Detached Eddy Simulation (DES)

16.2 Detached Eddy Simulation (DES)

The most popular hybrid method -detached eddy simulation- was proposed in 1997 by Spalart et al. [22]. The principle of DES is illustrated in Fig. 16.1. Close to the body the solution is calculated using the URANS mode. Far from the wall the LES equations are solved. The grey zone between URANS and LES is the mixed solution.

The classical version of the DES approach is based on the Spalart Almaras t =f

Figure

16.1: Zones of the Detached Eddy Simulation.

CN v

D j Q C b1 C w1 f w

@t

@x j

Generation

Destruction

C b2

@x k

@x k

@x k @x k

Diffusion

where

C b1 D 0:1355; C b2 D 0:622; C D 7:1;

C b1 1CC b2

C w1 D 2 C ;

C w2 D 0:3; C w3 D 2:0;

gDrCC w2 .r

r/; rD Q

SDSC Q

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Here d is the distance from the wall. The physical sense of different terms is illustrated in (16.1). Far from the wall the generation and the distruction terms are approaching each to other and the turbulence attains the equilib- rium state:

The kinematic viscosity is then calculated from the formula

b1 Sd Q 2

C w1

which is similar to the Smagorinsky one:

DES inventors proposed to use the following expression for d : dD minfd; C DE S

where C DE S is the DES constant. Now the main idea of the DES becomes obvious: At small wall distance d < C DE S the Spalart Almaras URANS model is active At large wall distance d > C DE S the Spalart Almaras URANS model is smoothly passed into the Smagorinsky model. Samples of DES applications are presented in Fig. 16.2 and 16.3. Despite of the wide application Detached Eddy Simulation technique is not free of disadvantages. Menter [24] notes: The essential concern with DES is that it does not continuously change from RANS to LES under grid re- finement. In order for LES structures to appear, the grid spacing and time step have to be refined beyond a case-dependent critical limit. In addition, a sufficiently large instability mechanism has to be present to allow the rapid formation of turbulent structures in regions where the DES limiter is acti- vated. If one of the two, or both requirements are violated, the resulting model is undefined and the outcome is largely unpredictable.

Figure 16.2: Flow around combat aircraft. (Squires K.D., Detached-eddy simulation: F igure 16.2: Squires K.D., Detached-eddy simulation: current status and current status and perspectives) perspectives.

Figure 16.3: Flow around combat aircraft. (Squires K.D., Detached-eddy simulation: Figure 16.3: Squires K.D., Detached-eddy simulation: current status and current status and perspectives) perspectives.