Comment on ''Supersonic Separation with Obstructions''

Abstract

V ERMA and Gupta 1 recently presented experimental data for the supersonic turbulent¯ow past a circular cylinder mounted on a¯at plate at a freestream Mach number of M = 1.6. Using their oil¯ow visualization data, Verma and Gupta 1 made an attempt to correlate the primary separation distance S with the cylinder diameter D and the thickness of the undisturbed boundary-layer d .Reference 1 concludedthat the appropriatelength scale for the separation distance is S/ p ( Dd ) (for H > d ) and proposed the following correlation:Reference 1 stated that ª the length scale chosen for nondimensionalizing S cannot be the cylinder diameter D.º This claim is not supported by the vast amount of experimental data reported in the literature. 2 ¡ 4 Westkaemper 3 was among the ® rst investigators who noted that S/ D correlated with H/ D. Settles and Dolling 4 and Dolling and Rodi 5 noted the similarities between the¯ow® elds of cylinders and hemicylindricallyblunted ® ns mounted on a¯at plate. For blunt ® ns, not only the separation distance but also the spanwise development of the¯ow® eld, as well as its vertical extent, depend primarily on diameter D (Ref. 5). The freestream Mach number M and Reynolds number Re have only secondary effects on the scaling in the turbulent¯ow regime. 5 These observations are supported by computational studies as well. 6 We used our own experimental results 7 ¡ 9 and the data of other experiments reported in the literature 1,2 to verify universal applicability of Eq. (1). All of the data utilized in our analysis were obtained for cylindersby oil¯ow visualization. Figure 1 gives the variationof S/ p (Dd ) with H/ d for seven different M and Re d values. Re d is the Reynolds number based on the undisturbed boundary-layer thickness d , which was measured in Ref. 2 and calculated for the other data sets by using the van Driest transformation.Equation(1) (which is shown by a dashed line in Fig. 1) has a maximum at H/ d = 10.2 and does not produce an asymptotic S value for in® nite H . The solid line in Fig. 1 is a plot of the correlation given bywhich ® ts the data more accurately than Eq. (1). However, there is considerable scatter in the data due, mainly, to the effect of D/ d on the correlation. D/ d values for large H/ d are indicated in Fig. 1. S/ p (Dd ) increases with increasing D/ d for H/ d > 6. A de® nite trend does not exist for H/ d < 6. The ranges of D/ d values for the data used in Fig. 1 are 4.2 < D/ d < 16 (Ref. 1), 0.7 < D/ d < 3.3 (Ref. 2), 0.Sedney and Kitchens 2 note that, when S/ D is plottedas a function of H/ d , a strong dependenceon D/ d is observed.(Figure 4 in Ref. 2 shows that S/ D decreaseswith increasing D/ d .) Figure 1 shows that plotting S/ p (Dd ), instead of S/ D, as a function of H/ d does not remove the dependenceon D/ d . Realizing that H/ d is not a suitable correlationparameter,Sedney and Kitchens 2 proposedthe following correlation:(3) where a and b are weak functions of Reynolds number and depend mainly on M (Refs. 2, 4, and 7). The results of Refs. 2 and 7 indic...