Nonequilibrium Hypersonic Flows Research Articles

Effect of Nonlocal Vacuum Ultraviolet Radiation on a Hypersonic Nonequilibrium Flow

Effect of Nonlocal Vacuum Ultraviolet Radiation on a Hypersonic Nonequilibrium Flow

Effect of Nonlocal Vacuum Ultraviolet Radiation on a Hypersonic Nonequilibrium Flow

during the excitation process of the same radiating gas species. This interaction affects the distribution of electronic state populations and, in turn, the radiative transport. The radiative transition rate in the excitation/deexcitation processes and the radiative transport equation must be coupled to account for nonlocal effects. A quasi-steady-state model is presented to predict the electronic state populations of radiating gas species taking into account nonlocal radiation. The definition of the escape factor that is dependent on the incoming radiative intensity from over all directions is presented. To perform accurate and efficient analyses of radiation from a chemically reacting flowfield, thedirect simulation MonteCarloandthefully three-dimensional photonMonteCarloradiative transportmethods are used. The effect of the escape factor on the distribution of electronic state populations of the atomic N and O radiating species is examined in a highly nonequilibrium flow condition, and the corresponding change of the radiative heat flux due to the nonlocal radiation is also investigated. It is found that inclusion of the escape factor increasestheupperelectronicstatepopulationsbyaboutafactorof2withasimilarincreaseintheradiativeheat flux to the vehicle surface.

Multiscale Part-Spectrum k-Distribution Database for Atomic Radiation in Hypersonic Nonequilibrium Flows

An accurate and compact part-spectrum k-distribution database has been developed for the two most important radiating species N and O encountered in hypersonic nonequilibrium flows. The database allows users to calculate the desired full-spectrum k-distributions through look-up and interpolation, providing an efficient means to perform radiative transfer calculations. A detailed methodology of the k-distribution data generation is presented. An optimized Gauss quadrature scheme is implemented for reducing the size of the database. The accuracy of the database is determined by comparing part-spectrum emissivities with those obtained from line-by-line calculations. The application of the database to construct full-spectrum k-distributions at arbitrary gas states is discussed. Heat transfer results for the stagnation line of the Stardust vehicle are discussed and CPU-time studies are presented, demonstrating the accuracy and efficiency of the k-distribution database.

High-order shock-fitting methods for direct numerical simulation of hypersonic flow with chemical and thermal nonequilibrium

In recent years, much progress has been made in the direct numerical simulation of laminar-turbulent transition of hypersonic boundary layer flow. However, most of the efforts at the direct numerical simulation of transition previously have been focused on the idealized perfect gas flow or “cold” hypersonic flows. For practical problems in hypersonic flows, high-temperature effects of thermal and chemical nonequilibrium are important and cannot be modeled by a perfect gas model. Therefore, it is necessary to include the real gas models in the numerical simulation of hypersonic boundary layer transition in order to accurately predict flow field parameters. Currently most numerical methods for hypersonic flow with thermo-chemical nonequilibrium are based on shock-capturing approach at relatively low order of accuracy. Shock capturing schemes reduce to first-order accuracy near the shock and have been shown to produce spurious oscillations behind curved strong shocks. There is a need to develop new methods capable of simulating nonequilibrium hypersonic flow fields with uniformly high-order accuracy and avoid spurious oscillations near the shock. This paper presents a fifth-order shock-fitting method for numerical simulation of thermal and chemical nonequilibrium in hypersonic flows. The method is developed based on the state-of-the-art real gas models for thermo-chemical nonequilibrium and transport phenomena. Shock-fitting approach is used because it has the advantage of capturing the entire flow field with high-order accuracy and without any oscillations near the shock. The new method has been tested and validated for a number of test cases over a wide span of free stream conditions. The developed method is applied for the study of receptivity of free stream acoustic waves over a blunt cone for hypervelocity flow. Some preliminary results of the computations of the high order shock fitting method for the above mentioned study have also been presented.

Simulating Stardust Earth Reentry with Radiation Heat Transfer

A multigroup spectral method is integrated into an interdisciplinary formulation for nonequilibrium radiative hypersonic flows. The developed simulation capability has been successfully applied to study the Stardust capsule Earth reentry via an axisymmetric approximation. The predicted total heat transfer rates at different stages of reentry achieve a reasonable agreement with results in literature. The computational results reveal a close correlation between the relaxation of vibrational excitations and diffusive heat transfer in the wake, as well as a diminished radiative intensity and a shifted emission spectrum in the shock layer toward the lower-frequency domain from the earlier to the later stages of the reentry.

Multi-scale k-distribution model for gas mixtures in hypersonic nonequilibrium flows

A k-distribution model is presented for gas mixtures in thermodynamic nonequilibrium, containing strongly radiating atomic species N and O together with molecular species of N 2, N 2 +, NO and O 2. In the VUV range of the spectrum there is strong absorption of atomic radiation by bands of N 2. For this spectral range, a multi-scale model is presented, where RTEs are solved separately for each emitting species and overlap with other species is treated in an approximate way. Methodology for splitting the gas mixture into scales and evaluation of the overlap parameter between different scales is presented. The accuracy of the new model is demonstrated by solving the radiative transfer equation along the stagnation line flow field of the Crew Exploration Vehicle (CEV).

Implicit methods for fluid dynamics

This paper represents the contributions to the development of implicit procedures for solving the equations of fluid dynamics made by Briley and McDonald (1975) [1], Beam and Warming (1976, 1978) [2,3] and Lombard et al. (1983) [4]. The contributions of Briley and McDonald and Beam and Warming are well known, but Lombard has not been fully recognized for his innovative contributions to flux vector splitting and use of the DDADI (Diagonally Dominate Alternating Direction Implicit) algorithm. Their contributions are presented herein. Fully implicit algorithms are applied to two complex flow problems of current interest, (1) hypersonic non-equilibrium flow about a blunt nosed body and (2) flow within an MFD (magneto-fluid dynamics) accelerator. These two applications would be exceeding costly without the use of fully implicit methods.

Nonequilibrium jet boundary layer in a polyatomic gas

The two-dimensional nonequilibrium hypersonic free jet boundary layer gas flow in the near wake of a body is studied using a closed system of macroscopic equations obtained (as a thin-layer version) from moment equations of kinetic origin for a polyatomic single-component gas with internal degrees of freedom. (This model is can be used to study flows with strong violations of equilibrium with respect to translational and internal degrees of freedom.) The solution of the problem under study (i.e., the kinetic model of a nonequilibrium homogeneous polyatomic gas flow in a free jet boundary layer) is shown to be related to the known solution of the well-studied simpler problem of a Navier-Stokes free jet boundary layer, and a method based on this relation is proposed for solving the former problem. It is established that the gas flow velocity distribution along the separating streamline in the kinetic problem of a free jet boundary layer coincides with the distribution obtained by solving the Navier-Stokes version of the problem. It is found that allowance for the nonequilibrium nature of the flow with respect to the internal and translational degrees of freedom of a single-component polyatomic gas in a hypersonic free jet boundary layer has no effect on the base pressure and the wake angle.

Advanced Radiation Calculations of Hypersonic Reentry Flows Using Efficient Databasing Schemes

Efficient schemes for databasing emission and absorption coefficients are developed to model radiation from hypersonic nonequilibrium flows. For bound-bound transitions, spectral information including the line-center wavelength and emission and absorption coefficients is stored for typical air plasma species. Since the flow is nonequilibrium, a rate equation approach including both collisional and radiatively induced transitions is used to calculate the electronic state populations, assuming quasi steady state. The general Voigt line-shape function is assumed for modeling the line-broadening. The accuracy and efficiency of the databasing scheme was examined by comparing results of the databasing scheme with those of NEQAIR for the Stardust flowfield. An accuracy of approximately 1 % was achieved with an efficiency about three times faster than the NEQAIR code.

Unstructured Cartesian Grid Methodology for Inviscid Nonequilibrium Hypersonic Flows

In this work, a solution-adaptive unstructured Cartesian grid solver for thermochemical nonequilibrium hypersonic flows with a two-temperature model is developed. The Cartesian grid methodology offers the convenience of automatic grid generation over three-dimensional complex geometries with minimum user intervention. At the same time, an accurate higher-order flux calculation over unstructured-grid topologies is provided. To avoid convergence problems in the explicit flow solver, a point-implicit method is adopted to discretize the source terms. The AUSMPW+ numerical scheme with MUSCL data reconstruction is used, preventing nonphysical oscillations and carbuncle phenomena. The accuracy of the present methodology was verified against DPLR (NASA Ames Research Center's structured-grid nonequilibrium flow solver), showing a good agreement between the two codes. As expected, the AUSMPW+ scheme effectively resolved the large gradients of the flow properties at the shock waves. In parallel, the point-implicit technique used for the source terms allows the original Courant-Friedrichs- Lewy constraints of the explicit solver to be maintained.

Arc-jet testing of ultra-high-temperature-ceramics

The article deals with arc-jet experiments on different ultra high temperature ceramics (UHTC) models in high enthalpy hypersonic non-equilibrium flow. Typical geometries of interest for nose tip or wing leading edges of hypersonic vehicles, as rounded wedge, hemisphere, and cone are considered. Temperature and spectral emissivity measurements have been performed using pyrometers, an IR thermocamera and thermocouples. The details of the experimental set-up, the test procedure and the measurement are discussed in the text. The UHTC materials have been tested for several minutes to temperatures up to 2050 K showing a good oxidation resistance in extreme conditions. Differences between the various model shapes have been analyzed and discussed. Numerical–experimental correlations have been carried out by a computational fluid-dynamic code. The numerical rebuilding also allowed to evaluate the catalytic efficiency and the emissivity of the materials at different temperature.

Spectral Module for Photon Monte Carlo Calculations in Hypersonic Nonequilibrium Radiation

In this paper, efficient spectral modules and random number databases are developed for atomic and diatomic species for use in photon Monte Carlo (PMC) modeling of hypersonic nonequilibrium flow radiation. To model nonequilibrium flow conditions, the quasisteady state assumption was used to generate electronic state populations of atomic and diatomic gas species in the databases. For atomic species (N and O), both bound-bound transitions and continuum radiation were included and were separately databased as a function of electron temperature and number density as well as the ratio of atomic ion to neutral number density. For the radiating diatomic species of N2+, N2, O2, and NO databases were generated for each electronic molecular electronic system. In each molecular electronic system, the rovibrational transition lines were separately databased for each electronic upper state population forming the electronic system. The spectral module for the PMC method was optimized toward computational efficiency for emission calculations, wavelength selections of photon bundles and absorption coefficient calculations in the ray tracing scheme.

Effects of Chemistry in Nonequilibrium Hypersonic Flow Around Blunt Bodies

In this paper, the influence of a chemical kinetic model in hypersonic flow past blunt bodies is examined. Slow and fast chemical kinetic models are investigated to identify the reliable model for applications with a wide range of Mach numbers. Solutions from the Gardiner reaction-rate set, the Moss reaction-rate set, the Park rate set of 1993, and the Dunn and Kang reaction rate are compared. High-temperature, equilibrium-constant curve fits proposed by Gupta are also examined. The new Hansen's formulation for the rate controlling temperature for the dissociation reaction is compared with Park's approach. Particular attention has been devoted to backward reaction rates, because the methods of calculation affect the flowfield structure. Sample hypersonic flowfields, typical of spacecraft reentry conditions in which reactions play an important role, are presented and compared with results from experiments and other computational fluid dynamics simulations. The differences are discussed and evaluated.

Numerical and theoretical study of the shock stand-off distance in non-equilibrium flows

A theoretical model based on a quasi-one-dimensional formulation is developed which allows determination of the shock stand-off distance at the stagnation point of blunt bodies in hypersonic non-equilibrium flows. Despite the simple ideal dissociating gas model implemented in the theoretical approach, it gives insight into the main physics governing the shock stand-off problem. More detailed and precise data are obtained by a numerical simulation where vibrational and chemical relaxation processes as well as their interactions are taken into account. The physical modelling of these processes is based on a kinetic approach and on a generalized Chapman–Enskog method of solving the Boltzmann equation. Explicit formulae for rate constants and vibrational energy consumption are derived and incorporated into the general conservation equations. Good agreement between theoretical, numerical and experimental results is achieved which ensures a reliable and mutual validation of the different methods.

Computation of non-equilibrium hypersonic flow with artificially upstream flux vector splitting (AUFS) schemes

The AUFS scheme has been presented for solving the Euler equations [Sun, M., Takayama, K., 2003. An artificially upstream flux vector splitting scheme for the Euler equations. Journal of Computational Physics, 189, 305–329]. An extension of this high resolution scheme-based on upwind numerical methods has been developed to calculate a two-dimensional hypersonic viscous flowfield in thermochemical non-equilibrium. The time-dependent Navier–Stokes governing equations are computed by using a multi-block finite volume technique on a structured mesh. The convective fluxes at the interfaces are evaluated using a flux vector splitting (FVS) method with a second-order reconstruction of the interface values and the viscous terms are discretised by second-order central differences. A better evaluation of aerodynamic parameters are obtained with this AUFS scheme and they are also compared to those obtained by previous works. The freestream flow conditions of these computations correspond to high-enthalpy flows with a Mach number range between 6.4 and 25.9. The obtained numerical results indicate that the AUFS scheme is accurate, robust, and efficient for the calculation of hypersonic flow.

Possible uses of optical methods for determining the structure of nonequilibrium hypersonic flows

Results are given of the investigation of self-luminosity of flow in hypersonic wind tunnels with electric-arc heaters, and the possibilities of using this luminosity for the visualization of flow past bodies are analyzed. It is demonstrated that the luminosity is caused by nonequilibrium physicochemical processes in nozzles and is defined by the excitation of low-potential electron-vibrational levels of molecules and atoms of impurities in the flow. It follows from comparison of flow patterns obtained by the shadow method with photographs of flow in the vicinity of bodies that the use of luminosity for determining the structure of flow past models is not always justified. Results are given of applying the method of induced resonance fluorescence for the visualization of flow past bodies.

A hybrid particle-continuum method applied to shock waves

A hybrid numerical scheme designed for hypersonic non-equilibrium flows is presented which solves the Navier–Stokes equations in regions of near-equilibrium and uses the direct simulation Monte Carlo method where the flow is in non-equilibrium. Detailed analysis of each stage of the hybrid cycle illustrates the difficulty in defining physically correct DSMC boundary conditions in regards to both macroscopic state and velocity distribution. However, results also show that DSMC boundary conditions have little effect on a previously initialized interior particle domain. A sub-relaxation technique capable of determining macroscopic, hydrodynamic properties in a DSMC simulation is used to determine low-scatter boundary conditions for the NS domain. Particle and continuum domains adapt during the hybrid simulation through application of a continuum breakdown parameter based on the gradient-length Knudsen number. The hybrid code reproduces experimental results and full DSMC simulations in half the time for a large range of 1D shock waves in argon and diatomic nitrogen gas.

Numerical prediction of nonequilibrium hypersonic flow around Brazilian satellite SARA

Hypersonic flows past Brazilian satellite SARA at zero angle of attack in chemical and thermal nonequilibrium are investigated using an axisymmetric Navier-Stokes solver. The numerical solutions were carried out for freestream conditions equivalent to a typically re-entry trajectory with a range of Mach numbers from 10 to 25. The gas was chemically composed by seven air species O;N;NO;O2, N2;NO+; e- with 24 steps chemical reactions scheme and thermically characterized by a multi-temperature model. Comparisons have been made between the present computation and the distribution of pressure coefficient and the heat transfer obtained recently with Direct Simulation Monte Carlo Method[1]. The study also points out the influence of nonequilibrium phenomena like ionization, vibrational and electronic excitation on aerothermodynamic flow parameters.

Preconditioned Newton-Method for Computing Supersonic and Hypersonic Nonequilibrium Flows

Preconditioned Krylov subspace methods and a Jacobi line relaxation method are tested in an implicit scheme to solve the three-dimensional Navier‐Stokes equations for nonequilibrium supersonic and hypersonic flows. Special attention has been paid to the development of vectorizable preconditioners. In the numerical scheme the Jacobian of the fluxes is computed using the first-order inviscid fluxes and a thin shear-layer approximation of the viscous fluxes. In the second part, the influence of these approximations of the Jacobian is examined. Starting from a matrix-free implicit method, the scheme is developed to an exact Newton method without approximations in the Jacobian.

Reactive and nonreactive vibrational energy exchanges in nonequilibrium hypersonic flows

The generalized depletion equations, considering state-to-state kinetics of dissociating nitrogen, were solved to predict the extent of vibrational depletion for 4000 and 6000 K. Two different vibrational transition rate sets were used in the depletion analysis. One was based on the Schwartz–Slawsky–Herzfeld (SSH) theory and the other based on the analytical methods of Capitelli, Billing, Fisher, Doroshenko and co-workers. Transition rates based on the SSH theory predicted a lower depletion due to very high rates in the upper levels. With the objective of delineating the vibration–vibration (V–V) exchanges and vibration–translation (V–T) transfers in nonreactive, vibrationally excited gas dynamic flows, the flowfield simulations of blunt body and expanding nozzles were performed. For vibrational cooling cases (where vibrational temperature is greater than translational temperature) of flow past blunt body and the nozzle flows, the population distribution showed the Treanor-like distribution only at low translational temperatures. This non-Boltzmann behavior and the corresponding low state densities establish the dominance of the V–T energy transfers and the relatively minor role of V–V exchanges for hypersonic gasdynamic flows.