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Valve with a sliding ball control mechanism

**Library:**Hydraulics (Isothermal) / Valves / Flow Control Valves

The Ball Valve block models an orifice with a
variable opening area controlled by a sliding ball mechanism. The
opening area changes with the relative position of the ball—the *valve
lift*. A displacement toward the orifice decreases flow
while a displacement away increases flow. The interface between the
orifice and the ball—the *valve seat*—can
be `Sharp-edged`

, shown left in the figure,
or `Conical`

, shown right.

**Ball Valve Seat Types**

The valve lift is a function of the displacement signal specified
through port **S**. The two can, but generally do
not, have the same value. The valve lift differs from the displacement
whenever the **Ball displacement offset** parameter
is nonzero:

$$h(x)={x}_{0}+\text{}s,$$

where:

is the valve lift.*h**x*_{0}is the ball displacement offset.is the ball displacement (relative to the specified offset).*s*

The valve is fully closed when the valve lift is equal
to zero or less. It is fully open when the valve lift reaches or exceeds
a (geometry-dependent) value sufficient to completely clear the orifice.
A fully closed valve has an opening area equal to the specified **Leakage
area** parameter while a fully open valve has the maximum
possible opening area. Adjusting for internal leakage:

$${A}_{Max}=\pi {r}_{O}^{2}+{A}_{Leak},$$

where:

*A*_{Max}is the maximum opening area.*r*_{O}is the orifice radius.*A*_{Leak}is the internal leakage area between the ports.

At intermediate values of the valve lift, the opening
area depends on the valve seat geometry. If the **Valve seat
specification** parameter is set to `Sharp-Edged`

,
the opening area as a function of valve lift is:

$$A(h)=\pi {r}_{O}\left(1-{\left[\frac{{r}_{B}}{{d}_{OB}}\right]}^{2}\right){d}_{OB},$$

where:

is the opening area at a given valve lift value.*A**r*_{B}is the ball radius.*d*_{OB}is the clearance distance between the ball surface and the orifice edge.

If the **Valve seat specification** parameter
is set to `Conical`

, the opening area becomes:

$$A(h)=\pi hcos(\theta )\text{}\text{sin(}\theta )\left({d}_{OB}+\text{}h\mathrm{sin}(\theta )\right),$$

where * θ* is
the angle between the conical surface and the orifice centerline.
The geometrical parameters and variables used in the equations are
shown in the figure.

**Valve Geometries**

The volumetric flow rate through the valve is a function of
the opening area, * A(h)*, and of the pressure differential
between the valve ports:

$$q={C}_{D}A(h)\sqrt{\frac{2}{\rho}}\frac{\Delta p}{{\left({(\Delta p)}^{2}+{p}_{Cr}^{2}\right)}^{1/4}},$$

where:

*C*_{D}is the flow discharge coefficient.is the hydraulic fluid density.*ρ*is the pressure differential between the valve ports, defined as:*Δp*$$\Delta p={p}_{A}-{p}_{B},$$

where

*p*_{A}is the pressure at port**A**and*p*_{B}is the pressure at port**B**.*p*_{Cr}is the minimum pressure required for turbulent flow.

The critical pressure *p*_{Cr} is
computed from the critical Reynolds number as:

$${p}_{Cr}=\frac{\rho}{2}\left(\frac{R{e}_{Cr}\nu}{{C}_{D}{D}_{H}}\right),$$

where:

*Re*_{Cr}is the critical Reynolds number.(*ν**nu*) is the hydraulic fluid dynamic viscosity.*D*_{H}is the orifice hydraulic diameter:$${D}_{H}=\pi {r}_{O}^{2}$$

Fluid inertia is ignored.

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