Session: 09-01: Computational Methods in Micro/ Nanoscale Transport

Paper Number: 132089

132089 - Developing Code_saturne for Advanced Micro-Scale Gas Transport 

Abstract: 

Non-equilibrium gas flows represent a fundamental modelling challenge and exist in many industrial applications and scientific research facilities, including mass spectrometry, low-pressure environments, vacuum pumps, micro-electro-mechanical systems (MEMS), high-altitude vehicles, and porous media. The extent of the non-equilibrium state is usually measured by the Knudsen number,Kn, which is the ratio of the gas molecular mean free path to the characteristic macroscopic length scale of the flow. If the Knudsen number is very small (Kn<0.001), continuum theory is considered to be valid and the no-slip boundary condition can be applied i.e. the Navier-Stokes-Fourier (NSF) equations can be used in the prediction of flowfields. When the Knudsen number lies in the range (0.001<Kn<0.1), the flow is in the slip regime and the NSF equations can only be used if the wall boundary conditions are modified to account for velocity-slip and temperature-jump. For (0.1<Kn<10), the flow enters the transition regime and the NSF equations are no longer able to predict the flow field with any degree of accuracy. Kinetic theory approaches, such as the Boltzmann equation or direct simulation Monte Carlo (DSMC), can be used in this regime. For the Boltzmann equation, the complexity of the collision term makes it difficult to use in all but simple problems. In the case of DSMC, the computational cost is prohibitive and, apart from the flow with high, simulations are limited to 2-D and low-speed problems can take weeks to solve. When Kn>10, the flow is in the free-molecular regime and molecular collisions can be ignored. Without collisions, kinetic methods offer a computationally efficient approach. However, in the early transition regime(0.1<Kn<1), the moment method offers the best approach for capturing rarefied phenomena. More physics is embedded in the moment equations than in the NSF equations with only a modest increase in computational cost.
We have successfully demonstrated that the moment equations can be used to study a range of classic problems including Couette flow, Poiseuille flow, and Kramers’ problem which have all been studied theoretically. Numerical investigations of 2-D-driven cavity flow and flow past a circular cylinder have demonstrated that the moment method has great potential. However, there is currently no software available that can solve non-equilibrium flows in the early transition regime (0.1<Kn<1) in 3-D complex geometries with a computational efficiency similar to conventional computational fluid dynamics (CFD) problems. An understanding of the flow in the transition regime is essential to design, predict, and operate a wide range of practical devices. It is now timely and beneficial to develop software which will bridge the gap between the continuum approach and kinetic theory. The open-source CFD software, Code_Saturne [1], provides a well-defined and flexible platform to solve moment equations. It already has a wide and growing range of academic and industrial users and this enhancement will expand its capability into a new research and industrial dimension by developing and implementing a rarefied gas dynamics module with the moment equations.
We will present the development of the moment method in the well-established open-source software, Code_Saturne. Detailed computed results for Poiseuille flow, lid-driven cavity flow, thermally induced flow and flow past a square cylinder will be given to validate the implementation.

[1] Y. Fournier, J. Bonelle, C. Moulinec, Z. Shang, A. Sunderland, J. Uribe, Optimizing Code_Saturne computations on Petascale systems. Computers & Fluids (2011) 45:103-108.

Presenting Author: Xiao-Jun Gu Scientific Computing Department, STFC Daresbury Laboratory

Presenting Author Biography: Professor Xiaojun Gu is a principal scientist in the Scientific Computing Department of STFCDaresbury Laboratory and a visiting Professor at the University of Leeds with experience in modelling and simulating a broad range of fluid dynamic problems. He is a recipient of the Sugden Award from the Combustion Institute (British Section) for significant contributions to combustion research. His pioneering work on extended thermodynamics into MEMS has been well-recognised internationally.

Authors:

Xiao-Jun Gu Scientific Computing Department, STFC Daresbury Laboratory
Adam Greenbank STFC Daresbury Labotratory
Charles Moulinec Scientific Computing Department, STFC Daresbury Laboraotry
David R Emerson Scientific Computing Department