Augmentation of flat surface forced convection by a pair of rectangular strips – A wavelet analysis

Turbulent flow downstream of a pair of 12.7-mm wide (W) and 25.4-mm high rectangular flexible strips was characterized using a 3D hotwire anemometer. The rectangular strips were at a separation distance of 3 W, 2 W, and 1 W and the Reynolds number based on the strip width was fixed at 8500. Discrete wavelet transform was employed to investigate the effect of various segments of the turbulence cascade on convective heat transfer augmentation over a flat surface. The fluctuating turbulent velocity was decomposed into 12 levels of Detail, D components, in addition to Approximation, A. The turbulence kinetic energy (ke) between 78 and 156 Hz (D9 component) was found to be largest. The corresponding ke peak of D9 increased from 0.0064 to 0.0074 to 0.0084 with decreasing separation from 3 W to 2 W to 1 W, respectively. Regression analysis was performed to correlate the normalized Nusselt number (Nu/Nu0) with the turbulence fluctuations at various wavelet levels. For the 3W-separation strip pair, the standardized regression coefficient has a value of larger than 0.90 for D7 to D4 levels (300 Hz to 5000 Hz). Level D1 (20 kHz to 40 kHz) followed by level D2 (10 Hz to 20 kHz) gave the largest standardized regression coefficient of 0.86 and 0.84, respectively, for the 2W-separation case. On the other hand, the lower frequencies at D12 (9 Hz to 20 Hz) and A12 (0 to 10 Hz) levels were found to be most involved in heat transfer enhancement for the 1W-separation strip pair. The corresponding standardized regression coefficient values of 0.77 and 0.79 seem to indicate that the organized large-scale vortical structures have been broken down and randomized into potent convection motions with frequencies up to 20 Hz