Colocated-grid finite volume formulation for the large eddy simulation of incompressible and compressible turbulent flows
Date
1998
Authors
Chidambaram, Narayanan
Major Professor
Advisor
Pletcher, Richard H.
Committee Member
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Abstract
A colocated-grid finite volume scheme has been developed for large eddy simulations of both incompressible and compressible low speed flows. The algorithm solves the Favre filtered Navier-Stokes system of equations in a fully coupled and implicit manner with the use of a time derivative preconditioning technique to enable computation of nearly incompressible flows. Basic schemes such as the second-order and fourth-order central difference and an upwind scheme were implemented, so as to finally select an appropriate scheme for future large eddy simulations of complex flows. A modification called the momentum-interpolation correction was also implemented in order to overcome the pressure-velocity decoupling problems typical of colocated-grid algorithms.
The schemes were evaluated using both two-dimensional laminar test cases and by performing a large eddy simulation tracking the evolution of an isotropic decaying turbulence field. The basic algorithm was validated by simulating the lid-driven and buoyancy-driven cavity flows. The momentum-interpolation correction to the basic schemes, was necessary to alleviate the pressure-velocity decoupling problem found in all the different schemes tried. The large eddy simulation of an isotropic decaying turbulence showed that the upwind scheme was very dissipative in the higher wave numbers as compared to the central difference schemes which captured the three-dimensional energy spectra significantly better. Both the Smagorinsky and dynamic sub-grid scale models were tried. The Smagorinsky model was found to perform better. For the central difference schemes, the dynamic model resulted in some accumulation of energy at the smaller scales.
Behavior of the different schemes was explained using a truncation error analysis. It was found that the fourth-order central difference scheme was not energy-preserving. Criteria for creating and testing new higher-order accurate schemes were suggested. Finally, the large eddy simulation was performed using the second-order central difference scheme with the momentum-interpolation correction. This scheme was found to give very good agreement with the experimental data. The performance of the dynamic model was much improved with this scheme. It was concluded that the second-order central difference in conjunction with the momentum-interpolation scheme was the most appropriate scheme from among the schemes tested.
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thesis