Ball Valve (IL)

Ball valve in an isothermal liquid network

Since R2022b

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Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Flow Control Valves

Description

The Ball Valve (IL) block represents a ball valve in an isothermal liquid network. A ball valve consists of a ball with a bore that can pivot inside of a valve body. When the valve is open, the bore fully overlaps with the valve body port. As the valve shuts, the ball rotates and reduces the amount of overlap, thereby reducing the effective area of the orifice. Ball valves are common for flow isolation purposes because they can securely shut off flow for many cycles. Ball valves are less common in applications where precise throttling is necessary.

You can parameterize the block analytically or by using tabulated data. When you set Opening characteristic to Area of overlapping circles, the block considers the area of the overlap between the valve port and the ball bore as the opening area such that

$$\begin{array}{l}{A}_{open}=\sin \left(\phi \right)R_{bore}^2\left[{\cos }^{-1}\left({\lambda }_{bore}\right)-{\lambda }_{bore}\sqrt{1-{\lambda }^2{}_{bore}}\right]+R_{port}^2\left[{\cos }^{-1}\left({\lambda }_{port}\right)-{\lambda }_{port}\sqrt{1-{\lambda }^2{}_{port}}\right]\\ {\lambda }_{bore}=\frac{R_{bore}^2-R_{port}^2+l^2}{2R_{bore}l}\\ {\lambda }_{port}=\frac{R_{port}^2-R_{bore}^2+l^2}{2R_{port}l}\end{array}$$

where:

• R_port and R_bore are the radii of the valve port and the ball bore, respectively.

• l is the displacement of the bore center from the valve port center.

• φ is the rotation of the ball valve given by the physical signal S. The valve is fully shut at 0 rad and fully open at π/2 rad.

Mass Flow Rate

The block calculates flow through the valve using the pressure-area relationship for orifices such that

$$\dot{m}=C_{d}A\sqrt{2\overline{\rho }}\frac{\Delta p}{{\left(\Delta p^2+\Delta p_{crit}^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}},$$

where:

• C_d is the discharge coefficient.

• $$\overline{\rho }$$ is the average fluid density.

• A is the area open to flow, where A = A_open + A_leak, and A_leak is the Leakage area parameter.

• Δp_crit is the critical pressure differential associated with the critical Reynolds number, Re_crit.

The block calculates Δp_crit as

$$\Delta p_{crit}=\frac{\pi \overline{\rho }}{8A}{\left(\frac{vR{e}_{crit}}{C_d}\right)}^2.$$

When you set Valve parameterization to Orifice area based on geometry, you can specify C_d using the Discharge coefficient parameter. When you set Valve parameterization to Cv flow coefficient, the block calculates C_d as

$$C_d=\frac{C_v}{A}\sqrt{\frac{{\rho }_{water,60°\text{F}}}{2\Delta p_{C_v}}},$$

where C_v is the Maximum Cv flow coefficient parameter. When you set Valve parameterization to Kv flow coefficient, the block uses

$$C_d=\frac{K_v}{A}\sqrt{\frac{{\rho }_{water,15°\text{C}}}{2\Delta p_{K_v}}},$$

where K_v is the Maximum Kv flow coefficient parameter. In either equation, Δp_Cv is 1 psi and Δp_Kv is 1 bar.

Ports

Input

S — Valve position, rad

physical signal

Physical signal port associated with the position of the valve, in rad. A value of 0 represents a fully shut valve and a value of π/2 represents a fully open valve.

Conserving

A — Valve port A

isothermal liquid

Isothermal liquid conserving port associated with valve port A.

B — Valve port B

isothermal liquid

Isothermal liquid conserving port associated with valve port B.

Parameters

Valve parameterization — Option to parameterize given flow coefficient

Orifice area based on geometry (default) | Cv flow coefficient | Kv flow coefficient

Whether to parameterize the flow using K_v, C_v, or C_d. The block uses these coefficient definitions:

• K_v is the flow capacity of water through the fully open valve at 15℃ with a pressure drop of 1 bar, in m³/h.

• C_v is the flow capacity of water through the fully open valve at 60℉ with a pressure drop of 1 psi, in gpm.

• C_d is the unitless discharge coefficient that defines the efficiency of the valve.

Opening characteristic — Ball valve parameterization

Area of overlapping circles (default) | Tabulated

Option to parameterize the block using the method of area of overlapping circles or to use tabulated data.

Maximum Cv flow coefficient — Maximum valve flow coefficient

32 gpm (default) | positive scalar

Maximum value of the valve flow coefficient. This value should correspond to the fully open position.

Dependencies

To enable this parameter, set Opening characteristic to Area of overlapping circles and Valve parameterization to Cv flow coefficient.

Maximum Kv flow coefficient — Maximum valve flow factor

49 m^3/hr (default) | positive scalar

Maximum value of the valve flow factor. This value should correspond to the fully open position.

Dependencies

To enable this parameter, set Opening characteristic to Area of overlapping circles and Valve parameterization to Kv flow coefficient.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Discharge coefficient of the valve. This value is a correction factor that accounts for losses in the theoretical flow.

Dependencies

To enable this parameter, set Valve parameterization to Orifice area based on geometry.

Cross-sectional area at ports A and B — Valve port cross-sectional area

pi * (25 ^ 2) / 4 mm^2 (default) | positive scalar

Cross-sectional area of the valve ports. The valve ports are the paths in the valve body where the flow meets the ball bore.

Dependencies

To enable this parameter, set Opening characteristic to Area of overlapping circles.

Ball bore area — Area of ball bore

pi * (20 ^ 2) / 4 mm^2 (default) | positive scalar

Cross-sectional area of the bore in the valve ball.

Dependencies

To enable this parameter, set Opening characteristic to Area of overlapping circles.

Cv flow coefficient vector — Flow coefficient for given ball rotation

[1e-06, .58, 1.15, 1.9, 2.8, 4.3, 7, 10.5, 17, 26, 32] gpm (default) | vector

Valve flow coefficient for a given ball rotation. Each element corresponds one-to-one with the Ball rotation vector parameter. The first element corresponds to the valve leakage and must be nonzero.

Dependencies

To enable this parameter, set Opening characteristic to Tabulated and Valve parameterization to Cv flow coefficient.

Kv flow coefficient vector — Flow factor for given ball rotation

[1e-06, .34, .76, 1.6, 2.45, 4.1, 5.75, 9.4, 13, 28, 50] m^3/hr (default) | vector

Valve flow factor for a given ball rotation. Each element corresponds one-to-one with the Ball rotation vector parameter. The first element corresponds to the valve leakage and must be nonzero.

Dependencies

To enable this parameter, set Opening characteristic to Tabulated and Valve parameterization to Kv flow coefficient.

Area vector — Area for given ball rotation

[1e-10, 62.5, 125, 187.5, 250, 312.5, 375, 437.5, 500, 562.5, 625] mm^2 (default) | vector

Flow area for a given ball rotation. Each element corresponds one-to-one with the Ball rotation vector parameter. The first element corresponds to the valve leakage and must be nonzero.

Dependencies

To enable this parameter, set Opening characteristic to Tabulated and Valve parameterization to Orifice area based on geometry.

Ball rotation vector — Ball rotation

pi / 2 .* [0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1] rad (default) | vector

Ball rotation for a given flow coefficient or area. The elements is this vector must align one-to-one with the elements in either the Cv flow coefficient vector parameter, the Kv flow coefficient vector parameter, or the Area vector parameter.

Dependencies

To enable this parameter, set Opening characteristic to Tabulated.

Leakage area — Valve gap area when in fully shut position

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the valve is in the fully shut position. The block saturates any area smaller than this value to the specified leakage area. This value contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, set Opening characteristic to Area of overlapping circles.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022b

R2024b: Updated parameter and parameter setting names

The names of the parameter and parameter settings in the Ball Valve (IL) block have been updated to be consistent with other valve blocks. The behavior of the block has not changed. This table summarizes the new parameter and parameter setting names.

Previous Parameter or Setting Name	Updated Parameter or Setting Name
Ball valve parameterization	Opening characteristic
Flow coefficient parameterization	Valve parameterization
Kv coefficient (SI)	Kv flow coefficient
Cv coefficient (USCS)	Cv flow coefficient
Cd coefficient and area	Orifice area based on geometry
Discharge coefficient (Cd)	Discharge coefficient
Maximum valve flow coefficient (Cv)	Maximum Cv flow coefficient
Maximum valve flow factor (Kv)	Maximum Kv flow coefficient
Valve flow coefficient (Cv) vector	Cv flow coefficient vector
Valve flow factor (Kv) vector	Kv flow coefficient vector