On wave harmonics of heated circular cylinders

A hybrid (FV + FE) acoustic damping method, which is investigated and optimized in terms of wave harmonics behavior of the method, is utilized at Ma = 0.01 for heated circular cylinders. Discretization of nonlinear convective terms is a modified approximate Riemann solver. Modification is realized through multiplication of dissipation term with an acoustic damping matrix. This is necessary to avoid drawbacks of standard algorithm and to improve accuracy of results, if low speed applications are concerned. Later, harmonics of velocity and temperature fields behind a heated circular cylinder are investigated numerically for moderate Reynolds numbers between 70 and 110. A parametric study of the first harmonics is carried out precisely by increasing temperature ratios, T∗ = Twall/T∞ from 1.03 to 1.8. Results agree well for high temperature ratios, T∗ = 1.5, 1.8 and Re ⩾ 100, with the key issues stated in the experimental work of Ezersky et al. [Ezersky AB, Lecordier JC, Paranthoën P, Soustov PL, Structure of vortices in a Karman street behind a heated cylinder. Phys Rev E 2000;61:2107]. Moreover, it is found that decrease in frequency of oscillations can be explained as heated cylinders have larger vortex formation region as a result of heat flux from walls in comparison to non-heated cylinders. At lower temperature ratios, T∗ = 1.03, 1.1, temperature can be taken as passive scalar field.