In order to use Ansys Polyflow’s internal optimizer, you must first define your mesh deformation problem as described in Die Shape Parameterization (if you are optimizing the die shape) and set up the flow problem in Ansys Polydata. Then you must define the following items for the optimization:
objective functions
The objective functions are the aspects of the simulation that you want to minimize or maximize. Examples of such aspects include the flow balance at the die exit, the pressure drop through the die land, the difference between the radius of the free jet at a given position with respect to a prescribed value, the temperature at a point, swelling, and viscous heating.
design variables
The design variables are quantities whose values you allow to vary in order to find the optimum solution. When optimizing the die shape (see Figure 35.1: The Main Sections of a Die for an illustration), the amplitudes of displacement you assigned on the topological entities when defining the mesh deformation can be design variables. Besides the displacement amplitudes, you can also define the design variables to be the flow rates in different inlet sections, material data parameters, and certain boundary condition and sub-model parameters. For a complete list of the quantities that can be designated as design variables, see Design Variables.
constraints
The constraints define the bounds and in/equalities that the objective functions, design variables, and other solution functions must observe.
After the previous items have been defined, the internal optimizer can then find the values of the design variables that minimize all the objectives functions, while respecting the set of constraints. In many ways, the optimizer functions as an evolution scheme (see Evolution), but with a different goal: optimization intends to minimize an objective function, rather than reach the final value of an evolution function.
During the optimization, Ansys Polyflow has to perform two CPU-consuming tasks: the evaluation of the solution (including the cost function), and the evaluation of the sensitivities of the cost function with respect to the design parameters. Ansys Polyflow will perform an optimization loop in which it computes the new values for the design variables (for example, the shape of the geometry), the flow solution, and the objective and constraint functions. When it is required by the optimizer, Ansys Polyflow will also compute the sensitivities of the solution with respect to the design variables.
In order to reduce the CPU time, the optimizer does not search for a global optimum. The assumption is that the number of minima within the range of the design variables is small; when this condition is met, a global optimum is generally found, but it is possible that it is instead a local minimum. In the case of die shape optimization, the number of minima is reduced when the initial geometry is close to the optimized geometry, so you should start with your best estimation.
In this chapter, Theory presents the method implemented for the optimizer under constraints, independently of any mesh deformation and the flow problem. Optimization in Ansys Polyflow describes the links that exist between any defined mesh deformation, the flow problem, and the optimizer. Problem Setup explains how to define an optimization problem in Ansys Polydata, and Files and Output for Optimization describes the output of the optimization. To view examples that demonstrate the setup and results of optimization problems, see Example 95, 98, and 100 in the Ansys Polyflow Examples Manual, which you can find on the Ansys Help site.