Abstract
Abstract In this paper, we deal with topology optimization attributed to the non stationary Navier-Stokes equations. We propose an approach where we analyze the sensitivity of a shape function relating to a perturbation of the flow domain. A numerical optimization algorithm based on topological gradient method is built and applied to the 2D Tesla micro valve reconstruction. Some numerical results confirm the efficiency of the proposed approach.
Highlights
Tesla valves are no-moving-part valves that utilize uidic inertial forces to inhibit ow in the reverse direction
We propose an approach where we analyze the sensitivity of a shape function relating to a perturbation of the ow domain
A numerical optimization algorithm based on topological gradient method is built and applied to the 2D Tesla micro valve reconstruction
Summary
Tesla valves are no-moving-part valves that utilize uidic inertial forces to inhibit ow in the reverse direction. The topological sensitivity method idea is to study the variation of a given shape function j relating to a perturbation in the uid ow domain geometry. Ε where Wd ∈ L ( , T; H (Ω)) is a datum representing a desired uid ow state This example concerns the L -norm shape function that has been used in geometric control problems like the optimization of location of some obstacle in a tank to approximate an object ow Wd (see [16]). The problem is to optimize numerically the design of the 2D Tesla micro-valve at Re=100 To solve this problem we consider the objective function as the forward energy dissipation and the diodicity as a constraint. It is nearly identical to literature [1, 15] (see Figure 5)
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