Ball valve (TL)

Block appearance in REPEAT VISION

 The Ball valve (TL) simulates the operation of this shutoff and control device in a thermal hydraulic system.

Note

The user has the ability to adjust the maximum area of liquid flow through the crane and the maximum throughput of the crane in dimensions:

• [m\(^3\)/h] - for coefficient \(K_v\);

• [gpm] - for coefficient \(С_v\), through which one can calculate the recovery factor \(C_d\) using the following formulas (1) and (2):

(1)\[C_d=\frac{K_v}{A}\cdot\sqrt{\frac{\rho_{water, 15^0C}}{2\cdot \Delta p_{K_v}}}\]

(2)\[C_d=\frac{C_v}{A}\cdot\sqrt{\frac{\rho_{water, 60^0F}}{2\cdot \Delta p_{C_v}}}\]

 The degree of valve opening in degrees is set through the external automation port.

Note

Zero signal means a fully closed valve.

 Calculation of the open area for liquid flow is made according to Idelchik handbook for cylindrical pipe according to the following figure :

Calculation of open area for liquid flow

Note

Also, the user can select a table data setting by specifying a pair of vectors in three different ways:

First way:

Coefficient vector \(K_v\) and valve rotation angle vector

Second way:

Coefficient vector \(C_v\) and valve rotation angle vector

Third way:

Crane cross-sectional area vector and valve rotation angle vector

 The block retains mass so that (3) :

(3)\[\dot m_{A}\:+\:\dot m_{B}\:=\:\rho\:\cdot \:\nu_{A}\:\cdot \:A_{A}\:+\: \rho\:\cdot \:\nu_{B}\:\cdot \:A_{B}\:=\:0\]

 This mass balance implies that the velocity increases as the area decreases and decreases when the flow discharges over a larger area. According to Bernoulli’s principle, this change in velocity results in a region of lower pressure in the hole and higher pressure in the expansion area. The resulting increase in pressure, called pressure recovery, depends on the pressure recovery loss ratio and the area ratio of the hole and port.

Mass flow rate calculation

 The block calculates the mass flow rate (4) :

(4)\[ \dot m\:=\:\frac{C_{d}\:\cdot A_{orifice}\:\cdot \:\sqrt{2\:\cdot \:\bar \rho}}{\sqrt{PR_{loss}\:\cdot \:(1-(\frac{A_{orifice}}{A_{port}})^2)}}\:\cdot \:\sqrt{p_{A}-p_{B}}\:\approx\:\frac{C_{d}\cdot A_{orifice}\cdot \:\sqrt{2\cdot \:\bar \rho}}{\sqrt{PR_{loss}\cdot (1-(\frac{A_{orifice}}{A_{port}})^2)}}\cdot \:\frac{p_{A}-p_{B}}{[(p_{A}-p_{B})^2+\:\Delta p_{crit}]^{1/4}} \]

where:

 \(C_d\) – coefficient of losses during pressure recovery;

 \(A_{orifice}\) - hole area, [m\(^2\)];

 \(A_{port}\) — cross-sectional area of ports A and B, [m\(^2\)];

 \(\bar ρ\) – average liquid density, [kg/m\(^3\)].

Pressure loss

 Pressure loss describes a decrease in valve pressure due to a decrease in area. Pressure loss, \(PR_{loss}\) calculated as (5) :

(5)\[ PR_{loss}\:=\:\frac{\sqrt{1-(\frac{A_{orifice}}{A_{port}})^2\cdot (1-C_{d}^2)}-C_{d}\cdot \:\frac{A_{orifice}}{A_{port}}}{\sqrt{1-(\frac{A_{orifice}}{A_{port}})^2\cdot (1-C_{d}^2)}+C_{d}\cdot \:\frac{A_{orifice}}{A_{port}}} \]

Critical pressure

 Critical pressure drop, \(Δp_{crit}\) , is the pressure drop associated with the critical Reynolds number, \(Re_{crit}\), which is the transition point between laminar and turbulent liquid flow (6) :

(6)\[\Delta p_{crit}\:=\:\frac{\Pi\:\cdot \:\bar \rho}{8\cdot A_{orifice}}\cdot \:(\frac{\nu\:\cdot Re_{crit}}{C_{d}})^2\]

Law of conservation of energy

\[\phi_А+\phi_В=0\]

where:

 \(\phi_A\) - energy flow at the input, [W];

 \(\phi_B\) - energy flow at the output, [W].

1.  Properties

Property	Default Value	Description	Units of measurement
Valve parametrization: Area; Table	Area	-	-
Flow coefficient parametrization: \(K_v\); \(C_v\); \(C_d\) And Area	\(K_v\)	-	-
\(K_v\), when selecting Valve parametrization - Area, Flow coefficient parametrization - $K_v$	49.0	-	m\(^3\)/h
\(C_v\), when selecting Valve parametrization - Area, Flow coefficient parametrization - $C_v$	32.0	-	gpm
Discharge coefficient, when selecting Valve parametrization - Area, Flow coefficient parametrization - $C_d$ And Area	0.64	-	-
Critical Reynolds number	150.0	-	-
Leakage area, when selecting Valve parametrization - Area	1.0E-10	-	m\(^2\)
Area port, when selecting Valve parametrization - Area	0.09	-	m\(^2\)
Area ball bore, when selecting Valve parametrization - Area	0.07	-	m\(^2\)
\(K_v\) vector, when selecting Valve parametrization - Table, Flow coefficient parametrization - $K_v$	{1.0E-6; 0.34; 0.76; 1.6; 2.45; 4.1; 5.75; 9.4; 13.0; 28.0; 50.0}	-	-
\(C_v\) vector, when selecting Valve parametrization - Table, Flow coefficient parametrization - $C_v$	{1.0E-6; 0.58; 1.15; 1.9; 2.8; 4.3; 7.0; 10.5; 17.0; 26.0; 32.0}	-	-
Area vector, when selecting Valve parametrization - Table, Flow coefficient parametrization - $C_d$ And Area	{1.0E-10;62.5;125.0;187.5;250.0;312.5;375.0;437.0;500.0;562.5;625.0}	-	-
Ball rotation vector, when selecting Valve parametrization - Table	{0.0; 0.15707963267948966; 0.3141592653589793; 0.47123889803846897; 0.6283185307179586; 0.7853981633974483; 0.9424777960769379; 1.0995574287564276; 1.2566370614359172; 1.413716694115407; 1.5707963267948966}	-	-

2.  Inputs and outputs

Parameters	Input/Output	Description	Units of measurement	Port type
Opening angle	Input	-	degrees	Automation
Input	Input	-	-	Thermohydraulics
Output	Output	-	-	Thermohydraulics

In order to see the connection capabilities of the block, you need to go to page Description of block ports