Ball Valve

(To be removed) Valve with a sliding ball control mechanism

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead. (since R2020a)

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

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Libraries:
Simscape / Fluids / Hydraulics (Isothermal) / Valves / Flow Control Valves

Description

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

Opening Area

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:

• h is the valve lift.

• x₀ is the ball displacement offset.

• s is the ball displacement (relative to the specified offset).

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:

$$A(h)=\pi r_O\left(1-{\left[\frac{r_B}{d_{OB}}\right]}^2\right)d_{OB}(h),$$

where:

• A is the opening area at a given valve lift value.

• r_B is the ball radius.

• d_OB(h) is the distance from the center of the ball (point O in the figure) to the edge of the orifice (point B). This distance is a function of the valve lift (h).

If the Valve seat specification parameter is set to Conical, the opening area becomes:

$$A(h)=\pi hcos(\theta )\text{}\text{sin(}\theta )\cdot \left(2r_B+\text{}h\sin (\theta )\right),$$

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

Flow Rate

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.

• ρ is the hydraulic fluid density.

• Δp is the pressure differential between the valve ports, defined as:

  $$\Delta p=p_A-p_B,$$

  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:

$$p_{Cr}=\frac{\rho }{2}{\left(\frac{R{e}_{Cr}\nu }{C_D{D}_H}\right)}^2,$$

where:

• Re_Cr is the critical Reynolds number.

• ν (nu) is the hydraulic fluid dynamic viscosity.

• D_H is the orifice hydraulic diameter:

  $$D_H=\{\begin{array}{ll}{D}_H^{Min},\hfill & \text{if }h\le 0\hfill \\ D_H^{Max}+D_H^{Min},\hfill & \text{if }h\ge h_{Max}\hfill \\ \frac{4A}{l}+D_H^{Min},\hfill & \text{otherwise}\hfill \end{array},$$

  in which:

  • D_H^Min is the minimum hydraulic diameter, corresponding to the smallest attainable flow area, the leakage flow area.

  • D_H^Max is the maximum hydraulic diameter, corresponding to the largest attainable flow area, that of the valve in the fully open position.

  • l is the wetted length of the valve perimeter—which can, but need not, be that of a circle.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Assumptions

Fluid inertia is assumed to be negligible.

Ports

Input

S — Ball displacement, m

physical signal

Physical signal input port for the ball displacement.

Conserving

A — Valve inlet

hydraulic (isothermal liquid)

Hydraulic (isothermal liquid) conserving port associated with the valve inlet.

B — Valve outlet

hydraulic (isothermal liquid)

Hydraulic (isothermal liquid) conserving port associated with the valve outlet.

Parameters

Valve seat specification — Valve seat geometry type

Sharp-edged (default) | Conical

Geometry of the valve seat. The choice of geometry impacts the opening characteristics of the valve. See the block description for the valve opening calculations.

Cone angle — Angle between sloping edges of transverse seat cross section

120 deg (default) | scalar in units of rotation

Angle between the sloping edges of the seat in a transverse cross-sectional view.

Ball diameter — Diameter of the ball control element

0.01 m (default) | scalar in units of length

Diameter of the ball control element. This diameter must be greater than that specified for the orifice.

Orifice diameter — Diameter of the valve orifice

0.005 m (default) | scalar in units of length

Diameter of the valve orifice. This diameter must be smaller than that specified for the ball control element.

Ball displacement offset — Neutral position of ball control element

0 m (default) | scalar in units of length

Neutral position of the ball control element. The neutral position is that to which the ball returns when the displacement signal is zero. This parameter must be greater than or equal to zero.

Discharge coefficient — Semi-empirical parameter for valve capacity characterization

0.7 (default) | unitless scalar between 0 and 1

Ratio of the actual and theoretical flow rates through the valve. This parameter depends on the geometrical properties of the valve. Values are usually provided in textbooks and manufacturer data sheets.

Leakage area — Internal leakage area between valve inlets

1e-12 m^2 (default) | positive scalar in units of area

Total area of internal leaks in the completely closed state. The purpose of this parameter is to maintain the numerical integrity of the fluid network by preventing a portion of that network from becoming isolated when the valve is completely closed.

Laminar transition specification — Choice of parameter used to define the laminar-turbulent transition

Pressure ratio (default) | Reynolds number

Select the parameter to base the laminar-turbulent transition on. Options include:

• Pressure ratio — Flow transitions between laminar and turbulent at the pressure ratio specified in the Laminar flow pressure ratio parameter. Use this option for the smoothest and most numerically robust flow transitions.

• Reynolds number — The transition occurs at the Reynolds number specified in the Critical Reynolds number parameter. Flow transitions are more abrupt and can cause simulation issues at near-zero flow rates.

Laminar flow pressure ratio — Pressure ratio at the laminar-turbulent flow transition

0.999 (default) | unitless scalar between 0 and 1

Pressure ratio at which the flow transitions between the laminar and turbulent regimes. The pressure ratio is the fraction of the outlet pressure over the inlet pressure.

Dependencies

This parameter is active when the Laminar transition specification parameter is set to Pressure ratio.

Critical Reynolds number — Reynolds number at the laminar-turbulent flow transition

12 (default) | unitless positive scalar

Maximum Reynolds number for laminar flow. This parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value, 12, corresponds to a round orifice in thin material with sharp edges.

Dependencies

This parameter is active when the Laminar transition specification parameter is set to Reynolds number.

Extended Capabilities

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

Version History

Introduced in R2006a

R2023a: To be removed

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead.

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.