Documentation

Flow Coefficient Parameterized Valve (TL)

Generic valve model with flow coefficient parameterization

Library

Thermal Liquid/Valves

Description

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:

  • Cv — Valve flow coefficient in imperial units of USG/min. Cv data is often provided at a temperature of 60 °F and a valve pressure differential of 1 lb/in^2 [1].

  • Kv — Valve flow coefficient in metric units of m^3/h. Kv 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.

Valve Opening Characteristics

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:

    f(L)=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.

  • Quick opening — Model the valve open fraction f(L) as a power function of the lift input signal L:

    f(L)=L1/α

    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.

  • Equal percentage — Model the valve open fraction f(L) as an exponential function of the valve lift input signal:

    f(L)=RL1

    The parameter 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.

Mass Balance

The mass conservation equation in the valve is

m˙A+m˙B=0,

where:

  • m˙A is the mass flow rate into the valve through port A.

  • m˙B is the mass flow rate into the valve through port B.

Momentum Balance

The momentum conservation equation in the valve is

pApB=m˙m˙2+m˙2crρAvgS2,

where:

  • pA is the pressure at port A.

  • pB is the pressure at port B.

  • ρAvg is the average fluid density.

  • S is the valve opening area.

  • m˙cr is the critical mass flow rate.

The valve opening area is

S={SMaxf(L),SMaxf(L)>SMinSMin,Else

where:

  • SMax is the maximum valve opening area.

  • SMin is the minimum valve opening area.

  • f(L) is the inherent valve flow characteristic.

The critical mass flow rate is

m˙cr=RecrμAvgπ4S,

where:

  • Recr is the critical Reynolds number at which the flow regime transitions between laminar and turbulent.

  • μAvg is the average dynamic viscosity.

Energy Balance

The energy conservation equation in the valve is

ϕA+ϕB=0,

where:

  • ϕA is the energy flow rate into the valve through port A.

  • ϕB is the energy flow rate into the valve through port B.

Parameters

Parameters Tab

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)=L1/α

  • Equal percentage — Models the valve open fraction f(L) as an exponential function of the valve lift input signal:

    f(L)=RL1

Exponent number

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

f(L)=L1/α

The exponent number determines how rapidly the valve open fraction approaches its maximum value. This parameter is active only when the 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:

f(L)=RL1

The rangeability parameter determines the minimum valve opening fraction, a number generally different from zero. This parameter is active only when the 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.

Variables Tab

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.

Ports

  • 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

References

[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.

Introduced in R2016a

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