Development of a boundary layer parameters identification method for transition prediction with complex grids

Abstract

Predicting boundary layer transition accurately is important to thermal protection and drag reduction of flight vehicles. Up to now, there has been many transition prediction methods. However, most of those methods need boundary layer parameters, which are difficult to obtain in massively parallel execution since some parameters are nonlocal variables, thus greatly limiting the application of those methods. A grid-reorder method is developed to obtain the boundary layer parameters, which is suitable for parallel computing in this paper. With the grid-reorder method the wall normal grid cells can be easily found, and two criteria are used to determine the boundary layer edge in the wall normal direction, then the boundary layer parameters such as boundary layer thickness, boundary layer momentum thickness, boundary layer edge velocity, cross-flow velocity, and so on, can be obtained accurately and efficiently. The method has been coupled to three transition prediction methods, the γ-Reθ model, the k-ω-γ model, and the transition correlations, to validate its effectiveness. For the γ-Reθ model, the cross-flow velocity is obtained with the grid-reorder method, then a cross-flow intermittency factor is developed and introduced into the model, and the inclined prolate spheroid case is used to test the performance of the model. For the k-ω-γ model, the grid-reorder method is applied to obtain the boundary layer edge velocity and the inflection point velocity which are of vital importance to form the second-mode timescale for hypersonic transition prediction. For the transition correlations, Reθ/ Me is obtained effectively with the grid-reorder method. The X-51 forebody is selected to test the effectiveness of Reθ/Me for complex geometries and the results show a good correspondence with the experiment results. The successful application in three transition prediction methods demonstrates that the grid-reorder method has an excellent performance in obtaining the boundary layer parameters and can broaden the application of the existing transition prediction method in engineering.

Coherent structure tracking of the second Mack mode in transitional hypersonic boundary layers

“…The u-velocity and temperature profiles obtained from the DNS are plotted at the end of the computational domain in Figure 4. The normalized wall-normal coordinate is determined using the local boundary-layer thickness, which is based on the total enthalpy criterion h 0 (δ h0 ) = C h h ∞ [42], with C h = 1.008. Over the insulated wall, the developed boundary layer is thicker, approximately δ h0 ≃ 14 mm, in contrast to δ h0 ≃ 8 mm over the cold wall.…”