A Morphing Continuum Simulation of Transonic Flow over an Axisymmetric Hill

TL;DR

This paper applies Morphing Continuum Theory (MCT) to simulate transonic flow over an axisymmetric hill, demonstrating improved visualization of turbulent structures and better agreement with experimental data compared to traditional DNS methods.

Contribution

It introduces a novel MCT-based finite volume simulation approach that captures turbulent structures with fewer computational resources and enhances flow visualization techniques.

Findings

MCT simulations match experimental surface pressure data closely.

The new Q-criterion visualizes three-dimensional turbulent structures effectively.

MCT achieves comparable accuracy with significantly fewer mesh cells.

Abstract

Finite volume simulations of turbulent boundary layer flow over an axisymmetric hill are performed for $Re_H$ = 6500 using Morphing Continuum Theory (MCT), and compared with DNS data from Castagna et. al. and experimental data obtained by Simpson. The inlet profile was specified by inputting values from the profile specified by Castagna et. al. Root- mean-square velocity fluctuations are inputted using the new variable of gyration from MCT. Additional terms introduced by MCT lead to a new formulation of the Q-criterion, which allows for the visualization of three-dimensional turbulent structures including a 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. MCT data was obtained on a $6.72 \times 10^6$ cell mesh containing a smaller number of cells by an order of magnitude than that of the DNS mesh of $5.4 \times 10^7$ by Castagna et. al. The effects of the particle on the larger structures are inferred from the variation in the new variable of gyration.