# How to use the fluids.core.Reynolds function in fluids

## To help you get started, we’ve selected a few fluids examples, based on popular ways it is used in public projects.

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CalebBell / fluids / fluids / two_phase.py View on Github
``````Frictional Pressure Drop and Void Fraction in Mini-Channel."
International Journal of Heat and Mass Transfer 53, no. 1-3 (January 15,
2010): 453-65. doi:10.1016/j.ijheatmasstransfer.2009.09.011.
.. [2] Kim, Sung-Min, and Issam Mudawar. "Universal Approach to Predicting
Two-Phase Frictional Pressure Drop for Adiabatic and Condensing Mini/
Micro-Channel Flows." International Journal of Heat and Mass Transfer
55, no. 11-12 (May 2012): 3246-61.
doi:10.1016/j.ijheatmasstransfer.2012.02.047.
.. [3] Xu, Yu, Xiande Fang, Xianghui Su, Zhanru Zhou, and Weiwei Chen.
"Evaluation of Frictional Pressure Drop Correlations for Two-Phase Flow
in Pipes." Nuclear Engineering and Design, SI : CFD4NRS-3, 253 (December
2012): 86-97. doi:10.1016/j.nucengdes.2012.08.007.
'''
# Actual Liquid flow
v_l = m*(1-x)/rhol/(pi/4*D**2)
Re_l = Reynolds(V=v_l, rho=rhol, mu=mul, D=D)
fd_l = friction_factor(Re=Re_l, eD=roughness/D)
dP_l = fd_l*L/D*(0.5*rhol*v_l**2)

# Actual gas flow
v_g = m*x/rhog/(pi/4*D**2)
Re_g = Reynolds(V=v_g, rho=rhog, mu=mug, D=D)
fd_g = friction_factor(Re=Re_g, eD=roughness/D)
dP_g = fd_g*L/D*(0.5*rhog*v_g**2)

# Actual model
X = (dP_l/dP_g)**0.5
Co = Confinement(D=D, rhol=rhol, rhog=rhog, sigma=sigma)

if flowtype == 'adiabatic vapor':
C = 21*(1 - exp(-0.142/Co))
elif flowtype == 'adiabatic gas':``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````Engineering Progress 45 (1), 39-48.
.. [2] Chisholm, D."A Theoretical Basis for the Lockhart-Martinelli
Correlation for Two-Phase Flow." International Journal of Heat and Mass
Transfer 10, no. 12 (December 1967): 1767-78.
doi:10.1016/0017-9310(67)90047-6.
.. [3] Cui, Xiaozhou, and John J. J. Chen."A Re-Examination of the Data of
Lockhart-Martinelli." International Journal of Multiphase Flow 36, no.
10 (October 2010): 836-46. doi:10.1016/j.ijmultiphaseflow.2010.06.001.
.. [4] Kim, Sung-Min, and Issam Mudawar. "Universal Approach to Predicting
Two-Phase Frictional Pressure Drop for Adiabatic and Condensing Mini/
Micro-Channel Flows." International Journal of Heat and Mass Transfer
55, no. 11-12 (May 2012): 3246-61.
doi:10.1016/j.ijheatmasstransfer.2012.02.047.
'''
v_l = m*(1-x)/rhol/(pi/4*D**2)
Re_l = Reynolds(V=v_l, rho=rhol, mu=mul, D=D)
v_g = m*x/rhog/(pi/4*D**2)
Re_g = Reynolds(V=v_g, rho=rhog, mu=mug, D=D)

if Re_l &lt; Re_c and Re_g &lt; Re_c:
C = 5.0
elif Re_l &lt; Re_c and Re_g &gt;= Re_c:
# Liquid laminar, gas turbulent
C = 12.0
elif Re_l &gt;= Re_c and Re_g &lt; Re_c:
# Liquid turbulent, gas laminar
C = 10.0
else: # Turbulent case
C = 20.0

# Frictoin factor as in the original model
fd_l =  64./Re_l if Re_l &lt; Re_c else 0.184*Re_l**-0.2``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````.. [3] Shoham, Ovadia. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in
Pipes. Pap/Cdr edition. Richardson, TX: Society of Petroleum Engineers,
2006.
'''
A = 0.25*pi*D*D
# Liquid-superficial properties, for calculation of dP_ls, dP_ls
# Paper and Brill Beggs 1991 confirms not v_lo but v_sg
v_ls =  m*(1.0 - x)/(rhol*A)
Re_ls = Reynolds(V=v_ls, rho=rhol, mu=mul, D=D)
fd_ls = friction_factor(Re=Re_ls, eD=roughness/D)
dP_ls = fd_ls/D*(0.5*rhol*v_ls*v_ls)

# Gas-superficial properties, for calculation of dP_gs
v_gs = m*x/(rhog*A)
Re_gs = Reynolds(V=v_gs, rho=rhog, mu=mug, D=D)
fd_gs = friction_factor(Re=Re_gs, eD=roughness/D)
dP_gs = fd_gs/D*(0.5*rhog*v_gs*v_gs)

X = (dP_ls/dP_gs)**0.5

F = (rhog/(rhol-rhog))**0.5*v_gs*(D*g*cos(angle))**-0.5

# Paper only uses kinematic viscosity
nul = mul/rhol

T = (dP_ls/((rhol-rhog)*g*cos(angle)))**0.5
K = (rhog*v_gs*v_gs*v_ls/((rhol-rhog)*g*nul*cos(angle)))**0.5

F_A_at_X = XA_interp_obj(X)

X_B_transition = 1.7917 # Roughly``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````# Handle x = 0, x=1:
if x == 0:
return dP_lo
elif x == 1:
return dP_go

# Actual Liquid flow
v_l = m*(1-x)/rhol/(pi/4*D**2)
Re_l = Reynolds(V=v_l, rho=rhol, mu=mul, D=D)
fd_l = friction_factor(Re=Re_l, eD=roughness/D)
dP_l = fd_l*L/D*(0.5*rhol*v_l**2)

# Actual gas flow
v_g = m*x/rhog/(pi/4*D**2)
Re_g = Reynolds(V=v_g, rho=rhog, mu=mug, D=D)
fd_g = friction_factor(Re=Re_g, eD=roughness/D)
dP_g = fd_g*L/D*(0.5*rhog*v_g**2)

# The model
n1 = log(dP_l/dP_lo)/log(1.-x)
n2 = log(dP_g/dP_go)/log(x)
n = (n1 + n2*(dP_g/dP_l)**0.1)/(1 + (dP_g/dP_l)**0.1)
epsilon = 3 - 2*(2*(rhol/rhog)**0.5/(1.+rhol/rhog))**(0.7/n)
dP = (dP_lo**(1./(n*epsilon))*(1-x)**(1./epsilon)
+ dP_go**(1./(n*epsilon))*x**(1./epsilon))**(n*epsilon)
return dP``````
CalebBell / fluids / fluids / drag.py View on Github
``````Examples
--------
&gt;&gt;&gt; integrate_drag_sphere(D=0.001, rhop=2200., rho=1.2, mu=1.78E-5, t=0.5,
... V=30, distance=True)
(9.686465044053476, 7.8294546436299175)

References
----------
.. [1] Timmerman, Peter, and Jacobus P. van der Weele. "On the Rise and
Fall of a Ball with Linear or Quadratic Drag." American Journal of
Physics 67, no. 6 (June 1999): 538-46. https://doi.org/10.1119/1.19320.
'''
# Delayed import of necessaray functions
from scipy.integrate import odeint, cumtrapz
import numpy as np
laminar_initial = Reynolds(V=V, rho=rho, D=D, mu=mu) &lt; 0.01
v_laminar_end_assumed = v_terminal(D=D, rhop=rhop, rho=rho, mu=mu, Method=Method)
laminar_end = Reynolds(V=v_laminar_end_assumed, rho=rho, D=D, mu=mu) &lt; 0.01
if Method == 'Stokes' or (laminar_initial and laminar_end and Method is None):
try:
t1 = 18.0*mu/(D*D*rhop)
t2 = g*(rhop-rho)/rhop
V_end = exp(-t1*t)*(t1*V + t2*(exp(t1*t) - 1.0))/t1
x_end = exp(-t1*t)*(V*t1*(exp(t1*t) - 1.0) + t2*exp(t1*t)*(t1*t - 1.0) + t2)/(t1*t1)
if distance:
return V_end, x_end
else:
return V_end
except OverflowError:
# It is only necessary to integrate to terminal velocity
t_to_terminal = time_v_terminal_Stokes(D, rhop, rho, mu, V0=V, tol=1e-9)
if t_to_terminal &gt; t:``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````Two-Phase Frictional Pressure Drop for Adiabatic and Condensing Mini/
Micro-Channel Flows." International Journal of Heat and Mass Transfer
55, no. 11-12 (May 2012): 3246-61.
doi:10.1016/j.ijheatmasstransfer.2012.02.047.
.. [3] Xu, Yu, Xiande Fang, Xianghui Su, Zhanru Zhou, and Weiwei Chen.
"Evaluation of Frictional Pressure Drop Correlations for Two-Phase Flow
in Pipes." Nuclear Engineering and Design, SI : CFD4NRS-3, 253 (December
2012): 86-97. doi:10.1016/j.nucengdes.2012.08.007.
'''
# Liquid-only flow
v_lo = m/rhol/(pi/4*D**2)
Re_lo = Reynolds(V=v_lo, rho=rhol, mu=mul, D=D)

# Actual Liquid flow
v_l = m*(1-x)/rhol/(pi/4*D**2)
Re_l = Reynolds(V=v_l, rho=rhol, mu=mul, D=D)
fd_l = friction_factor(Re=Re_l, eD=roughness/D)
dP_l = fd_l*L/D*(0.5*rhol*v_l**2)

# Actual gas flow
v_g = m*x/rhog/(pi/4*D**2)
Re_g = Reynolds(V=v_g, rho=rhog, mu=mug, D=D)
fd_g = friction_factor(Re=Re_g, eD=roughness/D)
dP_g = fd_g*L/D*(0.5*rhog*v_g**2)

# Actual model
X = (dP_l/dP_g)**0.5
Co = Confinement(D=D, rhol=rhol, rhog=rhog, sigma=sigma)
C = 0.227*Re_lo**0.452*X**-0.320*Co**-0.820
phi_l2 = 1 + C/X + 1./X**2
return dP_l*phi_l2``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````.. [1] Taitel, Yemada, and A. E. Dukler. "A Model for Predicting Flow
Regime Transitions in Horizontal and near Horizontal Gas-Liquid Flow."
AIChE Journal 22, no. 1 (January 1, 1976): 47-55.
doi:10.1002/aic.690220105.
.. [2] Brill, James P., and Howard Dale Beggs. Two-Phase Flow in Pipes,
1994.
.. [3] Shoham, Ovadia. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in
Pipes. Pap/Cdr edition. Richardson, TX: Society of Petroleum Engineers,
2006.
'''
A = 0.25*pi*D*D
# Liquid-superficial properties, for calculation of dP_ls, dP_ls
# Paper and Brill Beggs 1991 confirms not v_lo but v_sg
v_ls =  m*(1.0 - x)/(rhol*A)
Re_ls = Reynolds(V=v_ls, rho=rhol, mu=mul, D=D)
fd_ls = friction_factor(Re=Re_ls, eD=roughness/D)
dP_ls = fd_ls/D*(0.5*rhol*v_ls*v_ls)

# Gas-superficial properties, for calculation of dP_gs
v_gs = m*x/(rhog*A)
Re_gs = Reynolds(V=v_gs, rho=rhog, mu=mug, D=D)
fd_gs = friction_factor(Re=Re_gs, eD=roughness/D)
dP_gs = fd_gs/D*(0.5*rhog*v_gs*v_gs)

X = (dP_ls/dP_gs)**0.5

F = (rhog/(rhol-rhog))**0.5*v_gs*(D*g*cos(angle))**-0.5

# Paper only uses kinematic viscosity
nul = mul/rhol``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````and the Correlation Development."  International Journal of Heat and
Mass Transfer 49, no. 11-12 (June 2006): 1804-12.
doi:10.1016/j.ijheatmasstransfer.2005.10.040.
.. [2] Kim, Sung-Min, and Issam Mudawar. "Universal Approach to Predicting
Two-Phase Frictional Pressure Drop for Adiabatic and Condensing Mini/
Micro-Channel Flows." International Journal of Heat and Mass Transfer
55, no. 11-12 (May 2012): 3246-61.
doi:10.1016/j.ijheatmasstransfer.2012.02.047.
.. [3] Xu, Yu, Xiande Fang, Xianghui Su, Zhanru Zhou, and Weiwei Chen.
"Evaluation of Frictional Pressure Drop Correlations for Two-Phase Flow
in Pipes." Nuclear Engineering and Design, SI : CFD4NRS-3, 253 (December
2012): 86-97. doi:10.1016/j.nucengdes.2012.08.007.
'''
# Liquid-only flow
v_lo = m/rhol/(pi/4*D**2)
Re_lo = Reynolds(V=v_lo, rho=rhol, mu=mul, D=D)

# Actual Liquid flow
v_l = m*(1-x)/rhol/(pi/4*D**2)
Re_l = Reynolds(V=v_l, rho=rhol, mu=mul, D=D)
fd_l = friction_factor(Re=Re_l, eD=roughness/D)
dP_l = fd_l*L/D*(0.5*rhol*v_l**2)

# Actual gas flow
v_g = m*x/rhog/(pi/4*D**2)
Re_g = Reynolds(V=v_g, rho=rhog, mu=mug, D=D)
fd_g = friction_factor(Re=Re_g, eD=roughness/D)
dP_g = fd_g*L/D*(0.5*rhog*v_g**2)

# Actual model
X = (dP_l/dP_g)**0.5
Co = Confinement(D=D, rhol=rhol, rhog=rhog, sigma=sigma)``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````1973): 347-58. doi:10.1016/0017-9310(73)90063-X.
.. [2] Mekisso, Henock Mateos. "Comparison of Frictional Pressure Drop
Correlations for Isothermal Two-Phase Horizontal Flow." Thesis, Oklahoma
State University, 2013. https://shareok.org/handle/11244/11109.
.. [3] Thome, John R. "Engineering Data Book III." Wolverine Tube Inc
(2004). http://www.wlv.com/heat-transfer-databook/
.. [4] Chisholm, D. "Research Note: Influence of Pipe Surface Roughness on
Friction Pressure Gradient during Two-Phase Flow." Journal of Mechanical
Engineering Science 20, no. 6 (December 1, 1978): 353-354.
doi:10.1243/JMES_JOUR_1978_020_061_02.
'''
G_tp = m/(pi/4*D**2)
n = 0.25 # Blasius friction factor exponent
# Liquid-only properties, for calculation of dP_lo
v_lo = m/rhol/(pi/4*D**2)
Re_lo = Reynolds(V=v_lo, rho=rhol, mu=mul, D=D)
fd_lo = friction_factor(Re=Re_lo, eD=roughness/D)
dP_lo = fd_lo*L/D*(0.5*rhol*v_lo**2)

# Gas-only properties, for calculation of dP_go
v_go = m/rhog/(pi/4*D**2)
Re_go = Reynolds(V=v_go, rho=rhog, mu=mug, D=D)
fd_go = friction_factor(Re=Re_go, eD=roughness/D)
dP_go = fd_go*L/D*(0.5*rhog*v_go**2)

Gamma = (dP_go/dP_lo)**0.5
if Gamma &lt;= 9.5:
if G_tp &lt;= 500:
B = 4.8
elif G_tp &lt; 1900:
B = 2400./G_tp
else:``````
CalebBell / fluids / fluids / two_phase.py View on Github
``````55, no. 11-12 (May 2012): 3246-61.
doi:10.1016/j.ijheatmasstransfer.2012.02.047.
.. [3] Xu, Yu, Xiande Fang, Xianghui Su, Zhanru Zhou, and Weiwei Chen.
"Evaluation of Frictional Pressure Drop Correlations for Two-Phase Flow
in Pipes." Nuclear Engineering and Design, SI : CFD4NRS-3, 253 (December
2012): 86-97. doi:10.1016/j.nucengdes.2012.08.007.
'''
# Actual Liquid flow
v_l = m*(1-x)/rhol/(pi/4*D**2)
Re_l = Reynolds(V=v_l, rho=rhol, mu=mul, D=D)
fd_l = friction_factor(Re=Re_l, eD=roughness/D)
dP_l = fd_l*L/D*(0.5*rhol*v_l**2)

# Actual gas flow
v_g = m*x/rhog/(pi/4*D**2)
Re_g = Reynolds(V=v_g, rho=rhog, mu=mug, D=D)
fd_g = friction_factor(Re=Re_g, eD=roughness/D)
dP_g = fd_g*L/D*(0.5*rhog*v_g**2)

# Actual model
X = (dP_l/dP_g)**0.5
C = 21*(1 - exp(-0.319E3*D))
phi_l2 = 1 + C/X + 1./X**2
return dP_l*phi_l2``````

## fluids

Fluid dynamics component of Chemical Engineering Design Library (ChEDL)

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