Optimal control of a transitional jet using a continuous adjoint method

Abstract

The use of active flow control with unsteady means gains increasing interest in engineering designs. The main bottleneck of the methodology is the strong dependence on trial and error to find the right set of control parameters. In this context, adjoint-based control using high-fidelity simulations is a promising method to explore optimal values in large parameter spaces. However, the applicability of the methodology to complex engineering geometries remains extremely limited. In this work, we employ adjoint-based optimal control using unsteady high-fidelity simulations in a generic unstructured grid framework. To this end, an optimal flow control study is conducted in OpenFOAM R using the continuous adjoint method and DNS simulations. To demonstrate the methodology, we study control of an incompressible axisymmetric jet at Re D = 2000, with focus on improving its mixing properties. The gradient of the cost functional is calculated with a newly developed unsteady-adjoint solver based on a classical incremental projection scheme. Particular attention is paid into the presentation of mathematical and algorithmic details. Moreover, we address three main issues that remained relatively undiscussed in common practise: the choice of adjoint boundary conditions on computational boundaries, the failure of the adjoint methodology for long optimization horizons in turbulent flows and the treatment of the additional transposed convective term in the adjoint equations. Practical solutions are employed for these issues. Two optimization cases with different initial conditions are designed. To this end, we considered

Coherent structures in interacting vortex rings

“…The dynamics of a vortex ring has been found to be dominated by large-scale structures, for instance in the breakdown of a vortex ring [7], and in turbulent transport and subsequently the efficient and environmentally-clean operation of a combustor [8]. The manipulation, either excitation or suppression, of such large-scale coherent structures by means of passive or active control has been found to enhance mass entrainment rate [9][10][11][12] or reduce noise [13]. In Ref.…”

A vortex pair in ground effect, dynamics and optimal control

“…This optimal system is based on a set of nonlinear partial differential equations. While this nonlinearity could lead to difficulties in converging an optimal solution, in the present case the dynamics of the vortex to be controlled follows a deterministic evolution, so that similarly to Önder & Meyers (2016), a steepest descent algorithm with a generic backtracking line search is successfully used in order to perform the optimization. The whole procedure is sketched in figure 7.…”

“…The technique has been successfully applied for boundary layers and wakes (Walther, Airiau & Bottaro 2001;Homescu, Navon & Li 2002;Airiau et al 2003;Guégan, Schmid & Huerre 2006;Flinois & Colonius 2015). In Önder & Meyers (2016), the optimal control method is used to improve the mixing of an incompressible axisymmetric jet and in Bewley, Moin & Temam (2001) flow relaminarization and drag reduction in a plane channel are demonstrated. The control algorithm for an unsteady flow and nonlinear dynamics typically requires a large amount of storage as the full flow field information is needed at each time step.…”

A reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows

“…The resolution of this problem determines the distribution of a basis of parameters (typical choices are boundary / initial conditions) which optimizes the flow configuration. Recent applications deal both with fundamental studies [10,11] and industrial oriented analyses [12,13].…”

“…While these approaches are very precise and they allow for sensitivity analyses considering a very large number of variables, their application to turbulent flow investigation over a long observation window is problematic [13,14]. A much less commonly investigated path for CFD is represented by the use of sequential methods, which are based on Bayesian inference and they occasionally require the resolution of Riccati-type equations.…”