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The HART II international workshop: an assessment of the state-of-the-art in comprehensive code prediction

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Abstract

Significant advancements in computational fluid dynamics (CFD) and their coupling with computational structural dynamics (CSD, or comprehensive codes) for rotorcraft applications have been achieved recently. Despite this, CSD codes with their engineering level of modeling the rotor blade dynamics, the unsteady sectional aerodynamics and the vortical wake are still the workhorse for the majority of applications. This is especially true when a large number of parameter variations is to be performed and their impact on performance, structural loads, vibration and noise is to be judged in an approximate yet reliable and as accurate as possible manner. In this article, the capabilities of such codes are evaluated using the HART II International Workshop database, focusing on a typical descent operating condition which includes strong blade–vortex interactions. A companion article addresses the CFD/CSD coupled approach. Three cases are of interest: the baseline case and two cases with 3/rev higher harmonic blade root pitch control (HHC) with different control phases employed. One setting is for minimum blade–vortex interaction noise radiation and the other one for minimum vibration generation. The challenge is to correctly predict the wake physics—especially for the cases with HHC—and all the dynamics, aerodynamics, modifications of the wake structure and the aero-acoustics coming with it. It is observed that the comprehensive codes used today have a surprisingly good predictive capability when they appropriately account for all of the physics involved. The minimum requirements to obtain these results are outlined.

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Notes

  1. The name conventions MN and MV were taken from the HART I test of 1994, despite larger HHC control angles used there.

Abbreviations

\(a_\infty\) :

Speed of sound (m/s)

c :

airfoil chord (m)

C m M 2 :

Section moment coefficient, \(C_mM^2=(dM_{c/4}/dy)/[(\rho/2)a_\infty^2c^2]\)

C n M 2 :

Section loading coefficient, \(C_nM^2=(dL/dy)/[(\rho/2)a_\infty^2c]\)

C T :

Thrust coefficient, \(C_T=T/(\rho\pi\Upomega^2R^4)\)

dL/dy :

Section lift (N/m)

dM c/4/dy :

Section moment (Nm/m)

M :

Mach number

M h :

Hover tip Mach number, \(M_h=\Upomega R/a_\infty\)

M x :

Rotor hub rolling moment (Nm)

M y :

Rotor hub pitching moment (Nm)

M ∞ :

Free-stream Mach number, \(M_\infty=V_\infty/a_\infty\)

N b :

Number of blades

p ∞ :

Static air pressure (kPa)

P :

Rotor power (kW)

r :

Non-dimensional radial coordinate

r a :

Non-dimensional root cut-out radius

r c :

Vortex core radius (m)

r c0 :

Vortex initial core radius (m)

r tw :

Non-dimensional zero twist radius

R :

Rotor radius (m)

t :

Time (s)

T :

Thrust (N)

T ∞ :

Air temperature (°C)

V ∞ :

Airspeed (m/s)

y :

Radial coordinate (m)

α :

Oseen parameter, α = 1.25643

α S :

Rotor shaft angle of attack (°)

\(\Upgamma\) :

Circulation (m2/s)

δ:

Effective viscosity coefficient, δ = 1000

\(\Updelta\alpha\) :

Wind tunnel interference angle (°)

\(\Uptheta_C\) :

Lateral cyclic pitch angle (°)

\(\Uptheta_S\) :

Longitudinal cyclic pitch angle (°)

\(\Uptheta_{el}\) :

Elastic twist angle (°)

\(\Uptheta_{tw}\) :

Linear blade twist per span (°)

\(\Uptheta_{75}\) :

Collective pitch angle at 0.75R (°)

\(\Uptheta_3\) :

HHC pitch angle at 3/rev (°)

μ :

Advance ratio, \(\mu=V_\infty\cos\alpha_S/(\Upomega R)\)

ν :

Kinematic viscosity of air (m2/s)

\(\rho_\infty\) :

Air density (kg/m3)

σ :

Rotor solidity, σ = N b c/(πR 2)

ψ :

Azimuth, \(\psi=\Upomega\)t (°)

ψ v :

Vortex age (°)

ψ 3 :

Phase of 3/rev HHC pitch angle (°)

\(\Upomega\) :

Rotor rotational frequency (rad/s)

bpf:

Blade passage frequency

BL:

Baseline case without HHC

BVI:

Blade–vortex interaction

CFD:

Computational fluid dynamics

CSD:

Computational structural dynamics

HART:

HHC aeroacoustics rotor test

HHC:

Higher harmonic control

MN:

Minimum noise case

MV:

Minimum vibration case

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Acknowledgments

The authors would like to thank all of their colleagues, students, and advisors for their collaboration. These are: Dr. Jae-Sang Park (KU), Dr. Jianping Yin (DLR), Dr. Yves Delrieux (Onera), Mathieu Amiraux and Sebastian Thomas (UM), Michael Acierno, Nicolas Reveles, and C. Eric Lynch (GIT).

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Authors and Affiliations

  1. German Aerospace Center (DLR), Institute of Flight Systems, Lilienthalplatz 7, 38108, Braunschweig, Germany

    Berend G. van der Wall

  2. Ames Research Center, US Army Aeroflightdynamics Directorate, Moffett Field, CA, 94035, USA

    Joon W. Lim

  3. Georgia Institute of Technology, School of Aerospace Engineering, 270 Ferst Drive, Atlanta, GA, 30332-0150, USA

    Marilyn J. Smith

  4. Department of Aerospace Information Engineering, Konkuk University, Seoul, 143-701, Republic of Korea

    Sung N. Jung

  5. Onera, 8 rue des Vertugadins, 92190, Meudon, France

    Joëlle Bailly

  6. Department of Aerospace Engineering, University of Maryland, College Park, MD, 20742, USA

    James D. Baeder

  7. NASA Langley Research Center, Aeroacoustics Branch, Hampton, VA, 23681-2199, USA

    D. Douglas Boyd Jr.

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  1. Berend G. van der Wall
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Correspondence to Berend G. van der Wall.

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Condensed form of a paper first presented at the 68th Annual Forum of the American Helicopter Society, Ft. Worth, TX, USA, 2012.

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van der Wall, B.G., Lim, J.W., Smith, M.J. et al. The HART II international workshop: an assessment of the state-of-the-art in comprehensive code prediction. CEAS Aeronaut J 4, 223–252 (2013). https://doi.org/10.1007/s13272-013-0077-9

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