A Multiscale Morphing Continuum Analysis of Energy Cascade of Compressible Turbulence

Student Research Assistant: Mohamad Ibrahim Cheikh

The goal of this project is to construct a statistical morphing continuum theory to model the complex and non-equilibrium physics of microstructured eddies in compressible turbulence. This multiscale phenomenon is largely composed of subscale eddies, strongly affecting the macroscale flow behaviors. Morphing continuum theory (MCT) contains one length scale for macroscale translation and the other one for subscale eddy motion.

Although MCT can be formulated under the framework of rational continuum thermomechanics, the physical picture it describes for compressible turbulence is still unclear. This project will propose the statistical foundation of the morphing continuum theory to describe the statistics of the turbulent eddy structures, and connect this description with compressible turbulence physics, such as energy cascade. Hence, the research objective is to investigate the energy cascade in compressible turbulence through the multiscale morphing continuum theory along with a high performance numerical solver without any ad hoc turbulence closure model.

In order to accomplish this objective, three specific research tasks are proposed: (1) establish the non-equilibrium eddy mechanics with the multiscale morphing continuum theory through the lens of statistical kinetic theory for compressible turbulence; (2) validate the morphing continuum theory with known turbulence characteristics through a portable, robust and efficient numerical simulation tool; and (3) identify the mechanism of multiscale energy transfer among translation, eddy motion and heat for compressible turbulence under free-stream and wall-bounded disturbances.

Although the goal is to propose a new multiscale continuum theory for compressible turbulence, the outcome of the project will be transformed into (1) a major component in the PI’s career plan in theoretical turbulence physics, and (2) collaboration opportunities in other aerospace-related research. Thus, this initiative is a research project that fulfills the United States Air Force mission and significantly impacts academia and industry.