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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1985

The numerical viscosity of entropy stable schemes for systems of conservation laws

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes, is quantified and related to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones.

Tadmor, E.↗

NASA NTRS1987

The numerical viscosity of entropy stable schemes for systems of conservation laws. I

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison.To this end, conservative schemes which are also entropy-conservative are constructed. These entropy-conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise-linear finite-element methods, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.

Tadmor, Eitan↗

NASA NTRS1988

An entropy and viscosity corrected potential method for rotor performance prediction

An unsteady Full-Potential Rotor code (FPR) has been enhanced with modifications directed at improving its drag prediction capability. The shock generated entropy has been included to provide solutions comparable to the Euler equations. A weakly interacted integral boundary layer has also been coupled to FPR in order to estimate skin-friction drag. Pressure distributions, shock positions, and drag comparisons are made with various data sets derived from two-dimensional airfoil, hovering, and advancing high speed rotor tests. In all these comparisons, the effect of the nonisentropic modification improves (i.e., weakens) the shock strength and wave drag. In addition, the boundary layer method yields reasonable estimates of skin-friction drag. Airfoil drag and hover torque data comparisons are excellent, as are predicted shock strength and positions for a high speed advancing rotor.

Bridgeman, John O.↗

NASA NTRS1983

Numerical viscosity and the entropy condition for conservative difference schemes

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Tadmor, E.↗

NASA NTRS1984

Numerical viscosity and the entropy condition for conservative difference schemes

Tadmor, E.↗

NASA NTRS1975

Theoretical study of production of unique glasses in space

The potential of producing the glassy form of selected materials in the weightless, containerless nature of space processing is examined through the development of kinetic relationships describing nucleation and crystallization phenomena. Transformation kinetics are applied to a well-characterized system (SiO2), an excellent glass former (B2O3), and a poor glass former (Al2O3) by conventional earth processing methods. Viscosity and entropy of fusion are shown to be the primary materials parameters controlling the glass forming tendency. For multicomponent systems diffusion-controlled kinetics and heterogeneous nucleation effects are considered. An analytical empirical approach is used to analyze the mullite system. Results are consistent with experimentally observed data and indicate the promise of mullite as a future space processing candidate.

Larsen, D. C.↗

NASA NTRS1991

The development of a CFD potential method for the analysis of tilt-rotors

A new CFD potential code, FPX (eXtended Full-Potential), has been developed for application to both helicopters and tilt-rotors. The code solves the unsteady, three-dimensional full potential equation and is an extension of the rotor code, FPR. Both entropy and viscosity corrections are included to enhance the physical modeling capabilities. A number of efficiency related modifications have yielded a factor of two speed-up in the code. An axial flow capability has been added to treat tilt-rotor in forward flight (cruise mode). In order to employ streamwise periodicity and accurately solve for the propagation of acoustic signals in the tip region, an H-H topology has been added to the basic O-H grid system. Computations are performed for the XV-15 Standard and ATB blades at high-speed conditions. Comparisons are made for the blade aerodynamics and the induced fuselage cabin pressure for a range of Mach numbers. Grid generation, wake treatment, and far-field wall treatment are identified as problem areas with recommendations for future research.

Bridgeman, John O.↗

NASA NTRS1956

Compressibility factor, density, specific heat, enthalpy, entropy, free-energy function, viscosity, and thermal conductivity of steam

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Fano, Lilla↗

NASA NTRS2000

On the Coupling of CDISC Design Method with FPX Rotor Code

A rotor section aerodynamics design package is developed by coupling Constrained Direct Iterative Surface Curvature (CDISC) design method with the FPX rotor code. The coupling between the CDISC design and the FPX flow analysis is fully automated. The CDISC design method employs a predictor-corrector procedure iteratively to determine a surface geometry which produces a target pressure distribution, where the target pressure distributions is either pre-defined or automatically generated through flow and geometry constraints. The FPX code is an eXtended Full-Potential rotor Computational Fluid Dynamics (CFD) code, which solves the three-dimensional unsteady full-potential equation in a strong conservative form using an implicit approximate factorization finite-difference scheme with entropy and viscosity corrections. Application of the CDISC design method coupled with the FPX rotor code is made for rotor blades in hovering motions. Several design examples are presented to demonstrate the capability of the new package in rotor section design.

Hu, Hong↗

NASA NTRS1972

Computer programs for thermodynamic and transport properties of hydrogen (tabcode-II)

The thermodynamic and transport properties of para and equilibrium hydrogen have been programmed into a series of computer routines. Input variables are the pair's pressure-temperature and pressure-enthalpy. The programs cover the range from 1 to 5000 psia with temperatures from the triple point to 6000 R or enthalpies from minus 130 BTU/lb to 25,000 BTU/lb. Output variables are enthalpy or temperature, density, entropy, thermal conductivity, viscosity, at constant volume, the heat capacity ratio, and a heat transfer parameter. Property values on the liquid and vapor boundaries are conveniently obtained through two small routines. The programs achieve high speed by using linear interpolation in a grid of precomputed points which define the surface of the property returned.

Roder, H. M.↗

NASA NTRS1975

Normal- and oblique-shock flow parameters in equilibrium air including attached-shock solutions for surfaces at angles of attack, sweep, and dihedral

Normal- and oblique-shock flow parameters for air in thermochemical equilibrium are tabulated as a function of shock angle for altitudes ranging from 15.24 km to 91.44 km in increments of 7.62 km at selected hypersonic speeds. Post-shock parameters tabulated include flow-deflection angle, velocity, Mach number, compressibility factor, isentropic exponent, viscosity, Reynolds number, entropy difference, and static pressure, temperature, density, and enthalpy ratios across the shock. A procedure is presented for obtaining oblique-shock flow properties in equilibrium air on surfaces at various angles of attack, sweep, and dihedral by use of the two-dimensional tabulations. Plots of the flow parameters against flow-deflection angle are presented at altitudes of 30.48, 60.96, and 91.44 km for various stream velocities.

Hunt, J. L.↗

NASA NTRS1993

Computer program for thermal and transport properties of parahydrogen from 20 to 10,000 K

A computer program was recently developed to provide thermal and transport properties for parahydrogen across a wide temperature and pressure range. The program, NBS+/-pH2, matches the most recent parahydrogen property data from the National Bureau of Standards up to 3000 K and property data from the NASA Lewis Research Center's Chemical Equilibrium Computer Program up to 10,000 K. The pressure range of NBS+/-pH2 is from 1 x 10(exp 4) to 1.6 x 10(exp 7) Pa. The program was developed to meet the need for accurate parahydrogen properties from liquid to dissociated conditions as required by propulsion simulation programs being developed under the Space Exploration Initiative. NBS+/-pH2 is a machine-independent, standard Fortran 77 program which provides density, thermal conductivity, viscosity, Prandtl number, entropy, specific heats, and speed of sound given pressure and either temperature or enthalpy. This program is described and a comparison to programs previously available is provided.

Walton, James T.↗

NASA NTRS1996

Transport Coefficients in weakly compressible turbulence

A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa's two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, a prediction unique to Yoshizawa's two-scale approximation is that terms containing gradients of incompressible turbulence quantities also appear in the mean flow equations. The form these terms take is described.

Rubinstein, Robert↗

NASA NTRS1975

Perturbation solution of the Navier-Stokes equations and its relation to the Lighthill-Curle solution of aerodynamic sound

The aerodynamic sound described by the Lighthill-Curle solution is reexamined using a method of matched asymptotic expansions. The governing Navier-Stokes equations written in nondimensional form are expanded for a small Mach number. First- and second-order solutions for the pressure field are obtained, and the singular nature of the expansion at large distances is indicated. The nearfield pressure is governed by the Poisson equation, whereas the farfield equations describe a linear wave system in a dissipative medium. The pseudosound is related to the incompressible Reynolds stresses associated with a solenoidal velocity field, the velocity, the pressure perturbation, and their derivatives on the boundaries. A uniformly valid first-order solution for the pressure is obtained. It is shown that viscosity, thermal conductivity, and entropy in the flow do not contribute to the first-order noise generation, while the viscous stress contributes to noise only from some boundaries. The application of the proposed perturbation method to a subsonically moving surface and a hot jet is discussed.

Pan, Y. S.↗

NASA NTRS1986

Entropy conservative finite element schemes

The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.

Tadmor, E.↗

NASA NTRS1993

Energy considerations in computational aeroacoustics

A finite-volume multistage time-stepping Euler code is used to investigate the use of CFD algorithms for the direct calculation of acoustics. The 2D compressible inviscid flow about an accelerating or decelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder to the fluid, as the cylinder is moved from rest to some nonnegligible velocity, is clearly seen. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy contained in the local aerodynamic field. Systematic variation of the cylinder acceleration shows that the radiated acoustic energy depends strongly upon the rate of acceleration or deceleration. The computational grid has a large effect on the ratio of acoustic energy to nonphysical entropy associated energy, while the role of the explicit artificial viscosity seems to be of second order. The entropy term was nearly negligible in all cases the cylinder was started slowly.

Brentner, Kenneth S.↗

NASA NTRS1973

WASP: A flexible FORTRAN 4 computer code for calculating water and steam properties

A FORTRAN 4 subprogram, WASP, was developed to calculate the thermodynamic and transport properties of water and steam. The temperature range is from the triple point to 1750 K, and the pressure range is from 0.1 to 100 MN/m2 (1 to 1000 bars) for the thermodynamic properties and to 50 MN/m2 (500 bars) for thermal conductivity and to 80 MN/m2 (800 bars) for viscosity. WASP accepts any two of pressure, temperature, and density as input conditions. In addition, pressure and either entropy or enthalpy are also allowable input variables. This flexibility is especially useful in cycle analysis. The properties available in any combination as output include temperature, density, pressure, entropy, enthalpy, specific heats, sonic velocity, viscosity, thermal conductivity, surface tension, and the Laplace constant. The subroutine structure is modular so that the user can choose only those subroutines necessary to his calculations. Metastable calculations can also be made by using WASP.

Hendricks, R. C.↗

NASA NTRS1975

Computer program for calculating water and steam properties

Computer subprogram calculates thermodynamic and transport properties of water and steam. Program accepts any two of pressure, temperature, and density as input conditions. Pressure and either entropy or enthalpy are also allowable input variables. Output includes any combination of temperature, density, pressure, entropy, enthalpy, specific heats, sonic velocity, viscosity, thermal conductivity, surface tension, and the Laplace constant.

Hendricks, R. C.↗