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At least 505 records · Page 28

Analytical study of He II flow characteristics in the SHOOT transfer line

Pressure and temperature profiles for He II flow in the transfer line for the Superfluid Helium On-Orbit Transfer (SHOOT) experiment are determined using a finite difference method to solve the one-dimensional two-fluid conservation equations. For practical purposes, forced flow of He II with Re greater than 10 to the 6th can be treated as a classical turbulent flow For a maximum SHOOT transfer rate of 800 cu dm/h, the temperature rise between the pump outlet and the receiver tank is about 80 mk with a 7-W heat load imposed on the 4-m-long transfer line. A pump outlet pressure of 160 torr is required to sustain the 800 cu dm/h flow without causing vapor formation within the transfer line.

Lee, J. H.↗

Unsteady stagnation-point heat transfer during passage of a concentrated vortex

The unsteady boundary layer due to a single rectilinear vortex filament approaching a two-dimensional stagnation point is investigated. The unsteady boundary-layer equations are solved by an alternating-direction-implicit finite-difference method. Two mechanisms which cause fluctuations in heat transfer are the unsteady velocity field in the boundary layer and secondly, the unsteady total temperature at the edge of the boundary layer. The relative importance of these mechanisms is dependent upon the total temperature fluctuations relative to the imposed temperature difference.

Rigby, David L.↗

Numerical studies of the effects of jet-induced mixing on liquid-vapor interface condensation

Numerical solutions of jet-induced mixing in a partially full cryogenic tank are presented. An axisymmetric laminar jet is discharged from the central part of the tank bottom toward the liquid-vapor interface. Liquid is withdrawn at the same volume flow rate from the outer part of the tank. The jet is at a temperature lower than the interface, which is maintained at a certain saturation temperature. The interface is assumed to be flat and shear-free and the condensation-induced velocity is assumed to be negligibly small compared with radial interface velocity. Finite-difference method is used to solve the nondimensional form of steady state continuity, momentum, and energy equations. Calculations are conducted for jet Reynolds numbers ranging from 150 to 600 and Prandtl numbers ranging from 0.85 to 2.65. The effects of above stated parameters on the condensation Nusselt and Stanton numbers which characterize the steady-state interface condensation process are investigated. Detailed analysis to gain a better understanding of the fundamentals of fluid mixing and interface condensation is performed.

Lin, Chin-Shun↗

Numerical Study of Three-dimensional Spatial Instability of a Supersonic Flat Plate Boundary Layer

The behavior of spatially growing three-dimensional waves in a supersonic boundary layer was studied numerically by solving the complete Navier-Stokes equations. Satisfactory comparison with linear parallel and non-parallel stability theories, and experiment are obtained when a small amplitude inflow disturbance is used. The three-dimensional unsteady Navier-Stokes equations are solved by a finite difference method which is fourth-order and second-order accurate in the convection and viscous terms respectively, and second-order accurate in time. Spanwise periodicity is assumed. The inflow disturbance is composed of eigenfunctions from linear stability theory. By increasing the amplitude of the inflow disturbance, nonlinear effects in the form of a relaxation type oscillation of the time signal of rho(u) are observed.

Maestrello, Lucio↗

Effect of spatial resolution on apparent sensitivity to initial conditions of a decaying flow as it becomes turbulent

Grids with 32(exp 3), 64(exp 3), and 128(exp 3) points are used in numerical solutions for a decaying flow. The sensitivity of initially neighboring solutions to small changes in initial conditions increases as the spatial resolution improves. A fourth-order finite-difference method is used for the solutions with 32(exp 3) and 64(exp 3) grid points, and a pseudospectral method is used for 128(exp 3) grid points. The latter solutions appear to be rather well-resolved, in spite of the formation of steep velocity gradients in the flow.

Deissler, Robert G.↗

Vapor condensation on liquid surface due to laminar jet-induced mixing: The effects of system parameters

The effects of system parameters on the interface condensation rate in a laminar jet induced mixing tank are numerically studied. The physical system consists of a partially filled cylindrical tank with a slightly subcooled jet discharged from the center of the tank bottom toward the liquid-vapor interface which is at a saturation temperature corresponding to the constant tank pressure. Liquid is also withdrawn from the outer part of the tank bottom to maintain the constant liquid level. The jet velocity is selected to be low enough such that the free surface is approximately flat. The effect of vapor superheat is assumed to be negligible. Therefore, the interface condensation rate can be determined from the resulting temperature field in the liquid region alone. The nondimensional form of the steady state conservation equations are solved by a finite difference method for various system parameters including liquid height to tank diameter ratio, tank to jet diameter ratio, liquid inflow to outflow area ratio, and a heat leak parameter which characterizes the uniform wall heat flux. Detailed analyses based on the numerical solutions are performed and simplified equations are suggested for the prediction of condensation rate.

Lin, Chin-Shun↗

On the application of subcell resolution to conservation laws with stiff source terms

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Chang, Shih-Hung↗

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗

A parametric heat transfer study for cryogenic ball bearings in SSME HPOTP

A numerical modeling is to examine the effects of coolant convective heat transfer coefficient and frictional heating on the local temperature characteristics of a ball element in Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP) bearing. The present modeling uses a control-volume based, finite-difference method to solve the non-dimensionalized heat conduction equation in spherical coordinate system. The dimensionless temperature is found as a function of Biot number, heat flux ratio between the two race contacts, and location in the ball. The current results show that, for a given cooling capability, the ball temperature generally increases almost linearly with the heat input from the race-contacts. This increase is always very high at one of the two contacts. An increase in heat transfer coefficient generally reduces the ball temperature and alleviates the temperature gradient, except for the regions very close to the race contacts. For a 10-fold increase of heat transfer coefficient, temperature decrease is 35 percent for the average over entire ball, and 10 percent at the inner-race contact. The corresponding change of temperature gradient displays opposing trends between the regions immediately adjacent to the contacts and the remaining portion of the ball. The average temperature gradient in the vicinity of both contacts increases approximately 70 to 100 percent. A higher temperature gradient produces excessive thermal stress locally which may be detrimental to the material integrity. This, however, is the only unfavorable issue for an increase of heat transfer coefficient.

Chyu, Mingking K.↗

Graphics applications utilizing parallel processing

The results are presented of research conducted to develop a parallel graphic application algorithm to depict the numerical solution of the 1-D wave equation, the vibrating string. The research was conducted on a Flexible Flex/32 multiprocessor and a Sequent Balance 21000 multiprocessor. The wave equation is implemented using the finite difference method. The synchronization issues that arose from the parallel implementation and the strategies used to alleviate the effects of the synchronization overhead are discussed.

Rice, John R.↗

Numerical investigation of the thermal stratification in cryogenic tanks subjected to wall heat flux

The flow pattern and thermal stratification of a cryogenic cylindrical tank are numerically studied. The tank sidewall is subjected to either a uniform heat-flux or two discrete levels of uniform heat-flux at the upper and lower halves of the tank wall. The tank bottom is kept at a constant temperature controlled by the heat exchanger of a thermodynamic vent system. The tank pressure is also assumed constant resulting in a constant saturation temperature at the interface which is higher than the tank bottom temperature. The effects of vapor motion and vapor superheat on the mass and heat transfer processes at the interface are assumed negligible such that the calculations of liquid region can be decoupled from the vapor region. Dimensionless steady-state conservation equations are solved by a finite-difference method. The effects of modified Rayleigh number, Prandtl number, tank aspect ratio, wall heat-flux parameter, and wall heat-flux distribution on the liquid velocity and temperature fields are investigated. Also, their effects on the rate of heat transfer through the interface and the tank bottom are examined.

Lin, Chin-Shun↗

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Numerical calculations of turbulent reattaching shear layers in a divergent channel are presented. The turbulence is described by a multiple-time-scale turbulence model. The turbulent flow equations are solved by a control-volume based finite difference method. The computational results are compared with those obtained using k-epsilon turbulence models and algebraic Reynolds stress turbulence models. It is shown that the multiple-time-scale turbulence model yields significantly improved computational results than the other turbulence models in the region where the turbulence is in a strongly inequilibrium state.

Kim, S.-W.↗

Efficient estimation of diffusion during dendritic solidification

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.

Yeum, K. S.↗

Vapor condensation on liquid surface due to laminar jet-induced mixing - The effects of system parameters

The effects of system parameters on the interface condensation rate in a laminar jet induced mixing tank are numerically studied. The physical system consists of a partially filled cylindrical tank with a slightly subcooled jet discharged from the center of the tank bottom toward the liquid-vapor interface which is at a saturation temperature corresponding to the constant tank pressure. Liquid is also withdrawn from the outer part of the tank bottom to maintain the constant liquid level. The jet velocity is selected to be low enough such that the free surface is approximately flat. The effect of vapor superheat is assumed to be negligible. Therefore, the interface condensation rate can be determined from the resulting temperature field in the liquid region alone. The nondimensional form of the steady state conservation equations are solved by a finite difference method for various system parameters including liquid height to tank diameter ratio, tank to jet diameter ratio, liquid inflow to outflow area ratio, and a heat leak parameter which characterizes the uniform wall heat flux. Detailed analyses based on the numerical solutions are performed and simplified equations are suggested for the prediction of condensation rate.

Lin, Chin-Shun↗

Global simulation of the solar wind-magnetosphere interaction - The importance of its numerical validity

This paper examines the global interaction of the solar wind with the geomagnetic field, using a newly developed three-dimensional high-precision MHD simulation code which employs the fourth-order Runge-Kutta-Gill scheme in time and the direct finite-difference method in space, and which allows much less numerical error than the conventional code. The simulation reveals in detail the formation processes of the magnetosphere and the bow shock, as well as the plasma sheet formation process. It is shown that, contrary to the conventional understanding, no Kelvin-Helmholtz instability occurs along the magnetopause in an ideal MHD.

Watanabe, K.↗

Analysis of the transient compressible vapor flow in heat pipes

The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual vapor flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds and high mass flow rates are successfully predicted. The one-dimensional model also describes the vapor flow dynamics in cylindrical heat pipes at high temperatures.

Jang, J. H.↗

Numerical investigation of the thermal stratification in cryogenic tanks subjected to wall heat flux

The flow pattern and thermal stratification of a cryogenic cylindrical tank are numerically studied. The tank sidewall is subjected to either a uniform heat-flux or two discrete levels of uniform heat-flux at the upper and lower halves of the tank wall. The tank bottom is kept at a constant temperature controlled by the heat exchanger of a thermodynamic vent system. The tank pressure is also assumed constant resulting in a constant saturation temperature at the interface which is higher than the tank bottom temperature. The effects of vapor motion and vapor superheat on the mass and heat transfer processes at the interface are assumed negligible such that the calculations of liquid region can be decoupled from the vapor region. Dimensionless steady-state conservation equations are solved by a finite-difference method. The effects of modified Rayleigh number, Prandtl number, tank aspect ratio, wall heat-flux parameter, and wall heat-flux distribution on the liquid velocity and temperature fields are investigated. Also, their effects on the rate of heat transfer through the interface and the tank bottom are examined.

Lin, Chin-Shun↗

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

Bodonyi, R. J.↗