Elliptic relaxation second moment closure for the turbulent heat fluxes

Jong Keun Shin, Jeong Soo An, Young Don Choi, Young Chan Kim, Min Soo Kim

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-29
Number of pages29
JournalJournal of Turbulence
Publication statusPublished - 2008


  • Elliptic blending model
  • Heat transfer
  • Rotation
  • Second moment closure
  • Turbulence
  • Turbulent heat flux

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Physics and Astronomy(all)


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