Mean-flow measurements in an axisymmetric compressible turbulent wake.

Abstract

The mean flowfield of the axisymmetric turbulent wake shed by a very slender body at Mach 3 has been mapped with the aid of the pilot and static pressure probes and the hot-wire anemometer. The experimental geometry was chosen so that no inviscid wake existed, and the measurements were carried out to about 100 diam downstream of the base. The axial variation of the velocity and temperature defects appears to obey classical decay laws following a relaxation distance of at least 40 diam from the transition region. By contrast, the radial profiles of these properties relax quickly to a self-preserving form; both the temperature and the velocity radial variations fit single-parameter Gaussian distributions quite well. The proper radial similarity variable is the radius divided by the transverse wake scale; equally good agreement obtains for a Howarth-Dorodnitzyn-transformed radius, although this issue is still unsettled because of the low Mach number used. The turbulent Reynolds and Prandtl numbers computed indirectly from the data agree well with similar results from low-speed turbulent flows. Nomenclature 6* = wake half-diameter c p = specific heat at constant pressure (Cz>A) 1/2 = virtual wake diameter D = model diameter / = nondimensional radial distribution of velocity g = nondimensional radial distribution of density h = static enthalpy I = pure number [see Eq. (16)] L = transverse wake scale L' = defined by Eq. (18) p = static pressure r = radial coordinate f = Howarth-Dorodnitzyn radial coordinate r* = wake half-radius RT = turbulent Reynolds number REO( 1) = indirectly measured wire Reynolds number RERD = directly measured wire Reynolds number 5 = function of the turbulent Prandtl number T = static temperature T = nondimensional static temperature To = stagnation temperature u = axial velocity u = nondimensional axial velocity U -local velocity scale w == velocity defect [Eq. (1)] x = axial coordinate x = nondimensional axial coordinate #o = axial location of virtual origin y = radial direction z = radial direction (normal to y) T} = nondimensional radial coordinate [Eq. (17)] YI' = defined by Eq. (13) 6 = temperature defect [Eq. (2)] 9= temperature scale T(Q) -T m