Entropy production calculation for turbulent shear flows and their implementation in cfd codes

Entropy production in turbulent shear flows with heat transfer is calculated locally and afterwards integrated over the whole flow domain. This quantity can serve as a parameter to determine the efficiency of turbulent heat transfer processes. Based on the time averaged entropy balance equation, four different mechanisms of entropy production can be identified and cast into mathematical equations. They are: dissipation in the mean and the fluctuating velocity fields and heat flux due to the mean and the fluctuating temperature fields. It turns out that no additional balance equation has to be solved, provided the turbulent dissipation rate is known in the flow field together with the mean velocity and temperature distribution. Since all four entropy production rates show very steep gradients close to the wall numerical solutions are far more effective with wall functions for the production terms. These wall functions are mandatory when high Reynolds number turbulent models are used, as for example the high Reynolds number k-epsilon; model, like in our case. As an example, flow through a heated pipe with a twisted tape inserted is calculated in detail including the local entropy production rate. For this configuration experimental results show an increase in heat transfer as well as in pressure drop when the spiral slope of the twisted tape is increased. Therefore, no optimum of the spiral slope can be found in the experiments. An analysis based on entropy production, however, reveals that there is a distinct optimum for a certain slope of the twisted tape. Thus, entropy production can be used as an efficiency parameter with respect to minimizing the loss of available work in a process. (c) 2005 Elsevier Inc. All rights reserved.