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GENERALIZATION OF THE RANS EQUATIONS USING MEAN MODAL DECOMPOSITION OF THE NAVIER STOKES EQUATIONS

机译:利用Navier Stokes方程的均值模态分解对Rans方程进行广义化

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摘要

A generalization in the Reynolds decomposition and averaging are proposed in this paper. The method is directly applied to the Navier Stokes(N-S) equations to construction of a generalized Reynolds Averaged Navier Stokes(RANS) equations. The formulation which is presented for the fields realized in a suitable ensemble, is based on a two part decomposition. One part is an approximate unique representation of the field and when reconstruction of the field, will repeat in all ensemble elements. The other part represents deviation of the real field from the approximate part and therefore is different in any mode and each ensemble element. The decomposition is applied in both spatial and temporal fashions. In the temporal decomposition, a system of Partial Differential Equations(PDEs) is obtained that is non-closed, coupled and second order in space and its zeroth mode is the classical Reynolds averaged values of the field. In the spatial decomposition whereas, a first order system of nonclosed PDEs is obtained which could be seen as an alternative version of the Proper Orthogonal Decomposition(POD) or the Coherent Vortex Simulation(CVS) methods. In both fashions however, there are some terms that must be modeled just like as the classical closure problem in the RANS method. The method is applied on a one dimensional mixed random-nonrandom field and successfully extracted the coherent part of the field.
机译:本文提出了雷诺分解和平均的一个概括。该方法直接应用于Navier Stokes(N-S)方程,以构造广义雷诺平均Navier Stokes(RANS)方程。针对在合适的集合中实现的领域提出的公式是基于两部分分解的。一部分是该场的近似唯一表示,当重建该场时,将在所有合奏元素中重复。另一部分表示实际场相对于近似部分的偏差,因此在任何模式和每个集合元素中都不同。分解以空间和时间方式应用。在时间分解中,获得了一个偏微分方程组(PDEs),该系统在空间上是非封闭的,耦合的和二阶的,其零阶模式是该场的经典雷诺平均值。在空间分解中,获得了非封闭PDE的一阶系统,该系统可以看作是Proper Orthogonal Decomposition(POD)或Coherent Vortex Simulation(CVS)方法的替代版本。但是,两种方式都必须像RANS方法中的经典闭包问题一样对某些术语进行建模。该方法应用于一维混合随机非随机场,并成功提取了场的相干部分。

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