# Gaskinetic Modeling on Dilute Gaseous Plume Impingement Flows

## Abstract

**:**

## 1. Introduction

## 2. Background and Gaskinetic Methods to Investigate Plume and Impingement Flows

## 3. Gaseous Jet Impingement on a 2D Inclined Planar Plate

## 4. 3D Diffuse and Specular Reflective Plate Surface Properties

## 5. Averaged Surface Properties for Gaseous Plume Impinging Flows

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Several Important Integrals

## References

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**Figure 1.**Free jet impingement on an inclined planar diffuse reflective plate, $\angle POX={\theta}_{0}$, $\angle PBF={\theta}_{1}$, $\angle PAG={\theta}_{2}$, $\angle PEH={\theta}_{3}={\alpha}_{0}+{\beta}_{2}$, and $\angle ICP={\theta}_{4}={\alpha}_{0}+\pi -{\beta}_{1}$.

**Figure 2.**Velocity spaces for jet impinging on a planar, flat, diffuse reflective plate.

**Left**: $\angle HFu={\theta}_{1}$, $\angle GFu={\theta}_{2}$;

**Right**: $\angle uoI={\theta}_{3}={\alpha}_{0}+{\beta}_{2}$, $\angle Jou={\theta}_{4}={\alpha}_{0}+\pi -{\beta}_{1}$. Integration ${\mathrm{\Omega}}_{1}$ is for the free jet, and ${\mathrm{\Omega}}_{2}$ is for the reflected particles.

**Figure 3.**Free jet impingement on an inclined specular planar reflective plate. $\angle PBI={\theta}_{1}$, $\angle PAJ={\theta}_{2}$, $\angle PoX={\theta}_{0}$, $\angle PFK={\theta}_{5}$, $\angle PEL={\theta}_{6}$.

**Figure 4.**Velocity space for jet impinging on a specular planar reflective plate. $\angle TRu={\theta}_{1}$, $\angle SRu={\theta}_{2}$, $\angle QMP={\theta}_{5}$, $\angle NMP={\theta}_{6}$. Integration domain, ${\mathrm{\Omega}}_{1}$ is for the free jet, and ${\mathrm{\Omega}}_{2}$ is for the reflected particles.

**Figure 5.**Temperature contours for free jet impingement on an inclined, planar, flat, diffuse reflective plate. Solid: analytical; dashed: DSMC (Direct Simulation Monte Carlo).

**Figure 6.**Temperature contours for free jet impingement on an inclined, flat, planar, specular reflective plate. Solid: analytical; dashed: DSMC.

**Figure 7.**Diffuse planar plate, surface ${C}_{p,d}(s)$, ${T}_{w}/{T}_{0}=1.5$. Lines: analytical; symbols: DSMC.

**Figure 9.**Diffuse planar plate: surface ${C}_{f,d}(s)$, ${T}_{w}/{T}_{0}=1.5$. Lines: analytical; symbols: DSMC.

**Figure 10.**Diffuse planar plate: surface ${C}_{q,d}(s)$, ${T}_{w}/{T}_{0}=1.5$. Lines: analytical; symbols: DSMC.

**Figure 12.**Velocity phases for the problem of a round jet impinging on a diffuse reflective plate.

**Left**: for the free jet;

**Right**for the reflected particles.

**Figure 13.**Illustration of the problem of a round jet impinging on a specular reflective plate. Dashed lines: virtual nozzle.

**Figure 14.**Velocity phases for the specular reflective plate impingement problem. Solid cone: for the free jet; dashed red cone: reflected particles.

**Figure 15.**Pressure contours for free jet impingement on an inclined diffuse rectangular reflective plate, from a round exit, in the middle vertical plane. Results normalized by the static pressure at the nozzle exit. Dashed: analytical; solid: DSMC.

**Figure 16.**Pressure contours for free jet impingement on an inclined specular rectangular reflective plate, from a round exit, in the middle vertical plane. Results normalized by the static pressure at the nozzle exit. Dashed: analytical; solid: DSMC.

**Figure 17.**Diffuse plate, pressure contours, ${C}_{p,d}(s,\tau )$, ${S}_{0}=2.0$, ${T}_{w}/{T}_{0}=1.5$, ${\alpha}_{0}={60}^{\circ}$. Plate lengths are normalized by the nozzle diameter. Solid: analytical; dashed: DSMC.

**Figure 18.**Specular plate, pressure contours, ${C}_{p,s}(s,\tau )$, ${S}_{0}=2.0$, ${\alpha}_{0}={60}^{\circ}$, ${T}_{w}/{T}_{0}=1.5$. Plate lengths are normalized by the nozzle diameter. Solid: analytical; dashed: DSMC.

**Figure 19.**Diffuse plate, friction coefficient, ${C}_{{f}_{1},d}(s,\tau )$, ${S}_{0}=2.0$, ${T}_{w}/{T}_{0}=1.5$, ${\alpha}_{0}={60}^{\circ}$. Plate lengths are normalized by the nozzle diameter. Solid: analytical; dashed: DSMC.

**Figure 20.**Diffuse plate, friction coefficient, ${C}_{{f}_{2},d}(s,\tau )$, ${S}_{0}=2.0$, ${T}_{w}/{T}_{0}=1.5$, ${\alpha}_{0}={60}^{\circ}$. Plate lengths are normalized by the nozzle diameter. Solid: analytical; dashed: DSMC.

**Figure 21.**Diffuse plate, heat flux, ${C}_{q,d}(s,\tau )$, ${S}_{0}=2.0$, ${T}_{w}/{T}_{0}=1.5$, ${\alpha}_{0}={60}^{\circ}$. Plate lengths are normalized by the nozzle diameter. Solid: analytical; dashed: DSMC.

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Cai, C.
Gaskinetic Modeling on Dilute Gaseous Plume Impingement Flows. *Aerospace* **2016**, *3*, 43.
https://doi.org/10.3390/aerospace3040043

**AMA Style**

Cai C.
Gaskinetic Modeling on Dilute Gaseous Plume Impingement Flows. *Aerospace*. 2016; 3(4):43.
https://doi.org/10.3390/aerospace3040043

**Chicago/Turabian Style**

Cai, Chunpei.
2016. "Gaskinetic Modeling on Dilute Gaseous Plume Impingement Flows" *Aerospace* 3, no. 4: 43.
https://doi.org/10.3390/aerospace3040043