Extension of morphing continuum theory to numerical simulations of transonic flow over a bump

Finite-volume simulations of turbulent boundary layer flow over an axisymmetric bump are performed for Re = 6709 using Morphing Continuum Theory (MCT), and compared with DNS simulations performed by Castagna¹ and experimental data obtained by Simpson.² Additional terms introduced by MCT allow for the visualization of three-dimensional turbulent structures through the newly derived Q-criterion of the MCT governing equations. Streamline plots of the separation bubble agree well with that of Castagna while the pressure matches Simpson much more closely than Castagna.^{1, 2} MCT data was obtained with a smaller mesh size by an order of magnitude than Castagna’s DNS data.¹ Eddy structures are clearly visualized through isosurfaces of the new Q-criterion. The effects of the inner structure on the larger eddy structures are inferred from the variation in the new variable of gyration.