Internal Report

Direct numerical simulation of turbulent flow in plane and cylindrical geometries

Author Document Type Year Download File size
Jukka Komminaho Doctoral thesis 2000 Download 2.6 Mb
ISSN 0348-467X


This thesis deals with numerical simulation of turbulent flows in geometrically simple cases. Both plane and cylindrical geometries are used. The simplicity of the geometry allows the use of spectral methods which yield a very high accuracy using relatively few grid points. A spectral method for plane geometries is implemented on a parallel computer. The transitional Reynolds number for plane Couette flow is verified to be about 360, in accordance with earlier findings. Turbulent Couette flow at twice the transitional Reynolds number is studied and the findings of large scale structures in earlier studies of Couette flow are substantiated. These large structures are shown to be of limited extent and give an integral length scale of six half channel heights, or about eight times larger than in pressure-driven channel flow. Despite this, they contain only about 10% of the turbulent energy. This is demonstrated by applying a very small stabilising rotation, which almost eliminates the large structures. A comparison of the Reynolds stress budget is made with a boundary layer flow, and it is shown that the near-wall values in Couette flow are comparable with high-Reynolds number boundary layer flow. A new spectrally accurate algorithm is developed and implemented for cylindrical geometries and verified by studying the evolution of eigenmodes for both pipe flow and annular pipe flow. This algorithm is a generalisation of the algorithm used in the plane channel geometry. It uses Fourier transforms in two homogeneous directions and Chebyshev polynomials in the third, wall-normal, direction. The Navier--Stokes equations are solved with a velocity-vorticity formulation, thereby avoiding the difficulty of solving for the pressure. The time advancement scheme used is a mixed implicit/explicit second order scheme. The coupling between two velocity components, arising from the cylindrical coordinates, is treated by introducing two new components and solving for them, instead of the original velocity components. The Chebyshev integration method and the Chebyshev tau method is both implemented and compared for the pipe flow case.