Poppet valve (TL)#

The Poppet valve (TL) block is a flow control valve in a thermal hydraulic network.

Depending on the specified value of the Seat and poppet geometry property, the user can select the following valve configuration options:

Conical seat, ball poppet:

Diameter of a spherical plate, [m];
Seat orifice diameter, [m];
Seat cone angle, \(^о\);
Offset, [m].

Conical seat, cylindrical stem. For this type of valve the user can set the following parameters:

Diameter of cylindrical rod, [m];
Seat cone angle, \(^о\);
Offset, [m].

Sharp-edged seat, ball poppet. For this type of valve, the user can set the following parameters:

Diameter of a spherical plate, [m];
Seat orifice diameter, [m];
Offset, [m].

For the valve configuration Conical seat, ball poppet, the valve flow area is defined as (1):

(1)#\[A_{open,conical}=G_{conical}\cdot h + \frac{\pi}{2}\cdot sin(\theta)\cdot sin(\frac{\theta}{2})\cdot h^2 + A_{leak}\]

where the parameter \(G_{conical}\) is defined as (2):

(2)#\[G_{conical}=\pi \cdot r_B \cdot sin(\theta)\]

Maximum distance between valve seat and plate, [m] (3):

(3)#\[h_{max}=\frac{\sqrt{r^2_B+\frac{r_O^2}{cos(\frac{\theta}{2})}}-r_B}{sin(\frac{\theta}{2})}\]

where:

\(r_B\) – radius of a spherical plate, [m];

\(r_O\) – valve seat radius, [m];

\( heta\) – angle of the conical valve seat, \(^o\);

h – distance between valve seat and valve plate, [m].

For valve configuration Conical seat, cylindrical stem valve flow area is determined by the formula (4):

(4)#\[A_{open}=П\cdot h\cdot sin(\theta /2)\cdot (d_s+\frac{h}{2}\cdot sin(\theta))+A_{leak}\]

where:

h - distance between cylinder and seat, [m];

\(\theta\) - inclination angle of the seat cone, [rad];

d\(_s\) - diameter of cylindrical valve, [m];

A\(_{leak}\) - leakage area, [m\(^2\)].

The cross-section area of the valve is limited by the maximum displacement h\(_{max}\) (5):

(5)#\[h_{max}=\frac{d_s\cdot (\sqrt {1+cos(\theta/2)}-1)}{sin(\theta)}\]

For valve configuration Conical seat, cylindrical stem the cross-sectional area of the valve is defined as (6):

(6)#\[A_{open,sharp-edged}=\pi \cdot r_O \cdot \sqrt{(G_{sharp}+h)^2+r_O^2}\cdot (1- \frac{r_B^2}{(G_{sharp}+h)^2+r_O^2})+A_{leak}\]

where the parameter \(G_{sharp}\) is defined as (7):

(7)#\[G_{sharp}=\sqrt{r_B^2-r_O^2}\]

Maximum distance between valve seat and plate, [m] (8):

(8)#\[h_{max}=\sqrt{\frac{2\cdot r^2_B-r_O^2+r_O\cdot \sqrt{r_O^2+4\cdot r_B^2}}{2}}-G_{sharp}\]

where:

\(r_B\) – radius of a spherical plate, [m];

\(r_O\) – valve seat radius, [m];

h – distance between valve seat and valve plate, [m].

Calculating the distance between the saddle and the plate

For all valve configurations considered, the distance h between the seat and the plate is determined as follows (9):

(9)#\[\begin{split}h =\begin{cases}0 , & \ (S-S_{min})\leq 0\\h_{max}, & (S-S_{min})\geq h_{max}\\(S-S_{min}),&Else \end{cases}\end{split}\]

where:

S – plate position signal, [m];

Note

Transmitted via the Automation port

\(S_{min}\) – Offset, [m].

Saturation of the valve cross-sectional area

For all the valve configurations considered, saturation of the valve cross-sectional area occurs both on the right and on the left.

For any stem displacement, which is greater than \(h_{max}\) , \(A_{open}\) is the sum of the maximum cross-section of valve and the leakage area (10):

(10)#\[A_{open}=\frac{\pi}{4}\cdot d_s^2+A_{leak}\]

Equation of mass flow rate

Law of conservation of mass (11):

(11)#\[\dot{m_A}+ \dot{m_B}=0 \]

The mass flow rate through the valve is calculated using the following formula (12):

(12)#\[{\dot{m}}=\frac{C_d \cdot A_{valve}\cdot \sqrt {2 \cdot \bar\rho}}{\sqrt {PR_{loss}\cdot (1-(\frac{A_{valve}}{A_{port}})^2)}}\cdot \frac{\Delta p}{(\Delta \rho^2+\Delta p^2_{crit})^{1/4}} \]

where:

С\(_d\) - loss coefficient at pressure recovery;

A\(_{valve}\) - current cross-section area of the valve, [m\(^2\)];

A\(_{port}\) - cross-section area of flow, [m\(^2\)];

\(\bar ho\) - average density of liquid, [kg/\(m^3\)];

\(\Delta p\) - is the pressure drop at valve, [Pa].

Critical pressure drop \(\Delta p_{crit}\) is the pressure drop associated with the critical Reynolds number, the point of transition of the flow mode from laminar to turbulent (6):

(13)#\[\Delta p_{crit}=\frac {П\cdot \bar\rho }{8\cdot A_{valve}} \cdot (\frac{\nu \cdot Re_{crit}}{C_d})^2\]

Pressure decrease describes the pressure decrease in the valve when the valve cross-section area is decreased.

PR\(_{loss}\) is calculated using the following formula (7):

(14)#\[PR_{loss}=\frac{\sqrt {1-(\frac{A_{valve}}{A_{port}})^2\cdot (1-C_d^2)}-C_d \cdot \frac{A_{valve}}{A_{port}}}{\sqrt {1-(\frac{A_{valve}}{A_{port}})^2\cdot (1-C_d^2)}+C_d \cdot \frac{A_{valve}}{A_{port}}}\]

Pressure recovery describes a positive pressure change in the valve when the area increases.

Law of conservation of energy (15):

(15)#\[\phi_А+\phi_B=0\]

where:

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

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

1. Properties#

Property	Default value	Description	Units of measurement
Seat and poppet geometry: Conical seat, ball poppet; Conical seat, cylindrical stem; Sharp-edged seat, ball poppet	Conical seat, ball poppet	-	-
Ball diameter, available when `Seat and poppet geometry` - `Conical seat, ball poppet` or `Sharp-edged seat, ball poppet`	0.01	-	m
Seat orifice diameter, available when `Seat and poppet geometry` - `Conical seat, ball poppet` or `Sharp-edged seat, ball poppet`	0.007	-	m
Offset	0.01	-	m
Seat cone angle	120.0	-	\(^о\)
Leakage area	1.0e-10	-	m\(^2\)
Port area	0.1	-	m\(^2\)
Discharge coefficient	0.64	-	-
Critical Reynolds number	150.0	The Reynolds number at which the transition from laminar to turbulent flow occurs	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Displacement	Input	-	m	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