Flow control valve actuated by transverse motion of circular gate

Thermal Liquid/Valves/Flow Control Valves

The Gate Valve (TL) block represents a flow control valve with a circular opening and a circular gate. The gate moves in a direction orthogonal to the fluid flow. The opening and gate are equal in diameter. The figure shows a schematic of the gate valve in three different positions—closed, partially open, and fully open.

**Gate Valve in Different Positions**

A smoothing function allows the valve opening area to change smoothly between the fully closed and fully open positions. The smoothing function does this by removing the abrupt opening area changes at the zero and maximum ball positions. The figure shows the effect of smoothing on the valve opening area curve.

**Opening-Area Curve Smoothing**

The block computes the valve opening area directly from valve geometry parameters using the expression

$$A=\frac{\pi {d}_{0}^{2}}{4}-{A}_{Covered},$$

*A*is the valve opening area.*d*_{0}is the valve orifice diameter.*A*_{Covered}is the portion of the valve orifice area covered by the gate:$${A}_{Covered}=\frac{{d}_{0}^{2}}{2}\text{acos}\left(\frac{\Delta l}{{d}_{0}}\right)-\frac{\Delta l}{2}\sqrt{{d}_{0}^{2}-{\left(\Delta l\right)}^{2}}$$

*Δl*is the net displacement of the gate center relative to the orifice center.$$\Delta l=\{\begin{array}{ll}0,\hfill & \left({x}_{0}+{S}_{d}\right)\le 0\hfill \\ {d}_{0},\hfill & \left({x}_{0}+{S}_{d}\right)\ge {d}_{0}\hfill \\ \left({x}_{0}+S\right),\hfill & \text{Else}\hfill \end{array},$$

*x*_{0}is the**Gate displacement offset**specified in the block dialog box.*S*_{d}is the gate displacement specified through physical signal input port S.

The valve opening expressions introduce undesirable discontinuities at the fully open and fully closed positions. The block eliminates these discontinuities using polynomial expressions that smooth the transitions to and from the fully open and fully closed positions. The valve smoothing expressions are

$${\lambda}_{L}=3{\overline{\Delta l}}_{L}^{2}-2{\overline{\Delta l}}_{L}^{3}$$

$${\lambda}_{R}=3{\overline{\Delta l}}_{R}^{2}-2{\overline{\Delta l}}_{R}^{3}$$

$${\overline{\Delta l}}_{L}=\frac{\Delta l}{\Delta {l}_{smooth}}$$

$${\overline{\Delta l}}_{R}=\frac{\Delta l-\left({d}_{0}-\Delta {l}_{smooth}\right)}{{d}_{0}-\left({d}_{0}-\Delta {l}_{smooth}\right)}.$$

*λ*_{L}is the smoothing expression for the fully closed portion of the valve opening curve.*λ*_{R}is the smoothing expression applied to the fully open portion of the valve opening curve.*Δl*_{smooth}is the gate displacement smoothing region:where$$\Delta {l}_{smooth}={f}_{smooth}\frac{{d}_{0}}{2},$$

*f*_{smooth}is a smoothing factor between 0 and 1.

The smoothed valve opening area is given by the piecewise conditional expression

$${S}_{R}=\{\begin{array}{ll}{S}_{Leak},\hfill & \Delta l\le 0\hfill \\ {S}_{Leak}\left(1-{\lambda}_{L}\right)+\left(A+{S}_{Leak}\right){\lambda}_{L},\hfill & \Delta l<\Delta {l}_{smooth}\hfill \\ A+{S}_{Leak},\hfill & \Delta l\le {d}_{0}-\Delta {l}_{smooth}\hfill \\ \left(A+{S}_{Leak}\right)\left(1-{\lambda}_{R}\right)+\left({S}_{Leak}+{S}_{Max}\right){\lambda}_{R},\hfill & \Delta l<{d}_{0}\hfill \\ {S}_{Leak}+{S}_{Max},\hfill & \Delta l\ge {d}_{0}\hfill \end{array},\text{\hspace{0.17em}}$$

*S*_{R}is the smoothed valve opening area.*S*_{Leak}is the valve leakage area.*S*_{Max}is the maximum valve opening area:$${S}_{Max}=\frac{\pi {d}_{0}^{2}}{4}.$$

The mass conservation equation in the valve is

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

$${\dot{m}}_{A}$$ is the mass flow rate into the valve through port A.

$${\dot{m}}_{B}$$ is the mass flow rate into the valve through port B.

The energy conservation equation in the valve is

$${\varphi}_{A}+{\varphi}_{B}=0,$$

*ϕ*_{A}is the energy flow rate into the valve through port A.*ϕ*_{B}is the energy flow rate into the valve through port B.

The momentum conservation equation in the valve is

$${p}_{A}-{p}_{B}=\frac{\dot{m}\sqrt{{\dot{m}}^{2}+{\dot{m}}_{cr}^{2}}}{2{\rho}_{Avg}{C}_{d}^{2}{S}^{2}}\left[1-{\left(\frac{{S}_{R}}{S}\right)}^{2}\right]P{R}_{Loss},$$

*p*_{A}and*p*_{B}are the pressures at port A and port B.$$\dot{m}$$ is the mass flow rate.

$${\dot{m}}_{cr}$$ is the critical mass flow rate:

$${\dot{m}}_{cr}={\mathrm{Re}}_{cr}{\mu}_{Avg}\sqrt{\frac{\pi}{4}{S}_{R}}.$$

*ρ*_{Avg}is the average liquid density.*C*_{d}is the discharge coefficient.*S*is the valve inlet area.*PR*_{Loss}is the pressure ratio:$$P{R}_{Loss}=\frac{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\left({S}_{R}/S\right)}{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\left({S}_{R}/S\right)}.$$

**Orifice diameter**Diameter of the valve flow area in the fully open position. The default value is

`7e-3`

m.**Gate displacement offset**Gate offset from the zero position. The instantaneous gate displacement is the sum of the gate offset and input signal S. The default value is

`0`

m.

**Leakage area**Aggregate area of all fluid leaks in the valve. The leakage area helps to prevent numerical issues due to isolated fluid network sections. For numerical robustness, set this parameter to a nonzero value. The default value is

`1e-12`

.

**Smoothing factor**Portion of the opening-area curve to smooth expressed as a fraction. Smoothing eliminates discontinuities at the minimum and maximum flow valve positions. The smoothing factor must be between

`0`

and`1`

. Enter a value of`0`

for zero smoothing. Enter a value of`1`

for full-curve smoothing. The default value is`0.01`

.**Cross-sectional area at ports A and B**Flow area at the valve inlets. The inlets are assumed equal in size. The default value is

`0.01`

m^2.

**Characteristic longitudinal length**Approximate length of the valve. This parameter provides a measure of the longitudinal scale of the valve. The default value is

`0.1`

m^2.**Discharge coefficient**Semi-empirical parameter commonly used as a measure of valve performance. The discharge coefficient is defined as the ratio of the actual mass flow rate through the valve to its theoretical value.

The block uses this parameter to account for the effects of valve geometry on mass flow rates. Textbooks and valve data sheets are common sources of discharge coefficient values. By definition, all values must be greater than 0 and smaller than 1. The default value is

`0.7`

.**Critical Reynolds number**Reynolds number corresponding to the transition between laminar and turbulent flow regimes. The flow through the valve is assumed laminar below this value and turbulent above it. The appropriate values to use depend on the specific valve geometry. The default value is

`12`

.

**Mass flow rate into port A**Mass flow rate into the component through port

**A**at the start of simulation. The default value is`1 kg/s`

.

A — Thermal liquid conserving port representing valve inlet A

B — Thermal liquid conserving port representing valve inlet B

S — Physical signal input port for the control member displacement

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