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Optimal control of a turbulent fibre suspension flowing in a planar contraction. (English) Zbl 1115.76038

Summary: We consider the fibre orientation distribution in a turbulent fibre suspension flowing in a planar contraction. The fibre orientation is modelled using a diffusion-convection-type equation, while the average flow velocity of the suspension is modelled using a simple one-dimensional model. Our aim is to control the fibre orientation distribution at the end of the contraction by changing its shape. The shape is discretized with Bezier function, and the diffusion-convection equation with streamline upwind Petrov-Galerkin finite element method. Algebraic sensitivity analysis for the discretized optimization problem is done with the aid of automatic differentiation techniques. Numerical examples are given.

MSC:

76F70 Control of turbulent flows
76T20 Suspensions
76M10 Finite element methods applied to problems in fluid mechanics
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References:

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