Elliptic relaxation second moment closure for the turbulent heat fluxes

Abstract

This study describes the development of near-wall second moment turbulent heat flux model and its application to various turbulent flows with heat transfer to test the performance of the model. The second moment models for turbulent heat fluxes based on the elliptic concept are proposed and closely linked to the elliptic blending model, which is used for the prediction of Reynolds stresses. The new models satisfy the near-wall balance between viscous diffusion, viscous dissipation and pressure–temperature gradient correlation, and also have the characteristics of approaching their respective conventional high Reynolds number model far away from the wall. On the other hand, the traditional heat flux model using the wall-normal vector expression in the wall-reflection model is tested in the present study with the new unit wall-normal vector formulation that appears in the elliptic blending model. To develop and calibrate the new heat flux models, firstly, the distributions of the mean temperature and the scalar flux in a fully developed non-rotating channel flow are solved by the present models in constant wall temperature difference boundary condition. And then, the fully developed rotating channel and square duct flows with heat transfer and the wall bounded turbulent flows with buoyancy are simulated by the new elliptic concept models to show their applicability to the complex flows. The results of prediction are directly compared to the DNS and the LES to assess the performance of new model predictions and show the reasonable agreement with the DNS and the LES data for all the flow fields adopted in the present study.

Keywords:

• second moment closure
• elliptic blending model
• turbulence
• turbulent heat flux
• heat transfer
• rotation

Acknowledgments

This work was supported by Korea Science and Engineering Foundation (grant no. R05–2003-000–12391-0) and (grant no. R01–2003-000–10571-0). We are grateful for the specific comments and suggestions from the reviews.

This article is a modified version of the original article from the Proceedings of the 4th International Symposium on Turbulence and Shear Flow Phenomena held at Williamsburg, VA, USA, 27–29 June, 2005.

This work was supported by Korea Science and Engineering Foundation (grant no. R01–2003-000–10571-0).