# Simulation of Tail Boom Vibrations Using Main Rotor-Fuselage Computational Fluid Dynamics (CFD)

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## Abstract

**:**

## 1. Introduction

## 2. Fuselage Aerodynamics

^{TM}mesh generation tool has been used. The length of the wind tunnel model (Figure 1a) was ${L}_{F}$ = 1.8 m. The computational grid for this model contained 964 blocks and 13.5 × 10

^{6}cells. The surface grid and grid details are shown in Figure 1b–d.

^{6}and Mach number of 0.1.

## 3. Rotor-Fuselage Computations

^{TM}. The topology of the blocks and the parameters of the computational grids correspond to what was used for the isolated fuselage of the helicopter. The fixed part of the mesh contains 688 blocks and 9 × ${10}^{6}$ cells.

^{6}cells. The simulation concerns forward flight for a 1:6 scaled helicopter model, and all geometric and flight parameters are presented in Table 1.

- -
- Rigid blades;
- -
- No flapping motion of the blades, only pitch input is considered;
- -
- No lead-lag.

## 4. Mathematical Model of Tail Boom Vibrations

## 5. Calculation of the Tail Boom Vibrations

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

T = rotor thrust | L = tail boom length |

D = fuselage drag | ${c}_{Bz}$ = vertical load coefficient |

$Cp$ = pressure coefficient | E = Young’s modulus |

${C}_{T\text{}}$ = rotor thrust coefficient | $I\text{}$ = moment of inertia |

${C}_{D}$ = fuselage drag coefficient | ${m}_{L}\text{}$ = mass per unit length |

${M}_{tip}$ = tip Mach number | ${F}_{L}\text{}$ = per unit length tail boom force |

N = number of blades | ${c}_{F\text{}}$ = normal force coefficient |

${q}_{\infty}$ = free stream dynamic pressure | $v\text{}$ = vertical deformation |

${q}_{tip}\text{}$ = blade tip dynamic pressure | ${v}_{0}$ = natural deformation |

R = rotor radius | ${v}_{1\text{}}$ = forced deformation |

$\overline{r\text{}}$ = normalized rotor radius | Greek symbols |

x = longitudinal tail boom coordinate | ${\rho}_{b}$ = beam material density |

t = time coordinate | ψ = rotor azimuth angle |

${S}_{F}\text{}$ = reference fuselage area | ω = angular velocity of rotor |

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**Figure 1.**(

**a**) Ansat-P fuselage model in the T-1K wind tunnel of KNRTU-KAI, (

**b**) surface grid for fuselage, (

**c**) multi-block topology, and (

**d**) surface mesh near exhausts.

**Figure 2.**Computational Fluid Dynamics (CFD) and experimental drag coefficients vs. lift coefficient for Ansat-P model.

**Figure 3.**Pressure coefficients along the rotor section: (

**a**) $\text{}\overline{r}$ = 0.68, (

**b**) $\text{}\overline{r}$ = 0.96.

**Figure 7.**Surface pressure coefficient on the fuselage and blades at the conditions of Table 1.

**Figure 10.**Load Z and Load Y present sectional forces along the tail boom projected in the vertical (Z) and lateral directions for different azimuthal positions: (

**a**) ψ = 0°, (

**b**) ψ = 40°, (

**c**) ψ = 80°.

**Figure 11.**Vertical aerodynamic load on the tail boom, as a function of the azimuth of the main rotor blades.

**Figure 13.**Functions ${S}_{1}(\overline{t})\text{}$ (

**left column**) and ${S}_{2}(\overline{t})\text{}$ (

**right column**) for different $\gamma $ values (variant numbers).

**Figure 14.**Forced free end tail boom oscillations ${v}_{1}\left(0,L\right)\text{}$ (in mm) at different $\gamma $ values (variant numbers).

Geometry Parameters | |
---|---|

Number of blades, N | 4 |

Rotor diameter, 2R (m) | 1.92 |

Root cut-out, (m) | 0.19 |

Blade twist, φ (deg) | −5.3 |

Blade chord, c (mm) | 52 |

Blade thickness, f (%c) | 12 |

Operation Parameters | |

Collective pitch angle, θ_{0} (deg) | 8 |

Cyclic pitch angle, θ_{1s} (deg) | −2 |

Cyclic pitch angle, θ_{1c} (deg) | 2 |

Coning angle, β (deg) | 0 |

Angle of attack, α (deg) | −4 |

Tip Mach number | M_{tip} = 0.64 |

Advance ratio, μ | 0.15 |

Direction of rotation | Counter clockwise |

Parameters | |
---|---|

Diameter of the fixed beam end, D_{1} (m) | 0.546 |

Diameter of the free beam end, D_{2} (m) | 0.346 |

Beam length, L (m) | 4 |

Wall thickness of the beam, δ (m) | 0.001 |

Thickness of the stringer, δ_{S} (m) | 0.003 |

Length of the stringer, L_{S} (m) | 0.015 |

Number of stringers, N_{S} | 10 |

Beam material density, ${\rho}_{b}$ (kg/m^{3}) | 2.7 × 10^{3} |

Young’s modulus, E (MPa) | 72 × 10^{3} |

Variant, N | Parameter $\mathit{\gamma}$ | Diameter D, m | Mass Per Unit Length ${\mathit{m}}_{\mathit{L}}$, (kg/m) | Dimensionless Rotor Frequency $\mathit{N}\overline{\mathsf{\omega}}$ |
---|---|---|---|---|

1 | 0.224 | 0.546 | 40.48 | 9.07 |

2 | 0 | 0.446 | 38.78 | 10.52 |

3 | −0.02914 | 0.433 | 38.56 | 10.9 |

4 | −0.03812 | 0.4293 | 38.498 | 11.0168 |

5 | −0.04484 | 0.426 | 38.44 | 11.12 |

6 | −0.06502 | 0.417 | 38.29 | 11.41 |

7 | −0.225 | 0.346 | 37.08 | 14.27 |

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**MDPI and ACS Style**

Batrakov, A.; Kusyumov, A.; Kusyumov, S.; Mikhailov, S.; Barakos, G.N.
Simulation of Tail Boom Vibrations Using Main Rotor-Fuselage Computational Fluid Dynamics (CFD). *Appl. Sci.* **2017**, *7*, 918.
https://doi.org/10.3390/app7090918

**AMA Style**

Batrakov A, Kusyumov A, Kusyumov S, Mikhailov S, Barakos GN.
Simulation of Tail Boom Vibrations Using Main Rotor-Fuselage Computational Fluid Dynamics (CFD). *Applied Sciences*. 2017; 7(9):918.
https://doi.org/10.3390/app7090918

**Chicago/Turabian Style**

Batrakov, Andrey, Alexander Kusyumov, Sergey Kusyumov, Sergey Mikhailov, and George N. Barakos.
2017. "Simulation of Tail Boom Vibrations Using Main Rotor-Fuselage Computational Fluid Dynamics (CFD)" *Applied Sciences* 7, no. 9: 918.
https://doi.org/10.3390/app7090918