# Effects of Nozzle Pressure Ratio and Nozzle-to-Plate Distance to Flowfield Characteristics of an Under-Expanded Jet Impinging on a Flat Surface

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Facility and Particle Image Velocimetry (PIV) Experimental Setup

#### 2.1. Experimental Facility of Impinging Jet

#### 2.2. PIV Experimental Setup

## 3. Results from PIV Measurements of Under-Expanded Free Jets and Impinging Jets

#### 3.1. Experimental Results of Under-Expanded Free Jets for Various Values of NPRs

#### 3.2. Experimental Results of Under-Expanded Impinging Jets for Various Nozzle-to-Plate Gaps and NPRs

## 4. Proper Orthogonal Decomposition Analysis to the Free Jet and Impinging Jet Flows

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overview of the experimental facility of the free jet and impinging jet. (

**a**,

**b**) Experimental rig and PIV experimental setup, (

**c**,

**d**) a close-view and dimensions of the tested nozzle.

**Figure 2.**PIV results obtained from experimental measurements of under-expanded free jets at $NP{R}_{4}=2.77$. (

**a**) Mean in-plane velocity field, color contour of velocity magnitude (m/s) and velocity streamlines, color contours of (

**b**) RMS fluctuating velocity ${v}_{rms}^{\prime}$ (m/s), (

**c**) Reynolds stress $\langle {u}^{\prime}{v}^{\prime}\rangle $ (m${}^{2}$/s${}^{2}$), and (

**d**) turbulent kinetic energy k (m${}^{2}$/s${}^{2}$). Vectors were de-sampled for better visibility.

**Figure 3.**Comparisons of statistical results obtained from PIV measurements of under-expanded free jets for various values of NPRs, i.e., $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. Profiles were interpolated to Line 1 ($y=-2.54$) mm, Line 2 ($y=-12.7$) (mm), and Line 3 ($y=-25.4$) (mm). (

**a**) Normalized mean axial velocity, $V/c$, (

**b**) normalized RMS fluctuating axial velocity ${v}_{rms}^{\prime}/c$, (

**c**) normalized Reynolds stress $\langle {u}^{\prime}{v}^{\prime}\rangle /{c}^{2}$, and (

**d**) normalized turbulent kinetic energy $k/{c}^{2}$.

**Figure 4.**PIV results obtained from experimental measurements of under-expanded impinging jets with the nozzle-to-plate $e=30$ mm ($e/{D}_{j}=2.46$) and at $NP{R}_{2}=2.2$ (left) and $NP{R}_{4}=2.77$ (right). (

**a**) Mean in-plane velocity fields, color contour of velocity magnitude (m/s) and velocity streamlines, color contours of (

**b**) turbulent kinetic energy k (m${}^{2}$/s${}^{2}$), and (

**c**) Reynolds stress $\langle {u}^{\prime}{v}^{\prime}\rangle $ (m${}^{2}$/s${}^{2}$). Vectors were de-sampled for better visibility.

**Figure 5.**PIV results obtained from experimental measurements of under-expanded impinging jets with the nozzle-to-plate $e=20$ mm ($e/{D}_{j}=1.64$) and at $NP{R}_{2}=2.2$ (left) and $NP{R}_{4}=2.77$ (right). (

**a**) Mean in-plane velocity fields, color contour of velocity magnitude (m/s) and velocity streamlines, color contours of (

**b**) turbulent kinetic energy k (m${}^{2}$/s${}^{2}$), and (

**c**) Reynolds stress $\langle {u}^{\prime}{v}^{\prime}\rangle $ (m${}^{2}$/s${}^{2}$). Vectors were de-sampled for better visibility.

**Figure 6.**PIV results obtained from experimental measurements of impinging jets with the nozzle-to-plate $e=10$ mm ($e/{D}_{j}=0.82$) and at $NP{R}_{2}=2.2$ and $NP{R}_{4}=2.77$. (

**a**) Mean in-plane velocity fields, color contour of velocity magnitude (m/s) and velocity streamlines, color contours of (

**b**) turbulent kinetic energy k (m${}^{2}$/s${}^{2}$), and (

**c**) Reynolds stress $\langle {u}^{\prime}{v}^{\prime}\rangle $ (m${}^{2}$/s${}^{2}$). Vectors were de-sampled for better visibility.

**Figure 7.**Comparisons of statistical results obtained from PIV measurements of under-expanded impinging jets with $e=30$ mm ($e/{D}_{j}=2.46$) for various values of NPRs, i.e., $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. (

**a**) Normalized mean axial velocity $V/c$ and normalized RMS fluctuating axial velocity ${v}_{rms}^{\prime}/c$ along the jet centerline ($x=0$); (

**b**,

**c**) showed normalized statistical profiles of $V/c$ and ${v}_{rms}^{\prime}/c$, respectively, obtained along Line 1 ($y=-2.54$) mm, Line 2 ($y=-12.7$) mm, and Line 3 ($y=-27.46$) mm.

**Figure 8.**Comparisons of statistical results obtained from PIV measurements of under-expanded impinging jets with $e=20$ mm ($e/{D}_{j}=1.64$) for various values of NPRs, i.e., $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. (

**a**) Normalized mean axial velocity, $V/c$ and normalized RMS fluctuating axial velocity ${v}_{rms}^{\prime}/c$ along the jet centerline ($x=0$); (

**b**,

**c**) showed normalized statistical profiles of $V/c$ and ${v}_{rms}^{\prime}/c$, respectively, obtained along Line 1 ($y=-2.54$) mm, Line 2 ($y=-12.7$) mm, and Line 3 ($y=-17.46$) mm.

**Figure 9.**Comparisons of statistical results obtained from PIV measurements of under-expanded impinging jets with $e=10$ mm ($e/{D}_{j}=0.82$) for various values of NPRs, i.e., $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. (

**a**) Normalized mean axial velocity, $V/c$ and normalized RMS fluctuating axial velocity ${v}_{rms}^{\prime}/c$ along the jet centerline ($x=0$); (

**b**,

**c**) showed normalized statistical profiles of $V/c$ and ${v}_{rms}^{\prime}/c$, respectively, obtained along Line 1 ($y=-2.54$) mm, Line 2 ($y=-3.35$) mm, and Line 3 $y=-7.46$ (mm).

**Figure 10.**POD analysis of the velocity fields obtained from the 2D2C PIV measurements of under-expanded free jets for $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. (

**a**) Kinetic energy spectra; (

**b**) cumulative energy. Low-order POD velocity modes (

**c**) ${\mathsf{\Psi}}_{1}$, (

**d**) ${\mathsf{\Psi}}_{2}$, (

**e**) ${\mathsf{\Psi}}_{3}$, and (

**f**) ${\mathsf{\Psi}}_{4}$. Vectors were de-sampled for better visibility.

**Figure 11.**POD analysis of the velocity fields obtained from the 2D2C PIV measurements of under-expanded impinging jets with $e=30$ mm ($e/{D}_{j}=2.46$) for $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$ (

**a**) Kinetic energy spectra; (

**b**) cumulative energy. Low-order POD velocity modes (

**c**)$\phantom{\rule{3.33333pt}{0ex}}Ps{i}_{1}$, (

**d**) ${\mathsf{\Psi}}_{2}$, (

**e**) ${\mathsf{\Psi}}_{3}$, and (

**f**) ${\mathsf{\Psi}}_{4}$. Vectors were de-sampled for better visibility.

**Figure 12.**POD analysis of the velocity fields obtained from the 2D2C PIV measurements of impinging jets with $e=20$ mm ($e/{D}_{j}=1.64$) for $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. (

**a**) Kinetic energy spectra; (

**b**) cumulative energy. Low-order POD velocity modes (

**c**) ${\mathsf{\Psi}}_{1}$, (

**d**) ${\mathsf{\Psi}}_{2}$; (

**e**) ${\mathsf{\Psi}}_{3}$, and (

**f**) ${\mathsf{\Psi}}_{4}$. Vectors were de-sampled for better visibility.

**Figure 13.**POD analysis of the velocity fields obtained from the 2D2C PIV measurements of impinging jets with $e=10$ mm ($e/{D}_{j}=0.82$) for $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$. (

**a**) Kinetic energy spectra; (

**b**) cumulative energy. Low-order POD velocity modes (

**c**) ${\mathsf{\Psi}}_{1}$, (

**d**) ${\mathsf{\Psi}}_{2}$; (

**e**) ${\mathsf{\Psi}}_{3}$, and (

**f**) ${\mathsf{\Psi}}_{4}$. Vectors were de-sampled for better visibility.

**Table 1.**Physical exit flow conditions for under-expanded free jets and impinging jets at various nozzle-to-plate gaps and various values of NPRs.

NPR | 2 | 2.2 | 2.5 | 2.77 | |

Nozzle Outlet Temperature (K) | 287.1 | 287.0 | 286.5 | 274.1 | |

Exit Air Density (kg/m${}^{3}$) | 2.46 | 2.73 | 3.08 | 3.42 | |

Exit Air Viscosity (Pa/s) | $1.791\times {10}^{-5}$ | $1.792\times {10}^{-5}$ | $1.789\times {10}^{-5}$ | $1.787\times {10}^{-5}$ | |

Ambient Sound Speed (m/s) | 339 | 339 | 339 | 339 | |

Free Jet | Exit Centerline Velocity (m/s) | 273.4 | 309.1 | 343.1 | 353.1 |

Reynolds number | 458,037.3 | 574,651.6 | 720,724.8 | 824,301.7 | |

Impinging Jet | Exit Centerline Velocity (m/s) | 291.9 | 326.6 | 351.1 | 354.7 |

$e/{D}_{j}=2.46$ | Reynolds number | 489,031.1 | 607,186.1 | 737,529.8 | 828,036.9 |

Impinging Jet | Exit Centerline Velocity (m/s) | 285.4 | 306.8 | 335.5 | 336.3 |

$e/{D}_{j}=1.64$ | Reynolds number | 478,141.4 | 570,375.7 | 700,558.8 | 785,082.6 |

Impinging Jet | Exit Centerline Velocity (m/s) | 273.1 | 308.5 | 334.7 | 348.1 |

$e/{D}_{j}=0.82$ | Reynolds number | 457,534.7 | 573,536.2 | 703,079.6 | 812,629.4 |

**Table 2.**Flow kinetic energy fractions contained in low-order POD modes obtained from POD velocity decomposition to 2D2C PIV velocity vector fields for free jets and impinging jets with various nozzle-to-plate distances $e=30$ mm, 20 mm, and 10 mm, and different values of NPRs, i.e., $NP{R}_{1}=2$, $NP{R}_{2}=2.2$, $NP{R}_{3}=2.5$, and $NP{R}_{4}=2.77$.

Free Jets | Impinging Jet ($\mathit{e}=30$ mm) | ||||||||
---|---|---|---|---|---|---|---|---|---|

NPRs | ${\mathsf{\Psi}}_{1}$ (%) | ${\mathsf{\Psi}}_{2}$ (%) | ${\mathsf{\Psi}}_{3}$ (%) | ${\mathsf{\Psi}}_{4}$ (%) | NPRs | ${\mathsf{\Psi}}_{1}$ (%) | ${\mathsf{\Psi}}_{2}$ (%) | ${\mathsf{\Psi}}_{3}$ (%) | ${\mathsf{\Psi}}_{4}$ (%) |

2 | 85.65 | 1.5 | 0.85 | 0.65 | 2 | 84.48 | 1.39 | 0.66 | 0.45 |

2.2 | 88.8 | 1.12 | 0.59 | 0.44 | 2.2 | 86.03 | 1.18 | 0.60 | 0.44 |

2.5 | 91.8 | 0.80 | 0.42 | 0.33 | 2.5 | 88.43 | 1.13 | 0.42 | 0.34 |

2.77 | 94.37 | 0.58 | 0.26 | 0.25 | 2.77 | 90.44 | 0.78 | 0.30 | 0.24 |

Impinging Jet ($\mathit{e}=\mathbf{20}$mm) | Impinging Jet ($\mathit{e}=\mathbf{10}$mm) | ||||||||

NPRs | ${\mathsf{\Psi}}_{1}$ (%) | ${\mathsf{\Psi}}_{2}$ (%) | ${\mathsf{\Psi}}_{3}$ (%) | ${\mathsf{\Psi}}_{4}$ (%) | NPRs | ${\mathsf{\Psi}}_{1}$ (%) | ${\mathsf{\Psi}}_{2}$ (%) | ${\mathsf{\Psi}}_{3}$ (%) | ${\mathsf{\Psi}}_{4}$ (%) |

2 | 84.07 | 1.81 | 0.72 | 0.48 | 2 | 81.72 | 2.37 | 0.85 | 0.59 |

2.2 | 86.21 | 1.29 | 0.62 | 0.46 | 2.2 | 85.67 | 1.84 | 0.73 | 0.44 |

2.5 | 90.28 | 0.8 | 0.42 | 0.29 | 2.5 | 88.10 | 1.21 | 0.70 | 0.46 |

2.77 | 90.51 | 0.68 | 0.43 | 0.27 | 2.77 | 87.07 | 1.78 | 0.71 | 0.47 |

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**MDPI and ACS Style**

Nguyen, D.T.; Maher, B.; Hassan, Y. Effects of Nozzle Pressure Ratio and Nozzle-to-Plate Distance to Flowfield Characteristics of an Under-Expanded Jet Impinging on a Flat Surface. *Aerospace* **2019**, *6*, 4.
https://doi.org/10.3390/aerospace6010004

**AMA Style**

Nguyen DT, Maher B, Hassan Y. Effects of Nozzle Pressure Ratio and Nozzle-to-Plate Distance to Flowfield Characteristics of an Under-Expanded Jet Impinging on a Flat Surface. *Aerospace*. 2019; 6(1):4.
https://doi.org/10.3390/aerospace6010004

**Chicago/Turabian Style**

Nguyen, Duy Thien, Blake Maher, and Yassin Hassan. 2019. "Effects of Nozzle Pressure Ratio and Nozzle-to-Plate Distance to Flowfield Characteristics of an Under-Expanded Jet Impinging on a Flat Surface" *Aerospace* 6, no. 1: 4.
https://doi.org/10.3390/aerospace6010004