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Hydraulic gate valve
The Gate Valve block models a valve consisting of a round orifice in the valve housing and a flat gate, which moves perpendicular to the orifice axis. The orifice in the gate has the same diameter as the orifice in the housing. As the gate moves, it opens or closes the valve passage (shown as a shaded area in the following illustration).
The flow rate through the valve is proportional to the valve opening and to the pressure differential across the valve. The flow rate is determined according to the following equations:
$$q={C}_{D}\cdot A(h)\sqrt{\frac{2}{\rho}}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$
$$p={p}_{A}-{p}_{B}$$
$${p}_{cr}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{H}}\right)}^{2}$$
$$h={x}_{0}+x$$
$$A(h)=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}h=0\text{or}h2D\text{}\hfill \\ {D}^{2}\cdot \left(\frac{\alpha}{2}-\frac{\mathrm{sin}\left(2\alpha \right)}{4}\right)\text{,}\alpha =a\mathrm{cos}\left|1-\frac{h}{D}\right|\hfill & \text{for}0h=2D\hfill \end{array}$$
$${D}_{H}=\sqrt{\frac{4A(h)}{\pi}}$$
where
q | Flow rate |
p | Pressure differential |
p_{A}, p_{B} | Gauge pressures at the block terminals |
C_{D} | Flow discharge coefficient |
A(h) | Instantaneous orifice passage area |
x_{0} | Initial opening |
x | Gate displacement from initial position |
h | Valve opening |
D | Orifice diameter |
ρ | Fluid density |
ν | Fluid kinematic viscosity |
p_{cr} | Minimum pressure for turbulent flow |
Re_{cr} | Critical Reynolds number |
D_{H} | Valve instantaneous hydraulic diameter |
A_{leak} | Closed valve leakage area |
Connections A and B are hydraulic conserving ports. Connection S is a physical signal port that controls the gate displacement. The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B, and the pressure differential is determined as $$p={p}_{A}-{p}_{B}$$. Positive signal at the physical signal port S opens the valve.
The diameter of the valve orifice. The orifices in the valve housing and in the gate have the same diameter. The default value is 0.01 m.
The initial opening of the valve. The parameter can take both positive and negative values. The default value is 0.
Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 0.65.
The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is 10.
The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. An isolated or "hanging" part of the system could affect computational efficiency and even cause simulation to fail. Therefore, MathWorks recommends that you do not set this parameter to 0. The default value is 1e-12 m^2.
Parameters determined by the type of working fluid:
Fluid density
Fluid kinematic viscosity
Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.