Modeling heat transfer and skin friction frequency responses of a cylinder in cross-flow : a unifying perspective

Abstract

The dynamic behavior of skin friction and heat release of a cylinder in pulsating cross-flow are investigated. Existing analytical solutions are presented as transfer functions versus frequency, known from control theory. Newly found expressions are given for Reynolds number ranges, where no appropriate model exist until now. These expressions are obtained by the combination of CFD simulation and system identification (CFD/SI). In the CFD/SI approach time series are generated by exciting inlet velocity fluctuations over a wide range of frequencies in one single CFD simulation. Time series are acquired for heat release, skin friction and velocity forcing, and then post-processed with system identification tools. Direct numerical simulations are conducted for mean flow Reynolds numbers between 0.1 and 40, solving the incompressible Navier-Stokes equations in a 2D domain using a finite volume approach. The system identification framework provides methods to identify a mathematical model for the response in heat release and skin friction to velocity fluctuations from data series. It can be confirmed that Bayly’s model for heat release fluctuations performs well at low Reynolds numbers. Lighthill’s model, often used in the assessment of Rijke tubes, is more accurate for high Reynolds numbers, but the time constant was underpredicted for Reynolds numbers of order 10. For the range above a Reynolds number of 0.4 a unifying model could be developed. This model especially excels at Reynolds numbers of order 10. Available models for skin friction usually match the simulated data up to a point, but do not give any dependence on Reynolds number which is corrected here. The expressions presented allow insight in the physics of the dynamic behavior of a cylinder in pulsating cross flow and also facilitate the use of these models in further investigations.