A study of the thermal law of the wall for separated flow caused by a backward facing step
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A thermal law of the wall provides important information to predict the surface temperature of an object in turbulent flow. Surface temperature predictions for an Radial Jet Reattachment (RJR)nozzle were overpredicted particularly inside the reattachment dome using the conventional thermal law of the wall. As a result, the convective heat transfer coefficient was underpredicted in that region. The present research was motivated to more accurately predict the surface temperature of a heated surface subject to turbulent recirculating flow caused by a sudden geometry change using a new thermal law of the wall. To determine a new thermal law of the wall, thermal and hydrodynamic characteristics of turbulent airflow inside the recirculation region caused by a sudden change in geometry with no external pressure gradient were investigated experimentally. A backward facing step was utilized to predict the recirculation region over a heated flat surface. Temperature and velocity data were measured inside the recirculation region using a thermocouple and an X hot-film probe respectively for step heights of 0.043, 0.057, and 0.072 m and Reynolds numbers of 4452, 6678, and 8904. The turbulent Prandtl number was calculated inside the recirculation region and was found to be 0.25. Using the maximum backflow velocity inside the recirculation region as the reference velocity and the measured experimental data, a new thermal law of the wall for separated flows caused by sudden geometry changes was obtained by using the mixing length theory. The new thermal law of the wall was utilized in a Computational Fluid Dynamics (CFD) code to predict surface temperature distribution and air temperature distribution within the recirculation region of a backward facing step geometry. The average error from the wall temperature predictions using the new thermal law of the wall decreased by 77.4% when compared to predictions that used the conventional thermal law of the wall.