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# -*- coding: utf-8 -*- Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.'''
#N9 = 2.60E1 # m^3/hr kPa K at 15 deg C #N22 = 1.84E1 # m^3/hr kPa K at 15 deg C
r'''Calculates the cavitation index of a valve with upstream and downstream absolute pressures `P1` and `P2` for a fluid with a vapor pressure `Psat`.
.. math:: \sigma = \frac{P_1 - P_{sat}}{P_1 - P_2}
Parameters ---------- P1 : float Absolute pressure upstream of the valve [Pa] P2 : float Absolute pressure downstream of the valve [Pa] Psat : float Saturation pressure of the liquid at inlet temperature [Pa]
Returns ------- sigma : float Cavitation index of the valve [-]
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:
.. math:: \sigma = \frac{P_2 - P_{sat}}{P_1 - P_2}
Another definition and notation series is:
.. math:: K = xF = \frac{1}{\sigma} = \frac{P_1 - P_2}{P_1 - P_{sat}}
Examples -------- >>> cavitation_index(1E6, 8E5, 2E5) 4.0
References ---------- .. [1] ISA. "RP75.23 Considerations for Evaluating Control Valve Cavitation." 1995. '''
r'''Calculates FF, the liquid critical pressure ratio factor, for use in IEC 60534 liquid valve sizing calculations.
.. math:: F_F = 0.96 - 0.28\sqrt{\frac{P_{sat}}{P_c}}
Parameters ---------- Psat : float Saturation pressure of the liquid at inlet temperature [Pa] Pc : float Critical pressure of the liquid [Pa]
Returns ------- FF : float Liquid critical pressure ratio factor [-]
Examples -------- From [1]_, matching example.
>>> FF_critical_pressure_ratio_l(70100.0, 22120000.0) 0.9442375225233299
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 '''
r'''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.
.. math:: \Delta P > F_L^2(P_1 - F_F P_{sat})
\Delta P >= \left(\frac{F_{LP}}{F_P}\right)^2(P_1 - F_F P_{sat})
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 []
Returns ------- choked : bool Whether or not the flow is choked [-]
Examples -------- >>> is_choked_turbulent_l(460.0, 680.0, 70.1, 0.9442375225233299, 0.9) False >>> is_choked_turbulent_l(460.0, 680.0, 70.1, 0.9442375225233299, 0.6) True
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 ''' else:
r'''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.
.. math:: x \ge F_\gamma x_T
x \ge F_\gamma x_{TP}
Parameters ---------- x : float Differential pressure over inlet pressure, [-] Fgamma : float Specific heat ratio factor [-] xT : float, optional Pressure difference ratio factor of a valve without fittings at choked flow [-] xTP : float Pressure difference ratio factor of a valve with fittings at choked flow [-]
Returns ------- choked : bool Whether or not the flow is choked [-]
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
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 ''' else:
r'''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.
.. math:: Re_v = \frac{N_4 F_d Q}{\nu \sqrt{C F_L}}\left(\frac{F_L^2 C^2} {N_2D^4} +1\right)^{1/4}
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 Kv flow coefficient [m^3/hr at a dP of 1 bar]
Returns ------- Rev : float Valve reynolds number [-]
Examples -------- >>> Reynolds_valve(3.26e-07, 360, 150.0, 0.9, 0.46, 165) 2966984.7525455453
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 '''
r'''Calculates the sum of loss coefficients from possible inlet/outlet reducers/expanders around a control valve according to IEC 60534 calculations.
.. math:: \Sigma \xi = \xi_1 + \xi_2 + \xi_{B1} - \xi_{B2}
\xi_1 = 0.5\left[1 -\left(\frac{d}{D_1}\right)^2\right]^2
\xi_2 = 1.0\left[1 -\left(\frac{d}{D_2}\right)^2\right]^2
\xi_{B1} = 1 - \left(\frac{d}{D_1}\right)^4
\xi_{B2} = 1 - \left(\frac{d}{D_2}\right)^4
Parameters ---------- d : float Diameter of the valve [m] D1 : float Diameter of the pipe before the valve [m] D2 : float Diameter of the pipe after the valve [m]
Returns ------- loss : float Sum of the four loss coefficients [-]
Examples -------- In example 3, non-choked compressible flow with fittings:
>>> loss_coefficient_piping(0.05, 0.08, 0.1) 0.6580810546875
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 '''
r'''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:
.. math:: F_{R,1a} = 1 + \left(\frac{0.33F_L^{0.5}}{n_1^{0.25}}\right)\log_{10} \left(\frac{Re_v}{10000}\right)
F_{R,2} = \min(\frac{0.026}{F_L}\sqrt{n_1 Re_v},\; 1)
n_1 = \frac{N_2}{\left(\frac{C}{d^2}\right)^2}
F_R = F_{R,2} \text{ if Rev < 10 else } \min(F_{R,1a}, F_{R,2})
Otherwise :
.. math:: F_{R,3a} = 1 + \left(\frac{0.33F_L^{0.5}}{n_2^{0.25}}\right)\log_{10} \left(\frac{Re_v}{10000}\right)
F_{R,4} = \frac{0.026}{F_L}\sqrt{n_2 Re_v}
n_2 = 1 + N_{32}\left(\frac{C}{d}\right)^{2/3}
F_R = F_{R,4} \text{ if Rev < 10 else } \min(F_{R,3a}, F_{R,4})
Parameters ---------- FL : float Liquid pressure recovery factor of a control valve without attached fittings [] C : float Kv flow coefficient [m^3/hr at a dP of 1 bar] d : float Diameter of the valve [m] Rev : float Valve reynolds number [-] full_trim : bool Whether or not the valve has full trim
Returns ------- FR : float Reynolds number factor for laminar or transitional flow []
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
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 ''' else: else: else:
r'''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 Diameter of the pipe before the valve [m] D2 : float Diameter of the pipe after the valve [m] d : float Diameter of the valve [m] FL : float Liquid pressure recovery factor of a control valve without attached fittings [] Fd : float Valve style modifier []
Returns ------- C : float Kv flow coefficient [m^3/hr at a dP of 1 bar]
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
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 ''' # Pa to kPa, according to constants in standard # m to mm, according to constants in standard
# Choked flow, equation 3 else: # non-choked flow, eq 1 # liquid, using Fp and FLP # Choked flow with piping, equation 4 else: # Non-Choked flow with piping, equation 4
# Laminar else: Ci = iterate_piping_laminar(Ci) # pragma: no cover
#print [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=0.09, d=0.08, FL=0.9, Fd=0.46)] #print [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)] #print [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=0.95, FL=0.6, Fd=0.98)] #print [size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-2, P1=680E3, P2=220E3, Q=0.001, D1=0.01, D2=0.01, d=0.01, FL=0.6, Fd=0.98)]
r'''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 Diameter of the pipe before the valve [m] D2 : float Diameter of the pipe after the valve [m] d : float Diameter of the valve [m] FL : float Liquid pressure recovery factor of a control valve without attached fittings [] Fd : float Valve style modifier [] xT : float Pressure difference ratio factor of a valve without fittings at choked flow [-]
Returns ------- C : float Kv flow coefficient [m^3/hr at a dP of 1 bar]
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) 72.58664545391052
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
References ---------- .. [1] IEC 60534-2-1 / ISA-75.01.01-2007 ''' # Pa to kPa, according to constants in standard # m to mm, according to constants in standard # Convert dynamic viscosity to kinematic viscosity
# Choked, and flow coefficient from eq 14a else: # Non-choked, and flow coefficient from eq 8a
# gas, using xTP and FLP # Choked flow with piping, equation 17a else: # Non-choked flow with piping, equation 11a # Laminar; else:
#print [size_control_valve_g(T=433., MW=44.01, mu=1.4665E-4, gamma=1.30, Z=0.988, P1=680E3, # P2=30E3, Q=38/36., D1=0.08, D2=0.1, d=0.05, FL=0.85, Fd=0.42, xT=0.60)] #print [size_control_valve_g(T=320., MW=39.95, mu=5.625E-5, gamma=1.67, Z=1.0, P1=2.8E5, # P2=2.7E5, Q=0.1/3600., D1=0.015, D2=0.015, d=0.001, FL=0.98, Fd=0.07, xT=0.8)] |