Connecting dispersion models and wall temperature prediction for laminar and turbulent flows in channels

In a former paper, Drouin et al. [6] proposed a model for dispersion phenomena in heated channels that works for both laminar and turbulent regimes. This model, derived according to the double averaging procedure, leads to satisfactory predictions of mean temperature. In order to derive dispersion coefficients, the so called “closure problem” was solved, which gave us access to the temperature deviation at sub filter scale. We now propose to capitalize on this useful information in order to connect dispersion modeling to wall temperature prediction. As a first step, we use the temperature deviation modeling in order to connect wall to mean temperatures within the asymptotic limit of well established pipe flows. Since temperature in wall vicinity is mostly controlled by boundary conditions, it might evolve according to different time and length scales than averaged temperature. Hence, this asymptotic limit provides poor prediction of wall temperature when flow conditions encounter fast transients and stiff heat flux gradients. To overcome this limitation we derive a transport equation for temperature deviation (Tw-〈T¯f〉f). The resulting two-temperature model is then compared with fine scale simulations used as reference results. Wall temperature predictions are found to be in good agreement for various Prandtl and Reynolds numbers, from laminar to fully turbulent regimes and improvement with respect to classical models is noticeable.