Restriction in flow area in thermal liquid network
Simscape / Foundation Library / Thermal Liquid / Elements
The Local Restriction (TL) block models the pressure drop due to a localized reduction in flow area, such as a valve or an orifice, in a thermal 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 mass balance in the restriction is
$$0={\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}},$$
where:
$${\dot{m}}_{\text{A}}$$ is the mass flow rate into the restriction through port A.
$${\dot{m}}_{\text{B}}$$ is the mass flow rate into the restriction through port B.
The pressure difference between ports A and B follows from the momentum balance in the restriction:
$$\begin{array}{l}\Delta p=\frac{1}{2\rho}\left(1\frac{{S}_{\text{R}}^{2}}{{S}^{2}}\right){v}_{R}\sqrt{{v}_{R}^{2}+{v}_{Rc}^{2}}\\ {v}_{R}=\frac{{\dot{m}}_{A}}{{C}_{d}\rho {S}_{R}}\\ {v}_{Rc}=\frac{{\mathrm{Re}}_{c}\mu}{{C}_{d}\rho}\sqrt{\frac{\pi}{4{S}_{R}}}\end{array}$$
where:
Δp is the pressure differential.
ρ is the liquid density.
μ is the liquid dynamic viscosity.
S is the crosssectional area at ports A and B.
S_{R} is the crosssectional area at the restriction.
v_{R} is fluid velocity at the restriction.
v_{Rc} is the critical fluid velocity.
Re_{c} is the critical Reynolds number.
C_{d} is the discharge coefficient.
If pressure recovery is off, then
$${p}_{\text{A}}{p}_{\text{B}}=\Delta p,$$
where:
p_{A} is the pressure at port A.
p_{B} is the pressure at port B.
If pressure recovery is on, then
$${p}_{\text{A}}{p}_{\text{B}}=\Delta p\frac{\sqrt{1{\left(\frac{{S}_{R}}{S}\right)}^{2}\left(1{C}_{\text{d}}^{2}\right)}{C}_{d}\frac{{S}_{R}}{S}}{\sqrt{1{\left(\frac{{S}_{R}}{S}\right)}^{2}\left(1{C}_{\text{d}}^{2}\right)}+{C}_{d}\frac{{S}_{R}}{S}}.$$
The energy balance in the restriction is
$${\varphi}_{\text{A}}+{\varphi}_{\text{B}}=0,$$
where:
ϕ_{A} is the energy flow rate into the restriction through port A.
ϕ_{B} is the energy flow rate into the restriction through port B.
The restriction is adiabatic. It does not exchange heat with its surroundings.
The dynamic compressibility and thermal capacity of the liquid in the restriction are negligible.