CEAS Aeronautical Journal

, Volume 10, Issue 3, pp 665–685

# Aerodynamic design optimization of a helicopter rotor blade-sleeve fairing

• P. Pölzlbauer
• D. Desvigne
• C. Breitsamter
Original Paper

## Keywords

Design optimization CFD Helicopter aerodynamics Blade-sleeve fairing Drag reduction RACER

## Abbreviations

$$(C_{\text {d}})_{\text {ref}}$$

Reference drag coefficient (Symmetric reference geometry)

$$(C_{\text {d}})_{\text {rel}}$$

Normalized drag coefficient, $$(C_{\text {d}})_{\text {rel}}=\frac{C_{\text {d}}}{|(C_{\text {d}})_{\text {ref}}|}$$

$$(C_{\text {l}})_{\text {ref}}$$

Reference lift coefficient (Symmetric reference geometry)

$$(C_{\text {l}})_{\text {rel}}$$

Normalized lift coefficient, $$(C_{\text {l}})_{\text {rel}}=\frac{C_{\text {l}}}{|(C_{\text {l}})_{\text {ref}}|}$$

$$\alpha$$

Angle of attack

$$\lambda$$

Thermal conductivity

$$\mu _{\infty }$$

Dynamic viscosity

$$\nu$$

Kinematic viscosity

$$\psi$$

$$\rho _{\infty }$$

Density

$$\tau _{\text {w}}$$

Wall shear stress

x

Design variable vector

z

Optimization objective vector, $$\mathbf {z}=f(\mathbf {x})$$

B(t)

Bézier curve function

$${b}_{{i,n}}$$(t)

Bernstein basis polynomial

$${B}_{{i}}\text {P}_{{jx}}$$

x-position of the Bézier control point

$${B}_{{i}}\text {P}_{{jz}}$$

z-position of the Bézier control point

c

Chord length

$${C}_{{\text {d}}}$$

Drag coefficient, $$C_{\text {d}}=\frac{D}{q_{\infty }\cdot S_{\text {ref}}}$$

$${C}_{{\text {f}}}$$

Skin-friction coefficient, $$C_{f}=\frac{\tau _{\text {w}}}{q_{\infty }}$$

$${C}_{{\text {l}}}$$

Lift coefficient, $$C_{\text {l}}=\frac{L}{q_{\infty }\cdot S_{\text {ref}}}$$

$${C}_{{\text {p}}}$$

Pressure coefficient, $$C_{{\text{p}}} = \frac{{p - p_{\infty } }}{{q_{\infty } }}$$

$${C}_{{\text {p}}}$$

Specific heat capacity

D

Drag

d

Diameter

f(x)

Objective function

$${g}_{{i}}$$(x)

Inequality constraint

$${h}_{{i}}$$(x)

Equality constraint

L

Lift

l

Length

M

Mach number

n

Rotor speed

$${p}_{{\infty }}$$

Ambient pressure

$${P}_{{1}}$$

Non-dominated set of candidates

$${P}_{{i}}$$

Bézier curve control point

$${q}_{{\infty }}$$

Dynamic pressure, $$q_{\infty }=\frac{\rho _{\infty }\cdot V_{\infty }^{2}}{2}$$

R

r

$${S}_{\text{ref}}$$

Reference area, $$S_{\text {ref}}=c\cdot 0.001m$$

T

Total simulation time

t

Local coordinate

$${T}_{{\infty }}$$

Ambient temperature

$${t}_{\text{ave}}$$

Time-averaging interval

Tu

Turbulence intensity, $${\text{Tu}}=\frac{\sqrt{\frac{2}{3}k}}{U}$$

U

Mean velocity, $$U=\sqrt{U_{x}^{2}+U_{y}^{2}+U_{z}^{2}}$$

$${u}_\tau$$

Friction velocity, $$u_{\tau }=\sqrt{{\tau _{\text {w}}}/{\rho }}$$

V

Velocity magnitude

$${V}_{\infty }$$

Freestream velocity

x, y, z

Cartesian coordinates

$${y}^{+}$$

Dimensionless wall distance, $$y^{+}=\frac{u_{\tau }\cdot y}{\nu }$$

## Notes

### Acknowledgements

The authors would like to thank the European Union for the funding of the FURADO research project within the framework of Clean Sky 2 and under the Grant agreement number 685636. Further, the fruitful collaboration and valuable support of the project partner Airbus Helicopters is highly acknowledged. Special thanks are addressed to ANSYS for providing the flow simulation software. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (http://www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (http://www.lrz.de).

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© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2018

## Authors and Affiliations

• P. Pölzlbauer
• 1
• D. Desvigne
• 2
• C. Breitsamter
• 1
1. 1.Technical University of MunichGarchingGermany
2. 2.Airbus HelicoptersMarignane CedexFrance