Spalart-Allmaras Model

Spalart-Allmaras模型是一个相对简单的单方程模型,解决了针对湍流运动学粘度输运方程模型，这体现了一类相对较新的单方程模型，在这类模型中剪切层的厚度尺度计算显得无关紧要。

Spalart-Allmaras模型是专门为航空航天应用所设计的,涉及wall边界内的流动。该模型在逆(负)压梯度边界层也具有良好的效果。同时它也获得了叶轮机械应用的普及。但不适合用于模拟复杂的内部流

    It is the 1-equation model analyzing turbulence flow by integral with respect to the wall.This model is developed from the mixing length model,and shows accuracy in the level of 2-equation model. The Spalart-Allmaras model suggests the transport equation with respect to the modified turbulent kinematic viscosity v and is expressed as follows.

v : modified turbulent kinematic viscosity

S: modified vorticity

R: circular pipe radius or open channel flow depth

S is modified from the vorticity S calculated as like the equation (4.3.7) and is calculated as the equation(4.3.8). Functionsandandin the equation (4.3.8) are damping functions and are expressed as the equation (4.3.9) respectively. x is the actual, non-dimensional and modified turbulent kinematic viscosity and it is calculated as the equation (4.3.10).

:damping functions

In addition, g in the equation (4.3.9) is derived as follows

:constants

Finally, the turbulent viscosity is calculated as follows

   The Spalart-Allmaras model does not require fine mesh for wall bounded flow as like the 2-equation turbulence model and exhibits excellent convergence for simple flow. In addition, it is more accurate to predict the flow around airfoil as well as the adverse pressure gradient flow compared to themodel or the model. On the other hand, it is known less accurate in analysis on the strongly separated flow such as jet flow or the decaying turbulence flow

模型无法准确模拟逆压力梯度adverse pressure gradient下的边界层运动

因此在空气动力学和涡轮机械领域，为了得到逆压力梯度条件下更好的模拟结果，Spalart-Allmaras Model被提出