Breakdown of the Reynolds Analogy in a Stagnation Region Under Inflow Disturbances

Abstract

A systematic analysis is performed for the Reynolds analogy breakdown at stagnation-region flow and heat transfer in the presence of inflow disturbances. The Reynolds analogy breakdown between momentum and energy transfers in a stagnation region is scrutinized by varying the Reynolds number (5000≤Re≤20000), the amplitude (0.00075≤A≤0.003) and the length scale (λ/δ=10.6). A spanwise sinusoidal variation is superimposed on the velocity component normal to the wall. Self-similarity solutions are obtained with trigonometric series expansions. The Reynolds analogy criterion demonstrates that the rate of change of skin friction is different from that of wall heat transfer. Different evolutions of the rates of skin friction and wall heat transfer are due to the difference between 〈s'v'〉 and 〈v'T'〉. An in-depth analysis on 〈s'v'〉 and 〈 v'T'〉 is performed by analysis using disturbance correlations based on the fluctuating velocity transport equations in vorticity form. It is found that the pressure fluctuations, the wall blocking and the Lamb vectors are responsible for the breakdown of the Reynolds analogy. A direct comparison is made between momentum and energy balances associated with the three responsible mechanisms. A common finding is that their profiles are changed significantly at a location where the evolution of the streamwise vortex is strong.