Defining the Optimization Objective and the Constraint

The objective of the topology optimization is to minimize the pressure drop between the inlet boundary (high pressure) and the outlet boundary (low pressure).

One constraint accompanies this objective: the fraction of solid material in the topology optimization domain must not be less than 65%.

You define the pressure drop objective by using adjoint cost functions. The cost function is solved by the adjoint solver.

The ratio of fluid volume to solid volume is a built-in constraint that you are advised to always apply alongside any user-defined constraints. The volume ratio constraint determines the tightness of the topology.

The penalty parameter of the topology optimization solver governs how strongly the optimizer attempts to satisfy the constraints. A default value of 1000 for this parameter is sufficient for this simulation.

To define the optimization objective and the constraint:
  1. Create a report to calculate the pressure drop between inlet and outlet:
    1. Right-click the Reports node and select New > Flow / Energy > Pressure Drop.
    2. Rename the Pressure Drop 1 node to Pressure Drop.
    3. Select the Pressure Drop node and set the following properties:
      PropertySetting
      High PressureRegions > Inlet > Inlet
      Low PressureRegions > Outlet > Outlet
  2. Create a report to track the solid volume ratio:
    1. Right-click the Reports node and select New > Metrics > Volume Average.
    2. Rename the Volume Average 1 node to Fluid Volume Ratio.
    3. Select the Fluid Volume Ratio node and set the following properties:
      PropertySetting
      Field FunctionMaterial Indicator
      PartsRegions > Topology Optimization Domain
    4. Right-click the Reports node again and select New > User > Expression.
    5. Rename the Expression 1 node to Solid Volume Ratio.
    6. Select the Solid Volume Ratio node and set Definition to 1-${Fluid Volume Ratio}.
  3. To create a report for the current optimization loop counter, right-click the Reports node and select New > System > Optimization Iteration.
  4. To use these reports later in plots and stopping criteria, multi-select the Pressure Drop, Solid Volume Ratio, and the Optimization Iteration node, right-click on one of the selected nodes and select Create Monitor from Report.
  5. Create a pressure drop cost function:
    1. Right-click the Solvers > Adjoint > Adjoint Cost Functions node and select New.
    2. Rename the report node as Pressure Drop Cost Function.
    3. Select the Pressure Drop Cost Function node and set Report to Pressure Drop.
  6. Create the pressure drop objective together with the volume ratio constraint:
    1. Edit the Solvers > Topology Optimization node and set the following properties:
      NodePropertySetting
      Topology OptimizationObjectivePressure Drop Cost Function
      Optimization SettingsPenalty1000
    2. Right-click the Constraints node and select New > Volume Ratio Constraint.
    3. Select the Volume Ratio Constraint node and set the following properties:
      PropertySetting
      Minimum0.65
      PhaseSolid Phase
  7. Save the simulation.