Renormalization group analysis of the Reynolds stress transport equation
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Engineering topics
Publications and source records attributed to Barton, J. M..
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The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.
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An implicit approximate factorization scheme in conjunction with a new boundary treatment was used to compute the inviscid flow field about an advanced high-speed propeller. The method of characteristics was used to apply impermeable boundary conditions. The convergence history of numerical calculations shows substantial decrease in the residual error decay. Euler solutions were computed for SR-3 propeller geometry and the results were compared with the experimental data and previous numerical results.
A three-dimensional Euler code, previously developed for high speed propellers, was rewritten and vectorized for the Cray computer. Calculations were compared with previous results and measurements. The new code requires less memory and is more than two times faster than its predecessor. The new boundary conditions produced more accurate results and improved stability. The accuracy and stability characteristics also resulted in reduced manual intervention required to obtain solutions. The code is a useful tool for examining the fluid dynamics and performance of propellers.
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