Reduced-Order Model for Viscous Aerodynamic Flow Past an Airfoil

Alonso, Diego Hayashi; Vega, José M.; Velázquez, A.

doi:10.2514/1.j050153

Cited by 43 publications

(61 citation statements)

References 24 publications

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“…In particular, both the snapshots and the POD amplitudes were calculated using the Euler equations. More recently, Alonso et al (2010) calculated POD modes using a R ANS approximation but determined the POD-mode amplitudes projecting the Euler equations. To our knowledge, this is the first paper in the literature in which a ROM based on Euler equations has been derived that uses snapshots resulting from viscous CFD calculations, which has both conceptual and practical consequences.…”

Section: Introductionmentioning

confidence: 99%

“…To our knowledge, this is the first paper in the literature in which a ROM based on Euler equations has been derived that uses snapshots resulting from viscous CFD calculations, which has both conceptual and practical consequences. Alonso et al (2010) considered a wide parameter range (0.4 < M < 0.8, -3° < AoA < 3°) in the Mach-number/angle-of-attack plane. A special shock wave treatment was necessary because of the presence of shock waves that move up to one-third of the chord as the parameters are varied.…”

Section: Introductionmentioning

confidence: 99%

“…The first difficulty (A) will deal with projecting the Euler equations onto the POD manifold. As explained and checked by Alonso et al (2010), the use of the Euler equations to project the equations, while the original problem is turbulent (and the snapshots have been CFD-computed using the NS equations with a turbulence model and, possibly, some small stabilizing terms added for numerical reasons) relies on three related arguments:…”

Section: Introductionmentioning

confidence: 99%

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Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

et al. 2012

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

et al. 2012

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“…f. Steep spatial gradients (e.g. shock waves in transonic aerodynamic flows) may require specific treatment (Alonso et al 2010). g. Variable geometry can be accounted for using a common, virtual mesh to define POD modes (Bache et al 2010).…”

Section: Steady Romsmentioning

confidence: 99%

Reduced order modeling of some fluid flows of industrial interest

Alonso

Terragni²,

Velázquez³

et al. 2012

Fluid Dyn. Res.

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Some basic ideas are presented for the construction of robust, computationally efficient reduced order models amenable to be used in industrial environments, combined with somewhat rough computational fluid dynamics solvers. These ideas result from a critical review of the basic principles of proper orthogonal decomposition-based reduced order modeling of both steady and unsteady fluid flows. In particular, the extent to which some artifacts of the computational fluid dynamics solvers can be ignored is addressed, which opens up the possibility of obtaining quite flexible reduced order models. The methods are illustrated with the steady aerodynamic flow around a horizontal tail plane of a commercial aircraft in transonic conditions, and the unsteady lid-driven cavity problem. In both cases, the approximations are fairly good, thus reducing the computational cost by a significant factor.

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“…Such reduction of the computational cost has been used in the reduced modeling of several systems, arising in nonlinear elasticity (Ryckelynck 2009), steady aerodynamic forces (Alonso et al 2009(Alonso et al , 2010, and unsteady incompressible flows (Terragni et al 2011). Mode libraries (both customized and generic) can also be used to further decrease the computational effort (Rapun et al 2015).…”

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confidence: 99%

Computationally efficient simulation of unsteady aerodynamics using POD on the fly

2016

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Modern industrial aircraft design requires a large amount of sufficiently accurate aerodynamic and aeroelastic simulations. Current computational fluid dynamics (CFD) solvers with aeroelastic capabilities, such as the NASA URANS unstructured solver FUN3D, require very large computational resources. Since a very large amount of simulation is necessary, the CFD cost is just unaffordable in an industrial production environment and must be significantly reduced. Thus, a more inexpensive, yet sufficiently precise solver is strongly needed. An opportunity to approach this goal could follow some recent results (Terragni and Vega 2014 SIAM J. Appl. Dyn. Syst. 13 330-65; Rapun et al 2015 Int. J. Numer. Meth. Eng. 104 844-68) on an adaptive reduced order model that combines 'on the fly' a standard numerical solver (to compute some representative snapshots), proper orthogonal decomposition (POD) (to extract modes from the snapshots), Galerkin projection (onto the set of POD modes), and several additional ingredients such as projecting the equations using a limited amount of points and fairly generic mode libraries. When applied to the complex Ginzburg-Landau equation, the method produces acceleration factors (comparing with standard numerical solvers) of the order of 20 and 300 in one and two space dimensions, respectively. Unfortunately, the extension of the method to unsteady, compressible flows around deformable geometries requires new approaches to deal with deformable meshes, high-Reynolds numbers, and compressibility. A first step in this direction is presented considering the unsteady compressible, two-dimensional flow around an oscillating airfoil using a CFD solver in a rigidly moving mesh. POD on the Fly gives results whose accuracy is comparable to that of the CFD solver used to compute the snapshots.

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Reduced-Order Model for Viscous Aerodynamic Flow Past an Airfoil

Cited by 43 publications

References 24 publications

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

Reduced order modeling of some fluid flows of industrial interest

Computationally efficient simulation of unsteady aerodynamics using POD on the fly

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