Study of turbulent hypersonic flow past elongated blunt-nosed cones

Abstract

Axisyrmnetdc turbulent hypersonic perfect-gas flow past slightly blunted cones is considered. The influence of the absorption of the entropy layer, developing on an elongated body, on friction and heat transfer to the body surface is studied using the viscous shock layer model. Correlations are established for the heat flux and the friction coefficient along the cone surface at large distances from the forward stagnation point. The results are presented together with their correlations in the framework of the viscous shock layer model and an approximate model of the boundary layer type, taking into account the entropy layer absorption. A generalization of the Reynolds analogy is obtained. There are many paper.s dealing with the calculation of the friction and heat transfer in flow past blunt bodies within the framework of the classical theory of the turbulent boundary layer (see [1]). The absorption of the entropy layer by the boundary layer may be regarded as the principal second-order effect in boundary layer theory. Approximate methods have been developed to take this effect into account (see [2--6]). It should be noted that the entropy layer is absorbed more rapidly by a turbulent than by a laminar boundary layer, due to the greater boundary layer thickness; in this case the absorption length is 5--50 bluntness radii. In [2--4] the effect of the absorption of the entropy layer by the boundary layer was taken into account by means of additional calculations for the flow parameters at the outer edge of the boundary layer, using the mass flow rate global balance method. The authors of [5] and [6] have proposed a technique based on the mass-average method. All these approaches enable the entropy layer absorption to be taken into account without solving a set of equations more intricate than that of boundary layer theory. All these approaches need theoretical or experimental verification. The similitude criteria for turbulent boundary layers on blunt-nosed cones were analyzed in [4, 6]. In [4] the similitude parameters determining the heat transfer to the cone surface were established for the entropy layer absorption regime over the following ranges of the governing parameters: cone half-angle 0k= 10 deg, Reynolds number Re~ =1.0-105--3.1-105, Mach number Mo. =6--8, temperature factor tw=0.40--0.52 (here, tw=Tw/To, T w being the wall temperature and T O -- the stagnation temperature). The similitude criteria governing hypersonic flow past slender blunt bodies in the turbulent boundary layer regime were determined in [6]. Our aim is to study numerically the problem of hypersonic turbulent flow past blunt-nosed cones using the viscous shock layer model; to estimate the errors of the various approximate theories; and to establish the similitude criteria for the heat transfer at large distances from the bluntness and for the friction at both large and intermediate distances.