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About this book

This is the first volume of a two volume set which presents the results of the 31st International Symposium on Shock Waves (ISSW31), held in Nagoya, Japan in 2017. It was organized with support from the International Shock Wave Institute (ISWI), Shock Wave Research Society of Japan, School of Engineering of Nagoya University, and other societies, organizations, governments and industry. The ISSW31 focused on the following areas: Blast waves, chemical reacting flows, chemical kinetics, detonation and combustion, ignition, facilities, diagnostics, flow visualization, spectroscopy, numerical methods, shock waves in rarefied flows, shock waves in dense gases, shock waves in liquids, shock waves in solids, impact and compaction, supersonic jet, multiphase flow, plasmas, magnetohyrdrodynamics, propulsion, shock waves in internal flows, pseudo-shock wave and shock train, nozzle flow, re-entry gasdynamics, shock waves in space, Richtmyer-Meshkov instability, shock/boundary layer interaction, shock/vortex interaction, shock wave reflection/interaction, shock wave interaction with dusty media, shock wave interaction with granular media, shock wave interaction with porous media, shock wave interaction with obstacles, supersonic and hypersonic flows, sonic boom, shock wave focusing, safety against shock loading, shock waves for material processing, shock-like phenomena, and shock wave education. These proceedings contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 31 and individuals interested in these fields.

Table of Contents

Frontmatter

Aerodynamic Testing at Duplicating Hypersonic Flight Conditions with Hyper-Dragon

In this paper, aerodynamic testing carried out with the JF12 hypervelocity shock tunnel is reported, and three experiments are discussed. The first experiment is aerodynamic heat test in hypersonic boundary layer, and a new thermal sensor for heat flux measurement at the extreme high-temperature condition is described, and the hypersonic boundary physics is explored. The second one is the aerodynamic force testing, and a new concept is proposed for optimizing the force and moment measurement system in shock tunnels. With this technology, the real gas effect is investigated, and its dominating mechanism is considered to be the gas molecular vibration. The last is the scramjet test from which two engine operation models are observed, that is, the continuous and pulsed combustion. Because most of the scramjet tests were conducted in combustion-based test facilities, the experimental data at the duplicated hypersonic flight condition would be of fundamental importance for exploring coupling of combustion, supersonic flow, and shock dynamics.

Z. Jiang, H. Yu

Shock Wave Research: Remembrance of Professor I. I. Glass

The paper reviews the author’s shock wave research inspired by Professor I. I Glass of UTIAS. Firstly, a preliminary underwater shock wave research by using a shock tube is briefly described. Secondly, small-scale underwater explosions of primary explosives visualized by means of double exposure holographic interferometry. Results of experiments performed by the refurbished hypervelocity shock tube donated from UTIAS to IFS in 1994 are presented.

Kazuyoshi Takayama

Ray Stalker Memorial Lecture: Legacy at T5

Ray Stalker’s invention of the free piston driver concept as uniquely suited to the study of high-enthalpy nonequilibrium phenomenon has resulted in a worldwide legacy of facilities such as the T1–T4 tunnels in Australia, HEG in Germany, T5 at Caltech, and HIEST at JAXA, Kakuda, Japan. In this talk, I will discuss recent and ongoing research in our group at Caltech that has focused on hypervelocity flows in which gas dynamics and thermochemistry are tightly coupled. To this end, we perform experiments in two impulse facilities which build on Ray Stalker’s legacy, including the T5 reflected shock tunnel and the Hypervelocity Expansion Tube facility.

J. M. Austin

Experimental Studies of Shock Wave-Related Phenomena at the Ben-Gurion University: A Review

The shock tube laboratory at the Ben-Gurion University was founded at the early 1970s by Profs. Ozer Igra and Gabi Ben-Dor. About two decades later, the system was reassembled and altered to investigate the Richtmyer-Meshkov instability (RMI). Recruiting new students (including myself) and a well-known scientist, Dr. Alex Britan RIP, the research activities expanded and became deeper. New shock tubes were constructed, new diagnostic techniques were implemented, and new equipment were purchased. In the presentation, some studies that were conducted during the past two decades and not published yet in the open literature will be presented. One of the main objectives of the study in the laboratory has been the RMI. In this study, a shock wave crosses the interface between two fluids having different densities and accelerates it. As a result, the interface becomes unstable and small perturbations grow nonlinearly. We were interested in the evolution of a well-defined multimode initial perturbation. Another subject that was intensely investigated was the starting process in a nozzle. We investigated the problem with two aims: (a) to better understand the effect of asymmetry of the nozzle on the flow inside it and (b) to better understand the flow in the nozzle when different pressure profiles initiated the flow.

O. Sadot

Shock Compression Spectroscopy Under a Microscope

In this paper, I will describe recent progress in developing a tabletop apparatus for shock compression spectroscopy based on laser-driven flyer plates synchronized with high-speed lasers and optical and infrared detectors. The primary focus of the paper is technique development, although examples of applications are also provided. The flyer plates can be launched up to 6 km/s, but they are tiny, typically 0.5 mm in diameter and 50 μm thick, so the main limitations of this technique are the short duration of the shock, typically <15 ns, and the small sample size needed. The flyer launch and impact, monitored by photon Doppler velocimetry (PDV) and ultrafast strobe photography, show the flyers make exceptionally reproducible impacts with minimal tilt. Using fabricated shock target arrays containing 50–200 individual samples, hundreds of experiments can be conducted every day. Examples are presented involving time-resolved spectroscopy of quantum dot photoemission to measure compressional strain at high speed, time-resolved optical pyrometry to study shock initiation of plastic-bonded explosives and liquid explosives, and ultrafast spectroscopy to measure molecular photophysics under extreme conditions.

Dana D. Dlott

Research on Shock-Induced Aerothermodynamics for Future Planetary Explorations

Researches on shock-induced aerothermodynamics are conducted at Chofu Aerospace Center (CAC) of Japan Aerospace Exploration Agency (JAXA) for future planetary explorations currently entertained in JAXA. The hyper-velocity shock tube (HVST) simulates the thermochemical properties in the shock layer of hypersonic systems in flight, while the hyper-velocity expansion tube (HVET) reproduces those in the wake region of the test model. The hypersonic rarefied wind tunnel (HRWT) enables us to directly measure the rarefied aerodynamics of hypersonic systems in transition flows. The light-gas gun (LGG) allows us to clearly understand the wake flow structure of capsules in supersonic flight, from which the parachute ejection conditions are determined. Numerical investigations of shock-induced aerothermodynamics are overviewed as well.

K. Fujita, T. Suzuki, H. Takayanagi, T. Ozawa, S. Nomura, N. Takizawa, S. Matsuyama, A. Lemal, M. Mizuno

Kinetic Shock Tubes: Recent Developments for the Study of Homogeneous and Heterogeneous Chemical Processes

Shock tubes have been successfully used for more than 50 years to study high-temperature chemical kinetics. The main advantages of this ideal reactor are the quasi-instantaneous increase of the temperature and pressure, the absence of mass diffusion, and the clear definition of the initial time. The ability of shock tubes to generate very easily pressures and temperatures over a very large domain (from as low as a few kPa to MPa and from as low as a few hundred Kelvin to several thousands) made them uniquely suitable for various studies from the classical homogeneous autoignition delay times to elementary reaction rate measurements and nanoparticle formation. It has been also used to characterize the shock-to-detonation transition for many chemical systems for propellants such as hydrazine and its derivatives, of light hydrocarbons. The aim of the present paper is to give an overview of different studies related to the kinetics of gaseous and heterogeneous systems with applications related to the chemistry of detonation as well as internal combustion engines. Examples of studies performed at ICARE laboratory as well as in the literature will be given as an illustration.

Nabiha Chaumeix

Structure and Unsteadiness of Swept-Ramp Shock Wave/Turbulent Boundary Layer Interactions

In this study we investigate the flow structure and large-scale unsteadiness of a 3D shock wave/turbulent boundary layer interaction generated by a swept compression ramp in a Mach 2 flow. The unsteady dynamics of the flow are investigated using 50 kHz particle image velocimetry (PIV) in side-view and plan-view planes. The 50 kHz PIV velocity data are bandpass-filtered to investigate potential mechanisms that drive the large-scale unsteadiness. Our analysis shows that strong correlation exists between velocity fluctuations in the upstream boundary layer and motion of the separation-line surrogate for frequencies lower than 10 kHz (0.25 U ∞/δ 99). This frequency band correlates well with the characteristic frequency range of boundary layer superstructures. Separated flow motions in the high-frequency band (10–50 kHz) do not seem to be strongly correlated to the upstream flow, instead significant correlation is observed with structures within the separation region that move primarily in the cross-stream direction.

L. Vanstone, N. T. Clemens

Propagation Behavior and Mitigation of Shock Wave Along the Water Inside a Rectangular Tube

This report presents our numerical study of a simple system in which a shock wave generated by the explosion of 10 mg of AgN3 propagates through water inside a rectangular tube. In such a system, the reflection of the shock wave from the water surface and from the tube wall can be neglected, facilitating the discussion of how water mitigates the shock wave. The shock wave propagates through the tube and compresses the fluid adiabatically. The high-temperature air in the shock wave makes thermal contact with the ambient-temperature water, allowing thermal energy to transfer through the air-water interface. The simulation results show that the speed of the shock wave inside the tube is significantly decreased when water is present. The results show that (i) thermal-energy transfer at the interface between water and air is a dominant factor in mitigating the shock wave, and (ii) water absorbs approximately 10–30% of the energy released by the explosion inside the tube.

Y. Sugiyama, Y. Nakayama, K. Ohtani, K. Nishimura, A. Matsuo

Dust Lofting Behind Shock Waves: What Is the Dominate Lofting Mechanism?

Blast waves formed by aerial explosion above dust and coal mine explosion lift dust. The lofted dust particles couple to the flow field and are carried by it. The dust lofting phenomenon behind blast/shock waves is studied over seven decades. Yet, a clear identification of the dominated dust lofting mechanism behind blast and shock waves is still lacking.

Y. Leler, S. Pistinner, A. Yafe, O. Sadot

Contribution to the Development of a Fast Running Method for Blast Waves Propagation

Direct numerical simulation of airborne blast waves, from source location to long distance, is a challenging task due to the wide range of spatial and temporal scales. Billions of cells are necessary for 3D codes. Taking into account topography, obstacles, and variable atmospheric conditions is further restricting. In this paper we present a simplified model for blast wave propagation designed to obtain reasonably accurate results at low computational cost in the near field. This new model is an extension to blast waves of earlier simplified models for shock propagation. It gives the first arrival time and the overpressure at the front.

J. Ridoux, N. Lardjane, F. Coulouvrat, L. Monasse

An Investigation of Stationary and Moving Cased Charge Detonations in Stone Lined Pipes

This paper describes the application of a coupled CFD and CSD methodology to the simulation of a thick-cased explosive-filled cylinder placed inside a pipe composed of either steel or various strength stones. The objective is to better understand the energy exchange mechanisms between the impacting case debris produced by either stationary or moving charges on the surrounding pipe material and its affect on the energy propagation in the pipe.

J. D. Baum, O. A. Soto, F. Togashi, R. Löhner, Michael E. Giltrud, J. Bell

Interaction of a Blast Wave with a Material Interface

Hydrodynamic instabilities are important drivers of mixing in many engineering applications and physical phenomena. Blast waves, e.g., originating from explosions in these systems, interact with interfaces between materials of different densities. This interaction deposits baroclinic vorticity along the interface, leading to characteristic rollups and late-time mixing of the materials. As opposed to instabilities driven by a shock wave (Richtmyer-Meshkov) or constant acceleration (Rayleigh-Taylor), the blast wave exhibits a complex acceleration history due to the combination of the leading shock and the following rarefaction. In addition to the induced interface acceleration, the shock and rarefaction compress and decompress the material, further modifying the perturbation growth. Finally, after the blast-wave interaction with the interface, residual circulation at the interface continues to drive the perturbation growth.

Eric Johnsen, M. T. Henry de Frahan

Laboratory Simulation of Explosions Using Conical Shock Tubes

Shock tubes are routinely used across laboratories to simulate and understand blast events that are beyond a standoff distance of 5 m from an explosive charge. If we wish to simulate distances which are even closer, we find a formidable barrier in the form of shock formation distance, which is inherent to these facilities. In this work, we propose to use a (conical) shock tube having a continuously diverging cross-section to overcome this limitation. This paper puts forward the rationale behind using such a facility, some analytical relations using Chisnell’s work to characterize the conical shock tube, and some experiments that validate our assumptions.

I. Obed Samuelraj, G. Jagadeesh

Shock Tube Study of Nitric Oxide Addition on Ignition Delay Time of n-Dodecane/Air Mixture

In engine applications, small concentrations of very reactive chemical species such as nitric oxide (NO) can have a very important impact on the onset of combustion. The small amount of NO can come from various sources including EGR, residual gas, and vitiated oxidizer streams. Combustion of distillate fuels and their surrogates with NO addition affects many practical propulsion and power systems and is of particular interest in gas turbines. As part of our efforts to understand these phenomena, shock tube ignition delay times have been studied for n-dodecane/air mixtures with the addition of 500 ppm and 1000 ppm NO over temperatures of 1083–750 K, near 30 atm and ϕ = 1. Laser absorption was used to quantify in situ fuel and NO concentrations. The current ignition delay time measurements should provide needed targets for NO addition model development and refinement.

Jiankun Shao, Yangye Zhu, Chris Almodovar, David F. Davidson, Ronald K. Hanson

Ignition Delay Times of Methane and Hydrogen Highly Diluted in Carbon Dioxide

As part of the effort to understand oxy-fuel combustion with large CO2 dilution, we have measured shock tube ignition delay times for methane/O2/CO2 mixtures and hydrogen/O2/CO2 mixtures. Ignition delay times (IDT) were measured using sidewall pressure and OH* emission near 306 nm. IDT measurements were performed near 80 atm for 3.91% methane/9.92% oxygen/carbon dioxide mixtures and near 110 atm for 7.5% methane/15% oxygen/carbon dioxide mixtures. IDT measurements for 10% hydrogen/5% oxygen/carbon dioxide mixtures were also performed near 110 atm. IDT measurements were compared to several current mechanisms. Excellent agreement was seen between the ARAMCO and USC Mech 2 models and the data under the current operating conditions.

Jiankun Shao, David F. Davidson, Ronald K. Hanson, Barak Samuel, Subith Vasu

A Study of the Chemiluminescence of СН*, ОН*, С2*, and СО2* During the Ignition of C2H2/O2/Ar Mixture Behind Reflected Shock Waves

The self-ignition of a number of near-stoichiometric acetylene−oxygen mixtures diluted with argon are experimentally and computationally studied to gain additional insights into the nature of the chemiluminescence that accompanies this process and to obtain some of its quantitative characteristics. The experiments are performed behind reflected shock waves at temperatures of 1270–1820 K and a pressure of ∼1 bar. The time evolution of the intensity of the luminescence of the electronically excited C2*, CH*, and OH* radicals and CO2* molecule is concurrently monitored. The measured temperature dependences of the ignition delay time are demonstrated to be in satisfactory agreement with the published data and the results of simulations within the framework of our own and a number of published mechanisms. To achieve a better description of the behavior of CO2* and C2*, and to improve the agreement between the experimental data and the results of kinetic simulation of CO2*, a novel kinetic mechanism wherein the reaction СН2 + О2 = СО2* + Н + Н is replaced by the reaction СН + О2 = СО2* + Н has been proposed.

V. N. Smirnov, A. M. Tereza, P. A. Vlasov, I. V. Zhiltsova

A Study on Soot Formation Characteristics of a Gasoline Surrogate Fuel Using a Shock Tube

Soot formation characteristics of gasoline surrogate fuels have been studied using a shock tube. Soot yield from thermal decomposition of mixed hydrocarbons including a gasoline surrogate fuel was obtained from measured soot volume fraction by the laser extinction method. The soot particle temperature was estimated based on spectral dependence of monochromatic emissive power of thermal radiation from the soot particles. The gasoline surrogate fuel used in the present work was basically composed of five hydrocarbons (isopentane, n-heptane, isooctane, toluene, 1,2,4-trimethylbenzene), and its composition was determined to emulate the distillation characteristic of a commercial gasoline fuel. In addition, a binary-, three- and four-component hydrocarbon fuels were tested for comparison. The shock tube tests were conducted at various temperatures ranging from 1700 to 2400 K and at a pressure of 200–260 kPa. The experimental results show that decrease in aromatic hydrocarbon in the fuel leads to less soot yield and delay of soot formation. The temperature at which maximum soot yield for the gasoline surrogate fuel is obtained is shifted to higher temperature as compared to the binary fuels containing 50% isooctane and 50% toluene.

Y. Nagata, K. Ishii

Effect of Dimethyl Methylphosphonate (DMMP) Addition on H2, CH4, and C2H4 Ignition Behind Reflected Shock Waves

Dimethyl methylphosphonate (DMMP) is both a fire suppressant and a surrogate for Sarin, a deadly nerve agent. To improve and validate the detailed kinetics model for DMMP, ignition delay times of mixtures of H2, CH4, and C2H4 seeded with DMMP where investigated in a heated shock tube. Results showed a strong promoting effect of DMMP on the ignition delay time of methane, whereas nearly no differences were observed for C2H4. The comparison of the experimental results with the most recent model from the literature exhibited the necessity to revisit the phosphorus combustion chemistry.

O. Mathieu, W. D. Kulatilaka, E. L. Petersen

CO and H2O Time Histories in a Shock-Heated H2S/CH4 Blend Near Atmospheric Pressure

Hydrogen sulfide (H2S) makes up a significant percentage of certain natural gas resources (sour gas) and is known to have significant effects on a variety of fuel systems. Key to the understanding of sour gas chemistry are H2S and methane (CH4) interactions, although relatively few data are available for this system. In this study, a fuel-lean (φ = 0.5) 30/70 H2S/CH4 blend in 99% argon by volume was shock-heated to temperatures between 1538 and 1889 K and pressures near 1 atm. Time histories of CO and H2O were measured using laser absorption diagnostics at 4.5 and 1.4 μm. The diagnostics were employed in two high-purity, stainless steel shock tubes. The predictions of several recent chemical kinetics mechanisms were compared to the measured profiles and induction times for CO and H2O. Based on these comparisons, it was concluded that the interactions of species containing both carbon and sulfur are negligible at the conditions studied herein. It was also concluded that the CH4 chemistry dominates at these conditions. To the best of the authors’ knowledge, this is the first shock tube study of the H2S/CH4 system.

C. R. Mulvihill, O. Mathieu, E. L. Petersen

Thermochemical Nonequilibrium Modeling of O2

The vibrational nonequilibrium in the electronically excited states of O 2 X 3 Σ g − a 1 Δ g b 1 Σ g + $$ {\mathrm{O}}_2\left({X}^3{\Sigma}_g^{-}, {a}^1{\Delta}_g,{b}^1{\Sigma}_g^{+}\right) $$ is investigated in the one-dimensional post-shock flows. The electronic and rovibrational state-to-state kinetics due to the heavy-particle collisions are employed to describe the electronic and rovibrational energy transitions. In the 1D post-shock flow calculations, it is observed that the vibrational relaxations of O 2 X 3 Σ g − $$ {\mathrm{O}}_2\left({X}^3{\Sigma}_g^{-}\right) $$ are more significant than those of the O 2 a 1 Δ g b 1 Σ g + $$ {\mathrm{O}}_2\left({a}^1{\Delta}_g,{b}^1{\Sigma}_g^{+}\right) $$ because the electronic excitation due to the heavy-particle collisions is not efficient.

J. G. Kim

State-Resolved Transport Properties of Electronically Excited High-Temperature Flows Behind Strong Shock Waves

In the present study, a theoretical model of state-resolved transport coefficients in electronically and vibrationally excited ionized gas mixtures is developed. High-temperature chemically reacting flows of a five-component partially ionized mixture N 2 / N / N 2 + / N + / e − $$ {N}_2/N/{N}_2^{+}/{N}^{+}/{e}^{-} $$ are considered in the state-to-state approach. Rotational, vibrational, and electronic states of molecular species as well as electronic degrees of freedom of atoms, both neutral and ionized, are taken into account. Nonequilibrium reactions of ionization, dissociation, and transitions of electronic and vibrational energy are included in the kinetic scheme. The developed model is applied for evaluating transport properties in strongly nonequilibrium flows behind the plane shock wave under conditions characteristic for the spacecraft reentry from an interplanetary flight (Hermes and Fire II experiments). The range of temperature and the distance behind the shock where the contribution of electronic and vibrational degrees of freedom to the flow parameters is of importance are indicated, and the effect of vibrational and electronic excitation on transport coefficients is analyzed.

V. A. Istomin, E. V. Kustova, G. P. Oblapenko

Oxygen Catalytic Recombination on Titanium Surface

In this paper, the theoretical concept to compute catalytic recombination efficiency for tertiary gas mixture is elaborated. The theory is an extension of Goulard and Park’s work in the catalytic phenomenon occurring in the binary mixture and tertiary mixture, respectively. The solution of this theory is solved by utilizing the concept of multicomponent diffusion velocity proposed by Chapman-Enskog combined with eigenvalue approach. This theory gives the relation between the heat transfer rate and the catalytic recombination efficiency. With this concept, the oxygen catalytic recombination efficiency is evaluated based on the experimental heat transfer on titanium-coated end-wall surface in a shock tube. The end-wall model is assumed to have smooth surface without any preheating condition. The heat transferred is measured using a thin-film gauge sensor in a shock tube with driven gas consisting of 21% oxygen and 79% argon by volume ratio. By utilizing the proposed concept of tertiary gas mixture, it is found that the oxygen catalytic recombination efficiency on titanium surface is 0.0034.

Yosheph Yang, Gisu Park

Computations of a Shock Layer Flow with a Vibrational-Specific Kinetics Model

The present work shows the ability of Navier-Stokes codes to handle detailed chemical kinetics models to compute the reactive and vibrational nonequilibrium gases in shock layers and the recent development done in our laboratories toward this goal. The detailed model used in the present study is a simplified version of a collisional-radiative model for N2 that has been implemented step-by-step in a Navier-Stokes code in order to show the effect of each group of chemical and vibrational processes. The processes taken into account are the vibration-vibration exchanges and the vibration-translation exchanges through molecular or atomic impact, leading to dissociation or not. The question of how the vibrational levels reach the Boltzmann distribution is also assessed. Comparisons of results obtained with global and detailed chemical kinetics models are performed.

Marie-Claude Druguet, Arnaud Bultel, Vincent Morel, Julien Annaloro

A One-Dimensional Modeling of Seed Electron Generation and Electron Avalanche in Laser-Supported Detonation

A one-dimensional numerical analysis has been conducted to investigate the laser-induced discharge mechanism in the laser-supported detonation. The radiative transfer equations for the laser and ultraviolet lights are coupled with the fluid equations of electrons and heavy particles. Photoionization and electron avalanche are considered in the ionization model. The steady-state problem of ionization wave propagation is computed by using the reference frame fixed to the ionization wave. The electron density distribution and electron temperature distribution are compared between the simulation and experiment. Quantitative agreements are confirmed in the peak electron density and electron temperature with differences of 38% and 24%, respectively. The simulation results indicated the existence of the precursor region, where the seed electrons are generated by the photoionization rather than avalanche ionization. In the condition of argon gas and 10.6 μm laser, the location of precursor region is estimated as 0.03–0.14 mm from the ionization wave front. The ionization wave propagation is governed by the self-consistent discharge mechanism consisting of photoionization, electron avalanche, and ultraviolet light radiation.

R. Kawashima, K. Matsui, K. Komurasaki, J. A. Ofosu, T. Shimano, H. Koizumi

PLIF-Based Concentration Measurement of OH Behind the Blast Wave Emanating from an Oxyhydrogen Detonation-Driven Shock Tube

The amount of OH species behind the shock wave from detonation-driven shock tubes is of prime importance. In this paper, the flow emanating from a miniature detonation-driven shock tube (m-DDST), which uses 5 bar of in situ generated oxyhydrogen mixture, is investigated. OH-PLIF is employed to characterize the relative OH distribution in the flow. Schlieren-shadowgraph imaging is also carried out to understand the flow features and to monitor the temporal evolution of the flow. Due to multiple reflections in the detonation driver, there are two distinct flashes observed during flow evolution which are captured in the OH-PLIF experiments. Predominant amount of OH radicals is observed after the Mach disc in the evolving flow field. Future studies are planned to map the absolute concentration of the OH radicals and ultimately to obtain the temperature distribution in the flow regime.

S. K. Karthick, P. R. Rajitha, S. Janardhanraj, Y. Krishna, G. Jagadeesh

Flame Propagation Over the Heat Absorbing Substrate

The paper presents experimental study of hemispherical flame propagation in a hydrogen-air mixture. The flame propagates over a solid aluminum wall and a layer of steel wool. Velocities of flame propagation are comparing at flame radii up to 0.4 m. Before and after passing through the flame, front steel wool has been investigated by the scanning electron microscope using energy-dispersive analysis system. Calculation of heat absorption in the steel wool layer shows that the heat losses due to the absorption are sufficient to reduce the flame front speed, which is observed in the experiments.

V. V. Golub, A. Korobov, A. Mikushkin, V. Volodin

Propagation Mechanism of Detonations in Rough-Walled Tube

Detonation propagation mechanism in rough-walled tube has been examined in the present study. To generate wall roughness, spirals with rectangular cross section of various wire lengths are used. Detonation velocity is measured by photodiodes along the length of the tube as well as a high-speed camera for detonations with weak illumination. A short length of the smoked foil is inserted into the core of the tube at the end of the test section to register the cellular pattern. It is observed that in rough tubes with spirals, detonation velocity can vary continuously from close to the theoretical Chapman-Jouguet value far from the limit to about 40% VCJ where the detonation fails. This contrasts with the detonations in smooth tubes, where the detonation velocity seldom decreases to less than 80% VCJ at the limit. It is found that an abrupt drop in velocity exists when decreasing the initial pressure for mixtures with high argon dilution, indicating a transition from a quasi-detonation to a high-speed deflagration. Smoke-foil studies indicate a transition criterion from a quasi-detonation to a fast deflagration in a rough walled tube, is d/λ ≈ 1.

J. Li, T. Yang, X. Wang, J. Ning

Effect of Hydrodynamic Instabilities on the Development of Hydrogen-Air Flames

The paper describes experimental investigation of hydrodynamic instabilities in lean hydrogen-air mixtures. The shock tube of 138 × 138 mm square section was used to experimentally study of evolution of flames in lean hydrogen-air mixtures. Obtained data demonstrate how flame development depends on the Rayleigh-Taylor instability in conditions of the superimposed artificial G-field.Two modes of turbulent flame development are identified, i.e., convex and concave flames. Modes depend on the mixture concentration. Transition between modes takes place in the 16 ± 2% range of hydrogen concentration in the air. The convex flame mode is realized below the 16% hydrogen concentration in the air, and the concave flame mode is realized above the 16% hydrogen concentration. The 16% hydrogen concentration realizes the transition mode of the periodic oscillating flame. The flame development in the transition mode is driven by the Rayleigh-Taylor instability as far as superposition of the artificial G-field sharply intensifies development of the instability that preconditions the flame evolution in this mode.

N. B. Anikin, V. A. Simonenko, A. V. Pavlenko, A. A. Tiaktev, I. L. Bugaenko, Yu. A. Piskunov

Crumpling Behavior of Graphene Oxide in Jet A-1 Vapor in Air and Its Effects on Combustion Process

This paper presents the crumpling behavior of graphene oxide (GO) nanosheets in Jet A-1 vapor in air and its effects in Jet A-1 fuel on the combustion process. The results indicate that a longer vaporized duration and higher chamber temperature are helpful to gain smaller and more crumpling GO particles which retain high surface area as potential micro-catalyst for enhancing combustion reaction. From Schlieren photography, the combustion test of GO-Jet A-1 mixtures in the closed single-shot facilities demonstrated that the addition of GO nanosheets can accelerate the initial linear burning velocity and reduce the ignition delay times. For 17.9% Jet A-1 in air, the addition of GO (2 mg/ml) increased the initial linear burning velocity from 4.52 to 5.15 m/s (13.8%) and reduced the ignition delay times from 8.195 to 3.045 ms (30%).

Jiun-Ming Li, Po-Hsiung Chang, Lei Li, Yiyuan Liu, Van Bo Nguyen, Chiang Juay Teo, Boo Cheong Khoo, Van Cuong Mai, Hongwei Duan

Detonation Decay and Flame Propagation Through a Channel with Porous Walls

Detonation decay and flame propagation in hydrogen–air mixture were experimentally investigated in the channels with solid walls and two types of porous materials on the walls: steel wool and polyurethane foam. Shock wave pressure dynamics inside the section with porous coating were studied using pressure sensors; flame front propagation was studied using photodiodes and high-speed camera. For all mixtures, the detonation wave was formed before entering the section with porous coating. In both porous materials, the stationary detonation wave was decoupled in the porous section of the channel into the shock wave and the flame front with velocity around the Chapman–Jouguet acoustic velocity. By the end of the porous section, the velocity and shock wave pressure were significantly lower in case of using steel wool.

G. Yu Bivol, S. V. Golovastov, V. V. Golub

Gas Flow with Stabilized Detonation in a Plane Channel

Using a detailed kinetic mechanism of the chemical interaction, detonation combustion of a stoichiometrical hydrogen-air mixture flowing at a supersonic velocity into a plane symmetrical channel with a constriction has been investigated with the purpose of both determination of conditions that provide detonation stabilization in the flow and study of methods of stabilized wave location control.In case of detonation initiation by energy input, the investigation of conditions of formation in the channel of a thrust developing flow with a stabilized detonation wave was carried out. The effect of variations of the inflow Mach number, the dustiness of the incoming gas mixture, and the width of the outflow channel cross section on stabilized detonation location was examined. Some methods of controlling of detonation location in the flow that ensure a thrust increase have been proposed. The possibility of formation of the thrust developing flow with a stabilized detonation wave in the channel under consideration without any energy consumption has been detected.

V. Levin, T. Zhuravskaya

Investigation on Vibrational Nonequilibrium Effect on ZND Detonation Model

This paper reports a modified steady one-dimensional Zel’dovich–von Neumann–Döring detonation model that considers a vibrational nonequilibrium effect. The Landau–Teller model is adapted for the translational–rotational to vibrational mode exchange rate, and Park’s two-temperature model is applied in the single-step Arrhenius equation. The Millikan and White method is chosen to model the vibrational relaxation time. In this modified model, α is introduced and is defined as the ratio of the specific heat capacity related to the translational–rotational mode only versus the total specific heat capacity at constant pressure. Changes in half-reaction zone length and predicted postshock thermodynamic properties are observed in this modified profile across the postshock state to the Chapman–Jouguet state. The findings agree with a previous numerical simulation of gas detonation with detailed chemistry assessment, in which detonation cell size changes under a vibrational nonequilibrium assumption.

Ken C. K. Uy, L. S. Shi, C. Y. Wen

Instabilities of Rotating Detonation

In order to investigate the combustion phenomena of rotating detonation of H2/air, ground experiments under different airflow rates at equivalence ratio of 1.0 are operated in an annular rotating detonation combustor (RDC), which uses the non-premixed mixture injection scheme. The airflow rates vary from 75 to 225 g/s. Qualitative and quantitative analysis of pressure signals at different circumferential positions are made to study the behaviors and instabilities of rotating detonation. The stable one-wave detonation is obtained, and four types of instabilities are found in the experiments: strong-weak wave alternation, unstable multi-wave detonation, direction inversion, and pulsed detonation. The possible physical mechanism is further analyzed.

Haocheng Wen, Qiaofeng Xie, Bing Wang

The Influence of Shock Reflections on Detonation Re-initiation

The objective of the present study is to investigate the mechanisms of detonation re-initiation. In addition, experiments were employed to further look into the discrepancies of the critical geometry conditions summarized from the previous research. Multiple measurement techniques have been applied. It is found that the discrepancies are mainly caused by the differences in the channel length. As the length of the bifurcation channel directly determines the shock reflection times, it can affect the re-initiation if the channel doesn’t allow sufficient times of shock reflection to take place. Another topic regarding the influence of the channel width to the detonation re-initiation phenomenon is also addressed. It is revealed that a wider channel width is preferable for detonation re-initiation because of the longer induction length during diffraction which can result in a strong explosion during the first shock reflection process.

L. Li, C. J. Teo, B. C. Khoo, J. Li, P. H. Chang

Experimental Studies Around Shock Tube for Dynamic Calibrations of High-Frequency Pressure Transducers

Shock tube facilities are well suited in the dynamic calibration of high-amplitude and high-frequency pressure transducers. This paper presents an overview of the experimental dynamic calibrations performed on pressure sensors and reports on the principles of the different diagnoses that will be implemented on the CEA-laboratory shock tube.

M. Lavayssière, J. Luc, A. Lefrançois

Effect of Imaging Blurring on 3D Computed Tomography of Chemiluminescence

Chemiluminescence measurements are commonly employed in the study of flame geometry and excited species concentrations. Computed tomography of chemiluminescence (CTC) is potential for the three-dimensional diagnostics of combustion both on high spatial and temporal resolution. It uses 2D multidirectional projections as inputs incorporated with iterative algorithms to get the 3D distribution. In general, a good simulation of projection processing by charge-coupled device (CCD) is important for the reconstruction solution. Bokeh effect out of focus may have an effect on the projections, which is produced by lenses of finite aperture. In order to verify the influence of imaging blurring on 3D-CTC, three different projection models were studied, including clear-imaging model, out-of-focus imaging model, and deconvolution model. The results suggest that the model taken the consideration of Bokeh effects has the best reconstruction accuracy, but it is time consuming. The projection deconvolution processing can improve reconstruction accuracy without increasing computation time.

K. Wang, F. Li, X. Yu

Time-Resolved Optical Flow of Supersonic Bevelled Nozzles

Time-resolved Schlieren photography-based image velocimetry using optical flow techniques (SIVOF) was applied to supersonic jet flows issued from a 30° bevelled nozzle. A modified Z-type Schlieren system and a high-speed camera was used to obtain the Schlieren images, before they were post-processed using an in-house optical flow code. Convective velocities are recovered at significantly high resolutions, where the corresponding vorticity maps are observed to offer reasonably accurate identification and velocimetry of supersonic jet shear layer structures. Results are subsequently compared to and showcased against particle image velocimetry (PIV) measurements of the same supersonic bevelled jet. Behaviour of the vortical structures, shear layer growth rate, shock wave location and potential core length obtained from SIVOF agrees well with historical findings and previous studies conducted with the same nozzle design and nozzle pressure ratio (NPR) value. Lastly, the present study also highlights both the potentials and limitations of SIVOF in supersonic flow studies.

H. D. Lim, T. H. New, Y. D. Cui, Shengxian Shi

The Effect of Adaptive Sampling on Fluorescence Velocimetry Measurements in High-Speed Flows

An adaptive sampling technique has been assessed experimentally for determining the peak location of Doppler-shifted lineshapes for fluorescence velocimetry measurements in high-speed flows. Acquired data from three regions of an imaged leading-edge separation in hypersonic flow were fitted with Gaussian profiles and the Doppler-shift compared with that of a uniform sampling technique. Lineshape peak locations from both methods were similar, although significant scatter in fluorescence intensity values were found to reduce the effectiveness of adaptive sampling, which led to an almost uniformly spaced distribution of sample frequencies. Additional longitudinal laser modes were identified as the cause of the intensity scatter, which originated from an intra-cavity etalon not performing at factory specifications. The experimental implementation of the adaptive sampling technique using the current setup rendered its performance to be approximately the same as a uniformly spaced sampling approach.

L. M. Le Page, S. O’Byrne, S. L. Gai

High-Resolution Background-Oriented Schlieren Technique for a Laser-Induced Underwater Shock Wave

Background-oriented schlieren (BOS) technique is a nonintrusive method to obtain global pressure field via refraction of light induced by the density change in fluid. Although the cross-correlation method so-called PIV-BOS is commonly used for computing the displacement field, this method induces to decrease the accuracy of the pressure field due to poor spatial resolution. In order to improve the spatial resolution, we apply the optical flow to computation of displacement field. The pressure field of a laser-induced underwater shock wave is used to validate the techniques. We show that the profile of shock wave is successfully captured by the optical-flow-based BOS (OF-BOS). Poor spatial resolution of pass-integrated displacement field deteriorates the accuracy of three-dimensional reconstruction.

M. Kameda, K. Hayasaka, Y. Tagawa, T. Liu

Evaluation of the Radiance of Shock-Heated Air in the 120–400-nm Spectral Range

The need to evaluate the radiative heat flux to a descending spacecraft motivated a series of ongoing studies aimed at measuring radiation fluxes behind the shock-wave front over a wide range of wavelengths at low initial pressures and high flow velocities. In the present chapter, the experimental results are presented for the emission intensity of shock-heated air behind the front of an incident shock wave at an initial pressure of 0.25 Torr and shock-wave velocities from 6.3 up to 8.4 km/s. The radiation intensity was measured in absolute units in the form of spectral distribution over a wavelength range of 120−400 nm. It was shown that the radiation flux is significantly higher at the wavelength 120 nm than the radiation flux from the same source within the wavelength range of 200−400 nm. Our experimental results demonstrated that the duration of the radiation of shock-heated air was about 1μs for all shock-wave velocities over the entire spectral range at pressure upstream of shock-wave front of 0.25 Torr. The intensities of the radiation of the N and O atomic lines at 120, 130, 141, and 149 nm were found to be much higher than the intensity of the background radiation.

S. V. Stovbun, N. G. Bykova, I. E. Zabelinskii, A. M. Tereza, O. P. Shatalov, P. A. Vlasov

Application of NO Laser-Induced Fluorescence in JF-10 Detonation-Driven Shock Tunnel

We have presented our recent progress in the application of γ(0,0) band NO LIF in the hypersonic flow with total enthalpy of 16.2 MJ/kg generated by JF-10, a H2/O2-detonation-driven shock tunnel. The strong luminosity behind the shock wave is competing against the fluorescence signal, and the photon collecting efficiency of such facilities is limited by its large dimension. To cope with the problems, the laser sheet of a conventional planar LIF is rotated 90° along its propagation direction, so that the fluorescence signal collected by the camera concentrates on a sharp line. This setup makes LIF signal stand out even after the shock wave. With this setup, the S/N ratio is also increased; thus single-shot measurement is achievable. In this paper, the rotational temperature of the flow is estimated based on two-line thermometry.

H. Yan, S. Zhang, X. Yu

Molecular Tagging Velocimetry of NH Fluorescence in a High-Enthalpy Rarefied Gas Flow

In this paper, a new type molecular tagging velocimetry based on NH fluorescence was developed and validated for the velocity measurements of a high-enthalpy rarefied gas wind tunnel where the maximum flow velocity exceeds 7 km/s at 0.2 Pa. The feasibility of this technique using the short-lived NH fluorescence was demonstrated in the hypersonic rarefied gas flow with yielding velocity profiles at multiple downstream locations from the nozzle exit. The total uncertainty of the measured flow velocities was estimated to be less than 6% when the flow velocity above 2000 m/s. For the new tagging technique, only a single laser and a single time-gated camera are required for velocity measurement, due to the existence of NH radicals in the arc-discharged N2 mixed with small an amount of H2. Therefore, the NH-MTV not only shows great promise for tagging in high-enthalpy rarefied gas of nitrogen or air flows without seeding but also possesses high practicability and facility for velocity measurement.

S. Zhang, X. Yu, H. Yan, H. Huang, L. Liu

Measurements of Jet A Vapor Concentration Using Interband Cascade Laser

The nonintrusive laser-based sensor is developed to measure the concentration of vapor-phase Jet A in the pulse detonation engines (PDEs). The sensor utilizes a distributed feedback (DFB) interband cascade laser (ICL), whose centered wavelength is at 3.411 μm. The concentration of vapor-phase Jet A is determined via tunable diode-laser absorption spectroscopy (TDLAS) technique using Beer’s absorption law. Calibration measurements have been carried out in a static cell to determine the line strength of vapor-phase Jet A-1, and the results have been applied to the concentration measurements. The sensor has been used to determine the time-resolved fuel concentration during the fuel injection as well as the arrival time of fuel to the head end of the PDE tube. The stoichiometry data shows fuel distribution is not uniform along the PDE tube wherein there exists a rising portion, a constant fuel concentration portion, and a descending portion. At the cases of nearly stoichiometry and fuel rich, the measured fuel concentrations are close to assumed concentration; however, at the case of fuel lean, there is an overestimation in the measured fuel concentration. The reasons could be attributed to fuel aerosols. The laser light can be also attenuated by droplet scattering when fuel aerosols are present in the laser beam. Nevertheless, there is a discrepancy between the measured fuel concentration and assumed concentration; the stoichiometry data still provide the information about the fuel distribution in the PDE tube and also give a better understanding of heterogeneous jet-fuel/air mixture sensing techniques.

Po-Hsiung Chang, Jiun-Ming Li, Chiang Juay Teo, Boo Cheong Khoo, Christopher M. Brophy, Robert G. Wright

Temperature Measurement in a Shock Tunnel Using Tunable Diode Laser Absorption Spectroscopy

Quantitative measurement of the freestream temperature in the test section of a hypersonic shock tunnel, obtained using tunable diode laser absorption spectroscopy (TDLAS) technique, is presented in this work. Water vapor absorption lines near 1392 nm were probed using a vertical-cavity surface-emitting laser scanned at 25,000 Hz to get the time-resolved measurement of temperature in a Mach number M = 8 hypersonic flow. Three different enthalpy cases – 2.57, 2.23, and 2.01 MJ/kg – were studied in the shock tunnel. Freestream temperature was extracted from the absorbance spectra obtained using direct absorption scheme, by using two-line ratio method. The measured temperatures were compared with the theoretically predicted values.

M. Kannan, Y. Krishna, G. Jagadeesh, K. P. J. Reddy

Measurement and Formulation of Velocity, Attitude, and Trajectory of Moving Object Using Magnet–Coil Method for High-Speed Penetration Experiment

Objects penetrating sand produce various phenomena; however, most phenomena are still unknown. It is necessary to observe the behavior of objects penetrating to sand elucidate these gaps in knowledge. Therefore, the study of projectile impacts requires accurate determination of projectile path and velocity. In order to clarify the location of a projectile after penetrating into opaque material (e.g., sand), the previously developed magnet–coil method using electromagnetic induction was applied. The method provides multipoint measurements of the location of a moving magnet in opaque material. Previous experiments confirmed that it has sufficient measurement accuracy in the case of straight penetration. However, our previous experiments demonstrated that the penetrating projectile meandered. Therefore, in this study, we conducted free-fall experiments in consideration of eccentricity, inclination, and oblique passage of a falling object and evaluated the output signal of the coil. As a result, theoretical equations were formulated for the output voltage induced by the attitude and trajectory of the magnet.

S. Iwata, K. Watanabe

Investigations of Density Field of a Flat Plate Shock Wave Boundary Layer Interaction at Hypersonic Speeds Using BOS

Shock wave boundary layer interaction with leading-edge bluntness problem has great effect on the performance of the aerospace vehicles. Strong interactions of the shock wave with the boundary layer lead to separation of the boundary layer and unsteadiness in the flow. These effects increase drag and reduce the efficiency of the nozzles. Moreover, the leading-edge bluntness influences the separation length of the flow. The objective of the present work is to obtain quantitative information of density flow field to understand the flow physics in a shock wave boundary layer interaction at hypersonic flow. Background-Oriented Schlieren (BOS) technique was used to map the density flow field. Based on earlier studies, a flat plate with sharp and blunt leading edge at M ∞ = 5 was chosen. Separation length correlations based on the surface pressure measurements obtained from the previous studies were compared with the density flow field correlations.

P. Suriyanarayanan, L. Venkatakrishnan, L. Srinath, G. Jagadeesh

Schlieren Tomography to Visualize Three-Dimensional Supersonic Flows

This work describes a way to deduce the 3D density gradient field using a set of focusing schlieren images taken close to each other. Focusing schlieren gives density gradient information corresponding to a narrow focal plane. However, it still contains contributions from adjacent planes, and it depends on the focusing optics. This work used 3D deconvolution algorithm to solve this problem. The point spread function (PSF) of the optical system is estimated experimentally, and the noise is modeled statistically. The deconvolution results show that the contribution from adjacent planes is minimized, and thus this tomographic approach can lead to better understanding of 3D compressible flows.

S. Vaisakh, T. M. Muruganandam

Interaction of a Planar Shock Wave with a Water Surface

This work is about experimental study of a planar shock wave which slides over a water surface. The aim is to observe the air-water interface and the droplet entrainment. Experiments are performed at atmospheric pressure in a 200 × 200-mm2-square-cross-section shock tube for depths of 10, 20, and 30 mm and two incident planar shock waves having Mach number of 1.11 and 1.43. We recorded the pressure histories and high-speed visualization to study the flow patterns, surface waves, and spray layers behind the shock wave.We observed two different flow patterns with ripples formed at the air-water interface for the weaker shock wave and the dispersion of a droplet mist for the stronger shock wave. We analyzed pressure signals both in the air and in the water at the same location. From these pressure signals, we extracted the delay time between the arrival of the compression wave into the water and the shock wave in air at the same location. We show that the delay time evolves with the distance traveled over the water layer, the depth of the water layer, and the Mach number of the incident shock wave.

V. Rodriguez, G. Jourdan, A. Marty, A. Allou, J.-D. Parisse

Basic Experiment on Focusing Schlieren PIV Method with LED Light Source

The focusing schlieren PIV technique is being done to investigate the velocity vector, and it is considered as the useful measurement technique in the compressible flow. In this study, the LED light sources of a focusing schlieren system was used to visualize the flow fields of helium jets. And the flow vector was estimated by using PIV software as the first step. The system was constructed by an extended light source, a Fresnel lens, source and cutoff grids, focusing lens, and a CCD camera. The three source grids were prepared. The light source was designed by consisting of four LEDs. This system was used to visualize free jets from the convergent nozzle. The helium gas was used as the test gas to obtain large density gradient in low-speed flows. As the result, the density gradient could be seen though the condition was low speed. And the flow field from the nozzle was visualized by the LEDs as the extended light source. The jet at the focal plane could be seen clear, and the flow vector due to the turbulence was seen by the PIV analysis.

Masashi Kashitani, S. Nakao, Y. Miyazato

Boundary-Layer Transition Detection at High-Enthalpy Flow Using Temperature-Sensitive Paint

Temperature-sensitive paint technique was applied to high-enthalpy shock tunnel JAXA-HIEST. The test model was circular cone model with the total length of 1100 mm. The model was equipped with thermocouples, and Temperature-Sensitive Paint was painted on the side of the model. Measured heat flux distributions were compared between Temperature-Sensitive Paint and thermocouples to evaluate temperature-sensitive paint measurement in High-Enthalpy Shock Tunnel. Near the end of the test model, the trend that heat flux increase with the distance from nosetip was same in two measurement techniques. Temperature-Sensitive Paint could detect the locations of boundary-layer transition. Furthermore, heat flux measurement quantitatively showed good agreement with the thermocouple measurement result by using in situ calibration.

H. Nagai, T. Nagayama, H. Tanno, T. Komuro

Development of Sprayable Ultrafast-PSP for Unsteady Flow

Intensive efforts have been made to enhance the time response of sprayable pressure-sensitive paint (PSP) to measure the global pressure distribution on a model with a high time resolution. However, conventional sprayable PSPs showed lower time responsibility than an anodized aluminum PSP (AA-PSP). In addition, sprayable fast-responding PSPs have higher temperature sensitivity and much rougher surface than conventional polymer-based PSPs. In this paper, ultrafast-PSP has been developed to achieve a time response comparable to AA-PSP. As a pressure-sensitive dye of the ultrafast-PSP, ruthenium complex Ru(dpp)3 was employed. It has shorter luminescence lifetime than PtTFPP, which is widely used as a dye for fast-PSP. In addition, we investigated the many PSP formulations of polymers, nano-particles, and solvents. It was found that the combination of these materials strongly influenced PSP properties. Finally, we successfully found the optimum formulation of materials to achieve an ultrafast-PSP with a time response of 2–3 μs, which is comparable to the fastest AA-PSP.

Y. Egami, Y. Sato, Y. Shimizu, K. Yamashita, A. Natsubori, T. Fukuzumi

Three-Dimensional Measurement of the Lateral Jet/Cross-Flow Interaction Field by Colored-Grid Background-Oriented Schlieren (CGBOS) Technique

The colored-grid background-oriented schlieren (CGBOS) technique is applied to the lateral jet/cross-flow interaction field. The background pattern composed of inclined stripes is tested to capture the flow information near the test model in wind tunnel test. As a result, boundary layer and separation shock are captured quantitatively.

Masanori Ota, Ken Kurihara, Takumi Ito, Tatsuro Inage

Numerical Investigation of Dust Lifting Induced by Vertical Shock Wave

In this paper, two-dimensional CFD-DEM was conducted to investigate the effect of Magnus force for the dust dispersion by vertical shock wave. Magnus force is mainly driven by the gas rotation inside the boundary layer near the surface of dust layer, and the particle rotation generated by collisions has smaller contribution for Magnus force. The gas rotation only has large value inside the boundary layer, so that Magnus force becomes insignificant with dust lifting.

K. Shimura, A. Matsuo

Gas Surface Interaction of Carbon Endwall in a Shock Tube

This paper shows qualitative results about surface catalytic reaction of carbon with low-temperature air through shock tube experiments. In the shock tube experiments, air is used as test gas, and its temperature reaches about 3500 K behind reflected shock wave. Carbon powder is attached at the surface of acrylic endwall which is located at the end of driven tube of the shock tube. From the observation of pressure trace, 100 μs of quasi-steady-state test time is maintained. High-speed camera and visible-range spectrometry methods are used to observe flow luminescence and to detect molecule or spectrum of test gas. The orange-color luminescence is detected form the high-speed camera and is maintained for about 250 μs. Continuous radiation from carbon dust and atomic emission from C, O, and He is detected by the spectroscope. At the temperature tested, molecules of species from the gas surface interaction are not detected in spectrometric range considered.

Hanseul Shim, Gisu Park

Numerical Simulation of a Water Column Deformation and Breakup by Shock Wave

The numerical simulation of a water column breakup by shock wave is simulated. The sharp interface method that was constructed with level-set method and ghost fluid method was adopted as compressible two-phase flow numerical method. We simulate various Weber number conditions. The detail behavior of water column deformation is clarified by these simulations. Except the least Weber number for this paper, the tips are formed lateral side of a water column, deflected in flow direction by high-speed gas flow. In relatively large Weber number, the wavy shape is observed at upstream side interface. This wavy interface evolves with time.

T. Kamiya, M. Asahara, T. Miyasaka

Hybrid Compact-WENO Finite Difference Schemes for Hyperbolic Conservation Laws

The hybrid scheme reduces the dissipation and dispersion errors inherited by the characteristic-wise weighted essentially nonoscillatory finite difference scheme and improves the efficiency by using a cheap and fast high-order compact scheme for the solution of nonlinear hyperbolic conservation laws. The key component in the hybrid scheme is a high-order, robust, and efficient shock detection algorithm, such as those based on the multiresolution analysis, conjugate Fourier analysis, and radial basis function. Classical examples for solving Euler equations will be presented to demonstrate the performance of the hybrid schemes in terms of resolution power, dissipation, and efficiency.

W. S. Don

A Fast Mathematical Modeling Method for Aerodynamic-Heating Predictions

Prediction of aerodynamic heating under different flight conditions is a critical and challenging step in developing a new hypersonic vehicle. The prediction model usually involves a large number of variables, and this makes genetic programming converge too slow. This paper presents a fast mathematical modeling method, divide and conquer, for aerodynamic-heating predictions. It can use the separability feature of the target model to decompose a high-dimensional function into many low-dimensional sub-functions. The separability is detected by a special algorithm, bi-correlation test (BiCT), and the sub-functions could be determined by general genetic programming (GP) algorithms one by one. Thus the computational cost will be increased almost linearly with the increase of function dimension. This can help to break the curse of dimensionality and greatly improved the convergence speed to get the underlying target models from a set of sample data.

C. Luo, Z. Jiang

A Multi-space Interrelation Theory for Correlating Aerodynamic Data from Hypersonic Ground Testing

Prediction of aerodynamic force/heating acting on hypersonic vehicles in flight conditions with experimental data is a critical yet challenging step in developing hypersonic vehicles. A multi-space interrelation (MSI) theory and its correlation algorithms have been presented. MSI considers the flight condition as an ideal wind tunnel and then aims at detecting an inherent invariant of aerodynamic data from different wind tunnels. The invariant detection is carried out by special supervised self-learning schemes, adaptive space transformation (AST), and/or parse-matrix evolution (PME). The invariant is then used to predict the aerodynamic force/heating coefficients. The study indicates that the multi-space interrelation theory agrees well with physical phenomena. The correlation algorithm can make use of hypersonic wind-tunnel experimental data effectively, and the correlation function is capable of unifying all the experimental data in an analytical form. With the proposed theory and algorithm, one can expect to find a reliable correlation formula with high accuracy based on plenty of wind-tunnel experimental data, provided that the physical condition has not essentially changed.

Z. Jiang, C. Luo

Reynolds Stress Models for Shock-Turbulence Interaction

A systematic deficiency of current turbulence models which are based on the Reynolds-averaged Navier-Stokes equations (RANS) is their inability to correctly predict the interaction of turbulence with shocks. This is because RANS models do not account for the unsteady motion or fragmentation of the shock wave within the interaction zone. Typically, significant over-prediction of the turbulent energy amplification occurs without dedicated adjustment of the applied turbulence model.An empirical shock correction for Reynolds stress models (RSM) is proposed. This corrective model is based on rescaling of the production and redistribution terms in the Reynolds stress and length scale equations. The method is tested for two common RSM models and enables them to correctly predict the turbulence amplification, anisotropy, and dissipation downstream of the interaction with a normal shock wave.

Sebastian Karl, Jean-Pierre Hickey, Francis Lacombe

On the Analysis of Full-Spectrum k-Distribution Databases for Thermal Radiation in Shock Waves Within CO2-Rich Atmospheres

Future interplanetary missions encourage the investigation of fast and reliable methods to estimate the radiative heat loads on space vehicles for a better design of their thermal protection systems. Shock waves around entering blunt bodies cause highly nonhomogenous fields under thermal non-equilibrium conditions. The calculations of such radiative flows imply large computational times, often forcing the reduction of the analysis to one dimension. Investigations propose the k-distribution approach as an improvement in calculation times while delivering reliable results, allowing full flow field calculations. This work presents an approach of the method to thermal non-equilibrium regimes at entry conditions into Mars atmosphere. The full-spectrum k-distribution method and its coupling with the NSMB flow solver are briefly described. A description of the k-distribution database and its particularities for shock wave applications is given. A first sensitivity analysis of the database parameters shows good results compared to exact methods, which motivate future investigations on its applications.

J. García-Garrido, Ch. Mundt

Measurement of Electron Density by Heterodyne Interferometer for Atmospheric Pressure Plasmas

A sample return mission from Jupiter trojans is proposed in JAXA. Reentry velocity in this mission is estimated at 14 km/s. It is reported that there is a discrepancy between predictions and experimental results with regard to the electron number density in the shock layer. Precursor photoionization is one candidate to cause the discrepancy. To clarify the phenomenon, it is necessary to measure the electron density ne distribution from across a strong shock wave. Then, we are developing a heterodyne interferometer whose measurement range and time resolution is n e = 1019–1022 m−3, above 1 μs, respectively. In this study, the limit of phase shift was evaluated by the variation of ZnSe window thickness. Measured value is in agreement with theoretical curve. However the error is 5.8 × 1019 m−3. Variability of phase is 5.35°, it is equivalent to n e of 4.4 × 1019 m−3 with l = 70 mm and λ = 10.6 μm, and it is found out that phase stability of laser is a major factor of phase variability. It is required for the enhancement of sensitivity. It is required for the enhancement of phase stability of laser beam.

T. Yamada, M. Matsui

Parametrical Quasi-resonant Amplification of Alfven Waves in Heat-Releasing Isentropically Unstable Media

Three-wave interactions of the powerful magnetoacoustic wave with the Alfvén waves in heat-releasing ionized media are considered. The system describing the parametrical decay of the acoustic wave is obtained. The solution of the obtained system is found analytically for long-wave and weak nonlinearity approximations. The obtained solutions for the Alfvén waves strongly depend on the frequency detuning ∆ω. When ∆ω equals zero, the amplification of Alfvén waves is resonant, non-threshold and bi-exponential. With frequency detuning increase, the parametrical amplification of Alfvén waves becomes slower; further on, modulation is observed before bi-exponential amplification; and, finally, there is only Alfvén wave modulation. The cause of the modulation, which is observed before the amplification, is the existence of a threshold for amplitude. Conditions of the Alfvén wave amplification caused by the quasi-resonant parametrical energy transfer from unstable magnetoacoustic waves are obtained.

S. A. Belov, N. E. Molevich, D. I. Zavershinsky, D. S. Ryashchikov, S. Yu. Pichugin

Two-Dimensional MHD Structures in Heat-Releasing Plasma

Thermal instability has been the subject of intensive research for several decades. It is considered to be responsible for various spatio-temporal structures formation in the solar atmosphere, interstellar media, planetary nebulae and other media. Nevertheless, a convincing explanation of these structures appearance remains an open question. In this paper, we focus our attention on the isentropic type of thermal instabilities only, which causes MHD waves amplification in plasma. It is well-known that MHD waves are highly anisotropic and the patterns formed cannot be properly described using one-dimensional approach. Therefore, this work aims to study the features of 2D structures and compare them with one-dimensional ones. It is shown that both 1D and 2D initial Gaussian density perturbations lead to the formation of travelling autowave (self-sustaining) magnetoacoustic (MA) pulse sequence. Moreover, one-dimensional slice of the pulses corresponding to the fast MA waves coincides with the results of previous one-dimensional simulations. Furthermore, the investigation reveals that highly anisotropic wave patterns become more pronounced with the increase of magnetic field magnitude.

D. S. Riashchikov, N. E. Molevich, D. I. Zavershinsky

Mode Transition from Fast-Gas Ionization Wave to Laser-Supported Detonation Wave

In this study, the FIW and the LSDW were experimentally observed by shadowgraph in air. A TEA CO2 laser with 10 J output was used. A 532 nm DPSS laser with 1.4 W output power was used as a probe light. It projected the shadow of the laser-induced plasma and the shock wave onto a high-speed ICCD camera.

K. Shimamura, N. Ozaki, K. Matsui, K. Komurasaki

Gas-Dynamic Flow Behind Shock Wave Initiated by a Sliding Surface Discharge Channel

The dynamics of a blast (shock) wave from a pulsed single-channeled surface discharge and the flow velocity behind it are studied experimentally, numerically, and theoretically. The evolution of the flow field forming after the discharge initiation is captured using the Particle Image Velocimetry (PIV) method and the shadow method in a single-frame and multi-frame mode (with a high-speed camera). In experiments, the distance traveled by the shock wave is measured by the shadow technique; the flow velocity fields are obtained by the PIV method within 100 μs after the discharge initiation. The three-dimensional computational fluid dynamics (3D CFD) simulation based on the assumption of instantaneous energy deposition is in agreement with the experimental results. It is shown that, for a voltage pulse of 25 kV and an air pressure of 240 Torr, up to 30% of the total electric energy is instantly released into heat. The experimental and numerical results are also compared with that of the Sedov’s theory.

Irina Mursenkova, Ekaterina Koroteeva, Yugan Liao, Irina Znamenskaya

Jet Formation of SF6 Bubble Induced by Incident and Reflected Shock Waves

We present computational results of two different cases on the evolution of shock-SF6 heavy bubble interaction. And the shock-focusing processes and jet formation mechanisms are analyzed by using the high resolution of computation schemes, and the influence of reflected shock wave is also investigated. It is concluded that there are two stages in the shock-focusing process behind the incident shock wave. However, different jet formation mechanisms are found behind the reflected shock wave in case 2, owing to the gas being with a rightward velocity before the reflected shock wave impinges. The multi-influences of different shock waves and high-pressure zones in the vicinity of the bubble interface could induce a leftward velocity, which can promote the formation of jets. In addition, the time for the bubble evolution before the impingement of reflected shock wave in case 1 is larger than that in case 2, so the distorted bubble is getting more flat, which would induce the weakening of the influence of reflected shock in the bubble.

Yuejin Zhu, Lei Yu, Jianfeng Pan

Interaction of Cylindrical Converging Shock Wave with SF6 Gas Bubble

Interaction of cylindrical converging shock wave with an SF6 gas bubble is studied experimentally and numerically. A high-speed schlieren photography and three-dimensional (3D) program are adopted to capture the detailed flow field. Due to the variance of shock curvature, the distributions of vorticity deposition on two mutually perpendicular views of the interface are different. Besides, the gradually intensified strength of converging shock as well as additional pressure gradient in the post-shock flow also influences the interface evolution, which is different from planar shock case. The results indicate that both of the shape and strength of converging shock play an important role in the interface evolution.

Yu Liang, Zhigang Zhai, Xisheng Luo

Numerical Study on the Single-Mode Richtmyer-Meshkov Instability in a Cylindrical Geometry

Evolution of a single-mode air/SF6 interface accelerated by a converging shock is investigated numerically. For comparison, a planar case with the same perturbation amplitude and wavelength as well as the initial shock strength is also simulated. Temporal variations of the perturbation amplitudes for both cases indicate that the converging Richtmyer-Meshkov (RM) instability develops more quickly than the planar counterpart, which is mainly ascribed to the Bell-Plesset (BP) effect. Furthermore, the interface growth rate suffers from a rapid decrease at late stages due to the Rayleigh-Taylor (RT) effect related to the interface deceleration motion in convergent geometry.

Lili Liu, Juchun Ding, Zhigang Zhai, Ting Si, Xisheng Luo

Light/Heavy Converging Richtmyer-Meshkov Instability in a Conventional Shock Tube

A new experimental investigation of the Richtmyer-Meshkov instability in a cylindrical geometry was conducted in the light/heavy configuration using a conventional shock tube equipped with a new specifically designed three-zone He/air/SF6 convergent test section. The first experimental results show the expected phases of the Richtmyer-Meshkov instability development.

L. Biamino, G. Jourdan, L. Houas, M. Vandenboomgaerde, D. Souffland

The Imploding Cylindrical Richtmyer-Meshkov Instability with Ideal Two-Fluid Plasma Model

The shock-interface interaction in converging flow in the presence of magnetic field is numerically studied with two-fluid plasma model. Two-fluid effect on the density field is investigated by varying Debye length: the electron and ion dynamics essentially decouple for large Debye length, and the dynamics is similar to that of a single-fluid for small Debye lengths. The influence of an initially unidirectional uniform seed magnetic field on Richtmyer-Meshkov instability in ion fluid is studied with a given Debye length.

Y. Li, R. Samtaney, W. Cheng, V. Wheatley, Daryl Bond

Experimental Study on a Single-Mode Interface Impacted by a Converging Shock

Experiment of a single-mode air/SF6 interface impacted by a converging shock is performed in a semi-annular converging shock tube, and complete evolution of the shock propagation and the interface deformation is well captured by a high-speed schlieren photography. Time variation of the perturbation amplitude measured from schlieren pictures agrees well with the linear theory of Bell at early stages. Later, before secondary impact of the reflected shock, the growth rate decreases gradually even to be a negative, which is first discovered in experiment. Rayleigh-Taylor (RT) stabilization is found to be the main factor contributing to the growth rate reduction. A modification of Bell equation by introducing a decaying factor is proposed to reasonably evaluate the RT stabilization effect on the perturbation growth.

Juchun Ding, Zhigang Zhai, Ting Si, Xisheng Luo

The Richtmyer-Meshkov Instability of a Flat Interface Initiated by a Perturbed Shock

The Richtmyer-Meshkov (RM) instability of a flat density interface that is induced by a perturbed shock is simulated in this study. A rigid circular cylinder perturbs a planar shock wave that interacts with a flat density interface, initiating the RM instability. The compressible Euler equations that govern the dynamics of the inviscid shock wave are numerically solved by a second-order multidimensional upwind embedded boundary method wherein the cylinder geometry is implicitly represented by a level-set function. A block-based adaptive mesh is employed to refine the local complex areas and capture wave patterns and interfaces effectively. Three different distances η (the ratio of distance L from cylinder to interface over cylinder diameter D) are considered. The results show the interaction of the perturbed shock and the flat interface leads to the formation of overall “Λ”−shaped structures that characterize the interface perturbation. The growth of the perturbation width and depth is affected by distance L, and the width of the shock perturbation is determined by diameter D. Furthermore, the computational shape of incident perturbed shock and geometrical sizes of distorted interface are compared and analyzed with experimental results quantitatively.

M. Al-Marouf, R. Samtaney, L. Zou

A Study of Shock-Induced, Variable Density Mixing

Experiments and simulations of shock-driven Richtmyer-Meshkov mixing between air and SF6 show strong dependence of initial interface perturbations on the evolution of the mixing structures. Experiments focus on two-dimensional versus three-dimensional initial perturbations at Mach 1.3, showing differences in the development of the large-scale structures that drive mixing. Simulations using experimentally measured initial conditions reproduce 3-D effects and peak vorticity observed in the experiments. The 3-D initial conditions create more patches of vorticity that drive the mixing more quickly than the 2-D initial conditions.

Swathi M. Mula, Adam A. Martinez, Nick Denissen, Kathy Prestridge

Wave Patterns in the Interaction of an Incident Shock with an Elliptic Gas Cylinder

The wave patterns in the interaction between a planar incident shock and an elliptic gas cylinder are studied by two-dimensional Eulerian simulations. The finite volume weighted essential non-oscillatory (WENO) scheme with interface and shock-capturing algorithm is employed. The aspect ratio of the heavy/light elliptic gas cylinder ranging from 0.25 to 4.0 is defined as the ratio of streamwise length to spanwise length. For the heavy cases, numerical results show that the transmitted shock splits in the cylinders with aspect ratio less than one while reflects in the cylinders with aspect ratio greater than one. On the other hand, for the light cases, the wave patterns are similar, and the interaction time is relatively short. As the incident shock propagates downward, the wave patterns change from “free precursor refraction” to “twin von Neumann refraction” in the light cases. Irrespective of cylinder gas species, the greater aspect ratio results in more primary circulation deposition, and the normalized linear deposition rate is nearly the same for different aspect ratio cases.

Wenbin Zhang, Liyong Zou

Investigation of the Interface Stretching Within a Reshocked Mixing Zone Produced by the Richtmyer-Meshkov Instability

The spatiotemporal evolution of a bidimensional (2D) and three-dimensional (3D) air/SF6 mixing layer issued from the development of a Richtmyer-Meshkov instability (RMI) under reshock is investigated using direct numerical simulations (DNS) at moderate Mach number (M = 1.2) and high Atwood number (A = 0.67). This study discusses the relevance of an original criterion based on the measurement of the gaseous interface stretching in the analysis of the mixing process. The first part of the work provides an estimation of the validity of a 2D approach in time for the retained simulation cases. To this avail, a 2D simulation for one typical parameter set is compared to its 3D counterpart. As a means of comparing the development of the mixing layer in both simulations, the classical criterion relying on the evaluation of the mixing layer thickness has been chosen. This criterion is commonly used to characterize baroclinic instability as it is intuitive and easy to compute and to analyze. However, this criterion only provides the mixing zone frontiers but does not provide information about the length scale content and its evolution on the interface. In order to tackle this issue, it is proposed to adapt a still documented criterion for the determination of the interface stretching, based on the computation of the temporal evolution of the mixing interface length for the study of various cases involving different initial interface perturbations, with reshock consideration.

P. Graumer, S. Jamme, Y. Bury

Self-generated Magnetic Fields in the Plasma Richtmyer-Meshkov Instability

Self-generated magnetic fields that arise in initially unmagnetized plasma during the ideal two-fluid plasma Richtmyer-Meshkov instability of a thermal interface are investigated computationally. These fields are of significant interest as they may adversely affect the coupling between the laser energy and the fuel in inertial confinement fusion implosions. We explore the mechanism by which these fields are generated and how their strength depends on the plasma parameters.

V. Wheatley, Daryl Bond, Y. Li, R. Samtaney, D. I. Pullin

The Evolution of a Square SF6 Gas Cylinder Impacted by a Converging Shock Wave

Based on the large-eddy simulation, combined with the fifth-order weighted essentially non-oscillatory scheme and the two-order central difference scheme, the evolution of a square SF6 gas cylinder impacted by a converging shock wave has been numerically simulated. The numerical results present clearly the deformation of cylinder interface induced by the Richtmyer-Meshkov instability due to the interaction of converging shock wave with SF6 cylinder, which accords well with the previous experimental results. In addition, our results reveal more details about generation process of the Mach configuration when the converging shock wave interacts with the SF6 gas interface. The pattern and the development of the transmitted shocks and the transmitted reflected shocks are also expatiated before the shock focusing. The complex wave structures and the pressure distributions at different moments after refracted shock focusing are discussed in detail. The reflected shock waves moving along the interface and rarefaction waves generated due to the expansion of the interface are the main reasons to form the pressure difference between the inside and the outside of the interface, resulting in bubble-spike structure reversing on the evolving interface.

C. Zheng, Z. Chen, H. Zhang, S. Zhu

Electron Shock Dynamics in the Two-Fluid Plasma Richtmyer-Meshkov Instability

The dynamics of the electron shock in a two-fluid plasma simulation of the planar Richtmyer-Meshkov instability of a thermal interface are presented. In this study the electron shock is generated by a general Riemann problem before processing the electron density interface. The interface then undergoes significant oscillation which is coupled to a breakdown of the electron shock into an oscillatory wave packet. The evolution of the electron fluid is shown to be heavily dominated by electromagnetic effects due to the presence of charge separation. Acceleration of the electron fluid by the Lorentz force is found to be equal in magnitude to that provided by the pressure gradient leading to the observed oscillatory behavior.

Daryl Bond, V. Wheatley, R. Samtaney, D. I. Pullin

The Evolution of Concentration and Velocity Fluctuations in the Richtmyer-Meshkov Instability

The Richtmyer-Meshkov instability (RMI) is studied experimentally in the Wisconsin Shock Tube Laboratory (WiSTL) using a broadband, shear layer initial condition at the interface between a helium-acetone mixture and argon. This interface (Atwood number A = 0.7) is accelerated by either a M = 1.6 or M = 2.2 planar shock wave, and the development of the RMI is investigated through simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) measurements at the initial condition and four post-shock times. Simultaneously measuring concentration and velocity allows us, for the first time, to experimentally determine turbulence quantities in this regime, such as the Reynolds stresses, as well as study the effect of incident shock strength on turbulent mass-flux velocities, and the evolution of the planar turbulent kinetic energy (TKE) spectrum.

D. Reese, C. Noble, A. Ames, J. Oakley, D. Rothamer, R. Bonazza

Numerical Investigation of High-Temperature Effects in a Shock-Bubble Interaction

A numerical investigation of the interaction of a planar shock with an isolated cylindrical gas inhomogeneity, often termed “shock-bubble interaction (SBI),” is performed in this work. This interaction is a representative situation of the Richtmyer-Meshkov instability. Most of the simulations performed to analyze this interaction have employed the calorically perfect gas model, resulting in constant values of the specific heats and the specific heat ratios for both the ambient and the bubble gases. If the incident shock Mach number is sufficiently high, the high post-shock temperatures can excite the vibration modes in polyatomic gases rendering them calorically imperfect. In such a case, the specific heats and the specific heat ratio become a function of temperature. The effect of calorically imperfect gases on the dynamics of the SBI is investigated by performing simulations with the incident shock Mach number of 6. In particular, three gas combinations are investigated, namely, “air-Ar,” “air-He,” and “air-N2.” For each combination, the bubble and ambient media are interchanged. Furthermore, air and nitrogen are considered as calorically perfect as well as calorically imperfect to study the effect of temperature-dependent specific heats. The simulation results indicate that that effect of change in specific heat ratio is significant only when the Atwood number is small.

M. P. Ray, B. P. Puranik, U. V. Bhandarkar

Numerical Investigation of the Interaction Between a Planar Shock Wave with a Square Bubble Containing Different Gases

The interaction between a planar shock wave and a rectangular bubble containing either SF6, He, Ar, or CO2 is studied numerically. It is shown that due to the existing large differences in the molecular weight and the specific heat ratio between these gases, different wave patterns are developed during the interaction process. As expected, the fastest transmitted shock is witnessed in the He case, while the slowest is the transmitted shock wave in the SF6 case.

D. Igra, O. Igra

Underwater Shock Waves by Explosion in a Closed Space

This paper reports an experimental result of underwater shock wave generation by an explosion in a closed space for an establishment of shock wave amplitude method related to the shock wave medical and biomedical application. In this study, a metal tube made of stainless steel (SS304) was used as a closed space. The metal tube was placed only partly under the water surface in a water-filled chamber. A shock wave was generated in the metal tube by detonating a micro-explosive (10 mg silver azide pellet) which was placed about 5, 10, and 15 mm from the bottom of the tube. The process of underwater shock wave propagation from the tube was visualized by shadowgraph method and recorded by a high-speed framing camera. The pressure history of a generated shock wave was measured simultaneously by a spatiotemporal pressure sensor.

K. Ohtani, T. Ogawa, A. Nakagawa, K. Nakagawa

Collision of Underwater Explosion with Compressible Porous Wall

Interaction between complex structure with underwater explosion (UNDEX) is related to extensive damage of structures and ship at sea or undersea from explosion hazards. This study is predicting for the pressure and momentum attenuation of UNDEX environment. Porous compressible material will be able to disperse the inertia and momentum of shock loading, bubble pulse, and bubble jet of UNDEX. Results show that semicircle wall in low-porosity foam shows good performance with attenuation of UNDEX environment.

K. Kitagawa, D. Nagahiro, K. Ohtani, A. Abe

Disturbance Waves Behind the Shock Propagating Through Nonuniform Gas

A one-dimensional shock propagation through nonuniform gas at rest is considered. Disturbance waves behind the shock have been analyzed. In addition, we found a particular nonlinear solution for the disturbances behind the shock wave.

A. P. Kalinchenko, F. V. Shugaev

Study on Mach Stem Shape of the Asymmetric Overall Mach Reflection

In this paper, the Mach stem shape of the asymmetric overall Mach reflection is studied analytically. Based on the experimental results, we can conclude that the angle difference between two wedges would result in the flow deflection. Then, we assume the Mach stem is ellipse shaped. Afterward, the analytical method is applied to describe the Mach stem shape. Compared to the fine structures using nano-tracer planar laser scattering (NPLS) technique, the analytical results agree well with the experimental results.

Y. Tao, W. D. Liu, X. Q. Fan

Experimental and Numerical Investigation of a Shock Wave Propagation Through a Bifurcation

The propagation of a planar shock wave through a “Y” bifurcation duct system is both experimentally and numerically studied. Experiments were conducted in an 80 × 80 mm square shock tube section at atmospheric pressure, for incident planar shock waves having Mach numbers of 1.12 and 1.36, respectively. We show that the pressure prevailing behind the reflected shock wave from the end wall of the Y-shaped duct is less than half of what exists behind a reflected shock wave from a similar straight duct under the same initial conditions. Furthermore, numerical results allow pointing out that the expansion ratio of the cross-sectional area where the shock wave propagates is a preponderant parameter in attenuating the strength of a shock wave compared to the duct geometry.

A. Marty, L. Biamino, G. Jourdan, E. Daniel, J. Massoni, L. Houas, D. Leriche

The Reflection of Cylindrical Shock Wave Segments on Cylindrical Wall Segments

The reflection of a two-dimensional cylindrical shock wave segment on a concave-cylindrical wall segment was investigated from an experimental and numerical perspective. The images obtained from experiment show no qualitative difference between cylindrical shock behavior and how a plane shock would behave in terms of the features developed. The length of the shock’s Mach stem was plotted against subtending angle. Two limits are highlighted, one where the shock’s radius is much larger than the wall’s radius and another where the wall has the larger radius: the former being akin to a plane shock interacting with a cylindrical wall segment. The increase in initial shock Mach number was observed to affect the type of Mach reflection that is formed as well as the transition point to a transitioned Mach reflection.

Bright Ndebele, B. Skews

On InMR-TRR Transition on a Concave Cylindrical Reflector

The paper presents experimental, numerical, and analytical work aiming at the reexamination of the current state of knowledge regarding the transition from inverse Mach reflection (InMR) to transitioned regular reflection (TRR) on a concave cylindrical surface. The obtained experimental and inviscid numerical wall angles at the InMR-TRR transition agree well with each other, while their values are considerably higher as compared to the experimental results of the early 1980s, which can be largely attributed to lower resolution of the latter. A number of available analytical approaches are compared with the present experiments and simulations, leading to the conclusion that there is still no fully satisfactory analytical model of the transition.

F. Alzamora Previtali, E. Timofeev, H. Kleine

Reflection of a Planar Shock Wave Over a Concave Double Wedge

The concave double wedge is the simplest model of the reflecting surface which can elucidate the MR→RR transition problem. Both experimental and numerical investigations have been conducted for different concave double wedges. The dynamics of the shock wave configurations arising on the first and the second surfaces of a double wedge is carefully studied.

M. K. Berezkina, I. V. Krassovskaya

Jetting in Strong Shock Reflections Through Low Isentropic Exponent Gases: Experiments and Navier-Stokes Simulations

Forward jetting and Mach stem bifurcation of irregular shock reflections are studied numerically and experimentally for a wedge angle of 30°. Simulations of the Navier-Stokes equations, resolving the shock width, show increasing Mach stem bulging with Mach number and decreasing isentropic exponent. Experiments in rich propane-oxygen and in hexane are performed using a plane of symmetry as the reflecting surface. Wall jetting and Mach stem bulging are shown to increase with Mach number, and Mach stem bifurcation is observed.

S. SM. Lau-Chapdelaine, Q. Xiao, M. I. Radulescu

The Influence of a Pulsed Driver on the Micro Shock Propagation

A high-speed magnetic valve is applied to generate a shock wave with an initial Mach number of 1.6 in a square shock tube with 200 μm hydraulic diameter. Different from previous works, the current work focuses on the effects of a pulsed driver. These effects are caused by unsteady conditions resulting from the short duration of the valve opening τ time. Experiments are performed for different values of τ. The results show that τ correlates with the micro shock attenuation and the friction. Different from expectation, a pulsed driver does not necessarily result in a weaker shock wave.

Y. Kai, W. Garen, U. Teubner

Investigation of an Expansion Fan/Shock Wave Interaction Between High Aspect Ratio Wedges

Shock waves and expansion fans form in supersonic flows as a mechanism to allow fluid to flow conformally over a body. When bodies are in close proximity – such as in the aerospace applications of store carriage and release from aircraft, engine inlet design, and formation flying – these shock waves and expansion fans interact and give rise to an interesting flow field warranting further investigation. The present research focused on modelling an expansion fan/shock wave interaction both experimentally and numerically, and these results were used to validate the basic flow physics of the interaction as well as the analytical model to predict the shock curvature originally published by Li and Ben-Dor. From the results, it can be concluded that both the curvature of the shock and the deflection of the expansion fan increase with increasing shock generator angle of attack. The analytical solution for predicting the shock curvature derived by Li and Ben-Dor is valid for predicting the amount of curvature of the shock (i.e., the concavity of the shock, given by the second derivative of the equation for the shock curvature) but underpredicts the range over which the expansion fan/shock wave interaction occurs and is thus invalid for analyses concerned with the extent of the shock curvature and modelling the full interaction.

Lara Nel, B. Skews

Interaction of Multiple Cylindrical Expanding Shock Waves

The study of shock-shock interaction has interested researchers since the days of Ernst Mach. The nonlinearity of the shocks yields a complex interaction featuring a Mach stem. This phenomenon is very similar to the reflection patterns of a planar shock wave over an inclined wedge. As the shocks expand, the two-shock system is no longer able to turn the flow as much as needed, and a Mach stem is generated. As the shocks continue to expand, so too does the Mach stem. The expansion of a shock wave has been studied analytically by Lin (J Appl Phys 25:54–57, 1950) and Taylor (Proc R Soc Ser A Math Phys Sci 201:159–174, 1954) for two and three dimensions, respectively. In these cases, however, there is only a single blast. For shock-shock interaction, von Neumann’s (Oblique Reflection of Shocks. Bureau of Ordinance, Washington, DC, 1943) work using a planar shock wave over a wedge, while similar, does not consider the decaying properties behind an expanding shock wave. This study will focus on two separate numerical methods; geometrical shock dynamics (GSD) and Euler simulations. Each of them was used to study a two-dimensional shock interaction case with two cylindrically expanding shock waves. The results from the GSD and Euler simulations were then compared to analogous experimental work conducted by Higashino et al. (Shock Waves 1:275, 1991). Good agreement is seen between the three cases apart from early times in the case of GSD.

S. Qiu, N. Amen, V. Eliasson

Shock Interaction on a V-Shaped Blunt Leading Edge

A V-shaped blunt leading edge configuration brings unavoidable hypersonic shock interactions which can result in an extremely high aerothermal load. Experiments and numerical simulations were carried out to study the behaviors of those complex shock interactions on V-shaped blunt leading edges. An abnormal Mach reflection (MR) configuration which includes two inverse Mach reflections (InMR+InMR) was found surprisingly in the experiment for the first time. And a new kind of hysteresis process in the regular reflection (RR) to InMR transition was found with the Mach number variation in numerical result.

Zhiyu Zhang, Zhufei Li, Fengshou Xiao, Yujian Zhu, Jiming Yang

Partial Confinement of Detonation Products by Shock Reflection from a Convergent Nozzle Opening

Following an explosion in a partially confined chamber, such as a room with a door or a window, a shock wave will emerge from the opening followed immediately by a mixed flow of air and detonation products (DP). We designed a truncated cone-shaped nozzle opening that reflects the initial blast wave in such a way that it postpones venting and reduces the amount of DP that vent out of the chamber. We conducted a series of experiments with a C4 charge in a cylindrical tank of volume 0.57 m3 and multiple nozzle designs. Pressure inside the tank was recorded, and fast imaging of the exhaust cone was used to find the exit time and amount of DP venting through the opening. The measurements’ results were compared to OpenFOAM® simulations, and some of them were found to be in a good agreement. The tests show that a smaller amount of DP is ejected from the tank when a convergent conical nozzle is used compared to a flat flange with the same opening size. We therefore conclude that such an opening shape gives the desired use of shock reflection to hold the DP inside the tank for a considerably longer time.

Y. Schweitzer, Y. Lefler, A. Ravid, D. Sidilkover, S. Pistinner, A. Fedotov-Gefen, G. Lifshitz

Geometrical Perception of Convex Surface Reflections

Experiments and inviscid numerical computations were performed in air at an incident shock wave Mach number of 1.3. The incident shock waves were reflected over cylindrical convex surfaces. The models differed in the radii and initial angles. Great agreement was obtained between the high-resolution computations and the high-resolution experiments. Examination of the flow Mach number distributions revealed a fundamental difference between pseudo-steady and unsteady reflections. As the radius of the surface increases, the orientation of the reflected shock wave, with respect to the incident shock wave, approaches its orientation in a pseudo-steady reflection. This means that the radius of curvature does play a rule in the RR reflection. Therefore, it is reasonable to assume that the RR→MR transition is also affected by the radius of curvature. This observation is in contrast with the claim that variation between the RR→MR unsteady and pseudo-steady transitions is a result of optical limitations as was previously suggested by several studies. The problematic estimation of the RR→MR transition is also discussed. This study is a section of an extensive ongoing research dealing with the unsteady mechanism that leads to transition.

M. Geva, O. Ram, O. Sadot, G. Ben-Dor

Numerical Simulation of Supersonic/Hypersonic Flow for TSTO’s Staging Separation

For the next-generation space transportation system, two-stage-to-orbit (TSTO) is one of the possible concepts. This paper discusses the aerodynamic effects around the TSTO which consisted of orbiter and booster at the hypersonic ascend and the separation using the computational fluid dynamics. The effects of shock wave interaction to aerodynamic coefficients were investigated with changing freestream velocity, angle of attack, and relative position between the orbiter and booster. Firstly, the aerodynamics at the separation of the ascending booster and orbiter was investigated. It was found that the orbiter and the booster behave oppositely on the lift and the moment. It means both vehicles can come to separate each other without any control. The shock wave interactions and reflections between booster and orbiter moment showed oppositely. At the separation, although the moment of the booster had negative value and decreases when α decrease from α = 0, orbiter kept positive value. In this study, the model changed relative positions were also investigated. Orbiter’s horizontal position Δx-changed model indicated higher moment than that of standard one. Separation angle θ-changed model had negative moment value. To investigate the effects due to the combination of the orbiter and the booster, two configurations (the combined and uncombined (booster)) are compared. As horizontal direction force; the drag was not related to shock wave interaction. On the contrary, the lift (perpendicular direction force in the freestream direction) was related to shock wave interaction. Accordingly, in all phase moment, it was showed that the orbiter and the booster can separate successfully due to the shock interactions.

H. Iwafuji, Y. Kurata, M. Kanazaki, T. Fujikawa, K. Yonemoto

Experimental Study of Normal Shock Wave-Isotropic Turbulence Interaction Using Counter-Driver Shock Tube

A counter-driver shock tube, which realized a normal shock wave-grid turbulence interaction in various conditions, was developed. Also, a new method to calibrate constant temperature hot-wire anemometer using shock wave experiments was developed. Using the shock tube, an interaction experiment between a normal shock wave (M s = 1.01) and isentropic turbulence (rms velocity fluctuation was 6.8 m/s) was conducted. Although frequency analysis on overpressure history measured by a pressure transducer was practiced, clear difference caused by the interaction has not been obtained yet.

T. Tamba, M. Kayumi, H. Kawasaki, H. Fujiwara, A. Iwakawa, Akihiro Sasoh

Numerical Studies on the Form of Weak Shock Reflection Over Wedges

A transition from regular to Mach reflection of shock waves over wedges was investigated experimentally and numerically. Experimental and numerical results showed good agreements on trajectory of shock triple point. It was demonstrated that the influence of boundary layer is very significant on the transition condition.

Kazuaki Hatanaka, M. Hirota, T. Saito, Kazuyoshi Takayama

Shock Wave Generation Method Using High-Speed Jet

The shock wave generation in a closed tube using the high-speed jet injection was experimentally investigated. The unsteady behavior of the gas compression by the jet injection was visualized by the schlieren method, and the temporal history of the overpressure was measured by the pressure transducers which flush mounted in a tube. The injected jet can compress the gas in the tube, and the shock wave generation was observed by schlieren visualization and the pressure measurement. The characteristics of the jet and the relation between the cross-sectional area of the jet and the tube had an important role for the shock wave generation.

A. Iwakawa, H. Kawasaki, M. Kayumi, Akihiro Sasoh, T. Yamashita, Y. Furuta

Analytical Prediction of Mach Stem Height for Asymmetric Wedge Reflection in 2-D Steady Flows

An analytical formulation for the prediction of Mach stem height for asymmetric wedge reflection in 2-D steady flows is presented. The present model is based on a previous model for Mach stem height in a symmetric reflection. The asymmetric Mach reflection configuration is approached as the combination of upper and lower domains of symmetric Mach reflection. Assumptions made for closing the combined set of equations are discussed. The Mach stem heights are calculated using each set of closing equations. The von Neumann condition for Mach reflection to regular reflection transition in asymmetric case is satisfied by this model for all closing equations.

Shobhan Roy, G. Rajesh

Upstream Pressure Induced MR-RR Shock Transitions

This study investigates the effect of upstream total pressure on shock transition from Mach reflection (MR) to regular reflection (RR). In the present work, the shock transitions in two geometric configurations are studied: (1) underexpanded confined jet and (2) convergent- divergent (C-D) nozzle with extended wall from the exit plane. The experimental study reveals that a MR shock structure is formed initially, for both cases, which then transforms to an RR with increase in primary jet total pressure. It was found that an increase in primary jet total pressure results in the downstream movement of the Mach stem with upstream Mach number and the shock angle of the first oblique shock leg in the MR remaining constant. This is in contradiction to the classical MR-RR transformations. The transformation in the present case is found to be a total pressure variation-induced transformation, which is a new kind of shock transformation.

R. Arun Kumar, G. Rajesh

Revisiting Shock Propagation in a Temperature Gradient

Shock wave propagation through an inclined inhomogeneity is investigated experimentally and numerically. The shock wave is generated by exploding wire technique, and its propagation is captured using shadowgraph technique. The numerical simulation is performed using an in-house code. When a shock wave encounters such a medium, the flow field is no longer symmetric. The transmitted shock rotates itself to travel along the inclination axis, the precursor regions are relatively elongated, and the baroclinicity-induced vortices are skewed with respect to the inclination axis. This study also explores the possibility of using the inhomogeneity as wave guides.

S. Sembian, M. Liverts, N. Apazidis

On Hysteresis at Axisymmetric Curved Shock Reflection from an Axial Cylinder

The phenomena of hysteresis in the process of transition from regular to Mach reflection and back to regular reflection are studied using CFD to simulate the impingement of a curved axisymmetric incident shock on a cylinder placed along the axis of the flow. Pseudo-steady calculations conducted with decreasing and increasing cylinder radius are performed, causing a change in the incident shock strength that is sufficient to traverse the dual-solution domain in both directions. Hysteresis is shown to be present, although the points of transition are inconsistent with the detachment and von Neumann criteria.

B. Shoesmith, E. Timofeev

Singularity Formation in the Geometry of Perturbed Shocks of General Mach Number

While planar shock waves are known to be stable to small perturbations in the sense that the perturbation amplitude decays over time, it has also been suggested that plane propagating shocks can develop singularities in some derivative of their geometry (Whitham (1974) Linear and nonlinear waves. Wiley, New York) in a nonlinear, wave reinforcement process. We present a spectral-based analysis of the equations of geometrical shock dynamics that predicts the time to singularity formation in the profile of an initially perturbed planar shock for general shock Mach number. We find that following an initially sinusoidal perturbation, the shock shape remains analytic only up to a finite, critical time that is a monotonically decreasing function of the initial perturbation amplitude. At the critical time, the shock profile ceases to be analytic, corresponding physically to the incipient formation of a “shock-shock” or triple point. We present results for gas-dynamic shocks and discuss the potential for extension to shock dynamics of fast MHD shocks.

W. Mostert, D. I. Pullin, R. Samtaney, V. Wheatley

A Generalized Form of the Simplified Bernoulli Trial Collision Scheme Applied to Shock Waves

The motivation of this research is to present a generalization of the intermolecular collision schemes in the framework of the direct simulation Monte Carlo (DSMC) method derived from the Kac stochastic equation. Here, we derive a generalized form of the Bernoulli Trial collision scheme (GBT) where the number of selected pairs is any desired value smaller than (N (l) − 1), i.e., N sel < (N (l) − 1). The present generalization further improves the computational efficiency of the Bernoulli Trial-based collision models compared to the standard no time counter (NTC) and nearest neighbor (NN) collision models. We evaluate the accuracy and performance of the GBT scheme in treating flows with shock waves.

Ehsan Roohi, Stefan Stefanov

On the Problem of Shock Wave Structure

We consider the problem of internal structure of the triple point appearing in Mach reflection, which is considered to be important for the cause study of the von Neumann paradox as well as the shock reflection itself in rarefied gas. We investigate it in an adequately made finite region near the triple point and use analytical approach rather than numerical to have a solution of 2D Navier-Stokes equations system, by which we can avoid the difficulties such as the need for ever finer mesh size for the region not known in the beginning. We consider first one-dimensional flow in a finite region, which gives a flow with a hump unlike conventional one of monotonous change for the infinite region. Then we seek a solution of the 2D Navier-Stokes equations system in polar coordinates to the flow field between two curved boundaries. Results show the incoming parallel flow bents to the direction of the slip flow and the density distribution along the streamline increases similar to that for one-dimensional shock structure but a small hump as the solution over to the flow for a finite range.

A. Sakurai, S. Kobayashi

Ab Initio Simulation of Shock Waves Propagating Through Gaseous Mixtures

A structure of planar shock wave propagating through a helium-argon mixture is calculated applying the direct simulation Monte Carlo method based on ab initio interatomic potential for several values of the Mach number in the range between 1.5 and 10. To characterize the density and temperature variations along the shock wave, dimensionless slopes of these quantities, defined through their maximum derivative with respect to the spatial coordinate, are calculated. A comparison of the slopes and density distributions for different values of molar fraction shows that the chemical composition strongly affects the shock wave characteristics.

Felix Sharipov, Fernanda C. Dias

Comparison of DSMC Chemistry Models for Rarefied Shock Tube Simulations with Nitrogen

Shocks encountered in high Mach number flows lead to dissociation of gas molecules. At present, the DSMC codes that simulate such flows under rarefied conditions account for dissociations using phenomenological models such as the total collision energy (TCE) model. However, these models calculate the cross sections using equilibrium rate constants and are not appropriate to use during non-equilibrium situations. The present work calculates cross sections using ab initio methods that first calculate a highly accurate potential energy surface (PES), followed by using the quasi-classical trajectory (QCT) method to generate cross sections. A shock tube under rarefied conditions containing nitrogen gas is simulated wherein cross sections are implemented using the ab initio method as well as the classical TCE model for comparison. The comparison shows a difference in the prediction of nitrogen dissociation for high enthalpy areas where non-equilibrium is expected.

Tapan K. Mankodi, Upendra V. Bhandarkar, Bhalchandra P. Puranik

Experimental and Numerical Studies on the Plume Structure of Micro-nozzles Operating at High-Vacuum Conditions

Recently micro-thruster-based miniature nozzles are gaining research interest due to the advent of micro-propulsion technology for micro-spacecraft and attitude management requirements of micro- and nano-satellites. Micro-nozzles experience all types of flow regimes from continuum to free-molecular flows when they are operated at high-vacuum conditions. Experimental and numerical analysis of cold-flow plume structure of a typical conical micro-nozzle is presented here. The plume structure is visualized using glow discharge flow visualization (GDFV) technique and surveyed the entire plume axially with a static pressure probe. Numerical modeling of a micro-nozzle operating in rarefied condition is done using a coupled Navier-Stokes (NS)-DSMC method, and the pressure profile of the nozzle plume is compared with that obtained in experiment.

K. M. M. Rafi, B. A. H. Fahd, M. Deepu, G. Rajesh

Study of Rarefied Flow Around Rectangular Cylinder Using DSMC

The rarefied flow around a rectangular cylinder is studied using in-house developed DSMC solver. When the flow becomes rarefied, the nature of the shock system will be affected and also the cases with high Knudsen number will be difficult to simulate using Navier–Stokes equation. 2D-DSMC solver is developed to study high Knudsen number flows or rarefied flow regimes. Particle collisons are treated by variable hard sphere model with Larsen–Borgnakke model for rotation which is adopted in the present code. In the present simulation, a rectangular cylinder of 6 × 6 mm is investigated for a range of Mach number 2.0–5.0 with different Knudsen numbers. The result indicates that the shock gets smeared with increasing Knudsen number. Also, the increasing Knudsen number shows that pressure load acting on the rectangular cylinder gets reduced.

P. S. Vignesh Ram, Heuy Dong Kim, Minoru Yaga

Influence of Phase Transitions Components of Mixtures on Thermodynamic Parameters of Shock-Wave Loading

The results of modeling the thermodynamic parameters of shock-wave loading of heterogeneous mixtures are presented in this work. Thermodynamic equilibrium model TEC is used in the modeling. The possibility of a phase transition of the components of the mixtures under high dynamic loads is taken into account. The model allows reliably describe area of polymorphic phase transition, considering the material in the field of phase transition as a mixture of the phase of low- and high-pressure phases. It is shown that the conditions for the start of the phase transition for a pure substance can also be used in the modeling of mixtures comprising one or more components experiencing a phase transition under shock-wave loading. The data of the model calculations are in good agreement with the data of different authors defined on the basis of the experiments. Thermodynamic parameters of mixtures of nitrides, solid and porous mixtures of quartz SiO2, and mixtures containing bismuth Bi as a component are modeled reliably.

K. K. Maevskii, S. A. Kinelovskii

Experimental Study of Ejection of Particles from Shock-Loaded Metals

When a strong shock wave reaches a free surface of metals, there occurs an ejection of microparticles from the surface. The number and size of particles depend on the metal, finishing of its surface, incident wave shape, and many other factors. Most experimental studies investigate the particle ejection in dependence on the shape and size of irregularities (notches and grooves) on the surface of metals. The resulting data are necessary for numerical simulation of particle ejection processes. The existing methods of particle detection enable determination of the maximum particle velocities (optical, X-ray, and piezoelectric sensors), particle momentum (piezoelectric sensors), and microparticle sizes (optical and holographic sensors). The greatest difficulties arise in the measurement of the particle mass distribution and particle distribution by size. In this paper, the mass distribution along the jet was measured using the “soft” synchrotron radiation spectrum of the VEPP-3 collider.

K. Ten, E. Pruuel, A. Kashkarov, I. Rubtsov, A. Muzyrya, K. Prosvirnin, G. Rykovanov, E. Smirnov, M. Stolbikov, L. Shekhtman, V. Zhulanov, B. Tolochko

Phase Transitions of Titanium Under Dynamic Loading

The authors present results of sound velocity measurement in shock-compressed samples of VT1-0 titanium and VT-20. The measurements were accomplished by the rarefaction overtake technique with use of indicator liquids and by the reverse impact method with use of laser interferometer. In titanium, kinks were recorded at the dependence of sound velocity on pressure at the pressures of 20–40 and 60–90 GPa. These kinks can be explained by phase transitions. X-ray structural analysis revealed presence of the ω-phase in the samples, which had been recovered after loading by pressures in steel ampoules in the range from 9 to 23 GPa. Beginning of VT-20 alloy melting relates to pressure of 130 GPa at shock adiabat.

M. V. Zhernokletov, O. N. Aprelkov, A. E. Kovalev, M. G. Novikov, L. I. Kanunova, D. N. Zamotaev, A. N. Malyshev, E. V. Koshatova, D. V. Kryuchkov, A. M. Ivin, V. I. Skokov, А. M. Podurets, M. I. Tkachenko, S. N. Ulanov, S. I. Kirshanov, A. B. Mezhevov, O. V. Myasoedov

Results of Investigations of Phase Transitions of Shock-Compressed Metals

The authors present results of investigations of phase transitions of shock-compressed cerium, pure titanium, its alloy VT-20, tin, and zinc. Loading of the investigated samples was provided by impactors accelerated with use of explosives detonation products or compressed helium.PVDF sensors recorded a two-wave structure consisting of a head wave of isentropic compression and a sequent shock wave in cerium in a range of load pressures from 0.6 up to 6 GPa.In titanium, kinks were recorded in the pressure dependence of sound velocity at the pressures of 20–40 and 60–90 GPa. These kinks can be explained by phase transitions. The X-ray structural analysis revealed the presence of the ω-phase in the samples, which had been recovered after loading by pressures in steel ampoules in the range from 9 to 23 GPa. The onset of the VT-20 alloy melting relates to pressure of 130 GPa at shock adiabats.Jumps of sound velocities, which were revealed in tin and zinc at the pressures of 60–90 GPa and 105–130 GPa, can be, respectively, associated with the beginning and the completion of melting at their shock adiabats.

M. V. Zhernokletov, V. V. Glushchenko, A. E. Kovalev, P. V. Matveev, A. M. Podurets, V. G. Simakov

Shock Wave Propagation Through Heterogeneous Cementitious Composites

Because of the current geopolitical situation, research on improving the resistance of the civil and transport infrastructure to blast or impact loads has gained considerable attention in recent years. This paper presents the results of full-scale blast experiments designed to characterize the resistance of steel-fibre-reinforced concrete full-scale bridge decks subjected to near-field blast loading. Twenty-five kilogrammes of TNT charges were placed on steel chairs in the middle of each slab. The specimens were concrete slabs 6 m in length, 1.5 m in width and 0.3 m in thickness. Following, slabs with multiple placements of basalt mesh were used. The basalt mesh was placed at the half of both upper and lower concrete cover and three times in between both layers of panel reinforcement. To conclude, slabs with deformable layer were used. The layer was made of shredded textiles slabs, 80 mm thick. These slabs were placed in the middle of the slab cross section. The experimental programme was recorded by high-speed cameras, and the recordings were supplemented by PDV (Photon Doppler Velocimetry) measurements of the acceleration of the bottom surface of the studied specimens. Conclusions are drawn from the utilization of the PDV measurements to studying of shock wave propagation through heterogeneous cementitious composites.

M. Foglar, A. Horska, R. Hajek, J. Pachman

Equation of State and Phase Transformations of Zirconium in Shock Waves

An equation-of-state model that represents the relation of pressure with density and internal energy is applied for zirconium in the bcc and liquid phases. Thermodynamic parameters at the principal Hugoniot are calculated for the metal and compared with available data from shock-wave experiments.

K. V. Khishchenko

Reynolds Number Effects on Shock Wave Boundary Layer Interaction in a Hypersonic Flow

The Reynolds number is found to affect the separation bubble for shock impingement locations away from the leading edge where finite separation occurs. A decrease in separation bubble was observed with an increase in Reynolds number. However, as the shock impingement moved closer to the leading edge, a leading edge separation was observed, and the separation flow dynamics was found to be Reynolds number independent.

L. Srinath, S. Mohammed Ibrahim, R. Sriram, K. P. J. Reddy, G. Jagadeesh

Numerical Study for Interactions Between Separation on Supersonic Flow and Laser-Induced Blast Wave

Flow separation on an airfoil was numerically reproduced by integrating a two-dimensional Navier-Stokes equation. We found that the flow separation on the upper surface of the airfoil was suppressed when repetitive pulses were irradiated to the undersurface. An expansion region was induced at a trailing edge of the wing when the blast wave propagated from the under- to upper surfaces. The separation region became smaller because an inverse pressure gradient on the upper surface was relaxed when the expansion wave at the trailing edge interacted with the separation region. A new contactless flow control technique proposed by us was effective to improve an aerodynamic performance of the wing.

M. Takahashi, N. Ohnishi

Unsteady Separation Shock Dynamics in a Mach 4 Shock-Wave/Turbulent Boundary Layer Interaction

High-speed schlieren image processing is applied to characterise the unsteady separation shock dynamics of a step-induced axisymmetric shock-wave/turbulent boundary layer interaction at Mach ∼4, enabling shock motion to be tracked from frame to frame and subsequently analysed within the frequency domain. Two approaches are tested: a first one which assumes the separation shock to be linear and which relies on the Hough line transform for edge detection and a second one which tracks axial shock motions at selected wall-normal heights. Results yield clear qualitative detail into the formation of the shear layer upon boundary layer separation and go on to show that both schlieren-based methods capture well the low-frequency pulsations of the separation bubble, finding good agreement with fast-response wall pressure measurements near separation. Clear evidence on the influence of the separated shear layer on interaction unsteadiness is further provided, with both methods documenting the relative enhancement in higher-frequency motions associated to shear layer shedding (acoustic disturbances from shear layer eddies are clearly shown in the visualisations as well). Given the linearity assumptions within the first method – which intrinsically averages the shear layer jitter effects along the shock wave – the latter is found to perform better in this sense.

X. Huang, G. Chandola, D. Estruch-Samper

Experimental Study of Hypersonic Shock Wave/Transition Boundary Layer Interaction

The experiment based on 15° compression corner model was performed in FD-20 wind tunnel to research shock wave/boundary layer interaction which occurs around transition boundary layer. The pressure sensors, film resistance thermometers, and high-speed schlieren were used in the experiment to study shock wave structures, parameter distributions, and fluctuation distribution. According to the state of boundary layer around separation region, the interactions were divided into “laminar/turbulent interaction” and “transition/turbulent interaction.” For laminar/turbulent interaction, separation bubble and transition boundary layer dominate interaction region, which makes the pressure and heat transfer distribution be similar with pure laminar interaction. For transition/turbulent interaction, boundary layer transition comes to an end quickly downstream separation point, and then turbulence boundary layer and separation bubble dominate the interaction region, which makes the pressure and heat transfer distribution be similar with pure turbulent interaction. While transition occurs in interaction region, the nonlinear interaction between transition disturbances and separation bubble will appear, which makes fluctuation increase.

S. F. Xie, F. Ji, D. Yao, Q. Shen

Micro-vortex Generator Controlled Shock-Boundary Layer Interactions in Supersonic Intake

The efficient combustion necessitates the flow speed reduction from supersonic to subsonic level before entering the burner, which is achieved by a series of oblique and normal shocks in the isolator region of the intakes. However, the advantages of shock-induced compression are compromised by the associated penalties due to shock-boundary layer interactions (SBLIs), leading to intake unstart and abrupt thickening/separation of boundary layer. The micro-vortex generators (MVGs) are well-accepted boundary layer control in subsiding SBLIs. In the present investigation, the Mach 2.2 mixed compression intake controlled using MVGs with varied heights has been experimentally studied. The MVGs of height 200 μm are found to be efficient in promoting mixing near the boundary layer with minimized interaction losses.

G. Humrutha, Mrinal Kaushik, K. P. Sinhamahapatra

MVG Control on the Supersonic Compression Ramp Flow

The present paper is devoted to analyze the control effect of MVG (micro-vortex generator) on Ma = 3.0 supersonic flow over a 25° compression ramp. Visualization of the complex flow structures was gained by employing schlieren and planar laser scattering technique using nanoparticles as tracers. The interaction of vortex with shock waves and the separation zone was revealed. Kinetic parameters measured by PIV were analyzed by POD (proper orthogonal decomposition) to render the features of separation zone and shock unsteadiness.

Z. Chen, X. P. Kong, T. J. Li, K. Yang

Improvement of Pressure Recovery in a Duct by Repetitive Laser Energy Depositions

Impacts of energy deposition approach on performance of supersonic flow over a duct system were experimentally examined. Without using energy deposition, in the case of duct’s normal operation, supersonic flow was found being separated and weakly fluctuating at the duct’s compression surface. Additionally, in the case of unstable operation, supersonic flow was found strongly oscillating at both around the duct entrance and inside the duct chamber. To control these unfavorable influences to duct performance, energy deposition approach with repetition frequency up to 60 kHz was applied. Single energy pulse was confirmed to be able to suppressed flow separation. On the other hand, repetitive energy deposition not only could moderate flow separation but also increase total pressure of the internal flow, though the effectiveness highly depends on applied deposition frequency. Moreover, by applying repetitive energy pulses at 60 kHz, flow oscillation in the case of the duct’s unstable operation could be suppressed, and flow was stabilized.

H. S. Pham, M. Myokan, T. Tamba, A. Iwakawa, Akihiro Sasoh

Unsteadiness of Cowl Shock/Convex Corner Interaction in an Inlet

Experiments in 2-D inlets for both sharp and round shoulders were conducted to study the influence of shoulder shapes and the relative position between the incident cowl shock and the shoulder on the unsteadiness of shock wave/turbulent boundary layer interaction (SWBLI) in a shock tunnel at Mach 5.9. For the sharp shoulder, as the incident shock moves upstream, the position of the separation shock foot changes little, and the fluctuating pressure concentrates approximately at the same location. For the round shoulder, the separation shock foot moves upstream and then crosses over the corner, and the peak positions of fluctuating pressure move upstream. The pre-multiplied spectra of fluctuating pressure near the separation shock increase in a wide bandwidth of low and middle frequency at the round shoulder, whereas the trend is not obvious at the low frequency for sharp shoulder. The present results support that the sharp shoulder has an ability to restrict the low-frequency unsteadiness of separation shock.

Rong Huang, Zhufei Li, Jiming Yang

Incident Shock/Turbulent Boundary Layer Interactions on Concave Walls

Numerical simulations and experiments were performed to investigate the characteristics of incident shock/turbulent boundary layer interactions on concave walls. The concave walls were designed with constant adverse pressure gradients in the flow direction using the Prandtl-Meyer function. On the concave walls, decreasing boundary layer thickness and increasing wall shear stress were observed. The planar incident shock was distorted by the compression waves generated by the concave wall. The inviscid shock impingement position on the concave wall and the pressure rise caused by the shock impingement were calculated by the shock interaction theory. Under the impingement of the incident shocks with the same strength, the separation scale decreases as the adverse pressure gradient caused by the wall curvature increases.

Enlai Zhang, Zhufei Li, Jiming Yang

Experimental Study on the Unsteadiness of an Axisymmetric Shock-Wave/Turbulent-Boundary-Layer Interaction with Separation

An axisymmetric shock-wave/turbulent-boundary-layer interaction (STBLI) induced by a step is studied experimentally at M ∞ = 3.93. A detailed discussion of the unsteady flow field developed along the upstream and downstream separation regions – ahead and behind the step – is presented in terms of the time-dependent pressure data and its spectral analysis. The separation shock exhibits low-frequency motions at a dominant frequency of 391 Hz, and evidence suggests the dominance of downstream flow effects (in the recirculation region) on the large-scale low-frequency pulsations of the separation bubble. The dominant instabilities at the inception of the shear layer are found to be two orders of magnitude higher than the shock unsteadiness and decrease progressively along the interaction as shear layer eddies grow in size.

G. Chandola, X. Huang, D. Estruch-Samper

Numerical Study of Shock Wave-Boundary Layer Interaction in Cylinder-Flare Configuration

This study aims at characterizing shock wave/boundary layer interactions in conical configurations. This preliminary work focuses on the ramp configuration and presents some main differences observed in the statistical turbulence structure upstream and through the interaction region between the conical and planar case.

T. Nakano, G. Lehnasch, E. Goncalves

A Study on Turbulent Transition of Unsteady Boundary Layer Induced by Weak-Compression Wave

A high-speed train enters the tunnel and loud noise occurs at the tunnel exit. This is due to compression wave generated by a train entering into the tunnel. It is important for developing further speed train to clarify the mechanism of the compression wave propagation, which has been strongly affected by the boundary layer characteristics. The purpose of the present study is to clarify the turbulent transition characteristics of unsteady boundary layer, which is generated by sudden started flow induced by weak-compression wave (amount of pressure change: Δp ≈ 2 kPa). The boundary layer is transited by tripping wires, and the velocity distributions are measured by a hot wire anemometer. The results show that the boundary layer transition is confirmed by spectrum analysis of the velocity fluctuation. The transition process of the boundary layer is observed by changing the position of tripping wires, and the turbulent boundary layer is maintained down to about 310 of Reynolds number based on the momentum thickness in the case of inputting the large disturbance into the boundary layer.

D. Tanikawa, T. Hashimoto, S. Sakaue, Takakage Arai, T. Miyachi

Passive Control of Hypersonic Separated Flow Around Spiked Bodies

The occurrence of the two distinct unsteady flow modes, pulsation and oscillation, around axially symmetric spiked blunt bodies facing hypersonic flows leads to pressure fluctuations. Though earlier works have studied the nature of the unsteady flow modes, the influence of the relative afterbody shoulder roundness and shape of the spike tips is not well known. From the present study, it is found that even a slight modification to the shape of the spike tip may result in a change from pulsation mode to oscillation. Also, providing a small radius at the afterbody shoulder can have a significant stabilizing effect on the flow field.

G. Balakalyani, G. Jagadeesh

Surface Heat Transfer of Tertiary Gas Mixtures with Roughness Controlled

Catalytic phenomenon of titanium in a test gas consisting of a mixture of 21% oxygen and 79% argon has been investigated experimentally. The heat-transfer rates at the end-wall of the shock tube are measured using a thin-film gauge. The roughness of the thin-film gauge surface was controlled using a grinder and a sandpaper. The surface of the test model was coated with silicon dioxide or titanium. The heat-transfer rate of a titanium-coated model was approximately 18% higher than that of a silicon-dioxide-coated model. The heat-transfer rates are compared with the theory based on tertiary gas mixtures to obtain the catalytic efficiency. Catalytic efficiency of titanium is deduced to be 0.0044.

Ikhyun Kim, Gisu Park

Effect of Dielectric Barrier Discharge Plasma Actuator (DBD-PA) on Boundary Layer Separation Control in Hypersonic Flows

The experiments were carried out to observe the necessary control or elimination of the separation bubble which occurs during SWBLI (shock wave boundary layer interaction) in hypersonic flows. The dielectric barrier discharge plasma actuator (DBD-PA) as an active flow control technique has been used for this investigation. The study examines the effect of local active flow control of DBD-PA on the stability of laminar separation bubble. The Schlieren imaging is used to study the interaction between the DBD-PA and the SWBLI. The actuator was operated at pulsing frequency of 10 kHz, which generates the starting vortex at the frequency of 50 Hz. The results are presented in this paper. The actuator was arranged in two different fashions to observe its effect as a flow control mechanism in a hypersonic flow.

U. M. Snehal, Mohammed Ibrahim, G. Jagadeesh

Numerical Simulations of Transverse Jet in Supersonic Crossflow Toward an Understanding of Interaction Mechanism

In order to understand the flow mechanism of the self-ignition and the flame holding for the liquid rocket termination operation, the two-dimensional flow simulations on the under-expanded hydrogen jet injected into supersonic air crossflow were carried out at Mach numbers 1.9 and 6.3. Hydrogen and air mixing is mainly observed at the separated recirculation flow aft of the hydrogen jet and at the leeward shear layer between the hydrogen jet and the air free-stream. It was clarified that the size of the separated recirculation flow for Mach 6.3 is larger than that for Mach 1.9. It is mainly due to the high-speed downstream toward the wall generated by the free-stream impingement on the inclined under-expanded jet plume. It implies that the free-stream conditions such as Mach number, the momentum flux ratio J, and the pressure ratio PR should be considered to discuss the possibility of self-ignition and the flame holding.

T. Iwasa, K. Fujimoto, D. Muto, N. Tsuboi

Shock-Induced Corner Separation in Supersonic Duct Flows

The effect of wall separation control on multiple walls was investigated. This study used injection-assisted micro-vortex generators (MVGIs) in a duct flow. Three cases, namely, no control (case A), three-wall control (case B), and four-wall control (case C), were investigated using schlieren imaging, oil flow visualization, and wall pressure measurements. The various shock/compression waves from all the MVGIs were found to interact ahead of the normal shock. Oil flow visualizations on the bottom wall show that there are notable variations in center and corner separations when more walls are being controlled. Pressure recovery for three walls having control was higher than that for no control case, and the recovery for four-wall control case was much higher than that of three-wall control case. The separation zone sizes and the pressure recovery suggest that there is interaction between the separation zones in a duct at a cross section.

S. Vaisakh, A. Ramprakash, T. M. Muruganandam

Forced Boundary Layer Transition Experiments on a Multi-wedge in a Gun Tunnel

A series of wind tunnel experiments have been conducted to investigate the forced transition on hypersonic boundary layer transition on a multi-wedge in a gun tunnel. Two different trip configurations have been introduced on the first wedge, one is diamond shape and the other is swept ramp. The flow Mach number is 6 and the unit Reynolds number is 1.4 E + 07/m. The results show that when k/δ = 0.5, both of these two trips can cause transition and the diamond shape is much more effective than the swept ramp. When k/δ = 0.7, these two trips both can cause transition, but the diamond-shaped trip increases additional heating. Heat flux fluctuation results also show that when the trips are introduced, the flow goes directly to turbulence and rarely flow peaks can be found in the fluctuation signals.

Feng Ji, Xunhua Liu, Xinguo Sha, Zhixian Bi, Qing Shen

Aft-Body Effects on Lip Shock-Wave Laminar Free-Interaction

Compressible Navier-Stokes simulations have been performed to study the laminar near wake of two-dimensional adiabatic hypersonic blunt bodies. In particular, Hinman and Johansen’s modified free-interaction theory has been examined for cylindrical geometries with a truncated aft-body of finite shoulder radius. The geometries investigated were a single parameter family of geometries based on the ratio between the shoulder radius and the fore-body radius. Simulations were performed over a range of Mach (6 < M ∞ < 10) and Reynolds number (10,000 < Re ∞ < 100,000). The pressure rise due to the lip shock formation process was correlated to the properties of the boundary layer prior to the shock-wave boundary layer interaction. The correlation parameter F is shown to be a function of a Reynolds number calculated with post-shock properties and the shoulder radius as the relevant length scale (the shoulder Reynolds number). It has been shown that for a shoulder Reynolds number less than 1500, this interaction is highly Reynolds number dependent. For shoulder Reynolds number greater than 1500, it has been found that the correlation parameter F can be estimated as 0.5 with less than 10% error. Additionally, it has been shown that for a shoulder Reynolds number less than 300, the separation point exists past the shoulder on the base.

W. S. Hinman, C. T. Johansen

Temperature Distribution Measurement for the Comprehension of the Interaction Phenomena Between the Shock Wave and the DC Discharged Field

The temperature deduction method from the visualization data using the correlation between the shock wave velocity and the temperature was investigated and compared with the rotational temperature measured by the emission spectroscopy. The temperature deduced from the visualization data in the case with the discharge (31.9 [W]) was 800 [K] which was significantly higher than that (300 [K]) in the case without the discharge (0 [W]). However, there was discrepancy with the temperature obtained from the emission spectroscopy. In spite of this discrepancy, with some improvement, the temperature deduction method can be a promising method, since this method can deduce the temperature in the region where even the emission signal is weak and cannot determine the temperature from the emission spectroscopy.

Kenji Okada, Kohei Suwata, Takuhiro Kito, Atsushi Matsuda, Shinji Koizumi

An Interaction Between Shock Wave and Vortex Induced by Small Volume High-Pressure Shock Tube

In this research, the behavior and the interaction of a shock wave and a vortex ring using a small volume high pressure are experimentally studied. In order to make the shock wave and the vortex ring interact with each other, an elliptical cell is attached to the end of a shock tube of the low-pressure side. The function of the elliptical cell is to make the propagating shock wave inside the cell focus at the focal point and to generate the vortex ring from the exit of the elliptical cell. The visualization of the flow field took with a high-speed camera for the schlieren method. Pressure variations downstream of the exit are measured in order to figure out the results of the interaction between the shock wave and the vortex ring. As a result, the pressure variations downstream of the cell are found to be peaky compared to that by the straight shock tube. This is due to the effect of the focusing and spreading shock wave which generates the sudden induced velocity in the elliptical cell.

T. Maekawa, M. Yaga, H. Fukuoka, N. Kuniyoshi

Experimental Study on Grid Turbulence Interacting with a Spherical Shock Wave

Wind tunnel experiments are conducted to clarify the turbulence structure in grid-generated turbulence interacting with a spherical shock wave. The Mach number of the shock wave is 1.04 at the measurement location. Streamwise and vertical velocities are measured by the PIV at two instants. One is immediately after the passage of the shock wave and the following expansion fan is passing in the image, and the other is after the passage of the expansion fan and before the arrival of the reflected shock wave from the walls. The results show that the vorticity power spectrum is increased in the entire wavenumber region by the shock-wave interaction at both measured instants.

Y. Ito, Y. Ato, Y. Sakai, K. Iwano, K. Nagata, Akihiro Sasoh

Shock Propagation in Media with Non-uniform Density

Flow resolving shock-capturing and shock-resolving simulations are conducted to study the shock propagation in media with non-uniform density. Shock propagation in a simplified one-dimensional configuration is first examined for various types of density profiles. Both shock-capturing and shock-resolving simulations predict the same results, when there is a separation of scales between the shock width and flow scales. The numerical results agree well with theoretical solutions in the case of weak shocks and linearly varying density fields. In the strong shock limit, better agreement with previous results obtained by the method of characteristics is observed when compared with the theoretical solutions. The differences can be attributed to the effects of re-reflected waves immediately behind the shock, which are not considered in the theoretical solutions. For fluctuating density profiles, the numerical results further deviate from the theoretical solutions and exhibit additional long-wavelength oscillations, which are shown to be related to the re-reflected waves. 3D density variations, with and without turbulent velocity fluctuations, are also considered to examine the shock propagation in flows with strongly variable complex density fields.

Y. Tian, F. Jaberi, D. Livescu

Measurement of Velocity Fluctuations and Overpressure of Spherical Shock Wave in Grid Turbulence

Velocity fluctuations of grid turbulence and overpressure of spherical shock wave are measured simultaneously in wind tunnel experiments. The experiments are conducted for four different conditions of grid turbulence, where the turbulent intensity and the length scales are different. Probability density functions (PDFs) of the velocity fluctuation and the peak-overpressure fluctuation measured on the wall are calculated in each experimental condition, and both follow the Gaussian profile. In this study, the instantaneous spatial distributions of turbulent velocity are estimated with the Taylor hypothesis. Correlation coefficients are calculated for the peak-overpressure fluctuation and the spatial distribution of the low-pass filtered turbulent velocity fluctuation to evaluate the relation between them. The positive correlation is found for the velocity fluctuation at the location away from the wall. The correlation calculated for a wide range of the cutoff length shows that the turbulent motions of the order of the integral length scale have large influences on the peak-overpressure fluctuation.

K. Inokuma, S. Nishio, T. Watanabe, K. Nagata, Akihiro Sasoh, Y. Sakai

The Influence of the High-Pressure Part Length on Shock Waves Exiting from an Open Tube

The influence of the length of the high-pressure part on the flow field generated by an open shock tube is experimentally investigated, in particular with respect to the so-called critical length of the driver section. The differences seen when operating the shock tube with drivers below or above the critical length are presented. It is found that for an operation with short drivers (at or below critical length), the outflow following the shock and the vortex ring is unsteady, but the influence on the leading shock and the vortex is minimal.

C. Wilson, H. Kleine

Robust and Low-Dissipation Explicit Formulation of Improved Adaptive WCNS Scheme

In this paper, a novel adaptive central-upwind WCNS (weighted compact nonlinear scheme) based on an adjusting parameter of smoothness indicator is proposed. For the purpose of restraining numerical dissipation in smooth regions, avoiding spurious numerical oscillations dramatically, and preserving shock-capturing ability around discontinuity regions, an adaptive parameter is introduced in this modified WCNS scheme. Based on the above improvement, nonlinear weights could automatically fit discontinuity according to the local flow-field properties obtained by a discontinuity detector. In smooth regions, it is inclined toward optimal central scheme to minimize dissipations and capture turbulent features, while, in discontinuity regions, it is more likely inclined toward upwind scheme for stable shock-capturing ability and numerical robustness. Furthermore, to solve the problem of losing accuracy, the smoothness indicator with a mapping function is introduced. A variety of benchmark-test cases are tested to verify the modified WCNS scheme performance. Numerical results demonstrate that, compared with the EWENO-CU4 scheme, the modified WCNS scheme exhibits excellent shock-capturing ability, lower numerical dissipation, and higher numerical robustness in resolving complex flow features.

Zhao Guo-yan, Sun Ming-bo

Direct Numerical Simulations of Interaction Between Planar Shock Wave and Homogeneous Isotropic Turbulence at Low Turbulent Mach Number

We investigate interactions between a planar shock wave and homogeneous isotropic turbulence by employing direct numerical simulations. The shock wave at the shock Mach numbers 1.5 and 1.1 propagates through the turbulence without mean velocity. The interactions are studied for the statistical properties of turbulence and pressure increase of the shock wave. Fluid compression due to the shock wave causes velocity fluctuations to increase. This influence is more significant for the velocity component in the shock wave normal direction. The fluid compression in the shock wave normal direction also changes the spatial distribution of the vortical structures, resulting in the amplification of enstrophy. The characteristic length scales of turbulence, such as Taylor microscale, decrease by the interaction. The shock wave propagation in turbulence causes the fluctuation of pressure increase across the shock wave. We also show that the fluctuation of the pressure increase becomes stronger for the larger shock Mach number case.

K. Tanaka, T. Watanabe, K. Nagata, A. Sasoh, Y. Sakai, T. Hayase

Numerical Analysis of Shock Wave Diffraction

This work reports analysis of complex shock wave diffraction and longtime behavior of shock-vortex dynamics over splitter geometry encountered in both external and internal compressible flows. The simulation resolved the experimental findings of literature, and the insight of the flow topology is being presented with the probability density functions (PDFs) of various contributing terms of enstrophy transport equation and the invariants of the velocity gradient tensor. We use an artificial viscosity (AV)-based explicit discontinuous spectral element method (DSEM)-based compressible flow solver for this purpose. The numerical scheme utilizes entropy generation-based artificial viscosity and thermal conductivity to simulate the conservative form of the governing compressible flow equations. A shock sensor-based switch is used to reduce the addition of AV coefficients in rotation-dominated regions.

Arnab Chaudhuri, Gustaaf B. Jacobs, Xiao Hong

Investigations on Compressible Mixing Layers by Using Hot-Wire Velocimetry

A constant temperature hot-wire velocimetry (CTV) was used to evaluate the mixing characteristics of supersonic turbulent mixing layer. A hot-wire anemometer is calibrated against compressible air jet of flow Mach number 0.20 < M < 0.84 and Reynolds number around the wire 24 < Re < 109. It is then applied to compressible turbulent mixing layer generated between flows with Mach numbers of 1.5 and 2.0 in a rectangular duct. It is demonstrated how much the root mean square of the fluctuations in mass flux ρU RMS varies depending on the measuring point. The value of ρU RMS at x = 62 mm and y = 7.5 mm is higher than that at x = 25 mm and y = 7.5 mm. It is seen that the mixing layer at x = 62 mm is thicker about 2.5 mm than that at x = 25 mm. In addition, the maximum value of ρU RMS at x = 62 mm and y = 2.5 mm is higher about 30% than that at x = 25 mm and y = 2.5 mm. From these results, it is considered that the mixing at x = 62 mm is enhanced from that at the upstream location x = 25 mm.

T. Ikeda, R. Fuse, K. Hatanaka, M. Hirota, T. Saito, S. Rao

Spectral Radiant Intensity Calculation of Air in Shock Tube

Radiative heat may be greater than convective heat when flying at the velocity above 10 km/s. It is critical to precisely predict radiative heat for thermal protection system design. High-enthalpy flowfield solving and gas species’ radiant coefficient calculation are two main contents in computing radiation heat. A series of tests to obtain quantitative emission spectral radiation of air at high velocity have been conducted in a detonation-driven shock tube. Based on optical calibration and measurement, volumetric spectral radiant intensities of N2 and air have been acquired in the spectrum range of 310–380 nm and in the velocity range of 5.5–8 km/s. Unsteady non-equilibrium Navier-Stokes equations were numerically solved for temperature and gas concentration in the shock tube under test conditions. A narrowband model was used to calculate the gas spectral intensity at the specific position behind the shock corresponding to test time delay. The comparison between the computational results and the test measurement shows that the predictions of the flowfield parameters and the gas spectral radiation intensities are accurate and reliable.

Jun Ming Lyu, X. L. Cheng, J. J. Yu, F. Li, X. L. Yu
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