Why does a Simscape Pressure Source (MA) with zero pressure input introduce a temperature change proportional to mass flow rate?

I have a simscape model of a vehicle cooling system with a pressure source to represent the differential pressure between air inlet and outlet when the vehicle is moving, a fan and a radiator from which I am rejecting the engine heat.

In the simplist condition I set the pressure source input to zero and my fan drives the flow through the radiator.

When I run it in this configuration there is a temperature rise between the input and output flows of the Pressure Source (MA) block that appears to be in proportion to the mass flow rate through the pressure source block. I can't understand why it is introducing this temperature change across my pressure source.

This is a plot of the Pressure Source (MA) plots from the simscape logger:

Simscape model with the Pressure Source block highlighted:

Simplified model attached:

This model exhibits the same temperature rise across the pressure source block.

Upon further investigation I have found that the heating appears to be due to the port areas. I had set my fan area and radiator area in my original model to the value that I wanted (0.2m^2), but not updated the port areas to the reservoirs and pressure source from the default values of 0.01m^2. Can anyone explain why the port areas result in heating of the moist air?

[Yifeng Tang]

If you could share the model, or a simplified model that exhibits the same behavior, it'll help the community better understand and diagnose the issues.

[Guy]

@Yifeng Tang I have updated the question with a simplified model that replicates the same behaviour, it appears to be due to differences in the port areas, although I still don't understany why this would lead to such a significant increase in temperature.

Answer 1

[Yifeng Tang]

@Guy, thanks for the update.

Your observation on the port area makes sense. Let me point you to the mathematical explanation behind this.

For fluids domains with internal energy contents (G, MA, TL & 2P), two through variables are tracked at each port: mass flow (mdot) and energy flow (Phi). The Phi term is the sum of the internal energy/enthalpy carried by the mass flow (mdot*h), the kinetic term (mdot*v^2/2), and a conduction-like term as described here for numerical smoothing. The temperature change due to area you saw is the result of the v^2/2 term, where the velocity for any given mass flow is dependent on the port area.

As no power is added by the pressure source, the mass and energy flow at the A & B ports are conserved. The sudden change of area at the Fan, which is connected to the B port of the pressure source, now will "slow" down the local velocity, reducing the v^2/2 term. Now the h+v^2/s term has to be conserved, so the value of h will go up, and you'll see the temperature went up as the result.

You may have already observed this in your model: (1) if you make all the port area consistent, the temperature jump disappears and (2) higher flow rate will cause more temperature change, as the difference in the v^2/2 term grows with mdot.

Lesson learned here: make the port area consistent and physically meaningful. This is particularly important for G and MA domains, and the 2P domain in vapor phase. The velocity term tends to be more significant because the density is lower. It's less likely to be an issue for the TL domain in my experience, but it's still a good practice to keep port area consistent.

Hope this makes sense. You can view the Simscape code related to this by opening the "port_convection" subroutine:

where you can find the calculation of the "total" enthalpy including the velocity term: