Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls

Abstract

AbstractInterest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo‐spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant‐property, turbulent fluid in a two‐dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions.Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half‐height of 180 or 2800 based on channel half‐height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two‐point velocity correlations are given.Deficiencies are that the calculation requires many hours on a fast computer with a large high‐speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.