Poppet Valve (IL)

Poppet valve in an isothermal liquid network

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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:

$$A_{open}=\pi h\sin \left(\frac{\theta }{2}\right)\left[d_s+\frac{h}{2}\sin \left(\theta \right)\right]+A_{leak},$$

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.

• d_s is the Stem diameter.

• A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$$h_{\max }=\frac{d_s\left[\sqrt{1+\cos \left(\frac{\theta }{2}\right)}-1\right]}{\sin \left(\theta \right)}.$$

For any stem displacement larger than h_max, A_open 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.

• 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: $$G_{sharp}=\sqrt{r_B^2-r_O^2}.$$

• A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$$h_{\max }=\sqrt{\frac{2r_B^2-r_O^2+r_O\sqrt{r_O^2+4r_B^2}}{2}}-G_{sharp}.$$

For any ball displacement larger than h_max, A_open 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:

$$A_{open,conical}=G_{conical}h+\frac{\pi }{2}\sin \left(\theta \right)\sin \left(\frac{\theta }{2}\right)h^2+A_{leak},$$

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.

• G_conical is the geometric parameter: $$G_{conical}=\pi r_B\sin \left(\theta \right),$$ where r_B is the ball radius.

• A_leak is the Leakage area.

The opening area is bounded by the maximum displacement h_max:

$$h_{\max }=\frac{\sqrt{r_B^2+\frac{r_O^2}{\cos \left(\frac{\theta }{2}\right)}}-r_B}{\sin \left(\frac{\theta }{2}\right)}.$$

For any ball displacement larger than h_max, A_open 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.

Numerically-Smoothed Displacement

At the extremes of the orifice opening range, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. When the smoothing factor is nonzero, a smoothing function is applied to every calculated displacement, but primarily influences the simulation at the extremes of this range.

The normalized orifice opening is:

$$\widehat{h}=\frac{h}{h_{\max }}.$$

The Smoothing factor, s, is applied to the normalized opening:

$${\widehat{h}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{h}}_{}^2+{\left(\frac{s}{4}\right)}^2}-\frac{1}{2}\sqrt{{\left(\widehat{h}-1\right)}^2+{\left(\frac{s}{4}\right)}^2}.$$

The smoothed opening is:

$$h_{smoothed}={\widehat{h}}_{smoothed}{h}_{\max }.$$

This smoothed opening is used in the valve opening area, either A_open,conical or A_{open,sharp-edged}.

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:

$$\dot{m}=\frac{C_d{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\right)}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where:

• 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.

• $$\overline{\rho }$$ 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:

$$\Delta p_{crit}=\frac{\pi \overline{\rho }}{8A_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{C_d}\right)}^2.$$

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PR_loss 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, PR_loss is 1.

Ports

Conserving

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

S — Stem displacement, m

physical signal

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

Parameters

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. 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.

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.

Version History

Introduced in R2020a