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Blade planform improvement and airfoil shape optimization of helicopters in hover flight

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Abstract

In this paper, blade planform effects and airfoil shape coefficients on aerodynamic efficiency of helicopters in hover flight are investigated. The procedure emphasizes small composite data (SCD), airfoil representation method, and numerical optimization and is presented as generalized process to the rotor blade design optimization problem. Therefore, the systematic evaluation of blade taper, taper point on the blade, linear twist, tip sweep, and airfoil shape coefficients on figure of merit (FM), rotor thrust, and power required is provided with the proposed procedure. The SCD data were generated through the in-house flight dynamic simulation program in which the model of rotor is a nonlinear dynamic model developed for rotors and the unsteady aerodynamic representation with a three-state dynamic inflow model. The results show that this procedure alleviates the challenges associated with complex and time-consuming approaches required computational fluid dynamics CFD analysis. The results also confirm that the optimum swept-tapered blade with cambered airfoil lowers the power required in hover by about 7% and enhances the FM up to 10% with an acceptable improvement relative to the rectangular planform with NACA 0012 cross section.

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Abbreviations

a :

Lift curve slope (1/rad)

A :

Rotor disk area (m2)

A i :

Airfoil weighting factor

b :

Number of blades

c e :

Equivalent chord (m)

c r :

Root chord (m)

c t :

Tip chord (m)

\( C_{N2}^{N1} \) :

Airfoil class function

\( \bar{C}_{\text{l}} \) :

Mean lift coefficient

C l_max :

Maximum lift coefficient

C P :

Power coefficient

C T :

Thrust coefficient

CT/σe :

Blade loading

d :

Individual desirability function

D :

Overall desirability function

DL:

Disk loading (N/m2)

f i :

Binomial coefficients

FM:

Figure of merit

k :

Induced power correction factor, number of design variables

k*:

Center point

N :

Bernstein polynomial order

\( N_{1} , N_{2} \) :

Class function constants

P i :

Rotor induced power

P o :

Rotor profile power

PL:

Power loading (N/kW)

r :

Distance from rotor hub (m)

R :

Blade radius (m)

S :

Airfoil shape function

S u :

Upper surface shape function

S l :

Lower surface shape function

swp:

Quarter-chord tip sweep (°)

tr:

Taper ratio, ct/cr

trst:

Taper ratio start point on the blade (r/R)

tw:

Blade twist (°)

T :

Rotor thrust (N)

μ :

Advance ratio, \( V_{\infty } \cos \alpha /\varOmega R \)

ρ :

Air density (kg/m3)

σ :

Rotor solidity, bc/πR

σ e :

Thrust weighted solidity, \( \sigma_{\text{e}} = 3\mathop \smallint \limits_{0}^{1} \sigma r^{2} {\text{d}}r \)

ψ :

Blade azimuth angle (°)

\( \varOmega \) :

Rotor speed (rad/s)

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Authors and Affiliations

  1. Department of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, 15875-1774, Iran

    Farid Shahmiri & Mahdi Ebrahimnejad Badihi

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  1. Farid Shahmiri
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  2. Mahdi Ebrahimnejad Badihi
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Correspondence to Farid Shahmiri.

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Technical Editor: André Cavalieri.

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Shahmiri, F., Badihi, M.E. Blade planform improvement and airfoil shape optimization of helicopters in hover flight. J Braz. Soc. Mech. Sci. Eng. 42, 417 (2020). https://doi.org/10.1007/s40430-020-02499-9

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