Sensitivities, adjoints and flow optimization

Gunzburger, Max

doi:10.1002/(sici)1097-0363(19990915)31:1<53::aid-fld955>3.0.co;2-z

Cited by 67 publications

(23 citation statements)

References 10 publications

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“…The adjoint was constructed directly from the source code of the original discrete nonlinear model, circumventing di culties that would appear if one were to ÿrst obtain the continuous adjoint model and then discretize the adjoint equations (for more about the di erences between the di erentiate-then-discretize approach and the discretize-then-di erentiate approach see Gunzburger [46]). …”

Section: Introductionmentioning

confidence: 99%

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Homescu

Navon

2001

Numerical Methods in Fluids

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SUMMARYAdjoint formulation is employed for the optimal control of ow around a rotating cylinder, governed by the unsteady Navier-Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time-dependent. Since the numerical control problem is ill-posed, regularization is employed. An empirical logarithmic law relating the regularization coe cient to the Reynolds number was derived for 606Re6140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re = 60 to Re = 1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A signiÿcant reduction of the amplitude of the variation of the drag coe cient is obtained for the optimized values of the rotation rate.

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Section: Introductionmentioning

confidence: 99%

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Homescu

Navon

2001

Numerical Methods in Fluids

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“…Similarly, ∇ u w λ and ∇ T w λ de¦ne the sensitivity of the eigenvalue to a wall velocity and temperature. The analytical expression of these gradients is derived using a Lagrangian method relying on the de¦nition of adjoint variables, an approach similar to that widely used in the context of optimization problems [6]:…”

Section: Progress In Flight Physicsmentioning

confidence: 99%

Adjoint-based control of afterbody flow unsteadiness in the compressible regime

Ph.

Sipp

Chomaz

2012

Progress in Flight Physics

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The theoretical study of a compressible afterbody §ow in the subsonic regime is presented. It relies on sensitivity analyses developed in the framework of the linear global stability theory and aims at predicting beforehand the e¨ect of a steady bulk and wall forcing on the growth rate of linear global modes. Such an analysis stands as a step in the perspective of a full control of afterbody §ow unsteadiness. The sensitivity functions are derived analytically using adjoint methods and presented for the global mode responsible for the onset of a periodic regime. Various control methods are investigated, including an additional control device in the lee of the main body, heat sources, and boundary forcing. The obtained results show that the global mode is sensitive to momentum forcing along the separation line, to a localized heating in the core of the recirculating bubble, and to a blowing velocity close to the edge of the base.

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“…Such an approach is classically used in flow control and optimization problems. 46,47 It is worthwhile noting that although the definition of the gradients depends on the choice of the inner product through the computation of the adjoint quantities, the eigenvalue variation computed from Eq. ͑16͒ does not.…”

Section: -5mentioning

confidence: 99%

Open-loop control of compressible afterbody flows using adjoint methods

Méliga¹,

Sipp²,

Chomaz

2010

Physics of Fluids

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International audienceThe flow past an axisymmetric body is generically unstable to a steady and a time-periodic global instability, the latter being thought to lead the low-frequency unsteadiness of the wake even at larger Reynolds numbers. The present paper examines how the growth rate of the oscillatory unstable mode developing in the wake of bullet-shaped objects can be reduced by a steady forcing, whose effect is to modify the base flow. The use of the compressible Navier-Stokes equations allows to consider control through steady mass, momentumheat forcing applied in the bulk and at the wall. To do so, we extend to compressible flows and axisymmetric geometries the method first proposed by Hill (NASA Technical Report No. 103858, 1992) to analyze the control of the two-dimensional mode of the incompressible cylinder wake. This method aims at evaluating the sensitivity of one particular eigenvalue to forcing by resolution of adjoint equations. Considering control at the wall, it allows to compute directly the eigenvalue gradient with respect to the wall variables. We show that the oscillating mode can be stabilized by a steady blowing at the wall (the so-called base-bleed control). Expressing the gradient as a sum of production, streamwise advectioncross-stream advection terms, we show that this stabilizing effect is due to cross-stream advection, in contradiction with the up to now accepted interpretation based on the local absolute and convective instability analysis of parallel profiles. The same technique allows to compute the gradient of the oscillatory eigenvalue to bulk mass, momentumheat sources. Momentum control can be achieved by placing a small ring in the lee of the afterbody. Similar to the two-dimensional case studied by Hill, the effect of such a ring is twofold, as it induces a steady drag force which modifies the base flow and a fluctuating drag force proportional to the perturbation momentum at the ring location. We show that the efficiency of the control can be improved by heating the ring, which then acts as an additional heat source. © 2010 American Institute of Physics

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Sensitivities, adjoints and flow optimization

Cited by 67 publications

References 10 publications

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Adjoint-based control of afterbody flow unsteadiness in the compressible regime

Open-loop control of compressible afterbody flows using adjoint methods

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