Hi akhtarzeb,

Some of the fluid components in the Modelica Standard Library offer different possibilities to switch the mass, energy and momentum balances between static and dynamic. As far as I recall, only the DynamicPipe model implements a dynamic momentum balance.

The three balance equations are tightly coupled and will affec each other. But popularly speaking, you can say that the dynamics of the three balance equations do the following:
- Mass balance: pressure inertia — i.e. increasing inlet pressure will create a lagging outlet pressure
- Energy balance: thermal inertia — i.e. increasing fluid inlet temperature will create a laggin outlet temperature
- Momentum balance: mass flow inertia — creates a reluctance toward changing the mass flow rate. Much like and inductor in electrical systems.

A practical use of the dynamic momentum balance is in the study of water hammer effect. For example in long pipelines, shutting a valve instantaneously will (statically) cause the mass flow to stop immediately. If the dynamics are switched on, the reluctance towards reducing the flow will result in pressure shockwaves due to the energy stored in the moving fluid — which in real applications can destroy the equipment if the valve is closed too fast.

So why isn't the momentum balance dynamic by default? Because the time constant of the momentum balance is orders of magnitude smaller than the time constant of the energy balance. This will result in a stiff equation system which is slow to solve.

Best regards,
Rene Just Nielsen

Dear Rene Just Nielsen,

Thank you very much. That's very helpful. In the current case, the waterhammer effect is out of our interest. And I have another query,

Does the static momentum balance allow the reversing of the flow direction, i.e. acausality in this respect?


Best Regards,
Akhtar

Hi akhtarzeb,

Causality and flow-reversal should not be confused:

Causality refers to a way of modelling. Causal modelling is done in e.g. Simulink and in the Modelica.Blocks package and can be very easy to comprehead for the user because you can track the "signal path" in your models. Also algorithms in Modelica are causal i.e. "first do this, then that"...
In acausal modelling you write down relations in terms of equations and unknowns, not considering the order in which the problem is solved. You only need to end up with the same numbers of equation and uknowns. However, in order to be able to solve the model the translation causalizes the system using e.g. time varying boundaries as inputs to the model.

Flow-reversal: in thermo-fluid systems this is a choice by the component designer. Sometimes restricting component models to only allow flow in the "normal" direction will make the simulation faster. In the Modelica.Fluid components most of the components (including DynamicPipe) allow flow reversal. This can be set with the parameter "AllowFlowReversal". This is independent of your choice of static/dynamic balance equations.

Really appreciated. Thank you very much.

Sincerely,
akhtar