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NASA NTRS1977

Vorticity interaction effects on blunt bodies

Numerical solutions of the viscous shock layer equations governing laminar and turbulent flows of a perfect gas and radiating and nonradiating mixtures of perfect gases in chemical equilibrium are presented for hypersonic flow over spherically blunted cones and hyperboloids. Turbulent properties are described in terms of the classical mixing length. Results are compared with boundary layer and inviscid flowfield solutions; agreement with inviscid flowfield data is satisfactory. Agreement with boundary layer solutions is good except in regions of strong vorticity interaction; in these flow regions, the viscous shock layer solutions appear to be more satisfactory than the boundary layer solutions. Boundary conditions suitable for hypersonic viscous shock layers are devised for an advanced turbulence theory.

Anderson, E. C.↗

NASA NTRS1974

Experimental study of the shock-induced unsteady laminar boundary layer on a flat plate

The behavior of the unsteady laminar boundary layer induced by the incident shock wave passing over a flat plate mounted in a shock tube has been experimentally studied for shock speeds ranging from 2.35 to 7.34 km/sec by measuring unsteady heat transfer rates to the plate using thin-film heat-flux gages. Theoretical heat-transfer rates were predicted from analytical solutions in the literature which describe the unsteady flat plate boundary layer development for equilibrium real-gas flows. Experimental results obtained for both air and nitrogen were found to be in good agreement with the theoretical predictions.

Cook, W. J.↗

NASA NTRS2002

Aeroheating Environments for a Mars Smart Lander

A proposed Mars Smart Lander is designed to reach the surface via lifting-body atmospheric entry (alpha = 16 deg) to within 10 km of the target site. CFD (computational fluid dynamics) predictions of the forebody aeroheating environments are given for a direct entry from a 2005 launch. The solutions were obtained using an 8-species gas in thermal and chemical nonequilibrium with a radiative-equilibrium wall temperature boundary condition. Select wind tunnel data are presented from tests at NASA Langley Research Center. Turbulence effects are included to account for both smooth body transition and turbulence due to heatshield penetrations. Natural transition is based on a momentum-thickness Reynolds number value of 200. The effects of heatshield penetrations on turbulence are estimated from wind tunnel tests of various cavity sizes and locations. Both natural transition and heatshield penetrations are predicted to cause turbulence prior to the nominal trajectory peak heating time. Laminar and turbulent CFD predictions along the trajectory are used to estimate heat rates and loads. The predicted peak turbulent heat rate of 63 W/sq cm on the heatshield leeward flank is 70% higher than the laminar peak. The maximum integrated heat load for a fully turbulent heat pulse is 38% higher than the laminar load on the heatshield nose. The predicted aeroheating environments with uncertainty factors will be used to design a thermal protection system.

Edquist, Karl T.↗

NASA NTRS2005

Afterbody Heating Predictions for a Mars Science Laboratory Entry Vehicle

The Mars Science Laboratory mission intends to deliver a large rover to the Martian surface within 10 km of its target site. One candidate entry vehicle aeroshell consists of a 3.75-m diameter, 70-deg sphere-cone forebody and a biconic afterbody similar to that of Viking. This paper presents computational fluid dynamics predictions of laminar afterbody heating rates for this configuration and a 2010 arrival at Mars. Computational solutions at flight conditions used an 8-species Mars gas model in chemical and thermal non-equilibrium. A grid resolution study examined the effects of mesh spacing on afterbody heating rates and resulted in grids used for heating predictions on a reference entry trajectory. Afterbody heating rate reaches its maximum value near 0.6 W/sq cm on the first windward afterbody cone at the time of peak freestream dynamic pressure. Predicted afterbody heating rates generally are below 3% of the forebody laminar nose cap heating rate throughout the design trajectory. The heating rates integrated over time provide total heat load during entry, which drives thermal protection material thickness.

Edquist, Karl T.↗

NASA NTRS1989

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

Liou, May-Fun↗

NASA NTRS1972

Solution of non-isoenergetic supersonic flows by method of characteristics, volume 3

The calculation of supersonic flow fields by the method of characteristics. The theoretical approach to the solution of these flow fields and a computer program to implement the numerical solution of the flow equations are discussed. This versatile program has a flexible set of boundary conditions enabling the calculation of nozzles, plumes and many other complex flow fields. A complete derivation of the equations of motion for reacting gas systems is presented. An important consequence of this derivation is that, for the reaction assumptions which were made, the thermochemistry was shown to be uncoupled from the flow solution and as such could be solved separately. The methods of characteristics equations are shown to be formally the same for ideal, frozen, and equilibrium reacting gas mixtures.

Prozan, R. J.↗

NASA NTRS1992

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Shuen, J.-S.↗

NASA NTRS1984

Flowfield computation of an aerobrake orbital transfer vehicle

Viscous real gas and ideal gas supersonic flowfields over the forebody of a aeroassisted orbital transfer vehicle are determined using a unsteady factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are obtained for both real and ideal gases at a Mach number of 30 and at angles of attack up to 20 degrees. Shock stand-off distances and surface pressure distributions are presented for the gas models with and without viscous effects. For the freestream conditions considered, viscous effects dominate the flow.

Balakrishnan, A.↗

NASA NTRS1975

The NATA code; theory and analysis. Volume 2: User's manual

The NATA code is a computer program for calculating quasi-one-dimensional gas flow in axisymmetric nozzles and rectangular channels, primarily to describe conditions in electric archeated wind tunnels. The program provides solutions based on frozen chemistry, chemical equilibrium, and nonequilibrium flow with finite reaction rates. The shear and heat flux on the nozzle wall are calculated and boundary layer displacement effects on the inviscid flow are taken into account. The program contains compiled-in thermochemical, chemical kinetic and transport cross section data for high-temperature air, CO2-N2-Ar mixtures, helium, and argon. It calculates stagnation conditions on axisymmetric or two-dimensional models and conditions on the flat surface of a blunt wedge. Included in the report are: definitions of the inputs and outputs; precoded data on gas models, reactions, thermodynamic and transport properties of species, and nozzle geometries; explanations of diagnostic outputs and code abort conditions; test problems; and a user's manual for an auxiliary program (NOZFIT) used to set up analytical curvefits to nozzle profiles.

Bade, W. L.↗

NASA NTRS1977

Computational models for the analysis of three-dimensional internal and exhaust plume flowfields

This paper describes computational procedures developed for the analysis of three-dimensional supersonic ducted flows and multinozzle exhaust plume flowfields. The models/codes embodying these procedures cater to a broad spectrum of geometric situations via the use of multiple reference plane grid networks in several coordinate systems. Shock capturing techniques are employed to trace the propagation and interaction of multiple shock surfaces while the plume interface, separating the exhaust and external flows, and the plume external shock are discretely analyzed. The computational grid within the reference planes follows the trace of streamlines to facilitate the incorporation of finite-rate chemistry and viscous computational capabilities. Exhaust gas properties consist of combustion products in chemical equilibrium. The computational accuracy of the models/codes is assessed via comparisons with exact solutions, results of other codes and experimental data. Results are presented for the flows in two-dimensional convergent and divergent ducts, expansive and compressive corner flows, flow in a rectangular nozzle and the plume flowfields for exhausts issuing out of single and multiple rectangular nozzles.

Dash, S. M.↗

NASA NTRS1996

Progress Toward an Efficient and General CFD Tool for Propulsion Design/Analysis

The simulation of propulsive flows inherently involves chemical activity. Recent years have seen substantial strides made in the development of numerical schemes for reacting flowfields, in particular those involving finite-rate chemistry. However, finite-rate calculations are computationally intensive and require knowledge of the actual kinetics, which are not always known with sufficient accuracy. Alternatively, flow simulations based on the assumption of local chemical equilibrium are capable of obtaining physically reasonable results at far less computational cost. The present study summarizes the development of efficient numerical techniques for the simulation of flows in local chemical equilibrium, whereby a 'Black Box' chemical equilibrium solver is coupled to the usual gasdynamic equations. The generalization of the methods enables the modelling of any arbitrary mixture of thermally perfect gases, including air, combustion mixtures and plasmas. As demonstration of the potential of the methodologies, several solutions, involving reacting and perfect gas flows, will be presented. Included is a preliminary simulation of the SSME startup transient. Future enhancements to the proposed techniques will be discussed, including more efficient finite-rate and hybrid (partial equilibrium) schemes. The algorithms that have been developed and are being optimized provide for an efficient and general tool for the design and analysis of propulsion systems.

Cox, C. F.↗

NASA NTRS1984

Modelling the Local Interstellar Medium as a Supernova Remnant in a Multiphase Gas

The construction of supernova remnant which is consistent with the observations and what it talls about the theory was investigated. It is argued that thermal evaporation and local inhomogeneity are crucial elements which are essential to any satisfactory description. It is concluded that: (1) a multiphase supernova remnant (SNR) seems to provide a plausible description of the local interstellar medium (ISM); (2) the local region could have been deficient in cool gas prior to the supernova both on theoretical and observational grounds; (3) the Sun may lie in a region towards the outside of the supernova remnant which hasn't yet come into pressure equilibrium with the hot gas; and (4) evaporative models give a much more satisfactory description of the O VI observations than Sedov Solutions.

Cowie, L. L.↗

NASA NTRS1972

Thermodynamic models in cosmochemical systems.

Generalized computer methods are developed for inferring details of the formation of cosmochemical systems. Compositions of ideal gas mixtures existing in equilibrium with multicomponent solid and liquid phases are calculated. A comparison of computed results with experimental data is made for the ternary system MgO-FeO-SiO2. While the ideal-solution approximation is shown to be inaccurate in dealing with the silicate melts, the stable phases and compositions can be accurately calculated in a system where there are only solids and gas. A model system containing the elements H, O, Si, Mg, S, C, Cl, and F is investigated over a range of compositions involving the gas and ten solid phases, to show the power of the technique in dealing with complex gas-solid equilibria. Systems close to cosmic composition are next considered, both with and without iron.

Griffiths, P. R.↗

NASA NTRS1985

CAG12 - A CSCM based procedure for flow of an equilibrium chemically reacting gas

The Conservative Supra Characteristic Method (CSCM), an implicit upwind Navier-Stokes algorithm, is extended to the numerical simulation of flows in chemical equilibrium. The resulting computer code known as Chemistry and Gasdynamics Implicit - Version 2 (CAG12) is described. First-order accurate results are presented for inviscid and viscous Mach 20 flows of air past a hemisphere-cylinder. The solution procedure captures the bow shock in a chemically reacting gas, a technique that is needed for simulating high altitude, rarefied flows. In an initial effort to validate the code, the inviscid results are compared with published gasdynamic and chemistry solutions and satisfactorily agreement is obtained.

Green, M. J.↗

NASA NTRS1976

Helium emission from model flare layers

The emission of visible and UV He I and He II line radiation from a plane-parallel model flare layer characterized by electron temperatures of 10,000 to 50,000 K and electron densities of 10 to the 10th power to 10 to the 15th power per cu cm is analyzed by solving the statistical-equilibrium equations for a 30-level He I-II-III system, using parametric representations of the line and continuum radiation fields. The atomic model was chosen to provide accurate solutions for the first two resonance lines of He I and He II as well as for the D3 and 10,830-A lines of He I. Reaction rates are discussed, and sample solutions to the steady-state population equations are given for a generally optically thin gas assumed to be irradiated over 2pi sr by a blackbody spectrum at 6000 K. Specific results are examined for ionization equilibrium, level populations, approximate optical depths of a 1000-km-thick flare layer, line intensities, and upper-level population rates.

Kulander, J. I.↗

NASA NTRS1992

Development of a 3-D upwind PNS code for chemically reacting hypersonic flowfields

Two new parabolized Navier-Stokes (PNS) codes were developed to compute the three-dimensional, viscous, chemically reacting flow of air around hypersonic vehicles such as the National Aero-Space Plane (NASP). The first code (TONIC) solves the gas dynamic and species conservation equations in a fully coupled manner using an implicit, approximately-factored, central-difference algorithm. This code was upgraded to include shock fitting and the capability of computing the flow around complex body shapes. The revised TONIC code was validated by computing the chemically-reacting (M(sub infinity) = 25.3) flow around a 10 deg half-angle cone at various angles of attack and the Ames All-Body model at 0 deg angle of attack. The results of these calculations were in good agreement with the results from the UPS code. One of the major drawbacks of the TONIC code is that the central-differencing of fluxes across interior flowfield discontinuities tends to introduce errors into the solution in the form of local flow property oscillations. The second code (UPS), originally developed for a perfect gas, has been extended to permit either perfect gas, equilibrium air, or nonequilibrium air computations. The code solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that was modified to account for real gas effects. The dissipation term associated with this algorithm is sufficiently adaptive to flow conditions that, even when attempting to capture very strong shock waves, no additional smoothing is required. For nonequilibrium calculations, the code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. This code was used to calculate the hypersonic, laminar flow of chemically reacting air over cones at various angles of attack. In addition, the flow around the McDonnel Douglas generic option blended-wing-body was computed and comparisons were made between the perfect gas, equilibrium air, and the nonequilibrium air results.

Tannehill, J. C.↗

NASA NTRS1985

Three-dimensional viscous-shock-layer applications for the Space Shuttle orbiter

A nonorthogonal three-dimensional viscous-shock-layer code was modified and used to compute the windward surface flowfield over a Shuttle-like configuration. Code modifications were made in the methods used to evaluate shock boundary conditions and in the implementation of the equilibrium air models. Additional viscous terms were also retained in the governing equations. Effects of these modifications are demonstrated. Three-dimensional flowfield solutions obtained with the modified code showed good comparison of surface heating and pressure with actual flight data. An apparently three-dimensional effect, characterized by a drop in surface heating on the Shuttle windward centerline in the wing root area, was predicted by the present method. A preliminary review of Shuttle ground-based experimental and flight data confirmed this trend. The present three-dimensional solutions were also compared with the predictions of several approximate methods. Those comparisons showed the approximate methods to be valid for predicting heating along the Shuttle windward centerline uner both perfect gas and equilibrium air conditions.

Thompson, R. A.↗

NASA NTRS1986

On star formation in stellar systems. I - Photoionization effects in protoglobular clusters

The progressive ionization and subsequent dynamical evolution of nonhomogeneously distributed low-metal-abundance diffuse gas after star formation in globular clusters are investigated analytically, taking the gravitational acceleration due to the stars into account. The basic equations are derived; the underlying assumptions, input parameters, and solution methods are explained; and numerical results for three standard cases (ionization during star formation, ionization during expansion, and evolution resulting in a stable H II region at its equilibrium Stromgren radius) are presented in graphs and characterized in detail. The time scale of residual-gas loss in typical clusters is found to be about the same as the lifetime of a massive star on the main sequence.

Tenorio-Tagle, G.↗