Poppet Valve (IL)

Poppet valve in an isothermal liquid network

Since R2020a

Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Flow Control Valves

Description

The Poppet Valve (IL) block represents a flow-control valve in an isothermal liquid system. The poppet can either be a cylinder or a ball. You can choose between sharp-edged and conical seats. The poppet opens or closes according to the displacement signal at port S. A positive signal retracts the poppet and opens the valve.

Poppet Valve Schematic

Side-view schematic explaining the relationship between the seat, the poppet, and the open area. The seat is a V-shape. The poppet is rectangular. The open area is the orange trapezoid depicting where flow occurs.

Poppet Valve Top View

Top-view schematic explaining the relationship between the seat, the poppet, and the open area. The seat is the outside ring. The poppet is the filled-in inner circle. The open area is the ring between the poppet and the seat.

Cylindrical Stem Poppet Opening Area

The opening area of the valve is calculated as:

$A_{o p e n} = π h \sin (\frac{θ}{2}) [d_{s} + \frac{h}{2} \sin (θ)] + A_{l e a k},$

where:

h is the vertical distance between the outer edge of the cylinder and the seat, indicated in the schematic above.
θ is the Seat cone angle.
d_s is the Stem diameter.
A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$h_{\max} = \frac{d_{s} [\sqrt{1 + \cos (\frac{θ}{2})} - 1]}{\sin (θ)} .$

For any stem displacement larger than h_max, A_open is the sum of the maximum orifice area and the Leakage area:

$A_{o p e n} = \frac{π}{4} d_{s}^{2} + A_{l e a k} .$

For any combination of the signal at port S and the cylinder offset less than 0, the minimum valve area is the Leakage area.

Round Ball Poppet Opening Area

Sharp-edged Seat Geometry

The opening area of the valve is calculated as:

$A_{o p e n, s h a r p - e d g e d} = π r_{O} \sqrt{{(G_{s h a r p} + h)}^{2} + r_{O}^{2}} [1 - \frac{r_{B}^{2}}{{(G_{s h a r p} + h)}^{2} + r_{O}^{2}}] + A_{l e a k},$

where:

h is the vertical distance between the outer edge of the cylinder and the seat, indicated in the schematic above.
r_O is the seat orifice radius, calculated from the Seat orifice diameter.
r_B is the radius of the ball, calculated from the Ball diameter.
G_sharp is the geometric parameter: $G_{s h a r p} = \sqrt{r_{B}^{2} - r_{O}^{2}} .$
A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$h_{\max} = \sqrt{\frac{2 r_{B}^{2} - r_{O}^{2} + r_{O} \sqrt{r_{O}^{2} + 4 r_{B}^{2}}}{2}} - G_{s h a r p} .$

For any ball displacement larger than h_max, A_open is the sum of the maximum orifice area and the Leakage area:

$A_{o p e n} = \frac{π}{4} d_{O}^{2} + A_{l e a k} .$

For any combination of the signal at port S and the ball offset that is less than 0, the minimum valve area is the Leakage area.

Conical Seat Geometry

The opening area of the valve is calculated as:

$A_{o p e n, c o n i c a l} = G_{c o n i c a l} h + \frac{π}{2} \sin (θ) \sin (\frac{θ}{2}) h^{2} + A_{l e a k},$

where:

h is the vertical distance between the outer edge of the cylinder and the seat, indicated in the schematic above.
θ is the Seat cone angle.
G_conical is the geometric parameter: $G_{c o n i c a l} = π r_{B} \sin (θ),$ where r_B is the ball radius.
A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$h_{\max} = \frac{\sqrt{r_{B}^{2} + \frac{r_{O}^{2}}{\cos (\frac{θ}{2})}} - r_{B}}{\sin (\frac{θ}{2})} .$

For any ball displacement larger than h_max, A_open is the sum of the maximum orifice area and the Leakage area:

$A_{o p e n} = \frac{π}{4} d_{O}^{2} + A_{l e a k} .$

For any combination of the signal at port S and the ball offset that is less than 0, the minimum valve area is the Leakage area.

Numerically Smoothed Displacement

The block calculates the poppet displacement, h, such that

$h = {\begin{array}{l} 0, & (S - S_{\min}) \leq 0 \\ h_{M a x}, & (S - S_{\min}) \geq h_{M a x} \\ (S - S_{\min}), & Else \end{array}$

where:

S is the physical signal input.
S_min is the Poppet position when in the seat parameter.
h_Max is the maximum displacement.

If the Smoothing factor parameter is nonzero, the block smoothly saturates the poppet displacement between 0 and h_Max.

For more information, see Numerical Smoothing.

Mass Flow Rate Equation

Mass is conserved through the valve:

${\dot{m}}_{A} + {\dot{m}}_{B} = 0.$

The mass flow rate through the valve is calculated as:

$\dot{m} = \frac{C_{d} A_{v a l v e} \sqrt{2 \bar{ρ}}}{\sqrt{P R_{l o s s} (1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2})}} \frac{Δ p}{{[Δ p^{2} + Δ p_{c r i t}^{2}]}^{1 / 4}},$

where:

C_d is the Discharge coefficient.
A_valve is the current valve open area.
A_port is the Cross-sectional area at ports A and B.
$\bar{ρ}$ is the average fluid density.
Δp is the valve pressure difference p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number, Re_crit, the flow regime transition point between laminar and turbulent flow:

$Δ p_{c r i t} = \frac{π \bar{ρ}}{8 A_{v a l v e}} {(\frac{ν {Re}_{c r i t}}{C_{d}})}^{2} .$

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PR_loss is calculated as:

$P R_{l o s s} = \frac{\sqrt{1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2} (1 - C_{d}^{2})} - C_{d} \frac{A_{v a l v e}}{A_{p o r t}}}{\sqrt{1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2} (1 - C_{d}^{2})} + C_{d} \frac{A_{v a l v e}}{A_{p o r t}}} .$

Pressure recovery describes the positive pressure change in the valve due to an increase in area. If you do not wish to capture this increase in pressure, clear the Pressure recovery check box. In this case, PR_loss is 1.

Ports

Conserving

expand all

A — Liquid port
isothermal liquid

Liquid entry or exit port to the valve.

B — Liquid port
isothermal liquid

Liquid entry or exit port to the valve.

Input

expand all

S — Stem displacement, m
physical signal

Displacement of the valve control member in m, specified as a physical signal.

Parameters

expand all

Poppet geometry — Type of poppet
`Cylindrical stem` (default) | `Round ball`

Type of poppet. You can choose either a cylindrical or ball-shaped control member.

Valve seat specification — Geometry of valve seat
`Sharp-edged` (default) | `Conical`

Geometry of valve seat. The block uses this parameter to calculate the open area between the poppet and seat.

Dependencies

To enable this parameter, set Poppet geometry to Round ball.

Ball diameter — Diameter of ball control member
`0.01 m` (default) | positive scalar

Diameter of the ball control member.

Dependencies

To enable this parameter, set Poppet geometry to Round ball.

Seat orifice diameter — Seat orifice diameter
`7e-3 m` (default) | positive scalar

Seat orifice diameter.

Dependencies

To enable this parameter, set Poppet geometry to Round ball.

Stem diameter — Diameter of cylindrical stem
`0.01 m` (default) | positive scalar

Diameter of the cylindrical stem.

Dependencies

To enable this parameter, set Poppet geometry to Cylindrical stem.

Seat cone angle — Angle of seat opening
`120 deg` (default) | positive scalar

Angle of the seat opening.

Dependencies

To enable this parameter, set either:

Poppet geometry to Cylindrical stem
Poppet geometry to Round ball and Valve seat specification to Conical

Poppet position when in the seat — Control member offset
`0 m` (default) | positive scalar

Poppet offset when valve is closed. A positive, nonzero value indicates a partially open valve. A negative, nonzero value indicates an overlapped valve that remains closed for an initial displacement set by the physical signal at port S.

Leakage area — Gap area when in fully closed position
`1e-10 m^2` (default) | positive scalar

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Cross-sectional area at ports A and B — Area at conserving ports
`inf` `m^2` (default) | positive scalar

Areas at the entry and exit ports A and B, which are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

Upper Reynolds number limit for laminar flow through the orifice.

Smoothing factor — Numerical smoothing factor
`0.01` (default) | positive scalar in the range [0,1]

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Pressure recovery — Whether to account for pressure increase in area expansions
`off` (default) | `on`

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

Extended Capabilities

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

Version History

Introduced in R2020a

Poppet Valve (IL)

Description

Cylindrical Stem Poppet Opening Area

Round Ball Poppet Opening Area

Numerically Smoothed Displacement

Mass Flow Rate Equation

Ports

Conserving

A — Liquid port isothermal liquid

B — Liquid port isothermal liquid

Input

S — Stem displacement, m physical signal

Parameters

Poppet geometry — Type of poppet Cylindrical stem (default) | Round ball

Valve seat specification — Geometry of valve seat Sharp-edged (default) | Conical

Dependencies

Ball diameter — Diameter of ball control member 0.01 m (default) | positive scalar

Dependencies

Seat orifice diameter — Seat orifice diameter 7e-3 m (default) | positive scalar

Dependencies

Stem diameter — Diameter of cylindrical stem 0.01 m (default) | positive scalar

Dependencies

Seat cone angle — Angle of seat opening 120 deg (default) | positive scalar

Dependencies

Poppet position when in the seat — Control member offset 0 m (default) | positive scalar

Leakage area — Gap area when in fully closed position 1e-10 m^2 (default) | positive scalar

Cross-sectional area at ports A and B — Area at conserving ports inf m^2 (default) | positive scalar

Discharge coefficient — Discharge coefficient 0.64 (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow 150 (default) | positive scalar

Smoothing factor — Numerical smoothing factor 0.01 (default) | positive scalar in the range [0,1]

Pressure recovery — Whether to account for pressure increase in area expansions off (default) | on

Extended Capabilities

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

Version History

See Also

A — Liquid port
isothermal liquid

B — Liquid port
isothermal liquid

S — Stem displacement, m
physical signal

Poppet geometry — Type of poppet
`Cylindrical stem` (default) | `Round ball`

Valve seat specification — Geometry of valve seat
`Sharp-edged` (default) | `Conical`

Ball diameter — Diameter of ball control member
`0.01 m` (default) | positive scalar

Seat orifice diameter — Seat orifice diameter
`7e-3 m` (default) | positive scalar

Stem diameter — Diameter of cylindrical stem
`0.01 m` (default) | positive scalar

Seat cone angle — Angle of seat opening
`120 deg` (default) | positive scalar

Poppet position when in the seat — Control member offset
`0 m` (default) | positive scalar

Leakage area — Gap area when in fully closed position
`1e-10 m^2` (default) | positive scalar

Cross-sectional area at ports A and B — Area at conserving ports
`inf` `m^2` (default) | positive scalar

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

Smoothing factor — Numerical smoothing factor
`0.01` (default) | positive scalar in the range [0,1]

Pressure recovery — Whether to account for pressure increase in area expansions
`off` (default) | `on`

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