Flow Resistance (2P)

It is assumed that the volume of liquid inside the hydraulic resistance is negligible. Then the mass expenses through the ports are equal

where and — mass expenses via ports A and B respectively.

Energy can enter and exit the hydraulic resistance only through the ports of the two-phase fluid. There is no heat exchange between the walls and the environment, and the liquid does not perform any work. The amount of energy entering per unit of time through one port is equal to the amount of energy exiting through the other port per unit of time:

where and — energy flow through ports A and B respectively.

External forces acting on the liquid include forces due to pressure on the ports and forces due to viscous friction on the walls. Gravity, like other volumetric forces, is not taken into account. Expression of friction forces in terms of the loss coefficient gives a semi-empirical expression:

where

The differential pressure equation is implemented in two modifications. The first one takes into account the change in sign when the flow direction changes, then the equation is rewritten as follows:

where the pressure drop is positive only if the mass flow rate is also positive. The second modification is designed to eliminate singularities caused by a change in the flow direction, which may pose a problem for numerical solvers during simulation. In this modification, linearization is performed in a small area with almost zero consumption.:

where — the threshold mass flow rate below which the pressure drop is linearized. The figure shows a modified pressure drop depending on the local mass flow (curve ):

For ease of modeling, the loss factor is it is not required as a block parameter. Instead, it is automatically calculated based on the nominal conditions specified in the block parameters.:

where is the asterisk ( ) indicates the value at the nominal operating mode. All these calculations are based on the assumption that the threshold mass flow rate significantly less than the nominal value . Replacing fractions in the expression for the pressure drop, it gives

or, equivalently:

where — the coefficient of proportionality between the pressure drop on the hydraulic resistance and the local mass flow rate, which is defined as

If we assume that the specific volume — and, consequently, the density — is unchanged, then its nominal and actual values should always be equal. This is true if the nominal value is specified in the block parameter as 0 — a special value used to indicate to the block that the specific volume is constant. Then the ratio of these two values is 1, and the product it boils down to the expression