# Poppet Valve (IL)

Poppet valve in an isothermal liquid network

• Library:
• Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Flow Control Valves

## Description

The Poppet Valve (IL) block models a flow-control valve in an isothermal liquid system. The poppet can either have a cylindrical or ball control member. For ball valves, 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

Poppet Valve Top View

### Cylindrical Stem Poppet Opening Area

The opening area of the valve is calculated as:

`${A}_{open}=\pi h\mathrm{sin}\left(\frac{\theta }{2}\right)\left[{d}_{s}+\frac{h}{2}\mathrm{sin}\left(\theta \right)\right]+{A}_{leak},$`

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.

• ds is the Stem diameter.

• Aleak is the Leakage area.

The opening area is bounded by the maximum displacement hmax:

`${h}_{\mathrm{max}}=\frac{{d}_{s}\left[\sqrt{1+\mathrm{cos}\left(\frac{\theta }{2}\right)}-1\right]}{\mathrm{sin}\left(\theta \right)}.$`

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

`${A}_{open}=\frac{\pi }{4}{d}_{s}^{2}+{A}_{leak}.$`

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:

`${A}_{open,sharp-edged}=\pi {r}_{O}\sqrt{{\left({G}_{sharp}+h\right)}^{2}+{r}_{O}^{2}}\left[1-\frac{{r}_{B}^{2}}{{\left({G}_{sharp}+h\right)}^{2}+{r}_{O}^{2}}\right]+{A}_{leak},$`

where:

• h is the vertical distance between the outer edge of the cylinder and the seat, indicated in the schematic above.

• rO is the seat orifice radius, calculated from the Seat orifice diameter.

• rB is the radius of the ball, calculated from the Ball diameter.

• Gsharp is the geometric parameter: ${G}_{sharp}=\sqrt{{r}_{B}^{2}-{r}_{O}^{2}}.$

• Aleak is the Leakage area.

The opening area is bounded by the maximum displacement hmax:

`${h}_{\mathrm{max}}=\sqrt{\frac{2{r}_{B}^{2}-{r}_{O}^{2}+{r}_{O}\sqrt{{r}_{O}^{2}+4{r}_{B}^{2}}}{2}}-{G}_{sharp}.$`

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

`${A}_{open}=\frac{\pi }{4}{d}_{O}^{2}+{A}_{leak}.$`

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:

`${A}_{open,conical}={G}_{conical}h+\frac{\pi }{2}\mathrm{sin}\left(\theta \right)\mathrm{sin}\left(\frac{\theta }{2}\right){h}^{2}+{A}_{leak},$`

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.

• Gconical is the geometric parameter: ${G}_{conical}=\pi {r}_{B}\mathrm{sin}\left(\theta \right),$ where rB is the ball radius.

• Aleak is the Leakage area.

The opening area is bounded by the maximum displacement hmax:

`${h}_{\mathrm{max}}=\frac{\sqrt{{r}_{B}^{2}+\frac{{r}_{O}^{2}}{\mathrm{cos}\left(\frac{\theta }{2}\right)}}-{r}_{B}}{\mathrm{sin}\left(\frac{\theta }{2}\right)}.$`

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

`${A}_{open}=\frac{\pi }{4}{d}_{O}^{2}+{A}_{leak}.$`

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.

### Mass Flow Rate Equation

Mass is conserved through the valve:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0.$`

The mass flow rate through the valve is calculated as:

`$\stackrel{˙}{m}=\frac{{C}_{d}{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$`

where:

• Cd is the Discharge coefficient.

• Avalve is the current valve open area.

• Aport is the Cross-sectional area at ports A and B.

• $\overline{\rho }$ is the average fluid density.

• Δp is the valve pressure difference pApB.

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

`$\Delta {p}_{crit}=\frac{\pi \overline{\rho }}{8{A}_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$`

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

`$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}.$`

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, set the Pressure recovery to `Off`. In this case, PRloss is 1.

## Ports

### Conserving

expand all

Liquid entry or exit port to the valve.

Liquid entry or exit port to the valve.

### Input

expand all

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

## Parameters

expand all

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

Geometry of valve seat. This parameter is used for calculating the open area between the poppet and seat.

#### Dependencies

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

Diameter of the ball control member.

#### Dependencies

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

Seat orifice diameter.

#### Dependencies

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

Diameter of the cylindrical stem.

#### Dependencies

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

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 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 .

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.

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.

Correction factor that accounts for discharge losses in theoretical flows.

Upper Reynolds number limit for laminar flow through the orifice.

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.