Poppet Valve (TL)

Poppet flow control valve in a thermal liquid network

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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_cr is the value of the Critical Reynolds number parameter.

  • μ_Avg is the average fluid dynamic viscosity.

• 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_leak is the leakage area.

The maximum displacement, h_max, is

$$h_{\max }=\sqrt{\frac{2r_p^2-r_o^2+r_o\sqrt{r_o^2+4r_p^2}}{2}}-\sqrt{r_p^2-r_o^2}.$$

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

$$A=\pi r_p\sin \left(\theta \right)h+\frac{\pi }{2}\sin \left(\frac{\theta }{2}\right)\sin \left(\theta \right)h^2+A_{leak}.$$

The maximum displacement, h_max, is:

$$h_{\max }=\frac{\sqrt{r_p^2+\frac{r_o^2}{\cos \left(\frac{\theta }{2}\right)}}-r_p}{\sin \left(\frac{\theta }{2}\right)},$$

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

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

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.

Ports

Conserving

A — Liquid port

thermal liquid

Thermal liquid conserving port associated with valve inlet A.

B — Liquid port

thermal liquid

Thermal liquid conserving port associated with valve inlet B.

Input

S — Poppet displacement, m

physical signal

Physical signal port associated with the displacement of the poppet, in m.

Parameters

Valve seat specification — Geometry of valve seat

Sharp-edged (default) | Conical

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

Cone angle — Angle of seat opening

120 deg (default) | positive scalar

Angle of the seat opening.

Dependencies

To enable this parameter, set Valve seat specification to Conical.

Ball diameter — Poppet diameter

0.01 m (default) | positive scalar

Diameter of the poppet.

Orifice diameter — Seat orifice diameter

7e-3 m (default) | positive scalar

Seat orifice diameter.

Poppet position when in the seat — Poppet offset

0 m (default) | nonnegative scalar

Poppet offset when valve is shut. A positive, nonzero value indicates a partially open valve. A negative, nonzero value indicates an overlapped valve that remains shut 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 shut position. The block saturates smaller numbers to this value. This parameter contributes to numerical stability by maintaining continuity in the flow.

Smoothing factor — Gap area when in fully closed position

0.01 (default) | 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 the near-open or near-shut positions. Set this value to a nonzero number less than one to increase the stability of your simulation in these regimes.

Cross-sectional area at ports A and B — Area at conserving ports

0.01 m^2 (default) | positive scalar

Area at 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.

Extended Capabilities

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

Version History

Introduced in R2016a