On URANS Congruity with Time Averaging: Analytical laws suggest improved models
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The standard 1-equation model of turbulence was first derived by Prandtl and has evolved to be a common method for practical flow simulations. Five fundamental laws that any URANS model should satisfy are < a r r a y > This report proves that a kinematic specification of the model's turbulence lengthscale by l(x,t)=√(2)k^1/2(x,t)τ, where τ is the time filter window, results in a 1-equation model satisfying Conditions 1,2,3,4 without model tweaks, adjustments or wall damping multipliers.
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