Based on the analysis of the direct numerical simulation (DNS) database of the heated and unheated turbulent boundary layers at supercritical pressures (Kawai J. Fluid Mech. 865 , 563 2019 ), this paper proposes a Reynolds-averaged Navier-Stokes (RANS) turbulence modeling for predicting the turbulent boundary layers at supercritical pressure where large density fluctuations are induced by the pseudo-boiling phenomena. The proposed approach is to model the mass flux contribution term M τ = u i ′ ′ ¯ ∂ τ i j ¯ / ∂ x j $M_{\tau }=\overline {u_{i}^{\prime \prime }} \partial \overline {\tau _{ij}}/\partial x_{j}$ in the turbulent kinetic energy equation (more specifically the turbulent mass flux u i ′ ′ ¯ = − ρ ′ u i ′ ¯ / ρ ¯ $\overline {u_{i}^{\prime \prime }}= -\overline {\rho ^{\prime } u_{i}^{\prime }}/\overline {\rho }$ in M τ term) and add the modeled M τ to the k -transport equation in the RANS model in order to incorporate the effects of the large density fluctuations on turbulence observed in the DNS. The key idea of modeling the turbulent mass flux in M τ is to employ the gradient diffusion hypothesis and we propose to model u i ′ ′ ¯ $\overline {u_{i}^{\prime \prime }}$ as a function that is proportional to the density gradient (i.e. u i ′ ′ ¯ ∝ μ ¯ t ∂ ρ ¯ / ∂ x j $\overline {u_{i}^{\prime \prime }} \propto \overline {\mu }_{t} \partial \overline {\rho }/\partial x_{j}$ ). The proposed RANS model shows significant improvements over existing models for predicting the logarithmic law for the mean velocity and temperature in the turbulent boundary layers at supercritical pressure, something that existing RANS models fail to do robustly.

中文翻译：

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超临界压力下湍流边界层的湍流建模：湍流质量通量模型

建议的方法是模拟质量通量贡献项 M τ = ui ′ ′ ¯ ∂ τ ij ¯ / ∂ xj $M_{\tau }=\overline {u_{i}^{\prime \prime }} \partial \湍动能方程中的上划线 {\tau _{ij}}/\partial x_{j}$（更具体地说是湍流质量通量 ui ′ ′ ¯ = − ρ ′ ui ′ ¯ / ρ ¯ $\overline {u_{ i}^{\prime \prime }}= -\overline {\rho ^{\prime } u_{i}^{\prime }}/\overline {\rho }$ in M τ term) 并添加建模的 M τ 到 RANS 模型中的 k 传输方程，以便将大密度波动对 DNS 中观察到的湍流的影响结合起来。在 M τ 中模拟湍流质量通量的关键思想是采用梯度扩散假设，我们建议将 ui ′ ′¯ $\overline {u_{i}^{\prime \prime }}$ 建模为一个函数，即与密度梯度成正比（即 ui ′ ′ ¯ ∝ μ ¯ t ∂ ρ ¯ / ∂ xj $\overline {u_{i}^{\prime \prime }} \propto \overline {\mu }_{t} \partial \overline {\rho } //部分 x_{j}$ )。提出的 RANS 模型比现有模型显着改进，用于预测超临界压力下湍流边界层中平均速度和温度的对数定律，这是现有 RANS 模型无法稳健地做到的。