# Research and Application of Filtering Grid Scale in Detached Eddy Simulation Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{sst}into DES to reduce the excessive dependence on grid density based on the two-equation SST k-ω model. Although compared with the original DES hybrid model the real flow could be simulated more accurately, it was not universal. Spalart [9] constructed another kind of delay function f

_{d}. It was firstly applied in the RANS/LES switching function, which effectively delayed the switching from RANS to LES and solved the problem of grid-induced separation [10,11,12]. To further enhance the ability to resolve turbulence in the boundary layer, Shur [13] combined the Delayed Detached Eddy Simulation (DDES) with Wall-modeled Large-eddy Simulation (WMLES), namely IDDES. Although the IDDES method can improve the calculation accuracy in the boundary layer, the introduced WMLES means there is a complete LES method within the whole flow field. In a sense, this contradicts the original intention of DES-type models (RANS in the boundary layer and LES in other regions).

## 2. DES Grid

#### 2.1. Boundary Layer Mesh

#### 2.2. Filtering Grid Scale

- (1)
- As the main component of the DES switching function, it is used to determine whether the flow region is suitable for RANS or LES.
- (2)
- As the sub-grid grid scale of LES, large and small vortexes in the flow field are separated. There are two definition methods for filtering grid scales.

#### 2.2.1. ${\Delta}_{\mathit{max}}$ (Maximum Criterion)

#### 2.2.2. ${\Delta}_{\mathit{IDDES}}$ (IDDES Grid Scale Definition)

_{IDDES}.

## 3. Comparison of Three Grid Scale Definition Methods

#### 3.1. Arithmetic Mean (${\Delta}_{\mathit{AM}}$)

#### 3.2. Geometric Mean (${\Delta}_{\mathit{GM}}$)

_{i}is the weight ($i=1,\text{}2,\text{}\dots ,\text{}n$).

#### 3.3. Quadratic Mean (${\Delta}_{\mathit{QM}}$)

#### 3.4. Relations between Three Filtering Grid Scales

## 4. Internal Flow Simulation in Curved Elbow

#### 4.1. Physical Model

#### 4.2. Calculation Settings

#### 4.3. Calculation Results

#### 4.3.1. Comparison of the Average Speed Curve in the Mainstream Direction

#### 4.3.2. External Arc Surface Flow Static Pressure Distribution (${r}^{*}=0,{Z}^{*}=0$)

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Three types of grid in the boundary layer [9]. (

**a**) Boundary layer grid type I; (

**b**) Boundary layer grid type II; (

**c**) Boundary layer grid type III.

**Figure 6.**Time-averaged velocity distribution of flow cross section. (

**a**) The mainstream time-averaged velocity distribution curve obtained by the DES model at ${r}^{*}=0.9$; (

**b**) the mainstream time-averaged velocity distribution curve obtained by the DES model at ${r}^{*}=0.5$; (

**c**) the mainstream time-averaged velocity distribution curve obtained by the DES model at ${r}^{*}=0.1$.

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**MDPI and ACS Style**

Dong, L.; Guo, C.; Wang, Y.; Liu, H.; Dai, C.
Research and Application of Filtering Grid Scale in Detached Eddy Simulation Model. *Symmetry* **2020**, *12*, 1252.
https://doi.org/10.3390/sym12081252

**AMA Style**

Dong L, Guo C, Wang Y, Liu H, Dai C.
Research and Application of Filtering Grid Scale in Detached Eddy Simulation Model. *Symmetry*. 2020; 12(8):1252.
https://doi.org/10.3390/sym12081252

**Chicago/Turabian Style**

Dong, Liang, Chao Guo, Ying Wang, Houlin Liu, and Cui Dai.
2020. "Research and Application of Filtering Grid Scale in Detached Eddy Simulation Model" *Symmetry* 12, no. 8: 1252.
https://doi.org/10.3390/sym12081252