Morphing continuum simulation of transonic flow over axisymmetric hill

Finite volume simulations of turbulent boundary layer flow over an axisymmetric hill are performed for Re_H 6500 using morphing continuum theory and compared with direct numerical simulation data from Castagna et al. (“Direct Numerical Simulation of a Turbulent Flow over an Axisymmetric Hill,” Computers and Fluids Journal, Vol. 95, May 2014, pp. 116-126.) and experimental data obtained by Simpson. The inlet profile is specified by inputting values from the profile specified by Castagna et al. Root-mean-square velocity fluctuations are input using the new variable of gyration from morphing continuum theory. Additional terms introduced by morphing continuum theory lead to a new formulation of the Q criterion, which allows for the visualization of three-dimensional turbulent structures including hairpin vortices. Streamline plots of the separation bubble show a more confined bubble than Castagna et. al. but agree well on the separation and reconnection points. The surface pressure coefficient matches Simpson much more closely than Castagna et al. Morphing continuum theory data were obtained on a 6.72 × 10⁶ cell mesh containing a smaller number of cells by an order of magnitude than that of the direct numerical simulation mesh of 5.4 × 10⁷ by Castagna et al. The effects of the particle on the larger structures are inferred from the variation in the new variable of gyration.