Control valve sizing and rating (fluids.control_valve)¶
This module contains equations for modeling control valves subject to gas or liquid flow.
For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.
Sizing Functions¶
- fluids.control_valve.size_control_valve_l(rho, Psat, Pc, mu, P1, P2, Q, D1=None, D2=None, d=None, FL=0.9, Fd=1, allow_choked=True, allow_laminar=True, full_output=False)[source]¶
Calculates flow coefficient of a control valve passing a liquid according to IEC 60534. Uses a large number of inputs in SI units. Note the return value is not standard SI. All parameters are required. This sizing model does not officially apply to liquid mixtures, slurries, non-Newtonian fluids, or liquid-solid conveyance systems. For details of the calculations, consult [1].
- Parameters
- rho
float
Density of the liquid at the inlet [kg/m^3]
- Psat
float
Saturation pressure of the fluid at inlet temperature [Pa]
- Pc
float
Critical pressure of the fluid [Pa]
- mu
float
Viscosity of the fluid [Pa*s]
- P1
float
Inlet pressure of the fluid before valves and reducers [Pa]
- P2
float
Outlet pressure of the fluid after valves and reducers [Pa]
- Q
float
Volumetric flow rate of the fluid [m^3/s]
- D1
float
,optional
Diameter of the pipe before the valve [m]
- D2
float
,optional
Diameter of the pipe after the valve [m]
- d
float
,optional
Diameter of the valve [m]
- FL
float
,optional
Liquid pressure recovery factor of a control valve without attached fittings (normally 0.8-0.9 at full open and decreasing as opened further to below 0.5; use default very cautiously!) []
- Fd
float
,optional
Valve style modifier (0.1 to 1; varies tremendously depending on the type of valve and position; do not use the default at all!) []
- allow_chokedbool,
optional
Overrides the automatic transition into the choked regime if this is False and returns as if choked flow does not exist
- allow_laminarbool,
optional
Overrides the automatic transition into the laminar regime if this is False and returns as if laminar flow does not exist
- full_outputbool,
optional
If True, returns intermediate calculation values as well as Kv in the form of a dictionary containing ‘Kv’, ‘Rev’, ‘choked’, ‘FL’, ‘FLP’, ‘FR’, ‘FP’, and ‘laminar’. Some may be None if they are not used in the calculation.
- rho
- Returns
- Kv
float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
- Kv
Notes
It is possible to use this model without any diameters specified; in that case, turbulent flow is assumed. Choked flow can still be modeled. This is not recommended. All three diameters need to be None for this to work. FL and Fd are not used by the models when the diameters are not specified.
References
Examples
From [1], matching example 1 for a globe, parabolic plug, flow-to-open valve.
>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-4, ... P1=680E3, P2=220E3, Q=0.1, D1=0.15, D2=0.15, d=0.15, ... FL=0.9, Fd=0.46) 164.9954763704956
From [1], matching example 2 for a ball, segmented ball, flow-to-open valve.
>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-4, ... P1=680E3, P2=220E3, Q=0.1, D1=0.1, D2=0.1, d=0.1, ... FL=0.6, Fd=0.98) 238.05817216710483
- fluids.control_valve.size_control_valve_g(T, MW, mu, gamma, Z, P1, P2, Q, D1=None, D2=None, d=None, FL=0.9, Fd=1, xT=0.7, allow_choked=True, allow_laminar=True, full_output=False)[source]¶
Calculates flow coefficient of a control valve passing a gas according to IEC 60534. Uses a large number of inputs in SI units. Note the return value is not standard SI. All parameters are required. For details of the calculations, consult [1]. Note the inlet gas flow conditions.
- Parameters
- T
float
Temperature of the gas at the inlet [K]
- MW
float
Molecular weight of the gas [g/mol]
- mu
float
Viscosity of the fluid at inlet conditions [Pa*s]
- gamma
float
Specific heat capacity ratio [-]
- Z
float
Compressibility factor at inlet conditions, [-]
- P1
float
Inlet pressure of the gas before valves and reducers [Pa]
- P2
float
Outlet pressure of the gas after valves and reducers [Pa]
- Q
float
Volumetric flow rate of the gas at 273.15 K and 1 atm specifically [m^3/s]
- D1
float
,optional
Diameter of the pipe before the valve [m]
- D2
float
,optional
Diameter of the pipe after the valve [m]
- d
float
,optional
Diameter of the valve [m]
- FL
float
,optional
Liquid pressure recovery factor of a control valve without attached fittings (normally 0.8-0.9 at full open and decreasing as opened further to below 0.5; use default very cautiously!) []
- Fd
float
,optional
Valve style modifier (0.1 to 1; varies tremendously depending on the type of valve and position; do not use the default at all!) []
- xT
float
,optional
Pressure difference ratio factor of a valve without fittings at choked flow (increasing to 0.9 or higher as the valve is closed further and decreasing to 0.1 or lower as the valve is opened further; use default very cautiously!) [-]
- allow_chokedbool,
optional
Overrides the automatic transition into the choked regime if this is False and returns as if choked flow does not exist
- allow_laminarbool,
optional
Overrides the automatic transition into the laminar regime if this is False and returns as if laminar flow does not exist
- full_outputbool,
optional
If True, returns intermediate calculation values as well as Kv in the form of a dictionary containing ‘Kv’, ‘Rev’, ‘choked’, ‘Y’, ‘FR’, ‘FP’, ‘xTP’, and ‘laminar’. Some may be None if they are not used in the calculation.
- T
- Returns
- Kv
float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
- Kv
Notes
It is possible to use this model without any diameters specified; in that case, turbulent flow is assumed. Choked flow can still be modeled. This is not recommended. All three diameters need to be None for this to work. FL and Fd are not used by the models when the diameters are not specified, but xT definitely is used by the model.
When this model does not converge, the result is normally because of the specified delta P being less than that caused by the piping diameter changes.
References
Examples
From [1], matching example 3 for non-choked gas flow with attached fittings and a rotary, eccentric plug, flow-to-open control valve:
>>> size_control_valve_g(T=433., MW=44.01, mu=1.4665E-4, gamma=1.30, ... Z=0.988, P1=680E3, P2=310E3, Q=38/36., D1=0.08, D2=0.1, d=0.05, ... FL=0.85, Fd=0.42, xT=0.60) 72.5866454539105
From [1], roughly matching example 4 for a small flow trim sized tapered needle plug valve. Difference is 3% and explained by the difference in algorithms used.
>>> size_control_valve_g(T=320., MW=39.95, mu=5.625E-5, gamma=1.67, Z=1.0, ... P1=2.8E5, P2=1.3E5, Q=0.46/3600., D1=0.015, D2=0.015, d=0.015, FL=0.98, ... Fd=0.07, xT=0.8) 0.016498765335995726
Intermediary Sizing Calculations¶
- fluids.control_valve.FF_critical_pressure_ratio_l(Psat, Pc)[source]¶
Calculates FF, the liquid critical pressure ratio factor, for use in IEC 60534 liquid valve sizing calculations.
- Parameters
- Returns
- FF
float
Liquid critical pressure ratio factor [-]
- FF
References
- 1
IEC 60534-2-1 / ISA-75.01.01-2007
Examples
From [1], matching example.
>>> FF_critical_pressure_ratio_l(70100.0, 22120000.0) 0.9442375225233299
- fluids.control_valve.is_choked_turbulent_l(dP, P1, Psat, FF, FL=None, FLP=None, FP=None)[source]¶
Calculates if a liquid flow in IEC 60534 calculations is critical or not, for use in IEC 60534 liquid valve sizing calculations. Either FL may be provided or FLP and FP, depending on the calculation process.
- Parameters
- dP
float
Differential pressure across the valve, with reducer/expanders [Pa]
- P1
float
Pressure of the fluid before the valve and reducers/expanders [Pa]
- Psat
float
Saturation pressure of the fluid at inlet temperature [Pa]
- FF
float
Liquid critical pressure ratio factor [-]
- FL
float
,optional
Liquid pressure recovery factor of a control valve without attached fittings [-]
- FLP
float
,optional
Combined liquid pressure recovery factor with piping geometry factor, for a control valve with attached fittings [-]
- FP
float
,optional
Piping geometry factor [-]
- dP
- Returns
- chokedbool
Whether or not the flow is choked [-]
References
- 1
IEC 60534-2-1 / ISA-75.01.01-2007
Examples
>>> is_choked_turbulent_l(460.0, 680.0, 70.1, 0.94, 0.9) False >>> is_choked_turbulent_l(460.0, 680.0, 70.1, 0.94, 0.6) True
- fluids.control_valve.is_choked_turbulent_g(x, Fgamma, xT=None, xTP=None)[source]¶
Calculates if a gas flow in IEC 60534 calculations is critical or not, for use in IEC 60534 gas valve sizing calculations. Either xT or xTP must be provided, depending on the calculation process.
- Parameters
- Returns
- chokedbool
Whether or not the flow is choked [-]
References
- 1
IEC 60534-2-1 / ISA-75.01.01-2007
Examples
Example 3, compressible flow, non-choked with attached fittings:
>>> is_choked_turbulent_g(0.544, 0.929, 0.6) False >>> is_choked_turbulent_g(0.544, 0.929, xTP=0.625) False
- fluids.control_valve.Reynolds_valve(nu, Q, D1, FL, Fd, C)[source]¶
Calculates Reynolds number of a control valve for a liquid or gas flowing through it at a specified Q, for a specified D1, FL, Fd, C, and with kinematic viscosity nu according to IEC 60534 calculations.
- Parameters
- nu
float
Kinematic viscosity, [m^2/s]
- Q
float
Volumetric flow rate of the fluid [m^3/s]
- D1
float
Diameter of the pipe before the valve [m]
- FL
float
,optional
Liquid pressure recovery factor of a control valve without attached fittings []
- Fd
float
Valve style modifier [-]
- C
float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
- nu
- Returns
- Rev
float
Valve reynolds number [-]
- Rev
References
- 1
IEC 60534-2-1 / ISA-75.01.01-2007
Examples
>>> Reynolds_valve(3.26e-07, 360, 150.0, 0.9, 0.46, 165) 2966984.7525455453
- fluids.control_valve.Reynolds_factor(FL, C, d, Rev, full_trim=True)[source]¶
Calculates the Reynolds number factor FR for a valve with a Reynolds number Rev, diameter d, flow coefficient C, liquid pressure recovery factor FL, and with either full or reduced trim, all according to IEC 60534 calculations.
If full trim:
Otherwise :
- Parameters
- FL
float
Liquid pressure recovery factor of a control valve without attached fittings []
- C
float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
- d
float
Diameter of the valve [m]
- Rev
float
Valve reynolds number [-]
- full_trimbool
Whether or not the valve has full trim
- FL
- Returns
- FR
float
Reynolds number factor for laminar or transitional flow []
- FR
References
- 1
IEC 60534-2-1 / ISA-75.01.01-2007
Examples
In Example 4, compressible flow with small flow trim sized for gas flow (Cv in the problem was converted to Kv here to make FR match with N32, N2):
>>> Reynolds_factor(FL=0.98, C=0.015483, d=15., Rev=1202., full_trim=False) 0.7148753122302025
- fluids.control_valve.loss_coefficient_piping(d, D1=None, D2=None)[source]¶
Calculates the sum of loss coefficients from possible inlet/outlet reducers/expanders around a control valve according to IEC 60534 calculations.
- Parameters
- Returns
- loss
float
Sum of the four loss coefficients [-]
- loss
References
- 1
IEC 60534-2-1 / ISA-75.01.01-2007
Examples
In example 3, non-choked compressible flow with fittings:
>>> loss_coefficient_piping(0.05, 0.08, 0.1) 0.6580810546875
- fluids.control_valve.control_valve_choke_P_l(Psat, Pc, FL, P1=None, P2=None, disp=True)[source]¶
Calculates either the upstream or downstream pressure at which choked flow though a liquid control valve occurs, given either a set upstream or downstream pressure. Implements an analytical solution of the needed equations from the full function
size_control_valve_l
. For some pressures, no choked flow is possible; for choked flow to occur the direction if flow must be reversed. If disp is True, an exception will be raised for these conditions.- Parameters
- Psat
float
Saturation pressure of the liquid at inlet temperature [Pa]
- Pc
float
Critical pressure of the liquid [Pa]
- FL
float
,optional
Liquid pressure recovery factor of a control valve without attached fittings [-]
- P1
float
,optional
Absolute pressure upstream of the valve [Pa]
- P2
float
,optional
Absolute pressure downstream of the valve [Pa]
- dispbool,
optional
Whether or not to raise an exception on flow reversal, [-]
- Psat
- Returns
- P_choke
float
Pressure at which a choke occurs in the liquid valve [Pa]
- P_choke
Notes
Extremely cheap to compute.
Examples
>>> control_valve_choke_P_l(69682.89291024722, 22048320.0, 0.6, 680000.0) 458887.5306077305 >>> control_valve_choke_P_l(69682.89291024722, 22048320.0, 0.6, P2=458887.5306077305) 680000.0
- fluids.control_valve.control_valve_choke_P_g(xT, gamma, P1=None, P2=None)[source]¶
Calculates either the upstream or downstream pressure at which choked flow though a gas control valve occurs, given either a set upstream or downstream pressure. Implements an analytical solution of the needed equations from the full function
size_control_valve_g
. A singularity arises as xT goes to 1 and gamma goes to 1.4.- Parameters
- Returns
- P_choke
float
Pressure at which a choke occurs in the gas valve [Pa]
- P_choke
Notes
Extremely cheap to compute.
Examples
>>> control_valve_choke_P_g(1.0, 1.3, 1E5) 7142.857142857143 >>> control_valve_choke_P_g(1.0, 1.3, P2=7142.857142857143) 100000.0
- fluids.control_valve.convert_flow_coefficient(flow_coefficient, old_scale, new_scale)[source]¶
Convert from one flow coefficient scale to another; supports the Kv Cv, and Av scales.
Other scales are Qn and Cg, but clear definitions have yet to be found.
- Parameters
- Returns
- converted_flow_coefficient
float
Flow coefficient converted to the specified scale.
- converted_flow_coefficient
Notes
Qn is a scale based on a flow of air in units of L/minute as air travels through a valve and loses one bar of pressure (initially 7 bar absolute, to 6 bar absolute). No consistent conversion factors have been found and those from theory do not match what have been found. Some uses of Qn use its flow rate as in normal (STP reference conditions) flow rate of air; others use something like the 7 bar absolute condition.
Examples
>>> convert_flow_coefficient(10, 'Kv', 'Av') 0.0002776532068951358
- fluids.control_valve.cavitation_index(P1, P2, Psat)[source]¶
Calculates the cavitation index of a valve with upstream and downstream absolute pressures P1 and P2 for a fluid with a vapor pressure Psat.
- Parameters
- Returns
- sigma
float
Cavitation index of the valve [-]
- sigma
Notes
Larger values are safer. Models for adjusting cavitation indexes provided by the manufacturer to the user’s conditions are available, making use of scaling the pressure differences and size differences.
Values can be calculated for incipient cavitation, constant cavitation, maximum vibration cavitation, incipient damage, and choking cavitation.
Has also been defined as:
Another definition and notation series is:
References
- 1
ISA. “RP75.23 Considerations for Evaluating Control Valve Cavitation.” 1995.
Examples
>>> cavitation_index(1E6, 8E5, 2E5) 4.0
Representative Control Valve Curves¶
- fluids.control_valve.Cv_char_linear(opening)¶
- fluids.control_valve.Cv_char_quick_opening(opening)¶
- fluids.control_valve.Cv_char_equal_percentage(opening)¶
Noise Generated by Control Valves¶
- fluids.control_valve.control_valve_noise_l_2015(m, P1, P2, Psat, rho, c, Kv, d, Di, FL, Fd, t_pipe, rho_pipe=7800.0, c_pipe=5000.0, rho_air=1.2, c_air=343.0, xFz=None, An=- 4.6)[source]¶
Calculates the sound made by a liquid flowing through a control valve according to the standard IEC 60534-8-4 (2015) [1].
- Parameters
- m
float
Mass flow rate of liquid through the control valve, [kg/s]
- P1
float
Inlet pressure of the fluid before valves and reducers [Pa]
- P2
float
Outlet pressure of the fluid after valves and reducers [Pa]
- Psat
float
Saturation pressure of the fluid at inlet temperature [Pa]
- rho
float
Density of the liquid at the inlet [kg/m^3]
- c
float
Speed of sound of the liquid at the inlet conditions [m/s]
- Kv
float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
- d
float
Diameter of the valve [m]
- Di
float
Internal diameter of the pipe before and after the valve [m]
- FL
float
,optional
Liquid pressure recovery factor of a control valve without attached fittings (normally 0.8-0.9 at full open and decreasing as opened further to below 0.5) [-]
- Fd
float
,optional
Valve style modifier [-]
- t_pipe
float
Wall thickness of the pipe after the valve, [m]
- rho_pipe
float
,optional
Density of the pipe wall material at flowing conditions, [kg/m^3]
- c_pipe
float
,optional
Speed of sound of the pipe wall material at flowing conditions, [m/s]
- rho_air
float
,optional
Density of the air surrounding the valve and pipe wall, [kg/m^3]
- c_air
float
,optional
Speed of sound of the air surrounding the valve and pipe wall, [m/s]
- xFz
float
,optional
If specified, this value xFz is used instead of estimated; the calculation is sensitive to this value, [-]
- An
float
,optional
Valve correction factor for acoustic efficiency
- m
- Returns
- LpAe1m
float
A weighted sound pressure level 1 m from the pipe wall, 1 m distance dowstream of the valve (at reference sound pressure level 2E-5), [dB]
- LpAe1m
Notes
For formulas see [1]. This takes on the order of 100 us to compute. This model can also tell if noise is being produced in a valve just due to turbulent flow, or cavitation. For values of An, see [1]; it is normally -4.6 for global valves, -4.3 for butterfly valves, and -4.0 for expanders.
This model was checked against three examples in [1]; they match to all given decimals.
A formula is given in [1] for multihole trim valves to estimate xFz as well; this is not implemented here and xFz must be calculated by the user separately. The formula is
Where N0 is the number of open channels and dH is the multihole trim hole diameter.
References
- 1(1,2,3,4,5)
IEC 60534-8-4 : Industrial-Process Control Valves - Part 8-4: Noise Considerations - Prediction of Noise Generated by Hydrodynamic Flow. (2015)
Examples
>>> control_valve_noise_l_2015(m=40, P1=1E6, P2=6.5E5, Psat=2.32E3, ... rho=997, c=1400, Kv=77.848, d=0.1, Di=0.1071, FL=0.92, Fd=0.42, ... t_pipe=0.0036, rho_pipe=7800.0, c_pipe=5000.0,rho_air=1.293, ... c_air=343.0, An=-4.6) 81.58200097996
- fluids.control_valve.control_valve_noise_g_2011(m, P1, P2, T1, rho, gamma, MW, Kv, d, Di, t_pipe, Fd, FL, FLP=None, FP=None, rho_pipe=7800.0, c_pipe=5000.0, P_air=101325.0, rho_air=1.2, c_air=343.0, An=- 3.8, Stp=0.2, T2=None, beta=0.93)[source]¶
Calculates the sound made by a gas flowing through a control valve according to the standard IEC 60534-8-3 (2011) [1].
- Parameters
- m
float
Mass flow rate of gas through the control valve, [kg/s]
- P1
float
Inlet pressure of the gas before valves and reducers [Pa]
- P2
float
Outlet pressure of the gas after valves and reducers [Pa]
- T1
float
Inlet gas temperature, [K]
- rho
float
Density of the gas at the inlet [kg/m^3]
- gamma
float
Specific heat capacity ratio [-]
- MW
float
Molecular weight of the gas [g/mol]
- Kv
float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
- d
float
Diameter of the valve [m]
- Di
float
Internal diameter of the pipe before and after the valve [m]
- t_pipe
float
Wall thickness of the pipe after the valve, [m]
- Fd
float
Valve style modifier (0.1 to 1; varies tremendously depending on the type of valve and position; do not use the default at all!) [-]
- FL
float
Liquid pressure recovery factor of a control valve without attached fittings (normally 0.8-0.9 at full open and decreasing as opened further to below 0.5; use default very cautiously!) [-]
- FLP
float
,optional
Combined liquid pressure recovery factor with piping geometry factor, for a control valve with attached fittings [-]
- FP
float
,optional
Piping geometry factor [-]
- rho_pipe
float
,optional
Density of the pipe wall material at flowing conditions, [kg/m^3]
- c_pipe
float
,optional
Speed of sound of the pipe wall material at flowing conditions, [m/s]
- P_air
float
,optional
Pressure of the air surrounding the valve and pipe wall, [Pa]
- rho_air
float
,optional
Density of the air surrounding the valve and pipe wall, [kg/m^3]
- c_air
float
,optional
Speed of sound of the air surrounding the valve and pipe wall, [m/s]
- An
float
,optional
Valve correction factor for acoustic efficiency, [-]
- Stp
float
,optional
Strouhal number at the peak fp; between 0.1 and 0.3 typically, [-]
- T2
float
,optional
Outlet gas temperature; assumed T1 if not provided (a PH flash should be used to obtain this if possible), [K]
- beta
float
,optional
Valve outlet / expander inlet contraction coefficient, [-]
- m
- Returns
- LpAe1m
float
A-weighted sound pressure level 1 m from the pipe wall, 1 m distance dowstream of the valve (at reference sound pressure level 2E-5), [dB]
- LpAe1m
Notes
For formulas see [1]. This takes on the order of 100 us to compute. For values of An, see [1].
This model was checked against six examples in [1]; they match to all given decimals.
Several additional formulas are given for multihole trim valves, control valves with two or more fixed area stages, and multipath, multistage trim valves.
References
- 1(1,2,3,4)
IEC 60534-8-3 : Industrial-Process Control Valves - Part 8-3: Noise Considerations - Control Valve Aerodynamic Noise Prediction Method.”
Examples
>>> control_valve_noise_g_2011(m=2.22, P1=1E6, P2=7.2E5, T1=450, rho=5.3, ... gamma=1.22, MW=19.8, Kv=77.85, d=0.1, Di=0.2031, FL=None, FLP=0.792, ... FP=0.98, Fd=0.296, t_pipe=0.008, rho_pipe=8000.0, c_pipe=5000.0, ... rho_air=1.293, c_air=343.0, An=-3.8, Stp=0.2) 91.67702674629604