Similarity-solution-based improvement of γ-Reθt model for hypersonic transition prediction

The improvement of γ-Reθt model for hypersonic transition prediction is conducted based on the compressible similarity solutions. The Wilcox's correlation of vorticity Reynolds number and momentum thickness Reynolds number adopted in the original γ-Reθt model is not suitable for hypersonic boundary layer. The new correlation is obtained from similarity solutions of compressible boundary layer equations, which includes parameters such as Mach number and temperature of boundary edge and wall temperature. Then the new correlation as well as several modifications are applied to improve the γ-Reθt model for hypersonic transition prediction. Four test cases are selected to assess the performance of the improved γ-Reθt model, including a wide range flows from two-dimensional flat plate and double ramp to three-dimensional X-51A forebody and scramjet intake. The predicted pressure coefficient and Stanton number are consistent with the available experimental data, which validate the transition prediction capacity of the improved γ-Reθt model in different hypersonic conditions. For complex scramjet intake, the predicted results by the improved γ-Reθt model show a good agreement with experimental data, especially in the interior region, which demonstrates that the improved γ-Reθt model can be an effective tool for the design and optimization of hypersonic vehicles.