The so-called coaxial compound helicopter features two rigid coaxial rotors, and possesses high-speed capabilities. Nevertheless, the small separation of the coaxial rotors causes severe aerodynamic interactions, which require careful analysis. In the present work, the aerodynamic interaction between the various helicopter components is investigated by means of a numerical method considering both hover and forward flight conditions. While a sliding mesh method is used to deal with the rotating coaxial rotors, the Reynolds-Averaged Navier-Stokes (RANS) equations are solved for the flow field. The Caradonna & Tung (CT) rotor and Harrington-2 coaxial rotor are considered to validate the numerical method. The results show that the aerodynamic interaction of the two rigid coaxial rotors significantly influences hover’s induced velocity and pressure distribution. In addition, the average thrust of an isolated coaxial rotor is smaller than that of the corresponding isolated single rotor. Compared with the isolated coaxial rotor, the existence of the fuselage results in an increment in the thrust of the rotors. Furthermore, these interactions between the components of the considered coaxial compound helicopter decay with an increase in the advance ratio.

Although conventional helicopters possess excellent hover-ability and low-speed maneuverability, the maximum forward speed of conventional helicopters is restricted by the adverse effects of the compressibility on the advancing blades and stalling on the retreating blades of the main rotor [

The methods to investigate the aerodynamic characteristics of coaxial configurations include experimental tests, vortex methods, and computational fluid dynamics (CFD) simulations. Experimental tests focus on the static-thrust performance in hover [

CFD simulations have been widely employed to investigate the aerodynamic characteristics of coaxial configurations with acceptable costs and high fidelity. Based on the structured overset-mesh method and Reynolds-Averaged Navier-Stokes (RANS) solver, Lakshminarayan et al. [

Most of the literature focuses on the rigid coaxial rotor, and the fuselage is not involved. In this paper, a numerical simulation for a compound helicopter is constructed based on the sliding mesh method and the RANS method. The cases of the isolated single rotor, isolated coaxial rotor, and whole helicopter are calculated. Then, the aerodynamic interactions between the components of the compound helicopter are analyzed. The simulated states include hover and forward flights.

Although the Navier-Stokes (NS) equations are applicable for all turbulence flow, the direct numerical simulation of the turbulence flow is prohibitively expensive. The RANS method provides a way to reduce the cost, focusing on the time-averaged flow and the effects of turbulence on time-averaged flow properties. The RANS equations contain the continuity equation, the momentum equations, and the scalar transport equation, as follows [

where

where

In this paper, the compressible RANS equations are solved by the Finite Volume Method (FVM) [

where

The sliding mesh method is a special case of general dynamic mesh motion wherein the nodes move rigidly in a given dynamic mesh zone. There are at least two cell zones that connect through non-conformal interfaces. This means that one boundary face has at least two neighboring cells. In practice, the two interfaces of the neighboring zones are replaced with a new set of faces formed by their intersections [

A typical coaxial compound helicopter is the X2, which utilizes a similar rotor system to the XH-59A [

Parameter | Value |
---|---|

Rotor blade | |

Rotor radius | 5.5 m |

Rotor angular velocity | 34.2 rad/s |

Rotor separation | 0.763 m |

Root cut | 0.66 m |

Solidity | 0.127 |

Chord | Tapered (2:1) |

Airfoil section | NACA23012 |

Parameter | Value |
---|---|

Fuselage length | 11.22 m |

Tailplane airfoil section | NACA0012 |

Tailplane span | 3.74 m |

Tailplane chord | 0.935 m |

Vertical fin airfoil section | NACA0012 |

Vertical fin span | 1.5 m |

Vertical fin tip cord | 0.75 m, tapered (2:1) |

Three unstructured poly-hex-core mesh regions, including two rotating cylindrical regions and a stationary region, are generated for this numerical simulation. The poly-hex-core mesh contains the polyhedral mesh and the hex-core mesh. The polyhedral mesh is used in the field close to the boundaries, while the hex-core mesh is used inside the core of the domain. The poly-hex-core mesh has a lower mesh count than the equivalent tetrahedral mesh, and it can handle complex geometries.

The rotating cylindrical mesh regions cover the upper and lower rotor blades. Mesh refinement is performed on the blades’ leading edge and trailing edge. The mesh size of the rotating region interface is set to march the length when the rotor rotates

To speed up the convergence and reduce computation time, the steady-state simulation of the flow field is firstly calculated by the moving reference frames method, and then the steady-state results are used as the initial values of transient analysis of the sliding mesh method. The time step of transient analysis is set as the time when the main rotor rotates

The Caradonna & Tung (CT) rotor with experimental data [

The Harrington 2 rotor is a coaxial rotor from the reference [

In this section, cases of the isolated single rotor, isolated coaxial rotor, and the whole helicopter are calculated, and the aerodynamic interactions between these components are analyzed in hover and forward flights. The simulation conditions are 500 m height, 0.566 Mach number of the blade tip, and

The hover state of the isolated single rotor is calculated with three kinds of grid sizes. Each grid is divided into two regions, the rotating region, and the stationary region. The grids of both regions are refined. The average thrust coefficient (

Mesh | Rotating region (million) | Stationary region (million) | Total number (million) | Average thrust coefficient | Difference |
---|---|---|---|---|---|

Grid 1 | 1.94 | 0.68 | 2.62 | 0.005739 | - |

Grid 2 | 3.75 | 1.48 | 5.23 | 0.005789 | 0.87% |

Grid 3 | 4.39 | 3.02 | 7.41 | 0.005795 | 0.10% |

The cases of the isolated single rotor, the isolated coaxial rotor, and the whole helicopter are calculated at advance ratios of 0.1, 0.2, and 0.3.

To identify the interactions of the coaxial rotors in forward flights, the pressure distributions of the isolated single rotor and coaxial rotors at the advancing and retreating sides are compared, as shown in

Advance ratio | Isolated coaxial rotor | The whole helicopter | Difference |
---|---|---|---|

0.1 | 0.01148 | 0.01165 | 1.48% |

0.2 | 0.01621 | 0.01626 | 0.31% |

0.3 | 0.02000 | 0.02008 | 0.40% |

Based on the sliding mesh method, a numerical method for coaxial rotor helicopter aerodynamic interaction simulation is constructed. The rotor-rotor interactions and rotor-fuselage interactions are analyzed in hover and forward flights. The following conclusions are obtained:

Compared with the isolated single rotor, the aerodynamic interaction of the two rigid coaxial rotors significantly influences the induced velocity and pressure distribution in hover. This interaction also reduces the thrust of the isolated coaxial rotor.

Compared with the hover state, the periodic thrust variation of the upper rotor and lower rotor changes from six-per-revolution to three-per-revolution in forward flights. The encounter of the upper and lower rotors results in the oscillation of the transient thrusts.

The thrust of the coaxial rotor increases due to the fuselage’s blocked downwash of the coaxial rotor. This indicated that the fuselage positively affects the lift capability of the coaxial rotor.

The interactions between the components of the coaxial helicopter decay with the advance ratio increasing.

Chord of the rotor blade section

Fuselage lift

Air pressure

Freestream pressure

Rotor torque

Radial distance to the blade section

Rotor radius

Rotor thrust

Forward flight speed

Air density

Rotor angular velocity

Advance ratio

Lift coefficient of the fuselage

Pressure coefficient of the blade section

Rotor thrust coefficient

Rotor torque coefficient

^{TM}demonstrator