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.

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.

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.

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.

NON-STATIONARY EFFECTS IN HYPERSONIC NONUNIFORM DUSTY-GAS FLOW PAST A BLUNT BODY

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found.

Gao's interacting shear flows( ISF) theory and its inferences and their applications

Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dynamics （CFD） are reviewed and some subjects worthy to be studied are pro- posed in this paper. The flow-field and motion law of ISF, mathematics definition of strong viscous shear layer flow in ISF, ISF equations, wall-surface compatibility criteria （Gao＇s criteria ）, space scale variety law of strong viscous shear layer reveals flow mechanism and local space small scale triggered by strong interaction that cause some abnormal severe local pneumatic heating phenomenon in hypersonic flow. Gao＇s ISF theory was used in near wall flow, free ISF flow simulation and design of computing grids, Gao＇s wall-surface criteria were used to verify calculation reliability and accuracy of near wall flows, ISF theory approximate analytical result of shock waves-boundary layer interac- tion and ISF equations were used to obtain the numerical exact solution of local area flow （ such as stationary point flow）. Some new subjects, such as, improving near-wall turbulent models according to the turbulent flow simulation satisfying the wall-criteria and illustrating relation between grid-con- vergence based on the wall criteria and other convergence tactics, are suggested. The necessity of applying Gao＇s ISF theory and wall criteria is revealed. Difficulties and importance of hypersonic vis- cous/in-viscid interaction phenomenon were also emphasized.

Stable Runge-Kutta discontinuous Galerkin solver for hypersonic rarefied gaseous flow based on 2D Boltzmann kinetic model equations

A stable high-order Runge-Kutta discontinuous Galerkin(RKDG) scheme that strictly preserves positivity of the solution is designed to solve the Boltzmann kinetic equation with model collision integrals. Stability is kept by accuracy of velocity discretization, conservative calculation of the discrete collision relaxation term, and a limiter. By keeping the time step smaller than the local mean collision time and forcing positivity values of velocity distribution functions on certain points, the limiter can preserve positivity of solutions to the cell average velocity distribution functions. Verification is performed with a normal shock wave at a Mach number 2.05, a hypersonic flow about a two-dimensional(2D) cylinder at Mach numbers 6.0 and 12.0, and an unsteady shock tube flow. The results show that, the scheme is stable and accurate to capture shock structures in steady and unsteady hypersonic rarefied gaseous flows. Compared with two widely used limiters, the current limiter has the advantage of easy implementation and ability of minimizing the influence of accuracy of the original RKDG method.

Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat

When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.

Physical criterion study on forward stagnation point heat flux CFD computations at hypersonic speeds

In order to evaluate uncertainties in computational fluid dynamics （CFD） computations of the stagnation point heat flux, a physical criterion is developed. Based on a quasi-one-dimensional hypothesis along the stagnation line, a new stagnation flow model is applied to obtain the governing equations of the flow near the stagnation point at hypersonic speeds. From the above equations, the compatibility relations are given at the stagnation point and along the stagnation line, which consist of the physical criterion for checking the accuracy in the stagnation point heat flux computations. The verification of the criterion is made with various numerical results.

AN ANALYTIC SOLUTION ON HYPERSONIC FLOW OVER AN ARBTTRARY SLENDER BODY WITH NEAR POWER-LAW PROFILE

On the basis of a self-similar solution as well as of the assumption of the 'Transserse Motion',a general linear theory on hypersonic flow over a general slender body is set up in this paper By means of this theory, the problem concerned can he put into a universal system of O.D Eqs .which can be integrated manerically in adyance

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 mainly from the flux calculation in the boundary layer whereas the temperature gradient on the surface can be evaluated using a wall function.Numerical schemes having strong capability of boundary layer capture are therefore recommended for hypersonic heating prediction.

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.

NATURE OF THE SURFACE HEAT TRANSFER FLUCTUATION IN A HYPERSONIC SEPARATED TURBULENT FLOW

This paper presents the results of an experimental study of the unsteady nature of a hypersonic sepa- rated turbulent flow.The nominal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5x10^7/m.The separated flow was generated using finite span forward facing steps.An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make mul- ti-channel measurements of the fluctuating surface heat trtansfer within the separated flow.Conditional sampling ana- lysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness.The compression waves con- verge into a single leading shock beyond the boundary layer.The shock structure is unsteady and undergoes large-scale motion in the streamwise direction.The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave.There exists a wide band of frequency of oscillations of the shock system.Most of the frequencies are in the range of 1-3 kHz.The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave.This inter mittent phenomenon is considered as the consequence of the large-scale shock system oscillations.Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed.

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.

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.

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.