Fully consistent CFD methods for incompressible flow computations

D K Kolmogorov,J N Sørensen,N N Sørensen,W Z Shen

doi:10.1088/1742-6596/524/1/012128

Abstract

Nowadays collocated grid based CFD methods are one of the most efficient tools for computations of the flows past wind turbines. To ensure the robustness of the methods they require special attention to the well-known problem of pressure-velocity coupling. Many commercial codes to ensure the pressure-velocity coupling on collocated grids use the so-called momentum interpolation method of Rhie and Chow [1]. As known, the method and some of its widely spread modifications result in solutions, which are dependent of time step at convergence. In this paper the magnitude of the dependence is shown to contribute about 0.5% into the total error in a typical turbulent flow computation. Nevertheless if coarse grids are used, the standard interpolation methods result in much higher non-consistent behavior. To overcome the problem, a recently developed interpolation method, which is independent of time step, is used. It is shown that in comparison to other time step independent method, the method may enhance the convergence rate of the SIMPLEC algorithm up to 25 %. The method is verified using turbulent flow computations around a NACA 64618 airfoil and the roll-up of a shear layer, which may appear in wind turbine wake.

Highlights

During the last decade a large effort has gone into developing CFD tools for prediction of wind turbine aerodynamics
As will be later seen in the result section, if the Momentum Interpolation method (MMI) method is applied with SIMPLEC algorithm, it becomes advantageous in the convergence speed over other time step independent interpolation method
An idealized case of a shear layer, which appears in wind turbine wake, is computed at Re = 100 using SIMPLEC algorithm and the MMI interpolation method in Eq (4)

Summary

Introduction

During the last decade a large effort has gone into developing CFD tools for prediction of wind turbine aerodynamics. Nowadays in spite of the existence of the time step independent methods, the standard methods of Choi and Shen et al are widely used as can be seen in example in [26,27,28,29] On collocated grids both the solution accuracy and the convergence rate of the SIMPLE-like algorithms strictly depend on the choice of the interpolation method. Standard interpolation methods on collocated grids, such as the methods of Choi [21] and Shen et al [19], are known to result in solution, dependent of time step at convergence. There exist several interpolation methods on collocated grids, resulting in solutions, independent of time step at convergence [20, 22,23,24,25]. As will be later seen in the result section, if the MMI method is applied with SIMPLEC algorithm, it becomes advantageous in the convergence speed over other time step independent interpolation method

Results

Roll-up of a shear layer vortex

Turbulent flow around a NACA 64618 airfoil

Conclusions