Defining the Mass Flow Difference Indicator Report

The objective of this adjoint analysis is to optimize the shape of the Y-Junction manifold in order to achieve a uniform mass flow split between the two outlets.

To examine the mass flow imbalance between the two outlets, you define an expression report for the normalized squared difference of these mass flow rates defined as:

m ˙ d i f f = ( m ˙ 1 , o u t m ˙ 2 , o u t m ˙ 1 , o u t + m ˙ 2 , o u t ) 2

where m ˙ 1 , o u t and m ˙ 2 , o u t are the mass flow rates through Outlet 1 and Outlet 2, respectively. The use of the squared difference results in a convex cost function which is suitable for the gradient based minimization algorithm.

To define the mass flow difference indicator report:

  1. Create the mass flow reports and plot:
    1. Right-click the Reports node and select New > Flow/Energy > Mass Flow.
    2. Edit the Reports > Mass Flow 1 node and set the following properties:
      Property Setting
      Parts [Region: Manifold.Downstream Outlet 1]
      Representation Latest Surface/Volume
    3. Repeat Step 1 to create a second mass flow report Mass Flow 2.
    4. Edit the Reports > Mass Flow 2 node and set the following properties:
      Property Setting
      Parts [Region: Manifold.Downstream Outlet 2]
      Representation Latest Surface/Volume
    5. Multi-select the Mass Flow 1 and Mass Flow 2 reports, right-click and select Create Monitor and Plot from Report.
    6. In the Create Plots From Report... dialog box, click Single Plot.
    7. Rename the Plots > Reports Plot node to Mass Flows.
  2. Define an expression report to assess the deviation between Manifold.Downstream Outlet 1 and Manifold.Downstream Outlet 2:
    1. Right-click the Reports node and select New > User > Expression.
    2. Rename the report to Mass Flow Difference Indicator.
    3. Select the Reports > Mass Flow Difference Indicator node and set Definition to pow((${Mass Flow 1}-${Mass Flow 2})/(${Mass Flow 1}+${Mass Flow 2}),2).
  3. Save the simulation.