# Numerical Analysis of Supersonic Impinging Jet Flows of Particle-Gas Two Phases

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis

#### 2.1. Pressure Coefficient

_{p}is pressure coefficient on ground plate, P

_{s}, P

_{0}and P

_{∞}are surface pressure, inlet stagnation pressure, and ambient pressure, respectively.

#### 2.2. Particle Drag Coefficient

_{g}> 1.75),

_{D}is drag coefficient and Re is particle Reynolds number. M

_{g}is Mach number of gas phase, M is Mach number based on relative velocity between gas phase and particle phase, and S is the molecular speed ratio.

_{P}is particle density and D

_{p}is particle diameter. µ is dynamic viscosity of fluid and U and U

_{p}are the velocity of gas phase and particle phase, respectively. Based on different expressions of drag coefficients for supersonic and subsonic particle-gas flows, particle drag force F

_{D}can be obtained as shown in Equation (7):

#### 2.3. Stokes Number

_{0}is relaxation time and L is characteristic length of geometry. Particles at lower Stokes number follow flow streamlines more properly and show better tracing accuracy [27]. Relaxation time is regarded as a measurement of the responsiveness of particles to a change in flow velocity.

^{3}and nozzle pressure ratio is fixed to be 5. Relaxation time t

_{0}and Stokes number of particles were calculated to be 4.76 µs, 119 µs, 476 µs, and 0.112, 2.8, 11.2 as particle diameter is 1 µm, 5 µm, 10 µm respectively.

#### 2.4. Impinging Force on Plate Ground

_{I}is impinging force on calculated area and P

_{AV}is area average pressure on calculated area. A is the calculated area. Due to a large domain used as ground plate, the area where it is greatly affected by the pressure was used for calculating impinging force as shown in Figure 2a,b. Full ground plate was proved to be not suitable for showing the difference in impinging force between single gas flow and particle-gas flows.

## 3. Numerical Methods

#### 3.1. Computational Domain

#### 3.2. Numerical Schemes

#### 3.3. Boundary Conditions

^{3}was used as injected particles. Particle mass loading which defines as particle mass flow rate occupying the percent from total mass flow rate of gas-particle flows was fixed to be 10%. Effects of particle diameter varied from 1 to 10 µm on particle-gas flows were investigated.

#### 3.4. Mesh Independence Study

## 4. Results and Discussion

#### 4.1. Validation

#### 4.2. Particle-Gas Flows Induced by Different Nozzles

#### 4.3. Effect of Stokes Number

#### 4.4. Particle Effects

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Pressure contours on the ground plate and calculated area for calculating impinging force. (

**a**) Pressure contours on the ground plate; (

**b**) Calculated area.

**Figure 8.**Velocity magnitude contours of particle and gas flow. (

**a**) Particle velocity; (

**b**) Particle velocity; (

**c**) Gas velocity; (

**d**) Gas velocity.

**Figure 11.**Mach number contours for single gas flow and gas-particle flows. (

**a**) Single gas flow; (

**b**) Gas-particle flows.

**Figure 12.**Velocity contours and streamlines at different cross-sections for single gas flow. (

**a**) XOY plane; (

**b**) XOZ plane.

**Figure 13.**Velocity contours and streamlines at different cross-sections for gas-particle flows. (

**a**) XOY plane; (

**b**) XOZ plane.

**Figure 16.**Wall shear stress contours on the ground plate for single gas flow and particle-gas flows. (

**a**) Single gas flow; (

**b**) Particle-gas flows.

Cases | Single Gas Flow | Particle Mass Loading of 10% | Particle Mass Loading of 20% |
---|---|---|---|

F_{I} (N) | 109.42 | 192.14 | 223.67 |

Non-dimensional F_{I} | 1 | 1.756 | 2.044 |

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**MDPI and ACS Style**

Zhang, G.; Ma, G.F.; Kim, H.D.; Lin, Z.
Numerical Analysis of Supersonic Impinging Jet Flows of Particle-Gas Two Phases. *Processes* **2020**, *8*, 191.
https://doi.org/10.3390/pr8020191

**AMA Style**

Zhang G, Ma GF, Kim HD, Lin Z.
Numerical Analysis of Supersonic Impinging Jet Flows of Particle-Gas Two Phases. *Processes*. 2020; 8(2):191.
https://doi.org/10.3390/pr8020191

**Chicago/Turabian Style**

Zhang, Guang, Guang Fei Ma, Heuy Dong Kim, and Zhe Lin.
2020. "Numerical Analysis of Supersonic Impinging Jet Flows of Particle-Gas Two Phases" *Processes* 8, no. 2: 191.
https://doi.org/10.3390/pr8020191