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General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows

In this paper, the relation between skin friction and heat transfer along windward sides of blunt-nosed bodies in hypersonic flows is investigated. The self-similar boundary layer analysis is accepted to figure out the distribution of the ratio of skin friction to heat transfer coefficients along the wall. It is theoretically obtained that the ratio depends linearly on the local slope angle of the wall surface, and an explicit analogy expression is presented for circular cylinders, although the linear distribution is also found for other nose shapes and even in gas flows with chemical reactions. Furthermore, based on the theoretical modelling of the second order shear and heat transfer terms in Burnett equations, a modified analogy is derived in the near continuum regime by considering the rarefied gas effects. And a bridge function is also constructed to describe the nonlinear analogy in the transition flow regime. At last, the direct simulation Monte Carlo method is used to validate the theoretical results. The general analogy, beyond the classical Reynolds analogy, is applicable to both flat plates and blunt-nosed bodies, in either continuous or rarefied hypersonic flows.