Dynamics of unsteady heat transfer in pulsating flow across a cylinder

Abstract

The unsteady heat transfer between a cylinder and pulsating cross-flow is investigated for small perturbations of flow velocity. In this regime the cycle-averaged heat transfer is constant and fluctuations of flow variables can be described as linear, time-invariant dynamics. Numerical simulation of the response to a sudden increase of the free stream velocity allows to visualize and interpret physically the flow and heat transfer dynamics. Broadband excitation combined with linear system identification yields quantitative predictions of the frequency response of heat transfer over a range of Reynolds and Strouhal numbers. It is concluded that the heat transfer dynamics are governed by several time scales, corresponding to the response times of the velocity field and temperature field, respectively. The interaction of the different time lags leads to a non-trivial dependence of the heat transfer frequency response on Strouhal and Reynolds numbers. The frequency response functions exhibit a low-pass behavior with vanishing amplitudes and a phase lag slightly above -π/2 at high Strouhal numbers. Excess gain above the quasi-steady-state value of the heat transfer frequency response is observed for Strouhal numbers of order unity and Reynolds numbers of order ten.