Fixed flow resistance
The Local Restriction (2P) block models the pressure drop due to a fixed flow resistance such as an orifice. Ports A and B represent the restriction inlet and outlet. The restriction area, specified in the block dialog box, remains constant during simulation.
The restriction consists of a contraction followed by a sudden expansion in flow area. The contraction causes the fluid to accelerate and its pressure to drop. The expansion recovers the lost pressure though only in part, as the flow separates from the wall, losing momentum in the process.
Local Restriction Schematic
The mass balance equation is
and are the mass flow rates into the restriction through port A and port B.
The energy balance equation is
ϕA and ϕB are the energy flow rates into the restriction through port A and port B.
The local restriction is assumed to be adiabatic and the change in specific total enthalpy is therefore zero. At port A,
uA, uB, and uR are the specific internal energies at port A, at port B, and the restriction aperture.
pA, pB, and pR are the pressures at port A, port B, and the restriction aperture.
νA, νB, and νR are the specific volumes at port A, port B, and the restriction aperture.
wA, wB, and wR are the ideal flow velocities at port A, port B, and the restriction aperture.
The ideal flow velocity is computed as
is the ideal mass flow rate through the restriction.
S is the flow area at port A and port B.
SR is the flow area of the restriction aperture.
The ideal mass flow rate through the restriction is computed as:
CD is the flow discharge coefficient for the local restriction.
Local Restriction Variables
The pressure difference between the ports is derived from the momentum balances in the contraction zone (the region between the inlet and the restriction aperture) and expansion zone (the region between the restriction aperture and the outlet). In the turbulent flow regime, with the flow directed from port A to port B:
The equations indicate that the pressure difference between the ports varies with the square of the flow rate through the restriction. This relationship is characteristic of turbulent flows only. In the laminar regime, where the relationship becomes linear, the pressure difference is approximated as:
pavg as the average of the pressures at port A and port B:
Blam as the Laminar flow pressure ratio parameter.
The laminar pressure difference equation is the same for both flow directions—from port A to port B or from port B to port A.
The pressure at the restriction aperture is computed from the momentum balance in the flow contraction zone. In the turbulent flow regime, with the flow directed from port A to port B:
A cubic polynomial function is used to blend the pressure difference between the ports as well as the pressure at the restriction aperture between the laminar and turbulent flow regimes:
When then and
When then is smoothly blended between ΔpAB and Δplam and pR is smoothly blended between pR,AB and pR,lam.
When then is smoothly blended between ΔpBA and Δplam and pR is smoothly blended between pR,BA and pR,lam.
When then and
Use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector) to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.
The restriction is adiabatic. It does not exchange heat with its surroundings.
Area normal to the flow path at the restriction aperture—the
narrow orifice located between the ports. The default value,
is the same as the port areas.
Area normal to the flow path at the restriction ports. The ports
are assumed to be identical in cross-section. The default value,
is the same as the restriction aperture area.
Ratio of the actual to the theoretical mass flow rate through
the restriction. The discharge coefficient is an empirical parameter
used to account for non-ideal effects such as those due to restriction
geometry. The default value is
Ratio of the outlet to the inlet port pressure at which the
flow regime is assumed to switch from laminar to turbulent. The prevailing
flow regime determines the equations used in simulation. The pressure
drop across the restriction is linear with respect to the mass flow
rate if the flow is laminar and quadratic (with respect to the mass
flow rate) if the flow is turbulent. The default value is
A pair of two-phase fluid conserving ports labeled A and B represent the restriction inlet and outlet.