Shape Optimization of a Submerged Pump for Oil
Résumé
Submerged pumps are helico-axial turbo-machines, composed of a succession of identical stages arranged in series. The aim of a pump is to increase the pressure of the fluid between its inlet and outlet, at a given flow rate. The objective of the shape optimization of such a submerged pump is to minimize the pressure loss per length unit in one stage. The surfaces to re-design are the hub and the blades.
Parametric, 2D B-splines of the third degree are used for the parameterization of the whole 3D geometry. The coordinates of their control points are the control points of the optimization problem. Technical and geometric constraints are expressed as linear and non-linear equality and inequality constraints on the control points' coordinates. The CFD software Fluent is used to solve the Navier-Stokes turbulent equations.
We use an incomplete gradient method to solve the optimization problem. This method is supposed to provide a descent direction for the minimization process. The quality of the incomplete gradient can be measured by checking whether it gives a descent direction or not, and also by comparing it to the result of a finite differences method.
We first give the results of the optimization problem for a single hub, obtained with a classic descent method, with linear equality constraints. Then we present some tests for the validation of these results and, more generally, for the validation of the incomplete gradient method for our problem.
Parametric, 2D B-splines of the third degree are used for the parameterization of the whole 3D geometry. The coordinates of their control points are the control points of the optimization problem. Technical and geometric constraints are expressed as linear and non-linear equality and inequality constraints on the control points' coordinates. The CFD software Fluent is used to solve the Navier-Stokes turbulent equations.
We use an incomplete gradient method to solve the optimization problem. This method is supposed to provide a descent direction for the minimization process. The quality of the incomplete gradient can be measured by checking whether it gives a descent direction or not, and also by comparing it to the result of a finite differences method.
We first give the results of the optimization problem for a single hub, obtained with a classic descent method, with linear equality constraints. Then we present some tests for the validation of these results and, more generally, for the validation of the incomplete gradient method for our problem.
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