# Mesh Adaptation for Simulating Lateral Jet Interaction Flow

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hybrid Mesh Adaptive Method

#### 2.1. Numerical Simulation Method

**E**(including the inviscid term ${E}^{I}$ and the viscous term ${E}^{V}$), was used to simplify Equation (1) and discretize it as Formula (2):

**E**), including inflow and outflow grid units, and V is the reciprocal of the Jacobian. Due to overall change in the grid during the pitching process, no local deformation occurs, so the dynamic grid is realized with rigid rotation technology. Formula (2) is written as:

#### 2.2. Adaptation Strategy

#### 2.3. Adaptive Criteria

#### 2.3.1. Quasi-Gradient-Based Adaptation Criterion

#### 2.3.2. Adaptation Criterion Based on Curl and Gradient of Velocity

#### 2.3.3. Adaptation Criterion Based on Vortex Vector

#### 2.4. Combined Adaptation Criteria

- (1)
- If a mesh cell satisfies ${\tau}_{tI}>{\kappa}_{1}{\tau}_{t\mathrm{max}}$ and ${\tau}_{dI}>{\omega}_{2}{\sigma}_{d}$, then it needs to be refined. This identifies shock waves in the flow field.
- (2)
- If a mesh cell satisfies ${\tau}_{cI}>{\omega}_{1}{\sigma}_{c}$ or $R>{\omega}_{3}{\sigma}_{R}$, then it needs to be refined. This identifies vortex structures in the flow field.
- (3)
- If a mesh cell satisfies ${\tau}_{tI}<{\lambda}_{1}{\tau}_{t\mathrm{max}}$ or ${\tau}_{dI}<{\upsilon}_{2}{\sigma}_{d}$, then it needs to be coarsened. This identifies absence of shock waves in the flow field.
- (4)
- If a mesh cell satisfies ${\tau}_{cI}<{\upsilon}_{1}{\sigma}_{c}$ and $R<{\upsilon}_{3}{\sigma}_{R}$, then it needs to be coarsened. This identifies absence of a vortex in the flow field.

#### 2.5. Frequency Selection for Dynamic Grid Adaptation

_{min}) and characteristic length of the concerned flow structure (L

_{v}); its value is in the following range ($\Delta {t}_{G}$) [23]:

## 3. Adaptive Simulation of Lateral Jet Interaction Flow Field

#### 3.1. Generic Missile Model and Flow Conditions

_{cg}= 6.05 D. The free-stream condition was as follows: Mach number = 2.8, static temperature = 108.96 K, static pressure = 20,793.2 Pa, Reynolds number = $2.06\times {10}^{6}$ and angle of attack = 0°. The pressure ratio of the jet was ${P}_{j}/{P}_{\infty}=100$ (the total pressure of the jet divided by the static pressure of the free stream), and the static temperature of the jet was the same as that of the free stream.

#### 3.2. Transverse Jet Efficiency

#### 3.3. Simulation of a Steady Flow

#### 3.4. Simulation of an Unsteady Flow

## 4. Summary

- (1)
- A combined adaptation criterion for unstructured hybrid mesh is proposed for simulating lateral jet interaction flows. This can effectively capture complex structures in the lateral jet interaction flow field, such as shock waves and vortices.
- (2)
- The proposed adaptation criterion can significantly improve convergence of flow computation and resolution of flow structures. It also plays an important role in numerical simulation of lateral jet interaction flows and improves prediction accuracy of the aerodynamic characteristics of a missile.
- (3)
- Compared to the uniformly refined mesh, the adaptive mesh had a similar resolution to the flow field, while the total number of mesh cells was much smaller. Additionally, in this way, computational efficiency can be improved greatly.
- (4)
- The present adaptation criteria can identify characteristic structures in the unsteady flow field and effectively improve resolution of flow and accuracy of aerodynamic calculation.
- (5)
- In parallel computing, adaptive refined mesh may be concentrated in one processor in such a way that seriously imbalanced distributed mesh cannot reduce computational cost effectively. Implementation of dynamic load balancing in the solver for parallel computing will be the focus of future research.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Subdivision of different cells [20].

**Figure 7.**Meshes and contours of the Mach number on the symmetry plane: (

**a**) uniformly refined mesh, (

**c**) base mesh and (

**e**) adaptive mesh; (

**b**,

**d**,

**f**) contours of the Mach number on corresponding meshes in (

**a**,

**c**,

**e**).

**Figure 8.**Mesh and pressure contour on model: (

**a**) uniformly refined mesh, (

**c**) base mesh and (

**e**) adaptive mesh; (

**b**,

**d**,

**f**) contours of pressure on corresponding meshes in (

**a**,

**c**,

**e**).

**Figure 12.**Curves for aerodynamic coefficient: (

**a**) variation in pitching-moment coefficient with angle of attack, (

**b**) variation in normal-force coefficient with angle of attack, and (

**c**) variation in pitching-moment coefficient with time.

**Figure 13.**Amplification factors of transverse jet interaction: (

**a**) force-amplification factor against pitching angle and (

**b**) moment-amplification factor against pitching angle.

Mesh Adaptation | Total Number of Mesh Cells | Growth Rate |
---|---|---|

Base mesh | 1.71 million | / |

Once-adapted | 4.32 million | 155.5% |

Twice-adapted | 14.22 million | 731.6% |

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**MDPI and ACS Style**

Tian, S.; Peng, Z.
Mesh Adaptation for Simulating Lateral Jet Interaction Flow. *Aerospace* **2022**, *9*, 781.
https://doi.org/10.3390/aerospace9120781

**AMA Style**

Tian S, Peng Z.
Mesh Adaptation for Simulating Lateral Jet Interaction Flow. *Aerospace*. 2022; 9(12):781.
https://doi.org/10.3390/aerospace9120781

**Chicago/Turabian Style**

Tian, Shuling, and Zongzi Peng.
2022. "Mesh Adaptation for Simulating Lateral Jet Interaction Flow" *Aerospace* 9, no. 12: 781.
https://doi.org/10.3390/aerospace9120781