Oblique Shock Research Articles

Space debris interaction across a two-dimensional oblique shock wave

Space debris interaction across a two-dimensional oblique shock wave

Implementation of an OpenFOAM solver for shock and detonation simulation at high pressure

The high pressure condition widely used in industry makes it necessary to evaluate the impact of real gas behaviour in numerical simulation, especially for shock and detonation problems. Since most open source solvers are based on ideal or perfect gas assumption, we have developed an OpenFOAM solver for Real gas Shock and Detonation simulation, referred to as RSDFoam. We have considered the nonidealities in the equation of state, thermodynamic functions and mass action law brought about by the interaction between the fluid particles and by their finite volume. Connection between blastFoam and Cantera was built to utilize the CFD capabilities from the former and the efficient chemistry solver and real gas models in Cantera. The new solver has been thoroughly validated against analytical solutions, previous numerical simulation results and experimental data. For non-reactive flow, shock tube and oblique shock problems were solved. For reactive cases, constant volume reactor, steady detonation speed, reaction zone structure, and cellular structure were numerically studied. The satisfactory agreement demonstrates the accuracy and robustness of the solver for real gas based shock and detonation simulation.

Effect of Protrusions on the Surface Flow and Pressure Fluctuations in the Inter-stage Region of A Launch Vehicle Model

Experiments were carried out to assess the effects of geometrically scaled and viscous scaled protrusions on the surface flow and unsteady pressures in the inter-stage region of a typical launch vehicle model in the Mach number range 0.8 to 1.6. Formation of bow-waves due to the protrusions, and three-dimensional boundary layer separations and reattachments of the shear layer were seen from flow visualizations. Measurements of unsteady pressures show that protrusions cause substantial increases in fluctuation levels on the core vehicle. The highest levels on fluctuations were found to be at a location behind the viscous scaled protrusion, close to the shear layer reattachment. The spectra of pressure signals suggest that the reattachment may be periodic in the range 0.90 £ M £ 1.60; the associated frequency was found to vary in the range 1 kHz to 3.2 kHz (corresponding to Strouhal number in the range 0.034 to 0.051) depending on M. Streamlining the viscous-scaled protrusion was found to replace bow-waves with multiple oblique shocks, resulting in reduced levels of pressure fluctuations, comparable to the basic levels.

Distribution of Enthalpy in Rotating Detonation Engine

In Rotating Detonation Engine (RDE), the detonation wave rotates inside the annulus of thecombustor. After initiation by a pre-detonator, this detonation wave can be sustained by thecontinuous supply of fuel and oxidiser. The frequency of rotation is reported to be of the orderof 5-10 KHz indicating a near continuous operation which can be used in rocket andairbreathing propulsion systems. An experimental study on the RDE is being carried out atNational Centre for Combustion Research and Development (NCCRD), Indian Institute ofTechnology (IIT), Madras using hydrogen and air system. In addition,N2H4 - N2O4 hypergolicsystemreported in literature is considered for comparative study. In order to understand thevarious processes undergone by the flow through the RDE, a detailed thermodynamic analysisis performed. The procedure is explained in greater detail for the better understanding of thevarious state properties in the entire flow field. The flow field comprises of detonation wave,trailing oblique shock wave and Prandtl- Mayer expansion waves. There are two slip lines,one separating the fresh reactants and inert combustion products of the previous cycle ofdetonation wave propagation and another separating the products of detonation combustionand the shocked inert products. Though all the state properties will be evaluated, the enthalpydistribution is considered in the entire flow field of RDE and discussed. This provides theknowledge of the energy availability in various flow regimes and the extent of energyconversion due to detonative combustion, flow expansion, shock compression, and axial flowexciting through the combustor outlet. Propulsion parameters such as axial specific thrust andspecific impulse are computed to show the capability of this modelling approach.

A canonical numerical experiment to study detonation initiation from colliding subsonic auto-ignition waves

The collision of two subsonic auto-ignition fronts with initial constant velocity was found to transit to detonation only when the collision angle was acute. The interaction of the reactive phase wave with inert hot layers constituted a singularity providing a continuous source of vorticity due to barocline effect. For an acute angle, this singularity that propagated at supersonic speed induced oblique pressure waves, of which resonance, due to the reactivity gradient geometry, near the center of the channel in the fresh gases accelerated the reactive wave fronts until transition to detonation. The numerical results of the present study, even if based on drastic assumptions, were at least in good qualitative consistency with experiments. The geometry of the reactivity gradients can thus provide another seed for the coupling between gas dynamics and heat release. Continuous pressure fluctuations and oblique shocks coming from vorticity sources and sheets from barocline effects can considerably enhance this transition. This path to transition could be complementary to that invoking mixing burning within premixed non-planar turbulent flame brush.

Oblique dust-ion acoustic shock and oscillatory periodic wave excitations in space magnetized complex plasma regimes

The collisionless magnetized complex plasma (MCP) is considered to describe the nonlinear oblique propagation of dust-ion acoustic (DIA) shock wave and oscillatory wave having periodicity due to the impact of plasma parameters. Such plasma is composed of the dynamic ions having viscous influence, (α, q)-velocity distributed electrons, and static positive or negative dust charged particles. By implementing only the expansion of perturb quantities, the Burgers equation (BE) having quadratic nonlinearity (QN), cubic nonlinearity (CN), and composition of QN and CN are derived. Based on the useful exact solutions of these equations, the effect of physical parameters on the propagation of DIA shock wave, DIA oscillatory wave having periodicity and DIA double layer are discussed. It is found that the plasma system supports the shock and periodic wave excitations with both positive and negative polarity described by BE having QN. In addition, BE having CN supports shock and periodic wave excitations with only positive polarity. BE having a composition of QN and CN supports both shock wave excitations and double layer as well as both left to right and right to left propagating oscillatory waves having periodicity. The presented results would be applicable to space MCP regimes and further experimental verification.

Aerodynamic performance of a characteristic airfoil at low-Reynolds number and transonic flow under Mars sand-containing environment

The propeller tip of an unmanned aerial vehicle on Mars operates at a low-Reynolds number (Re = 1–5 × 104) and transonic velocity range (Ma = 0.7–1.2). Generally, this implies flow separation and shock waves in the flow field. Furthermore, the impact of Martian atmospheric sand particles significantly affects the aerodynamic performance, and numerical simulations of this issue have received increasing attention recently. Aimed at a characteristic airfoil, the study of a low-Reynolds number transonic flow and the influence of sand-containing flow on airfoil aerodynamic performance were analyzed in this study. The discrete phase model was adopted to simulate the two-phase flow considering Re = 8100–56 800 and Ma = 0.2–1.4. The results indicate that, compared with the atmospheric environment on Earth, the low-pressure atmosphere on Mars can delay the generation of the surface shock wave of the airfoil as well as alter the shock wave structure, significantly increasing the lift-to-drag ratio at high subsonic velocities (Ma = 0.6–0.8). Moreover, due to the weak compressive wave generated at the separation position, the low-pressure atmosphere weakens the strength of the trailing-edge oblique shock wave and reduces the drag when Ma = 0.9–1.4. Compared with a sand-free environment, sand-containing flow can affect the separation and transition positions of laminar separation bubbles, in addition to alter the shock wave structure. At different Mach numbers, the lift and drag of the airfoil first increased and then decreased as the sand particles flowed in the horizontal direction during the entire process of particles entering and exiting the airfoil flow field.

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

For an aeroelastic system of a two-dimensional elastic panel subjected to an impinging inviscid oblique shockwave, the nonlinear flutter characteristics are affected by many factors such as shock impingement location, cavity pressure and initial perturbation. The effects of the above factors on the variation of system bifurcation type and dynamic behaviors are investigated numerically. A low-fidelity computational method coupled with local piston theory and van Karman plate model, and a high-fidelity computational method coupled with Euler equations and finite element model are used for fluid-structure interaction simulations. Two sets of new findings are unveiled. First, either the variation of shock impingement location or cavity pressure can induce the aeroelastic system to transition between a subcritical bifurcation and a supercritical bifurcation. For some cases, the system bifurcation characteristics exhibit strong sensitivity to these two factors. Second, it is found that in addition to the limit cycle oscillation in the form of a combination of the second and third structural modes, multiple stable limit cycle oscillations due to the coupling of higher-order modes can be triggered by suitable initial perturbations. These limit cycle oscillations have high frequencies and amplitudes, which suggest a higher risk of structural fatigue failure.

Numerical study of the effect of micro vortices on chaotic flutter

The loading generated by shock wave boundary layer interaction (SBLI) plays a crucial role in the structural design of a high-speed vehicle. They can cause flow separation near the shock impingement, resulting in the onset of chaotic, self-sustained flutter leading to structural failure. This work investigates how a micro-ramp installed upstream of a flexible panel affects its flutter behavior. For this purpose, two-way coupled laminar fluid–structure interaction simulations are performed for two different oblique shock strengths impinging over a flexible panel. A comprehensive study with a micro-ramp, as high as half the boundary layer thickness, is conducted for a wide range of non-dimensional dynamic pressures expected for a supersonic flight. The study provides analysis methodology to characterize the nature of panel oscillations, and the influence of micro-ramp on fluid and structural unsteadiness is evaluated. The results indicate that the chaotic flutter is initiated because of the non-linear interaction between the high-frequency fluid and low-frequency structural unsteadiness. Micro vortices delay the onset of the chaotic flutter by lowering the fluid frequency, thereby synchronizing fluid and structure unsteadiness. The micro vortices also decreased flutter frequency for lower shock strength; however, MVG was somewhat ineffective for some higher shock strength. For the latter taller micro-ramps that can introduce stronger, low-frequency vortices are recommended.

Numerical study on the mixing enhancement induced by the interaction between the hydrogen/air coaxial jets and oblique shock wave at Mach 3 supersonic crossflow

The comprehensive performance of the scramjet is greatly influenced by the supersonic fuel mixing process. In the research, the mixing properties of the combination between the hydrogen/air coaxial jets and oblique shock at Mach 3 supersonic crossflow are investigated. The focus of the investigation is to reveal the mixing enhancement mechanism of coaxial jets and the impact of oblique shock on the mixing process. The numerical simulation is based on three-dimensional compressible RANS equations combined with the SST k-ω turbulence model. The hydrogen spatial distribution, flow features, vortex structure, penetration depth, stagnation pressure loss and mixing efficiency with different working conditions are evaluated and studied. Our computational results demonstrate that the coaxial jets enhance mixing through the intense shear action between the annular fuel jet with the inner and outer air layers, and the oblique shock contributes to the mixing process by strengthening the interaction between jet and airflow, improving fuel distribution and inducing streamwise vorticity. In addition, the hydrogen distribution and mixing properties are affected by the action position of the incident shock. According to the achieved results, the coaxial jets combined with the oblique shock impinging downstream of the jet have the highest mixing efficiency, which is improved by 63.27% compared to the reference case.

Scramjet combustion with bumpy struts

In this study, the following strut configurations were proposed to improve the combustion performance of a scramjet combustor with a strut: (1) BS-1: strut with periodic rectangular bumps and (2) BS-2: strut with periodic trapezoidal and triangular bumps. These bumps were arranged on both sides of the rear part of the struts. By using a validated numerical simulation method, the performance and combustion flow fields of scramjet combustors with a normal strut (NS) and two BSs were compared and analyzed under an inlet Mach number of 2.0 and hydrogen jet at sonic speeds. The effects of the two BSs on the performance of the scramjet combustor and their mechanisms were investigated. The results demonstrated that in the two BS combustors, the flow disturbance and streamwise vortices induced by the bumps, additional oblique shock waves at the leading edge of the rear straight section, and upstream shift in the interaction position between the reflected oblique shock wave and shear layer resulted in a significant increase in total pressure loss. However, the flow disturbance and streamwise vortices not only significantly increased the shear layer thicknesses and interfacial area between the fuel and air, which contributed to a more stable and efficient combustion by increasing the size of the near-field high-turbulent-kinetic-energy region and expanding the combustion region, but also enhanced heat and mass convection between the core region and main stream on both sides, yielding a higher flame propagation speed. Therefore, the combustion was significantly promoted in the two BS combustors. BS-2 had a stronger disturbance effect on the flow and induced stronger streamwise vortices, resulting in a greater total pressure loss compared with that observed in BS-1. However, the triangular bumps of BS-2 increased the width of the narrow part of the recirculation zone, which made the fuel distribution downstream of BS-2 combustor more conducive to maintaining a larger combustion region, thus achieving more efficient combustion. Compared with the NS combustor, BS-1 and BS-2 combustors reduced the distances by 49.4% and 54.1%, respectively, when the combustion efficiency reached 95%, and by 47.9% and 53.1%, respectively, when the combustion efficiency reached 100%, with the total pressure loss at the outlet increasing by 2.16% and 3%, respectively. Therefore, the results suggest that the two BSs have the potential to significantly enhance the combustion of scramjet combustors, making them a promising avenue for further research and optimization.

Numerical study on the dynamic process of ramjet/scramjet mode transition in the integrated full flow path for RBCC engine

As the inflow velocity increases, rocket-based combined cycle(RBCC) engine typically require a ramjet/scramjet mode transition within the flight range Ma∞ = 5.5 to 6.0. However, during the mode transition process, the reduction of the fuel mass flow rate usually causes the combustion intensity in the engine to drop sharply in a very short time, which will further lead to severe thrust fluctuations. So some technical methods need to be applied in this process to realize smooth mode transition. In this paper, different throttling strategies (kerosene mass flow rate dominant and rocket mass flow rate dominant) were designed and employed to study the dynamic mode transition process in the integrated RBCC engine flow path through three-dimensional numerical simulation for flight Ma∞ = 5.5 and Ma∞ = 6.0, respectively. The results show that when RBCC engine operates under the condition of large mass flow rate of fuel, the wall flow separation zone caused by oblique shock wave and combustion cannot be effectively improved by the bleed block and the inlet is still in the limit working state. Under flight Ma∞ = 5.5 condition, with the reduction of fuel equivalence ratio, RBCC engine successfully transited from ramjet mode to scramjet mode, and the flow separation zone near the bleed block disappeared. At this time, the high temperature gas of the rocket has no obvious effect on the thrust gain of the engine. By adjusting fuel mass flow rate in a small range and rocket mass flow rate in a large range, stable mode transition can be achieved, with relatively small time consumption and minimum thrust fluctuation during mode transition. With the increase of flight altitude, under flight Ma∞ = 6.0, the incoming flow speed increases, but the air capture ability of the inlet decreases, which is not conducive to the mixing of fuel and air combustion. When Ma∞ = 5.5, the mode transition by reducing the fuel equivalence ratio will cause the RBCC engine to produce huge thrust fluctuations, and the range of the high-pressure zone in the combustor will be greatly reduced. In order to ensure the stable operation of the RBCC engine, the rocket needs to operate at a larger mass flow rate.

Applicability analysis of inverse method of characteristics

The inverse method of characteristics (iMoC) is often employed to simulate the axisymmetric flow behind a predefined shock wave shape. Firstly, two marching schemes of iMoC were compared in this work: the intersection of the left- and right-running Mach lines and the intersection of the left-running Mach line and streamline. The intersection of the left-running Mach line and streamline is discovered to be simpler and more stable. Following that, the applicability of iMoC was analyzed by dividing the shock wave shapes into concave and convex curves, respectively. Based on the oblique shock relations, it is proved mathematically that iMoC is capable of computing the flow behind a concave shock wave. However, for the convex shock wave, if the shock wave angle declines too much along the axial coordinate, the clusters of left-running Mach lines may intersect, leading to iMoC failure. Furthermore, a method for enabling the implementation of iMoC is proposed by generating an expansion fan to replace the infeasible segment of the convex shock wave. Finally, computational fluid dynamics techniques were applied to validate the proposed methods and analysis. This study provides theoretical support to promote the application of iMoC in waverider and inward inlet design.

Isolation and phase-space energization analysis of the instabilities in collisionless shocks

We analyse the generation of kinetic instabilities and their effect on the energization of ions in non-relativistic, oblique collisionless shocks using a 3D-3V (three spatial with three velocity components) simulation by dHybridR, a hybrid particle-in-cell code. At sufficiently high Mach number, quasi-perpendicular and oblique shocks can experience rippling of the shock surface caused by kinetic instabilities arising from free energy in the ion velocity distribution due to the combination of the incoming ion beam and the population of ions reflected at the shock front. To understand the role of the ripple on particle energization, we devise a new instability isolation method to identify the unstable modes underlying the ripple and interpret the results in terms of the governing kinetic instability. We generate velocity-space signatures using the field–particle correlation technique to look at energy transfer in phase space from the isolated instability driving the shock ripple, providing a viewpoint on the different dynamics of distinct populations of ions in phase space. Together, the field–particle correlation technique and our new instability isolation method provide a unique viewpoint on the different dynamics of distinct populations of ions in phase space and allow us to completely characterize the energetics of the collisionless shock under investigation.

The Study of Surface Sliding Discharge Interacting with an Oblique Shock Wave

The Study of Surface Sliding Discharge Interacting with an Oblique Shock Wave

Numerical study on the integration of supersonic turbine guide vanes and three-dimensional hydrogen/air rotating detonation combustor

Hydrogen/air rotating detonation turbine engine is expected to become a new generation of aerospace power plant because of its compact structure, high cycle thermal efficiency, and superior thrust performance. It can also reduce fuel consumption, save energy, and reduce carbon emissions. However, the highly unsteady oscillation characteristics of the outlet flow of the rotating detonation combustor make it difficult to integrate the supersonic turbine with the rotating detonation combustor. In this paper, the supersonic turbine guide vanes are designed by the method of characteristics and Bessel parameterization and are integrated with three-dimensional hydrogen/air rotating detonation combustors for numerical studies. The effects of aligned mode and misaligned mode on the coupling of supersonic turbine guide vanes and rotating detonation combustor are discussed carefully. The results show that the supersonic turbine guide vanes can make the rotating detonation wave change from a single-wave mode to a double-wave alternating strength and weak propagation mode. It can effectively suppress the oscillation of the combustion chamber outlet airflow. In the aligned mode, the peak pressure at the outlet of the supersonic turbine is about 70% lower than that at the cascade inlet, the pressure oscillation amplitude is reduced by 93.33%, and the temperature amplitude is reduced by 23.81%; the average total pressure loss coefficient of the cascade is 11.63%. In the misaligned mode, compared with the cascade inlet, the peak value of the pressure signal at the cascade outlet decreases by about 50%, while the pressure oscillation amplitude decreases by about 33.33%, and the temperature oscillation amplitude decreases by 11.11%; the average total pressure loss coefficient of the cascade is 4.83%. The supersonic turbine guide vanes have a better suppression effect on the oscillation signal in the aligned mode, but the relative total pressure loss is relatively large. This is because that the oblique shock wave, channel shock wave, and supersonic turbine guide vanes interact to generate more complex wave system and secondary flow in the aligned mode. These features provide important reference information for the coupling of supersonic turbines and rotating detonation combustors.

Analysis of shock train leading shock structure under oscillatory backpressure

The leading shock in a steady shock train takes one of two forms: oblique or normal. However, the phenomenon and mechanism of the normal-to-oblique transition of the leading shock in a forced shock train have not been widely reported. In this study, leading normal and oblique shocks are experimentally observed at the same position and similar velocities in a forced oscillation shock train with an incoming Mach number of 1.83. The normal-to-oblique transition is found to be closely related to the self-excited oscillation of the shock train. In addition, we find that the direct use of free-interaction theory cannot accurately predict the leading shock angle in a moving shock train. Thus, free-interaction theory requires appropriate correction for this scenario.

Compressible correction for separated and shear flow based on structural compressibility

In this paper, different compressible correction strategies for k-ω turbulence model are proposed. The dilatation dissipation term, which is significant in compressible flow, is taken into account and modeled in the Favre-averaged k-equation and ω-equation. We propose correction model for the dilation dissipation term based on the gradient Mach number in this paper, the coefficients of which are calibrated from experimental data on compressible turbulent mixed layers, and compare it to the Wilcox, Sarkar, and Heinz correction models. In slope-cavity flow and oblique shock wave/boundary layer interactions, the performance of these corrections is evaluated and compared to experimental data. The new correction has a similar or even better effect in separation prediction, heat flux prediction, and other aspects, and the uncertainty of model form and coefficients can be investigated further.

Numerical Study of Shock Wave Boundary Layer Interaction Based on an Anisotropic Turbulence Model

This paper presents numerical simulations of incident oblique shock wave impinging on a flat plate with a turbulent boundary layer using a nonlinear anisotropic turbulence model. Three cases with different incident shock angles under the same free-stream Mach number are studied, including attachment flow, incipient separation flow and outstanding separation flows. Convection terms and diffusion terms are calculated using the third-order Roe’s flux difference splitting scheme and the second-order central difference scheme in the code, respectively. The Runge-Kutta time marching method is employed to solve the governing equations for steady state solutions. Comparisons between the simulated results and experimental data are carried out, which include density contours, pressure distribution, skin friction coefficients distribution and streamline vectors. To capture the essential behavior of this complex anisotropic turbulence separation flow caused by the shock-wave-boundary-layer-interaction (SWBLI), an anisotropic eddy viscosity tensor and a nonlinear Reynolds stress-strain constitutive relationship are used in this model. The anisotropic eddy viscosity tensor is composed of turbulent fluctuation velocity vector and characteristic length vector which are obtained by statistical partial average scheme. With proper modeling of anisotropic eddy viscosity tensor, the numerical results are in good agreement with the experimental data. It is worthy to point it out that the computation accuracy decreases with increasing interaction intensity.

Coupling study of supersonic turbine stage and two-dimensional hydrogen/air rotating detonation combustor

The hydrogen/air rotating detonation turbine engine has the advantages of self-supercharging, small entropy increase, high thermal efficiency, high thrust-to-weight ratio, low fuel consumption, and low carbon emissions. However, the high-frequency and high-speed oscillation characteristics of the outflow of the rotating detonation combustor pose challenges for the turbine to extract work efficiently. In this study, a supersonic turbine stage designed using the Python code of the method of characteristics coupled with a two-dimensional rotating detonation combustor is numerically investigated. The propagation characteristics of the detonation wave in the aligned mode and misaligned mode and interaction with the supersonic turbine stage are carefully discussed. The results show that the coupling of the supersonic turbine stage and the rotating detonation combustor will cause the detonation wave to change from a single-wave mode to a three-wave co-propagating mode. The Kelvin–Helmholtz instability of the slip line increases after passing through the induced oblique shock. In the multi-wave mode, the detonation wave is self-adaptive, and multiple detonation waves interact to automatically adjust the propagation velocity, intensity, and distance of each detonation wave, and finally achieve a dynamic balance. The supersonic turbine stage has good operating performance under the condition of rotating detonation flow, its power level can reach 110 kW, and the maximum stagnation adiabatic efficiency of the supersonic turbine stage can reach 86%. The supersonic turbine guide vanes can greatly reduce the oscillation amplitude of the incoming flow. In the aligned mode, the supersonic turbine guide vanes has a more obvious effect of suppressing the amplitude of the incoming flow. The total pressure loss of the supersonic turbine stage is smaller, and the supersonic turbine rotor can extract work more efficiently in the aligned mode. These findings provide a valuable reference for further research on the hydrogen/air rotating detonation turbine engine, ultimately leading to the practical application of an energy-saving, high-efficiency, and low-emission hydrogen/air rotating detonation turbine engine.