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This paper describes the numerical solutions of type‐IV shock‐on‐shock interactions in hypersonic thermochemical nonequilibrium air flows around blunt bodies. The Navier‐Stokes equation solver for a chemically reacting and vibrationally relaxing gas mixture was applied to the present problem, where the concepts of the Advection Upstream Splitting Method (AUSM) and the Lower‐Upper Symmetric Gauss‐Seidel (LU‐SGS) method were basically employed along with the two‐temperature thermochemical model of Park. The aerodynamic heating with or without the shock‐on‐shock interaction to a sphere and circular cylinders are simulated for a hypersonic nonequilibrium flow. The numerical results show that typical type‐IV shock‐on‐shock interaction pattern with a supersonic jet structure is also formed in a high‐enthalpy thermochemical nonequilibrium flow, and that the contribution of convective heat flux in the translational/rotational mode to the total heat flux is dominant. Furthermore, the inherent unsteadiness of nonequilibrium type‐IV shock‐on‐shock interaction flowfield is discussed briefly.

The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

The purpose of this paper is to perform the simulation to explore the gap flow field under a hypersonic air flow. Thermal protection systems of hypersonic vehicles generally consist of thermal insulation tiles, and gaps between these tiles probably cause a severe local aerodynamic thermal effect.

The discretizations of convection flux term and temporal term in the governing equation with chemical equilibrium, respectively, take AUSM+-up flux-vector splitting scheme and the implicit lower-upper symmetric Gauss–Seidel method. Based on these, the flow field in a deep gap is simulated by means of the computer codes that the authors have written.

The numerical results show that the heat flux distribution in a gap has a good agreement with experimental results. Importantly, the distribution of heat flux is “U” shaped and the maximum of the heat flux occurs at the windward corner of a gap.

To explore the gap flow field under a hypersonic air flow, which is a chemically reacting, all speed and viscous flow, a novel model with an equivalent ratio of specific heats is presented. The investigation in this paper has a guide for the design of the thermal protection system in hypersonic vehicles.

As to different angles of attack and nonlinear problems caused by high temperatures in coexisting hypersonic aircraft, people mainly rely on fluid software for research but lack analysis of flow mechanisms. Owing to computational difficulties, few people use numerical algorithms to combine them for discussion. Hence, this study aims to make a deep inquiry into the laminar flow and heat transfer of compressible Newtonian fluid in hypersonic aircraft with small attack angles.

In this paper, on the basis of mass, momentum and energy conservation laws, the governing equations of the hypersonic boundary layer are established. Viscosity, specific heat capacity and thermal conductivity are considered nonlinear functions concerning temperature. In virtue of the MacCormack finite difference method, the stationary numerical solutions are solved directly, and the validity of the algorithm is verified.

The results demonstrate that at Mach number 5, compared to the 0° attack angle, the maximum temperature near-wall at the 3° attack angle increases by about 25%. An enjoyable phenomenon is discovered, where the position corresponding to the maximum wall shear force shifts back as the attack angle and Mach number increase. The relationship between the near-wall maximum temperature versus attack angle and Mach number is fitted through numerical calculation results.

Empirical formulas can be used to estimate heat transfer characteristics at small attack angles, which will guide the design of aircraft thermal protection systems.

To compute the Navier‐Stokes equations of a non‐equilibrium weakly ionized air flow. This can help to have a better description of the flow‐field and the wall heat transfer in hypersonic conditions.

The numerical approach is based on a multi block finite volume method and using a Riemann's solver based on a MUSCL‐TVD algorithm. In the flux splitting procedure the modified speed of sound, due to the electronic mode, is implemented.

A good description of the shock standoff distance, of the wall heat fluxes and of the peak of electron density number in the shock layer.

The radiative effects are not included in this paper. For the very high Mach numbers, this can modify the shock layer parameters.

The knowledge of the wall heat transfer in the re‐entry body problems.

The building of a robust numerical code in order to well describe hypersonic air flow in high Mach numbers.

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

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.

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.

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.

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.

This 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.

The 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.

The 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.

The 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.

Non‐equilibrium hypersonic viscous flows with high enthalpy conditions have been computed with an implicit time‐dependent finite‐difference scheme. This scheme accounts for both chemical and vibrational non‐equilibrium processes in air flow around a hemispherical cylindrical body. The air was assumed to decompose into the following five species N, O, NO, N₂ and O₂ and only the two diatomic species N₂ and O₂ are taken in thermal non‐equilibrium. A range of Mach number from 14 to 18 has been investigated. The numerical results have been compared with those obtained by other workers and are in agreement with ballistic range data concerning the standoff shock distance at M = 15.3. The computed heat flux wall follows the trends of the experiments with an under prediction increasing with the Mach number. The influence of the thermal non‐equilibrium assumption on the computed standoff shock distance is investigated.

The purpose of this paper is to present an engineering inviscid‐boundary layer method for the calculation of convective heating rates on three‐dimensional non‐axisymmetric geometries at angle of attack.

Based on the axisymmetric analog, convective heating rates are calculated along the surface streamlines which are determined using the inviscid properties calculated on an unstructured grid.

Since the method is capable of using inviscid properties calculated on an unstructured grid, it is applicable to a variety of configurations and it requires much less computational effort than a Navier‐Stokes code. The results of the present method are evaluated on different wing body configurations in laminar and turbulent hypersonic equilibrium flows. In comparison to experimental data, the present results are found to be fairly accurate in the windward and leeward regions.

With this approach, heating rates can be predicted on general three‐dimensional configurations at hypersonic speeds in an accurate and fast scheme.

In order to calculate the heating rates at any specific point on the surface, a technique is developed to calculate the inviscid surface streamlines in a backward manner using the inviscid velocity components. The metric coefficients are also calculated using a new simple technique.