Restriction in flow area in isothermal liquid network
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The Local Restriction (IL) block models the pressure drop due to a localized reduction in flow area, such as a valve or an orifice, in an isothermal liquid network.
Ports A and B represent the restriction inlet and outlet. The input physical signal at port AR specifies the restriction area. Alternatively, you can specify a fixed restriction area as a block parameter.
The block icon changes depending on the value of the Restriction type parameter.
Restriction Type  Block Icon 





The restriction is adiabatic. It does not exchange heat with the environment.
The restriction consists of a contraction followed by a sudden expansion in flow area. The
fluid accelerates during the contraction, causing the pressure to drop. In the expansion zone,
if the Pressure recovery parameter is set to
off
, the momentum of the accelerated fluid is lost. If the
Pressure recovery parameter is set to on
,
the sudden expansion recovers some of the momentum and allows the pressure to rise slightly
after the restriction.
Local Restriction Schematic
The block equations express the mass flow rate in terms of the pressure difference between ports A and B:
$$\begin{array}{l}{\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}}=0\\ {\dot{m}}_{\text{A}}={C}_{d}{S}_{R}\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{cr}^{2}\right)}^{1/4}}\sqrt{\frac{2\overline{\rho}}{P{R}_{loss}\left(1{\left(\frac{{S}_{R}}{S}\right)}^{2}\right)}}\\ \Delta p={p}_{\text{A}}{p}_{\text{B}}\\ \Delta {p}_{cr}=\frac{\pi}{4}\cdot \frac{\overline{\rho}}{2{S}_{R}}{\left(\frac{{\mathrm{Re}}_{cr}{\nu}_{atm}}{{C}_{d}}\right)}^{2}\end{array}$$
$$\overline{\rho}=\frac{{\rho}_{A}+{\rho}_{B}}{2}$$
where:
Δp is the pressure differential.
p_{A} and p_{B} are pressures at ports A and B, respectively.
S_{R} is the crosssectional area at the restriction.
S is the crosssectional area at ports A and B.
Δp_{cr} is the critical pressure differential for the transition between the laminar and turbulent flow regimes.
Re_{cr} is the critical Reynolds number.
ν_{atm} is the liquid kinematic viscosity at atmospheric pressure, which is a global parameter defined by the Isothermal Liquid Properties (IL) block connected to the circuit.
C_{d} is the discharge coefficient.
$$\overline{\rho}$$ is the average fluid mixture density.
ρ_{A} and ρ_{B} are fluid mixture density values at ports A and B, respectively. Equations used to compute the fluid mixture density depend on the selected isothermal liquid model. For detailed information, see Isothermal Liquid Modeling Options.
PR_{loss} is the pressure loss ratio.
The pressure loss ratio, PR_{loss}, depends on the Pressure recovery parameter value:
If pressure recovery is off, then
$$P{R}_{\text{loss}}=1.$$
If pressure recovery is on, then
$$P{R}_{\text{loss}}=\frac{\sqrt{1{\left(\frac{{S}_{R}}{S}\right)}^{2}\left(1{C}_{\text{d}}^{2}\right)}{C}_{d}\frac{{S}_{R}}{S}}{\sqrt{1{\left(\frac{{S}_{R}}{S}\right)}^{2}\left(1{C}_{\text{d}}^{2}\right)}+{C}_{d}\frac{{S}_{R}}{S}}.$$
The crosssectional area at the restriction, S_{R}, depends on the Restriction type parameter value:
For variable restrictions,
$${S}_{\text{R}}=\{\begin{array}{ll}{S}_{\mathrm{min}},\hfill & AR\le {S}_{\mathrm{min}}\hfill \\ {S}_{\mathrm{max}},\hfill & AR\ge {S}_{\mathrm{max}}\hfill \\ AR,\hfill & {S}_{\mathrm{min}}<AR<{S}_{\mathrm{max}}\hfill \end{array},$$
where AR is the value of the input physical signal, and S_{min} and S_{max} are the values of the Minimum restriction area and Maximum restriction area block parameters, respectively.
For fixed restrictions, S_{R} is the value of the Restriction area parameter.
By default, the block assumes that the crosssectional area at the restriction ports is
much greater than the restriction area, setting the Crosssectional area at ports A
and B parameter value to inf
and all the
S_{R}/S terms in the equations to
0, to improve computation efficiency. Specify an actual value for the
Crosssectional area at ports A and B parameter if the two
crosssectional areas are comparable in size and their ratio has an impact on flow
computations.