Shape optimization in computational fluid dynamics

Dinh, Quang; Rogé, Gilbert; Sevin, Cyrille; Stoufflet, B.

doi:10.1080/12506559.1996.10511238

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…Thus, see by choosing

α MathClass-rel= MathClass-bin- λ ((), ρ^{MathClass-bin*} MathClass-bin+ \overset{U}{true} MathClass-bin\cdot \overset{{((), ρ U)}^{MathClass-bin*}}{true}) ((), \frac{\partial ((), ρ U_{n})}{\partial n} MathClass-bin- κ ρ U_{t})

for a small enough constant scalar λ , J will decrease because in this case,

δ J MathClass-rel= MathClass-bin- λ {MathClass-op\int}_{Σ} {((), ρ^{MathClass-bin*} MathClass-bin+ \overset{U}{true} MathClass-bin\cdot \overset{{(ρ U)}^{MathClass-bin*}}{true})}^{2} {((), \frac{\partial ((), ρ U_{n})}{\partial n} MathClass-bin- κ ρ U_{t})}^{2} MathClass-bin+ o (λ)

This method was used by B. Mohammadi in and G. Rogé et al in to reduce the sonic boom of a business jet by 30% without affecting the lift. Automatic differentiation was used, so we intend to reproduce the results with the code presented here in the future.…”

Section: Optimal Wing Profile With Least Sonic Boommentioning

confidence: 99%

Continuous and discrete adjoints to the Euler equations for fluids

Alauzet

Pironneau

2011

Numerical Methods in Fluids

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SUMMARY Adjoints are used in optimization to speed‐up computations, simplify optimality conditions or compute sensitivities. Because time is reversed in adjoint equations with first‐order time derivatives, boundary conditions, and transmission conditions through shocks can be difficult to understand. In this article, we analyze the adjoint equations that arise in the context of compressible flows governed by the Euler equations of fluid dynamics. We show that the continuous and discrete adjoints computed by automatic differentiation agree numerically; in particular, the adjoint is found to be continuous at the shocks and usually discontinuous at contact discontinuities by both.Copyright © 2011 John Wiley & Sons, Ltd.

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“…Thus, see by choosing

α MathClass-rel= MathClass-bin- λ ((), ρ^{MathClass-bin*} MathClass-bin+ \overset{U}{true} MathClass-bin\cdot \overset{{((), ρ U)}^{MathClass-bin*}}{true}) ((), \frac{\partial ((), ρ U_{n})}{\partial n} MathClass-bin- κ ρ U_{t})

for a small enough constant scalar λ , J will decrease because in this case,

δ J MathClass-rel= MathClass-bin- λ {MathClass-op\int}_{Σ} {((), ρ^{MathClass-bin*} MathClass-bin+ \overset{U}{true} MathClass-bin\cdot \overset{{(ρ U)}^{MathClass-bin*}}{true})}^{2} {((), \frac{\partial ((), ρ U_{n})}{\partial n} MathClass-bin- κ ρ U_{t})}^{2} MathClass-bin+ o (λ)

Section: Optimal Wing Profile With Least Sonic Boommentioning

confidence: 99%

Continuous and discrete adjoints to the Euler equations for fluids

Alauzet

Pironneau

2011

Numerical Methods in Fluids

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“…Schematically the CAD modeler can be represented by the following operator: ν −→ d(ν) where d(ν) denotes the surface mesh displacement. The mathematical optimization problem can be formulated as an optimal control problem (Lions, 1971) as follows (Dinh et al, 1996): Find a shape µ * within O (set of shapes) such that:…”

Section: A Numerical Platformmentioning

confidence: 99%

“…-CAD modeler, -Volume mesh deformation, -CFD solver (Bastin et al, 1999), -adjoint of CFD solver (Dinh et al, 1996), -adjoint of volume-mesh deformation, -cost and gradient, -optimizer.…”

Section: Optimization Platformmentioning

confidence: 99%

Multimodel design strategies applied to sonic boom reduction

Alauzet

Borel-Sandou²,

Daumas

et al. 2008

TECM

Self Cite

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“…Until recently, industrial heat exchangers have been designed with the assistance of computer-aided design (CAD) based geometry optimization software [18,14], which are compatible with all the stages of the design workflow from physical simulations relying on commercial codes to the automated manufacturing process. Unfortunately, these methods heavily rely on the choice of a parameterization for the geometry of the optimized shape, so that they usually yield very small modifications of the initially proposed geometry [49,23,38,36,69]. These already allow for substantial gains in performance in most industrial applications.…”

Section: Introductionmentioning

confidence: 99%

Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers

Feppon

Allaire

Dapogny

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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We present a topology optimization approach for the design of fluid-to-fluid heat exchangers which rests on an explicit meshed discretization of the phases at stake, at every iteration of the optimization process. The considered physical situations involve a weak coupling between the Navier-Stokes equations for the velocity and the pressure in the fluid, and the convection-diffusion equation for the temperature field. The proposed framework combines several recent techniques from the field of shape and topology optimization, and notably a level-set based mesh evolution algorithm for tracking shapes and their deformations, an efficient optimization algorithm for constrained shape optimization problems, and a numerical method to handle a wide variety of geometric constraints such as thickness constraints and non-penetration constraints. Our strategy is applied to the optimization of various types of heat exchangers. At first, we consider a simplified 2D cross-flow model where the optimized boundary is the section of the hot fluid phase flowing in the transverse direction, which is naturally composed of multiple holes. A minimum thickness constraint is imposed on the cross-section so as to account for manufacturing and maximum pressure drop constraints. In a second part, we optimize the design of 2D and 3D heat exchangers composed of two types of fluid channels (hot and cold), which are separated by a solid body. A non-mixing constraint between the fluid components containing the hot and cold phases is enforced by prescribing a minimum distance between them. Numerical results are presented on a variety of test cases, demonstrating the efficiency of our approach in generating new, realistic, and unconventional heat exchanger designs.

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Shape optimization in computational fluid dynamics

Cited by 6 publications

References 7 publications

Continuous and discrete adjoints to the Euler equations for fluids

Continuous and discrete adjoints to the Euler equations for fluids

Multimodel design strategies applied to sonic boom reduction

Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers

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