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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Turbulence energy and diffusion transport of third-moments in a separating and reattaching flow

For accurate prediction of turbulent flow in separated and reattaching regions, it is necessary to incorporate second- and third-moments of turbulent fluctuations. The turbulence energy and the energy dissipation rate equations are modified by incorporating second-order closure. Moreover, a transport equation model for the third-order closure with a near-wall correction is developed for the evaluation of the diffusive action of the second-moments. After comparison of the results with experimental data, it is concluded that the models developed here improve the prediction of triple-velocity correlations in both recirculating and redeveloping flow regions.

Amano, R. S.↗
NASA NTRS1988

Modified non-linear Burgers' equations and cosmic ray shocks

A reductive perturbation scheme is used to derive a generalized non-linear Burgers' equation, which includes the effects of dispersion, in the long wavelength regime for the two-fluid hydrodynamical model used to describe cosmic ray acceleration by the first-order Fermi process in astrophysical shocks. The generalized Burger's equation is derived for both relativistic and non-relativistic cosmic ray shocks, and describes the time evolution of weak shocks in the theory of diffusive shock acceleration. The inclusion of dispersive effects modifies the phase velocity of the shock obtained from the lower order non-linear Burger's equation through the introduction of higher order terms from the long wavelength dispersion equation. The travelling wave solution of the generalized Burgers' equation for a single shock shows that larger cosmic ray pressures result in broader shock transitions. The results for relativistic shocks show a steepening of the shock as the shock speed approaches the relativistic cosmic ray sound speed. The dependence of the shock speed on the cosmic ray pressure is also discussed.

Zank, G. P.↗
NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗
NASA NTRS1975

An experimental and analytical investigation of axisymmetric diffusers

A finite difference computer program for turbulent compressible flow was used to establish the performance of several diffuser shapes for experimental testing. The diffusers were designed to have a linear change in Mach number, a linear change in pressure, or a curvature fitted by a quadratic equation. Testing was performed with M = 0.1 to 0.9 with and without boundary layer bleed. Above M = 0.6, data were obtained with a normal shock upstream of the diffuser entrance. Peak static pressure recovery occurred with a diffuser inlet M0.75. The quadratic diffuser yielded the highest total pressure recovery.

Povinelli, L. A.↗
NASA NTRS1975

An experimental and analytical investigation of axisymmetric diffusers

A finite difference computer program for turbulent compressible flow was used to establish the performance of several diffuser shapes for experimental testing. The diffusers were designed to have a linear change in Mach number, a linear change in pressure or a curvature fitted by a quadratic equation. Testing was performed with M = 0.1 to 0.9 with and without boundary layer bleed. Above M = 0.6, data were obtained with a normal shock upstream of the diffuser entrance. Peak static pressure recovery occurred with a diffuser inlet M-0.75. The quadratic diffuser yielded the highest total pressure recovery.

Povinelli, L. A.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Towne, Charles E.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗
NASA NTRS1981

Stellar convection theory. III - Dynamical coupling of the two convection zones in A-type stars by penetrative motions

The thermal convection occurring over many density scale heights in an A-type star outer envelope, encompassing both the hydrogen and helium convectively unstable zones, is examined by means of anelastic modal equations. The single-mode anelastic equations for such compressible convection display strong overshooting of the motions into adjacent radiative zones, which would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. In addition, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The two solutions that the nonlinear single-mode equations admit for the same horizontal wavelength are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is suggested that strong horizontal shear flows should be present just below the surface of the star, and that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows.

Latour, J.↗
NASA NTRS1994

Design of a variable area diffuser for a 15-inch Mach 6 open-jet tunnel

The Langley 15-inch Mach 6 High Temperature Tunnel was recently converted from a Mach 10 Hypersonic Flow Apparatus. This conversion was effected to improve the capability of testing in Mach 6 air at relatively high reservoir temperatures not previously possible at Langley. Elevated temperatures allow the matching of the Mach numbers, Reynolds numbers, and ratio of wall-to-adiabatic-wall temperatures (TW/Taw) between this and the Langley 20-inch Mach 6 CF4 Tunnel. This ratio is also matched for Langley's 31-inch Mach 10 Tunnel and is an important parameter useful in the simulation of slender bodies such as National Aerospace Plane (NASP) configurations currently being studied. Having established the nozzle's operating characteristics, the decision was made to install another test section to provide model injection capability. This test section is an open-jet type, with an injection system capable of injecting a model from retracted position to nozzle centerline between 0.5 and 2 seconds. Preliminary calibrations with the new test section resulted in Tunnel blockage. This blockage phenomenon was eliminated when the conical center body in the diffuser was replaced. The issue then, is to provide a new and more efficient variable area diffuser configuration with the capability to withstand testing of larger models without sending the Tunnel into an unstart condition. Use of the 1-dimensional steady flow equation with due regard to friction and heat transfer was employed to estimate the required area ratios (exit area / throat area) in a variable area diffuser. Correlations between diffuser exit Mach number and area ratios, relative to the stagnation pressure ratios and diffuser inlet Mach number were derived. From these correlations, one can set upper and lower operating pressures and temperatures for a given diffuser throat area. In addition, they will provide appropriate input conditions for the full 3-dimensional computational fluid dynamics (CFD) code for further simulation studies.

Loney, Norman W.↗
NASA NTRS1986

Solvability condition for needle crystals at large undercooling in a nonlocal model of solidification

It is explicitly shown that, in a realistic model of diffusion-controlled dendritic solidification, Ivantsov's continuous family of steady-state needle crystals is destroyed by the addition of surface tension. The starting point is in the exact integro-differential equation for the one-sided model, in two dimensions, in a moving frame of reference. In the limit of large undercooling, where the range of the diffusion field is much smaller than the radius of curvature of the tip of the needle, this problem is reduced to a linear, inhomogeneous differential equation of infinite order. A solvability condition for this equation is derived and it is shown that solutions cease to exist for arbitrarily small but finite isotropic surface tension.

Caroli, B.↗
NASA NTRS1997

Shapes of Buoyant and Nonbuoyant Methane Laminar Jet Diffusion Flames

Laminar gas jet diffusion flames represent a fundamental combustion configuration. Their study has contributed to numerous advances in combustion, including the development of analytical and computational combustion tools. Laminar jet flames are pertinent also to turbulent flames by use of the laminar flamelet concept. Investigations into the shapes of noncoflowing microgravity laminar jet diffusion flames have primarily been pursued in the NASA Lewis 2.2-second drop tower, by Cochran and coworkers and by Bahadori and coworkers. These studies were generally conducted at atmospheric pressure; they involved soot-containing flames and reported luminosity lengths and widths instead of the flame-sheet dimensions which are of Greater value to theory evaluation and development. The seminal model of laminar diffusion flames is that of Burke and Schumann, who solved the conservation of momentum equation for a jet flame in a coflowing ambient by assuming the velocity of fuel, oxidizer and products to be constant throughout. Roper and coworkers improved upon this model by allowing for axial variations of velocity and found flame shape to be independent of coflow velocity. Roper's suggestion that flame height should be independent of gravity level is not supported by past or present observations. Other models have been presented by Klajn and Oppenheim, Markstein and De Ris, Villermaux and Durox, and Li et al. The common result of all these models (except in the buoyant regime) is that flame height is proportional to fuel mass flowrate, with flame width proving much more difficult to predict. Most existing flame models have been compared with shapes of flames containing soot, which is known to obscure the weak blue emission of flame sheets. The present work involves measurements of laminar gas jet diffusion flame shapes. Flame images have been obtained for buoyant and nonbuoyant methane flames burning in quiescent air at various fuel flow-rates, burner diameters and ambient pressures. Soot concentrations were minimized by selecting conditions at low flowrates and low ambient pressures; this allows identification of actual flame sheets associated with blue emissions of CH and CO2. The present modeling effort follows that of Roper and is useful in explaining many of the trends observed.

Sunderland, Peter B.↗
NASA NTRS1977

A second-order closure analysis of turbulent diffusion flames

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

Varma, A. K.↗
NASA NTRS1976

Modeling of three-dimensional mixing and reacting ducted flows

A computer code, based upon a finite element solution algorithm, was developed to solve the governing equations for three-dimensional, reacting boundary region, and constant area ducted flow fields. Effective diffusion coefficients are employed to allow analyses of turbulent, transitional or laminar flows. The code was used to investigate mixing and reacting hydrogen jets injected from multiple orifices, transverse and parallel to a supersonic air stream. Computational results provide a three-dimensional description of velocity, temperature, and species-concentration fields downstream of injection. Experimental data for eight cases covering different injection conditions and geometries were modeled using mixing length theory (MLT). These results were used as a baseline for examining the relative merits of other mixing models. Calculations were made using a two-equation turbulence model (k+d) and comparisons were made between experiment and mixing length theory predictions. The k+d model shows only a slight improvement in predictive capability over MLT. Results of an examination of the effect of tensorial transport coefficients on mass and momentum field distribution are also presented. Solutions demonstrating the ability of the code to model ducted flows and parallel strut injection are presented and discussed.

Zelazny, S. W.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗
NASA NTRS1981

Equatorial superrotation in a thermally driven zonally symmetric circulation

Near the equator where the Coriolis force vanishes, the momentum balance for the axially symmetric circulation is established between horizontal and vertical diffusion, which, a priori, does not impose constraints on the direction or magnitude of the zonal winds. Solar radiation absorbed at low latitudes is a major force in driving large scale motions with air rising near the equator and falling at higher latitudes. In the upper leg of the meridional cell, angular momentum is redistributed so that the atmosphere tends to subrotate (or corotate) at low latitudes and superrotate at high latitudes. In the lower leg, however, the process is reversed and produces a tendency for the equatorial region to superrotate. The outcome depends on the energy budget which is closely coupled to the momentum budget through the thermal wind equation; a pressure (temperature) maximum is required to sustain equatorial superrotation. Such a condition arises in regions which are convectively unstable and the temperature lapse rate is superadiabatic. It should arise in the tropospheres of Jupiter and Saturn; planetary energy from the interior is carried to higher altitudes where radiation to space becomes important. Upward equatorial motions in the direct and indirect circulations (Ferrel-Thomson type) imposed by insolation can then trap dynamic energy for equatorial heating which can sustain the superrotation of the equatorial region.

Mayr, H. G.↗