# CFD Study of an Annular-Ducted Fan Lift System for VTOL Aircraft

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Momentum Theory of the Ducted Lift Fan in Hover Mode

_{0}= 0) of incoming flow to the ducted lift fan, the thrust and power can be calculated:

^{3}; A is area of lift fan; σ is the duct diffusion ratio, σ = 0.5–1 and for an unducted rotor σ = 0.5; V

_{1}is the velocity under the rotor; and V

_{2}is the far wake velocity.

## 3. Geometry and Computational Mesh

#### 3.1. Geometry Definition

**Figure 2.**(

**a**) The annular-ducted lift fan system and the aircraft with the annular duct opened; (

**b**) the lift fans; (

**c**) the top front view of the aircraft with the annular duct system enclosed by upper aperture and lower louvers; (

**d**) the lift fan and its tip turbine in a gas chamber. The upper wall of the chamber has been removed to expose the tip turbine inside.

#### 3.2. Computational Mesh

^{+}value was within the range of 30–300 on most of the surface area.

^{8}), the viscous sublayer at the surface is very thin. As a result, a very high grid resolution is required close to the walls. This is important because boundary layer separation from the surface determines to a large extent the aerodynamic drag [10]. A value of y

^{+}< 1 was achieved for the attached flow on the surface of the aircraft.

**Figure 3.**(

**a**) Volume mesh of the annular-ducted lift fan system in the central plane for the hover and transition mode study. Different colors show different blocks; (

**b**) surface mesh on the surface of the aircraft and the symmetry plane for the aerodynamic drag study; (

**c**) volume mesh in the central plane of the gas chamber for the tip turbine study.

Parameters | Coarse Grid | Medium Grid | Fine Grid |
---|---|---|---|

Element number | 1.5M | 2.3M | 3.0M |

Power (kW) | 2117 | 2097 | 2085 |

Parameters | Coarse Grid | Medium Grid | Fine Grid |
---|---|---|---|

Element number | 323K | 650K | 1.26M |

C_{D} | 0.00842 | 0.00680 | 0.00676 |

Parameters | Coarse Grid | Medium Grid | Fine Grid |
---|---|---|---|

Element number | 323K | 670K | 1.7M |

Time-averaged moment (kN m) | 162 | 158 | 156 |

Parameters | Coarse Grid | Medium Grid | Fine Grid | Actual |
---|---|---|---|---|

Element number | 1.12M | 2.43M | 4.68M | |

Power (kW) | 2845 | 2688 | 2685 | 2676 |

Parameters | Coarse Grid | Medium Grid | Fine Grid | Experimental |
---|---|---|---|---|

Cell number | 355K | 638K | 1.55M | |

C_{L} | 0.266 | 0.260 | 0.258 | 0.241 |

C_{D} | 0.0110 | 0.0088 | 0.0075 | 0.0079 |

## 4. Boundary Condition and Simulation Setup

## 5. Numerical Model Validation

#### 5.1. Validation of Power Prediction

^{+}= 30–300.

^{2}.

**Figure 4.**(

**a**) Three-dimensional swirling streamlines in front of the central plane of the helicopter in hover mode; (

**b**) the rotor tip vortex in the central plane of the helicopter.

_{shaft}= 10,433/2685 = 3.88 kg/kW.

_{induced}/P = 0.603, and lift efficiency T/P = 3.89 kg/kW. Therefore, the prediction of the power is quite accurate.

#### 5.2. Validation of Transition Mode

^{6}, and rotation speed N = 21,000 rpm at different angles of attack were repeated to compare to the experimental data in [3]. The settings for the transition study were used. Ten chords were used in each direction from the wing to create the computational domain. The mesh contained 1.2 M tetrahedral cells. y

^{+}= 30–300 was achieved on the surface of the wing. However, for an angle of attack of 20°, flow separation happened, which caused significantly drop of lift, and the iterations could not converge; therefore, y

^{+}= ~1 on the surface of the wing was used.

**Figure 5.**Streamlines in the central plane of the generic fan-in-wing configuration at an angle of attack of 20°. Freestream velocity U = 30 m/s, and fan speed N = 21,000 rpm.

**Figure 6.**Lift and drag coefficients as a function of the angle of attack for U = 30 m/s and N = 21,000 rpm. The experimental data come from Thouault [3].

#### 5.3. Validation of Aerodynamic Drag Prediction

^{6}with the transition point fixed at 5% chord on both the upper and lower surfaces of the airfoil [17]. The unstructured grid and the settings for drag prediction were validated. Ten chord were used from the wing to create the computational domain with 1.55 M tetrahedral cells. y

^{+}= ~1 was achieved on the surface of the airfoil.

**Figure 7.**Comparison of computed and experimental data for the NACA-0012 airfoil at M = 0.7 and Re = 9 × 10

^{6}. (

**a**) Lift vs. angle of attack; (

**b**) lift vs. drag polar; (

**c**) pressure coefficient distribution at z = 1 and α = 1.55°. The experimental data come from Harris [17].

## 6. Numerical Simulation Results

#### 6.1. Annular-Ducted Fan Lift System in Hover Mode

_{rotor}= 58,361 N; thus, according to Equation (4) of the momentum theory:

**Figure 8.**(

**a**) Three-dimensional streamlines in front of the central plane in hover mode; (

**b**) surface streamlines in the central plane of the aircraft; (

**c**) static pressure on the upper surface of the fans, duct, fuselage and peripheral wing; (

**d**) pressure contour inside the annular-ducted lift fan system.

^{2}.

_{unducted}= 167.33 m

^{2}for the rotor of the Apache helicopter.

^{2}) is much larger than that of the lift fan system (103.62 m

^{2}), the induced power for the annular-ducted lift fan system to provide the same lift is even lower.

_{shaft}= 10,433/2085 = 5.00 kg/kW.

^{2}, so the rotor efficiency η = P

_{induced}/P = 0.603, and the lift efficiency T/P = 3.89 kg/kW. Therefore, compared to the Apache rotor, the 3-m lift fan system is more efficient and can save 22% of the power.

_{rotor}= 56,698 N and fan area A = 75.39; thus, σ = 0.902; the induced power P = 1791 kW; and P

_{ducted}/P

_{unducted}= 1.11.

_{shaft}= 2455 kW; the fan efficiency η = 0.73; and the lift efficiency T/P

_{shaft}= 4.25 kg/kW. Therefore the 2-m annular-ducted lift fan system also needs less power and has higher lift efficiency than the Apache rotor to provide the same lift. Furthermore, if the ground effect is considered and the distance from the aircraft to the ground is 10 m, the shaft power will be only 1880 kW, much lower than the Apache’s power. The lift efficiency T/P = 5.55, which is much higher than the Apache rotor.

#### 6.2. Transition from VTOL to Horizontal Flight

**Figure 9.**Computed time-averaged net drag and lift-to-aircraft weight ratio at different angles of attack in transition mode. The lift was maintained equal to the weight of the aircraft through the change of the rotational speed of the fans.

**Figure 10.**The aircraft attitudes and streamlines in the central plane of the aircraft in transition mode. The lift was maintained equal to the weight of the aircraft by adjusting the fan rotational speeds. (

**a**) Angle of attack α = 0°, freestream speed U = 20 m/s, fan speeds N = +108, −117 rpm; (

**b**) angle of attack α = −21°, U = 10 m/s, fan speeds N = +122, −121 rpm; (

**c**) angle of attack α = 15°, U = 20 m/s, fan speeds N = +91, −97 rpm.

#### 6.3. Aerodynamic Drag and Horizontal Cruise Speed Predictions

**Figure 11.**(

**a**) Streamlines in the central plane of the aircraft in cruise mode; (

**b**) pressure coefficient in the central plane of the aircraft at speed of 0.7 Ma.

**Figure 12.**The computed drag (the engines were not considered) of the aircraft increases with cruise speed at different angles of attack.

#### 6.4. Pneumatic Coupling of Tip Turbine and Engine Exhaust Gases

**Figure 14.**(

**a**) Velocity vector in the central plane of the gas chamber when the tip turbine was still; (

**b**) enlarged view of velocity vectors; (

**c**) enlarged view of velocity vectors when the tip turbine rotated at a speed n = 120 rpm; (

**d**) pressure contour in the central plane of the chamber; (

**e**) the enlarged view of pressure on the turbine blades to show the pressure difference on two sides of the blades.

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Jiang, Y.; Zhang, B.; Huang, T.
CFD Study of an Annular-Ducted Fan Lift System for VTOL Aircraft. *Aerospace* **2015**, *2*, 555-580.
https://doi.org/10.3390/aerospace2040555

**AMA Style**

Jiang Y, Zhang B, Huang T.
CFD Study of an Annular-Ducted Fan Lift System for VTOL Aircraft. *Aerospace*. 2015; 2(4):555-580.
https://doi.org/10.3390/aerospace2040555

**Chicago/Turabian Style**

Jiang, Yun, Bo Zhang, and Tao Huang.
2015. "CFD Study of an Annular-Ducted Fan Lift System for VTOL Aircraft" *Aerospace* 2, no. 4: 555-580.
https://doi.org/10.3390/aerospace2040555