Thermodynamical formulation of turbulent buoyant flows
A two-equation turbulence model that incorporates the effects of buoyancy within the limit of the Boussinesq approximation and is consistent with the second law of thermodynamics was developed. The model was derived by coupling the averaged equations of conservation of mass, balance of momentum, conservation of energy with the entropy inequality. Physical constraints imposed by the second law of thermodynamics were used to derive the constitutive equations for the turbulent stress tensor, heat flux, and energy flux vectors. With this formulation, the model can predict counter-gradient heat diffusion. Counter-gradient diffusion is a physical phenomenon that has been observed experimentally but has not been predicted theoretically. The new model contains empirical constants that were determined via comparison of analytical solutions of simple one-dimensional turbulent flows and with available experimental data. Four different simple flows were used in the calibration process. These flows are the decay of turbulence energy behind a grid, the diffusion of turbulence, the boundary layer near a no-slip solid wall, and the flow with high adverse pressure gradient. The equations were integrated numerically using an Euler, explicit, second order in space, finite differencing scheme. The resulting computer code was used to calculate various two-dimensional turbulent flow.
- Research Organization:
- Clarkson Coll. of Tech., Potsdam, NY (USA)
- OSTI ID:
- 5205324
- Country of Publication:
- United States
- Language:
- English
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