In the fluid aspect, capacitance has units (kg*mol/kPa). It is the amount of moles of fluid added to the node to raise its pressure by 1 kPa. For a fixed volume V:

C = n · β = V/MW · δρ/δp

See here for derivation.

MW and δρ/δp come from fluid properties.

GunnsFluidCapacitor and GunnsFluidTank assume constant volume so they stop there.

But constant liquid volumes tend to have very low capacitance because liquids have low compressibility. Most of the real capacitance in a liquid system comes from flexible volume containers, like accumulators.

The links that model flexible volume (GunnsFluidAccum, GunnsFluidAccumGas) add another term to their capacitance calculation:

C += ρ/MW · δV/δp,

Where δV/δp relates the container’s change in volume to pressure. For instance, as liquid is forced into the container, pressure rises. This causes the flexible balloon or bellows containing the liquid to expand to accommodate the incoming volume.

The implementation of volume, mass & capacitance is divided up among the capacitive link, the node, and the node’s fluid contents. Note this is attributes and behavior:

• Node: actual volume, content fluid, inflow fluid, thermal capacitance, compression effect, heat flows, thermal damping effect, isentropic expansion effect, computation & tracking of state error
• link: capacitance effect, initial volume, volume control & user edit, expansion scale factor, node fluid content user edits
• content fluid: fluid state, mass

In retrospect, this wasn’t the best design but it was convenient at the time. We have plans to redesign this so that all of the capacitance behavior belongs to the link and none in the node. This will simplify the nodes, make a cleaner representation of KCL in the nodes, and allow fancier modeling like nested balloons and having multiple capacitors sharing a node.

• We can’t use a fluid capacitor to connect between two normal nodes.
  • This would be equivalent to a flexible membrane between two fluids, like a balloon.
• Won’t explain here. The take-away is that the fluid capacitance effect must always connect between a normal node and the Ground node.

• Fluid’s δρ/δp is not constant, but varies with temperature, and for non-ideal fluids, also mixture and pressure. Therefore unlike thermal and electric capacitors, fluid capacitors do not have constant capacitance, even if volume is constant.

• The solution assumes that the capacitance represented in the system of equations is constant, but as soon as we flow in fluid of different mixture or temperature, on the next pass the capacitance is different. This leads to a disagreement between the new number of moles now in the node and what the number ought to be from the fluid’s PVT state equation. This is call “state error” and is actively corrected every pass by GUNNS so it doesn’t become obvious. More on that later.

• For different ideal gasses, the molar capacitance is always the same at the same temperature. And since all the gas in the node is at the same temperature, capacitance doesn’t vary with mixtures of ideal gasses. Therefore changing mixtures of ideal gas in the node doesn’t incur state error. The is the reason we use moles instead of mass as the system units.

• Because the capacitor link shares some capacitance implementation with the node, you must never put more than one capacitive link on any node, else they will fight over the node’s contents.

Previous Page / Next Page