A review of compressibility and rarefaction effects on spherical particle drag was conducted based on existing experimental data, theoretical limits, and direct simulation Monte Carlo method results. The data indicated a nexus point with respect to effects of Mach number and Knudsen number. In particular, it was found that a single drag coefficient (of about 1.63) is obtained for all particle conditions when the particle Reynolds number is about 45, and is independent of compressibility or rarefaction effects. At lower Reynolds numbers, the drag is dominated by rarefaction, and at higher Reynolds numbers, it is dominated by compressibility. The nexus, therefore, allows construction of two separate models for these two regimes. The compression-dominated regime is obtained using a modification of the Clift-Gauvin model to specifically incorporate Mach number effects. The resulting model was based on a wide range of experimental data and showed superior prediction robustness compared with previous models. For the rarefaction-dominated regime, the present model was constructed to directly integrate the theoretical creeping flow limits, including the incompressible continuum flow limit (Stokes drag), the incompressible weak rarefaction limit (Basset-Knudsen correction), and the incompressible free-molecular flow limit (Epstein theory). Empirical correlations are used to extend this model to finite particle Reynolds numbers within the rarefaction-dominated regime.

Compressibility and Rarefaction Effects on Drag of a Spherical Particle

In response to recent advances in numerical heat transfer research, the K-8 Committee of Theory and Fundamental Research of the ASME Heat Transfer Division has sponsored a symposium on the subject at the 1990 AIAA/ASME Thermophysics and Heat Transfer Conference in Seattle, Washington. This symposium volume contains the papers presented in three technical sessions. Works dealing with both the methodology and the results of numerical solutions of heat transfer problems are included in this volume. A large number of excellent manuscripts were submitted by researchers from this country and abroad. The papers collected here provide a representative cross section of current contributions to numerical methods in heat transfer.

Numerical heat transfer

An object-oriented serial implementation of a DSMC simulation package

Research on vacuum plume and its effects

Near-field plume-surface interaction and regolith erosion and dispersal during the lunar landing

In this paper, we investigate rarefied jet gas flows out of a circular exit impinging on a vertical flat plate. We employ a constraint relation about the velocity components of gas particles leaving a nozzle exit point and arriving at a given spatial point outside the nozzle. This relation leads to several analytical expressions for collisionless flow property distributions on the plate surface, including density, slip-velocity, temperature, pressure, shear stress, and heat flux. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical collisionless flow solutions. The impingement properties on the plate surface are accurate when the Knudsen number is large.

Surface properties for rarefied circular jet impingement on a flat plate

In this paper, we investigate highly rarefied jet gas flows out of a two-dimensional slit that impinges on a flat plate which is set vertically to the plume flow direction. The plate is assumed to be completely diffusive and the gaseous plume flow out of the slit is modeled with a Maxwellian distribution function which is characterized with known number density, nonzero exit velocity, and temperature. We present some analytical collisionless flow properties for a free plume and the impingement on the plate. The outcomes include simple results of the largest shear stress on the plate and the corresponding location. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical collisionless flow solutions.

Highly rarefied two-dimensional jet impingement on a flat plate

This paper presents exact density, velocity components, and temperature solutions for collisionless gasflows over a cylinder or a sphere. Possible real applications may include collisionless gas flows over a hot wire inside a vacuum chamber and rarefied gasflows aroundanaerosol at veryhigh altitude.At anypoint off the cylinder or the sphere, the local velocity distribution function consists of two pieces ofMaxwellian distribution functions: one for the freestream, which is characterized by the freestream density n0, temperature T0, and velocity U0; the other is characterized by density at the wall nw and wall temperature Tw, where nw is not constant at different surface locations. Directly integrating the distribution functions leads to the detailed flowfield solutions; the solutions are complex but exact.We performed numerical simulationswith the direct simulationMonteCarlomethod to validate these exact solutions. In general, the exact analytical and numerical results are virtually identical.

http://wordpress.nmsu.edu/mjwei/files/2014/06/sphere_cylinder_JSR_09.pdf

Collisionless Gas Flows over a Cylindrical or Spherical Object

This paper analyzes compressible gaseous slip flow through a three‐dimensional straight uniform rectangular microchannel, and reports a set of asymptotic solutions. By comparing the magnitudes of different forces in the compressible gas flow, we obtain a proper criteria to estimate the Reynolds and Mach numbers at the channel exit. We select two sets of Mach and Reynolds numbers and obtain asymptotic analytical solutions of velocities and pressure distributions; first order velocity slip and non‐slip boundary conditions are examined. The analytical results of pressure and velocities are compared with numerical simulation results of direct simulation Monte Carlo method and the results that are available in the literature.

https://eis.hu.edu.jo/deanshipfiles/conf110071118.pdf

Gaseous Slip Flow in Three‐Dimensional Uniform Rectangular Microchannel

A newly developed three‐dimensional direct simulation Monte Carlo (DSMC) simulation package, named GRASP (“Generalized Rarefied gAs Simulation Package”), is reported in this paper. This package utilizes the concept of simulation engine, many C++ features and software design patterns. The package has an open architecture which can benefit further development and maintenance of the code. In order to reduce the engineering time for three‐dimensional models, a hybrid grid scheme, combined with a flexible data structure compiled by C++ language, are implemented in this package. This scheme utilizes a local data structure based on the computational cell to achieve high performance on workstation processors. This data structure allows the DSMC algorithm to be very efficiently parallelized with domain decomposition and it provides much flexibility in terms of grid types. This package can utilize traditional structured, unstructured or hybrid grids within the framework of a single code to model arbitrarily complex...

http://www2.aero.psu.edu/RGD_2010/PaperSubmission_Full_Uploads/Hongli,%20Liu_332_revised2.pdf

Hongli Liu

Papers

Surface properties for rarefied circular jet impingement on a flat plate

Highly rarefied two-dimensional jet impingement on a flat plate

Collisionless Gas Flows over a Cylindrical or Spherical Object

Gaseous Slip Flow in Three‐Dimensional Uniform Rectangular Microchannel

An Object-Oriented Serial DSMC Simulation Package