Developments in turbulence modelling with Reynolds-averaged Navier-Stokes equations

Abstract

The performance of different low-Reynolds number turbulence models applied to various flows is described. The emphasis is put on Chien's k – ε model, an explicit algebraic Reynolds-stress model by Speziale et al., and a full Reynolds-stress closure. The Reynolds-stress closure of this work has been developed by the author by combining different existing models.

Accurate numerical methods are developed to couple the momentum equations and the low-Reynolds number Reynolds-stress equations. Two methods are introduced and these vary depending on how much the source terms are taken into account implicitly. The production of turbulence can be used to couple the inviscid part of the momentum equations and the Reynolds-stress equations in the approximate Riemann solution.

As demanding problems are computed, it has been essential to parallelize the computer code. This has been performed via a message passing package. The code shows an excellent parallel performance even in the most complex topologies simulated.

In this thesis, validations are presented for ten different fluid dynamic problems. The test cases vary from a simple channel flow to complicated flows in rotating machinery. In the validations it is found that the Reynolds-stress closure generally performs better than the two-equation models in complex flows. Especially streamline curvature is better captured by the Reynolds-stress closure. For the skin friction, the present Reynolds-stress closure does not give satisfactory results, and thus, some further development is needed. For simpler situations the two-equation models give comparable or even better results than the more complex models.