Simulation of two-Dimensional Supersonic Flow in Slip Regime in Microchannel with Finite Difference Lattice Boltzmann Method

Barootiha, Hamed | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41830 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, the simulation of two-dimensional supersonic flows through microchannels in slip flow regime is performed using a lattice Boltzmann model (LBM). Traditional LB models have been used to simulate incompressible fluid flows and there are not suitable for modeling compressible or thermo-fluid flows. Herein, a recently developed LB model, namely, the finite difference lattice Boltzmann method (FDLBM), is employed to simulate compressible flows with embedded shocks. In this model, one can select particle velocities independently from the lattice configuration, and therefore, a correct and numerically stable multispeed thermal model by adopting more isotropic particle velocities can be constructed. In FDLBM, particle velocities of octagonal directions are adopted which have up to seventh rank isotropic tensors and thus it can cover the compressible Navier-Stokes equations. In FDLBM, the convection term in the Boltzmann equation can be discretized using usual finite-difference schemes. In the present study, we use two finite-difference schemes, namely 1) second-order Lax-Wendroff method employing suitable dissipation and dispersion terms and 2) fourth-order compact scheme employing linear/nonlinear filters, for discretizing the convection term in the Boltzmann equation. The effects of linear/nonlinear filters on the accuracy of the results obtained by the compact finite-difference Lattice Boltzmann method (CFDLBM) developed are also examined For modeling fluid flows in complex geometries, we also solve FDLBM in curvilinear coordinates by mapping the Boltzmann equation from the physical space to the computational space. In addition, the implementation of different boundary conditions is explained and specifically the diffuse reflection boundary condition for simulation of slip flow regime using FDLBM is described. The accuracy and efficiency of both the second-order Lax–Wendroff and fourth-order compact schemes are examined by simulating shock tube and shock density wave interaction problems. Results for supersonic flow over a ramp and in a channel with circular arc bump are given to demonstrate the capability of the present methodology in calculating problems in curvilinear coordinates. The simulation of supersonic viscous flow in a 2D microchannel in slip flow regime is also performed for different Knudsen numbers to demonstrate the accuracy of FDLBM in predicting rarefied gas flow. Results obtained for these cases are in good agreement with the available theoretical and numerical results. The study shows the scheme is efficient and accurate for solving compressible flows in continuum and slip flow regime
  9. Keywords:
  10. Compressible Flow ; Slip Flow ; Microchannel ; Curvilinear Coordinates ; Finite Difference Lattice Boltzmann Method

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