Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors

Ekici, Kivanc; Hall, Kenneth C.; Dowell, Earl H.

doi:10.1016/j.jcp.2008.02.028

Cited by 81 publications

(12 citation statements)

References 33 publications

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“…Furthermore, it is necessary to simulate the entire rotor containing all the blades (all 360 • ) because each blade experiences different flow conditions at a given time, especially the relative velocity on each blade. While this is true for typical implicit time stepping schemes such the backward difference formula (BDF) by Jameson (1991), Ekici et al (2008) has shown that it is possible to simulate only one sector of the rotor when combined with a Fourier based time stepping scheme through a time-lagged boundary condition. The detail of this will be discussed in section 5.6.…”

Section: Helicopter In Forward Flightmentioning

confidence: 99%

“…The first group of people are from Syracuse University (Kumar & Murthy, 2007, and the second is from Duke University (Ekici et al, 2008). The first group's method is based on forward and backward Fourier transforms similar to the NLFD technique.…”

Section: Fourier-based Time Integration Solversmentioning

confidence: 99%

“…When Fourier based time integration is used for rotorcraft simulation, it is possible to use only one sector of a rotor for forward flight calculation by applying the boundary condition first proposed by Ekici et al (2008) at the upstream and downstream boundaries:…”

Section: Time Lagged Periodic Boundary Conditionmentioning

confidence: 99%

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Time Spectral Method for Rotorcraft Flow with Vorticity Confinement

Butsuntorn

2008

26th AIAA Applied Aerodynamics Conference

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Section: Helicopter In Forward Flightmentioning

confidence: 99%

Section: Fourier-based Time Integration Solversmentioning

confidence: 99%

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Time Spectral Method for Rotorcraft Flow with Vorticity Confinement

Butsuntorn

2008

26th AIAA Applied Aerodynamics Conference

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“…Although the pseudo-time integration for the inner iteration and a multigrid technique can make the solution converge faster, the time-marching computation is still expensive even with highly parallel computation as it needs to fully resolve unsteady transient flows before flows reach a periodic steady-state. On the other hand, a spectral method for time integration has been proposed [8][9][10][11][12][13][14][15][16] as an alternative to a time-marching, dual-time stepping 2 Mathematical Problems in Engineering method with much reduced computational cost at equivalent solution accuracy. With the flow solution approximation by a discrete Fourier series, a time derivative term of the governing equations reduces to a spectral derivative term and removes time dependence of the flow solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to the HBM developed by Thomas et al [9,10], it integrates the spectral derivative term of the governing equations directly in the time domain. Ekici et al [11] solved helicopter rotor flows using the harmonic balance method with periodic boundary conditions both in time and in space, which makes the computation domain more compact than that of the time-spectral method and contributes to further decreasing computation time and memory in comparison to the time-marching computation. Choi et al [17,18] used the time-spectral CFD computation method for fluidstructure interaction analysis of the rotor flows in unsteady forward flight of the UH60-A helicopter.…”

Section: Introductionmentioning

confidence: 99%

Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology

Choi

2018

Mathematical Problems in Engineering

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Unsteady helicopter rotor flows are solved by a Chebyshev pseudospectral method with overset mesh topology which employs Chebyshev polynomials for solution approximation and a Chebyshev collocation operator to represent the time derivative term of the unsteady flow governing equations. Spatial derivative terms of the flux Jacobians are discretized implicitly while the Chebyshev spectral derivative term is treated in explicit form. Unlike the Fourier spectral method, collocation points of standard Chebyshev polynomials are not evenly distributed and heavily clustered near the extremities of the time interval, which makes the spectral derivative matrix ill-conditioned and deteriorates the stability and convergence of the flow solution. A conformal mapping of an arcsin function is applied to redistribute those points more evenly and thus to improve the numerical stability of the linear system. A parameter study on the condition number of the spectral derivative matrix with respect to the control parameters of the mapping function is also carried out. For the validation of the proposed method, both periodic and nonperiodic unsteady flow problems were solved with two-dimensional problems: an oscillating airfoil with a fixed frequency and a plunging airfoil with constant plunging speed without considering gravitational force. Computation results of the Chebyshev pseudospectral method showed excellent agreements with those of the time-marching computation. Subsequently, helicopter rotor flows in hovering and nonlifting forward flight are solved. Moving boundaries of the rotating rotor blades are efficiently managed by the overset mesh topology. As a set of subgrids are constructed only one time at the beginning of the solution procedure corresponding to the mapped Chebyshev collocation points, computation time for mesh interpolation of hole-cutting between background and near-body grids becomes drastically reduced when compared to the time-marching computation method where subgrid movement and the hole-cutting need to be carried out at each physical time step. The number of the collocation points was varied to investigate the sensitivity of the solution accuracy, computation time, and memory. Computation results are compared with those from the time-marching computation, the Fourier spectral method, and wind-tunnel experimental data. Solution accuracy and computational efficiency are concluded to be great with the Chebyshev pseudospectral method. Further applications to unsteady nonperiodic problems will be left for future work.

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Aeroelastic analysis of a wind turbine blade using the harmonic balance method

2017

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An aeroelastic model for wind turbine blades derived from the unsteady Navier‐Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart‐Allmaras turbulence model. The computation times for the aerodynamic solution are significantly reduced using the harmonic balance method compared to a time‐accurate solution. This model is significantly more robust than standard aeroelastic codes that rely on blade element momentum theory to determine the aerodynamic forces. Comparisons with published results for the Caradonna‐Tung rotor in hover and the classical AGARD 445.6 flutter case are provided to validate the aerodynamic model and aeroelastic model, respectively. For wind turbines, flutter of the 1.5 MW WindPACT blade is considered. The results predict that the first flapwise and edgewise modes dominate flutter at the rotor speeds considered.

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Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors

Cited by 81 publications

References 33 publications

Time Spectral Method for Rotorcraft Flow with Vorticity Confinement

Time Spectral Method for Rotorcraft Flow with Vorticity Confinement

Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology

Aeroelastic analysis of a wind turbine blade using the harmonic balance method

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