Viscous-shock-layer analysis of hypersonic flows over long slender vehicles

An efficient and accurate method for solving the viscous shock layer equations for hypersonic flows over long slender bodies is presented. The two first order equations, continuity and normal momentum, are solved simultaneously as a coupled set. The flow conditions included are from high Reynolds numbers at low altitudes to low Reynolds numbers at high altitudes. For high Reynolds number flows, both chemical nonequilibrium and perfect gas cases are analyzed with surface catalytic effects and different turbulence models, respectively. At low Reynolds number flow conditions, corrected slip models are implemented with perfect gas case. Detailed comparisons are included with other predictions and experimental data

A review of reaction rates and thermodynamic and transport properties for the 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K

Reaction rate coefficients and thermodynamic and transport properties are provided for the 11-species air model which can be used for analyzing flows in chemical and thermal nonequilibrium. Such flows will likely occur around currently planned and future hypersonic vehicles. Guidelines for determining the state of the surrounding environment are provided. Approximate and more exact formulas are provided for computing the properties of partially ionized air mixtures in such environments

Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium

The conservation equations for simulating hypersonic flows in thermal and chemical nonequilibrium and details of the associated physical models are presented. These details include the curve fits used for defining thermodynamic properties of the 11 species air model, curve fits for collision cross sections, expressions for transport properties, the chemical kinetics models, and the vibrational and electronic energy relaxation models. The expressions are formulated in the context of either a two or three temperature model. Greater emphasis is placed on the two temperature model in which it is assumed that the translational and rotational energy models are in equilibrium at the translational temperature, T, and the vibrational, electronic, and electron translational energy modes are in equilibrium at the vibrational temperature, T sub v. The eigenvalues and eigenvectors associated with the Jacobian of the flux vector are also presented in order to accommodate the upwind based numerical solutions of the complete equation set

Computer codes for the evaluation of thermodynamic and transport properties for equilibrium air to 30000 K

The computer codes developed here provide self-consistent thermodynamic and transport properties for equilibrium air for temperatures from 500 to 30000 K over a temperature range of 10 (exp -4) to 10 (exp -2) atm. These properties are computed through the use of temperature dependent curve fits for discrete values of pressure. Interpolation is employed for intermediate values of pressure. The curve fits are based on mixture values calculated from an 11-species air model. Individual species properties used in the mixture relations are obtained from a recent study by the present authors. A review and discussion of the sources and accuracy of the curve fitted data used herein are given in NASA RP 1260

Stagnation-point heat-transfer rate predictions at aeroassist flight conditions

The results are presented for the stagnation-point heat-transfer rates used in the design process of the Aeroassist Flight Experiment (AFE) vehicle over its entire aeropass trajectory. The prediction methods used in this investigation demonstrate the application of computational fluid dynamics (CFD) techniques to a wide range of flight conditions and their usefulness in a design process. The heating rates were computed by a viscous-shock-layer (VSL) code at the lower altitudes and by a Navier-Stokes (N-S) code for the higher altitude cases. For both methods, finite-rate chemically reacting gas was considered, and a temperature-dependent wall-catalysis model was used. The wall temperature for each case was assumed to be radiative equilibrium temperature, based on total heating. The radiative heating was estimated by using a correlation equation. Wall slip was included in the N-S calculation method, and this method implicitly accounts for shock slip. The N-S/VSL combination of projection methods was established by comparison with the published benchmark flow-field code LAURA results at lower altitudes, and the direct simulation Monte Carlo results at higher altitude cases. To obtain the design heating rate over the entire forward face of the vehicle, a boundary-layer method (BLIMP code) that employs reacting chemistry and surface catalysis was used. The ratio of the VSL or N-S method prediction to that obtained from the boundary-layer method code at the stagnation point is used to define an adjustment factor, which accounts for the errors involved in using the boundary-layer method

Computer codes for the evaluation of thermodynamic properties, transport properties, and equilibrium constants of an 11-species air model

The computer codes developed provide data to 30000 K for the thermodynamic and transport properties of individual species and reaction rates for the prominent reactions occurring in an 11-species nonequilibrium air model. These properties and the reaction-rate data are computed through the use of curve-fit relations which are functions of temperature (and number density for the equilibrium constant). The curve fits were made using the most accurate data believed available. A detailed review and discussion of the sources and accuracy of the curve-fitted data used herein are given in NASA RP 1232

Surface-slip equations for multicomponent, nonequilibrium air flow

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip

A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K

Reaction rate coefficients and thermodynamic and transport properties are reviewed and supplemented for the 11-species air model which can be used for analyzing flows in chemical and thermal nonequilibrium up to temperatures of 3000 K. Such flows will likely occur around currently planned and future hypersonic vehicles. Guidelines for determining the state of the surrounding environment are provided. Curve fits are given for the various species properties for their efficient computation in flowfield codes. Approximate and more exact formulas are provided for computing the properties of partially ionized air mixtures in a high energy environment. Limitations of the approximate mixing laws are discussed for a mixture of ionized species. An electron number-density correction for the transport properties of the charged species is obtained. This correction has been generally ignored in the literature

DSMC simulations of OREX entry conditions

Results of direct simulation Monte Carlo (DSMC) solutions are presented for the Japanese Orbital Reentry Experiment (OREX) vehicle, a 50 deg half-angle spherically blunted cone with a nose radius of 1.35 m and a base diameter of 3.4 m. The flow conditions simulated are those for entry into the Earth's atmosphere at a nominal velocity of about 7.4 km/s and zero incidence. Calculations are made for the higher altitude portion of entry, encompassing the transitional flow regime (altitudes of 200 to 80 km). Comparisons with flight measured values are made for axial acceleration, surface pressure, and stagnation point heating

Assessment of thermochemical nonequilibrium and slip effects for Orbital Reentry Experiment (OREX)

Results are provided from a viscous shock layer (VSL) analysis of the reentry flowfield around the forebody of the Japanese Orbital Reentry Experiment (OREX) vehicle. This vehicle is a 50 deg. spherically blunted cone with a nose radius of 1.35 m and a base diameter of 3.4 m. Calculations are done for the OREX trajectory from 105 to 48.4 km altitude range. A 7-species chemical model is found adequate for the flowfield analysis. However, for altitudes greater than 84 km, the low density effects (such as thermal nonequilibrium and slip) are to be implemented for good agreement between the predictions and flight inferred heat-transfer rate data. Further, at altitudes lower than 84 km, a finite surface recombination probability is to be employed in place of a non-catalytic surface for better comparison between the calculations and data. VSL results are also compared with the direct simulation Monte Carlo (DSMC) predictions at high altitudes (greater than 80 km) and the electron number density data for three altitudes in the OREX trajectory. Overall, there is a good comparison between the flight data and calculated results. With the ongoing refinements in data extraction procedures, the OREX data should prove valuable for validating theoretical models employed in flowfield codes for calculation of reacting-gas flowfields