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ARTICLE INFO ABSTRACT Keywords: Reduced order model Proper Orthogonal Decomposition Incompressible nonisothermal flowA new method is presented to genérate reduced order models (ROMs) in Fluid Dynamics problems. The method is based on the expansión of the flow variables on a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. This means that the process is both computationally efficient (reconstructed flow fields require less than 1% of the time needed to compute a full CFD solution) and flexible (the projection window can avoid regions of large localized CFD errors). Also, various definitions of the residual are briefly discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors, to conclude that the method is numerically robust. This is because the results are largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications.

This study is motivated by the need to devise means to enhance heat transfer in configurations, like the back step, that appear in certain types of MEMS that involve fluid flow and that are not very efficient from the thermal transfer point of view. In particular, the work described in this paper studies the effect that a prescribed flow pulsation (defined by two control parameters: velocity pulsation frequency and pressure gradient amplitude at the inlet section) has on the heat transfer rate behind a backward facing step in the unsteady laminar 2-D regime. The working fluid that we have considered is water with temperature dependent viscosity and thermal conductivity. We have found that, for inlet pressure gradients that avoid flow reversal at both the upstream and downstream boundary conditions, the timeaveraged Nusselt number behind the step depends on the two above mentioned control parameters and is always larger than in the steady-state case. At Reynolds 100 and pulsating at the resonance frequency, the maximum time-averaged Nusselt number in the horizontal wall region located behind the step whose length is four times the step height is 55% larger than in the steady-case. Away from the resonant pulsation frequency, the time-averaged Nusselt number smoothly decreases and approaches its steady-state value.

Abstract:A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range 0.4 < Mach number < 0.8, -3° < angle of attack < 3°.

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