Investigation of hypersonic flows through a cavity with sweepback angle in near space using the DSMC method

Near space has been paid more and more attentionin recent years due to its military application value.However,flow characteristics of some fundamental configurations(e.g.,the cavity)in near space have rarely been investigated due to rarefied gas effects,which make the numerical simulation methods based on continuous flow hypothesis lose validity.In this work,the direct simulation Monte Carlo(DSMC),one of the most successful particle simulation methods in treating rarefied gas dynamics,is employed to explore flow characteristics of a hypersonic cavity with sweepback angle in near space by considering a variety of cases,such as the cavity at a wide range of altitudes 20-60 km,the cavity at freestream Mach numbers of 6-20,and the cavity with a sweepback angle of 30°-90°.By analyzing the simulation results,flow characteristics are obtained and meanwhile some interesting phenomena are also found.The primary recirculation region,which occupies the most area of the cavity,causes pressure and temperature stratification due to rotational motion of fluid inside it,whereas the pressure and temperature in the secondary recirculation region,which is a small vortex and locates at the lower left corner of the cavity,change slightly due to low-speed movement of fluid inside it.With the increase of altitude,both the primary and secondary recirculation regions contract greatly and it causes them to separate.A notable finding is that rotation direction of the secondary recirculation region would be reversed at a higher altitude.The overall effect of increasing the Mach number is that the velocity,pressure,and temperature within the cavity increase uniformly.The maximum pressure nearby the trailing edge of the cavity decreases rapidly as the sweepback angle increases,whereas the influence of sweepback angle on velocity distribution and maximum temperature within the cavity is slight.

Experimental study on shock interaction control of double wedge in high-enthalpy hypersonic flow subject to plasma synthetic jet

The hypersonic shock-shock interaction flow field at double-wedge geometries controlled by plasma synthetic jet actuator is experimentally studied in a Ma = 8 high-enthalpy shock tunnel with the purpose of exploring a novel technique for reducing surface heat flux in a real flight environment. The results demonstrate that increasing the discharge energy is advantageous in eliminating the shock wave, shifting the shock wave interaction point, and shortening the control response time. The oblique shock wave can be completely removed when the actuator's discharge energy grows from 0.4 J to 11.5 J, and the displacement of the shock wave interaction point increases by 124.56%, while the controlled response time is shortened by 30 μs. Besides, the reduction in diameter of the jet exit is firstly proved to have a negative impact on energy deposition in a working environment with incoming flow, which reduces the discharge energy and hence decreases the control effect. The shock wave control response time lengthens when the jet exits away from the second wedge. Along with comparing the change in wall heat flux at the second wedge over time, the control effect of plasma synthetic jet actuator with and without inflation is also analyzed. When plasma synthetic jet works in inflatable mode, both the ability to eliminate shock waves and the shifting effect of the shock wave interaction point are increased significantly, and the wall heat flux is also reduced.

Oblique detonation wave triggered by a double wedge in hypersonic flow

Pressure-gain combustion has gained attention for airbreathing ramjet engine applications owing to its better thermodynamic efficiency and fuel consumption rate. In contrast with traditional detonation induced by a single wedge, the present study considers oblique shock interactions attached to double wedges in a hypersonic combustible flow. The temperature/pressure increases sharply across the interaction zone that initiates an exothermic reaction, finally resulting in an Oblique Detonation Wave(ODW). Compared with the case for a single-wedge ODW, the double-wedge geometry has great potential to control the initiation of the ODW. As a tentative study, two-dimensional compressible Euler equations with a two-step induction-reaction kinetic model are used to solve the detonation dynamics triggered by a double wedge. The effects of the wedge angles and wedge corner locations on the initiation structures are investigated numerically.The results show an ODW complex comprising three Oblique Shock Waves(OSWs), an induction zone, a curved detonation front, and an unburned/low-temperature gas belt close to the surface of the second wedge. Both the increasing wedge angle and downstream wedge corner location lead to an abrupt OSW–ODW transition type, whereas the former corresponds to the shock–shock interaction and the later has a greater effect on the exothermic chemical process. Analysis of the shock polar and flow scale confirms that the OSW–ODW initiation structure mainly depends on the coupling of shocks and heat release in a confined initiation zone.

SHOCK INTERACTIONS IN NONEQUILIBIUM HYPERSONIC FLOW

A shock interaction problem is solved with finite difference methods for a hypersonic fiow of air with chemical reactions. If a body has two concave cornerst a secondary shock is formed in the shock layer and it meets the main shock later.As the two shocks meet, the flow becomes singular at the interaction point, and a new main shock, a contact discontinuity and an expansion wave appear as a result of interaction between the two shocks. Therefore, the problem is very complicated.Using proper combinations of implicit and explicit finite difference schemes according to the property of the equations and the boundary conditions, we compute the fiow behind the interaction point successfully.

High-enthalpy hypersonic flows

Nearly all illuminating classic hypersonic flow theories address aerodynamic phenomena as a perfect gas in the high-speed range and at the upper limit of continuum gas domain.The hypersonic flow is quantitatively defined by the Mach number independent principle,which is derived from the asymptotes of the Rankine-Hugoniot relationship.However,most hypersonic flows encounter strong shock-wave compressions resulting in a high enthalpy gas environment that always associates with nonequilibrium thermodynamic and quantum chemical-physics phenomena.Under this circumstance,the theoretic linkage between the microscopic particle dynamics and macroscopic thermodynamics properties of gas is lost.When the air mixture is ionized to become an electrically conducting medium,the governing physics now ventures into the regimes of quantum physics and electromagnetics.Therefore,the hypersonic flows are no longer a pure aerodynamics subject but a multidisciplinary science.In order to better understand the realistic hypersonic flows,all pertaining disciplines such as the nonequilibrium chemical kinetics,quantum physics,radiative heat transfer,and electromagnetics need to bring forth.

Application of surrogate models to stability analysis and transition prediction in hypersonic flows

To increase the efficiency and robustness of stability-based transition prediction in flow simulations, simplified methods are introduced to substitute direct stability analyses for rapid disturbance growth prediction. For low-speed boundary layers, these methods are mainly established based on self-similar assumptions, which are not applicable to non-similar boundary layers in hypersonic flows. The objective of this article is to investigate the application of surrogate models to stability analysis of non-similar flows over blunt cones, focused on parameterization of boundary-layer (BL) profiles. Firstly, correlations between BL edge and profile parameters are analyzed, along with self-similar flow parameters and discrete points on BL profiles, which present four groups of BL characteristic parameters. Secondly, using these parameters as inputs, surrogate models are built for disturbance growth prediction over an MF-1 blunt cone. Results show that, surrogate models using four BL edge parameters and a BL shape factor {Ue, Te, ρe, ηe, H12} for stability analysis can achieve comparable accuracy with those using 16 discrete BL profile parameters, which are more precise than those using merely self-similar parameters or BL edge parameters. Thirdly, the established surrogate models are validated by stability analysis and transition prediction over the MF-1 blunt cone in flight experiments at the instants of t = 17 s ~ 22 s. Compared with direct linear stability analyses, the mean relative error of predicted disturbance growth rates by surrogate models is 8.0% and the maximum relative error of N factor envelopes is 6.6%, which indicates feasible applications of surrogate models to stability analysis and transition prediction of non-similar boundary layers in hypersonic flows.

A review of the mathematical modeling of equilibrium and nonequilibrium hypersonic flows

This paper systematically reviews the mathematical modeling based on the computational fluid dynamics(CFD)method of equilibrium and nonequilibrium hypersonic flows.First,some physicochemical phenomena in hypersonic flows(e.g.,vibrational energy excitation and chemical reactions)and the flow characteristics at various altitudes(e.g.,thermochemical equilibrium,chemical nonequilibrium,and thermochemical nonequilibrium)are reviewed.Second,the judgment rules of whether the CFD method can be applied to hypersonic flows are summarized for accurate numerical calculations.This study focuses on the related numerical models and calculation processes of the CFD method in a thermochemical equilibrium flow and two nonequilibrium flows.For the thermochemical equilibrium flow,the governing equations,chemical composition calculation methods,and related research on the thermodynamic and transport properties of air are reviewed.For the nonequilibrium flows,the governing equations that include one-,two-,and three-temperature models are reviewed.The one-temperature model is applied to a chemical nonequilibrium flow,whereas the two-and three-temperature models are applied to a thermochemical nonequilibrium flow.The associated calculations and numerical models of the thermodynamic and transport properties,chemical reaction sources,and energy transfers between different energy modes of the three models are presented in detail.Finally,the corresponding numerical models of two special wall boundary conditions commonly used in hypersonic flows(i.e.,slip boundary conditions and catalytic walls)and related research,are reviewed.

An Implicit Block LU-SGS Algorithm-Based Lattice Boltzmann Flux Solver for Simulation of Hypersonic Flows

This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volume method(FVM)is applied to discretize the Navier-Stokes equations,and the LBFS is utilized to evaluate the numerical flux at the cell interface.In LBFS,the local solution of discrete velocity Boltzmann equation(DVBE)with the non-free parameter D1Q4 lattice Boltzmann model is adopted to reconstruct the inviscid flux across the cell interface,and the viscous flux is approximated by conventional smooth function approach.In order to improve the robustness and convergence rate of the simulation for hypersonic flows,especially for problems with complex geometry,the implicit block LU-SGS algorithm is introduced to solve resultant discrete governing equations.A double cone model at Mach number of Ma=9.86 is firstly simulated to validate the proposed scheme,and a hypersonic flight vehicle with wings and rudders at Mach number of Ma=5.56 is then calculated to extend the application in practical engineering problems.Numerical results show that the proposed scheme could offer a more accurate and effective prediction for hypersonic flows.

An Empirical Method for Prediction of Hypersonic Rarefied Flow-Field Structure

Numerical simulations are presented about the effects of gas rarefaction on hypersonic flow field.Due to the extremely difficult experiment,limited wind-tunnel conditions and high cost,most problems in rarefied flow regime are investigated through numerical methods,in which the direct simulation Monte-Carlo(DSMC)method is widely adopted.And the unstructured DSMC method is employed here.Flows around a vertical plate at a given velocity 7 500 m/s are simulated.For gas rarefaction is judged by the free-stream Knudsen number(Kn),two vital factors are considered:molecular number density and the plate′s length.Cases in which Kn varies from 0.035 to13.36 are simulated.Flow characters in the whole rarefied regime are described,and flow-field structure affected by Knis analyzed.Then,the dimensionless position D*of a certain velocity in the stagnation line is chosen as the marker of flow field to measure its variation.Through flow-field tracing and least-square numerical method analyzing,it is proved that hypersonic rarefied flow field expands outward linearly with the increase of 1/2Kn.An empirical method is proposed,which can be used for the prediction of the hypersonic flow-field structure at a given inflow velocity,especially the shock wave position.

A reduced-order model for fast predicting ionized flows of hypersonic vehicles along flight trajectory

An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low-dimensional space by performing the Proper Orthogonal Decomposition(POD)on snapshots and is coupled with the Radial Basis Function(RBF)to achieve fast prediction speed.However,due to the disparate scales in the ionized flow field,the conventional ROM usually generates spurious negative errors.Here,this issue is addressed by performing flow-solution preprocessing in logarithmic space to improve the conventional ROM.Then,extra orthogonal polynomials are introduced in the RBF interpolation to achieve additional improvement of the prediction accuracy.In addition,to construct high-efficiency snapshots,a trajectory-constrained adaptive sampling strategy based on convex hull optimization is developed.To evaluate the performance of the proposed fast prediction method,two hypersonic vehicles with classic configurations,i.e.a wave-rider and a reentry capsule,are used to validate the proposed method.Both two cases show that the proposed fast prediction method has high accuracy near the vehicle surface and the free-stream region where the flow field is smooth.Compared with the conventional ROM prediction,the prediction results are significantly improved by the proposed method around the discontinuities,e.g.the shock wave and the ionized layer.As a result,the proposed fast prediction method reduces the error of the conventional ROM by at least 45%,with a speedup of approximately 2.0×105compared to the Computational Fluid Dynamic(CFD)simulations.These test cases demonstrate that the method developed here is efficient and accurate for predicting ionized hypersonic flows.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

Effects of mesh resolution on hypersonic heating prediction

Aeroheating prediction is a challenging and critical problem for the design and optimization of hypersonic vehicles.One challenge is that the solution of the Navier-Stokes equations strongly depends on the computational mesh.In this letter,the effect of mesh resolution on heat flux prediction is studied.It is found that mesh-independent solutions can be obtained using fine mesh,whose accuracy is confirmed by results from kinetic particle simulation.It is analyzed that mesh-induced numerical error comes m...

Numerical simulation of hypersonic thermochemical nonequilibrium flows using nonlinear coupled constitutive relations

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper.Three typical cases are intensively investigated for further validation,including hypersonic flows over a two-dimensional cylinder,a RAM-C II flight vehicle and a type HTV-2 flight vehicle.The results predicted by NCCR solution,such as heat flux coefficient and electron number densities,are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations,especially in the extremely nonequilibrium regions,which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects.The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.

Numerical exploration on the thermal invasion characteristics of two typical gap-cavity structures subjected to hypersonic airflow

In this paper,numerical investigation of hypersonic gas flow over two typical gap-cavity structures is carried out using all-speed preconditioned density-based solver.Such structures filled with porous seal in the gap are often present at the joint locations of control surfaces of the hypersonic vehicles.Single-domain approach is adopted to integrate the governing equations for both porous and fluid regions.The basic thermal invasion characteristic is first illustrated using the maze gap-cavity structure without sealing.Then,the influence of seal filling depth on the thermal invasion characteristic is investigated for the structure with sealing.Finally,a comparison of thermal invasion characteristics between maze and straight gap-cavity structures is performed to examine the influence of gap bending.Results show that the main source of hot airflow invading into the gap is from the millimeter scale gas layer within the boundary layer.And the invasion characteristic presents approximate stationary behavior.A primary vortex occurs in the gap adjacent to the leeward wall,which is ascribed to the impinging effect between the separate boundary flow and the windward wall.This effect is also the main driving force of thermal invasion.A treatment of filling the seal in certain depth inside the gap can significantly reduce the thermal load of seal and maintain an acceptable level of the invading mass flow rate.Additionally,it is found that the gap bending exerts a limited block effect on the thermal invasion without sealing,and this effect can be ignored with sealing.These results can provide a reference for optimizing the seal gap-cavity structure configuration.

Planar laser scattering visualization of streamwise vortex pairs in a Mach 6 flow

A series of cross-sectional flow fields of Counterrotating Vortex Pairs(CVPs) generated by a large-scale ramp vortex generator is observed using an ice-cluster-based Planar Laser Scattering(PLS) method in a shock tunnel with a nominal flow Mach number of 6. Combined with a numerical simulation, two streamwise CVPs with opposite rotating directions are identified in the wake flow of the vortex generator with an absence of a boundary layer, namely, a Primary CVP(PCVP) and a Secondary CVP(SCVP). The wake flow is divided into two stages with different features of the PCVP and SCVP. In Stage Ⅰ, the PCVP and SCVP gradually mature, and the flow is relatively stable. In Stage Ⅱ, the PCVP and SCVP depart from each other, and the flow becomes unstable. The profiles of the transverse velocity in the spanwise symmetry plane induced by the PCVP and SCVP do not obey the scaling law of CVPs immersed in the boundary layer. A new scaling law is proposed, in which the transverse distances between adjacent saddle points in the cross-sectional flow field are used as the characteristic lengths for the PCVP and SCVP. After this new scaling procedure, the profiles of transverse velocity induced by the PCVP and SCVP at different streamwise locations collapse well. Moreover, the PLS images show that the mixing between the CVPs and the outside high-momentum flow becomes evident at approximately 5.5 times the height of the vortex generator, which is earlier than that immersed in the boundary layer. These findings enrich the knowledge of CVPs in the hypersonic regime, especially in the absence of the boundary layer.

Variable High-Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows,Part II:Hypersonic Nonequilibrium Flows

The variable high-order multiblock overlapping(overset)grids method of Sj¨ogreen&Yee[CiCP,Vol.5,2009]for a perfect gas has been extended to nonequilibrium flows.This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts[Wang et al.,J.Comput.Phys.,2009,2010]that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations.Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields,even under the multiblock grid or adaptive grid refinement framework.While low dissipative sixth-or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets,second-and thirdorder shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence.It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow for an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow.In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries.The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks,including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components,depending on the flow conditions.

Rarefied gas effect in hypersonic shear flows

Recently,as aerodynamics was applied to flying vehicles with very high speed and flying at high altitude,the numerical simulation based on the Navier-Stokes(NS)equations was found that cannot correctly predict certain aero-thermo-dynamic properties in a certain range of velocity and altitude while the Knudsen number indicates that the flow is still in the continuum regime.As first noted by Zhou and Zhang(Science in China,2015),the invalidity of NS equations for such flows might be attributed to an non-equilibrium effect originating from the combined effects of gas rarefaction and strong shear in the boundary-layer flows.In this paper,we present the scope,physical concept,mathematical model of this shear non-equilibrium effect in hypersonic flows,as well as the way of considering this effect in conventional computational fluid mechanics(CFD)for engineering applications.Several hypersonic flows over sharp bodies and blunt bodies are analyzed by the proposed new continuum model,named direct simulation Monte Carlo(DSMC)data-improved Navier-Stokes(DiNS)model.

Scaling of interaction lengths for hypersonic shock wave/turbulent boundary layer interactions

The interaction length induced by Shock Wave/Turbulent Boundary-Layer Interactions(SWTBLIs)in the hypersonic flow was investigated using a scaling analysis,in which the interaction length normalized by the displacement thickness of boundary layer was correlated with a corrected non-dimensional separation criterion across the interaction after accounting for the wall temperature effects.A large number of hypersonic SWTBLIs were compiled to examine the scaling analysis over a wide range of Mach numbers,Reynolds numbers,and wall temperatures.The results indicate that the hypersonic SWTBLIs with low Reynolds numbers collapse on the supersonic SWTBLIs,while the hypersonic cases with high Reynolds numbers show a more rapid growth of the interaction length than that with low Reynolds numbers.Thus,two scaling relationships are identified according to different Reynolds numbers for the hypersonic SWTBLIs.The scaling analysis provides valuable guidelines for engineering prediction of the interaction length,and thus,enriches the knowledge of hypersonic SWTBLIs.

Numerical simulation of compression corner flows at Mach number 9

A hypersonic vehicle encounters a wide range of conditions during its complete flight regime.These flight conditions may vary from low to high Mach numbers with varying angles of attack.The near-wall viscous dissipation associated with flows at combined high Mach and Reynolds numbers leads to significant wall heat transfer rates and shear stresses.The shock wave/boundary-layer interaction results in a flow separation region,which commonly augments total pressure losses in the flow and lowers the efficiency of aerodynamic control surfaces such as fins installed on a vehicle.The standard turbulence models,when used to resolve such flows,result in incorrect separation bubble size for large separated flows.Therefore,it results in an inaccurate aerodynamic load,such as the wall pressures,skin friction distribution,and heat transfer rate.In previous studies,the application of the shock-unsteadiness correction to the standard two-equation k-ωturbulence model improved the separation bubble size leading to an accurate pressure prediction and shock definition with the assumption of constant Prandtl number.In the present work,the new shock-unsteadiness modification to the k-ωturbulence model is applied to the hypersonic compression corner flows.This new model with variable Prandtl number is based on the model parameter,which depends upon the local density ratio.The computed wall pressures,heat flux and flow field are compared to the experimental data.A parametric study is carried out by varying compression deflection angles,free stream Reynolds number and wall temperatures to compute the flow field and wall data accurately,particularly in the shock boundary layer interaction region.The new shockunsteadiness modified k-ωmodel with variable Prandtl number shows an accurate prediction of initial pressure rise location,pressure distribution in the plateau region and heat flux in comparison to the standard k-ωmodel.

Progress in flight tests of hypersonic boundary layer transition

Boundary layer transition(BLT)can cause a sharp rise in heat flux and skin friction,which can seriously affect the flight performance and safety of hypersonic flight vehicles.Therefore,the mechanism,prediction and control of transition have become important issues that must be dealt with for the development of advanced flight vehicles,and it is also a research hotspot of particular interest to major aerospace countries.Compared to other transition research approaches,model flight tests can better present the transition problems under real flight conditions,thus have been carried out extensively over the past 30 years.The United States,Germany,France,Australia,and other countries have carried out transition research based on flight tests,such as the Pegasus wing-glove crossflow transition and the Hypersonic Boundary Layer Transition(HyBOLT)transition control flight test of the United States,the joint research project of the Hypersonic International Flight Research and Experimentation-1(HIFiRE-1)circular cone and the HIFiRE-5 elliptic cone transition flight tests between the United States and Australia,the flight test of compression surface transition of the scramjet forebody(LEA)in France and so on.Although these flight tests suffered various setbacks,they still obtained valuable transition data.Recently,the United States is carrying out the concave-surface transition flight tests of Hypersonic Boundary Layer Transition(BOLT)and BOLT-II.Since its first model flight test mission for verification purpose launched successfully in 2015,several hypersonic BLT flight tests have been conducted by China Aerodynamics Research and Development Center(CARDC).The flight tests have measured valid transition data under flight conditions,obtained the transition front and its dynamical variation on blunt cones at various angles of attack and a lifting body Hypersonic Transition Research Vehicle(HyTRV).The crossflow traveling waves in high-altitude flight were measured for the first time,and our understanding of hypersonic BLT has been greatly improved.