# Ball Valve (IL)

Ball valve in an isothermal liquid network

Since R2022b

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 Ball valve parameterization 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

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

where:

• Rport and Rbore 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

`$\stackrel{˙}{m}={C}_{d}A\sqrt{2\overline{\rho }}\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right)}^{1}{4}}},$`

where:

• Cd is the discharge coefficient.

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

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

• Δpcrit is the critical pressure differential associated with the critical Reynolds number, Recrit.

The block calculates Δpcrit as

`$\Delta {p}_{crit}=\frac{\pi \overline{\rho }}{8A}{\left(\frac{vR{e}_{crit}}{{C}_{d}}\right)}^{2}.$`

When you set Flow coefficient parameterization to ```Cd coefficient and area```, you can specify Cd using the Discharge coefficient (Cd) parameter. When you set Flow coefficient parameterization to ```Cv coefficient (USCS)```, the block calculates Cd as

`${C}_{d}=\frac{{C}_{v}}{A}\sqrt{\frac{{\rho }_{water,60°\text{F}}}{2\Delta {p}_{{C}_{v}}}},$`

where Cv is the Maximum valve flow coefficient (Cv) parameter. When you set Flow coefficient parameterization to ```Kv coefficient (SI)```, the block uses

`${C}_{d}=\frac{{K}_{v}}{A}\sqrt{\frac{{\rho }_{water,15°\text{C}}}{2\Delta {p}_{{K}_{v}}}},$`

where Kv is the Maximum valve flow factor (Kv) parameter. In either equation, ΔpCv is 1 psi and ΔpKv is 1 bar.

## Ports

### Input

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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

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Isothermal liquid conserving port associated with valve port A.

Isothermal liquid conserving port associated with valve port B.

## Parameters

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

Whether to parameterize the flow using Kv, Cv, or Cd. The block uses these coefficient definitions:

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

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

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

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

#### Dependencies

To enable this parameter, set Ball valve parameterization to `Area of overlapping circles` and Flow coefficient parameterization to `Cv coefficient (USCS)`.

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

#### Dependencies

To enable this parameter, set Ball valve parameterization to `Area of overlapping circles` and Flow coefficient parameterization to `Kv coefficient (SI)`.

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 Flow coefficient parameterization to `Cd coefficient and area`.

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 Ball valve parameterization to ```Area of overlapping circles```.

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

#### Dependencies

To enable this parameter, set Ball valve parameterization to ```Area of overlapping circles```.

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 Ball valve parameterization to ```Tabulated data``` and Flow coefficient parameterization to ```Cv coefficient (USCS)```.

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 Ball valve parameterization to ```Tabulated data``` and Flow coefficient parameterization to ```Kv coefficient (SI)```.

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 Ball valve parameterization to ```Tabulated data``` and Flow coefficient parameterization to ```Cd coefficient and area```.

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 Valve flow coefficient (Cv) vector parameter, the Valve flow factor (Kv) vector parameter, or the Area vector parameter.

#### Dependencies

To enable this parameter, set Ball valve parameterization to ```Tabulated data```.

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 Ball valve parameterization to ```Area of overlapping circles```.

Upper Reynolds number limit for laminar flow through the valve.

## Version History

Introduced in R2022b