Hypersonic Thermochemical Nonequilibrium Flow Research Articles

Navier-Stokes characteristic boundary conditions for high-enthalpy compressible flows in thermochemical non-equilibrium

This fundamental study presents Navier-Stokes characteristic boundary conditions (NSCBCs) for high-enthalpy hypersonic flows in thermochemical non-equilibrium. In particular, the relevant locally one-dimensional inviscid (LODI) relations are derived within a two-temperature framework for high-enthalpy hypersonic flows undergoing finite-rate thermochemical processes, including air dissociation and vibrational relaxation. Using these LODI relations, a set of NSCBCs are proposed and later demonstrated in canonical test cases, including the interaction of homogeneous isotropic turbulence with a shock wave subject to high-enthalpy thermochemical non-equilibrium effects.

Computational study of lateral jet interaction in hypersonic thermochemical non-equilibrium flows using nonlinear coupled constitutive relations

The present study reports the numerical analyses of lateral jet interaction around a Terminal High Altitude Area Defense-type (THAAD-type) model in hypersonic rarefied flows, with the real gas effect incorporated. The computation approach employed is the recently developed thermochemical non-equilibrium nonlinear coupled constitutive relations (NCCR) model. Regarding the simulation conditions, the flight velocity and height are set to 20 Ma and 80 km, respectively. To disclose the flow mechanism of lateral jet interaction, the complex flowfield characteristics and surface pressure distributions are discussed at length. Additionally, the research explores the impact of two key factors, namely, the jet pressure ratio and the jet Mach number, on the control performance of an in-flight vehicle's reaction control system (RCS). The results demonstrate that the complicated flowfield structures in lateral jet interaction are successfully reproduced by the NCCR model. With an increase in either the jet pressure ratio or the jet Mach number, the force and moment amplification factors decrease, while the absolute value of the normal force coefficient increases. Notably, it is found that the rarefied gas effect captured by the NCCR model against the Navier–Stokes–Fourier solution affects the lateral jet interaction flowfield, e.g., weakening the compressibility of the barrel shock and the expansibility of the Prandtl–Meyer expansion fan, as well as strengthening the jet wraparound effect. Importantly, the rarefied gas effect also exerts a prominent influence on the performance of RCS, with the degree of influence diminishing as the jet Mach number or the jet pressure ratio increases.

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.

Thermochemical non-equilibrium effects on hypersonic shock wave/turbulent boundary-layer interaction

The research on shock wave/turbulent boundary-layer interactions is mainly limited to calorically perfect gases; little has been reported on the thermochemical non-equilibrium (real gas) effect. This effect is prominent at conditions of high Mach and Reynolds numbers. In this work, a household parallel solver for hypersonic thermochemical non-equilibrium flows with a Reynolds-averaged Navier–Stokes turbulence model is developed in which the coupling of turbulence with vibration and chemistry occurs under a gradient-law assumption. The thermal non-equilibrium is based on Park's two-temperature model, and the chemical non-equilibrium is based on Gupta's 11-species model. The method proposed in this paper is first validated using experimental data, including cases of a laminar cylinder flow at a high-enthalpy condition, a supersonic flat-plate turbulent boundary layer flow, a hypersonic transition flow, and a hypersonic compression corner flow at a low-enthalpy condition. This approach is then applied to assess the hypersonic flow characteristics past the 34° compression corner at a flight height of 30 km. Results show that the joint effects of turbulence and thermochemical non-equilibrium have a significant impact on the flow field organization, wall data, and separation length of the shock wave/boundary-layer interaction. Furthermore, the mechanism of the neck region accompanied by maximum heat flux, wall pressure and skin friction in both laminar and turbulent cases is well-interpreted. This study can be used as a reference tool for the aerodynamic design of future hypersonic vehicles accounting for multi-physics effects.

A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part II

Purpose This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes. Design/methodology/approach The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement. Findings The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions. Originality/value Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part I

PurposeThis paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.Design/methodology/approachThe solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.FindingsThe comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.Originality/valueThe FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

Aerothermodynamic Design Optimization of Hypersonic Vehicles

The objective of this study is to develop a reliable and efficient design optimization method for hypersonic vehicles focused on aerothermodynamic environments. Considering the nature of hypersonic flight, a high-fidelity aerothermodynamic analysis code is used for the simulation of weakly ionized hypersonic flows in thermochemical nonequilibrium. A gradient-based method is implemented for optimization. Bezier or nonuniform rational basis spline curves are used to parametrize the geometry or the geometry change. Linear elasticity theory is implemented for mesh deformation. Penalty functions are utilized to prevent undesired geometrical changes. The design objective is to minimize drag without increasing the total heat transfer rate and the maximum values of the surface heat flux, temperature, and pressure. Design optimizations are performed at different trajectory points of the IRV-2 vehicle. The effects of parametrizations, the number of design variables, and freestream conditions on design performance are studied.

Numerical investigation of oxygen thermochemical nonequilibrium on high-enthalpy double-cone flows

Hypersonic thermochemical nonequilibrium flows over a double-cone configuration are numerically investigated. Simulations with oxygen as the test gas are performed using different coupling models of vibrational excitation and dissociation, including a conventional two-temperature model as the baseline and an improved model established on elementary kinetics and validated against existing shock tube experimental data. For the condition with the highest total enthalpy, the improved model predicts a larger separation region and greater peak heat flux with relative differences of 20.3% and 29.2%, respectively, compared with the baseline two-temperature model. The differences are attributed to inaccurate modeling of the vibration–dissociation coupling effects by the conventional two-temperature model, which overestimates the post-shock degree of dissociation and underestimates the post-shock temperature. The size of the separation bubble is therefore altered due to the change in its density. These findings may help to explain the large discrepancies found between numerical results and experimental data for high-enthalpy double-cone flows in hypersonic studies.

Investigation of Unsteady Edney Type IV and VII Shock–Shock Interactions

Edney type IV and type VII shock–shock interactions are complex hypersonic flow phenomena. They are characterized by a supersonic jet that reaches far into the flowfield. An experimental investigation of the inner jet structure is difficult, especially in cases where the jet is subject to high-frequency unsteady movements. The present paper provides insight into the jet structure and its movement by means of a highly resolved computational fluid dynamics analysis in thermochemical nonequilibrium that significantly exceeds the resolution of existing publications. Simulations of an Edney type IV interaction in nitrogen flow are presented. Advanced adaptation strategies allow for the identification and analysis of the mechanisms of the jet unsteadiness, resulting in a new classification of the unsteady flowfield behavior with respect to the periodic jet movement. This classification is based not only on wall quantities, but also on the core flowfield. The computations are supplemented by a grid sensitivity study. The second configuration is an Edney type VII interaction. This shock–shock interaction type was observed and defined in nitrogen flow by Yamamoto et al (Numerical Investigation of Shock/Vortex Interaction in Hypersonic Thermochemical Nonequilibrium Flow, Journal of Spacecraft and Rockets, Vol. 36, No. 2, 1999, pp. 240–246. The present results demonstrate that this interaction may also be observed in carbon-dioxide-dominated flow with a gas composition similar to the Martian atmosphere. The results provide insight into the jet structure of this less known interaction.

Novel Method to Calculate Vibrational Thermal Conduction in Hypersonic Nonequilibrium Flow

A new method is proposed to express the vibrational thermal conduction in the computation of hypersonic thermochemical nonequilibrium flows with the two-temperature model. To overcome numerical difficulties such as the nonphysical oscillation of the vibrational temperature near the cold wall, the vibrational thermal conduction is modeled directly with the gradient of nonequilibrium vibrational energy and coupled to the diffusive flux of vibrational energy. In such a way, the proposed method needs neither the vibrational temperature nor the vibrational thermal conductivity, which are prerequisites in the conventional method to calculate vibrational thermal conduction. The effectiveness of the new method is demonstrated in the numerical simulation of the thermochemical nonequilibrium flow over a sphere–cylinder geometry. The results show that the sizes of the first grids away from the wall can be much larger than those with the conventional method, improving significantly the efficiency of the computation. Using the more primitive variable (nonequilibrium vibrational energy) rather than the representative variable (vibrational temperature), the new method has some theoretical advantages, especially under the extreme circumstances, where it is required to describe the microscopic processes directly and the meaning of vibrational temperature may have some ambiguity.

Conservative Residual Distribution Method for Viscous Double Cone Flows in Thermochemical Nonequilibrium

AbstractA multi-dimensionally upwind conservative Residual Distribution algorithm for simulating viscous axisymmetric hypersonic flows in thermo-chemical nonequilibrium on unstructured grids is presented and validated in the case of the complex flow-field over a double cone configuration. The resulting numerical discretization combines a state-of-the-art nonlinear quasi-monotone second order blended scheme for distributing the convective residual and a standard Galerkin formulation for the diffusive residual. The physical source terms are upwinded together with the convective fluxes. Numerical results show an excellent agreement with experimental measurements and available literature.

Overrelaxation Applied to Lower-Upper Symmetric Gauss-Seidel Method for Hypersonic Flow

An implicit time-marching method for acceleration of the convergence of solution for the compressible Navier-Stokes equations is presented. This is based on the lower-upper symmetric-Gauss-Seidel (LU-SGS) method proposed by Yoon and Jameson. A very simple overrelaxation is additionally executed in the LU-SGS method coupled with diagonal flux splitting. Then, an overrelaxation parameter w, a parameter similar to that in the well-known successive-overrelaxation method is introduced. The calculated results for a hypersonic viscous flows around a cylinder and through a compression corner indicate that the convergence is accelerated by a proper value of ω(1 < ω < 2). This method is also applied to a hypersonic thermochemical nonequilibrium flow around a sphere

Finite element adaptive method for hypersonic thermochemical nonequilibrium flows

Finite element adaptive method for hypersonic thermochemical nonequilibrium flows

Numerical Simulation of Hypersonic Non-Equilibrium Wake Flow Using a Higher-Resolution Method.

An object which flies hypersonic speed, such as an aeroassisted orbital transfer vehicle, is affected greatly by not only the bow shock but also the expansion around the shoulder and the recompression of separated flow. Though the experiments to analyze this flow have been performed by some groups recently, there are some difficulties in measuring the ow because of limitations of instrumentation. Both experimental and numerical approaches are necessary to analyze the phenomena. The efficient numerical code which has been developed by the authors for hypersonic thermochemical non-equilibrium flow is applied to simulate the problem. The calculated results of different accuracy's in space, the perfect gas and the experimental data are compared.

Computation of weakly ionized hypersonic flows in thermochemical nonequilibrium

A numerical method to compute a two-dimensional hypersonic flowfield that is weakly ionized and in thermochemical nonequilibrium has been developed. Such a flowfield is described by coupled partial differential equations for the conservation of species mass, mass-averaged momentum, vibrational energy of each diatomic species, electron energy, and total energy. The steady-state solution to these fully coupled equations has been obtained for a gas composed of seven chemical species and characterized by six temperatures using an implicit Gauss-Seidel line relaxation technique. The computed electron number densities in the flowfield of a sphere cone compare well with experimental results.