When I remove the MoodyFriction function from the equation and replace it with a constant, I'm still getting a warning when I declare "v" as a state variable.

[WARNING]: No unique solution for solving linear equation: -0.02 * pipelineSection1.medium.rho * pipelineSection1.v * pipelineSection1.L * $tmpBuf[4] + $tmpBuf[2] * der(pipelineSection2.flowPortb.mflow) = --0.02 * pipelineSection1.medium.rho * pipelineSection1.v * pipelineSection1.L * $tmpBuf[6]

I know these are custom models, but I'm hoping the message is generic enough to illustrate the problem.

I also simplified the model by removing the non-linearity.

dP = medium.rho * L * v * 0.01
(*instead of*)
dP = medium.rho * L * v^2 * 0.01

When I do that the errors go away, but it's not what I'm looking for which is...

dP = medium.rho * L * v^2 * MoodyFriction(Re, epsilon/D)
(*where*)
Re = v * D / medium.nue

Patrik,

I tried a few things, but am still struggling. I appreciate the help I've gotten so far.

I've stripped the model down to something extremely simple (not accurate equations). I'm still getting the "No unique solution for solving linear equation..." error. Setting start and fixed on dp and V_flow (via a modification) hasn't worked and results in an Overdetermined initial equation warning.

model PipelineSection
  extends Modelica.Thermal.FluidHeatFlow.Interfaces.Partials.TwoPort(V_flow(stateSelect=StateSelect.prefer));
equation
  dp = V_flow^2 * 0.01
  Q_flow = 0.0;

And I connect it with some standard components (see attached file).

And since you asked for the initialization debug output:

[INIT]: Initialized states to :
[INIT]:  pipelineSection.T = 288.15
[INIT]:  der(pipelineSection.T) = -0
[INIT]:  pipelineSection1.T = 288.15
[INIT]:  der(pipelineSection1.T) = -0
[INIT]:  pipelineSection2.T = 288.15
[INIT]:  der(pipelineSection2.T) = 0
[INIT]:  volumeFlow.T = 293.15
[INIT]:  der(volumeFlow.T) = -0
[INIT]:  $dummy = 0
[INIT]:  der($dummy) = 0
[GENERAL]: Checking events at initialization at time = 0.
[GENERAL]: Starting numerical solver at time 0
[INIT]: Initialization took 0.000432s.

Attachments:

Hi Eric!

The only variables that can be used for sensitivity analysis are those that the solver uses as states. You can influence how the solver selects states with the stateSelect attribute.

For example, in the following model:

model TestStates
  Real x(start = 1);
  parameter Real k=1;
  output Real y(stateSelect=StateSelect.always);
equation
  x*k=y;
  der(x)=1;
end TestStates;

y is forced to be used as a a state.

So the following code will bring up y's sensitivity to k:`

WSMPlot[WSMSimulateSensitivity[
  "TestStates", {0, 10}, {"k"}], {{"y", "k", 0.1}}]

The stateSelect attribute can take on the following values: StateSelect.never, StateSelect.avoid, StateSelect.default, StateSelect.prefer, StateSelect.always.

The difference between prefer and always is that in both cases the solver will prefer choosing the variable as a state, but if StateSelect.always is set, it will throw an error if it is unable to use the variable as a state. The same, but inverse is true for avoid and never.