Mixing length hypothesis

These models are usually categorized according to the number of supplementary partial differential transport equations which must be solved to supply the modeling parameters. The so-called zero-equation models do not use any differential equation to describe the turbulent quantities. The best known example is the Prandtl (19) mixing length hypothesis ... 

Prandtl mixing length hypothesis, 11 779 Prandtl number, JJ 746, 809 13 246-247 Praseodymium (Pr), J4 631t, 634t electronic configuration, J 474t Praseodymium bromide, physical properties of, 4 329 Prater equation, 25 270, 299 Prater number, 25 299, 300-301, 303 effect on maximum dimensionless intrapellet temperature, 25 304, 309 effect on maximum intrapellet temperature, 25 306 Prato reaction, 12 244 Pratsinis aluminum nitride, 17 212 Pravachol, 5 143... 

C. Prandtl s Mixing Length Hypothesis for Turbuient Fiow... 

Prandtl s mixing length hypothesis (Prandtl, 1925) was developed for momentum transport, instead of mass transport. The end result was a turbulent viscosity, instead of a turbulent diffusivity. However, because both turbulent viscosity and turbulent diffusion coefficient are properties of the flow field, they are related. Turbulent viscosity describes the transport of momentum by turbulence, and turbulent diffusivity describes the transport of mass by the same turbulence. Thus, turbulent viscosity is often related to turbulent diffusivity as... 

C. PRANDTL S MIXING LENGTH HYPOTHESIS FOR TURBULENT FLOW... 

Equation (5.36) is Prandtl s mixing length hypothesis, and it works well, considering that the basis for the equation is so empirical. However, equation (5.36) does present a challenge for us that mixing length, L, stiU needs to be specified. Measurements have shown us the following ... 

Adams, J.C., Jr and Hodge, B.K., The Calculation of Compressible, Transitional, T ir-bulent, and Relaminarizational Boundary Layers over Smooth and Rough Surfaces Using an Extended Mixing Length Hypothesis , AIAA Paper 77-682, Albuquerque, NM, 1977. 

Other suggestions were done for the mixing length l(z) present in the PrandtFs mixing length hypothesis vT = l2 dU/dz, some of them link the length with the forest density s [155] ... 

The constant A in Eq. 10.2.20 is the von Karman constant, equal to 0.4. Though the Prandtl mixing length hypothesis (Eq. 10.2.20) works for conditions in the turbulent core... 

Thereafter, the closure consists in determining the SGS eddy viscosity parameter. By analogy to the mixing length hypothesis, the Smagorinsky [150] model is defined as ... 

In the context of the two-dimensional problem considered here, the mixing-length hypothesis holds that the concentration fluctuation at any point (.v, t) is due to the arrival at that point of a fluid eddy that originated at some other location where the mean concentration (c) was different from that at(.v, y, t). 

Indeed, this is the exact form employed in the usual mixing-length hypothesis for an inert species. Substituting (17.19) into (17.15) and expanding (c(.y, 3 + Ij, t Zj)) in a first-order Taylor series about the point (j, y, r)i we get... 

Prandtl, [43] using boundary layer theory, mixing length hypothesis and law of the wall, developed the following theoretical law of friction for smooth pipes in turbulent flow... 

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