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NASA NTRS1982

Heat loss and drag of spherical drop tube samples

Analysis techniques for three aspects of the performance of the NASA/MSFC 32 meter drop tube are considered. Heat loss through the support wire in a pendant drop sample, temperature history of a drop falling through the drop tube when the tube is filled with helium gas at various pressures, and drag and resulting g-levels experienced by a drop falling through the tube when the tube is filled with helium gas at various pressures are addressed. The developed methods apply to systems with sufficiently small Knudsen numbers for which continuum theory may be applied. Sample results are presented, using niobium drops, to indicate the magnitudes of the effects. Helium gas at one atmosphere pressure can approximately double the amount of possible undercooling but it results in an apparent gravity levels of up to 0.1 g.

Wallace, D. B.↗

NASA NTRS1981

Insights into the gas dynamics in galaxies via a particle model

Techniques of rarefied gas dynamics are applied to the astrophysical problem of gas flow in disk galaxies. Historically, studies of the interstellar gas dynamics in spiral galaxies have assumed the medium could be regarded as both isothermal and continuous. However, it now appears that the gaseous interstellar medium may be better idealized as a rarefied gas or discrete system of interacting particles. Principal evidence for this is that the galaxies themselves exhibit a degree of disorder and raggedness that is characteristic of a rarefied gaseous system with a Knudsen number of approximately 0.02-0.2. In this paper a particle model for gas flow in a spiral galaxy is developed and some implications of the results are discussed. The results are compared to an analytical inviscid calculation to gain further physical insight.

Levinson, F. H.↗

NASA NTRS1983

The collapse of the local, Spitzer-Haerm formulation and a global-local generalization for heat flow in an inhomogeneous, fully ionized plasma

The breakdown of the classical (CBES) field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma as a mathematical issue of radius of convergence is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined. This paper shows the relationship to and points of departure of the present work from the CBES approach. The CBES heat law in current use is shown to be an especially restrictive special case of the new, more general GL result. A preliminary evaluation of the dimensionless heat function, using analytic formulas, shows that the dimensionless heat function profiles versus density of the type necessary for a conduction supported high speed solar wind appear possible.

Scudder, J. D.↗

NASA NTRS1986

Rarefied aerodynamics and upper atmosphere density from multiple orbiter flight measurements

Flight data from six flights of the experimental High Resolution Accelerometer Package (HIRAP), a micro-g accelerometer system, have been analyzed to produce rarefied flow aerodynamic coefficients of the Orbiter and freestream density in the altitude range from 60 km to 160 km. The direct measurements of the lift to drag ratio (L/D) are used to obtain individual normalized body-axis force coefficients in a least-squares regression scheme. An aerodynamics model based on an exponential function of Knudsen number is used for the individual coefficients. The calculated L/D from the flight determined coefficients agree with the multiple flight data measurements to within about 5 percent. Simultaneously, an upper altitude density variation is also obtained from the data. Density altitude profiles exhibit a wave feature on all flights. The wave has an amplitude of about + or - 25 percent relative to the 1962 Standard atmosphere model.

Buck, G. M.↗

NASA NTRS1986

The diffusion of individual molecules within a gas

The Direct Simulation Monte Carlo method is used to study the positional history of the individual molecules in a gas that is homogeneous at the macroscopic level and is in Maxwellian equilibrium at the microscopic level. The behavior at small times is characterized by 'persistence of velocity' effects, and a 'random walk' type of dispersal occurs over a longer timescale. It is shown that the rate of dispersal can be directly related to the self-diffusion coefficient. In addition, the diffusion coefficients are obtained directly from one-dimensional calculations, and the local Knudsen number at which the Chapman-Enskog theory breaks down is determined. Results are presented for both simple gases and gas mixtures.

Bird, G. A.↗

NASA NTRS1988

Rarefied flow past a flat plate at incidence

Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 deg incidence. The plate has zero thickness and a length of 1.0 m. The flow conditions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8.4, i.e., conditions that encompass most of the transitional flow regime. The DSMC simulations show that transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calculations show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag ratio by 90 percent over the free molecule value.

Dogra, Virendra K.↗

NASA NTRS1989

Rarefied gas flow through two-dimensional nozzles

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

De Witt, Kenneth J.↗

NASA NTRS1989

Side-wall gas 'creep' and 'thermal stress convection' in microgravity experiments on film growth by vapor transport

While 'no-slip' boundary conditions and the Navier-Stokes equations of continuum fluid mechanics have served the vapor transport community well until now, it is pointed out that transport conditions within highly nonisothermal ampoules are such that the nonisothermal side walls 'drive' the dominant convective flow, and the familiar Stokes-Fourier-Fick laws governing the molecular fluxes of momentum, energy, and (species) mass in the 'continuum' field equations will often prove to be inadequate, even at Knudsen numbers as small as 0.001. The implications of these interesting gas kinetic phenomena under microgravity conditions, and even under 'earth-bound' experimental conditions, are outlined here, along with a tractable approach to their systematic treatment.

Rosner, Daniel E.↗

NASA NTRS1989

Transition regime droplet growth and evaporation - An integrodifferential variational approach

A variational principle based on the integrodifferential form of the Boltzmann equation, which allows very general forms of the collision integral and of the boundary operator, has been used to compute the mass flux to a spherical particle. For simplicity the problem has been restricted to the one-speed, constant cross-section approximation, the black sphere problem of neutron transport theory. Using the Hilbert expansion of the solution far from the sphere as a trial function leads to a rational expression in the inverse Knudsen number for the extrapolation distance, which is simply related to the number flux to the sphere. A five-term expansion gives results that are no more than 6 percent in error when compared to an accurate numerical solution. The technique can be applied to other forms of the collision model and other boundary conditions.

Cipolla, J. W., Jr.↗

NASA NTRS1989

Rarefied flow past a flat plate at incidence

Dogra, Virendra K.↗

NASA NTRS1990

A continuous proportional low-thrust propulsion system

Helium gas flows continuously from a low-temperature dewar supplying propellant for satellite thrusters. Thrust is obtained by movement of a spool located between two opposing nozzles, thus differentially restricting the helium flow. The design procedure and test results of a high bandwidth, low power, linear electromagnetic actuator for the pool movement are presented. Two mathematical models are used to describe the helium flow through the thruster under different flow conditions. The experimental data measured in the vacuum chamber and the computational results from the mathematical models are compared. The models agree with the experiment to 3 percent except near a Knudsen number of 1.

Chen, J.-H.↗

NASA NTRS1991

Skin friction and heat transfer correlations for high-speed low-density flow past a flat plate

The independent and dependent variables associated with drag and heat transfer to a flat plate at zero incidence in high-speed, rarefied flow are analyzed anew to reflect the importance of kinetic effects occurring near the plate surface on energy and momentum transfer, rather than following arguments normally used to describe continuum, higher density flowfields. A new parameter, the wall Knudsen number Knx,w, based on an estimate of the mean free path length of molecules having just interacted with the surface of the plate, is introduced and used to correlate published drag and heat transfer data. The new parameter is shown to provide better correlation than either the viscous interaction parameter X or the widely-used slip parameter Voo for drag and heat transfer data over a wide range of Mach numbers, Reynolds numbers, and plate-to-freestream stagnation temperature ratios.

Woronowicz, Michael S.↗

NASA NTRS1991

An efficient DSMC algorithm applied to a delta wing

A new algorithm for 3D direct simulation Monte Carlo (DSMC) is tested and numerical results are compared with wind tunnel data and results obtained earlier with a more traditional DSMC code. The test case is the flowfield around a delta wing at incidence at Knudsen number of 0.016 and Mach number of 20.2. The results are shown to compare favorably with both experimental and earlier numerical results. The new algorithm is described with special emphasis placed on its distinctive features: Cartesian/unstructured combination grid, special body surface definition, discretization in physical space.

Rault, D. F. G.↗

NASA NTRS1992

Perspectives on hypersonic viscous and nonequilibrium flow research

An attempt is made to reflect on current focuses in certain areas of hypersonic flow research by examining recent works and their issues. Aspects of viscous interaction, flow instability, and nonequilibrium aerothermodynamics pertaining to theoretical interest are focused upon. The field is a diverse one, and many exciting works may have either escaped the writer's notice or been abandoned for the sake of space. Students of hypersonic viscous flow must face the transition problems towards the two opposite ends of the Reynolds or Knudsen number range, which represents two regimes where unresolved fluid/gas dynamic problems abound. Central to the hypersonic flow studies is high-temperature physical gas dynamics; here, a number of issues on modelling the intermolecular potentials and inelastic collisions remain the obstacles to quantitative predictions. Research in combustion and scramjet propulsion will certainly be benefitted by advances in turbulent mixing and new computational fluid dynamics (CFD) strategies on multi-scaled complex reactions. Even for the sake of theoretical development, the lack of pertinent experimental data in the right energy and density ranges is believed to be among the major obstacles to progress in aerothermodynamic research for hypersonic flight. To enable laboratory simulation of nonequilibrium effects anticipated for transatmospheric flight, facilities capable of generating high enthalpy flow at density levels higher than in existing laboratories are needed (Hornung 1988). A new free-piston shock tunnel capable of realizing a test-section stagnation temperature of 10(exp 5) at Reynolds number 50 x 10(exp 6)/cm is being completed and preliminary tests has begun (H. Hornung et al. 1992). Another laboratory study worthy of note as well as theoretical support is the nonequilibrium flow experiment of iodine vapor which has low activation energies for vibrational excitation and dissociation, and can be studied in a laboratory with modest resources (Pham-Van-Diep et al. 1992).

Cheng, H. K.↗

NASA NTRS1992

Aerodynamic characteristics of a hypersonic viscous optimized waverider at high altitudes

The present paper addresses the applicability of the basic concept of waveriding at high altitudes, and the extent to which the large viscous forces degrade the aerodynamic performance of waveriders. The waverider under consideration was designed using a continuum flow methodology. It is shown that the lift-to-drag ratio of high-altitude/high-Knudsen-number waveriders can be expected to be significantly lower than their low altitude/low Knudsen number counterparts. The aerodynamic performance of a representative waverider which was optimized for a 90-km, Mach-25 application is studied for altitudes ranging from 97 km to 145 km and incidence angles of 0 to 30 deg. Typical values of the lift-to-drag ratio were computed to be in the range of 0 to 0.3. Friction forces are mostly responsible for this poor performance. Friction forces account for more than 93 percent of the drag and significantly reduce lift.

Rault, Didier F. G.↗

NASA NTRS1992

Three dimensional particle simulation of high altitude rocket plumes

The interaction of two nozzles exhausting into vacuum generates a complex three-dimensional shock structure. The shock structure and resulting plume flowfield is characterized by the nozzle separation distance. For the appropriate range of penetration Knudsen numbers, the analysis of this shock structure can be suitably accomplished through a Monte Carlo simulation. This paper describes the application of a general three-dimensional Monte Carlo simulation on the Connection Machine CM-2 to the analysis of the plume self-interaction shock in the near field. Results are presented for two cases, corresponding to a small and a large nozzle separation distance. The results correctly reproduce the expected flow features and demonstrate the ability of this method to properly simulate the start of the plume self-interaction shock. This has significance not only for allowing analysis of the self-interacting plume in the near field, but also for allowing the subsequent simulation of the far field flow through the use of a continuation downstream exit boundary.

Dagum, Leonardo↗

NASA NTRS1993

Zonally-decoupled DSMC solutions of hypersonic blunt body wake flows

Direct simulation Monte Carlo (DSMC) solutions are presented for the hypersonic flow behind a blunt body in which the wake region is solved in a zonally-decoupled manner. The forebody flow is solved separately using either a DSMC or a Navier-Stokes method, and the forebody exit plane solution is specified as the inflow condition to the decoupled DSMC solution of the wake region. Results are presented for a 70-deg, blunted cone at flow conditions that can be accommodated in existing low-density wind tunnels with the Knudsen number based on base diameter ranging from 0.03 to 0.001. The zonally-decoupled solutions show good agreement with fully-coupled DSMC solutions of the wake flow densities and velocities. The wake closure predicted by the zonally-decoupled solutions is in better agreement with fully-coupled results than that predicted by a fully-coupled Navier-Stokes method indicating the need to account for rarefaction in the wake for the cases considered. The combined use of Navier-Stokes for the forebody with a decoupled DSMC solution for the wake provides an efficient method for solving transitional blunt-body flows where the forebody flow is continuum and the wake is rarefied.

Wilmoth, Richard G.↗

NASA NTRS1993

Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers

Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗