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About this book

This edited monograph contains the proceedings of the International Shock Interaction Symposium, which emerged as an heir to both the Mach Reflection and Shock Vortex Interaction Symposia. These scientific biannual meetings provide an ideal platform to expose new developments and discuss recent challenges in the field of shock wave interaction phenomena. The goal of the symposia is to offer a forum for international interaction between young and established scientists in the field of shock and blast wave interaction phenomena. The target audience of this book comprises primarily researchers and experts in the field of shock waves, but the book may also be beneficial for young scientists and graduate students alike.

Table of Contents

Frontmatter

Scale Effects on the Transition of Reflected Shock Waves

This is a summary of shock tube experiments performed at the Tohoku University from 1975 to 2005. Critical transition angles of reflected shock waves over concave and convex walls of radii from 20 to 300 mm were experimentally obtained and compared with the numerical simulation based on the Navier–Stokes equations. The experimental critical transition angles varied with the radii of curved walls and strongly affected by the presence of the boundary layer developing along curved walls. The effects of critical transition on shock wave dynamic, shock wave reflection from roughened wedges, double wedges, and shock focusing from curved walls were presented.
Kazuyoshi Takayama, Atsushi Abe, Mikhail Chernyshov

Transition Effect on Shock Wave Boundary Layer Interaction on Compressor Blade

Intensive research on the laminar flow is carried out nowadays. The main objective is to keep the laminar boundary layer as long as possible for the drag or losses reduction, depending on the application. Nevertheless, in some applications, the laminar layer interaction with the shock wave may lead to a strong flow separation. The process of separation usually becomes unsteady and causes buffeting at airfoils and shock oscillations in the internal flows. Shock oscillation causes pulsation of pressure, and consequently a change of the blade load. The main objective of this research is to study the effect of transition on the flow structure of the shock wave boundary layer interaction. This paper focuses on the influence of boundary layer transition on the flow pattern in the blade passage of a compressor cascade. The main question is whether the induced transition upstream of the shock can improve the pressure unsteadiness and the flow downstream of the interaction. The results presented here concern experimental investigations and the used combination of various methods allowed gaining an insightful analysis of the application of transition control devices into a complex flow structure in a compressor cascade passage.
Ryszard Szwaba, Piotr Doerffer, Piotr Kaczynski

Shock Wave Reflection and Attenuation in the Combined Blast Inhibitors

A robust blast-inhibiting bin is the most often used device for damage blast effects suppression. In particular, a top open cylindrical bin significantly reduces a fragmentation effect resulted from a detonation of an explosive device placed inside the bin. However, reduction of blast wave overpressure and impulse by such cylindrical bins is not sufficient (Gelfand et al, Shock Waves 20:317–321, 2010) [1]. A reasonable alternative to endless increase of height and thickness of robust blast-inhibiting bins is a development of destructible inhibitors having no solid elements in their structure and, therefore, excluding secondary fragmentation. So, the family of “Fountain” inhibitors (Vasil’ev et al, Izv Akad Nauk Energ 6:7–19, 2004) [2], (Silnikov and Mikhaylin, Acta Astronaut 97:30–37, 2014) [3] localizes and suppresses damaging blast effects due to multiphase working system. The present study is analyzing data obtained in testing of prototypes of new combined inhibitors. Their structure combines robust elements (bottoms, side surfaces) with elements responsible for blast loads reduction due to multiphase working system (top and low transverse embeddings) and fairings impeding wave propagation in undesirable directions.
M. V. Silnikov, M. V. Chernyshov, A. S. Kapralova, A. I. Mikhaylin, A. S. Pankov, V. N. Shishkin, A. I. Spivak, A. G. Tyapko

Overexpanded Jet Flow Type of Symmetry Influence on the Differential Characteristics of Flowfield in the Compressed Layer

The evolution of the incident shock in the plane overexpanded jet flow or in the axisymmetric one is analyzed theoretically at the whole range of governing flow parameters. Analytical results can be applied to avoid jet flow instability and self-oscillation effects at rocket launch, to improve launch safety and to suppress shock wave-induced noise harmful to environment and personnel.
M. V. Silnikov, M. V. Chernyshov

Shock Wave Interaction with a Solid Body Floating in the Air

A new shock tube system for the study of shock wave interaction with a solid body floating in the air has been developed. The system consists of a horizontally placed shock tube and a solid-body injecting device, which is mounted on the floor of the test section of the shock tube. A solid body initially placed on the shock tube floor was tossed into the air with the injecting device and then collided with a planar shock wave, which is generated by rapturing the diaphragm between the driver and the driven sections of the shock tube. By tuning the rapturing time of the diaphragm, we can make the shock wave interact with the solid body when it reaches the top of its trajectory almost at rest. In order to demonstrate the applicability of the present system, the shock-induced motion of a hexahedral solid body and the flow field around it were recorded using the shadowgraph technique coupled with a high-speed video camera. Representative results from the present experiments are reported in this paper.
M. Oshima, K. Nakayama, Y. Sakamura

Equation of State of Pure Water, Aqueous Solutions of Sodium Chloride, Gelatin Gel, and Glucose Syrup

For a medical application of shock waves, extracorporeal shock wave lithotripter (ESWL) has been established.
Hiroaki Yamamoto, Kazuyoshi Takayama, Hiroaki Shimokawa

Forecasting Method of Shock-Standoff Distance for Forward-Facing Cavity

Experiments are performed on a cylinder with a forward-facing cavity at the tip in the flow of \( M_{\infty } = 10 \) in FD-14A shock tunnel. The shock shape, shock-standoff distance, and oscillation characteristics are captured by the high-speed movie, and the dynamic pressure response is used to correlate with the acoustic characteristics of the cavity base through the transducer. By analyzing the amount of experimental and numerical results abroad, a forecasting method for shock-standoff distance is proposed. Combination of organ-pipe theory with experimental results of oscillation frequency validates the applicability and effectiveness of the method. Results of shock-standoff distance and oscillation frequency are also obtained for experiments in FD-14A shock tunnel. The forecasting results of oscillation frequency are in accordance with the experimental results. Furthermore, the oscillation amplitude and average velocity of the shock wave are analyzed for forward-facing nose cavity at \( M_{\infty } = 10 \).
Wang Gang, MA Xiao-wei, Jiang Tao, Gong Hong-ming, KONG Rong-zong, YANG Yan-guang

Shock Interactions in Continuum and Rarefied Conditions Employing a Novel Gas-Kinetic Scheme

Shock interactions can have a significant impact on heating rates and aerodynamic performance of hypersonic vehicles. The study presents different shock interactions in partially rarefied hypersonic flows predicted employing a recently developed gas-kinetic scheme for diatomic gases with rotational degrees of freedom. The new gas-kinetic schemes will be presented along with shock/wave boundary interactions as well as Edney Type IV shock–shock interactions. Various levels of rarefaction have been considered to highlight the effect of thermal relaxation between the translational and rotational modes. In addition, for the Edney test case, the imposed wall temperature on the shock-generating wedge and the cylinder surface has been varied, to evaluate the importance of the boundary layer thickness in the interaction region.
S. Colonia, R. Steijl, G. Barakos

Ballistic Range Experiment of Shock Stand-Off Distance for Spheres in Air with Flight Speeds Between 5.08 and 6.49 km/s

To measure the shock stand-off distance for spheres with flight speeds above 5 km/s in air and provide experimental data for validation of theory and numerical methods, measurement of shock stand-off distance for hypersonic sphere has been conducted in the hypervelocity ballistic range of China Aerodynamic Research and Development Center. The measurement was made for spheres with diameters of 8, 10, 12 and 15 mm, flight speeds between 5.08 and 6.49 km/s, and ambient pressures between 1.5 and 6.3 kPa. The shock stand-off distance was measured using transient shadowgraph and schlieren. The measurement error was analyzed and found to be between about ±3\(\%\) and ±8\(\%\). Under present test conditions, the flow near the stagnation point is speculated to be primarily nonequilibrium. The shock stand-off distance near stagnation point increases as the binary scaling parameter \(\rho \)R increases. The data match well with previous investigations of similar conditions. Different values of \(\rho \)R may have different influence on the state of the flow with different speed near the stagnation point.
Liao Dongjun, Sen Liu, Hexiang Jian, Xie Aimin, Zonghao Wang, Jie Huang

Oblique Shock Reflection over a Membrane

Oblique shock reflection phenomena have long been studied both theoretically and experimentally. In ordinary situations, incident shock is considered to be reflected off some solid hard material. In this case, the deformation of the reflection surface is negligible even if the pressure rise is high, and the boundary condition can be easily assigned.
S. Kobayashi, H. Hemmi, T. Adachi, T. Koita

Formation of Shock Wave Reflection Configurations in Unsteady Flows

In spite of the fact that the process of shock wave reflection has been the subject of considerable research effort over the last few decades [112], the question of the transition between the so-called regular and irregular reflection types is still of particular interest. The analytical approach to describing regular (RR) and Mach (MR) reflection pattern was initiated by von Neumann [13]. He developed the local theory of two- and three-shock configurations that are valid in the vicinity of the intersection point of shock waves. Von Neumann’s theory has been successfully applied to shock wave reflection in steady flows. As for the reflection in pseudo-steady flows, this case is more adequately described by a model proposed by Cabannes [14] for the reflection of a shock wave off an immobile wedge. The main assumption of the theory is that the Mach stem is rectilinear along all its length and perpendicular to the wedge surface. The Cabannes’s theory of pseudo-steady Mach reflection is valid in the finite flow domain. Both theories are mathematically equivalent to each other, and the formal difference is that the given and unknown variables swap places. In the case of the pseudo-steady straight wedge reflection, the given parameters are the Mach number \(M_s\) of an incident shock wave (or the ratio of densities at the shock front), the wedge angle \(\beta \) and the gas specific heat ratio \(\gamma \). Note that in the absence of experimental data one can describe the pseudo-steady reflection process using exclusively Cabannes’s theory, since without experimental data, only two initial parameters, the incident shock Mach number and the wedge angle, are known.
I. V. Krassovskaya, M. K. Berezkina

Experimental and Numerical Visualisation of Supersonic Flow over the British Isles

Colour schlieren experimental results for Mach 5 flow over an arbitrary geometry that generates complex shock structures and shock interactions are presented. The experiment is rebuilt using the rhoCentralFoam solver to solve the compressible Navier–Stokes equations and a numerical analogue, the density gradients (i.e. pseudo-schlieren), is compared to the experimental result, showing very good qualitative agreement. The numerical results give data that can be post-processed to visualise the shock waves by taking advantage of changes in pressure, entropy, velocity, etc. across a shock, in addition to the gradients of density. It is shown that, at least for the geometry and Mach number studied here, the divergence of the velocity field produces the best numerical shock detection method.
Craig White, Konstantinos Kontis

The Diffraction of a Two-Dimensional Curved Shock Wave Using Geometric Shock Dynamics

The diffraction of a cylindrical shock wave segment around convex sharp corners is considered. This investigation is approached from a numerical and analytical perspective. The numerical investigation was carried out using ANSYS Fluent while Whitham’s theory of geometric shock dynamics was used as a basis for the analytical approach. A model based on Whitham’s theory was developed, wherein the cylindrical shock profile is viewed as being composed of connected plane shocks with varying orientation. As the length of these plane shocks approaches zero, their combined shape approximates the cylindrical shock’s profile. Upon diffraction, disturbance waves propagate along this sequence of plane shocks; the theory of sound was used to model the propagation of these disturbances (taking into account the variation of shock orientation). Using this method, the inflection point (the point where the disturbed and undisturbed portions of the shock meet) was calculated. The results from the calculation were compared to those from ANSYS Fluent and they showed good correlation. A further attempt was made at modelling an elliptical shock, which produced unexpected results. In plane and cylindrical shocks, the disturbed region grows weaker; yet, it grows stronger in elliptical shock producing another wave between the reflected shock and the wall.
Bright B. Ndebele, Beric W. Skews

Viscous Correction and Shock Reflection in Stunted Busemann Intakes

Air intakes play a crucial role in hypersonic air-breathing propulsion by compressing incoming airflow to high pressure and temperature for combustion. Axisymmetric Busemann intakes can achieve highly efficient compression for scramjet engines in inviscid flow. In practice, however, viscous effects exert significant influence on the flowfield and performance of scramjet intakes, necessitating effective methods for viscous correction and intake shortening. The present study develops a robust correction methodology by coupling viscous flow simulations with a wall correction method based on local displacement thickness of the boundary layer, whose edge is detected based on the total enthalpy profile. This iterative correction process is applied to hypersonic stunted Busemann intakes and supersonic M-flow ring geometries. Flow features in the initial inviscid fields are successfully reproduced in the presence of viscosity for both applications, except for highly stunted Busemann intakes, where the mode transition to Mach reflection occurs at different shortening lengths.
H. Ogawa, B. Shoesmith, S. Mölder, E. Timofeev

Experimental and Numerical Results from Shock Propagation Through Dust Columns in a Shock Tube

This chapter presents experimental and numerical work in progress on shock propagation through dust columns in a shock tube environment. The shock tube consists of a short double driver chamber separated by membranes from the driven section. The shock tube is instrumented with pressure sensor and high-speed cameras. A specially designed window section allows Schlieren and shadow photography to be recorded simultaneously, in directions perpendicular to each other. The dust column is injected from below in the driven section, using a spark generator. The timing is such that the dust is in suspension before the shock arrives. The numerical method Regularized Smoothed Particle Hydrodynamics has been used to simulate shock–dust interaction problems, with a full multiphase description. Comparison with experimental data shows promising results for further studies on shock–dust interactions.
M. G. Omang, K. O. Hauge, J. Trulsen

Triple-Point Singularity and the Neumann Paradox of Mach Reflection

The singular nature of the flow near the triple point is investigated analytically based on a solution of the steady 2D Navier–Stokes equations system in polar coordinates, with special attention on the cause of the Neumann paradox. It gives a centered fan-like flow from the triple point in widening the slip flow region. Angles and curvatures of the reflected (R) and Mach stem (m) shock lines given in the solution are consistent with existing experiment data.
A. Sakurai, S. Kobayashi

Experimental Investigation of Mist Injection at the Stagnation Point of a Blunt Body in Hypersonic Flow

A spacecraft re-entering Earth’s atmosphere at orbital speeds or higher is subjected to severe aerodynamic heating. Generally, large angle sphere-cone configurations are preferred as forebody to minimize aerodynamic heating. Though these configurations reduce heat transfer to some extent, they are not alone sufficient to withstand the harsh conditions existing during re-entry.
J. L. K. Sindhu, S. Mohammed Ibrahim, K. P. J. Reddy

Shock Wave Development Within Expansive Flows

The propagation of two-dimensional expansion waves over a corner has received very little attention in the past. It can be studied experimentally in a standard shock tube by placing the test section at the end of the high-pressure section rather than the conventional method with placement at the driven section. It is found that reflected compression and shock waves can form as the wave propagates over the corner. An attached flow separation bubble develops at the corner and for a strong enough wave can develop a region of supersonic flow above it, and, in some cases, a transonic shock wave. Furthermore, for a sufficiently strong expansion wave, the flow behind the trailing edge of the expansion wave becomes supersonic. It has also been shown that when an expansion wave reflects off a wedge, shock waves can also develop due to the induced velocity flowing down the surface of the wedge striking the corner. The development of shock waves can also occur if the expansion wave focuses on a cavity.
Beric W. Skews, Randall T. Paton

Hypersonic Shock Wave Boundary Layer Interaction Studies on a Flat Plate at Elevated Surface Temperature

Experimental shock wave boundary layer interactions (SBLI) at a compression corner of a flat plate model with deflectable flap and variable surface temperature were studied in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) at Mach 7.4 and \({6.65\times 10^6}\,{\text {m}^{-1}}\) unit Reynolds number. The present paper focuses on the effect of the leading edge bluntness and surface temperature. The effects are discussed based on surface heat flux and surface pressure measurements as well as schlieren visualizations. The study confirms that the state of the incoming boundary layer is crucial for the interaction. A small change of the leading edge bluntness was found to affect the boundary layer stability and thus the SBLI. In contrast, surface heating was found to destabilize the boundary layer. Tests at different flap deflection angles and transitional incoming boundary layers revealed that the transition process was completed in the separated shear layer, leading to a fully turbulent reattachment on the flap. The experimental effort is complemented by Reynolds-Averaged Navier–Stokes (RANS) computations providing insights into fundamental trends. The 2D simulations underpredict the size of the separation bubble in the compression corner but qualitatively mirrored the experimental trends. The wall heating resulted in an increased boundary layer thickness, reduced the extent of the separation bubble and elevated the peak boundary layer temperature on the flap.
Alexander Wagner, Jan Martinez Schramm, Klaus Hannemann, Ryan Whitside, Jean-Pierre Hickey

Extinguishing Detonation in Pipelines—Optimization of the Process

The necessity of extinguishing detonation, which may occur in pipelines transporting gaseous fuels, creates nowadays a very important technological problem. The standard devices used for this purpose consist of matrices of very narrow channels. Cooling the gas by cold walls of such channels may extinguish the flame and stop detonation.
Z. A. Walenta, A. M. Słowicka

Triple-Shock Configurations, Vortices, and Instabilities Resulting from the Interaction of Energy Release with a Shock Layer in Gaseous Media

Triple-shock configurations and vortex structures are researched in problems of control of a high-speed flow past an aerodynamic body “plate-cylinder” at freestream Mach number M = 4. The effect of an energy source dislocated in the incoming flow ahead of a bow shock is evaluated for the gaseous media of different physical–chemical properties in a range of the ratio of specific heats γ from 1.1 to 1.4. The energy source is modeled as a heated rarefied channel. Changing the angles in triple-shock configuration and the effect of the stagnation pressure decreasing together with the front drag force reduction is studied depending on γ and rarefaction factor in the energy source. Generation of the Richtmyer–Meshkov instability accompanied the forming of the triple configuration is modeled for M = 8. Complex conservative difference schemes are used in the simulations.
O. A. Azarova, L. G. Gvozdeva

Analysis of Planar and Spherical Shock-Wave Mitigation by Wet Aqueous Foams

In a context where more and more Improvised Explosive Devices (IED) are found on national territories or theaters of external operations, the fight against IEDs has intensified since 2008, aiming, in particular, at designing reliable blast mitigation systems. Aqueous foams were identified in the 1970s as an efficient protective medium against blast and sound effects. They have been widely used because of their ease of application, but the quantification of the physical phenomena leading to mitigation remains unclear.
C. Breda, S. Kerampran, M.-O. Sturtzer, M. Arrigoni, J.-F. Legendre

The Effect of Increasing Rarefaction on the Edney Type IV Shock Interaction Problem

Two-dimensional direct simulation Monte Carlo simulations of the Edney Type IV shock interaction problem, where an oblique shock wave generated by a wedge encounters the bow shock from a cylinder, are carried out for three different Knudsen numbers using the dsmcFoam+ code. The numerical results for surface and flow properties are in good agreement with experiment for a Knudsen number of 0.0067. When the degree of rarefaction is increased, the oblique and normal shock waves become more diffuse and the bow shock standoff distance increases. The supersonic jet that forms in the interaction region becomes weaker as the Knudsen number increases and the point at where it impinges on the cylinder surface moves in a clockwise direction due to the jet being turned upward. The location of the peak heat transfer coefficient, peak pressure coefficient, and zero skin friction coefficient on the cylinder surface follow the supersonic jet impingement in a clockwise direction around the cylinder. The peak heat transfer and pressure coefficients decrease with increasing Knudsen number.
Craig White, Konstantinos Kontis

Laser Ignition for Pulse Detonation Engines

The high pressures and resultant momentum flux out of the chamber generate thrust. The ignition system of PDE has always posed problems in commercial applications. Microwave and laser-induced detonation in the mixture ofhydrogen with flake aluminum particles is simulated based on Eulerian approach. Minimum pulse energy of detonation is calculated for different parameters of laser pulse, mass fractions of particles, and compositions of gas mixture. The threshold intensity of optical breakdown on individual metal particle, and its dependence on contributing factors (particle radius, location of particle, total energy and time of laser pulse, radius of laser spot) are studied.
Pavel Bulat, Konstantin Volkov

Numerical Simulation of Reactive Gas Mixes Flows in the Detonation Engine

Mathematical modeling of gas flows with chemical reaction, with deflagration and detonation reactions, namely flows in detonation engines, demands taking into account a large number of physical factors: viscosity (laminar or turbulent), heat conductivity, multicomponents diffusion, changing of energy from chemical reactions, and so on.
S. N. Martyushov

On the Propagation of Planar Blast Waves Through Nonuniform Channels

The propagation of shock waves through nonuniform channels with slowly varying cross sections has been studied analytically from the 1950s.
J. T. Peace, F. K. Lu

Shock Reflection in Axisymmetric Internal Flows

The flow downstream of an axisymmetric conical shock wave, with a downstream pointing apex, can be predicted by solving the Taylor-Maccoll equations. Previous research, however, has suggested that these theoretical flowfields are not fully realisable in practice, and that a Mach reflection forms towards the centreline of the flow. This phenomenon is investigated for the case where the freestream Mach number is 3.0 and the shock angle is 150\(^\circ \). A range of complementary prediction techniques that include the solution to the Taylor-Maccoll equations, the method of characteristics, curved shock theory and CFD, are used to gain insight into this flow. The case where a cylindrical centrebody is placed along the axis of symmetry is studied for several values of centrebody radius that are expected to produce regular reflection at the centrebody surface. An analysis of pressure gradients suggests that the flowfield downstream of the reflected shock does not contribute to the process of transition from regular to Mach reflection at these conditions.
B. Shoesmith, S. Mölder, H. Ogawa, E. Timofeev

On Unsteady Shock Wave Reflection from a Concave Cylindrical Surface

The paper is devoted to a combined—analytical, numerical, and experimental—study of initially planar shock reflection from a full concave cylindrical surface with the emphasis on the transition from inverse Mach reflection to transitioned regular reflection. The numerically predicted and experimentally observed transition angles for a range of incident shock Mach numbers are found to be in good agreement with each other and at the same time significantly different from previous experimental observations in the literature. It is shown that among existing analytical predictions of the transition point location, the theory by Itoh et al. (JFM 108:383–400) provides the best agreement with new experimental and numerical data, even though this theory is in significant error with respect to the triple-point trajectory and Mach stem intensity. By tracking the corner signal, it is shown that it remains attached to the Mach stem during the entire course of flow development and, hence, effectively propagates with the Mach stem velocity. This finding is used for the initial development of another analytical treatment to predict the location of the transition point.
E. Timofeev, F. Alzamora Previtali, H. Kleine

New Findings on the Shock Reflection from Wedges with Small Concave Tips

Planar shock reflection from straight wedges and wedges with small concave tips is considered. It is demonstrated that, in shock tube experiments for a certain wedge angle and incident shock Mach number, the resulting reflection is of irregular type in the presence of a small concave tip with an arc radius as small as 4 mm while a straight wedge with the same wedge angle produces a regular reflection. In the numerical experiments, corner signal tracking is used to demonstrate that in the case of a concave tip wedge the corner signal is always merged with the Mach stem and never detaches. It is concluded that for the prediction of the Mach-to-regular reflection transition angle for wedges with concave tips, it is essential to predict as accurately as possible the strength of the Mach stem. An initial development of an analytical method to predict the transition angle is then provided.
F. Alzamora Previtali, H. Kleine, E. Timofeev

Normal Shock Wave Diffraction Over a Three-Dimensional Corner

The diffraction over a corner normal to the direction of travel of a shock wave has been well documented. This has also been extended to the diffraction of a shock wave over edges with discontinuous profiles in the flow direction. However, these studies have only considered the diffraction of a shock wave travelling over a single, plane surface initially. The current study extends this to consider the dynamics of a plane shock wave travelling simultaneously over two orthogonal surfaces, analogous to a shock wave travelling over the roof and wall of a rectangular building. The flow field bears similarity to the diffraction of a shock wave over a convex diffraction edge whereby there is thickening of the vortex tube formed at the axis defined by the common edge of the two surfaces with outboard thinning. However, as the Mach number of the incident shock wave increases, the vortex tubes shed from the two diffraction edges no longer merge into a single tube but rather each terminates in the downstream face. This also results in curvature of these vortex tubes away from the face rather than remaining approximately parallel to the downstream face as seen in most cases. These results were derived experimentally and computationally for a Mach number in the range M1.3–M1.6.
Randall T. Paton, Beric W. Skews, Cheryl M. Cattanach
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