Hydraulic ball valve

Flow Control Valves

The Ball Valve block models a variable orifice created by a spherical ball and a round sharp-edged orifice.

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:

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

$$p={p}_{A}-{p}_{B}$$

$${p}_{cr}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{H}}\right)}^{2}$$

$$h={x}_{0}+x$$

$$A(h)=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}h=0\hfill \\ \pi \cdot {r}_{O}\left(1-\frac{{r}_{B}}{{D}^{2}}\right)\cdot D\hfill & \text{for}0h{h}_{\mathrm{max}}\hfill \\ {A}_{\mathrm{max}}+{A}_{leak}\hfill & \text{for}h={h}_{\mathrm{max}}\hfill \end{array}$$

$$D=\sqrt{{\left(\sqrt{{r}_{B}^{2}-{r}_{O}^{2}}+{h}^{2}\right)}^{2}+{r}_{O}^{2}}$$

$${D}_{H}=\sqrt{\frac{4A(h)}{\pi}}$$

$${A}_{\mathrm{max}}=\frac{\pi {d}_{O}^{2}}{4}$$

$${h}_{\mathrm{max}}={r}_{O}\cdot \left(\sqrt{\frac{{\left(1+\sqrt{1+4\frac{{d}_{B}^{2}}{{d}_{O}^{2}}}\right)}^{2}}{4}-1}-\sqrt{\frac{{d}_{B}^{2}}{{d}_{O}^{2}}-1}\right)$$

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 | Ball displacement from initial position, controlled by the physical input signal at port S |

h | Valve opening |

d_{O} | Orifice diameter |

r_{O} | Orifice radius |

d_{B} | Ball diameter |

r_{B} | Ball radius |

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 |

A_{max} | Maximum valve open area |

h_{max} | Maximum valve opening |

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.

Fluid inertia is not taken into account.

The flow passage area is assumed to be equal to the side surface of the frustum of the cone located between the ball center and the orifice edge.

**Valve ball diameter**The diameter of the valve ball. It must be greater than the orifice diameter. The default value is

`0.01`

m.**Orifice diameter**The diameter of the orifice of the valve. The default value is

`0.005`

m.**Initial opening**The initial opening of the valve. Its value must be nonnegative. The default value is

`0`

.**Flow discharge coefficient**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`

.**Critical Reynolds number**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`

.**Leakage area**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. The parameter value must be greater than 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.

The block has the following ports:

`A`

Hydraulic conserving port associated with the valve inlet.

`B`

Hydraulic conserving port associated with the valve outlet.

`S`

Physical signal port to control ball displacement.

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