Morphing continuum theory for turbulence: Theory, computation, and visualization.

Area of Science:

• Computational fluid dynamics
• Continuum mechanics
• Turbulence modeling

Background:

• Modeling highly compressible turbulence presents significant computational challenges.
• Existing methods like Navier-Stokes (NS) simulations require substantial computational resources.
• Objective criteria for analyzing turbulent structures are limited in traditional frameworks.

Purpose of the Study:

• Introduce a high-order morphing continuum theory (MCT) for compressible turbulence.
• Develop a computationally efficient and accurate simulation method.
• Provide an objective criterion for analyzing turbulent eddy structures.

Main Methods:

• Formulated MCT within rational continuum mechanics.
• Derived linear constitutive equations and balance laws using Coleman-Noll procedure and Onsager's reciprocal relations.
• Solved governing equations in conservation form using a finite volume method with a second-order Lax-Friedrichs scheme.

Main Results:

• MCT-based direct numerical simulation (DNS) accurately predicted transonic flow over a 3D bump.
• Achieved better predictions than NS-based DNS using less than 10% of the mesh count.
• Developed a frame-indifferent MCT-based Q criterion to visualize coherent eddy structures objectively.

Conclusions:

• MCT offers a computationally efficient and accurate alternative for modeling compressible turbulence.
• The MCT-based Q criterion provides objective analysis of turbulence, overcoming Galilean invariance limitations.
• This approach enhances the prediction capabilities for complex turbulent flows.