Identification of velocity distribution in a turbulent flow inside parallel-plate ducts from wall temperature measurements

Abstract

An Inverse Heat Convection Problem is investigated in this numerical study. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, constant property flow inside a parallel-plate duct. Velocity and effective diffusivity distributions of the turbulent model are characterised by a Reynolds number b + based on the shear stress velocity. The identification of b + from simulated wall temperature measurements is presented. A heat flux density is applied along the channel length and temperature responses are taken at the wall external surface. Heat transfer has to act as a small but measurable perturbation of the flow. The inverse problem is recast into an optimisation problem solved with a Quasi-Newton method. Reynolds numbers 105 and 106, corresponding to two different values of b + , are considered. Effects of sensor number and location, as well as magnitude of measurement error on the estimation accuracy, are examined.