Statistics of high-speed turbulent wake boundaries.

Abstract

Some statistical characteristics of high-speed turbulent wake boundaries are presented. These were obtained by measuring the detailed turbulence outline structure appearing in shadowgraphs of three cone and three sphere wakes. The data cover downstream distances from 16 to 5000 body diam; freestream Reynolds numbers U m d/v m for the six cases range from 0.25(10 6 ) to 2(10 6 ). Statistical parameters measured include standard deviation and autocorrelation function of front deviations about the mean, correlation microscale, and intermittency factor. It is found that the random boundary structure of high-speed wakes produced by axisymmetric bodies has the same correlation function and probability distribution about the mean as a low-speed, two-dimensional boundary layer. Use of a Lagrangian model for front displacements perpendicular to the wake axis enables relationships between outline statistics and wake turbulence parameters to be obtained. Estimates are made thereby of turbulence dissipation rate, Kolmogoroff and energy-containing wave numbers, and the Lagrangian time integral scale. Results from these estimates allow some comparisons with low-speed experiments and other schlieren and shadowgraph diagnostic techniques to be made. Nomenclature 6= Jwake half-width, averaged over a sample d = body diameter (cm) kd = Kolmogoroff wave number (cm" 1 ) k e = energy-containing wave number (cm" 1 ) I = reference length L t = Lagrangian time integral scale Re\ = turbulence Reynolds number, u\ u /i> Ke m = Reynolds number, U m d/v m Re = front outline autocorrelation function 7 7 = static temperature (°K) u = Eulerian velocity, in body coordinate system U = average (axial) velocity, in body coordinate system v = Lagrangian velocity y f -front amplitude /3 = velocity ratio, Uf/U m r = intermittency factor e = deviation, yf -y t] = normalized axial distance, x/d \ a = Taylor (dissipation) microscale \ e = front (spatial) microscale v -kinematic viscosity £ = correlation lag distance (Te = standard deviation of front about mean TL = Lagrangian time microscale w = turbulence vorticity Subscripts oo = freestream / = turbulence front = above any symbol, denotes rms valuê = fluctuation component po = reference value 1.29 (10~3) g cm" 3