High resolution schemes for hyperbolic conservation laws

Chemical-kinetic parameters governing the e ow in the shock layer over a heat shield of a blunt body entering Earth’ s atmosphere from a hyperbolic orbit are derived. By the use of the assumption that the heat shield is made of carbon phenolic and by allowing for an arbitrary rateof pyrolysis-gasinjection, chemical reactions occurring in the shock layer are postulated, and the collision integrals governing the transport properties, the rate coefe cients of the reactions, and the parameters needed for the bifurcation model and for the e nite-rate kinetic wall boundary conditions are determined using the best available techniques. Sample e owe eld calculations are performed using this set of parameters to show that the heating and surface removal rates are substantially smaller than calculated using theexisting setofsuch parameters and traditionalassumptionsof gas ‐surfaceequilibrium and quasi-steadystate ablation.

Chemical-Kinetic Parameters of Hyperbolic Earth Entry

Analytical modeling of thermal and mechanical response is a fundamental step in the design process for ultra-high-temperature ceramic components, such as nose tips and wing leading edges for hypersonic applications. The purpose of the analyses is to understand the response of test articles to high-enthalpy flows in ground tests and to predict component performance in particular flight environments. Performing these analyses and evaluating the results require comprehensive and accurate physical, thermal, and mechanical properties. In this paper, we explain the nature of the analyses, highlight the essential material properties that are required and why they are important, and describe the impact of property accuracy and uncertainty on the design process.

Material property requirements for analysis and design of UHTC components in hypersonic applications

Statistical simulation of reactive rarefied flows - Numerical approach and applications

The manner in which the Navier–Stokes equations of fluid mechanics break down under conditions of low‐density, hypersonic flow is investigated numerically. This is performed through careful and detailed comparisons of solutions obtained with continuum and Monte Carlo simulation techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. Both normal shock waves and bow shocks formed by flow over a sphere are considered for argon and nitrogen. It is found that a Knudsen number based on local flow conditions and gradients is a convenient and accurate criterion for indicating breakdown of the continuum flow equations. Failure of the Navier–Stokes equations in hypersonic transitional flows occurs both in the shock front and in the region immediately adjacent to the body surface.

Predicting failure of the continuum fluid equations in transitional hypersonic flows

The Gauss‐Seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers. The resulting data-parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases.Thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata-parallel relaxation methods, but it reaches a steady-state solution in much less time for all cases tested to date. In addition, the data-parallel line relaxation method shows good convergence properties even on the high-cell-aspect-ratio grids required to simulate high-Reynolds-number e ows. The new method is implemented using message passing on the Cray T3E, and the parallel performance of the method on this machine is discussed. The data-parallel line relaxation method combines the fast convergence of the Gauss ‐Seidel line relaxation method with a high parallel efe ciency and thus shows promise for large-scale simulation of viscous e ows.

Data-Parallel Line Relaxation Method for the Navier -Stokes Equations

Theoretical determinations of the thermal rate constants and product energy distributions of the N2+O→NO+N reaction, which plays a crucial role in hydrocarbon air combustion and high temperature air chemistry, are carried out using a quasiclassical trajectory method. An analytical fit of the lowest 3A′ potential energy surface of this reaction based on the CCI ab initio data is obtained. The trajectory study is done on this surface and an analytical 3A″ surface proposed by Gilibert et al. [J. Chem. Phys. 97, 5542 (1992)]. The thermal rate constants computed from 3000 to 20 000 K are in good agreement with the available experimental data. In addition, the dependence of the rate constant on the N2 internal state is studied. It is found that a low vibrational excitation can reduce the rate constant of this reaction by a factor of 3. Also, we investigate the effect of the N2 vibrational state on the product NO vibrational distribution, and it is found that at low N2 vibrational states, the NO vibrational dist...

Thermal rate constants of the N 2 +O→NO+N reaction using ab initio 3 A″ and 3 A' potential energy surfaces

A detailed quasiclassical trajectory study of the O2+N→NO+O reaction is performed based on ab initio potential-energy surfaces of the 2A′ and 4A′ states. The study is aimed at generating a database of thermally averaged and O2 state-specific rate constants needed for accurate simulations of NO kinetics in high-temperature flow processes. The rate constants obtained show good agreement with the available experimental data and with other quasiclassical trajectory calculations. It is found that the reactant internal energy of the O2+N→NO+O reaction is less effective in enhancing the rate than in the N2+O→NO+N reaction. An analysis of the product vibrational energy shows that NO formed by the O2+N→NO+O reaction has a non-Boltzmann distribution. It is also found that the most populated NO vibrational level is determined by the reactant vibrational energy, while the terminal slope of the NO vibrational distribution is a strong function of the reactant translational temperature.

Thermal rate constants of the O2+N→NO+O reaction based on the A2′ and A4′ potential-energy surfaces

A Monte Carlo uncertainty and sensitivity analysis technique is presented to i) identify the major sources of uncertainty in the thermochemical models used for aerothermal analysis, and ii) track the propagation of these uncertainties through the system into the predicted quantities of interest, such as the vehicle heating, shock layer properties, etc. The technique is applied to the aerothermal analysis of Titan aerocapture, where CN shock layer radiation is the dominant source of vehicle heating. Several hundred model input parameters, including reaction rate constants, vibration-chemistry coupling parameters, vibrational relaxation times, and transport properties, are independently sampled over their range of uncertainties, and the vehicle heating is determined probabilistically. A massively parallel, axisymmetric CFD (Data-Parallel Line Relaxation) code was used to make the several thousand runs needed to statistically describe the variability in the heating predictions. It is found that major contributions to the uncertainty in the predicted heating originates from the uncertainties in the rates of N2 dissociation by H atom impact, and some atomic exchange reactions: N2+H→NH+N and N2+C→CN+N.

Uncertainty and Sensitivity Analysis of Thermochemical Modeling for Titan Atmospheric Entry

Assessment of nonequilibrium thermochemical models for shock-layer radiation in N 2 /CH 4 mixtures is presented via comparisons with spectrally and temporally resolved intensity measurements from a set of shock tube experiments. The experiments were carried out at the Electric Arc Shock Tube facility at NASA Ames Research Center in a rarified environment [13.3-133.3 Pa (0.1 and 1 torr)] representative of the peak heating conditions of a Titan aerocapture trajectory (5-9 km/s). The baseline model that assumes a Boltzmann population of the CN excited states consistently overpredicts the shock-layer radiation intensity at lower pressure [13.3 Pa (0.1 torr)]. A nonlocal collisional radiative model that solves a simplified master equation and includes radiative transport and nonlocal absorption in the shock tube is presented. The proposed model improves the prediction of the nonequilibrium radiation overshoot peak, but still underpredicts the intensity decay rate in the low-pressure case. Further analysis suggests possible reasons for the remaining disagreement, the most likely being a slow CN consumption in the current chemical kinetics model in the intensity fall-off region.

Deepak Bose

Papers

Data-Parallel Line Relaxation Method for the Navier -Stokes Equations

Thermal rate constants of the N 2 +O→NO+N reaction using ab initio 3 A″ and 3 A' potential energy surfaces

Thermal rate constants of the O2+N→NO+O reaction based on the A2′ and A4′ potential-energy surfaces

Uncertainty and Sensitivity Analysis of Thermochemical Modeling for Titan Atmospheric Entry

Modeling and experimental assessment of CN radiation behind a strong shock wave