Nonlinear, proper-orthogonal-decomposition-based model of forced convection heat transfer in pulsating flow
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2014
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Abstract
A nonlinear, low-order physics-based model for the dynamics of forced convection wall heat transfer in pulsating flow is formulated, based on the proper orthogonal decomposition technique. In a multivariate approach, proper orthogonal decomposition modes are constructed from computational fluid dynamics data for laminar flow and heat transfer over a flat plate in pulsating flow, spanning a range of pulsation frequencies and amplitudes. Then, the conservation equations for mass, momentum, and energy are projected onto the proper orthogonal decomposition modes, such that a system of ordinary differential equations for the modal amplitudes is obtained. The forcing at the inlet is written explicitly in the ordinary differential equations of the low-order model. The contribution of the nonvanishing pressure term resulting from the incompressible Navier-Stokes equation is included with a calibration method. The accuracy and stability of the low-order model are evaluated by comparison with computational fluid dynamics data. Possible applications of this heat source model to the computation of a describing function or the prediction of limit cycle amplitudes of thermoacoustic instabilities are discussed.
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Computational fluid dynamics , Heat transfer , Laminar flow , Navier Stokes equations , Ordinary differential equations , Principal component analysis , Conservation equations , Flow and heat transfer , Incompressible Navier Stokes equations , Physics-based modeling , Proper orthogonal decomposition techniques , Proper orthogonal decompositions , System of ordinary differential equations , Thermoacoustic instability , Forced convection