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The HART II international workshop: an assessment of the state of the art in CFD/CSD prediction

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Abstract

Over the past decade, there have been significant advancements in the accuracy of rotor aeroelastic simulations with the application of computational fluid dynamics methods coupled with computational structural dynamics codes (CFD/CSD). The HART II international workshop database, which includes descent operating conditions with strong blade–vortex interactions (BVI), provides a unique opportunity to assess the ability of CFD/CSD to capture these physics. In addition to a baseline case with BVI, two additional cases with 3/rev higher harmonic blade root pitch control are available for comparison. The collaboration during the workshop permits assessment of structured, unstructured, and hybrid overset CFD/CSD methods from across the globe on the dynamics, aerodynamics, and wake structure. Evaluation of the plethora of CFD/CSD methods indicates that the most important numerical variables associated with most accurately capturing BVI include the use of either a two-equation RANS model or detached eddy simulation-based turbulence model and a sufficiently small time step. An appropriate trade-off between grid fidelity and spatial accuracy schemes also appears to be important for capturing BVI on the advancing side of the rotor disk. Overall, the CFD/CSD methods generally fall within the same accuracy; cost-effective hybrid Navier-Stokes/Lagrangian wake methods tend to correlate less accurately with experiment and have larger data scatter than the full CFD/CSD methods for most parameters evaluated. The importance of modeling the fuselage is observed, and other requirements are discussed.

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Notes

  1. The MN and MV naming convention was adopted from the 1994 HART I. However, the HHC control angles from the HART I are larger than the HHC control angles in the HART II.

  2. The experimental data include 2,048 samples/rev for the aerodynamic loads and 256 samples/rev for the structural moments.

Abbreviations

\(a_\infty\) :

Speed of sound (m/s)

c :

Airfoil chord (m)

C m M 2 :

Section moment coefficient, \(C_mM^2 = ({\rm d}M_{c/4}/{\rm d}y)/(\rho_\infty a_{\infty}^2 c^2/2)\)

C n M 2 :

Section force coefficient, \(C_nM^2 = ({\rm d}L^\prime/{\rm d}y)/(\rho_\infty a_{\infty}^2 c/2)\)

C T :

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

f, g :

Function

\({\rm d}L^\prime/dy\) :

Section lift (N/m)

dM c/4/dy :

Section moment (Nm/m)

M h :

Hover tip Mach number, \(M_{\rm h} = \Upomega R/a_{\infty}\)

M x :

Rotor hub roll moment (Nm)

M y :

Rotor hub pitch moment (Nm)

\(M_\infty\) :

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

n :

Integer

N b :

Number of blades

\(p_\infty\) :

Static air pressure (kPa)

P :

Rotor power (kW)

r :

Pearson product moment coefficient

r a :

Non-dimensional root cut-out radius

r tw :

Non-dimensional zero twist radius

R :

Rotor radius (m)

s :

Standard deviation

t :

Time (s)

T :

Thrust (N)

\(T_\infty\) :

Air temperature (°C)

\(V_\infty\) :

Air speed, m/s

x, y, z :

Chord, radial, normal coordinates, respectively (m)

x el :

Elastic deflection (m)

x hub :

Hub center distance to nozzle (m)

y hub :

Hub position above centerline (m)

α :

Angle of attack (°)

α S :

Rotor shaft angle of attack (°)

\(\Updelta{\alpha_s}\) :

Wind tunnel interference angle (°)

ϕ :

Mode shape

\(\Uptheta_C\) :

Lateral cyclic pitch angle (°)

\(\Uptheta_S\) :

Longitudinal cyclic pitch angle (°)

\(\Uptheta_{\rm el}\) :

Elastic twist angle (°)

\(\Uptheta_{\rm tw}\) :

Linear blade twist (°/R)

\(\Uptheta_{75}\) :

Collective pitch angle at 0.75R (°)

\(\Uptheta_{3}\) :

HHC pitch angle at 3/rev (°)

μ :

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

\(\rho_\infty\) :

Air density (kg/m3)

σ :

Rotor solidity, σ = N b c/(πR 2)

ψ :

Azimuth, \(\psi = \Upomega t,\) (°)

ψ 3 :

Phase of 3/rev HHC pitch angle (°)

\(\Upomega\) :

Rotor rotational frequency (radians/s)

\(\bar{.}\) :

Mean

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Acknowledgments

The authors would like to acknowledge the support of HART II partners: DLR, DNW, NASA, ONERA, and AFDD. In addition, the authors would like to thank all of their colleagues, students, or advisors for their collaboration. These are: Andy Wissink, Anubhav Datta, Mark Potsdam, Venke Sankaran, Jay Sitaraman, and Roger Strawn of the Helios development team (AFDD-2), Michael Acierno, Nicolas Reveles, Eric Lynch, and Olivier Bauchau (GIT-1), Lakshmi N. Sankar, Kyle Collins and Olivier Bauchau (GIT-2), Young-Hyun You and Jeong-Hwan Sa (KU), Elizabeth M. Lee-Rausch (NL-2), and Mathieu Amiraux and Sebastian Thomas (UMD).

Author information

Author notes

  1. Byung-Young Min

    Present address: Aerodynamics Department, United Technologies Research Ctr, 411 Silver Lane, MS 129-89, East Hartford, CT, 06108, USA

Authors and Affiliations

  1. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0150, USA

    Marilyn J. Smith & Byung-Young Min

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

    Joon W. Lim

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

    Berend G. van der Wall

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

    James D. Baeder

  5. NASA Langley Research Center, Computational AeroSciences Branch, Hampton, VA, 23681-2199, USA

    Robert T. Biedron

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

    D. Douglas Boyd Jr.

  7. Science and Technology Corporation, Moffett Field, CA, 94035, USA

    Buvana Jayaraman

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

    Sung N. Jung

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  1. Marilyn J. Smith
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Correspondence to Marilyn J. Smith.

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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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Smith, M.J., Lim, J.W., van der Wall, B.G. et al. The HART II international workshop: an assessment of the state of the art in CFD/CSD prediction. CEAS Aeronaut J 4, 345–372 (2013). https://doi.org/10.1007/s13272-013-0078-8

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