General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows

TL;DR

This paper develops a generalized Reynolds analogy for skin friction and heat transfer on blunt-nosed bodies in hypersonic flows, incorporating effects of surface shape, rarefaction, and flow regime, validated by simulations.

Contribution

It introduces a new theoretical analogy linking skin friction and heat transfer for various nose shapes and flow regimes, including rarefied conditions.

Findings

Linear relation between skin friction and heat transfer ratio and wall slope angle.

Explicit analogy expression for circular cylinders and other nose shapes.

Validation of the analogy through direct simulation Monte Carlo results.

Abstract

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.