# A Comparison of Isolated and Ducted Fixed-Pitch Propellers under Non-Axial Inflow Conditions

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## Abstract

**:**

## 1. Introduction

**Figure 1.**Definition of the coordinate system. From [12].

**Figure 2.**Flow phenomena of a propeller under non-axial inflow. (

**a**) Illustration of the inflow, the rotational speed and the induced velocities, the flow around the blade tip, the radial flow and the vortex structures. (

**b**) Illustration of the resulting three-components’ pressure distributions and forces.

## 2. Experimental Approach

## 3. Numerical Approach

## 4. Results and Discussion

#### 4.1. Steady Loads

#### 4.2. Transient Loads

#### 4.3. Flow Field Analysis

#### 4.3.1. Axial Inflow, ${\alpha}_{disc}=0\xb0$

#### 4.3.2. Minor Inflow Angle, ${\alpha}_{disc}=30\xb0$

#### 4.3.3. Medium-High Inflow Angle, ${\alpha}_{disc}=60\xb0$

#### 4.3.4. High Inflow Angles, ${\alpha}_{disc}$ = 90–180$\xb0$

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

${c}_{F}$ | Force coefficient, ${c}_{F}=\frac{F}{\rho {n}^{2}{D}^{4}}$ [-] |

${c}_{m}$ | Pitching moment coefficient, ${c}_{m}=\frac{m}{\rho {n}^{2}{D}^{5}}$ [-] |

${c}_{p}$ | Pressure coefficient, ${c}_{p}=\frac{P}{q}$ [-] |

J | Propeller advance ratio, $J=\frac{{U}_{\infty}}{n{D}_{P}}$ [-] |

L | Lift force, $L=T\xb7sin{\alpha}_{disc}$ [N] |

n | Rotational speed [Hz] |

q | Stagnation pressure, $q=\frac{\rho}{2}\phantom{\rule{0.277778em}{0ex}}{U}^{2}$ [Pa] |

r | Radial position [m] |

R | Propeller radius [m] |

T | Thrust force [N] |

${T}_{eff}$ | Effective thrust, ${T}_{eff}=T\xb7cos{\alpha}_{disc}$ [N] |

${U}_{ind}$ | Induced velocity [m/s] |

${U}_{section}$ | Effective inflow velocity at local blade section [m/s] |

${U}_{\infty}$ | Inflow velocity [m/s] |

${U}_{x,y,z}$ | Velocities in x (axial), y and z-direction [m/s] |

${U}_{norm}$ | Normalized velocity magnitude, ${U}_{norm}=\sqrt{{U}_{x}^{2}+{U}_{y}^{2}+{U}_{z}^{2}}/{U}_{\infty}$ [-] |

${\alpha}_{disc}$ | Angle of attack of the propeller disc [$\xb0$] |

${\alpha}_{section}$ | Effective angle of attack at local blade section [$\xb0$] |

$\kappa $ | Axial advance ratio, $\kappa =J\xb7cos{\alpha}_{disc}$ [-] |

$\mu $ | Lateral advance ratio, $\mu =J\xb7sin{\alpha}_{disc}$ [-] |

$\varphi $ | Flow angle at local blade section, $\varphi =\theta -{\alpha}_{section}$ [$\xb0$] |

$\rho $ | Density of air [kg/m${}^{3}$] |

$\theta $ | Twist angle at local blade section [$\xb0$] |

${\omega}_{y}$ | Vorticity in y-direction [-] |

$\Omega $ | Angular velocity [$\xb0$/s] |

$\zeta $ | Propeller circumferential position [$\xb0$] |

## References

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**Figure 3.**Inflow characteristics of a propeller’s blade section under non-axial inflow. The non-axial inflow influences the local lift $dL$ and drag $dD$, and furthermore, the local thrust $dT$ and portion of propeller torque $dQ/r$ [12].

**Figure 4.**(

**a**) Size, (

**b**) twist angle and chord length distribution of the applied APC 18x8E propeller.

**Figure 6.**(

**a**) Rotatable wind tunnel support with mounted propeller. (

**b**) Instrumentation of the support with a one-sided illustration of the duct.

**Figure 7.**(

**a**) Stereo-PIV setup. The laser and the cameras were mounted on uniformly moving traverse systems. (

**b**) The laser illuminated the vertically aligned plane of measurement.

**Figure 9.**Computational grid. (

**a**) Blocking of the rotational propeller domain, (

**b**) grid around the airfoil at $r/R=0.7$, (

**c**) grid of propeller and outer domain at the symmetry plane ($z=0$).

**Figure 11.**Ratio of thrust coefficient to power coefficient ${c}_{T}/{c}_{P}$. (

**a**) Static thrust conditions ($J=0$), (

**b**) polar over the advance ratio J with $n=4000$ rpm. Wind tunnel data.

**Figure 12.**Thrust coefficient distribution. Polar over the advance ratio J, $n=4000$ rpm. URANS results.

**Figure 13.**(

**a**,

**b**) Thrust coefficient ${c}_{T}$ and (

**c**,

**d**) effective thrust coefficient ${c}_{T,eff}$. (

**a**,

**c**) $J=0.33$; black: open propeller; red: ducted propeller configuration. (

**b**,

**d**) Plot of total loads of the ducted configuration over $\mu $ and $\kappa $. Wind tunnel data.

**Figure 14.**(

**a**,

**b**) Lift coefficient ${c}_{L}$. (

**a**) $J=0.33$; black: open propelle; red: ducted propeller configuration. (

**b**) Plot of total loads of the ducted configuration over $\mu $ and $\kappa $. Wind tunnel data.

**Figure 16.**Time-resolved relative (

**a**) propeller and (

**b**) duct thrust coefficients over one propeller revolution for different inflow angles. Plotted in relation to their individual averaged thrust magnitudes. $J=0.33$, URANS calculation.

**Figure 17.**Normalized induced axial velocity component ${U}_{x,norm}$. (

**a**) Open propeller, (

**b**) ducted propeller. URANS calculation. $J=0.33$, ${\alpha}_{disc}=0\xb0$.

**Figure 18.**Pressure coefficient distribution on the duct contour. $n=4000$ rpm, ${\alpha}_{disc}=0\xb0$. URANS calculation.

**Figure 19.**Normalized vorticity components perpendicular to two intersecting planes. (

**a**) Open propeller, (

**b**) ducted configuration. URANS calculation, $J=0.33$, ${\alpha}_{disc}=0\xb0$.

**Figure 20.**Normalized induced axial velocity component ${U}_{x,norm}$ of the ducted propeller. (

**a**) PIV measurement with blanked areas due to shading of the PIV laser sheet. (

**b**) URANS calculation. $J=0.33$, ${\alpha}_{disc}=30\xb0$.

**Figure 21.**Normalized vorticity components perpendicular to two intersecting planes. URANS calculation, $J=0.33$, ${\alpha}_{disc}=30\xb0$.

**Figure 22.**Formation of the central duct vortices. Derived from URANS calculation, $J=0.33$, ${\alpha}_{disc}=30\xb0$.

**Figure 23.**Normalized induced axial velocity component ${U}_{x,norm}$. (

**a**) Open propeller, (

**b**) ducted propeller. URANS calculation. $J=0.33$, ${\alpha}_{disc}=60\xb0$.

**Figure 24.**Pressure distribution around the duct contour at the propeller’s cross-section ($z=0$). URANS calculation, $J=0.33$, ${\alpha}_{disc}=60\xb0$.

**Figure 25.**Normalized vorticity components perpendicular to two intersecting planes. URANS calculation, $J=0.33$, ${\alpha}_{disc}=60\xb0$.

**Figure 26.**Formation of the outer duct vortices. Derived from URANS calculation, $J=0.33$, ${\alpha}_{disc}=60\xb0$.

**Figure 27.**Three-dimensional illustration of the vortex structures under high inflow angles and reverse inflow, respectively. Normalized vorticity components perpendicular to two intersecting planes. URANS calculation, $J=0.33$, ${\alpha}_{disc}=90\u2013180\xb0$.

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**MDPI and ACS Style**

Cerny, M.; Breitsamter, C.
A Comparison of Isolated and Ducted Fixed-Pitch Propellers under Non-Axial Inflow Conditions. *Aerospace* **2020**, *7*, 112.
https://doi.org/10.3390/aerospace7080112

**AMA Style**

Cerny M, Breitsamter C.
A Comparison of Isolated and Ducted Fixed-Pitch Propellers under Non-Axial Inflow Conditions. *Aerospace*. 2020; 7(8):112.
https://doi.org/10.3390/aerospace7080112

**Chicago/Turabian Style**

Cerny, Michael, and Christian Breitsamter.
2020. "A Comparison of Isolated and Ducted Fixed-Pitch Propellers under Non-Axial Inflow Conditions" *Aerospace* 7, no. 8: 112.
https://doi.org/10.3390/aerospace7080112