Unsteady Transonic Aerodynamic Analysis for Oscillatory Airfoils using Time Spectral Method
This research proposes an algorithm for the simulation
of time-periodic unsteady problems via the solution unsteady Euler
and Navier-Stokes equations. This algorithm which is called Time
Spectral method uses a Fourier representation in time and hence
solve for the periodic state directly without resolving transients
(which consume most of the resources in a time-accurate scheme).
Mathematical tools used here are discrete Fourier transformations. It
has shown tremendous potential for reducing the computational cost
compared to conventional time-accurate methods, by enforcing
periodicity and using Fourier representation in time, leading to
spectral accuracy. The accuracy and efficiency of this technique is
verified by Euler and Navier-Stokes calculations for pitching airfoils.
Because of flow turbulence nature, Baldwin-Lomax turbulence
model has been used at viscous flow analysis. The results presented
by the Time Spectral method are compared with experimental data. It
has shown tremendous potential for reducing the computational cost
compared to the conventional time-accurate methods, by enforcing
periodicity and using Fourier representation in time, leading to
spectral accuracy, because results verify the small number of time
intervals per pitching cycle required to capture the flow physics.
[1] K.C. Hall, J.P. Thomas and W.S. Clark, "Computation of Unsteady
Nonlinear Flows in Cascades using a Harmonic Balance Technique,"
Technical report, 9th International Symposium on Unsteady
Aerodynamics, Aeroacoustics and Aeroelasticity Of Turbomachines,
Lyon, France, September 2000.
[2] M. McMullen, A. Jameson and J. J. Alonso, "Application of a Nonlinear
Frequency Domain Solver to the Euler and Navier- Stokes Equations,"
AIAA paper 02-0120, AIAA 40th Aerospace Sciences Meeting and
Exhibit, Reno, NV, January 2002,
[3] A. K. Gopinath and A. Jameson, "Time Spectral Method for Periodic
Unsteady Computations over Two- and Three- Dimensional Bodies," In
AIAA 43th Aerospace Sciences Meeting & Exhibit . Reno, NV, AIAA
Paper 2005-1220.
[4] S.S. Davis, "NACA 64A010 (NASA Ames Model) Oscillatory Pitching
," AGARD Report 702, AGARD, January 1982, Dataset 2.
[5] R.H. Landon., "NACA0012 Oscillatory and Transient Pitching,"
AGARD Report 702, AGARD, January 1982. Dataset 3.
[6] A. Jameson, W. Schmidt and E. Turkel, "Numerical solutions of the
Euler equations by finite volume methods with Runge-Kutta time
stepping schemes," AIAA paper 81-1259, January 1981.
[7] Baldwin, B. S. and Lomax H., "Thin layer approximation and algebraic
model for separated flows," AIAA paper 78-275, 1978.
[8] P. Moin, "Spectral Methods in Computational Physics, Supplementary
notes," Stanford University, Stanford, CA, ME 408, 2003.
[1] K.C. Hall, J.P. Thomas and W.S. Clark, "Computation of Unsteady
Nonlinear Flows in Cascades using a Harmonic Balance Technique,"
Technical report, 9th International Symposium on Unsteady
Aerodynamics, Aeroacoustics and Aeroelasticity Of Turbomachines,
Lyon, France, September 2000.
[2] M. McMullen, A. Jameson and J. J. Alonso, "Application of a Nonlinear
Frequency Domain Solver to the Euler and Navier- Stokes Equations,"
AIAA paper 02-0120, AIAA 40th Aerospace Sciences Meeting and
Exhibit, Reno, NV, January 2002,
[3] A. K. Gopinath and A. Jameson, "Time Spectral Method for Periodic
Unsteady Computations over Two- and Three- Dimensional Bodies," In
AIAA 43th Aerospace Sciences Meeting & Exhibit . Reno, NV, AIAA
Paper 2005-1220.
[4] S.S. Davis, "NACA 64A010 (NASA Ames Model) Oscillatory Pitching
," AGARD Report 702, AGARD, January 1982, Dataset 2.
[5] R.H. Landon., "NACA0012 Oscillatory and Transient Pitching,"
AGARD Report 702, AGARD, January 1982. Dataset 3.
[6] A. Jameson, W. Schmidt and E. Turkel, "Numerical solutions of the
Euler equations by finite volume methods with Runge-Kutta time
stepping schemes," AIAA paper 81-1259, January 1981.
[7] Baldwin, B. S. and Lomax H., "Thin layer approximation and algebraic
model for separated flows," AIAA paper 78-275, 1978.
[8] P. Moin, "Spectral Methods in Computational Physics, Supplementary
notes," Stanford University, Stanford, CA, ME 408, 2003.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:54758", author = "Mohamad Reza. Mohaghegh and Majid. Malek Jafarian", title = "Unsteady Transonic Aerodynamic Analysis for Oscillatory Airfoils using Time Spectral Method", abstract = "This research proposes an algorithm for the simulation
of time-periodic unsteady problems via the solution unsteady Euler
and Navier-Stokes equations. This algorithm which is called Time
Spectral method uses a Fourier representation in time and hence
solve for the periodic state directly without resolving transients
(which consume most of the resources in a time-accurate scheme).
Mathematical tools used here are discrete Fourier transformations. It
has shown tremendous potential for reducing the computational cost
compared to conventional time-accurate methods, by enforcing
periodicity and using Fourier representation in time, leading to
spectral accuracy. The accuracy and efficiency of this technique is
verified by Euler and Navier-Stokes calculations for pitching airfoils.
Because of flow turbulence nature, Baldwin-Lomax turbulence
model has been used at viscous flow analysis. The results presented
by the Time Spectral method are compared with experimental data. It
has shown tremendous potential for reducing the computational cost
compared to the conventional time-accurate methods, by enforcing
periodicity and using Fourier representation in time, leading to
spectral accuracy, because results verify the small number of time
intervals per pitching cycle required to capture the flow physics.", keywords = "Time Spectral Method, Time-periodic unsteadyflow, Discrete Fourier transform, Pitching airfoil, Turbulence flow", volume = "5", number = "2", pages = "345-8", }