Licentiatseminarium
Explicit algebraic turbulence modelling in buoyancy-affected shear flows
AbstractTurbulent flows affected by buoyancy forces occur in a large amount of applications, from heat transfer in industrial settings to the effects of stratification in Earth’s atmosphere. The two-way coupling between the Reynolds stresses and the turbulent heat flux present in these flows poses a challenge in the search for an appropriate turbulence model. The present thesis addresses this issue using the class of explicit algebraic models. Starting from the transport equations for the Reynolds stresses and the turbulent heat flux, an explicit algebraic framework is derived for two-dimensional mean flows under the influence of buoyancy forces. This framework consists of a system of 18 linear equations, the solution of which leads to explicit expressions for the Reynolds-stress anisotropy and a scaled heat flux. The model is complemented by a sixth-order polynomial equation for a quantity related to the total production-to-dissipation ratio of turbulent kinetic energy. Since no exact solution to such an equation can be found, various approximation methods are presented in order to obtain a fully explicit algebraic model. Several test cases are considered in this work. Special attention is given to the case of stably stratified parallel shear flows, which is also used to calibrate the model parameters. As a result of this calibration, we find a critical Richardson number of 0.25 in the case of stably stratified homogeneous shear flow, which agrees with theoretical results. Furthermore, a comparison with direct numerical simulations (DNS) for stably stratified channel flow shows an excellent agreement between the DNS data and the model. Other test cases include unstably stratified channel flow and vertical channel flow with either mixed convection or natural convection, and a reasonably good agreement between the model and the scarcely available, low-Reynolds-number DNS is found. Compared to standard eddy-viscosity/eddy-diffusivity models, an improvement in the predictions is observed in all cases. For each of the aforementioned test cases, model coefficients and additional corrections are derived separately, and a general formulation has yet to be given. Nevertheless, the results presented in this thesis have the potential of improving the prediction of buoyancy-affected turbulence in various application areas.
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