7.3.5 Detached Eddy Simulation 脱体涡模拟[cfd-7-3-5]
尽管上述壁面模型有助于大幅减少网格点（单元）数量，但对于复杂的工程外形，LES仍然过于昂贵。为此，Spalart最近提出了另一种方法——所谓的脱体涡模拟（Detached Eddy Simulation，DES），其目标是高雷诺数大范围分离流动的模拟[154]、[155]。该方法可以说是RANS与LES的混合体：其思想是在强拉伸网格上配合RANS湍流模型（大多是Spalart-Allmaras模型，见小节7.2.1，或Menter的SST模型，见小节7.2.3）来解析附着边界层，而在壁面区之外配合各向同性网格使用LES来捕捉脱体的三维涡。这样，DES试图在一个统一框架内结合两种方法的长处。en
Even though the above wall models help to reduce the number of grid points (cells) considerably, LES still remains too costly for complex engineering configurations. For this reason, Spalart recently suggested another approach, the so-called Detached Eddy Simulation (DES), which is aimed at the simulation of high Reynolds-number massively separated flows [154], [155]. The methodology represents a hybrid between the RANS and LES. The idea is to employ highly stretched grids together with a RANS turbulence model (mostly the Spalart-Allmaras model from Subsection 7.2.1 or Menter's SST model from Subsection 7.2.3) to resolve the attached boundary layer(s), and to use LES outside the wall region together with an isotropic grid to capture the detached 3-D eddies. Thus, DES tries to combine the strengths of both methods in a single framework.
该长度尺度取决于控制体的最大尺寸，即\(\Delta = \max(\Delta x, \Delta y, \Delta z)\)。常数\(C_{DES}\)在一定程度上依赖于流动类型：对均匀湍流，发现\(C_{DES} = 0.65\)最优[156]；而对跨声速和超声速射流，则建议取\(C_{DES} = 0.1\)[157]。方程(7.102)中长度尺度\(l\)的定义保证了：在边界层内，那里\(d < C_{DES}\Delta\)、因而\(l = d\)，恢复出原始的RANS模型；而在边界层之外\(l = C_{DES}\Delta\)，Spalart-Allmaras模型则充当LES的单方程SGS模型（对照方程(7.91)和式(7.24)）。在时间方向积分控制方程时，全局时间步长必须调整到能够解析脱体涡的时间尺度。这通常意味着时间步长会远远超出显式格式在边界层区域的稳定裕度。因此更高效的做法是采用时间精确的隐式格式，例如6.3节所述的双时间步进方法。关于DES方法的更多细节和模拟实例可参见上述文献或[158]-[161]。en
The length scale is dependent on the largest dimension of the control volume, i.e., \(\Delta = \max(\Delta x, \Delta y, \Delta z)\). The constant \(C_{DES}\) depends to some extent on the type of the flow. For a homogeneous turbulence, the value \(C_{DES} = 0.65\) was found optimal [156]. On the other hand, \(C_{DES} = 0.1\) was recommended for transonic and supersonic jets [157]. The definition of the length scale \(l\) in Eq. (7.102) makes sure that within the boundary layer, where \(d < C_{DES}\Delta\) and hence \(l = d\), the original RANS model is recovered. On the other hand, outside the boundary layer \(l = C_{DES}\Delta\) and the Spalart-Allmaras model serves as a one-equation SGS model for the LES (cf. Eq. (7.91) and (7.24)). When integrating the governing equations in time, the global time step has to be adjusted such as to resolve the time scales of the detached eddies. This usually means that the time step would by far exceed the stability margin of an explicit scheme for the boundary layer region. It is therefore more efficient to employ a time-accurate implicit scheme, such as the dual time-stepping approach described in Section 6.3. More details regarding the DES methodology and examples of simulations can be found in the above references or in [158]-[161].