Source code for ht.core

# -*- coding: utf-8 -*-
'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2016, 2017, 2018 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.'''

from __future__ import division
from math import log
from fluids.numerics import i1, i0, k1, k0

__all__ =['LMTD', 'wall_factor', 'is_heating_property',
'is_heating_temperature', 'wall_factor_fd', 'wall_factor_Nu',
'Kays_Crawford_turbulent_gas_Nu',
'Kays_Crawford_turbulent_gas_fd',
'Kays_Crawford_turbulent_liquid_Nu',
'Kays_Crawford_turbulent_liquid_fd',
'Kays_Crawford_laminar_gas_Nu',
'Kays_Crawford_laminar_gas_fd',
'Kays_Crawford_laminar_liquid_fd',
'Kays_Crawford_laminar_liquid_Nu', 'fin_efficiency_Kern_Kraus',
'countercurrent_hx_temperature_check']

[docs]def LMTD(Thi, Tho, Tci, Tco, counterflow=True): r'''Returns the log-mean temperature difference of an ideal counterflow or co-current heat exchanger. .. math:: \Delta T_{LMTD}=\frac{\Delta T_1-\Delta T_2}{\ln(\Delta T_1/\Delta T_2)} .. math:: \text{For countercurrent: } \\ \Delta T_1=T_{h,i}-T_{c,o}\\ \Delta T_2=T_{h,o}-T_{c,i} .. math:: \text{Parallel Flow Only:} \\ {\Delta T_1=T_{h,i}-T_{c,i}}\\ {\Delta T_2=T_{h,o}-T_{c,o}} Parameters ---------- Thi : float Inlet temperature of hot fluid, [K] Tho : float Outlet temperature of hot fluid, [K] Tci : float Inlet temperature of cold fluid, [K] Tco : float Outlet temperature of cold fluid, [K] counterflow : bool, optional Whether the exchanger is counterflow or co-current Returns ------- LMTD : float Log-mean temperature difference [K] Notes ----- Any consistent set of units produces a consistent output. For the case where the temperature difference is the same in counterflow, the arithmeric mean difference (either difference in that case) is the correct result following evaluation of the limit. For the same problem with the co-current case, the limit evaluates to a temperature difference of zero. Examples -------- Example 11.1 in [1]_. >>> LMTD(100., 60., 30., 40.2) 43.200409294131525 >>> LMTD(100., 60., 30., 40.2, counterflow=False) 39.75251118049003 >>> LMTD(100., 60., 20., 60) 40.0 >>> LMTD(100., 60., 20., 60, counterflow=False) 0.0 References ---------- .. [1] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011. ''' if counterflow: dTF1 = Thi-Tco dTF2 = Tho-Tci else: dTF1 = Thi-Tci dTF2 = Tho-Tco ratio = dTF2/dTF1 if not counterflow and (ratio <= 0.0 or ratio == 1.0): return 0.0 elif counterflow and (ratio <= 0.0 or ratio == 1.0): return dTF1 else: return (dTF2 - dTF1)/log(dTF2/dTF1)
[docs]def countercurrent_hx_temperature_check(T0i, T0o, T1i, T1o): r'''Perform a check on two sets of temperatures that could represent a countercurrent heat exchanger, and return whether they are possible or not. Parameters ---------- T0i : float Inlet temperature of one fluid, [K] T0o : float Outlet temperature of one fluid, [K] T1i : float Inlet temperature of another fluid, [K] T1o : float Outlet temperature of another fluid, [K] Returns ------- plausible : bool Whether the exchange is possilble, [-] Notes ----- Examples -------- ''' if T0i > T1i: Thi, Tho = T0i, T0o Tci, Tco = T1i, T1o else: Thi, Tho = T1i, T1o Tci, Tco = T0i, T0o if Thi < Tho: return False if Tci > Tco: return False return True
[docs]def is_heating_temperature(T, T_wall): r'''Checks whether or not a fluid side is being heated or cooled, from the temperature of the wall and the bulk temperature. Returns True for heating the bulk fluid, and False for cooling the bulk fluid. Parameters ---------- T : float Temperature of flowing fluid away from the heat transfer surface, [K] T_wall : float Temperature of the fluid at the wall, [K] Returns ------- is_heating : bool Whether or not the flow is being heated up by the wall, [-] Examples -------- >>> is_heating_temperature(298.15, 350) True ''' return T_wall > T
[docs]def is_heating_property(prop, prop_wall): r'''Checks whether or not a fluid side is being heated or cooled, from a property of the fluid at the wall and the bulk temperature. Returns True for heating the bulk fluid, and False for cooling the bulk fluid. Parameters ---------- prop : float Viscosity (or Prandtl number) of flowing fluid away from the heat transfer surface, [Pa*s] prop_wall : float Viscosity (or Prandtl number) of the fluid at the wall, [Pa*s] Returns ------- is_heating : bool Whether or not the flow is being heated up by the wall, [-] Examples -------- >>> is_heating_property(1E-3, 1.2E-3) False ''' return prop_wall < prop
WALL_FACTOR_VISCOSITY = 'Viscosity' WALL_FACTOR_PRANDTL = 'Prandtl' WALL_FACTOR_TEMPERATURE = 'Temperature' WALL_FACTOR_DEFAULT = 'Default' # All powers were originally for (wall/bulk)^power, but have been negated here. # Results for Deissler # -0.11 is also an option from another presented correlation Kays_Crawford_laminar_liquid_Nu = {'mu_heating_coeff': 0.14, 'mu_cooling_coeff': 0.14, 'property_option': WALL_FACTOR_VISCOSITY} Kays_Crawford_laminar_liquid_fd = {'mu_heating_coeff': -0.58, 'mu_cooling_coeff': -0.5, 'property_option': WALL_FACTOR_VISCOSITY} # 1.35 as a result suggested by an experiment byt the analysis is "preferred" Kays_Crawford_laminar_gas_fd = {'mu_heating_coeff': -1, 'mu_cooling_coeff': -1, 'property_option': WALL_FACTOR_VISCOSITY} # This is uncertain Kays_Crawford_laminar_gas_Nu = {'mu_heating_coeff': 0.0, 'mu_cooling_coeff': 0.0, 'property_option': WALL_FACTOR_VISCOSITY} # These seem fairly well measured Kays_Crawford_turbulent_liquid_fd = {'mu_heating_coeff': -0.25, 'mu_cooling_coeff': -0.25, 'property_option': WALL_FACTOR_VISCOSITY} # This is uncertain Kays_Crawford_turbulent_liquid_Nu = {'mu_heating_coeff': 0.11, 'mu_cooling_coeff': 0.25, 'property_option': WALL_FACTOR_VISCOSITY} # These see pretty accurate Kays_Crawford_turbulent_gas_fd = {'mu_heating_coeff': 0.1, 'mu_cooling_coeff': 0.1, 'property_option': WALL_FACTOR_VISCOSITY} Kays_Crawford_turbulent_gas_Nu = {'mu_heating_coeff': 0.5, 'mu_cooling_coeff': 0.0, 'property_option': WALL_FACTOR_VISCOSITY} # is_turbulent, is_liquid wall_factor_fd_defaults = {(True, True): Kays_Crawford_turbulent_liquid_fd, (True, False): Kays_Crawford_turbulent_gas_fd, (False, True): Kays_Crawford_laminar_liquid_fd, (False, False): Kays_Crawford_laminar_gas_fd} wall_factor_Nu_defaults = {(True, True): Kays_Crawford_turbulent_liquid_Nu, (True, False): Kays_Crawford_turbulent_gas_Nu, (False, True): Kays_Crawford_laminar_liquid_Nu, (False, False): Kays_Crawford_laminar_gas_Nu}
[docs]def wall_factor_fd(mu, mu_wall, turbulent=True, liquid=False): r'''Computes the wall correction factor for pressure drop due to friction between a fluid and a wall. These coefficients were derived for internal flow inside a pipe, but can be used elsewhere where appropriate data is missing. .. math:: \frac{f_d}{f_{d,\text{constant properties}}} = \left(\frac{\mu}{\mu_{wall}}\right)^n Parameters ---------- mu : float Viscosity (or Prandtl number) of flowing fluid away from the wall, [Pa*s] mu_wall : float Viscosity (or Prandtl number) of the fluid at the wall, [Pa*s] turbulent : bool Whether or not to use the turbulent coefficient, [-] liquid : bool Whether or not to use the liquid phase coefficient; otherwise the gas coefficient is used, [-] Returns ------- factor : float Correction factor for pressure loss; to be multiplied by the friction factor, or pressure drop to obtain the actual result, [-] Notes ----- The exponents are determined as follows: +-----------+--------+---------+---------+ | Regime | Phase | Heating | Cooling | +===========+========+=========+=========+ | Turbulent | Liquid | -0.25 | -0.25 | +-----------+--------+---------+---------+ | Turbulent | Gas | 0.1 | 0.1 | +-----------+--------+---------+---------+ | Laminar | Liquid | -0.58 | -0.5 | +-----------+--------+---------+---------+ | Laminar | Gas | -1 | -1 | +-----------+--------+---------+---------+ Examples -------- >>> wall_factor_fd(mu=8E-4, mu_wall=3E-4, turbulent=True, liquid=True) 0.7825422900366437 References ---------- .. [1] Kays, William M., and Michael E. Crawford. Convective Heat and Mass Transfer. 3rd edition. New York: McGraw-Hill Science/Engineering/Math, 1993. ''' params = wall_factor_fd_defaults[(turbulent, liquid)] return wall_factor(mu=mu, mu_wall=mu_wall, **params)
[docs]def wall_factor_Nu(mu, mu_wall, turbulent=True, liquid=False): r'''Computes the wall correction factor for heat transfer between a fluid and a wall. These coefficients were derived for internal flow inside a pipe, but can be used elsewhere where appropriate data is missing. It is also useful to compare these results with the coefficients used in various heat transfer coefficients. .. math:: \frac{Nu}{Nu_{\text{constant properties}}} = \left(\frac{\mu}{\mu_{wall}}\right)^n Parameters ---------- mu : float Viscosity (or Prandtl number) of flowing fluid away from the heat transfer surface, [Pa*s] mu_wall : float Viscosity (or Prandtl number) of the fluid at the wall, [Pa*s] turbulent : bool Whether or not to use the turbulent coefficient, [-] liquid : bool Whether or not to use the liquid phase coefficient; otherwise the gas coefficient is used, [-] Returns ------- factor : float Correction factor for heat transfer; to be multiplied by the Nusselt number, or heat transfer coefficient to obtain the actual result, [-] Notes ----- The exponents are determined as follows: +-----------+--------+---------+---------+ | Regime | Phase | Heating | Cooling | +===========+========+=========+=========+ | Turbulent | Liquid | 0.11 | 0.25 | +-----------+--------+---------+---------+ | Turbulent | Gas | 0.5 | 0 | +-----------+--------+---------+---------+ | Laminar | Liquid | 0.14 | 0.14 | +-----------+--------+---------+---------+ | Laminar | Gas | 0 | 0 | +-----------+--------+---------+---------+ Examples -------- >>> wall_factor_Nu(mu=8E-4, mu_wall=3E-4, turbulent=True, liquid=True) 1.1139265634480144 >>> wall_factor_Nu(mu=8E-4, mu_wall=3E-4, turbulent=False, liquid=True) 1.147190712947014 >>> wall_factor_Nu(mu=1.5E-5, mu_wall=1.3E-5, turbulent=True, liquid=False) 1.0741723110591495 >>> wall_factor_Nu(mu=1.5E-5, mu_wall=1.3E-5, turbulent=False, liquid=False) 1.0 References ---------- .. [1] Kays, William M., and Michael E. Crawford. Convective Heat and Mass Transfer. 3rd edition. New York: McGraw-Hill Science/Engineering/Math, 1993. ''' params = wall_factor_Nu_defaults[(turbulent, liquid)] return wall_factor(mu=mu, mu_wall=mu_wall, **params)
wall_factor_bad_option_msg = 'Supported options are %s' %( [WALL_FACTOR_VISCOSITY, WALL_FACTOR_PRANDTL, WALL_FACTOR_TEMPERATURE, WALL_FACTOR_DEFAULT])
[docs]def wall_factor(mu=None, mu_wall=None, Pr=None, Pr_wall=None, T=None, T_wall=None, mu_heating_coeff=0.11, mu_cooling_coeff=0.25, Pr_heating_coeff=0.11, Pr_cooling_coeff=0.25, T_heating_coeff=0.11, T_cooling_coeff=0.25, property_option=WALL_FACTOR_PRANDTL): r'''Computes the wall correction factor for heat transfer, mass transfer, or momentum transfer between a fluid and a wall. Utility function; the coefficients for the phenomenon must be provided to this method. The default coefficients are for heat transfer of a turbulent liquid. The general formula is as follows; substitute the property desired and the phenomenon desired into the equation for things other than heat transfer. .. math:: \frac{Nu}{Nu_{\text{constant properties}}} = \left(\frac{\mu}{\mu_{wall}}\right)^n Parameters ---------- mu : float, optional Viscosity of flowing fluid away from the surface, [Pa*s] mu_wall : float, optional Viscosity of the fluid at the wall, [Pa*s] Pr : float, optional Prandtl number of flowing fluid away from the surface, [-] Pr_wall : float, optional Prandtl number of the fluid at the wall, [-] T : float, optional Temperature of flowing fluid away from the surface, [K] T_wall : float, optional Temperature of the fluid at the wall, [K] mu_heating_coeff : float, optional Coefficient for viscosity - surface providing heating, [-] mu_cooling_coeff : float, optional Coefficient for viscosity - surface providing cooling, [-] Pr_heating_coeff : float, optional Coefficient for Prandtl number - surface providing heating, [-] Pr_cooling_coeff : float, optional Coefficient for Prandtl number - surface providing cooling, [-] T_heating_coeff : float, optional Coefficient for temperature - surface providing heating, [-] T_cooling_coeff : float, optional Coefficient for temperature - surface providing cooling, [-] property_option : str, optional Which property to use for computing the correction factor; one of 'Viscosity', 'Prandtl', or 'Temperature'. Returns ------- factor : float Correction factor for heat transfer; to be multiplied by the Nusselt number or heat transfer coefficient or friction factor or pressure drop to obtain the actual result, [-] Examples -------- >>> wall_factor(mu=8E-4, mu_wall=3E-4, Pr=1.2, Pr_wall=1.1, T=300, ... T_wall=350, property_option='Prandtl') 1.0096172023817749 ''' if property_option == WALL_FACTOR_DEFAULT: property_option = WALL_FACTOR_PRANDTL if property_option == WALL_FACTOR_VISCOSITY: if mu is None or mu_wall is None: raise TypeError('Viscosity wall correction specified but both ' 'viscosity values are not available.') heating = is_heating_property(mu, mu_wall) if heating: return (mu/mu_wall)**mu_heating_coeff else: return (mu/mu_wall)**mu_cooling_coeff elif property_option == WALL_FACTOR_TEMPERATURE: if T is None or T_wall is None: raise TypeError('Temperature wall correction specified but both ' 'temperature values are not available.') heating = is_heating_temperature(T, T_wall) if heating: return (T/T_wall)**T_heating_coeff else: return (T/T_wall)**T_cooling_coeff elif property_option == WALL_FACTOR_PRANDTL: if Pr is None or Pr_wall is None: raise TypeError('Prandtl number wall correction specified but both' ' Prandtl number values are not available.') heating = is_heating_property(Pr, Pr_wall) if heating: return (Pr/Pr_wall)**Pr_heating_coeff else: return (Pr/Pr_wall)**Pr_cooling_coeff else: raise ValueError(wall_factor_bad_option_msg)
[docs]def fin_efficiency_Kern_Kraus(Do, D_fin, t_fin, k_fin, h): r'''Returns the efficiency `eta_f` of a circular fin of constant thickness attached to a circular tube, based on the tube diameter `Do`, fin diameter `D_fin`, fin thickness `t_fin`, fin thermal conductivity `k_fin`, and heat transfer coefficient `h`. .. math:: \eta_f = \frac{2r_o}{m(r_e^2 - r_o^2)} \left[\frac{I_1(mr_e)K_1(mr_o) - K_1(mr_e) I_1(mr_o)} {I_0(mr_o) K_1(mr_e) + I_1(mr_e) K_0(mr_o)}\right] .. math:: m = \sqrt{\frac{2h}{k_{fin} t_{fin}}} .. math:: r_e = 0.5 D_{fin} .. math:: r_o = 0.5 D_{o} Parameters ---------- Do : float Outer diameter of bare pipe (as if there were no fins), [m] D_fin : float Outer diameter of the fin, from the center of the tube to the edge of the fin, [m] t_fin : float Thickness of the fin (for constant thickness fins only), [m] k_fin : float Thermal conductivity of the fin, [W/m/K] h : float Heat transfer coefficient of the finned pipe, [W/K] Returns ------- eta_fin : float Fin efficiency [-] Examples -------- >>> fin_efficiency_Kern_Kraus(0.0254, 0.05715, 3.8E-4, 200, 58) 0.8412588620231153 Notes ----- I0, I1, K0 and K1 are modified Bessel functions of order 0 and 1, modified Bessel function of the second kind of order 0 and 1 respectively. A number of assumptions are made in deriving this set of equations [5]_: * 1-D radial conduction * Steady-state operation * No radiative heat transfer * Temperature-independent fin thermal conductivity * Constant heat transfer coefficient across the whole fin * The fin base temperature is a constant value * There is no constant resistance between the tube material and the added fin * The surrounding fluid is at a constant temperature References ---------- .. [1] Kern, Donald Quentin, and Allan D. Kraus. Extended Surface Heat Transfer. McGraw-Hill, 1972. .. [2] Thulukkanam, Kuppan. Heat Exchanger Design Handbook, Second Edition. CRC Press, 2013. .. [3] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011. .. [4] Kraus, Allan D., Abdul Aziz, and James Welty. Extended Surface Heat Transfer. 1st edition. New York: Wiley-Interscience, 2001. .. [5] Perrotin, Thomas, and Denis Clodic. "Fin Efficiency Calculation in Enhanced Fin-and-Tube Heat Exchangers in Dry Conditions." In Proc. Int. Congress of Refrigeration 2003, 2003. ''' re = 0.5*D_fin ro = 0.5*Do m = (2.0*h/(k_fin*t_fin))**0.5 mre = m*re mro = m*ro x0 = i1(mre) x1 = k1(mre) num = x0*k1(mro) - x1*i1(mro) den = i0(mro)*x1 + x0*k0(mro) return float(2.0*ro/(m*(re*re - ro*ro))*num/den)