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At least 271 records · Page 15

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NASA NTRS1987

Numerical study of finite-rate supersonic combustion using parabolized equations

A set of partial differential equations, describing the two-dimensional supersonic chemically-reacting flow of the hydrogen-air system, is formulated such that the equations are parabolic in the streamwise direction. A fully-implicit fully-coupled finite-difference algorithm is used to develop a computer code which solves the governing equations by marching in the streamwise direction. The combustion process is modeled by a two-step finite-rate chemistry whereas turbulence is simulated by an algebraic turbulence model. Results of two calculations of internal supersonic reacting flow show fairly good agreement with the results obtained by the more costly full Navier-Stokes procedure.

Chitsomboon, T.↗

NASA NTRS1986

Scaling relations for heating during gliding entry at parabolic speed

The scaling relations presently derived illustrate the influence of ballistic coefficient and L/D primary vehicle parameters on the peak heating rate and total heating/unit area for gliding entry of the earth atmosphere at parabolic speed. Comparisons with stagnation-point and windward centerline laminar and turbulent heating during three Space Shuttle flights are presented. It is found that total heat input/unit area is reduced by decreasing both of the primary vehicle parameters.

Tauber, Michael E.↗

NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗

NASA NTRS1986

A relaxation technique for the parabolized Navier-Stokes (PNS) equations

A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.

Kaul, Upender K.↗

NASA NTRS1987

Parabolic heavy ion flow in the polar magnetosphere

Recent observations by the Dynamics Explorer 1 satellite over the dayside polar cap magnetosphere have indicated downward flows of heavy ions such as O(+), O(2+), N(+), and N(2+) with flow velocities of the order 1 km/s (Lockwood et al., 1985). These downward flows were interpreted as the result of 'parabolic' flow of these heavy ionospheric ions from a source region associated with the polar cleft topside ionosphere. Here, a two-dimensional kinetic model is utilized to elicit features of the transport of very low energy O(+) ions from the cleft ionosphere. Bulk parameter (density, flux, thermal energies, etc.) distributions in the noon-midnight meridian plane illustrate the effects of varying convection electric fields and source energies. The results illustrate that, particularly under conditions of weak convection electric fields and weak ion heating in the cleft region, much of the intermediate altitude polar cap magnetosphere may be populated by downward flowing heavy ions. It is further shown how two-dimensional transport effects may alter the characteristic vertical profiles of densities and fluxes from ordinary profiles computed in one-dimensional steady-state models.

Horwitz, J. L.↗

NASA NTRS1987

Estimation of discontinuous coefficients in parabolic systems - Applications to reservoir simulation

Spline-based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. In particular, the problem of determining discontinuous coefficients is discussed, estimating both the functional shape and points of discontinuity for such parameters. In addition, the ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces. Convergence results and a summary of numerical performance of the resulting algorithms are given.

Lamm, Patricia K.↗

NASA NTRS1986

Behavior of insoluble particles during parabolic flight solidification processing of Fe-C-Si and Fe-C-V alloys

In a high-g rapid solidification environment, Fe-base alloy insoluble particles at the solidification interface may be pushed ahead of the interface or may be trapped in the solid, depending on the correlation of various interface energies, the solidification rates, and the Stokes force; particle agglomeration due to buoyancy-driven convection further complicates the problem. Attention is presently given to results obtained for directionally solidified Fe-C-Si and Fe-C-V alloys during parabolic low-g flight and ground experiments. In these systems, graphite and vanadium carbide can be considered to be the insoluble particles.

Stefanescu, D. M.↗

NASA NTRS1987

Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

A new computer code for the solution of the three-dimensional parabolized Navier-Stokes equations has been developed. The code employs a state-of-the-art upwind algorithm to capture strong shock waves. The algorithm is implicit, uses finite volumes, and is second-order accurate in the crossflow directions. The new code is validated through application to laminar hypersonic flows past two simple body shapes: a circular cone of 10 deg half-angle, and a generic all-body hypersonic vehicle. Cone flow solutions were computed at angles of attack of 12, 20, and 24 deg and results are in agreement with experimental data. Results are also presented for the flow past the all-body vehicle at angles of incidence of 0 and 10 deg.

Lawrence, Scott L.↗

NASA NTRS1987

NASA Ames Research Center's parabolized Navier-Stokes code - A critical evaluation of heat-transfer predictions

The viscous supersonic/hypersonic flow over a biconic configuration was numerically simulated using the NASA Ames Research Center's Parabolized Navier-Stokes (PNS) code, and results obtained for the effects of various computational parameters on the heat transfer are compared with experimental results. The PNS code is found to provide accurate results for heat transfer parameters using low smoothing coefficient values, assuming that the radial spacing is at some small value and that the body is simple in cross section. For the cases considered, the nominal value of the spatial step size was 0.05, and the grid density was 45 points in the meridional direction and 30 points in the radial direction.

Chaussee, Denny S.↗

NASA NTRS1988

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Rosen, I. G.↗

NASA NTRS1988

An upwind parabolized Navier-Stokes code for real gas flows

A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the two-dimensional/axisymmetric hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence, Tannehill and Chaussee. The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. Simplified curve fits are used to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the hypersonic laminar flow of air over a flat plate, a wedge, a ramp, and a cone. The results of these computations are compared with the results from a conventional centrally-differenced, real gas, PNS code and the agreement is excellent, except in the vicinity of shock waves where the present code exhibits far superior shock capturing capabilities.

Tannehill, John C.↗

NASA NTRS1988

Explicit upwind algorithm for the parabolized Navier-Stokes equations

A new explicit upwind algorithm based on Roe's flux-difference splitting (FDS) method has been developed for the three-dimensional Parabolized Navier-Stokes (PNS) equations. For three-dimensional flows, FDS's are determined separately for the two nonmarching directions and modified to account for the calculated shock angle in the crossflow plane. Second-order FDS is applied to the pressure and convection terms with the streamwise pressure gradient limited in the subsonic region to maintain a hyperbolic inviscid equation set. Second-order central differencing is obtained in the two-step algorithm for the shear and heat flux terms. The new algorithm is demonstrated for three laminar flow test cases: supersonic flow over a flat plate, hypersonic flow over a 15 deg ramp, and hypersonic flow past a 10 deg cone at a 24 deg angle of attack. The computed results agree well with experimental measurements.

Korte, John J.↗

NASA NTRS1988

Computational validation of a parabolized Navier-Stokes solver on a sharp-nose cone at hypersonic speeds

Perfect gas computational results from a newly-developed upwind, parabolized Navier-Stokes (PNS) solver are compared with an existing set of experimental laminar results for a 10-deg half-angle circular cone at freestream Mach number of 7.95. Comparisons were performed with surface pressure and heat transfer data, as well as with flowfield pitot measurements. The PNS code predicted the surface quantities accurately up through 20-deg angle-of-attack, including crossflow separation, and correctly defined the location of the bow shock and the edge of the boundary layer. The importance of cell Reynolds number, grid density, and thermal boundary conditions to the accurate prediction of the flowfield are examined through numerical emamples.

Huebner, Lawrence D.↗

NASA NTRS1988

An upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow around two-dimensional or axisymmetric bodies. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. The algorithm solves the gas dynamic and species continuity equations in a 'loosely' coupled manner. The new code has been validated by computing the laminar flow (at free stream Mach number 25) of chemically reacting air over a wedge and a cone. The results of these computations are compared with the results from a centrally-differenced, fully coupled, nonequilibrium PNS code. The agreement is excellent, except in the vicinity of the shock wave where the present code exhibits superior shock capturing capabilities.

Tannehill, John C.↗

NASA NTRS1988

Real-time optical laboratory solution of parabolic differential equations

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Casasent, David↗

NASA NTRS1989

Dynamic loading of spur gears with linear or parabolic tooth profile modification

A computer simulation was conducted to investigate the effects of both linear and parabolic tooth profile modification on the dynamic response of low-contact-ratio spur gears. The effect of the total amount of modification and the length of the modification zone were studied at various loads and speeds to find the optimal profile modification for minimal dynamic loading. Design charts consisting of normalized maximum dynamic load curves were generated for gear systems operated at various loads and with different tooth profile modification. An optimum profile modification can be determined from these design charts to minimize the dynamic loads of spur gear systems.

Lin, Hsiang Hsi↗

NASA NTRS1988

Life science experiments during parabolic flight: The McGill experience

Over the past twelve years, members of the Aerospace Medical Research Unit of McGill University have carried out a wide variety of tests and experiments in the weightless condition created by parabolic flight. This paper discusses the pros and cons of that environment for the life scientist, and uses examples from the McGill program of the types of activities which can be carried out in a transport aircraft such as the NASA KC-135.

Watt, D. G. D.↗

NASA NTRS1989

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.↗