Orifice (2P)

Constant- or variable-area orifice in a two-phase fluid network

Since R2021a

Libraries:
Simscape / Fluids / Two-Phase Fluid / Valves & Orifices

Description

The Orifice (2P) block models pressure loss due to a constant or variable area orifice in a two-phase fluid network. The orifice can be constant or variable. When Orifice type is set to Variable, the physical signal at port S sets the position of the control member, which opens and closes the orifice.

Fluid properties inside the valve are calculated from inlet conditions. There is no heat exchange between the fluid and the environment, and therefore phase change inside the orifice only occurs due to a pressure drop or a propagated phase change from another part of the model.

A number of block parameters are based on nominal operating conditions, which correspond to the orifice rated performance, such as a specification on a manufacturer datasheet.

Constant Area

When you set Orifice type to Constant, the orifice has a constant area. The mass flow rate through the orifice is:

${\dot{m}}_{A} = {\dot{m}}_{n o m} [\sqrt{\frac{v_{n o m}}{2 Δ p_{n o m}}}] \sqrt{\frac{2}{v_{i n}}} \frac{Δ p}{{(Δ p^{2} + Δ p_{l a m}^{2})}^{0.25}},$

where:

Δp is the pressure drop over the orifice, p_A ̶ p_B.
Δp_lam is the pressure transition threshold between laminar and turbulent flow, which is calculated from the Laminar flow pressure ratio, B_lam:

$Δ p_{l a m} = \frac{(p_{A} + p_{B})}{2} (1 - B_{l a m}) .$
${\dot{m}}_{n o m}$ is the Nominal mass flow rate.
Δp_nom is the Nominal pressure drop rate.
v_nom is the nominal inlet specific volume. This value is determined from the fluid properties tabulated data based on the Nominal inlet condition specification parameter.
v_in is the inlet specific volume.

Variable Area

When you set Orifice type to Variable, the block is configured for a variable opening, which is set by the control member position at S. The block calculates the mass flow rate through the variable-area orifice as:

${\dot{m}}_{A} = λ {\dot{m}}_{n o m} [\sqrt{\frac{v_{n o m}}{2 Δ p_{n o m}}}] \sqrt{\frac{2}{v_{i n}}} \frac{Δ p}{{(Δ p^{2} + Δ p_{l a m}^{2})}^{0.25}},$

where λ is the orifice opening fraction.

Control Member Displacement

The orifice opening, which is expressed as a fraction of the total orifice open area, is determined by the input signal at S, the Control member travel between closed and open orifice parameter, ΔS, and a leakage value that improves numerical stability when the orifice is closed:

$λ = ε (1 - f_{l e a k}) \frac{(S - S_{\min})}{Δ S} + f_{l e a k},$

where:

ε is the Opening orientation. This value is +1 when the setting is Positive control member displacement opens orifice and -1 when the setting is Negative control member displacement opens orifice.
f_leak is the Closed orifice leakage as a fraction of nominal flow.
S_min is the Control member position at closed orifice.

Fluid Specific Volume Dynamics

When the fluid at the orifice inlet is a liquid-vapor mixture, the block calculates the specific volume as:

$v_{i n} = (1 - x_{d y n}) v_{l i q} + x_{d y n} v_{v a p},$

where:

x_dyn is the inlet vapor quality. The block applies a first-order lag to the inlet vapor quality of the mixture.
v_liq is the liquid specific volume of the fluid.
v_vap is the vapor specific volume of the fluid.

If the inlet fluid is liquid or vapor, v_in is the respective liquid or vapor specific volume.

Vapor Quality Lag

If the inlet vapor quality is a liquid-vapor mixture, the block applies a first-order time lag:

$\frac{d x_{d y n}}{d t} = \frac{x_{i n} - x_{d y n}}{τ},$

where:

x_dyn is the dynamic vapor quality.
x_in is the current inlet vapor quality.
τ is the Inlet phase change time constant.

If the inlet fluid is a subcooled liquid or superheated vapor, x_dyn is equal to x_in.

Mass Balance

Mass is conserved in the orifice:

${\dot{m}}_{A} + {\dot{m}}_{B} = 0,$

where:

${\dot{m}}_{A}$ is the mass flow rate at port A.
${\dot{m}}_{B}$ is the mass flow rate at port B.

Energy Balance

Energy is conserved in the orifice:

$Φ_{A} + Φ_{B} = 0,$

where:

Φ_A is the energy flow at port A.
Φ_B is the energy flow at port B.

Assumptions and Limitations

The block does not model pressure recovery downstream of the valve.
There is no heat exchange between the valve and the environment.
The block does not model choked flow.

Ports

Conserving

expand all

A — Fluid port
two-phase fluid

Fluid entry or exit port.

B — Fluid port
two-phase fluid

Fluid entry or exit port.

Input

expand all

S — Control member position
physical signal

Control member position that sets the orifice opening.

Dependencies

To enable this port, set Orifice type to Variable.

Parameters

expand all

Orifice type — Constant or variable orifice
`Variable` (default) | `Constant`

Type of orifice. When set to Variable, the orifice area varies according to the input signal received at port S.

Nominal mass flow rate — Rated mass flow rate
`0.1` kg/s (default) | positive scalar

Typical, rated, or design mass flow rate through a constant orifice.

Dependencies

To enable this parameter, set Orifice type to Constant.

Nominal pressure drop — Rated pressure drop
`0.001` MPa (default) | positive scalar

Typical, rated, or design pressure drop through a constant orifice.

Dependencies

To enable this parameter, set Orifice type to Constant.