Showing papers on "Slip ratio published in 1975"

Reacting Shock Layers with Slip and Catalytic Boundary Conditions

Abstract: The influence of wall slip and catalytic atom-recombination on the flowfield and wall heat flux are calculated for high-altitude flight and arcjet-flow conditions. Boundary equations, which include velocity slip, temperature jump, and wall catalytic atom-recombination, are coupled to the viscous reacting multicomponent NavierStokes equation. These equations are solved using a time-dependent finite difference technique applied to spheres in an arcjet flow (Reynolds number of 550) and a high-altitude flight case representative of the space shuttle orbiter (Reynolds number of 450). The results indicate that catalysis strongly influences the temperature jump, but not the velocity slip. Slip increases the atom fraction and temperature at both the wall and in the flowfield. Likewise, the shock stand-off distance, the wall heat flux, and friction coefficient are increased over the nonslip cases. The reacting gas calculations confirm the chemically frozen nature of the shock layer in arcjet flows. design the reusable space shuttle orbiter for highaltitude, low Reynolds number, atmospheric entry necessitates a more comprehensive treatment and understanding of the interaction between a high enthalpy gas flow and a relatively cold surface. At low densities the continuum model of the gas breaks down in regions of large gradients such as those near a cold body. Corrections to the equations for the boundary conditions are then required for the flow. These influences are reflected in the calculations of surface heat-transfer rate and chemical composition of the flow near the wall. The aim of this paper is to quantify how these low density phenomena interact, how they influence interpretation of test data obtained on thermal protection systems, and how they alter the predictions of heating rates and performance of the space shuttle orbiter thermal protection system (TPS) during its long high-altitude entry. The approach taken here is to obtain finite difference solutions to the reacting Navier-Stokes equations for the flow around spheres in both space shuttle flight and arcjet environments. The wall boundary conditions for these solutions are obtained from slip and jump relations for a nonequilibrium multicomponent gas mixture. They include the effects of catalytic atom recombination. From the solutions one can assess the effects. of the boundary conditions on the flow properties, the heat flux, etc. At low densities, the continuum-flow equations are no longer adequate close to the wall because the mean free path becomes long compared to characteristi c lengths associated with significant changes in macroscopic-flow parameters. The flow in a region next to the wall having a thickness on the order of a mean free path (the Knudsen layer) cannot be described by the Navier-Stokes description (Kogan1). To determine the flow properties within the Knudsen layer requires the direct solution of the Boltzmann equation matched to the solutions for the outer flow (Navier-Stokes equation) and the wall boundary condition. This is most conveniently done through the use of a slip model in which slip and jump properties are used for the boundary conditions for the Navier-Stokes equations.

Surface motions due to fault slip in the vertical mode with friction

Abstract: Approximations to the wave motions generated on the surface of an elastic half-space by slip in the vertical mode with friction on a fault plane of arbitrary dip are analyzed. The half-space is initially motionless under uniformly distributed tectonic stresses and hydrostatic stresses due to the weight of the material. The resistance to slip obeys the Coulomb model for static and kinetic friction. Slip is triggered along a line parallel to the fault surface trace. The moving edge of the slip zone extends toward the surface with a constant velocity. Homogeneous function techniques are used to derive the stresses and displacements for a general class of related problems as single integrals of analytic functions. The results are easily specialized to obtain approximate expressions for the wave-induced surface displacement and particle velocity components. For various values of the time, dip angle, coefficient of kinetic friction and rate of extension of the slip-zone edge, curves for the surface particle-velocity components are given. This paper will serve as a basis for future work.

A similarity solution of the Navier-Stokes equations with wall catalysis and slip for hypersonic, low Reynolds number flow over spheres

Abstract: The slip conditions for a multicomponent mixture with diffusion, wall-catalyzed atom recombination and thermal radiation are derived. The more realistic multicomponent species slip conditions are shown to be necessary for accurate merged shock layer solutions on a sphere. These slip conditions are used in a first-order similarity solution of the Navier-Stokes equations with nonequilibrium chemistry for the merged shock layer. Results of this quick numerical solution are compared with a time dependent solution around the sphere and with measured arc jet results at low Reynolds numbers. The similarity solution, unlike the time dependent solution, shows smooth radial profiles of the pressure and smooth variations of velocity slip, skin friction, temperature slip and heat transfer around the body. The present first-order similarity solution is valid up to 25 deg from the stagnation point and takes less than 1% of the computer time to run a time dependent scheme. The smaller stand-off distance obtained from the similarity solution is supported by experimental data. The measured heat flux is closer to the similarity solution than the time dependent method at the stagnation point and shows the proper variation with circumferential angle up to at least 40 deg.

Influence of Void and Velocity Variations on Two-Phase Liquid Metal MHD Induction Converter Characteristics

Abstract: An experimental study has been undertaken on the MHD induction power generation, with liquid-gas two-phase mixture as working fluid. The effect on the generator performance brought by variations of the electrical conductivity was experimentally proved by a model experiment in which the two-phase fluid flow was simulated by a solid metal plate of gradually changing cross-sectional area. A second experiment with actual NaK-N2 two-phase flow was performed, which proved that the effect on generator performance brought by the variations of electrical conductivity and of fluid velocity along the channel tended to cancel each other, resulting in substantially reduced distortion of the overall flow behavior. In an actual generator channel, a constant cross section would be unfavorable for realizing non-perturbation conditions, on account of the hydraulic behavior of two-phase flow, but nonetheless, the degradation of generator efficiency can be limited to within a few percent. A generator channel of gradually inc...

Use of vertical slip flow and flooding models in LOCA analysis

Abstract: Vertical slip flow and flooding models, which have been incorporated in a version of the RELAP4 computer code by Aerojet Nuclear Company have led to significant improvements in modeling nuclear reactor coolant system phenomena during postulated large and small break loss-of-coolant accidents. The vertical slip flow model computes the separated fluid component velocities and directions at vertical flow junctions. Use of the slip model allows the energy transfer between volumes to be based on individual liquid and vapor component flows rather than on the net junction flow. Continuity and momentum equations are unaffected by the addition of slip. The vertical flow slip model logic is based on the assumption that gravity forces dominate causing slip between phases. 7 references (auth)