Optimal electrostatic control of fluid films

Alex Wray

Controlling film flows has long been a central target for fluid dynamicists due to its numerous applications, in fields from heat exchangers to biochemical recovery, to semiconductor manufacture. However, despite its significance in the literature, most analyses have focussed on the “forward” problem: what effect a given control has on the flow. Often these problems are already complex, incorporating the - generally multiphysical - interplay of hydrodynamic phenomena with the mechanism of control. Indeed, many systems still defy meaningful agreement between models and experiments.
The inverse problem - determining a suitable control scheme for producing a specified flow - is considerably harder, and much more computationally expensive (often involving thousands of calculations of the forward problem). Performing such calculations for the full Navier-Stokes problem is generally prohibitive.

We examine the use of electric fields as a control mechanism. Solving the forward problem involves deriving a low-order model that turns out to be accurate even deep into the shortwave regime. We show that the weakly-nonlinear problem is Kuramoto-Sivashinsky-like, allowing for greater analytical traction. The fully nonlinear problem can be solved numerically via the use of a rapid solver, enabling solution of both the forward and adjoint problems on sub-second timescales, allowing for both terminal and regulation optimal control studies to be implemented. Finally, we examine the feasibility of controlling direct numerical simulations using these techniques.

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  • Industrial and Applied Mathematics Seminar