A Length-Scale Equation |
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Authors: | John L Lumley Zhigang Yang Tsan-Hsing Shih |
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Institution: | (1) Sibley School of Mechanical & Aerospace Engineering, Upson and Gumman Halls, Cornell University, Ithaca, NY, 14853, U.S.A.;(2) AYT Corporation, Boulder, CO, 80302, U.S.A.;(3) Ohio Aerospace Institute, Brook Park, OH, 44142, U.S.A. |
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Abstract: | We derive an equation for the average length-scale in a turbulent flow from a simple physical model. This is a tensorial length-scale.
We use as a model the evolution of a blob of turbulent kinetic energy under the influence of production, dissipation, and
transport, as well as distortion by the mean motion. A single length-scale is defined which is biased toward the smallest
of the scales in the various directions. Constants are estimated by consideration of homogeneous decay. Preliminary computations
are carried out in a mixing layer and a two-dimensional jet, using the new length-scale equation and the equation for the
turbulent kinetic energy. The results are compared with data and with the predictions of the classical k-epsilon equations;
the new results are quite satisfactory. In particular, the plane jet/round jet anomaly is approximately resolved.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | turbulence RANS modeling length-scale |
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