Methods for Measuring and Computing the Adiabatic-Wall Temperature

For convective heat transfer involving multiple sources of different temperatures in the flow field such as in film cooling, the adiabatic-wall temperature, T_ad, is used as the reference temperature to define the heat-transfer coefficient (HTC). Studies based on computational Fluid Dynamics (CFD) have always obtained T_ad by requiring the cooled or heated surface to be adiabatic. Similarly, most experimental studies that measured T_ad have sought to mimic adiabatic wall by using solids with very low thermal conductivity. Other experimental studies have obtained T_ad by making two assumptions: (1) T_ad at any given point on the cooled or heated surface is independent of the surface temperature, T_s, and the surface heat flux, $qs″$⁠, at that point and (2) the HTC, h_ad, which equals $qs″$/(T_s – T_ad), depends only on the ratio of $qs″$ to T_s – T_ad. With these two assumptions, measuring $qs″$ at two different T_s or vice versa at a point yields T_ad and h_ad at that point. In this study, CFD simulations, based on steady RANS, were performed to assess the assumptions invoked by CFD and experimental studies that seek to obtain T_ad and h_ad. The assessment was made by studying film cooling of a flat plate with an adiabatic wall and with isothermal walls, where the temperature of the isothermal wall, T_s, ranged from the lowest to the highest temperatures in the flow. Results from this study show T_ad obtained by enforcing an adiabatic wall does not satisfy the requirement: where and when T_s – T_ad = 0, $qs″$ = 0. Therefore, h_ad approaches infinity where T_s – T_ad is either zero or nearly zero, but $qs″$ ≠ 0. Also, obtaining T_ad and h_ad by measuring two sets of (T_s, $qs″$⁠) was found to yield non-unique values that depended strongly upon the pair of (T_s, $qs″$⁠) chosen. To overcome the shortcomings of existing methods, a new method was developed in this study to obtain T_ad that does satisfy the requirement: T_s – T_ad = 0 where and when $qs″$ = 0. Also, the method developed yields an h_ad that is continuous across T_s – T_ad = 0. By using the new method developed, errors in T_ad and h_ad obtained by existing methods were assessed.