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About this book

The book reports on the latest theoretical and experimental findings in the field of active flow and combustion control, in the context of energy conversion for power and propulsion systems. It covers new developments in actuator technology and sensing, robust and optimal open- and closed-loop control, model reduction for control purposes, and unsteady turbine cooling and performance, among other relevant topics. Gathering contributions to the Active Flow and Combustion Control (AFCC 2021), held virtually on September 28-29, 2021, from the Technische Universität Berlin, Germany, this book describes research that has been carried out within, and supported by, the collaborative research center SFB 1029 on “Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamics”, and funded by the German Research Foundation (DFG). It highlights theoretical and practical aspects, and corresponding solutions, that are important for the development of future energy conversion systems, thus offering a timely guide for researchers and practitioners in the field of aeronautics, turbomachinery, control and combustion.

Table of Contents


Part I: Constant Volume Combustion and Combustion Control


Pressure Gain and Specific Impulse Measurements in a Constant-Volume Combustor Coupled to an Exhaust Plenum

In the framework of air-breathing propulsion, the thermodynamic cycle of turbomachines is likely to be adapted to pressure-gain combustion (PGC) technology, which raises integration challenges. In this study, a constant-volume combustion chamber, fed with air and isooctane, was experimentally coupled to a nozzle assembly featuring a plenum with variable volume and throat diameter. The spark-ignited, direct-fueled combustion chamber allowed for time-resolved measurements of combustion pressure and axial thrust, as well as direct imaging of the reacting flow. The main parameters that drive the cyclic operation of the facility – regarding combustion dynamics and thrust generation – have been recorded as a function of the exhaust geometry, including the air stagnation pressure, the air/fuel equivalence ratio, and the cycle frequency. The pressure gain measured in the exhaust plenum proves to be a relevant parameter of the PGC facility, by representing the increase in stagnation pressure upstream of a turbine in turbomachine applications. The cycle frequency directly drives the pressure gain that reaches up to 31% in our constant-volume combustion facility, which yields an outstanding increase in specific impulse by up to 23% compared to conventional constant-pressure combustion.
Bastien Boust, Marc Bellenoue, Quentin Michalski

Control of Auto-ignitive Wave Propagation Modes from Hot Spots by Mixture Tailoring in Shockless Explosion Combustion

Shockless Explosion Combustion is a novel combustion concept that achieves pressure gain combustion by quasi-homogeneous auto-ignition of the fuel/air mixture. Shockless Explosion Combustion is, like other combustion concepts based on auto-ignition, prone to premature ignition and detonation formation in the presence of reactivity gradients, so called hot spots. Two measures to inhibit detonation formation and to achieve quasi-homogeneous auto-ignition, dilution and fuel blending, are investigated by means of zero-dimensional simulations of generic hot spots. Experimental ignition delay times measured in a high pressure shock tube are used to select suitable chemical-kinetic models for the numerical investigation and the calculation of temperature sensitivities of ignition delay times. The main focus of this investigation are the two non-dimensional regime parameters \(\xi \) and \(\varepsilon \), as they enable characterization of the mode of auto-ignitive wave propagation from hot spots. \(\xi \) is the ratio between the speed of sound and the auto-ignitive wave propagation velocity and \(\varepsilon \) describes the ratio between the time a pressure wave travels through the hot spot and the excitation time. Dilution of the combustion mixture with steam and CO\(_2\) aims at extending excitation times and therefore decreasing the parameter \(\varepsilon \). Fuel blending of Dimethyl ether with hydrogen or methane aims at reducing the temperature sensitivity of ignition delay time and low values of \(\xi \). It is demonstrated that both measures are effective at mitigating detonation development while maintaining quasi-homogeneous auto-ignition in presence of hot spots.
Lisa Zander, Johann Vinkeloe, Neda Djordjevic

Autoignition Modes in a Shockless Explosion Combustor

Pressure gain combustion as an alternative to isobaric combustion has been in the focus of research for the past decades as it potentially allows for increasing the thermal efficiency of conventional gas turbines significantly. Beside the most known concepts, such as pulse detonation and rotation detonation combustors, the shockless explosion combustor (SEC) has been proposed. In contrast to the previously mentioned detonation-based concepts the SEC process is based on a thermal explosion, hence avoiding entropy generation caused by propagating detonation waves. Conceptually, this is achieved through a homogeneous autoignition of the fuel–oxidizer mixture, which is realized by the proper stratification of the fuel concentration throughout the combustor, leading to a gradual rise in pressure. Since the process of autoignition is highly sensitive to perturbations, local deviations in the initial state of the mixture lead to a variety of autoignition modes. In this work, an SEC test rig is used to investigate the impact of different fuel injection profiles on the formation of autoignition modes. Pressure transducers are used to measure the pressure rise subsequent to the autoignition event. k-means clustering is applied to a set of pressure data to classify the measured pressure profiles. The same method was used to cluster the respective injection profiles. The results reveal that the gradient in reactivity is of major importance and can be used for increasing the pressure rise through ignition.
Fatma Cansu Yücel, Fabian Habicht, Myles Bohon, Christian Oliver Paschereit

Fuel-Rich Natural Gas Conversion in HCCI Engines with Ozone and Dimethyl Ether as Ignition Promoters: A Kinetic and Exergetic Analysis

Fuel-rich operated HCCI engines are suitable for the polygeneration of work, heat, and base chemicals like synthesis gas (CO + H2). Under favorable conditions, these engines are exergetically more efficient than separate steam reformer and cogeneration gas engines. However, to achieve ignition, reactive fuel additives like dimethyl ether or ozone must be supplied, which have some, probably negative and not yet quantified, impacts on the exergetic efficiency.
Therefore, the aim of this work is to compute and evaluate the effect of DME and ozone on the exergy input and exergetic efficiency of fuel-rich operated HCCI engines, which convert natural gas at equivalence ratios of 1.5 to 2.5.
Results of a single-zone-model (SZM) and a multi-zone model (MZM) are compared to analyze the influence of inhomogeneities in the cylinder on the system’s exergetic efficiency. Natural gas as fuel is compared with previous neat methane results.
The single-zone model results show that natural gas is much more reactive than methane. Ethane and propane convert partially in the compression stroke and lead to ethene, propene, and OH radicals. However, the ethane and propane conversions do not favor but slightly reduce the formation of methyl hydroperoxide, which is an important buffer molecule for fuel-rich methane ignition. But in addition, further buffer molecules like ethene or ethyl hydroperoxide are intermediately formed. The product selectivities are neither influenced by the natural gas composition, nor by the chosen additive.
Compared to ozone, the DME molar and mass fractions needed for ignition are up to 11 times higher, and its exergy contribution to the total mixture is even 95 times higher. Therefore, the system’s exergetic efficiency is much higher when ozone is chosen as additive: reasonable values of up to 82.8% are possible, compared to 67.7% with DME. The multi-zone model results show that the efficiency is strongly dependent on the fuel conversion and thus unconverted fuel should be recycled within the polygeneration system to maintain high efficiencies. Comparing the total exergetic efficiency, ozone is a favorable additive for fuel-rich operated HCCI polygeneration.
Dominik Freund, Christoph Horn, Burak Atakan

Enhancement of Blowout Limits in Lifted Swirled Flames in Methane-Air Combustor by the Use of Sinusoidally Driven Plasma Discharges

This study focuses on the effects of continuous volumetric discharge of sinusoidal plasma actuator at 20 kHz coupled directly with methane-air premixed flame in the near field of the injector exit. A plasma actuator composed of a needle-type electrode placed at the center of the nozzle, connected with high-voltage, while the nozzle was acted as a grounded electrode with different input electrical power values was designed to enhance lean blowout performance in a swirl model combustor. The ionic wind induced by the electrical body force given by the flow ionization leads to velocity disturbance and subsequently affects the flame. To investigate the possible mechanism of the combustion control by the plasma through the aerodynamic effect high speed flow visualization was analyzed under quiescent conditions. Flow visualizations showed that the plasma discharge affects the flow dynamics near the burner exit. It was observed that by increasing the electrical power used for the actuation a recirculation zone is formed in the non-reacting flow field. Furthermore, comparative experiments between conventional and plasma-assisted combustion were carried out to analyze the combustion enhancement in terms of lean blowout performance. The effect of the input electric power of the plasma actuator was studied, and it was seen that at coupled plasma powers corresponding to less than 1% of the thermal output power, there is a significant improvement in the blow-out limit.
Maria Grazia De Giorgi, Sara Bonuso, Ghazanfar Mehdi, Mohamed Shamma, Stefan Raphael Harth, Nikolaos Zarzalis, Dimosthenis Trimis

Part II: Combustor-Turbine-Integration: Pressure Fluctuations and Turbulence

Computational Simulation of an Exhaust Plenum Charged by a Multi-tube Pulsed Detonation Combustor

An efficient computational framework for the numerical simulation of multi-tube pressure-gain combustors for gas turbine applications is introduced. It is based on the open-source AMReX software platform (https://​amrex-codes.​github.​io/​amrex/​), enhanced to allow for the flexible coupling of multiple computational domains with possibly different dimensionality. Here, six pulsed detonation tubes represented by an efficient one-dimensional model are coupled at their outlets to a threedimensional plenum reservoir. The plenum outlet can be partially blocked to simulate the flow resistance of the first stage of a turbine. This paper presents a validation of this computational setup against measurements obtained from a laboratory experiment with unblocked plenum, and a numerical simulation study of the flow generated by periodic sequential firing of the six detonation tubes into a plenum with a partially blocked exit cross section simulating the flow resistance of a turbine.
Maikel Nadolski, Mohammad Rezay Haghdoost, Kilian Oberleithner, Rupert Klein

Pressure Fluctuations in an Annular Plenum Downstream of a Multi-tube Pulse Detonation Combustor

The generation of large pressure fluctuations at the combustor outlet due to the periodic combustion process involving propagating detonation waves is a major drawback on the way of integrating a pulse detonation combustor (PDC) into a gas turbine. Recently, the attachment of an annular plenum downstream of a multi-tube PDC was proposed to allow for the attenuation of the pressure amplitudes. In this work, pressure data is recorded at various axial and azimuthal positions in the annular plenum allowing for a quantification of pressure fluctuations. Furthermore, a systematic study was conducted to evaluate the effect of the firing pattern and an outlet blockage on both the longitudinal change of the peak amplitudes and the pressure fluctuations throughout the entire cycle duration. The results suggest that a sequential firing pattern should be preferred over the simultaneous firing of multiple PDC tubes, as it results in the lowest pressure fluctuations at the plenum outlet.
Fabian Habicht, Fatma Cansu Yücel, Myles Bohon, Mohammad Rezay Haghdoost, Kilian Oberleithner, Christian Oliver Paschereit

Reduction of Pressure Fluctuations in an Annular Pulsed Detonation Combustor Mockup by Iterative Learning Control Using Eigenvector-Based Binary Solution Sets and Iterative Model Identification

The approximation of constant volume combustion using a pulsed detonation engine is a promising approach to overcome the efficiency limitations of state-of-the-art gas turbines. It is assumed that the firing synchronization between different detonation tubes in an actual setup of such a machine significantly affects the overall performance. Therefore, to maintain reliable performance even under disturbances, the utilized firing pattern of the operation should be regulated using closed-loop control. A suitable control approach for such a machine that is cyclic in nature is iterative learning control (ILC). This contribution presents an advanced reformulation of a binary ILC method to minimize pressure fluctuations by altering the firing patterns of the detonation tubes. This method uses an eigenvector-based determination of the feasible binary solution set of control inputs to reduce the computational cost. Moreover, an ILC method using iterative model identification is introduced that minimizes pressure fluctuations under linear and nonlinear system behavior, allowing operation even if a linear model insufficiently describes the system. Both methods are tested on an acoustic mockup of an annular pulsed detonation combustor.
Daniel Topalovic, Florian Arnold, Rudibert King

Part III: Combustor-Turbine-Integration: Cooling and Unsteady Performance


Dynamic Forced Impingement Cooling: Latest Experimental Results Regarding Variations in Flow Guidance and Pulse Parameters

Convective heat transfer of a hot surface in a regime of a periodically pulsed 7 by 7 cooling air impingement jet array is experimentally investigated. In the category of geometrical parameters wall curvature was added. Based on a flat target plate configuration two additional wall curvatures for impingement jet flow guidance were focused on to enhance geometrical boundary conditions in style of real turbine blades. Thereby, internal structure of pressure and suction side is represented by a convex and a concave shaped impingement jet flow space with the same constant radius. For all three experimental configurations nozzle and impingement distance were kept constant at three nozzle diameters. Convective heat transfer behaviour achieved for flat plate setup is transferable for both additional investigated curvatures. The dynamic parameters, frequency, phase shift and duty cycle, separately as well as combined have a significant influence on convective heat transfer improvements compared to the corresponding steady blowing case.
Frank Haucke, Arne Berthold, Niklas Meyners

Time-Resolved Analysis of Film Cooling Effects Under Pulsating Inflow Conditions

The development of modern gas turbines requires higher turbine inlet temperatures for an increase in thermal efficiency. With a change to a pressure gain combustion concept to increase the efficiency significantly, more challenges for the cooling of the first turbine stages must be overcome. For this purpose an array of 777 fan-shaped cooling holes on a flat plate are exposed to a series of different pulsating inflow conditions. Varying the amplitude up to 100% to the mean differential pressure, the film cooling performance is analyzed and evaluated. Adjusting the pulsating frequencies from 1 Hz–5 Hz further allows to gain a comprehensive understanding of the influence of the main parameters affecting the cooling film development. The experimental data recorded with an infrared thermography system reveals a strong impact of the pulsating inflow conditions on the adiabatic film cooling effectiveness.
Alexander Heinrich, Markus Herbig, Dieter Peitsch

Rotating Detonation Combustor Downstream Transition Passage Design Considerations

A key enabler to integrate turbines downstream of rotating detonation combustors is the design of an optimal combustor-turbine passage. Precise estimates of fluctuations, losses, and heat loads are required for the turbine design as rotating detonation combustors feature transonic flow with rotating shocks moving at few kilohertz. This paper analyzes fluctuations and heat loads of the Purdue Turbine Integrated high-Pressure RDE through reactive unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. CFD++, a commercial CFD software package from Metacomp, is employed to solve the unsteady RANS equations through a one-step reaction mechanism. The inlet of the combustor is fed with a hydrogen-air mixture at mass flows of ~1 kg/s with two different back pressures to obtain supersonic and subsonic outlet flows. The mesh featured around 36 million grid points to ensure the resolving of the boundary layer. Finally, a methodology to lower computational time tenfold for the supersonic and subsonic passage is presented based on non-reacting unsteady RANS simulations.
James Braun, Guillermo Paniagua, Donald Ferguson

Part IV: Numerical Methods


Linear Forcing of Compressible Isotropic Turbulence in Rectangular Domains with Adapted Locally Refined Grids

This study investigates the applicability of the linear forcing method at rectangular domains with an adapted grid via local refinement. The advantages of the linear forcing method, using in a physical space solver for combustion simulations, are discussed. We present test cases for the different modifications of the forcing term and the major drawbacks occurring when using non-cubic domains. The use of a filtered velocity field within the forcing term is investigated, first as a solution for the described problems with rectangular domains and second as an attractive method to control the integral length scale of the turbulent field. Finally, we present results for various DNS computations in preparation for future studies of turbulence-flame interactions, and a few statistical properties of the turbulence are discussed.
Mario Sroka, Julius Reiss

Modal Decomposition of Flow Data via Gradient-Based Transport Optimization

In the context of model reduction, we study an optimization problem related to the approximation of given data by a linear combination of transformed modes, called transformed proper orthogonal decomposition (tPOD). In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper orthogonal decomposition. Allowing transformed modes in the approximation renders this approach particularly useful to compress data with transported quantities, which are prevalent in many flow applications. We prove the existence of a solution to the infinite-dimensional optimization problem. Towards a numerical implementation, we compute the gradient of the cost functional and derive a suitable discretization in time and space. We demonstrate the theoretical findings with three numerical examples using a periodic shift operator as transformation.
Felix Black, Philipp Schulze, Benjamin Unger

Towards Data-Driven Model Reduction of the Navier-Stokes Equations Using the Loewner Framework

The Loewner framework is extended to compute reduced order models (ROMs) for systems governed by the incompressible Navier-Stokes (NS) equations. For quadratic ordinary differential equations (ODEs) it constructs a ROM directly from measurements of transfer function components derived from an expansion of the system’s input-to-output map. Given measurements, no explicit access to the system is required to construct the ROM.
To extend the Loewner framework, the NS equations are transformed into ODEs by projecting onto the subspace defined by the incompressibility condition. This projection is used theoretically, but avoided computationally. This paper presents the overall approach. Currently, transfer function measurements are obtained via computational simulations; obtaining them from experiments is an open issue. Numerical results show the potential of the Loewner framework, but also reveal possible lack of stability of the ROM. A possible approach, which currently requires access to the NS system, to deal with these instabilities is outlined.
Alejandro N. Diaz, Matthias Heinkenschloss

Part V: Active Flow Control and Performance of Turbomachinery


The Effect of Periodic Disturbance Patterns on the Efficiency of Active Flow Control in a Linear Stator Cascade

Constant volume combustion (CVC) is a promising way to substantially increase gas turbine efficiency. Shockless explosion combustion and pulsed detonation combustion are potential candidates for CVC integration in gas turbines. Both these schemes operate with sequentially ignited tubes that introduce highly transient flow characteristics in neighboring machine components. One of the most critical parts of turbomachinery is the compressor. In this work, the impact of the firing pattern on the flow field in a compressor stator located upstream is studied. In particular, five combustion patterns are investigated in terms of local blockage and compressor performance. As wake measurements indicate, patterns with low fluctuations of local blockage exhibit less flow deflection, reduced losses, and higher pressure increases compared to those with large fluctuations. Furthermore, the effect of active flow control (AFC) utilizing end-wall blowing is investigated. Experiments show that the impact of AFC varies depending on the pattern, favoring patterns with low fluctuations of local blockage. The results indicate that closed-loop AFC is favorable when a disturbance rejection is of interest but does not significantly improve performance compared to steady blowing.
Karl Neuhäuser, Rudibert King

DBD Plasma Actuation on the Blades of Axial-Flow Turbomachinery

Flow separation, or stall, in axial flow turbomachinery results in a loss of pressure or compression in the case of fans and compressors, or the loss of power or thrust generation in the case of turbines. Wave-power-based Wells turbines, in particular, suffer so acutely from blade stall during normal operation, that it compromises their viability as a major renewable energy resource. In this research, pulsed dielectric barrier discharge (DBD) plasma actuators were implemented on the blades of a mono-plane Wells turbine impeller and its full-bandwidth performance was evaluated. An initial parametric study indicated that blade-tip reduced frequencies ≥2.5 produced the greatest impeller acceleration from rest. The corresponding physical pulsation frequency was then used as a basis for conducting nominally steady-state experiments as well as experiments involving acceleration and deceleration of the impeller. Data so acquired, corresponding to a reduced frequency range of 0.9 to 2.5, was compiled to construct an impeller performance map. Plasma pulsations dramatically increased the effective impeller bandwidth by producing useful net power well beyond flow ratios where mono-plane impellers spin down to a standstill. In fact, the shaft power at a 17° blade-tip angle of attack exceeded the plasma input power by a factor of 33. These findings are potentially game-changing for wave energy generation and axial flow turbomachinery in general.
David Greenblatt, Omer Pfeffermann, David Keisar

Numerical Analysis of Unsteady Compressor Performance Under Boundary Conditions Caused by Pulsed Detonation Combustion

Pressure gain combustion is a revolutionary concept to increase gas turbine efficiency and thus potentially reduces the environmental footprint of power generation and aviation. Pressure gain combustion can be realized through pulsed detonation combustion. However, this unsteady combustion process has detrimental effects on adjacent turbomachines. This paper identifies realistic time-variant compressor outlet conditions, which could potentially stem from pulsed detonation combustion. Furthermore, a low fidelity approach based on the 1D-Euler method is applied to investigate the performance of a compressor exposed to these outlet boundary conditions. The simulation results indicate that the efficiency penalty due to unsteady compressor operation remains below 1% point. Furthermore, between 80% and 95% of the fluctuations’ amplitudes are damped till the inlet of the 4-stage compressor.
Nicolai Neumann, Tim Rähse, Panagiotis Stathopoulos, Dieter Peitsch

Efficiency Increase and Start-Up Strategy of an Axial Turbine Stage Under Periodic Inflow Conditions Using Extremum Seeking Control

Since the efficiency increase of state-of-the-art gas turbines has become incrementally smaller, a significant improvement seems unlikely using the established concepts. Replacing the underlying constant pressure combustion with a constant volume combustion may change this and may yield significant efficiency increases. A possible realization of such a machine can be accomplished using firing tubes that utilize pulsed detonation combustion. This results in unsteady, periodic boundary conditions, generating challenges to the operation of the machine. A possible solution to operational difficulties is presented here using extremum seeking control (ESC). This model-free, easy to parameterize control approach is tested using a mock-up test rig designed specifically to mimic the pulsed flow conditions in front of an axial turbine. The ESC is defined in such a way that it maximizes either the calculated turbine efficiency or the specific work that is converted by the turbine by changing the synchronization between firing tubes only, leaving the parameter space of single firing events unaffected. Further, a concept for the start-up of such a gas turbine using ESC is introduced.
Daniel Topalovic, Rudibert King, Markus Herbig, Alexander Heinrich, Dieter Peitsch

Part VI: Active Flow Control Methods


Experimental Investigations of Active Flow Control Using a Piezo Adaptive Blade in a Compressor Cascade Under Periodic Boundary Conditions with High Strouhal-Number

As a consequence of constant volume combustion in gas turbines, pressure waves are generated that propagate upstream the main flow into the compressor system are generated leading to incidence variations. Numerical and experimental investigations of stator vanes have shown that Active Flow Control by means of adaptive blade geometries is beneficial when such periodic incidence variations occur. A less susceptible to stall and choking for compressors dealing with periodic disturbances can be achieved. Experimental investigations with high Strouhal numbers using such a method have not yet been done in order to demonstrate the effects. Therefore, this work investigates a linear compressor cascade that is equipped with a piezo-adaptive blade structure utilizing macro-fiber-composite actuators. A throttling device is positioned downstream of the trailing edge to emulate an unsteady combustion process. Periodic transient throttling events with Strouhal numbers up to 0.144 were being investigated due to incidence changes. Consequently, pressure fluctuations on the blade’s surface occur, having a significant impact on the pressure recovery downstream of the stator cascade. Experimental results of harmonically actuating the piezo-adaptive blade with Strouhal numbers of up to 0.72 show that the impact of disturbances at resonance can be nearly reduced to zero. Therefore, the blade design must be matched to the type of disturbances to achieve further improvements in the technology.
Tobias Werder, Lukas Kletschke, Robert Liebich

A Comparison of Optimal, Binary Closed-Loop Active Flow Control Applied to an Annular Compressor Stator Cascade with Periodic Disturbances

Pressure gain combustion has been proposed to exploit superior thermodynamic cycles in gas turbines. However, further research on their integration is needed to reduce the induced negative effects on the last stages of a compressor. In this contribution, mitigation results on the effects of periodic disturbances on an annular compressor stator rig are presented and compared for different closed-loop controllers. Instead of a real, unsteady combustion setup, a rotating disc was installed to create periodic disturbances downstream of each passage. Pneumatic active flow control served to influence the suction side of each stator blade.
With steady blowing actuation, the effects of periodically induced disturbances could not be explicitly addressed and led to worse results compared to the closed-loop versions. For closed-loop control, a clear recommendation for a class of learning approaches can be given. Finally, an evaluation of the efficiency of flow control is presented with a refined characterization of the actuation effort.
Benjamin Fietzke, Jan Mihalyovics, Rudibert King, Dieter Peitsch

Numerical Methodologies for Magnetohydrodynamic Flow Control for Hypersonic Vehicles

The concept of magnetohydrodynamic (MHD) flow control is of current interest for its applications in spacecraft reentry and aerodynamic control for hypersonic vehicles. This work presents an efficient approach for realistically simulating MHD effects in weakly ionised plasmas produced by hypersonic flows. The governing equations consists of the full Navier-Stokes resistive-MHD system under the low magnetic Reynold’s number assumption. The numerical approach employs a Cartesian mesh which facilitates hierarchical adaptive mesh refinement in a highly parallelised framework. Geometry is implemented via a rigid-body Ghost Fluid Method which permits arbitrarily complex embedded boundaries. An advanced 19-species equilibrium air-plasma equation of state (plasma19) has been adopted and extended in this work, for the study of test cases where the assumption of local thermodynamic equilibrium applies. The numerical methodology paired with plasma19 equation of state is shown to effectively capture boundary-layer shock wave interactions in a complex double-cone flow, with imposed magnetic field. The model predicts MHD flow control (augmented shock position) in line with experimental measurements, improving upon previous model predictions.
Heather Muir, Louisa Michael, N. Nikiforakis


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