ABSTRACT Motivated by the needs of wall modelled Large Eddy Simulation (LES), we introduce fits to numerical solutions of the Reynolds Averaged Navier–Stokes equations in their simplest near-wall, boundary layer approximation including a mixing-length model. We formulate the problem such that independent dimensionless variables are those directly available in LES. We provide practical fits for the dependent variable, fits that encompass a smooth transition between the viscous sublayer and inertial logarithmic layer, and then progress first considering moderate pressure gradients as well as roughness effects under the assumption that the mixing-length is not affected by the pressure gradient. An alternative fit based on the empirical wall model of Nickels (Inner scaling for wall-bounded flows subject to large pressure gradients. J Fluid Mech. 2004;521:217–239) is also provided, taking into account possible effects of pressure gradient on turbulence near-wall structure. We then consider the case of general pressure gradients, both favourable and adverse, up to conditions of separation, for both smooth and rough surfaces. The proposed fitting functions constitute a generalised Moody chart, comply with analytical solutions valid in various asymptotic regimes, and obviate the need for numerical iterative solution methods or near-wall numerical integration of ordinary differential equations during LES.

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关于为壁面建模大涡模拟拟合广义穆迪图的说明

摘要 受壁面建模大涡模拟 (LES) 需求的启发，我们在其最简单的近壁面边界层近似（包括混合长度模型）中引入了对雷诺平均 Navier-Stokes 方程数值解的拟合。我们将问题表述为独立的无量纲变量是那些在 LES 中直接可用的变量。我们为因变量提供了实际拟合，拟合包含粘性子层和惯性对数层之间的平滑过渡，然后首先考虑适度的压力梯度以及粗糙度影响，假设混合长度不受压力梯度。基于镍的经验壁模型的替代拟合（受大压力梯度影响的壁面流动的内部缩放。J Fluid Mech. 2004；521:217–239) 也提供，考虑到压力梯度对湍流近壁结构的可能影响。然后我们考虑一般压力梯度的情况，有利的和不利的，直到分离条件，对于光滑和粗糙的表面。所提出的拟合函数构成了广义穆迪图，符合在各种渐近状态下有效的解析解，并且在 LES 期间不需要数值迭代求解方法或常微分方程的近壁数值积分。