Heat transfer and skin friction: Beyond the Reynolds analogy

Abstract

This paper describes a variational method to determine a high-resolution skin friction field from a measured surface temperature field based on the exact relation between skin friction, surface temperature and heat flux in viscous flows. The focus is the application of this method to complex three-dimensional flows to explore the intrinsic relationship between skin friction and heat transfer beyond the Reynolds analogy. Further, the underlying condition for establishing the Reynolds analogy is examined in this general theoretical framework. Essentially, this method is considered as a global variational form of the Reynolds analogy. To demonstrate the application of this method, the skin friction fields are extracted from temperature sensitive paint measurements in normally and obliquely impinging jets, revealing complex flow structures in the impingement region where the Reynolds analogy does not hold.