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Cavity

CFD course project (Dr. Mashayek) Fall 2012
by

Zia Ghiasi

on 3 December 2012

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Transcript of Cavity

Formulation Variable Time Step Time Developing Flow in a Driven Cavity Seyyed Ziaoddin Ghiasi
Computational Fluid Dynamics
Prof. Farzad Mashayek
Fall 2012 Lid Driven Cavity Governing Equations Navier-Stokes Equations Nondimensionalizing Domain Discretization MAC method location of pressure and
velocity components
related to cells Equation Discretization How to label variables
for each cell Using FTCS discretization Viscous Terms Convective Terms Pressure Acceleration To calculate pressure in new time step Poisson
Solver Boundary Condition Use ghost cells to satisfy boundary conditions velocity pressure no penetration no slip Use Momentum and Continuity eqs. Algorithm Variable Mesh Scalar Transport Equation Additional Features CFL Two districtions for time step: Calculate CFL condition at each time step Start with a coarse mesh and increase number grids as marching in time Helps Poissin solver to converge faster at first time steps Convection Diffusion FTCS Discretization Explicit Solution for T: is solved at each time steps substituting Verifying The Results one-sided cavity two-sided cavity mid-plane u velocity for Re=400 Re=400 u at different x's v at different y's Flow Pattern one-sided two-sided one-sided two-sided Stability Accuracy mid-plane u velocity for one-sided cavity at Re=10 Movies Streamlines
Re=10,000 Vorticity
Re=10,000 Streamlines
Re=1,000 Vorticity
Re=1,000 Tansport Scalar
Re=1,000 Transport Scalar
Re=100 Transport Scalar
Re=1,000 Transport Scalar
Re=100 Transport Scalar
Re=1,000 one-sided cavity with n=100 Compare Variable Time Step Compare Variable Mesh one-sided cavity with n(max)=100 Thank you for your attention! Substituting in
Navier-Stokes to be solved... Streamlines
Re=3,200 Different Boundary Conditions mid-plane u
two-sided
Re=400
Full transcript