Generic valve model with flow coefficient parameterization

Thermal Liquid/Valves

The Flow Coefficient Parameterized Valve (TL) block models a generic valve using a parameterization based on the valve flow coefficient, a constant relating the flow rate to the pressure drop. The block accepts the flow coefficient in metric units or imperial units:

*C*_{v}— Valve flow coefficient in imperial units of USG/min.*C*_{v}data is often provided at a temperature of 60 °F and a valve pressure differential of 1 lb/in^2 [1].*K*_{v}— Valve flow coefficient in metric units of m^3/h.*K*_{v}data is often provided at a temperature at 5–30 °C and a valve pressure differential of 1 bar [2].

The physical signal L sets the valve opening fraction as a numerical value from 0 to 1. A value of 0 corresponds to a fully closed valve and leakage flow. A value of 1 corresponds to a fully open valve and maximum flow. The input signal saturates at these values.

At valve opening fractions between 0 and 1, the opening area depends on the valve opening parameterization selected in the block dialog box. The block provides three parameterizations:

`Linear`

— Model the valve open fraction*f*(*L*) as a linear function of the lift input signal L:This behavior is suitable at constant pressure drops in steady-state systems. The figure shows the relationship between the valve flow coefficient, expressed as a fraction of the maximum flow coefficient, and the valve lift input signal.$$f(L)=L$$

`Quick opening`

— Model the valve open fraction*f*(*L*) as a power function of the lift input signal L:The parameter α is an exponent number that you specify. This behavior is suitable for pressure-relief valves that must open quickly from a fully closed state. The figure shows the relationship between the valve flow coefficient, expressed as a fraction of the maximum flow coefficient, and the valve lift input signal.$$f(L)={L}^{1/\alpha}$$

`Equal percentage`

— Model the valve open fraction*f*(*L*) as an exponential function of the valve lift input signal:The parameter$$f(L)={R}^{L-1}$$

*R*is the valve rangeability—the ratio of the maximum and minimum valve flow rates. The figure shows the relationship between the valve flow coefficient, expressed as a fraction of the maximum flow coefficient, and the valve lift input signal.

The mass conservation equation in the valve is

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

$${\dot{m}}_{A}$$ 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.

The momentum conservation equation in the valve is

$${p}_{A}-{p}_{B}=\frac{\dot{m}\sqrt{{\dot{m}}^{2}+{\dot{m}}^{2}{}_{cr}}}{{\rho}_{Avg}{S}^{2}},$$

*p*_{A}is the pressure at port A.*p*_{B}is the pressure at port B.*ρ*_{Avg}is the average fluid density.*S*is the valve opening area.$${\dot{m}}_{cr}$$ is the critical mass flow rate.

The valve opening area is

$$S=\{\begin{array}{ll}{S}_{Max}f(L),\hfill & {S}_{Max}f(L)>{S}_{Min}\hfill \\ {S}_{Min},\hfill & \text{Else}\hfill \end{array}$$

*S*_{Max}is the maximum valve opening area.*S*_{Min}is the minimum valve opening area.*f*(*L*) is the inherent valve flow characteristic.

The critical mass flow rate is

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

*Re*_{cr}is the critical Reynolds number at which the flow regime transitions between laminar and turbulent.*μ*_{Avg}is the average dynamic viscosity.

The energy conservation equation in the valve is

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

*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.

**Flow coefficient specification**Flow coefficient to use in the block calculations. Options include Cv, defined in imperial units, and Kv, defined in metric units. The default setting is

`Cv coefficient (USG/min)`

.**Cv coefficient at maximum flow**Valve flow coefficient in the fully open position, specified in imperial units. The default value is

`1`

. This parameter is active only when the**Flow coefficient specification**parameter is set to`Cv coefficient (USG/min)`

.**Kv coefficient at maximum flow**Valve flow coefficient in the fully open position, specified in metric units. The default value is

`1`

. This parameter is active only when the**Flow coefficient specification**parameter is set to`Kv coefficient (m^3/h)`

.**Cv coefficient at minimum flow**Valve flow coefficient in the fully closed position, specified in imperial units. The default value is

`1e-4`

. This parameter is active only when the**Flow coefficient specification**parameter is set to`Cv coefficient (USG/min)`

.**Kv coefficient at minimum flow**Valve flow coefficient in the fully closed position, specified in metric units. The default value is

`1e-4`

. This parameter is active only when the**Flow coefficient specification**parameter is set to`Kv coefficient (m^3/h)`

.**Valve opening characteristics**Valve opening response to the lift input signal specified through port L. The block provides three valve opening models:

`Linear`

— Models the valve open fraction*f*(*L*) as a linear function of the lift input signal L:$$f(L)=L$$

`Quick opening`

— Models the valve open fraction*f*(*L*) as a power function of the lift input signal L:$$f(L)={L}^{1/\alpha}$$

`Equal percentage`

— Models the valve open fraction*f*(*L*) as an exponential function of the valve lift input signal:$$f(L)={R}^{L-1}$$

**Exponent number**Parameter α in the power expression of the quick opening valve model:

The exponent number determines how rapidly the valve open fraction approaches its maximum value. This parameter is active only when the$$f(L)={L}^{1/\alpha}$$

**Valve opening characteristics**parameter is set to`Quick opening`

. The exponent number must be greater than zero. The default value is`2`

.**Valve rangeability**Parameter R in the exponential expression of the equal-percentages valve model:

The rangeability parameter determines the minimum valve opening fraction, a number generally different from zero. This parameter is active only when the$$f(L)={R}^{L-1}$$

**Valve opening characteristics**parameter is set to`Equal-percentages`

. Typical values range from 20 to 50. The default value is`50`

.

**Cross-sectional area at ports A and B**Area normal to the direction of flow at inlets A and B. This area is assumed the same for the two inlets. The default value is

`0.01`

m^2.**Characteristic longitudinal length**Distance traversed by the fluid between inlets A and B. The default value is

`0.1`

m^2.**Critical Reynolds number**Reynolds number at which flow transitions between laminar and turbulent regimes. Flow is laminar below this number and turbulent above it. The default value is

`12`

.

**Mass flow rate into port A**Mass flow rate into the component through port

**A**at the start of simulation. The default value is`1 kg/s`

.

A — Thermal liquid conserving port representing valve inlet A

B — Thermal liquid conserving port representing valve inlet B

L — Physical signal input port for the valve opening control signal

[1] *Control Valve Handbook*. 4th ed.
Marshalltown, IA: Fisher Controls International. 2005.

[2] *Flow of Fluids through Valves, Fittings and
Pipe*. Stamford, CT: Crane, 2010.

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