Thermochemical Nonequilibrium Research Articles

Impact of Vibrational Nonequilibrium on the Supersonic Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic boundary layers has recently been shown to achieve a larger peak growth rate than the traditional second mode in particular circumstances relevant to free flight. In this environment, high levels of aerodynamic heating are encountered such that incorporation of chemical and vibrational nonequilibrium effects can become critical. The impact of thermal nonequilibrium (TNE) on the supersonic mode in particular has not been thoroughly and systematically investigated. This work uses thermochemical nonequilibrium (TCNE) direct numerical simulation (DNS) and TCNE linear stability theory (LST) to obtain a more complete investigation of the supersonic mode using both nonequilibrium and frozen gas models. The simulation is Mach 5 flow over a 1-mm-nose-radius axisymmetric cone 1 m in length, representative of experimental conditions in ground test facilities. Both LST and DNS results indicate that TNE effects are destabilizing compared with frozen flow and can lead to an -factor difference of approximately at the end of the cone. LST results also indicate that TNE effects are stabilizing to the second and supersonic modes in comparison with thermal equilibrium. The supersonic mode appeared to be slightly more affected by TNE than the second mode. Collectively, the findings in this work suggest that even in ground test facilities where TCNE effects are relatively small compared with free flight, incorporating nonequilibrium models in both the mean flow and stability solvers can have a practical effect on hypersonic boundary-layer transition prediction analyses.

Thermochemical nonequilibrium modeling of oxygen in hypersonic air flows

The thermochemical nonequilibrium model for oxygen, O2, in collisions with atmospheric gas species, is modified in the present work. The vibrational relaxation time with high temperature corrections, dissociation reaction rates, equilibrium constants for the reverse reactions, the vibrational energy loss ratio due to chemical reaction, and the collision integrals for nonequilibrium transport properties are proposed to describe the thermochemical nonequilibrium of O2. The proposed set of thermochemical nonequilibrium parameters for O2 successfully reproduces existing shock-tube experimental data and the flight and ground experimental data of the ELECTRE vehicle, orbital reentry experiments (OREX) flight modules, and double-cone geometry in the LENS-XX facility. In post-shock and hypersonic flow calculations, it is found that the vibrational relaxation and coupled chemical reactions calculated using the present parameters occur more slowly than using the previous parameters. The delayed nonequilibrium chemical reactions contribute to the extension of the shock stand-off distance, and drastically change the reverse reaction near the wall of the hypersonic vehicle.

Measurement of Radiative Nonequilibrium for Air Shocks Between 7 and

This paper describes a characterization of thermochemical nonequilibrium radiance for shock speeds between 7 and in the NASA Ames Electric Arc Shock Tube. Data are spectrally resolved from 190 to 1450 nm and spatially resolved behind the shock front on the order of 10 cm. The data are analyzed in terms of a spectral nonequilibrium metric, defined as the average radiance within of the peak radiance and presented in a format that may be used to test predictive nonequilibrium radiation tools. The data collected in two shock tubes of differing diameter (10 and 60 cm) at the same nominal shock condition agree within 30%. The spectra are compared with simulations using the DPLR/NEQAIR software tools using a combination of different modeling options (reaction rates, energy mode accounting, and electron impact excitation rates). The results show mixed agreement, with no one modeling option being a clear preference. This suggests that the data may be used to help to identify improvements to methodologies for modeling nonequilibrium air radiation.

Computation of High-Speed Plasma Flows in the Conditions of Thermochemical Non-Equilibrium

A numerical method is proposed for computing an ionized high-speed flow in the conditions of thermal and chemical nonequilibrium, taking into account the interaction of a moving electrically conductive continuous medium with an electromagnetic field. These flows are described by a fully coupled system of equations, which includes the equations of continuity, momentum, total energy, rotational energy, vibrational energy, electron energy, and mass conservation of chemical components. Electrical conductivity is determined using the kinetic theory. A special explicit-implicit scheme with alternation in half steps in time was proposed for numerical solution of rigid equations of chemical components and energy modes. That made it possible to solve a completely coupled system of equations with a large number of components and modes quickly and effectively. The developed method was used for numerical simulation of the physic process of interaction of a magnetic field with an ionized flow. The results of computations preformed by the proposed method are in satisfactory agreement with experimental data and computation results of other authors.

Infrared Optical Observability of an Earth Entry
 Orbital Test Vehicle Using Ground‐Based
 Remote Sensors

Optical design parameters for a ground-based infrared sensor rely strongly on the target’s optical radiation properties. Infrared (IR) optical observability and imaging simulations of an Earth entry vehicle were evaluated using a comprehensive numerical model. Based on a ground-based IR detection system, this model considered many physical mechanisms including thermochemical nonequilibrium reacting flow, radiative properties, optical propagation, detection range, atmospheric transmittance, and imaging processes. An orbital test vehicle (OTV) was selected as the research object for analysis of its observability using a ground-based infrared system. IR radiance contours, maximum detecting range (MDR), and thermal infrared (TIR) pixel arrangement were modeled. The results show that the distribution of IR radiance is strongly dependent on the angle of observation and the spectral band. Several special phenomena, including a strong receiving region (SRR), a characteristic attitude, a blind zone, and an equivalent zone, are all found in the varying altitude MDR distributions of mid-wavelength infrared (MWIR) and long-wavelength infrared (LWIR) irradiances. In addition, the possible increase in detectivity can greatly improve the MDR at high altitudes, especially for the backward and forward views. The difference in the peak radiance of the LWIR images is within one order of magnitude, but the difference in that of the MWIR images varies greatly. Analyses and results indicate that this model can provide guidance in the design of remote ground-based detection systems.

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.

Hypersonic aerodynamics of a deformed aeroshell in continuum and near-continuum regimes

The flexible inflatable aeroshell naturally deforms under aerodynamic loads during atmospheric entry. In this paper, we investigate the hypersonic aerodynamics of an inflatable aeroshell forebody with undulated surface deformation in the continuum and near-continuum flow regimes, where flow physics is complex involving rarefaction and thermochemical nonequilibrium effect. The aeroshell forebody shape is originated from a model of 8.3 m diameter stacked-tori hypersonic inflatable aerodynamic decelerator, and a series of surface deflections is generated by a parametric method based on the consistency of undulation with underlying structure. The trajectory points of 90, 80, and 68 km altitudes in a low Earth orbit reentry are considered. The thermochemical nonequilibrium Navier-Stokes equations with slip and no-slip boundary conditions are numerically solved to characterize flowfields and provide aerodynamic predictions. The results demonstrate that the undulated surface deflection induces local fluctuations of pressure and local Knudsen number, while the local variations of aerodynamic quantities create minor difference in total drag. The surface friction and drag are dependent on boundary conditions, i.e., either slip or no-slip model. The results also indicate that it is required to employ slip boundary conditions for the accurate prediction of friction and drag in the near continuum regime.

Assessment of Hypersonic Flow Physics on Aero-Optics

In a hypersonic environment, the high kinetic energy of the oncoming flow causes the molecules in the flow to be thermally excited, leading to dissociation. In such a flow field, an aero-optical analysis that considers thermochemical nonequilibrium may be necessary to assist in sensor design. The present study assesses the optical properties of a nonequilibrium, real gas flow field around a hemisphere cylinder. The simulations are conducted at freestream Mach numbers of 11, 13, and 15. The optical distortions are quantified using optical path length and optical path difference. Optical distortion is also predicted using a perfect gas assumption, and these distortions are provided for comparison. The primary contributions of nonequilibrium parameters on optical distortion are identified. For all Mach numbers, optical path lengths are higher when the effects of dissociation and vibrational relaxation are included. The computational results show that oxygen dissociation is the dominant nonequilibrium flow phenomena affecting the optical distortion. However, as the freestream Mach number increases, atomic nitrogen begins to have an additional influence on optical aberrations.

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.

Numerical investigation of hypervelocity shock-wave/boundary-layer interactions over a double-wedge configuration

Hypervelocity flows of nitrogen and air over a 30–55° double-wedge configuration are numerically investigated under the condition corresponding to recent experiments conducted with total enthalpy of 8.0 MJ/kg. Time-accurate two-dimensional and three-dimensional simulations are performed to resolve the unsteady shock interaction process. For the nitrogen flow, it is found that the three-dimensional simulation predicts a much smaller separation bubble and reduced surface heat flux and pressure peaks. Good agreement can be observed with the experiments in terms of the shock location, the flow structure, and the time-averaged surface heat flux when the three-dimensional effects are considered. For the air flow, the shock interaction mechanisms are similar to those in nitrogen. The real-gas effects tend to decrease the separation bubble and reduce the standoff distance of the detached shock induced by the second wedge, leading to a lower surface heat flux peak compared with the nitrogen result. However, the trend of the experimental heat flux data shows the opposite. To explain the discrepancies, effects of thermochemical nonequilibrium models are investigated. The results indicate that the air flow under the current condition is insensitive to air chemistry and vibration–dissociation coupling models. Suggestions for further study are presented.

Roughness-Induced Crossflow-Type Instabilities in a Hypersonic Capsule Boundary Layer Including Nonequilibrium

The current study investigates the unsteady disturbance development in a three-dimensional, high-enthalpy boundary layer on a capsule-like hemispherical geometry with pseudo-random distributed roughness. Direct Numerical Simulations are conducted for a typical reentry scenario at where chemical dissociation takes place. Unsteady disturbances at various frequencies are introduced into the flow to analyze the instabilities developing in the wake of the roughness patch. The amplification of small disturbances is shown for various chemical models (i.e., chemical equilibrium, chemical nonequilibrium, and thermochemical nonequilibrium). The largest disturbance amplification is observed for a crossflow-type vortex developing in the wake of the highest skewed protuberance of the roughness patch. The modes of instability of this crossflow-type vortex are analyzed and compared for different frequencies. The influence of the different nonequilibrium effects on the steady base flow as well as on the disturbance development is quantified and compared. The study highlights the necessity to include nonequilibrium effects in transitional scenarios as the unsteady development of the instabilities are affected strongly by the chemical modeling.

Numerical simulation of a CO2, CO, O2, O, C mixture: Validation through comparisons with results obtained in a ground-based facility and thermochemical effects

Various issues of numerical simulation of high-enthalpy non-equilibrium flows of a gas mixture of CO2, CO, O2, O, and C are discussed. Navier–Stokes equations are considered within the framework of one-, two-, and three-temperature approximations with allowance for chemical reactions. In the one-temperature approximation, chemical reactions are modelled by the Arrhenius law. In the multi-temperature approximations, simulations are performed with the use of the Treanor–Marrone model for carbon dioxide dissociation and the Park model for dissociation of diatomic gas molecules, which take into account vibrational non-equilibrium of molecules. The Arrhenius law is also used for calculating recombination reactions and also forward and backward exchange reactions. Translational-vibrational and vibrational-vibrational energy exchange is simulated by a simplified Landau–Teller model. Some examples of flows with the use of the above-mentioned approximations are calculated. It is demonstrated that the one-temperature approach ensures an adequate reproduction of experimental data on the shock standoff distance, heat flux, and pressure coefficient on the cone, which are obtained in a high-enthalpy wind tunnel. The calculation of the flow around a cylinder under Martian re-entry conditions reveals a significant effect of thermochemical non-equilibrium.

Three-Temperature Thermochemical Nonequilibrium Model with Application to Slender-Body Wakes

Hypersonic fluid dynamic simulations commonly model thermochemical nonequilibrium processes with the two-temperature model, which consists of a translational–rotational and vibrational–electronic–electron temperature. However, constricting the free-electron energy, by grouping it with the vibrational, the two-temperature model does not model certain nonequilibrium phenomena, which decreases the fidelity of the solution. A three-temperature model, consisting of a translational–rotational, vibrational, and electron–electronic temperature, increases the degrees of freedom of the simulation, permitting the electron temperature to be independent, and thus captures more nonequilibrium physics than the two-temperature model. Such a three-temperature model was implemented within a computational-fluid-dynamics framework for the simulation of hypersonic flows, with particular attention paid to wake flowfields. Validation was completed against the RAM C-II flight test data, and an assessment of the three-temperature model’s performance within the wake was completed. Finally, a study characterizing the wake behind a generic, slender cone geometry was completed, in which the nonequilibrium processes were shown to extend a significant distance into the wake.

Thermochemical Nonequilibrium Processes in Weakly Ionized Air Using Three-Temperature Models

Two three-temperature thermochemical nonequilibrium models were used to simulate the relaxation processes in weakly ionized air in compression and expansion regions. The three energy equations were the total energy, vibrational energy, and electron energy. The partition of electronic energy was investigated by considering it to be in equilibrium with the vibrational energy (free-electron model) or electron energy (electron–electronic model). Several zero-dimensional simulations were completed that demonstrated the potential of a three-temperature model to capture additional physics of the nonequilibrium processes above that of the legacy two-temperature model. The electron–electronic model consistently predicted, as expected, the electron temperature to be the last to equilibrate and for there to be significant electron nonequilibrium in all cases considered. However, the utility of the free-electron model to increase the fidelity of a simulation above that predicted by the two-temperature model was shown to be limited. Additionally, two vibrational–electron energy exchange relaxation times for the molecule were investigated; the resulting nonequilibrium processes were relatively insensitive to the use of a particular model.

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.

Numerical Analysis of an Actively Cooled Low-Reynolds-Number Hypersonic Diffuser

This paper presents a comprehensive numerical study of a low-Reynolds-number hypersonic diffuser designed for a 1.6 MW Arc-Heated Wind Tunnel facility. The numerical study includes the detailed computational fluid dynamics (CFD) investigation of the high-temperature, viscous, chemically reacting nonequilibrium hypersonic flowfield inside the diffuser with Reynolds-averaged Navier–Stokes simulations at a number of diffuser exit pressure conditions. The CFD analysis is used to evaluate the overall performance of the configuration at selected operating conditions and to provide wall heat flux values for the numerical analysis and design of an active cooling system for the thermal management of the diffuser. The CFD results are obtained with noncatalytic and fully catalytic wall assumptions to bound the estimated heat flux to the diffuser walls. The effects of surface catalyticity and thermochemical nonequilibrium on the flowfield are discussed, with the emphasis on diffuser and active cooling system design. A detailed numerical analysis focusing on active cooling of the diffuser is presented. The results of the CFD and thermal analyses presented in this paper are expected to be a valuable addition to the very limited literature on low-Reynolds-number hypersonic diffuser design.