The one-dimensional acoustic field in milli-scale flows with a mean axial temperature gradient and visco-thermal damping

Abstract

This work presents an analytical method for computing the one-dimensional (1-D) acoustic field in milli-scale flows with a streamwise mean temperature gradient, where visco-thermal damping occurs due to wall interactions. Such flows are relevant to compact, high-performance heat exchangers, whose flow area between the tubes is characterised by a hydraulic diameter of the order of millimetres. We propose for the first time that an inviscid acoustic model incorporating mean flow and mean temperature effects can be combined with a wave number correction to account for visco-thermal losses. The proposed hybrid model requires the 1-D mean flow field as input, which was approximated from Reynolds-averaged Navier–Stokes simulations in this work, thereby accounting for mean shear effects. To evaluate the model predictions, comparisons were made against linearised Navier–Stokes equations simulations for inlet shear and Helmholtz numbers in the ranges 26 $\le S{h}_{\text{in}}\le$ 94 and 0.03 $\le H{e}_{\text{in}}\le$ 0.20 respectively. The model showed very good agreement across these ranges, particularly at higher Helmholtz numbers.