Spalart—Allmaras湍流模型简介

redboy

该模型是NUMECA软件Version 6.1中新添加的一方程模型.
Spalart—Allmaras湍流模型直接根据经验和量纲分析，从简单流动开始，直到得到最终的控制方程。它相对于两方程模型计算量小和稳定性好，计算网格到壁面的加密程度可以与零方城模型有同等的量级。另外，模型是“当地”型的，所有在有多个物面的复杂流场的计算中不需要特殊处理。
Spalart—Allmaras一方程湍流模型的提出，最初是基于外流计算的考虑。由于外流与内流湍流流场在某种程度上有相当大的不同，所以它在内流计算中使用效果还需要进一步的验证。另外，最初的Spalart—Allmaras湍流模型是基于不可压缩流动，模型方城是非守恒的。
以上文字摘自文献
《Spalart—Allmaras湍流模型在内流流场数值模拟中的应用》
宁方飞，徐力平
工程热物理学报，Vol 22.3 2001

numeca

关于S-A的局限性不是在于内流、外流的区分。以下引用部分内容：
In zero-equation models, also called algebraic models, the eddy-viscosity is defined
from an algebraic relationship instead of a differential one. The earliest example of
such models comes from Prandtl [160], who introduced the concept of mixing length.
This hypothesis [206] forms the basis of all the algebraic turbulence models. From this
basis, Van Driest [188] devised a viscous damping correction which is now included
in almost all algebraic models. Other major improvements to these models were given
by Cebeci and Smith [30], then by Baldwin and Lomax [9]. Algebraic models
generally perform well for thin, attached shear layers at moderate Mach numbers.
However, they are incomplete since additional information other than initial and
boundary conditions must be known, namely the mixing length. Generally, incomplete models define this length scale in a prescribed manner from the mean flow, e.g. the
displacement thickness, , for an attached boundary layer. However, if this boundary
layer separates, or if a shear flow is met, other length scales are required, otherwise
inconsistencies are met. This is why algebraic models generally give poor predictions
in such cases. A second drawback is that, since these models cannot take into account
turbulence transport and diffusion, flow history effects cannot be simulated.
δ* In order to address the latter issue, Prandtl [161] postulated a model in which the eddyviscosity
depends on the kinetic energy of the turbulent fluctuations, . He proposed
a modeled partial-differential equation approximating the exact equation for . This
led to the concept of the one-equation turbulence model. Although these models
brought an improvement compared to algebraic ones, by making the turbulent eddyviscosity
depend upon flow history, the need to define a mixing length still remained
and the models were thus still incomplete. This may explain why one-equation models
where the turbulent kinetic energy transport equation was solved were not very
popular, since the advantage gained over algebraic models was modest. Recently, there
has been a renewed interest in a new generation of one-equation models based on a
postulated equation for the eddy viscosity. These models are complete, that is, they do
not require the specification of any length scale. Two of the most commonly used
models are due to Baldwin and Barth [8], and to Spalart and Allmaras [173]. While the
Baldwin-Barth model is quite inaccurate for attached boundary layers, in particular
with adverse pressure gradients [206], and therefore of little interest when having
general turbulent flow applications in mind, the Spalart-Allmaras model is of great
interest. Indeed, this model offers skin friction predictions for attached boundary
layers that are as close to experiments as algebraic models, and is superior to the latter
when separated flows are met. Furthermore, the differential equation offers no serious
numerical difficulties and its integration in an unstructured code is straightforward
compared to mixing-length models. The only drawback lies in its apparent failure to
accurately predict the asymptotic spreading rates for plane, circular and radial jets.
However, this model is quite attractive for engineering applications since it offers a
good compromise between accuracy and computational costs.........
The Spalart-Allmaras model [173] is a recent complete one-equation eddy-viscosity
model, which has been formulated based on empiricism and dimensional analysis to
give the right behavior in two-dimensional mixing layers, wakes, and flat plate
boundary layers, which were considered by the authors as the building blocks for
aerodynamic flows.
The model is local, that is, the equation at one point does not depend on the solution
at other points. It is therefore easily usable with any kind of grids, and in particular
unstructured grids. Another advantage is its relatively low additional computational
cost compared to the resolution of the RANS system itself. This model performs well
for a wide variety of flows, and can even outperform some two-equation models in
separating or reattaching flow prediction. Its failure to accurately reproduce jet
spreading rates should serve as a warning that the model has some shortcomings, but
remains a valuable engineering tool.
Spalart and Allmaras have also developed an additional term, which is used to trip the
solution from laminar to turbulent at a certain location, hence enabling the user to
specify transition points. This feature is appealing as subsequent downstream
predictions can critically depend on the appropriate choice for the onset of turbulence.  .......

HahaOcean

麻烦请教numeca，上述引文是摘录自哪里的？多谢

numeca

The contents are from the PhD thesis of Alpesh Patel, 2003

boling2000

这份文献能以附件形式上传吗？
或者能放到你们的网页上吗？

沈沉

学习了，很有用，谢谢

monday

考古贴啊。