On the Mixture Length and Shearing Stress Distribution in the Turbulent Boundary Layer with a Pressure Gradient

Abstract

The writers previously investigated the mixture length and shearing stress distribution in divergent and convergent flows of Nikuradse as typical flow under pressure gradient. The present paper is the extension of the former to general boundary layer flow. First of all they study an approximate expression of shearing stress distribution in the near wall region and show an advantage of using the effective pressure gradient instead of its nominal value. This idea is based on the correction due to acceleration terms in equation of motion. Through analogy to channel flows, they assume approximate distributions of mixture length and shearing stress in simple analytical forms as functions of η and β_<δe>. The notation used is listed below. By substituting the above quantities in their modified momentum relation velocity distribution is calculated. By the proper choice of β_<δe>, which is approximately a function of β_δ only, a fairly good agreement between calculated and observed results is obtained. This fact also implies that both the idea of the effective pressure gradient and expressions of mixture length and shearing stress distributions are proper in practical purpose. It is finally suggested that the ordinary method of solution using outer law of velocity distribution may be usefully improved by the adoption of the effective pressure gradient.