Assessment and recalibration of transition criteria for laminar-turbulent transition driven by crossflow instabilities

Kurzfassung

The major task of laminar-turbulent transition modeling for the boundary layer is to predict the transition line on solid surfaces in order to accurately compute the skin friction. A correct computation of the skin friction is important for the design of the surface geometry of new aircrafts, especially for the wing. One method of transition prediction is the local correlation-based transition modeling, which strongly relies on the use of transition criteria. There are separate transition criteria for different transition mechanisms. In this thesis, three different transition criteria for crossflow instability dominated transition (CFT) are analyzed: The C1 criterion of Arnal et al. (1984), the helicity criterion of Grabe et al. (2018), and the criterion of Langtry et al. (2015). They are assessed with regard to their accuracy, judged by means of simulations of several wind tunnel experiments reported in the literature. The transition in the simulations is either set manually (fixed transition) or computed by the gamma-Re_thetat transition model with CFT extension using the C1 criterion (free transition). The present analysis is motivated by the following facts: For certain test cases the prediction of the transition line based on the C1 and the helicity criteria is inaccurate in comparison to other test cases. In addition, the transition prediction using Langtry's criterion is not implemented in the used fluid dynamics solver TAU, yet. But evaluating the accuracy of Langtry's criterion with respect to transition prediction by means of fixed transition simulations is possible nevertheless. The analysis shows whether the implementation of approach of Langtry et al. (2015) would be worth the effort. These are the findings for the C1 criterion: For shape factors H12>2.43 the crosswise displacement thickness Reynolds number Re_delta2 at the transition location can be correlated well with the shape factor for many test cases. For lower shape factors the original correlation equation is suited good for the flow around a prolate spheroid and an infinite swept cylinder but not for the flow around two wing-like geometries. Therefore, for low shape factors a reformulation of the C1 criterion is proposed, which is implemented into the fluid dynamics solver. It is presented that computations with the gamma-Re_thetat transition model with CFT extension using the adapted C1 criterion yield almost no improvement of the transition lines compared to computations with the original C1 criterion. Explanations for that fact are suggested which show general deficiencies of the transition prediction model. The helicity Reynolds number Re_He relevant for the helicity criterion cannot be well-correlated with the shape factor H12 at the transition location among the several test cases. It is concluded that the parameters of the helicity criterion are less appropriate for CFT prediction than the ones of the C1 and Langtry's criteria. The momentum thickness Reynolds number Re_theta of Langtry's criterion can be correlated very well with the non-dimensional crossflow strength Hcf at the transition location. As the original equation of Langtry's criterion does not cover the test cases optimally, an improved formulation is proposed. The implementation of Langtry's approach into the fluid dynamics solver TAU is recommended. However, the sensitivity of the transition line prediction to an inaccurately computed momentum thickness Reynolds number is high, as the transition momentum thickness Reynolds number Re_thetat may have a streamwise slope similar to the one of the computed momentum thickness Reynolds number Re_theta. Generally, the parameters for the CFT-criteria are approximated locally in the frame of the gamma-Re_thetat transition model with CFT extension. For the C1 approach, the accuracy of this approximation is improved by recalibration of a certain model parameter, called critical-to-transition ratio C. In the formulation of Grabe et al. (2018) it is a constant, but in present work a dependency of the optimal value on the Reynolds number based on the streamwise chord length of the surface geometry and the boundary layer edge state is found. The new C-correlation is implemented into the fluid dynamics solver. Preliminary results for one test case are shown and discussed. Next steps for a continuation of the work are suggested.