Calculation of turbulent shear stress, heat flux, mass flux, and mixing length from mean flow measurements

Abstract

A numerical technique to calculate the turbulent mass flux, shear stress, heat flux, and mixing length directly from measurable mean flow quantities is presented. The development of this technique was motivated by the desire to make aero-optical calculations based directly on experimentally obtained mean flow data. The technique is based .upon the direct integration of the Navier-Stokes equations of compressible turbulent flow. The results of the integrations are the shear stress, heat flux, mass flux and mixing length distributions, (Le., all data that are necessary for application of the Aero-Optical Quality Code (AOQ). equations without appropriate closure assumptions and models. However, by restricting attention to twodimensional shear flows a reduced set of integrable equations which do not require closure assumptions is obtained. As first proposed by J.C. Rotta of Reference 5 and further developed in Schlichting (Reference 6) and Brown and Roshko (Reference 7) a reduced set of equations can be obtained. By straightforward extensions of the assumptions in these references, the Reynolds-averaged equations of continuity, specie conservatibn, x-momentum, ymomentum, and energy for turbulent compressible flow of an ideal binary gas mixture in a two-dimensional boundary layer or mixing layer are given in Table 1. Jntroduct ioQ If an experimental data set containing the measurements of the velocity (E) and density (P) In this paper. the direct integration technique is distributions is available, Equation 1, may be solved for examined. It is determined that the method presents a __ reasonable alternative to the very complex task of direct p * V ' . This together with the measurement of experimental measurement of shear mess (7'xy). mass flux concentration of specie A (Ti). can be used to solve for (J'A,.). heat flux (q',.). and mixing length. It has the added. J'Q in Equation 2. Likewise, knowledge of p 'Y' allows advantage of making prior experiments, in which only mean Equation 3 to be solved for . T ' ~ ~ . Further, measurements flow measurements data were acquired. useful for aeroof the temperature (T) distribution and knowledge of optical analysis code validation. In addition, the direct integration method can provide a useful consistency check p ' V I J ' A ~ , and 7lXy allow computation of q',. from on those experiments for which the turbulence transport Equalon 5, quantities have been measured. -