# Ball Valve with Conical Seat

Hydraulic ball valve with conical seat

## Library

Flow Control Valves

## Description

The Ball Valve with Conical Seat block models a valve created by a spherical ball and a conical seat.

The valve is characterized by the ball diameter, cone angle, and orifice diameter. The flow rate through the valve is proportional to the ball displacement and pressure differential. If passage area in the ball-cone contact exceeds the area of the orifice, the latter is assumed as the valve passage area. The flow rate is determined according to the following equations:

`$q={C}_{D}\cdot A\left(h\right)\sqrt{\frac{2}{\rho }}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$`
`$p={p}_{A}-{p}_{B}$`
`${p}_{cr}=\frac{\rho }{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu }{{C}_{D}\cdot {D}_{H}}\right)}^{2}$`
`$h={x}_{0}+x·or$`

`${D}_{H}=\sqrt{\frac{4A\left(h\right)}{\pi }}$`
`${A}_{\mathrm{max}}=\frac{\pi {d}_{O}^{2}}{4}$`

where

 q Flow rate p Pressure differential pA, pB Gauge pressures at the block terminals CD Flow discharge coefficient A(h) Instantaneous orifice passage area x0 Initial opening x Ball displacement from initial position h Valve opening dO Orifice diameter D Ball diameter Θ Cone angle of the valve seat ρ Fluid density ν Fluid kinematic viscosity pcr Minimum pressure for turbulent flow Recr Critical Reynolds number DH Valve instantaneous hydraulic diameter Aleak Closed valve leakage area Amax Maximum valve open area

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.

## Basic Assumptions and Limitations

• 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 and the conical seat.

## Dialog Box and Parameters

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.

Cone angle

The cone angle of the valve seat. The default value is `120` degrees.

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.

## Global Parameters

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.

## Ports

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.