Two-equation turbulence model consistent with the second law

Abstract

THE theory of a two-equation turbulence model that satisfies the second law of thermodynamic s is briefly reviewed. It is shown that the resulting governing equations resemble those of the k-e model with the e equation being different. The TEACH code is altered to account for the required modifications of the new model. Two test cases are considered in this study, a confined coaxial round jet expansion and a backward-facing plane step. The predicted velocity and turbulent kinetic energy profiles are compared with the experimental data and those obtained from the standard k-e model. It is shown that the new model predicts the features of these turbulent flows more accurately in comparison to the standard model. Contents Recently, Ahmadi1 derived the averaged form of the second law of thermodynamic s and discussed its implications in turbulence modeling. Based on thermodynamic al arguments, a two-equation turbulence model was also developed that resembles the k-e model. It was shown that although the k equation is unchanged, the e equation is quite different from the standard one. The purpose of the present study is to test the performance of the new turbulence model in predicting the flow properties in various engineering problems. The particular examples considered here are the flows in the mixing zone of confined coaxial round jets and the backward-facing plane step. The standard e equation in the TEACH code is replaced by the newly derived e equation. The mean velocity and the turbulent kinetic energy profiles are calculated and the results are compared with the experimental data of Johnson and Bennett,2 Kim et al., 3 Eaton and Johnston,4 and the predictions of the standard k-e model.5 It is shown that the new model describes, with reasonable accuracy, the basic features of the experimental data.