# Poppet Valve (TL)

Poppet flow control valve in a thermal liquid network

**Libraries:**

Simscape /
Fluids /
Thermal Liquid /
Valves & Orifices /
Flow Control Valves

## Description

The Poppet Valve (TL) block represents the flow control
within a thermal liquid network. You can specify the seat geometry as either sharp-edged
or conical. Set the poppet displacement with the physical signal at port
**S**.

### Mass Balance

The mass conservation equation in the valve is

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

where:

$${\dot{m}}_{A}$$ is the mass flow rate into the valve through port

**A**.$${\dot{m}}_{B}$$ is the mass flow rate into the valve through port

**B**.

### Momentum Balance

The pressure differential over the valve is:

$${p}_{A}-{p}_{B}=\frac{\dot{m}\sqrt{{\dot{m}}^{2}+{\dot{m}}_{cr}^{2}}}{2{\rho}_{Avg}{C}_{d}^{2}{S}^{2}}\left[1-{\left(\frac{{S}_{R}}{S}\right)}^{2}\right]P{R}_{Loss},$$

where:

*p*_{A}is the pressure at port**A**.*p*_{B}is the pressure at port**B**.$$\dot{m}$$ is the mass flow rate.

*ρ*_{Avg}is the average liquid density.*C*_{d}is the value of the**Discharge coefficient**parameter.$${\dot{m}}_{cr}$$ is the critical mass flow rate:

$${\dot{m}}_{cr}={\mathrm{Re}}_{cr}{\mu}_{Avg}\sqrt{\frac{\pi}{4}{S}_{R}}.$$

where:

*Re*is the value of the_{cr}**Critical Reynolds number**parameter.*μ*is the average fluid dynamic viscosity._{Avg}

*S*is the value of the**Cross-sectional area at port A and B**parameter.*PR*_{Loss}is the pressure ratio:$$P{R}_{Loss}=\frac{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\left({S}_{R}/S\right)}{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\left({S}_{R}/S\right)}.$$

### Energy Balance

The energy conservation equation in the valve is

$${\varphi}_{A}+{\varphi}_{B}=0,$$

where:

*ϕ*_{A}is the energy flow rate into the valve through port**A**.*ϕ*_{B}is the energy flow rate into the valve through port**B**.

### Opening Area With a Sharp-Edged Seat

When you set **Valve seat specification** to
`Sharp-edged`

, the block calculates the valve opening
area using

$$A=\pi {r}_{o}\left(1-{\left(\frac{{r}_{p}}{{d}_{OB}}\right)}^{2}\right){d}_{OB}(h)+{A}_{leak},$$

where:

*r*_{o}is the valve orifice radius.*r*_{p}is the valve poppet radius.*d*_{OB}(*h*) is the distance between the center of the poppet and the edge of the orifice. This distance is a function of the valve lift,*h*.*A*is the leakage area._{leak}

The maximum displacement, *h*_{max}, is

$${h}_{\mathrm{max}}=\sqrt{\frac{2{r}_{p}^{2}-{r}_{o}^{2}+{r}_{o}\sqrt{{r}_{o}^{2}+4{r}_{p}^{2}}}{2}}-\sqrt{{r}_{p}^{2}-{r}_{o}^{2}}.$$

The figure shows a schematic of a hard-edged seat.

### Opening Area With a Conical Seat

When you set **Valve seat specification** to
`Conical`

, the block calculates the valve opening area
using a geometric relationship, such that

$$A=\pi {r}_{p}\mathrm{sin}\left(\theta \right)h+\frac{\pi}{2}\mathrm{sin}\left(\frac{\theta}{2}\right)\mathrm{sin}\left(\theta \right){h}^{2}+{A}_{leak}.$$

The maximum displacement, *h*_{max}, is:

$${h}_{\mathrm{max}}=\frac{\sqrt{{r}_{p}^{2}+\frac{{r}_{o}^{2}}{\mathrm{cos}\left(\frac{\theta}{2}\right)}}-{r}_{p}}{\mathrm{sin}\left(\frac{\theta}{2}\right)},$$

where *θ* is the **Cone
angle**. The figure shows a schematic of a conical seat.

### Numerically Smoothed Displacement

The block calculates the poppet displacement, *h*, such that

$$h=\{\begin{array}{ll}0,\hfill & \left(S-{S}_{\mathrm{min}}\right)\le 0\hfill \\ {h}_{Max},\hfill & \left(S-{S}_{\mathrm{min}}\right)\ge {h}_{Max}\hfill \\ \left(S-{S}_{\mathrm{min}}\right),\hfill & \text{Else}\hfill \end{array}$$

where:

*S*is the physical signal input.*S*is the_{min}**Poppet position when in the seat**parameter.*h*is the maximum displacement._{Max}

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.

## Ports

### Conserving

### Input

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**