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Demonstration of Nonlinear Frequency Domain Methods Matthew McMullen,
 

Summary: Demonstration of Nonlinear Frequency Domain Methods
Matthew McMullen,
Antony Jameson,
and Juan Alonso
Stanford University, Stanford, California 94305 USA
DOI: 10.2514/1.15127
This paper demonstrates the accuracy of the nonlinear frequency domain method in applications to unsteady flow
calculations. The basis of the method is a pseudospectral approach to recast a nonlinear unsteady system of equations
in the temporal domain into a stationary system in the frequency domain. The nonlinear frequency domain method,
in principle, provides the rapid convergence of a spectral method with increasing numbers of modes, and, in this
sense, it is an optimal scheme for time-periodic problems. In practice it can also be effectively used as a reduced order
method in which users deliberately choose not to resolve temporal modes in the solution. A variable-time-period
method has been proposed such that the nonlinear frequency domain method can be applied to problems where the
time period of the unsteadiness is either known or unknown a priori. To validate the latter case, results from this
method have been compared with experimental results of vortex shedding in low Reynolds number flows past
cylinders. Validation of the first case utilizes experimental data of a pitching airfoil in transonic flow. These
comparisons demonstrate the efficiency of the nonlinear frequency domain method in representing complex
nonlinear flow field physics with a limited number of temporal modes.
Nomenclature
A, B, C, D = coefficients used in the Strouhal data curve fit

  

Source: Alonso, Juan J. - Department of Aeronautics and Astronautics, Stanford University
Stanford University - Aerospace Computing Laboratory

 

Collections: Engineering