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Knudsen Numbers (knudsen + number)

Distribution by Scientific Domains
Engineering60%

Selected Abstracts

The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2002
J.-S. Wu
Abstract The implementation of an adaptive mesh-embedding (h-refinement) scheme using unstructured grid in two-dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an-isotropic refinement in the interfacial cells between refined and non-refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high-speed driven cavity flow. The results show an improved flow resolution as compared with that of un-adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near-continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non-uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Acoustic limit for the Boltzmann equation in optimal scaling

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2010
Yan Guo
Based on a recent L2 , L, framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to the Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions. © 2009 Wiley Periodicals, Inc. [source]

Empirical slip and viscosity model performance for microscale gas flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005
Matthew J. McNenly
Abstract For the simple geometries of Couette and Poiseuille flows, the velocity profile maintains a similar shape from continuum to free molecular flow. Therefore, modifications to the fluid viscosity and slip boundary conditions can improve the continuum based Navier,Stokes solution in the non-continuum non-equilibrium regime. In this investigation, the optimal modifications are found by a linear least-squares fit of the Navier,Stokes solution to the non-equilibrium solution obtained using the direct simulation Monte Carlo (DSMC) method. Models are then constructed for the Knudsen number dependence of the viscosity correction and the slip model from a database of DSMC solutions for Couette and Poiseuille flows of argon and nitrogen gas, with Knudsen numbers ranging from 0.01 to 10. Finally, the accuracy of the models is measured for non-equilibrium cases both in and outside the DSMC database. Flows outside the database include: combined Couette and Poiseuille flow, partial wall accommodation, helium gas, and non-zero convective acceleration. The models reproduce the velocity profiles in the DSMC database within an L2 error norm of 3% for Couette flows and 7% for Poiseuille flows. However, the errors in the model predictions outside the database are up to five times larger. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Reducing energy availability losses with open parallel microchannels embedded in a micropatterned surface

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 13 2005
G. F. Naterer
Abstract This article develops a new technique of reducing exergy losses of external viscous flow over surfaces, based on optimized microchannels embedded within the surface. The rate of entropy production and loss of available optimized energy are formulated by an integral solution and modified Blasius profiles of boundary layer flow. The optimized number of microchannels, width and height of each microchannel and spacing between microchannels involve a selective compromise between added heat exchange due to surface area, together with reduced friction through slip conditions within each microchannel. Mixed Knudsen numbers across each microchannel require simultaneous modelling of both slip-flow and no-slip conditions at the wall. Results involving the minimal entropy production and optimized microchannel profiles are presented and compared to other benchmark results involving classical macro-scale configurations. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Hydrodynamic limits with shock waves of the Boltzmann equation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2005
Shi-Hsien Yu
We show that piecewise smooth solutions with shocks of the Euler equations in gas dynamics can be obtained as the zero Knudsen number limit of solutions of the Boltzmann equation for hard sphere collision model. The construction of the Boltzmann solutions is done in two steps. First we introduce a generalized Hilbert expansion with shock layer correction to construct approximations to the solutions of the Boltzmann equations with small Knudsen numbers. We then apply the recently developed macro-micro decomposition and energy method for Boltzmann shock layers to construct the exact Boltzmann solutions through the stability analysis. © 2004 Wiley Periodicals, Inc. [source]