Statistical Properties of the Turbulent Wake behind Hypervelocity Spheres

Abstract

Autocorrelation functions and spectra of the gas density fluctuations have been obtained from microdensitometer tracings of schlieren photographs of the turbulent wakes behind hypervelocity spheres ⅜ in. in diameter traveling with a velocity of about 8 kft/sec (≅ Mach 8). Schlieren photographs of wakes 100 to 10 000 body diameters behind the spheres at pressures ranging from 10 to 160 mmHg were taken and densitometer tracings from these films were analyzed. The relationship between the statistical properties of the film density and that of the gas density has been derived. The results show that the normalized autocorrelation functions and spectra of the turbulent wake of spheres are independent both of pressure and of position behind the body. Further, to the accuracy of the measurements, the turbulent wake appears to be statistically isotropic and homogeneous, and the three-dimensional spectrum of the gas density falls off as the 5.5 power of the wavenumber.

Application of Focusing Schlieren Deflectometry to an Isolator Shock Train

“…Early work involving time-resolved measurement of density gradient at a point in the flowfield had two main characteristics in common: the analysis of schlieren/shadowgraph images to obtain the time-resolved measurement, and the integral of flow properties along the entire light optical path length. [27][28][29] This earlier work was thus limited to image acquisition equipment frame rates (and other performance parameters of the particular system) and best suited for 2D approximated flows where the homogeneous assumption was valid. The former was addressed by work performed by McIntyre 15 , introduced above, utilizing fiber-optics and photomulitplier tubes (PMTs) together with a traditional schlieren method to record light intensity fluctuations at discrete locations with high spatial and temporal resolution.…”

Statistics of high-speed turbulent wake boundaries.

“…The apparent contradiction between this use of the long-time solution and the previous conclusion t/ <$C TL can perhaps be resolved by noting that the validity of Eq. (2) may not stem from strict applicability of the Lagrangian approach to front displacements from XQ to far downstream, but may be related to the asymptotic independence of particle displacements from particular t The data of Clay et al 6 were taken at range pressures 10 < POD < 160 mm Hg, in contrast to p™ = 1 atm for most of the present sphere measurements. There is some Reynolds number scaling for (\ D ) sc /d, but in addition the absolute level of p™ may have some effect on the optical sensitivity in relation to the turbulence scales, which has not been considered.…”

“…Slattery and Clay 5 and Clay et al 6 present measurements of RD(!~) from schlieren pictures of wakes behind spheres with d = 0.95 cm traveling at U m ~ 2.5 km/sec. "The results show that the normalized autocorrelation functions and spectra of the turbulent wake of spheres are independent both of pressure and of position behind the body."…”

Enthalpy and density fluctuations in high-speed wakes.

“…2 Parameter for enthalpy (density) fluctuation level determined by average of experimental points in Fig. 1 and an experimental point of Clay et al 2 Present estimates have a peak higher by about a factor of 2 than the experimental point, and peak at an x/d somewhat later. There is, however, qualitative agreement with experiment 2 in that high values of p/jo(>0.1) persist out to x/d ~ 10 4 .…”