Thermochemical Nonequilibrium Flow Research Articles

The implicit fully coupled numerical method for flows in thermochemical nonequilibrium

A new effective implicit fully coupled numerical method to compute a high-speed flowfield that is in thermochemical nonequilibrium has been developed. Such a flowfield is described by coupled partial differential equations for the conservation of mass, momentum, total energy, vibrational energies, rotational energy, mass conservation for each species, etc. The total number of equations can be very large, which greatly complicates the solution of general finite volume vector equation when using the standard fully implicit approach. The proposed method allows us to reduce operations with block tridiagonal matrices to inversion of 4x4 matrices and trivial matrix multiplication operations. Moreover, the approximation factorization error is minimized. The numerical procedures were applied to solve chemical and thermal nonequilibrium flow past a sphere body at Mach 27 and chemically nonequilibrium heterogeneous flow in the channel of a combined ramjet with a solid fuel gas generator. The results indicate that new method is 4-5 times more efficient than the standard fully implicit method.

Code-verification techniques for hypersonic reacting flows in thermochemical nonequilibrium

The study of hypersonic flows and their underlying aerothermochemical reactions is particularly important in the design and analysis of vehicles exiting and reentering Earth's atmosphere. Computational physics codes can be employed to simulate these phenomena; however, verification of these codes is necessary to certify their credibility. To date, few approaches have been presented for verifying codes that simulate hypersonic flows, especially flows reacting in thermochemical nonequilibrium. In this paper, we present our code-verification techniques for verifying the spatial accuracy and thermochemical source term in hypersonic reacting flows in thermochemical nonequilibrium. We demonstrate the effectiveness of these techniques on the Sandia Parallel Aerodynamics and Reentry Code (SPARC).

Development of a stagnation streamline model for thermochemical nonequilibrium flow

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.

Numerical Analysis of Thermochemical Nonequilibrium Flows in a Model Scramjet Engine

This numerical study was conducted to investigate the flow properties in a model scramjet configuration of the experiment in the T4 shock tunnel. In most numerical simulations of flows in shock tunnels, the inflow conditions in the test section are determined by assuming the thermal equilibrium of the gas. To define the inflow conditions in the test section, the numerical simulation of the nozzle flow with the given nozzle reservoir conditions from the experiment is conducted by a thermochemical nonequilibrium computational fluid dynamics (CFD) solver. Both two-dimensional (2D) and three-dimensional (3D) numerical simulations of the flow in a model scramjet were conducted without fuel injection. Simulations were performed for two types of inflow conditions: one for thermochemical nonequilibrium states obtained from the present nozzle simulation and the other for the data available using the thermal equilibrium and chemical nonequilibrium assumptions. The four results demonstrate the significance of the modelling approach for choosing between 2D or 3D, and thermal equilibrium or nonequilibrium.

Numerical Study of High-Temperature Nonequilibrium Flow around Reentry Vehicle Coupled with Thermal Radiation

Accurate aerodynamic heating prediction is of great significance to current manned space flight and deep space exploration missions. The temperature in the shock layer surrounding the reentry vehicle can reach up to 10,000 K and result in remarkable thermochemical nonequilibrium, as well as considerable radiative heat transfer. In general, high-temperature flow simulations coupled with thermal radiation require appropriate numerical schemes and physical models. In this paper, the equations governing hypersonic nonequilibrium flow, based on a three-temperature model combined with a thermal radiation solving approach, are used to investigate the radiation effects in the reentry shock layer. An axisymmetric spherical case shows that coupling the flow-field simulation with radiation has a scarce influence on the convective heating prediction, but has some impact on the radiative heating calculation. In particular, for the Apollo capsule reentry, both the absorption coefficient and incident radiation are remarkable inside the shock layer. The radiative heating maximum reaches nearly 38% of that of the convective heating making a considerable contribution to the total aerodynamic heating. These results indicate that in the hypersonic regime, in order to account for the total heating, it is necessary to simulate the high-temperature thermochemical nonequilibrium flows coupled with thermal radiation.

Analysis of Thermochemical Nonequilibrium Ablation Flow for a Hypersonic Hemispherical Nose

The thermal protection materials enveloping hypersonic vehicles ablate. This paper develops a numerical methodology of thermochemical nonequilibrium flow and structure temperature field to study the key flow and structure parameters of a hypersonic hemispherical nose under the condition of carbon-based thermal protection material ablation. The multi-species chemical reaction model of flow field and the corresponding numerical algorithm are constructed. Oxidation and sublimation ablation process are considered in ablation model coupled with flow field solver by gas-solid interaction method. The computational results of a hemispherical nose indicate that carbon-based thermal protection material ablation has significant effects on thermochemical nonequilibrium flow. Details of the ablation flow characteristics are reported to highlight the influences of ablation on microcosmic reaction species and macroscopic flow parameters including shock wave position, pressure and temperature.

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.

Numerical analysis of hypersonic thermochemical non-equilibrium environment for an entry configuration in ionized flow

A theoretical methodology for thermochemical non-equilibrium flow combing with the HLLC (Harten-Lax-van Leer Contact) scheme was applied to study the hypersonic thermochemical non-equilibrium environment of an entry configuration in ionized flow. A two-temperature controlling model was utilized and the Gupta’s 11 species (N2, O2, NO, O, N, NO+, N2+, O2+, N+, O+, e−) thermochemical non-equilibrium model was taken. Firstly, numerical calculations of hypersonic thermochemical non-equilibrium environments for different aerodynamic shapes were carried out to verify the reliability of the method above. Then, the method was used to research the effects of ionization and wall catalysis on the hypersonic thermochemical non-equilibrium environment of the entry configuration in ionized flow. The shock stand-off distance can be reduced by thermochemical reactions but doesn’t continue to decrease significantly when ionization occurs. The shock stand-off distance calculated by the 11 species model is 4.2% smaller than that calculated by the 5 species (N2, O2, NO, O, N) thermochemical non-equilibrium model without considering ionization. Ionization reduces wall heat flux but increases wall pressure a little. The effect of ionization on aerothermal loads is greater than that of aerodynamic loads. The thermochemical reactions of electrons and ions catalyzed at the wall increase wall heat flux significantly but make a small change in wall pressure. The maximum wall heat flux obtained by only considering the electrons and ions catalyzed at the partially catalytic wall condition is 11.8% less than that calculated at the super-catalytic wall condition.

Aerothermodynamic analysis for deformed membrane of inflatable aeroshell in orbital reentry mission

An inflatable aerodynamic decelerator with a membrane aeroshell is a promising key technology in the reentry, descent, and landing phases of future space transportation. The membrane aeroshell is generally deformed by the in-flight aerodynamic force; however, the effects of the deformation on the aerodynamic heating are unclear. Here, we investigated aerodynamic heating for an inflatable reentry vehicle, Titans, in the hypersonic regime using flow field simulation coupled with structural analysis. Thermochemical nonequilibrium flows around the Titans with a deformed membrane aeroshell were reproduced numerically for an angle of attack (AoA) values between 0° and 40°. The maximum displacements of the membrane aeroshell by deformation at the AoAs of 0° and 40° were 6.7% and 6.6% of the diameter of the Titans, respectively. The difference in heat fluxes between the deformed and rigid shapes was a remarkable 188.8% for a 0° AoA owing to the considerable changes in the front shock wave shape. Meanwhile, it was indicated that membrane deformation at an AoA of 40° insignificantly affected the peak heat flux value on the inflatable torus because the considerable change in the shock wave shape observed for the case of 0° AoA did not occur. It was found that local wrinkles on the membrane aeroshell were formed by deformation, thus causing the heat flux to increase owing to an increase in local temperature gradient on the surface.

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.

Lagrangian diffusive reactor for detailed thermochemical computations of plasma flows

The simulation of a thermochemical nonequilibrium for atomic and molecular energy level populations in plasma flows requires a comprehensive modeling of all the elementary collisional and radiative processes involved. Coupling detailed chemical mechanisms to flow solvers is computationally expensive and often limits their application to 1D simulations. We develop an efficient Lagrangian diffusive reactor moving along the streamlines of a steady baseline flow simulation to compute detailed thermochemical effects. In addition to its efficiency, the method allows us to model both continuum and rarefied flows, while including mass and energy diffusion. The Lagrangian solver is assessed for several testcases including strong normal shockwaves, as well as 2D and axisymmetric blunt-body hypersonic rarefied flows. In all the testcases performed, the Lagrangian reactor improves drastically the baseline simulations. The computational cost of a Lagrangian recomputation is typically orders of magnitude smaller with respect to a full solution of the problem. The solver has the additional benefit of being immune from statistical noise, which strongly affects the accuracy of calculations obtained by means of the Direct Simulation Monte Carlo method, especially considering minor species in the mixture. The results demonstrate that the method enables applying detailed mechanisms to multidimensional solvers to study thermochemical nonequilibrium flows.

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.

Effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider under different angles of attack

In order to research the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider, thermochemical non-equilibrium flow and perfect gas model are employed to study the aerodynamics of an osculating-cone waverider under different angles of attack. The obtained results show that the slope of the oblique shock wave has little difference when considering the thermochemical non-equilibrium effect under the condition of zero angle of attack. However, under the condition of other attack angles, the slope of the oblique shock wave diminishes when considering the thermochemical non-equilibrium effect. Furthermore, the non-equilibrium effect moves the pressure center of the osculating-cone waverider forward by as much as 1.53% of the whole craft's length, which must be taken into consideration in the balance design of aircraft.

Thermal protection performance of magnetohydrodynamic heat shield system based on multipolar magnetic field

In order to cover the shortage of dipole magnetic field in the magnetohydrodynamic(MHD) heat shield system, physical model of a multipolar magnetic field with central and peripheral solenoids is constructed. By employing the governing equations of three dimensional thermochemical nonequilibrium flow with electromagnetic source terms based on the low magneto-Reynolds assumption, the flow control performance of the dipole and multipolar magnetic fields are numerically simulated. To make the results comparable, two groups of cases are designed by first assuming equal stagnation magnetic induction strength and secondly assuming equal ampere-turns. Results show that, the five-magnet system, whose central polar orientation is the same with the peripheral ones, have stronger work capability and better shock control and thermal protection performance. Moreover, the five-solenoid systems are the best when the ampere-turns of the central solenoid are twice and fourth of the peripheral ones under those two circumstances respectively. Compared with the dipole magnetic field, the stagnation non-catalytic heat fluxes are decreased by a factor of 47.5% and 34.0% respectively.

Numerical solution procedure for Hall electric field of the hypersonic magnetohydrodynamic heat shield system

Magnetohydrodynamic (MHD) heat shield system is a novel-concept thermal protection technique for hypersonic vehicles, which has been proved by lots of researchers with both numerical and experimental methods. Most of researchers neglect the Hall effect in their researches. However, in the hypersonic reentry process, the Hall effect is sometimes so significant that the electric current distribution in the shock layer can be changed by the induced electric field. Consequently, the Lorentz force as well as the Joule heat is varied, and thus the efficiency of the MHD heat shield system is affected.In order to analyze the influence of Hall effect, the induced electric field must be taken into consideration. According to the weakly-ionized characteristics of hypersonic flow post bow shock, the magneto-Reynolds number is assumed to be small. Therefore, the Maxwell equations are simplified with the generalized Ohm's law, and the induced electric field is governed by the potential Possion equation. Numerical methods are hence established to solve the Hall electric field equations in the thermochemical nonequilibrium flow field. The electric potential Poisson equation is of significant rigidity and difficult to solve for two reasons. One is that the coefficient matrix may not be diagonally dominant when the Hall parameter is large in the shock layer, and the other is that this matrix including the electric conductivity is discontinuous across the shock. In this paper, a virtual stepping factor is included to strengthen the diagonal dominance and improve the computational stability. Moreover, approximate factor and alternating direction implicit method are employed for further improving the stability. With these methods, a FORTRAN code is written and validated by comparing the numerical results with the analytical ones as well as results available from previous references. After that, relation between the convergence property and the virtual stepping factor is revealed by theoretical analysis and numerical simulations. Based on these work, a local variable stepping factor method is proposed to accelerate the iterating process. Results show that the convergence property is closely related to the mesh density and Hall parameter, and there exists a best stepping factor for a particular mesh as well as a particular Hall parameter. Since the best stepping factor varies a lot for different meshes and different Hall parameter, its appropriate value is hard to choose. The best value of stepping factor coefficient still exists in the local step factor method, but its value range is relatively smaller. More importantly, the local stepping factor method yields better convergence property than the regular constant one when employing a locally refined mesh.

Investigation of Hall effect on the performance of magnetohydrodynamic heat shield system based on variable uniform Hall parameter model

There has been a resurgence in the field of magnetohydrodynamic (MHD) flow control in the past 20 years. An increasing demand for sustained hypersonic flight and rapid access to space, along with numerous mechanical and material advances in flight-weight MHD technologies, has aroused renewed interest in this subject area. As a novel application of MHD flow control in the thermal protection field, MHD heat shield system has been proved to be of great intrinsic value by lots of researchers in recent years. Although its theoretical feasibility has been validated, there are many problems that remain to be further investigated. Among those problems, the Hall effect is a remarkable one that may affect the effectiveness of MHD flow control. Considering the fact that it is not sufficient to evaluate the Hall effect by merely using the chemical reaction model implemented in the nonequilibrium flow simulation to calculate the Hall parameter, a parametric study is conducted under the assumption of simplified uniform Hall parameter. First, coupling numerical methods are constructed and validated to solve the thermochemical nonequilibrium flow field and the electro-magnetic field. Second, a series of numerical simulations of the MHD head shield system is conducted with different magnitudes of Hall parameter under two magnetic induction intensities (B0=0.2 T, 0.5 T). Finally, the influence of Hall effect on the performance of MHD heat shield system is analyzed. Results indicate that Hall effect is closely related to the wall conductivity. If the vehicle surface is regarded as an insulating wall, the heat flux variation is co-determined by varying the Lorentz forces within the boundary layer and the shock-control effect. Compared with the one neglecting the Hall effect, the heat flux with Hall effect is slightly mitigated as the increase of Lorentz forces in the boundary layer dominates when the stagnation magnetic induction intensity B0 equals 0.2 T. However, the heat flux is increased when B0 equals 0.5 T, because the decrease of shock stand-off distance dominates which increases the gas temperature outside the boundary layer. Moreover, in this case the larger the Hall parameter, the higher the heat flux will be. As for the conductive wall, the performance of MHD heat shield system becomes worse with the increase of Hall parameter, and while it is equal to or higher than 5.0, this system loses its effectiveness.

Numerical analysis of Hall effect on the performance of magnetohydrodynamic heat shield system based on nonequilibrium Hall parameter model

Magnetohydrodynamic (MHD) heat shield system, a novel thermal protection technique in the hypersonic field, has been paid much attention in recent years. In the real flight condition, not only the Lorentz force but also the Hall electric field is induced by the interaction between ionized air post shock and magnetic field. In order to analyze the action mechanisms of the Hall effect, numerical methods of coupling thermochemical nonequilibrium flow field with externally applied magnetic field as well as the induced electric field are constructed and validated. Based on the nonequilibrium model of Hall parameter, numerical simulations of the MHD heat shield system is conducted under two different magnetic induction strengths (B0=0.2T, 0.5T) on a reentry capsule forebody. Results show that, the Hall effect is the same under the two magnetic induction strengths when the wall is assumed to be conductive. For this case, with the Hall effect taken into account, the Lorentz force counter stream diminishes a lot and the circumferential component dominates, resulting that the heat flux and shock-off distance approach the case without MHD control. However, for the insulating wall, the Hall effect acts in different ways under these two magnetic induction strengths. For this case, with the Hall effect taken into account, the performance of MHD heat shield system approaches the case neglecting the Hall effect when B0 equals 0.2T. Such performance becomes worse when B0 equals 0.5T and the aerothermal environment on the capsule shoulder is even worse than the case without MHD control.

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.