A multiscale framework for unsteady conjugate heat transfer with turbulence resolving methods — With application to rotating cavities

Abstract

Carrying out unsteady conjugate heat transfer (CHT) with turbulence resolving methods is challenging due to the significant disparity in both time and length-scales that appear in the problem. The solid domain initial transient needs to be accelerated to a steady state, but time-accuracy for the solid domain temperatures fluctuations must be maintained. Many current state-of-the-art methods aim to do this by accelerating the solid domain timescale until the simulation is temporally converged, before switching to a non-accelerated solid solution that is assumed to be correct. However, this paper demonstrates that these current time domain CHT methods still introduce a long-lasting error in the solid domain temperature.To meet this challenge, we present a new multiscale framework that enables the interaction of all timescales in the fluid and solid domains to be consistently captured, without corruption by mesh resolution effects or the solid initial transient. Monochromatic low frequency temperature fluctuations from large coherent structures in the fluid domain are coupled to a time-spectral solid domain solution with a harmonic balance interface condition. Broadband higher frequency temperature fluctuations from turbulence are captured locally on the wall using a wall transfer function approach, reformulated using recursive convolution to simplify its application.The framework is applied to the simulation of rotating cavities with various disk materials and heating configurations. Various aspects of the framework and unsteady conjugate heat transfer in general are illustrated — in particular that starting from a roughly correct time-average solution can still lead to a large initial transient once an unsteady wall temperature is introduced. Comparison of the simulations yields new insight into the effect that different industrially relevant choices for the cavity material can have, even at the same non-dimensional operating conditions.