The renormalization group, the ɛ-expansion and derivation of turbulence models
The renormalization group, the ɛ-expansion and derivation of turbulence models
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DOI：
10.1007/bf01060210
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发表时间：
1992-03
影响因子：
2.5
通讯作者：
V. Yakhot;L. Smith
中科院分区：
文献类型：
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作者：
V. Yakhot;L. Smith
我们重新表述了重整化群（RNG）和推导湍流模型的展开。建立了Navier-Stokes方程和输运方程的动能和能量耗散率公式。推导借鉴了Yakhot和Orszag（1986）和Smith和Reynolds（1992）的工作，所有的结果都是在低阶的微扰展开中发现的。由于o （RT1/2）项在第一阶上的平衡，可知在e -方程中源项的和为o(1)。Smith和Reynolds（1992）展示了RNG过程产生的一些theO（RT1/2）项的消去。在这里，我们表明，包括随机力贡献的产生导致抵消所有theo （RT1/2）项。我们发现，关于平均耗散率的RNG方程中theO(1)项中的两个与广泛使用的模型方程中的theO(1)项具有相同的形式。熟悉项的系数值与实际使用的系数值接近。预测了一个额外的产生项，它对缓慢失真很小，但对快速失真很重要。因此，它可能是应该添加到模型方程中的一项。我们认为，目前的推导使模型方程有了更坚实的理论基础。
We reformulate the renormalization group (RNG) and theɛ-expansion for derivation of turbulence models. The procedure is developed for the Navier-Stokes equations and the transport equations for the kinetic energyKand energy dissipation rate ℰ. The derivation draws on the works of Yakhot and Orszag (1986) and Smith and Reynolds (1992), and all results are found at low order in the underlying perturbation expansion in powers ofɛ. The sum of the source terms in the ℰ-equation is known to beO(1) due to the balance at leading order ofO(RT1/2) terms. Smith and Reynolds (1992) showed the cancellation of some of theO(RT1/2) terms generated by the RNG procedure. Here we show that including the random-force contribution to ℰ-production results in the cancellation ofalltheO(RT1/2) terms. We find that two of theO(1) terms in the RNG equation for the mean dissipation rate ℰ have the same form as those in the widely used model -equation. The values of the coefficients of the familiar terms are close to those used in practice. An extra production term is predicted which is small for slow distortions, but important for rapid distortions. Hence, it may be a term that should be added to the model equation. We believe that the present derivation places the model equation on a more solid theoretical basis.