Poppet Valve (IH)#

The Poppet Valve (IH) block is a flow control valve in the isothermal hydraulic network.

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

Conical seat, ball poppet:

Ball poppet diameter, [m];
Seat orifice diameter, [m];
Seat conical angle , \(^о\);
Initial poppet offset, [m].

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

Cylindrical stem diameter, [m];
Seat conical angle , \(^о\);
Initial poppet offset, [m].

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

Ball poppet diameter, [m];
Seat orifice diameter, [m];
Initial poppet offset, [m].

For the valve configuration Conical seat, ball poppet, the valve cross-sectional 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 the cross-sectional area of the valve is determined by the formula (4):

(4)#\[A_{open}\:=\:\pi\: \cdot h\cdot\:sin(\frac{\theta}{2})\cdot[d_{s}+\frac{h}{2}\cdot sin(\theta)]+A_{leak}\]

where:

\(h\) — distance between cylinder and saddle, [m];

\(θ\) - saddle cone inclination angle, [rad];

\(d_s\) — diameter of cylindrical stem, [m];

\(A_{leak}\) — leakage area, [m\(^2\)].

The flow area of the valve is limited by the maximum displacement \(h_{max}\) (5):

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

For valve configuration Sharp-edged seat, ball poppet 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 \(G_{sharp}\) parameter is defined as (7):

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

Maximum distance between valve seat and poppet, [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 seat and the poppet

For all valve configurations considered, the distance h between the seat and the poppet 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

\(S_{min}\) – initial plate 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 rod displacement greater than \(h_{max}\), \(A_{open}\) is the sum of the maximum flow area of the valve and the leakage area (10):

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

Mass flow equation

Mass conservation principle (11):

(11)#\[\dot m_{A} + \dot m_{B}= 0\]

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

(12)#\[\dot m\:=\:\frac{C_{d} \cdot A_{valve} \cdot \:\sqrt{2 \cdot \:\rho_{av}}}{\sqrt{PR_{loss} \cdot (1-(\frac{A_{valve}}{A_{port}})^2)}} \cdot \:\frac{\Delta p}{[\Delta p^2+\:\Delta p_{crit}^2]^{1/4}}\]

where:

\(C_d\) – pressure recovery loss factor;

\(A_{valve}\) – current flow area of the valve, [m\(^2\)];

\(A_{port}\) – flow cross–section area, [m\(^2\)];

\(ρ_{av}\) – average density of liquid, [kg/m\(^3\)];

\(Δp\) – pressure differential across the valve, [Pa].

Critical pressure differential \(Δp_{crit}\) - is the pressure differential associated with the critical Reynolds number, the transition point of the flow mode from laminar to turbulent (13):

(13)#\[\Delta p_{crit} = \frac{\pi\: \cdot\:\rho_{av}}{8\: A_{valve}}\cdot (\frac{\nu\:\:Re_{crit}}{C_{d}})^2\]

The pressure loss describes the pressure differential in the valve as the flow area decreases.

\(PR_{loss}\) calculated by the following formula (14):

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

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

1. Properties#

Property	Default value	Description	Units of measurement
Seat and ball geometry: Conical seat, ball poppet; Conical seat, cylindrical stem; Sharp-edged seat, ball poppet	Conical seat, ball poppet	-	-
Ball poppet diameter, available when `Seat and ball geometry` - `Conical seat, ball poppet` or `Sharp-edged seat, ball poppet`	0.01	-	m
Seat orifice diameter, available when `Seat and ball geometry` - `Conical seat, ball poppet` or `Sharp-edged seat, ball poppet`	7e-3	-	m
Offset	0.0	-	m
Seat conical 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	Reynolds number at which the transition from the laminar regime occurs flow to turbulent	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Stem displacement	Input	-	m	Automation
Input	Input	-	-	Isothermal hydraulics
Output	Output	-	-	Isothermal hydraulics

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