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The exergy concept and compressible turbulence
Theoretical and Computational Fluid Dynamics ( IF 3.4 ) Pub Date : 2020-05-19 , DOI: 10.1007/s00162-020-00533-z Andreas Jocksch
Theoretical and Computational Fluid Dynamics ( IF 3.4 ) Pub Date : 2020-05-19 , DOI: 10.1007/s00162-020-00533-z Andreas Jocksch
Turbulence models facilitated by Kolmogorov’s theory play an important role for compressible flows. Typically the basis of these models is the power spectrum of the velocity $${\mathbf {u}}$$ u or of the density-weighted velocity $${\mathbf {w}}\equiv \rho ^{1/3}{\mathbf {u}}$$ w ≡ ρ 1 / 3 u . While for incompressible flow the quantity turbulent kinetic energy characterises turbulent motions, from the thermodynamic point of view, due to fluctuations of the density and the temperature other kinds of energies play a role at the different scales in compressible turbulence. We generalise the power spectrum of the velocity $${\mathbf {u}}$$ u from incompressible flows to compressible flows by introducing the exergy spectrum as an application of the exergy concept. Furthermore, we discuss the application of the concept of turbulent exergy to turbulence modelling and demonstrate this approach with a direct numerical simulation and a Large-Eddy-Simulation of homogeneous isotropic turbulence. The advantage of turbulence modelling based on turbulent exergy is shown on the example of the Approximate Deconvolution Model (ADM) where, at smallest scales for its newly introduced entropy formulation, more available energy is extracted from the flow, and this occurs in a more physical way than for the classical equation set of the model using the total energy.
中文翻译:
火用概念和可压缩湍流
Kolmogorov 理论促进的湍流模型对可压缩流动起着重要作用。通常,这些模型的基础是速度 $${\mathbf {u}}$$ u 或密度加权速度 $${\mathbf {w}}\equiv \rho ^{1/3 的功率谱}{\mathbf {u}}$$ w ≡ ρ 1 / 3 u 。而对于不可压缩流动,湍流动能的数量表征了湍流运动,从热力学的角度来看,由于密度和温度的波动,其他类型的能量在可压缩湍流中在不同尺度上发挥作用。我们通过引入火用能谱作为火用概念的应用,将速度 $${\mathbf {u}}$$ u 的功率谱从不可压缩流推广到可压缩流。此外,我们讨论了湍流火用概念在湍流建模中的应用,并通过直接数值模拟和均匀各向同性湍流的大涡模拟来证明这种方法。近似解卷积模型 (ADM) 的示例显示了基于湍流火用的湍流建模的优势,其中,在其新引入的熵公式的最小尺度上,从流动中提取了更多可用能量,这发生在更物理的比使用总能量的模型的经典方程组的方式。
更新日期:2020-05-19
中文翻译:
火用概念和可压缩湍流
Kolmogorov 理论促进的湍流模型对可压缩流动起着重要作用。通常,这些模型的基础是速度 $${\mathbf {u}}$$ u 或密度加权速度 $${\mathbf {w}}\equiv \rho ^{1/3 的功率谱}{\mathbf {u}}$$ w ≡ ρ 1 / 3 u 。而对于不可压缩流动,湍流动能的数量表征了湍流运动,从热力学的角度来看,由于密度和温度的波动,其他类型的能量在可压缩湍流中在不同尺度上发挥作用。我们通过引入火用能谱作为火用概念的应用,将速度 $${\mathbf {u}}$$ u 的功率谱从不可压缩流推广到可压缩流。此外,我们讨论了湍流火用概念在湍流建模中的应用,并通过直接数值模拟和均匀各向同性湍流的大涡模拟来证明这种方法。近似解卷积模型 (ADM) 的示例显示了基于湍流火用的湍流建模的优势,其中,在其新引入的熵公式的最小尺度上,从流动中提取了更多可用能量,这发生在更物理的比使用总能量的模型的经典方程组的方式。