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Extensions of prescribed wake modelling for helicopter rotor BVI noise investigations

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Abstract

The prediction of blade–vortex interaction noise is highly sensitive to the blade–vortex missdistance and thus requires the knowledge of the vortex position relative to the blade interacting with it. The generally accepted solution to the problem is to apply either free-wake codes (vortex lattice methods) or computational fluid dynamics (CFD) codes, both of which are very time consuming, especially CFD. Prescribed wake codes are computationally faster in comparison, since they are based on steady rotor operational conditions only, but they are considered to be not accurate enough due to the prescription of the geometry based on a few general parameters. First, they lack any wake geometry response due to variations in rotor loading distributions at constant thrust caused by, e.g., non-uniformity of the aerodynamic environment in forward flight, elastic blade motion, or by any means of active control. Second, wake deflections due to the presence of the fuselage are ignored. This paper provides an approximate solution to both problems, based on simple momentum theory considerations for the first problem, and based on the displacement flow of the fuselage for the second. This provides extensions for any existing prescribed wake model to account for rotor loading distribution and fuselage effects on the prescribed wake geometry to a first order of accuracy, sufficient for the investigations of the sensitivity analysis of noise radiation due to variations of blade design or due to applications of active control.

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Abbreviations

B :

Tip loss factor = effective non-dimensional blade radius

c nj :

Fourier coefficient of q n (ψ)

C T :

Thrust coefficient, \(C_{\rm T}=T/(\rho\pi\Upomega^{2}R^{4})\)

f(r):

Radial distribution function

f m :

Weight factor of f(r)

k x , k y :

Longitudinal and lateral inflow gradients

L n :

Blade lift at the nth harmonic, N

L nS, L nC :

Sin and cos part of L n

n, m :

Integer number

N b :

Number of blades

N rev :

Number of wake revolutions

N R :

Number of blade elements

N ψ :

Number of vortex segments per revolution

q n (ψ):

Fourier series of the nth mode of the fuselage-induced flow

r :

Non-dimensional radial coordinate

r a :

Non-dimensional root cut-out radius

r vr :

Radius of vortex release point

R :

Rotor radius, m

t :

Time, s

t vr :

Time of vortex release, s

T :

Thrust, N

v i :

Induced velocity normal to the disk, m/s

v if :

Fuselage-induced velocity, m/s

V :

Velocity, m/s

V ∞ :

Flight speed, m/s

x, y, z :

Non-dimensional coordinates

x e :

Rear end of the disk

x v, y v, z v :

Vortex position

x vr, y vr, z vr :

Coordinates of vortex release point

z te :

Vertical position of trailing edge

α:

Tip path plane angle of attack, rad

λi :

Induced inflow ratio, \(\lambda_{\rm i}=v_{\rm i}/(\Upomega R)\)

λ i0 :

Mean-induced inflow ratio

λin :

Induced inflow ratio, nth harmonic

λinh :

Induced inflow ratio computed in hover

μ:

Advance ratio, \(\mu=V_{\infty}\hbox{cos}\alpha/(\Upomega R)\)

μ z :

Axial inflow, μ z  =  − μ tan α

ρ:

Air density, kg/m3

ϕ n :

Radial distribution function

ψ:

Azimuth, \(\psi=\Upomega t, {\rm rad} \)

ψb :

Blade azimuth at vortex release, rad

\(\Upomega\) :

Rotor rotational frequency, rad/s

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Acknowledgments

The provision of data from CFD/CSD computations (Joon W. Lim, US Army AFDD) and from the Vorticity Transport Method (VTM; R. Brown and M. Kelly, University of Glasgow) in Fig. 16 is highly appreciated. The CFD data of the fuselage flow in Fig. 10c, d as well as those of Fig. 16b are kindly provided by S. Jung of Konkuk University in Seoul, Korea.

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  1. DLR, Institute of Flight Systems, Helicopter, Lilienthalplatz 7, 38108, Braunschweig, Germany

    Berend G. van der Wall

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Correspondence to Berend G. van der Wall.

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van der Wall, B.G. Extensions of prescribed wake modelling for helicopter rotor BVI noise investigations. CEAS Aeronaut J 3, 93–115 (2012). https://doi.org/10.1007/s13272-012-0045-9

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