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Renormalization group analysis for thermal turbulent transport.
1Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 10764, Taiwan, Republic of China.
Summary
This study analyzes incompressible turbulence using renormalization group methods to determine thermal transport properties. It derives the turbulent Prandtl number and thermal diffusivity, yielding constants for turbulent energy transport models.
Area of Science:
- Physics
- Fluid Dynamics
- Turbulence
Background:
- Incompressible turbulence analysis requires understanding thermal transport properties.
- Passive scalar transport, like temperature fields (T), is crucial in turbulent flows.
- Previous renormalization group (RG) analysis provides a foundation for this study.
Purpose of the Study:
- To determine thermal transport properties in incompressible turbulence.
- To derive the turbulent Prandtl number (Pr(t)) and thermal eddy diffusivity (sigma).
- To determine model constants for turbulent energy transport.
Main Methods:
- Renormalization group (RG) analysis of incompressible turbulence.
- Quasinormal approximation for statistical correlations between velocity and temperature fields.
- Derivation of turbulent Prandtl number (Pr(t)) as a function of turbulent Peclet number (Pe(t)) and eddy viscosity (nu(t)).
- Development of an inhomogeneous ordinary differential equation for thermal eddy diffusivity (sigma).
Main Results:
- A functional relationship between Pr(t) and Pe(t) consistent with simulations and experimental data.
- A closed-form solution for sigma as a function of wave number (k).
- Determination of the Batchelor constant (C(B)) and Smagorinsky model constant (C(P)).
Conclusions:
- The RG analysis provides a robust framework for understanding turbulent thermal transport.
- The derived relationships and constants are validated against existing data.
- This work contributes to improved modeling of turbulent heat and mass transfer.