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Aerodynamics and vibration analysis of a helicopter rotor blade

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Abstract

A computational model is developed to obtain a helicopter rotor blade's vibration characteristics and aerodynamic behavior. A mathematical model of the wake is also developed, consisting of fundamental wake geometry. A Bo 105 helicopter rotor blade is considered for computational aerodynamic analysis. A fluid–structure interaction model of the rotor blade with surrounding air is developed, where the finite element model of the blade is coupled with the computational fluid dynamics model of the surrounding air. The fluid–structure interaction model analyzes aerodynamic coefficients, velocity profiles, and pressure profiles. The resonance frequencies and mode shapes are also obtained by the computational method. A small-scale model of the rotor blade is manufactured, and experimental analysis of similar contemplation is conducted to validate the numerical results. Wind tunnel and vibration testing arrangements are used for the experimental validation of the aerodynamic and vibration characteristics, respectively. The wake and vortex analysis showed that the swirl velocity is minimum, and the axial velocity is maximum at the vortex center. The axial velocity decreases, and swirl velocity increases with increasing the distance from the vortex center to the core radius. Finally, an application of experimentally validated computational methodology for helicopter rotor blade to evaluate aerodynamic characteristics in a fluid–structure interaction environment along with the characterization of resonance properties is outlined where the results follow an expected pattern.

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Abbreviations

\({C}_{{\text{L}}}\) :

Coefficient of lift

\({C}_{{\text{D}}}\) :

Coefficient of drag

\(V\) :

Velocity

\({V}_{x}\) :

Velocity in \(x\)-direction

\({V}_{y}\) :

Velocity in \(y\)-direction

\({V}_{z}\) :

Velocity in \(z\)-direction

\({V}_{\infty }\) :

Freestream velocity

\(U\) :

Deformation

\({U}_{x}\) :

Deformation in \(x\)-direction

\({U}_{y}\) :

Deformation in \(y\)-direction

\({U}_{z}\) :

Deformation in \(z\)-direction

\(\alpha\) :

Angle of attack

\(\psi\) :

Azimuth angle

\(E\) :

Modulus of elasticity

\(\rho\) :

Density

\(\nu\) :

Poisson’s ratio

\(\mu\) :

Dynamic viscosity

\(L\) :

Characteristic length

\(l\) :

Length of the rotor blade

\(c\) :

Chord length of the airfoil

\(\overrightarrow{u}\) :

Flow velocity vector

\({\overrightarrow{u }}_{g}\) :

Mesh velocity of the moving mesh

\(\Gamma\) :

Diffusion coefficient

\({V}_{\theta }\) :

Tangential or swirl velocity

\({V}_{z}\) :

Axial velocity

\({V}_{r}\) :

Radial velocity

\({\Gamma }_{v}\) :

Vortex strength

\(\overline{r }\) :

Nondimensional radius

\(r\) :

Radial location

\({r}_{{\text{c}}}\) :

Vortex core radius

\(\alpha\) :

Constant

\(n\) :

Integer

\(\overrightarrow{\omega }\) :

Vorticity vector

\(\overrightarrow{V}\) :

Local velocity field

\(\overrightarrow{r}\) :

Position vector

\(t\) :

Time

\({\psi }_{\omega }\) :

Wake age

\({\psi }_{b}\) :

Azimuth angle

\(\Omega\) :

Rotation

\({\overrightarrow{V}}_{{\text{loc}}}\) :

Local velocity

\({\overrightarrow{V}}_{{\text{ind}}}\) :

Induced velocity

\({\psi }_{j}\) :

Location coordinate of jth vortex

\({z}_{{\text{tip}}}\) :

Axial displacement

\({y}_{{\text{tip}}}\) :

Radial displacement

\(R\) :

Maximum displacement

\({k}_{1}, {k}_{2}, {C}_{T}\) :

Empirical coefficients in the wake models

\({N}_{{\text{b}}}\) :

Number of blade

\({\theta }_{{\text{tw}}}\) :

Blade twist

\(\Lambda\) :

Coefficient for the radial contraction

\(A\) :

Constant

\(B, C, m, n\) :

Empirical coefficients in the Kocurek and Tanglers wake model

\(\lambda\) :

Contraction rate parameter

\({S}_{\phi }\) :

Source term of \(\phi\)

\({\text{Re}}\) :

Reynolds number

\(\partial V\) :

Boundary of the control volume \(V\)

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Acknowledgements

The authors would like to thank Dr. William Warmbrodt, who was the NASA technical monitor for the work presented in this paper. The authors are also thankful to Taylor Weidman, a Mechanical Engineering Technician of the College of Engineering at the University of New Orleans, for his support in conducting the laboratory experiments.

Funding

This research was supported by the NASA EPSCoR Research Infrastructure Development (RID) grant  (Contract No. LEQSF-EPS (2020)-RAP-29).

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  1. Department of Mechanical Engineering, The University of New Orleans, 2000 Lakeshore Drive, New Orleans, LA, 70148, USA

    Mohammad Khairul Habib Pulok & Uttam Kumar Chakravarty

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  1. Mohammad Khairul Habib Pulok
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Correspondence to Uttam Kumar Chakravarty.

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Pulok, M.K.H., Chakravarty, U.K. Aerodynamics and vibration analysis of a helicopter rotor blade. Acta Mech 235, 3033–3057 (2024). https://doi.org/10.1007/s00707-024-03871-9

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  • DOI: https://doi.org/10.1007/s00707-024-03871-9

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