Heat transfer from boundary layers undergoing an acceleration induced reverse transition

Abstract

An experimental and analytical investigation of heat transfer in an acceleration induced transitional flow regime is presented. A previously developed criterion for the onset of reverse transition of turbulent boundary layers is combined with a theory of forward transition to derive the effect of free-streom turbulence intensity on the critical value of an acceleration parameter for two initial velocity profiles within the turbulent boundary layer. The results are consistent with experimental observations. Local heot transfer measurements were obtained along converging walls of rectangular flow channels having convergence angles of 45, 60, and 70 deg. Free-,stream turbulence (1.6 to 11 %) was induced by grids upstream of the start of convergence, and the local Reynolds number were varied by variation in channel size and stagnation pressures (200 to 500 Ib./rq.in. abs.) at a gas stagnation temperature of 1,500"R.The results indicate a two-stage reverse transition process along the converging wall with a forword transition between the two stages of reverse transition. The local Nusselt numbers ob- Considerable experimental and analytical efforts have been expended for proper prediction of convective heat transfer coefficients in rapidly accelerating flows. A fair degree of success prevails if the boundary layer is either turbulent (1, 2) or laminar ( 3 ) . However, recent investigations at high rates of acceleration indicate that the boundary layer may be turbulent at the start of convergence but reverts to a transitional or near laminar state toward the sonic point (4, S), The process of reverse transition is seldom complete; that is, truly laminar heat transfer levels are seldom realized.For the transitional flow regime (between the turbulent and laminar with characteristics of neither), the velocity profile within the boundary layer and its associated shear stress relation cannot be described in a universal manner. Therefore, predictions of heat transfer coefficients for this flow regime are lacking, so that emphasis has to be placed on experimental or visual observations.The observed reduction in rocket nozzle heat transfer below that typical of a turbulent boundary layer (through the process of reverse transition) provides a strong motive to seek a method by which the phenomenon of reverse transition can be incorporated into design criteria. Two basic problems are involved: prediction of the onset of reverse transition (or laminarization) of a turbulent boundary layer, and estimation of heat transfer coefficients in the transitional flow regime.Several basic experimental investigations of acceleration induced reverse transition of turbulent boundary layers have been reported (6 to 9). However, the boundary layers investigated were developed on straight, nonconverging, side plates with the stream-by-stream pressure gradient being controlled by adjustments of an opposite converging wall, Such data are hardly applicable for the design of converging walls. This is well reflected by comparisons of the effect of ...