def test_bend_rounded_Miller():
# Miller examples - 9.12
D = .6
Re = Reynolds(V=4, D=D, nu=1.14E-6)
kwargs = dict(Di=D, bend_diameters=2, angle=90, Re=Re, roughness=.02E-3)
K = bend_rounded_Miller(L_unimpeded=30*D, **kwargs)
assert_close(K, 0.1513266131915296, rtol=1e-4)# 0.150 in Miller- 1% difference due to fd
K = bend_rounded_Miller(L_unimpeded=0*D, **kwargs)
assert_close(K, 0.1414607344374372, rtol=1e-4) # 0.135 in Miller - Difference mainly from Co interpolation method, OK with that
K = bend_rounded_Miller(L_unimpeded=2*D, **kwargs)
assert_close(K, 0.09343184457353562, rtol=1e-4) # 0.093 in miller
def calculate(doc_original):
doc = deepcopy(doc_original)
treeUnitConvert(doc, doc['units'], SI_UNITS)
K_pipe = 0
K_fittings = 0
K_entry = 0
K_exit = 0
K_fixed = 0
K_LbyD = 0
K_total = 0
LbyD_total = 0
deltaP_fixed = 0
deltaP_total = 0
size_definition = doc['input']['pipe']['size_definition']['_val']
if (size_definition == "NPS"):
nps = float(doc['input']['pipe']['NPS']['_val'])
schedule = doc['input']['pipe']['schedule']['_val']
NPS, Di, Do, t = nearest_pipe(NPS=nps, schedule=schedule)
else:
Di = float(doc['input']['pipe']['Dia_inner']['_val'])
NPS = math.nan
Do = math.nan
t = math.nan
doc['result'].update({'Di': {'_val': str(Di), '_dim': 'length_mili'}})
doc['result'].update({'Do': {'_val': str(Do), '_dim': 'length_mili'}})
doc['result'].update({'t': {'_val': str(t), '_dim': 'length_mili'}})
area = math.pi * pow(Di / 2, 2)
Q = float(doc['input']['fluidData']['Q']['_val'])
V = roundit(Q / area)
doc['result'].update({'V': {'_val': str(V), '_dim': 'speed'}})
mu = float(doc['input']['fluidData']['mu']['_val'])
rho = float(doc['input']['fluidData']['rho']['_val'])
Re = roundit(Reynolds(V=V, D=Di, rho=rho, mu=mu))
doc['result'].update({'Re': {'_val': str(Re)}})
Hdyn = roundit(rho * pow(V, 2) / 2)
doc['result'].update({'Hdyn': {'_val': str(Hdyn), '_dim': 'length'}})
#K calculation for straigth pipe
roughness_basis = doc['input']['pipe']['roughness_basis']['_val']
if (roughness_basis == "Material"):
material = doc['input']['pipe']['material']['_val']
roughness = get_roughness(material)
else:
roughness = float(doc['input']['pipe']['roughness']['_val'])
eD = roughness / Di
doc['result'].update({'eD': {'_val': str(eD)}})
fd = roundit(friction_factor(Re=Re, eD=eD, Method="Moody"))
doc['result'].update({'fd_Moody': {'_val': str(fd)}})
length = float(doc['input']['pipe']['length']['_val'])
K_pipe = roundit(K_from_f(fd=fd, L=length, D=Di))
doc['result'].update({'K_pipe': {'_val': str(K_pipe)}})
deltaP_pipe = roundit(dP_from_K(K_pipe, rho, V))
doc['result'].update(
{'deltaP_pipe': {
'_val': str(deltaP_pipe),
'_dim': 'pressure'
}})
#calculating pressure drop for entrance
entry_type = doc['input']['entrance']['entry_type']['_val']
print('entry type is')
print(entry_type)
if entry_type == 'none':
K_entry = 0
elif entry_type == 'Sharp':
K_entry = fluids.fittings.entrance_sharp()
elif entry_type == 'Rounded':
Rc = float(doc['input']['entrance']['Rc']['_val'])
K_entry = fluids.fittings.entrance_rounded(Di, Rc)
elif entry_type == 'Angled':
angle_radians = float(doc['input']['entrance']['angle']['_val'])
angle = angle_radians * 57.2958
K_entry = fluids.fittings.entrance_angled(angle)
elif entry_type == 'Projecting':
wall_thickness = float(
doc['input']['entrance']['wall_thickness']['_val'])
K_entry = fluids.fittings.entrance_distance(Di, wall_thickness)
K_entry = roundit(K_entry)
doc['result'].update({'K_entry': {'_val': str(K_entry)}})
deltaP_entry = roundit(dP_from_K(K_entry, rho, V))
doc['result'].update(
{'deltaP_entry': {
'_val': str(deltaP_entry),
'_dim': 'pressure'
}})
#calculating pressure drop for exit
exit_type = doc['input']['exit']['exit_type']['_val']
print('exit_type')
print(exit_type)
if (exit_type == 'Normal'):
K_exit = exit_normal()
else:
K_exit = 0
K_exit = roundit(K_exit)
doc['result'].update({'K_exit': {'_val': str(K_exit)}})
deltaP_exit = roundit(dP_from_K(K_exit, rho, V))
doc['result'].update(
{'deltaP_exit': {
'_val': str(deltaP_exit),
'_dim': 'pressure'
}})
#calculating pressure drop for fittings
fittings_list = doc['input']['fittings']
for fitting in fittings_list:
name = get_hooper_list()[fitting['index']]
Di_inch = Di * 39.3701
K_fitting = Hooper2K(Di_inch, Re, name=name)
K_fittings += K_fitting * fitting['quantity']
K_fittings = roundit(K_fittings)
doc['result'].update({'K_fittings': {'_val': str(K_fittings)}})
deltaP_fittings = dP_from_K(K_fittings, rho, V)
deltaP_fittings = roundit(deltaP_fittings)
doc['result'].update({
'deltaP_fittings': {
'_val': str(deltaP_fittings),
'_dim': 'pressure'
}
})
#calculating pressure drop for sharp contractions
deltaP_contractions_sharp = 0
contractions_sharp = doc['input']['contractions_sharp']['_list']
for contraction in contractions_sharp:
D1 = contraction['D1']
D2 = contraction['D2']
A2 = 3.1416 * (D2**2) / 4
V2 = Q / A2
K_contraction = fluids.fittings.contraction_sharp(D1, D2)
deltaP = dP_from_K(K_contraction, rho, V2)
deltaP_contractions_sharp += deltaP
deltaP_contractions_sharp = roundit(deltaP_contractions_sharp)
doc['result'].update({
'deltaP_contractions_sharp': {
'_val': str(deltaP_contractions_sharp),
'_dim': 'pressure'
}
})
#calculating pressure drop for rounded contractions
deltaP_contractions_rounded = 0
contractions_rounded = doc['input']['contractions_rounded']['_list']
for contraction in contractions_rounded:
D1 = contraction['D1']
D2 = contraction['D2']
Rc = contraction['Rc']
A2 = 3.1416 * (D2**2) / 4
V2 = Q / A2
K_contraction = fluids.fittings.contraction_round(D1, D2, Rc)
deltaP = dP_from_K(K_contraction, rho, V2)
deltaP_contractions_rounded += deltaP
deltaP_contractions_rounded = roundit(deltaP_contractions_rounded)
doc['result'].update({
'deltaP_contractions_rounded': {
'_val': str(deltaP_contractions_rounded),
'_dim': 'pressure'
}
})
#calculating pressure drop for conical contractions
deltaP_contractions_conical = 0
contractions_conical = doc['input']['contractions_conical']['_list']
for contraction in contractions_conical:
D1 = contraction['D1']
D2 = contraction['D2']
L = contraction['L']
A2 = 3.1416 * (D2**2) / 4
V2 = Q / A2
K_contraction = fluids.fittings.contraction_conical(D1, D2, fd=fd, l=L)
deltaP = dP_from_K(K_contraction, rho, V2)
deltaP_contractions_conical += deltaP
deltaP_contractions_conical = roundit(deltaP_contractions_conical)
doc['result'].update({
'deltaP_contractions_conical': {
'_val': str(deltaP_contractions_conical),
'_dim': 'pressure'
}
})
#calculating pressure drop for pipe reducers contractions
deltaP_contractions_reducer = 0
contractions_reducer = doc['input']['contractions_reducer']['_list']
for contraction in contractions_reducer:
reducer_size = contraction['reducer_size']
D1, D2, L = reducer_dimensions(reducer_size)
A2 = 3.1416 * (D2**2) / 4
V2 = Q / A2
K_contraction = fluids.fittings.contraction_conical(D1, D2, fd=fd, l=L)
deltaP = dP_from_K(K_contraction, rho, V2)
deltaP_contractions_reducer += deltaP
deltaP_contractions_reducer = roundit(deltaP_contractions_reducer)
doc['result'].update({
'deltaP_contractions_reducer': {
'_val': str(deltaP_contractions_reducer),
'_dim': 'pressure'
}
})
# calculating total pressure drop in all contractions
deltaP_contractions = deltaP_contractions_sharp + deltaP_contractions_rounded + deltaP_contractions_conical + deltaP_contractions_reducer
deltaP_contractions = roundit(deltaP_contractions)
doc['result'].update({
'deltaP_contractions': {
'_val': str(deltaP_contractions),
'_dim': 'pressure'
}
})
#calculating pressure drop for sharp expansions
deltaP_expansions_sharp = 0
expansions_sharp = doc['input']['expansions_sharp']['_list']
for contraction in expansions_sharp:
D1 = contraction['D1']
D2 = contraction['D2']
A1 = 3.1416 * (D1**2) / 4
V1 = Q / A1
K_contraction = fluids.fittings.diffuser_sharp(D1, D2)
deltaP = dP_from_K(K_contraction, rho, V1)
deltaP_expansions_sharp += deltaP
deltaP_expansions_sharp = roundit(deltaP_expansions_sharp)
doc['result'].update({
'deltaP_expansions_sharp': {
'_val': str(deltaP_expansions_sharp),
'_dim': 'pressure'
}
})
#calculating pressure drop for conical expansions
deltaP_expansions_conical = 0
expansions_conical = doc['input']['expansions_conical']['_list']
for contraction in expansions_conical:
D1 = contraction['D1']
D2 = contraction['D2']
L = contraction['L']
A1 = 3.1416 * (D1**2) / 4
V1 = Q / A1
K_contraction = fluids.fittings.diffuser_conical(D1, D2, fd=fd, l=L)
deltaP = dP_from_K(K_contraction, rho, V1)
deltaP_expansions_conical += deltaP
deltaP_expansions_conical = roundit(deltaP_expansions_conical)
doc['result'].update({
'deltaP_expansions_conical': {
'_val': str(deltaP_expansions_conical),
'_dim': 'pressure'
}
})
#calculating pressure drop for pipe reducer expansions
deltaP_expansions_reducer = 0
expansions_reducer = doc['input']['expansions_reducer']['_list']
for contraction in expansions_reducer:
reducer_size = contraction['reducer_size']
D2, D1, L = reducer_dimensions(reducer_size)
A1 = 3.1416 * (D1**2) / 4
V1 = Q / A1
K_contraction = fluids.fittings.diffuser_conical(D1, D2, fd=fd, l=L)
deltaP = dP_from_K(K_contraction, rho, V1)
deltaP_expansions_reducer += deltaP
deltaP_expansions_reducer = roundit(deltaP_expansions_reducer)
doc['result'].update({
'deltaP_expansions_reducer': {
'_val': str(deltaP_expansions_reducer),
'_dim': 'pressure'
}
})
# calculating total pressure drop in all expansions
deltaP_expansions = deltaP_expansions_sharp + deltaP_expansions_conical + deltaP_expansions_reducer
doc['result'].update(
{'deltaP_expansions': {
'_val': deltaP_expansions,
'_dim': 'pressure'
}})
fixed_K_loss = doc['input']['fixed_K_losses']['_list']
for loss in fixed_K_loss:
K_fixed += loss['K'] * loss['quantity']
deltaP_fixed_K = dP_from_K(K_fixed, rho, V)
fixed_LbyD_loss = doc['input']['fixed_LbyD_losses']['_list']
for loss in fixed_LbyD_loss:
L_D = loss['LbyD']
K_LbyD += K_from_L_equiv(L_D=L_D, fd=fd) * loss['quantity']
deltaP_fixed_LbyD = dP_from_K(K_LbyD, rho, V)
fixed_deltaP_loss = doc['input']['fixed_deltaP_losses']['_list']
for loss in fixed_deltaP_loss:
deltaP_fixed += loss['deltaP'] * loss['quantity']
deltaP_fixed_deltaP = deltaP_fixed
deltaP_fixed_all = deltaP_fixed_K + deltaP_fixed_LbyD + deltaP_fixed_deltaP
deltaP_fixed_all = roundit(deltaP_fixed_all)
doc['result'].update({
'deltaP_fixed_all': {
'_val': str(deltaP_fixed_all),
'_dim': 'pressure'
}
})
deltaP_total = deltaP_pipe + deltaP_entry + deltaP_exit + deltaP_fittings + deltaP_contractions + deltaP_expansions + deltaP_fixed_all
deltaP_total = roundit(deltaP_total)
doc['result'].update(
{'deltaP_total': {
'_val': str(deltaP_total),
'_dim': 'pressure'
}})
# doc_original['input'].update(doc['input'])
doc_original['result'].update(doc['result'])
treeUnitConvert(doc, SI_UNITS, doc['units'], autoRoundOff=True)
return True
def integrate_drag_sphere(D, rhop, rho, mu, t, V=0, Method=None,
distance=False):
r'''Integrates the velocity and distance traveled by a particle moving
at a speed which will converge to its terminal velocity.
Performs an integration of the following expression for acceleration:
.. math::
a = \frac{g(\rho_p-\rho_f)}{\rho_p} - \frac{3C_D \rho_f u^2}{4D \rho_p}
Parameters
----------
D : float
Diameter of the sphere, [m]
rhop : float
Particle density, [kg/m^3]
rho : float
Density of the surrounding fluid, [kg/m^3]
mu : float
Viscosity of the surrounding fluid [Pa*s]
t : float
Time to integrate the particle to, [s]
V : float
Initial velocity of the particle, [m/s]
Method : string, optional
A string of the function name to use, as in the dictionary
drag_sphere_correlations
distance : bool, optional
Whether or not to calculate the distance traveled and return it as
well
Returns
-------
v : float
Velocity of falling sphere after time `t` [m/s]
x : float, returned only if `distance` == True
Distance traveled by the falling sphere in time `t`, [m]
Notes
-----
This can be relatively slow as drag correlations can be complex.
There are analytical solutions available for the Stokes law regime (Re <
0.3). They were obtained from Wolfram Alpha. [1]_ was not used in the
derivation, but also describes the derivation fully.
.. math::
V(t) = \frac{\exp(-at) (V_0 a + b(\exp(at) - 1))}{a}
.. math::
x(t) = \frac{\exp(-a t)\left[V_0 a(\exp(a t) - 1) + b\exp(a t)(a t-1)
+ b\right]}{a^2}
.. math::
a = \frac{18\mu_f}{D^2\rho_p}
.. math::
b = \frac{g(\rho_p-\rho_f)}{\rho_p}
The analytical solution will automatically be used if the initial and
terminal velocity is show the particle's behavior to be laminar. Note
that this behavior requires that the terminal velocity of the particle be
solved for - this adds slight (1%) overhead for the cases where particles
are not laminar.
Examples
--------
>>> integrate_drag_sphere(D=0.001, rhop=2200., rho=1.2, mu=1.78E-5, t=0.5,
... V=30, distance=True)
(9.686465044053, 7.8294546436299)
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) < 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) < 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 > t:
raise ValueError('Should never happen')
V_end, x_end = integrate_drag_sphere(D=D, rhop=rhop, rho=rho, mu=mu, t=t_to_terminal, V=V, Method='Stokes', distance=True)
# terminal velocity has been reached - V does not change, but x does
# No reason to believe this isn't working even though it isn't
# matching the ode solver
if distance:
return V_end, x_end + V_end*(t - t_to_terminal)
else:
return V_end
# This is a serious problem for small diameters
# It would be possible to step slowly, using smaller increments
# of time to avlid overflows. However, this unfortunately quickly
# gets much, exponentially, slower than just using odeint because
# for example solving 10000 seconds might require steps of .0001
# seconds at a diameter of 1e-7 meters.
# x = 0.0
# subdivisions = 10
# dt = t/subdivisions
# for i in range(subdivisions):
# V, dx = integrate_drag_sphere(D=D, rhop=rhop, rho=rho, mu=mu,
# t=dt, V=V, distance=True,
# Method=Method)
# x += dx
# if distance:
# return V, x
# else:
# return V
Re_ish = rho*D/mu
c1 = g*(rhop-rho)/rhop
c2 = -0.75*rho/(D*rhop)
def dv_dt(V, t):
if V == 0:
# 64/Re goes to infinity, but gets multiplied by 0 squared.
t2 = 0.0
else:
# t2 = c2*V*V*Stokes(Re_ish*V)
t2 = c2*V*V*drag_sphere(float(Re_ish*V), Method=Method)
return c1 + t2
# Number of intervals for the solution to be solved for; the integrator
# doesn't care what we give it, but a large number of intervals are needed
# For an accurate integration of the particle's distance traveled
pts = 1000 if distance else 2
ts = np.linspace(0, t, pts)
# Perform the integration
Vs = odeint(dv_dt, [V], ts)
#
V_end = float(Vs[-1])
if distance:
# Calculate the distance traveled
x = float(cumtrapz(np.ravel(Vs), ts)[-1])
return V_end, x
else:
return V_end
def v_terminal(D, rhop, rho, mu, Method=None):
r'''Calculates terminal velocity of a falling sphere using any drag
coefficient method supported by `drag_sphere`. The laminar solution for
Re < 0.01 is first tried; if the resulting terminal velocity does not
put it in the laminar regime, a numerical solution is used.
.. math::
v_t = \sqrt{\frac{4 g d_p (\rho_p-\rho_f)}{3 C_D \rho_f }}
Parameters
----------
D : float
Diameter of the sphere, [m]
rhop : float
Particle density, [kg/m^3]
rho : float
Density of the surrounding fluid, [kg/m^3]
mu : float
Viscosity of the surrounding fluid [Pa*s]
Method : string, optional
A string of the function name to use, as in the dictionary
drag_sphere_correlations
Returns
-------
v_t : float
Terminal velocity of falling sphere [m/s]
Notes
-----
As there are no correlations implemented for Re > 1E6, an error will be
raised if the numerical solver seeks a solution above that limit.
The laminar solution is given in [1]_ and is:
.. math::
v_t = \frac{g d_p^2 (\rho_p - \rho_f)}{18 \mu_f}
Examples
--------
>>> v_terminal(D=70E-6, rhop=2600., rho=1000., mu=1E-3)
0.004142497244531304
Example 7-1 in GPSA handbook, 13th edition:
>>> from scipy.constants import *
>>> v_terminal(D=150E-6, rhop=31.2*lb/foot**3, rho=2.07*lb/foot**3, mu=1.2e-05)/foot
0.4491992020345101
The answer reported there is 0.46 ft/sec.
References
----------
.. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook,
Eighth Edition. McGraw-Hill Professional, 2007.
.. [2] Rushton, Albert, Anthony S. Ward, and Richard G. Holdich.
Solid-Liquid Filtration and Separation Technology. 1st edition. Weinheim ;
New York: Wiley-VCH, 1996.
'''
'''The following would be the ideal implementation. The actual function is
optimized for speed, not readability
def err(V):
Re = rho*V*D/mu
Cd = Barati_high(Re)
V2 = (4/3.*g*D*(rhop-rho)/rho/Cd)**0.5
return (V-V2)
return fsolve(err, 1.)'''
v_lam = g*D*D*(rhop-rho)/(18*mu)
Re_lam = Reynolds(V=v_lam, D=D, rho=rho, mu=mu)
if Re_lam < 0.01 or Method == 'Stokes':
return v_lam
Re_almost = rho*D/mu
main = 4/3.*g*D*(rhop-rho)/rho
V_max = 1E6/rho/D*mu # where the correlation breaks down, Re=1E6
# Begin the solver with 1/100 th the velocity possible at the maximum
# Reynolds number the correlation is good for
return secant(_v_terminal_err, V_max*1e-2, xtol=1E-12, args=(Method, Re_almost, main))
def h_Ganguli_VDI(m, A, A_min, A_increase, A_fin, A_tube_showing,
tube_diameter, fin_diameter, fin_thickness, bare_length,
pitch_parallel, pitch_normal, tube_rows, rho, Cp, mu, k,
k_fin):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with the formulas of [1]_ as modified in [2]_.
Inline:
.. math::
Nu_d = 0.22Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}
Staggered:
.. math::
Nu_d = 0.38 Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}
Parameters
----------
m : float
Mass flow rate of air across the tube bank, [kg/s]
A : float
Surface area of combined finned and non-finned area exposed for heat
transfer, [m^2]
A_min : float
Minimum air flow area, [m^2]
A_increase : float
Ratio of actual surface area to bare tube surface area
:math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
A_fin : float
Surface area of all fins in the bundle, [m^2]
A_tube_showing : float
Area of the bare tube which is exposed in the bundle, [m^2]
tube_diameter : float
Diameter of the bare tube, [m]
fin_diameter : float
Outer diameter of each tube after including the fin on both sides,
[m]
fin_thickness : float
Thickness of the fins, [m]
bare_length : float
Length of bare tube between two fins
:math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
pitch_parallel : float
Distance between tube center along a line parallel to the flow;
has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
pitch_normal : float
Distance between tube centers in a line 90° to the line of flow;
has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
tube_rows : int
Number of tube rows per bundle, [-]
rho : float
Average (bulk) density of air across the tube bank, [kg/m^3]
Cp : float
Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
mu : float
Average (bulk) viscosity of air across the tube bank, [Pa*s]
k : float
Average (bulk) thermal conductivity of air across the tube bank,
[W/m/K]
k_fin : float
Thermal conductivity of the fin, [W/m/K]
Returns
-------
h_bare_tube_basis : float
Air side heat transfer coefficient on a bare-tube surface area as if
there were no fins present basis, [W/K/m^2]
Notes
-----
The VDI modifications were developed in comparison with HTFS and HTRI data
according to [2]_.
For cases where the tube row count is less than four, the coefficients are
modified in [2]_. For the inline case, 0.2 replaces 0.22. For the stagered
cases, the coefficient is 0.2, 0.33, 0.36 for 1, 2, or 3 tube rows
respectively.
The model is also showin in [4]_.
Examples
--------
Example 12.1 in [3]_:
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=56, tube_length=36*foot,
... tube_diameter=1*inch, fin_thickness=0.013*inch, fin_density=10/inch,
... angle=30, pitch_normal=2.5*inch, fin_height=0.625*inch, corbels=True)
>>> h_Ganguli_VDI(m=130.70315, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
... pitch_parallel=AC.pitch_parallel, pitch_normal=AC.pitch_normal,
... rho=1.2013848, Cp=1009.0188, mu=1.9304793e-05, k=0.027864828, k_fin=238)
969.2850818578595
References
----------
.. [1] Ganguli, A., S. S. Tung, and J. Taborek. "Parametric Study of
Air-Cooled Heat Exchanger Finned Tube Geometry." In AIChE Symposium
Series, 81:122-28, 1985.
.. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
Berlin; New York:: Springer, 2010.
.. [3] Serth, Robert W., and Thomas Lestina. Process Heat Transfer:
Principles, Applications and Rules of Thumb. Academic Press, 2014.
.. [4] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers:
Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
PennWell Corp., 2004.
'''
V_max = m / (A_min * rho)
Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
Pr = Prandtl(Cp=Cp, mu=mu, k=k)
if abs(1 - pitch_normal / pitch_parallel
) < 0.05: # in-line, with a tolerance of 0.05 proximity
if tube_rows < 4:
coeff = 0.2
else:
coeff = 0.22
else: # staggered
if tube_rows == 1:
coeff = 0.2
elif tube_rows == 2:
coeff = 0.33
elif tube_rows == 3:
coeff = 0.36
else:
coeff = 0.38
# VDI example shows the ratio is of the total area, to the original bare tube area
# Serth example would match Nu = 47.22 except for lazy rounding
Nu = coeff * Re**0.6 * Pr**(1 / 3.) * (A_increase)**-0.15
h = k / tube_diameter * Nu
efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
D_fin=fin_diameter,
t_fin=fin_thickness,
k_fin=k_fin,
h=h)
h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
h_bare_tube_basis = h_total_area_basis * A_increase
return h_bare_tube_basis
def h_ESDU_low_fin(m,
A,
A_min,
A_increase,
A_fin,
A_tube_showing,
tube_diameter,
fin_diameter,
fin_thickness,
bare_length,
pitch_parallel,
pitch_normal,
tube_rows,
rho,
Cp,
mu,
k,
k_fin,
Pr_wall=None):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with low fins using the formulas of [1]_ as
presented in [2]_ (and also [3]_).
.. math::
Nu = 0.183Re^{0.7} \left(\frac{\text{bare length}}{\text{fin height}}
\right)^{0.36}\left(\frac{p_1}{D_{o}}\right)^{0.06}
\left(\frac{\text{fin height}}{D_o}\right)^{0.11}
Pr^{0.36} \cdot F_1\cdot F_2
.. math::
h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h
.. math::
h_{bare,total} = A_{increase} h_{A,total}
Parameters
----------
m : float
Mass flow rate of air across the tube bank, [kg/s]
A : float
Surface area of combined finned and non-finned area exposed for heat
transfer, [m^2]
A_min : float
Minimum air flow area, [m^2]
A_increase : float
Ratio of actual surface area to bare tube surface area
:math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
A_fin : float
Surface area of all fins in the bundle, [m^2]
A_tube_showing : float
Area of the bare tube which is exposed in the bundle, [m^2]
tube_diameter : float
Diameter of the bare tube, [m]
fin_diameter : float
Outer diameter of each tube after including the fin on both sides,
[m]
fin_thickness : float
Thickness of the fins, [m]
bare_length : float
Length of bare tube between two fins
:math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
pitch_parallel : float
Distance between tube center along a line parallel to the flow;
has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
pitch_normal : float
Distance between tube centers in a line 90° to the line of flow;
has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
tube_rows : int
Number of tube rows per bundle, [-]
rho : float
Average (bulk) density of air across the tube bank, [kg/m^3]
Cp : float
Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
mu : float
Average (bulk) viscosity of air across the tube bank, [Pa*s]
k : float
Average (bulk) thermal conductivity of air across the tube bank,
[W/m/K]
k_fin : float
Thermal conductivity of the fin, [W/m/K]
Pr_wall : float, optional
Prandtl number at the wall temperature; provide if a correction with
the defaults parameters is desired; otherwise apply the correction
elsewhere, [-]
Returns
-------
h_bare_tube_basis : float
Air side heat transfer coefficient on a bare-tube surface area as if
there were no fins present basis, [W/K/m^2]
Notes
-----
The tube-row count correction factor `F2` can be disabled by setting `tube_rows`
to 10. The property correction factor `F1` can be disabled by not specifying
`Pr_wall`. A Prandtl number exponent of 0.26 is recommended in [1]_ for
heating and cooling for both liquids and gases.
There is a third correction factor in [1]_ for tube angles not 30, 45, or
60 degrees, but it is not fully explained and it is not shown in [2]_.
Another correction factor is in [2]_ for flow at an angle; however it would
not make sense to apply it to finned tube banks due to the blockage by the
fins.
Examples
--------
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=8, tube_length=0.5,
... tube_diameter=0.0164, fin_thickness=0.001, fin_density=1/0.003,
... pitch_normal=0.0313, pitch_parallel=0.0271, fin_height=0.0041, corbels=True)
>>> h_ESDU_low_fin(m=0.914, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
... pitch_normal=AC.pitch_normal, pitch_parallel=AC.pitch_parallel,
... rho=1.217, Cp=1007., mu=1.8E-5, k=0.0253, k_fin=15)
553.853836470948
References
----------
.. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press,
1994.
.. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986).
.. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
in Cross Flow." Heat Transfer Engineering 8, no. 2 (January 1987):
49-62.
'''
fin_height = 0.5 * (fin_diameter - tube_diameter)
V_max = m / (A_min * rho)
Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
Pr = Prandtl(Cp=Cp, mu=mu, k=k)
Nu = (0.183 * Re**0.7 * (bare_length / fin_height)**0.36 *
(pitch_normal / fin_diameter)**0.06 *
(fin_height / fin_diameter)**0.11 * Pr**0.36)
staggered = abs(1 - pitch_normal / pitch_parallel) > 0.05
F2 = ESDU_tube_row_correction(tube_rows=tube_rows, staggered=staggered)
Nu *= F2
if Pr_wall is not None:
F1 = wall_factor(Pr=Pr,
Pr_wall=Pr_wall,
Pr_heating_coeff=0.26,
Pr_cooling_coeff=0.26,
property_option=WALL_FACTOR_PRANDTL)
Nu *= F1
h = k / tube_diameter * Nu
efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
D_fin=fin_diameter,
t_fin=fin_thickness,
k_fin=k_fin,
h=h)
h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
h_bare_tube_basis = h_total_area_basis * A_increase
return h_bare_tube_basis
def h_ESDU_high_fin(m,
A,
A_min,
A_increase,
A_fin,
A_tube_showing,
tube_diameter,
fin_diameter,
fin_thickness,
bare_length,
pitch_parallel,
pitch_normal,
tube_rows,
rho,
Cp,
mu,
k,
k_fin,
Pr_wall=None):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with the formulas of [2]_ as presented in [1]_.
.. math::
Nu = 0.242 Re^{0.658} \left(\frac{\text{bare length}}
{\text{fin height}}\right)^{0.297}
\left(\frac{P_1}{P_2}\right)^{-0.091} P_r^{1/3}\cdot F_1\cdot F_2
.. math::
h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h
.. math::
h_{bare,total} = A_{increase} h_{A,total}
Parameters
----------
m : float
Mass flow rate of air across the tube bank, [kg/s]
A : float
Surface area of combined finned and non-finned area exposed for heat
transfer, [m^2]
A_min : float
Minimum air flow area, [m^2]
A_increase : float
Ratio of actual surface area to bare tube surface area
:math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
A_fin : float
Surface area of all fins in the bundle, [m^2]
A_tube_showing : float
Area of the bare tube which is exposed in the bundle, [m^2]
tube_diameter : float
Diameter of the bare tube, [m]
fin_diameter : float
Outer diameter of each tube after including the fin on both sides,
[m]
fin_thickness : float
Thickness of the fins, [m]
bare_length : float
Length of bare tube between two fins
:math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
pitch_parallel : float
Distance between tube center along a line parallel to the flow;
has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
pitch_normal : float
Distance between tube centers in a line 90° to the line of flow;
has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
tube_rows : int
Number of tube rows per bundle, [-]
rho : float
Average (bulk) density of air across the tube bank, [kg/m^3]
Cp : float
Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
mu : float
Average (bulk) viscosity of air across the tube bank, [Pa*s]
k : float
Average (bulk) thermal conductivity of air across the tube bank,
[W/m/K]
k_fin : float
Thermal conductivity of the fin, [W/m/K]
Pr_wall : float, optional
Prandtl number at the wall temperature; provide if a correction with
the defaults parameters is desired; otherwise apply the correction
elsewhere, [-]
Returns
-------
h_bare_tube_basis : float
Air side heat transfer coefficient on a bare-tube surface area as if
there were no fins present basis, [W/K/m^2]
Notes
-----
The tube-row count correction factor is 1 for four or more rows, 0.92 for
three rows, 0.84 for two rows, and 0.76 for one row according to [1]_.
The property correction factor can be disabled by not specifying
`Pr_wall`. A Prandtl number exponent of 0.26 is recommended in [1]_ for
heating and cooling for both liquids and gases.
Examples
--------
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=20, tube_length=3,
... tube_diameter=1*inch, fin_thickness=0.000406, fin_density=1/0.002309,
... pitch_normal=.06033, pitch_parallel=.05207,
... fin_height=0.0159, tube_thickness=(.0254-.0186)/2,
... bundles_per_bay=1, parallel_bays=1, corbels=True)
>>> h_ESDU_high_fin(m=21.56, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
... pitch_normal=AC.pitch_normal, pitch_parallel=AC.pitch_parallel,
... rho=1.161, Cp=1007., mu=1.85E-5, k=0.0263, k_fin=205)
1390.888918049757
References
----------
.. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press,
1994.
.. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986).
.. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
in Cross Flow." Heat Transfer Engineering 8, no. 2 (January 1987):
49-62.
'''
fin_height = 0.5 * (fin_diameter - tube_diameter)
V_max = m / (A_min * rho)
Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
Pr = Prandtl(Cp=Cp, mu=mu, k=k)
Nu = 0.242 * Re**0.658 * (bare_length / fin_height)**0.297 * (
pitch_normal / pitch_parallel)**-0.091 * Pr**(1 / 3.)
if tube_rows < 2:
F2 = 0.76
elif tube_rows < 3:
F2 = 0.84
elif tube_rows < 4:
F2 = 0.92
else:
F2 = 1.0
Nu *= F2
if Pr_wall is not None:
F1 = wall_factor(Pr=Pr,
Pr_wall=Pr_wall,
Pr_heating_coeff=0.26,
Pr_cooling_coeff=0.26,
property_option=WALL_FACTOR_PRANDTL)
Nu *= F1
h = k / tube_diameter * Nu
efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
D_fin=fin_diameter,
t_fin=fin_thickness,
k_fin=k_fin,
h=h)
h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
h_bare_tube_basis = h_total_area_basis * A_increase
return h_bare_tube_basis
def h_Briggs_Young(m, A, A_min, A_increase, A_fin, A_tube_showing,
tube_diameter, fin_diameter, fin_thickness, bare_length,
rho, Cp, mu, k, k_fin):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with the formulas of Briggs and Young [1], [2]_
[3]_.
.. math::
Nu = 0.134Re^{0.681} Pr^{0.33}\left(\frac{S}{h}\right)^{0.2}
\left(\frac{S}{b}\right)^{0.1134}
Parameters
----------
m : float
Mass flow rate of air across the tube bank, [kg/s]
A : float
Surface area of combined finned and non-finned area exposed for heat
transfer, [m^2]
A_min : float
Minimum air flow area, [m^2]
A_increase : float
Ratio of actual surface area to bare tube surface area
:math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
A_fin : float
Surface area of all fins in the bundle, [m^2]
A_tube_showing : float
Area of the bare tube which is exposed in the bundle, [m^2]
tube_diameter : float
Diameter of the bare tube, [m]
fin_diameter : float
Outer diameter of each tube after including the fin on both sides,
[m]
fin_thickness : float
Thickness of the fins, [m]
bare_length : float
Length of bare tube between two fins
:math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
rho : float
Average (bulk) density of air across the tube bank, [kg/m^3]
Cp : float
Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
mu : float
Average (bulk) viscosity of air across the tube bank, [Pa*s]
k : float
Average (bulk) thermal conductivity of air across the tube bank,
[W/m/K]
k_fin : float
Thermal conductivity of the fin, [W/m/K]
Returns
-------
h_bare_tube_basis : float
Air side heat transfer coefficient on a bare-tube surface area as if
there were no fins present basis, [W/K/m^2]
Notes
-----
The limits on this equation are :math:`1000 < Re < `8000`,
11.13 mm :math:`< D_o < ` 40.89 mm, 1.42 mm < fin height < 16.57 mm,
0.33 mm < fin thickness < 2.02 mm, 1.30 mm < fin pitch < 4.06 mm, and
24.49 mm < normal pitch < 111 mm.
Examples
--------
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=20, tube_length=3,
... tube_diameter=1*inch, fin_thickness=0.000406, fin_density=1/0.002309,
... pitch_normal=.06033, pitch_parallel=.05207,
... fin_height=0.0159, tube_thickness=(.0254-.0186)/2,
... bundles_per_bay=1, parallel_bays=1, corbels=True)
>>> h_Briggs_Young(m=21.56, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
... fin_thickness=AC.fin_thickness,
... rho=1.161, Cp=1007., mu=1.85E-5, k=0.0263, k_fin=205)
1422.8722403237716
References
----------
.. [1] Briggs, D.E., and Young, E.H., 1963, "Convection Heat Transfer and
Pressure Drop of Air Flowing across Triangular Banks of Finned Tubes",
Chemical Engineering Progress Symp., Series 41, No. 59. Chem. Eng. Prog.
Symp. Series No. 41, "Heat Transfer - Houston".
.. [2] Mukherjee, R., and Geoffrey Hewitt. Practical Thermal Design of
Air-Cooled Heat Exchangers. New York: Begell House Publishers Inc.,U.S.,
2007.
.. [3] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers:
Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
PennWell Corp., 2004.
'''
fin_height = 0.5 * (fin_diameter - tube_diameter)
V_max = m / (A_min * rho)
Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
Pr = Prandtl(Cp=Cp, mu=mu, k=k)
Nu = 0.134 * Re**0.681 * Pr**(1 / 3.) * (bare_length / fin_height)**0.2 * (
bare_length / fin_thickness)**0.1134
h = k / tube_diameter * Nu
efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
D_fin=fin_diameter,
t_fin=fin_thickness,
k_fin=k_fin,
h=h)
h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
h_bare_tube_basis = h_total_area_basis * A_increase
return h_bare_tube_basis
def Aggour(m, x, alpha, D, rhol, Cpl, kl, mu_b, mu_w=None, L=None,
turbulent=None):
r'''Calculates the two-phase non-boiling laminar heat transfer coefficient
of a liquid and gas flowing inside a tube of any inclination, as in [1]_
and reviewed in [2]_.
Laminar for Rel <= 2000:
.. math::
h_{TP} = 1.615\frac{k_l}{D}\left(\frac{Re_l Pr_l D}{L}\right)^{1/3}
\left(\frac{\mu_b}{\mu_w}\right)^{0.14}
Turbulent for Rel > 2000:
.. math::
h_{TP} = 0.0155\frac{k_l}{D} Pr_l^{0.5} Re_l^{0.83}
.. math::
Re_l = \frac{\rho_l v_l D}{\mu_l}
.. math::
V_l = \frac{V_{ls}}{1-\alpha}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval [-]
alpha : float
Void fraction in the tube, [-]
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
kl : float
Thermal conductivity of liquid [W/m/K]
mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet
temperature) [Pa*s]
mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
L : float, optional
Length of the tube, [m]
turbulent : bool or None, optional
Whether or not to force the correlation to return the turbulent
result; will return the laminar regime if False
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
Developed with mixtures of air-water, helium-water, and freon-12-water and
vertical tests. Studied flow patterns were bubbly, slug, annular,
bubbly-slug, and slug-annular regimes. Superficial velocity ratios ranged
from 0.02 to 470.
A viscosity correction is only suggested for the laminar regime.
If the viscosity at the wall temperature is not given, the liquid viscosity
correction is not applied.
Examples
--------
>>> Aggour(m=1, x=.9, D=.3, alpha=.9, rhol=1000, Cpl=2300, kl=.6, mu_b=1E-3)
420.9347146885667
References
----------
.. [1] Aggour, Mohamed A. Hydrodynamics and Heat Transfer in Two-Phase
Two-Component Flows, Ph.D. Thesis, University of Manutoba, Canada
(1978). http://mspace.lib.umanitoba.ca/xmlui/handle/1993/14171.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vls = m*(1-x)/(rhol*pi/4*D**2)
Vl = Vls/(1.-alpha)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mu_b)
if turbulent or (Rel > 2000.0 and turbulent is None):
hl = 0.0155*(kl/D)*Rel**0.83*Prl**0.5
return hl*(1-alpha)**-0.83
else:
hl = 1.615*(kl/D)*(Rel*Prl*D/L)**(1/3.)
if mu_w:
hl *= (mu_b/mu_w)**0.14
return hl*(1.0 - alpha)**(-1/3.)
def Martin_Sims(m, x, D, rhol, rhog, hl=None,
Cpl=None, kl=None, mu_b=None, mu_w=None, L=None):
r'''Calculates the two-phase non-boiling heat transfer coefficient of a
liquid and gas flowing inside a tube of any inclination, as in [1]_ and
reviewed in [2]_.
.. math::
\frac{h_{TP}}{h_l} = 1 + 0.64\sqrt{\frac{V_{gs}}{V_{ls}}}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
hl : float, optional
Liquid-phase heat transfer coefficient as described below, [W/m^2/K]
Cpl : float, optional
Constant-pressure heat capacity of liquid [J/kg/K]
kl : float, optional
Thermal conductivity of liquid [W/m/K]
mu_b : float, optional
Viscosity of liquid at bulk conditions (average of inlet/outlet
temperature) [Pa*s]
mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
L : float, optional
Length of the tube [m]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
No specific suggestion for how to calculate the liquid-phase heat transfer
coefficient is given in [1]_; [2]_ suggests to use the same procedure as
in `Knott`.
Examples
--------
>>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, hl=141.2)
5563.280000000001
>>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
... mu_b=1E-3, mu_w=1.2E-3, L=24)
5977.505465781747
References
----------
.. [1] Martin, B. W, and G. E Sims. "Forced Convection Heat Transfer to
Water with Air Injection in a Rectangular Duct." International Journal
of Heat and Mass Transfer 14, no. 8 (August 1, 1971): 1115-34.
doi:10.1016/0017-9310(71)90208-0.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m*x/(rhog*pi/4*D**2)
Vls = m*(1-x)/(rhol*pi/4*D**2)
if hl is None:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=D, mu=mu_b, mu_w=mu_w)
hl = Nul*kl/D
return hl*(1.0 + 0.64*(Vgs/Vls)**0.5)
def Knott(m, x, D, rhol, rhog, Cpl=None, kl=None, mu_b=None, mu_w=None, L=None,
hl=None):
r'''Calculates the two-phase non-boiling heat transfer coefficient of a
liquid and gas flowing inside a tube of any inclination, as in [1]_ and
reviewed in [2]_.
Either a specified `hl` is required, or `Cpl`, `kl`, `mu_b`, `mu_w` and
`L` are required to calculate `hl`.
.. math::
\frac{h_{TP}}{h_l} = \left(1 + \frac{V_{gs}}{V_{ls}}\right)^{1/3}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval [-]
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
Cpl : float, optional
Constant-pressure heat capacity of liquid [J/kg/K]
kl : float, optional
Thermal conductivity of liquid [W/m/K]
mu_b : float, optional
Viscosity of liquid at bulk conditions (average of inlet/outlet
temperature) [Pa*s]
mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
L : float, optional
Length of the tube [m]
hl : float, optional
Liquid-phase heat transfer coefficient as described below, [W/m^2/K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
The liquid-only heat transfer coefficient will be calculated with the
`laminar_entry_Seider_Tate` correlation, should it not be provided as an
input. Many of the arguments to this function are optional and are only
used if `hl` is not provided.
`hl` should be calculated with a velocity equal to that determined with
a combined volumetric flow of both the liquid and the gas. All other
parameters used in calculating the heat transfer coefficient are those
of the liquid. If the viscosity at the wall temperature is not given, the
liquid viscosity correction in `laminar_entry_Seider_Tate` is not applied.
Examples
--------
>>> Knott(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mu_b=1E-3,
... mu_w=1.2E-3, L=4)
4225.536758045839
References
----------
.. [1] Knott, R. F., R. N. Anderson, Andreas. Acrivos, and E. E. Petersen.
"An Experimental Study of Heat Transfer to Nitrogen-Oil Mixtures."
Industrial & Engineering Chemistry 51, no. 11 (November 1, 1959):
1369-72. doi:10.1021/ie50599a032.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m*x/(rhog*pi/4*D**2)
Vls = m*(1-x)/(rhol*pi/4*D**2)
if not hl:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=D, mu=mu_b, mu_w=mu_w)
hl = Nul*kl/D
return hl*(1 + Vgs/Vls)**(1/3.)
def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in [1]_ and again by the same
author in [2]_; also given in [3]_. Requires no properties of the gas.
Uses the Dittus-Boelter correlation for single phase heat transfer
coefficient, with a Reynolds number assuming all the flow is liquid.
.. math::
h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}}
{P_r^{0.38}}\right]
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval [-]
D : float
Diameter of the channel [m]
rhol : float
Density of the liquid [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
P : float
Pressure of the fluid, [Pa]
Pc : float
Critical pressure of the fluid, [Pa]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ is well written an unambiguous as to how to apply this equation.
Examples
--------
>>> Shah(m=1, x=0.4, D=.3, rhol=800, mul=1E-5, kl=0.6, Cpl=2300, P=1E6, Pc=2E7)
2561.2593415479214
References
----------
.. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film
Condensation inside Pipes." International Journal of Heat and Mass
Transfer 22, no. 4 (April 1, 1979): 547-56.
doi:10.1016/0017-9310(79)90058-9.
.. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and
Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no.
3, pp. 1086-1100, 1981.
.. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
'''
VL = m / (rhol * pi / 4 * D**2)
ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
hL = turbulent_Dittus_Boelter(ReL, Prl) * kl / D
Pr = P / Pc
return hL * ((1 - x)**0.8 + 3.8 * x**0.76 * (1 - x)**0.04 / Pr**0.38)
def Cavallini_Smith_Zecchin(m, x, D, rhol, rhog, mul, mug, kl, Cpl):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in
[1]_, also given in [2]_ and [3]_.
.. math::
Nu = \frac{hD_i}{k_l} = 0.05 Re_e^{0.8} Pr_l^{0.33}
.. math::
Re_{eq} = Re_g(\mu_g/\mu_l)(\rho_l/\rho_g)^{0.5} + Re_l
.. math::
v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}
.. math::
v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval [-]
D : float
Diameter of the channel [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
Examples
--------
>>> Cavallini_Smith_Zecchin(m=1, x=0.4, D=.3, rhol=800, rhog=2.5, mul=1E-5, mug=1E-3, kl=0.6, Cpl=2300)
5578.218369177804
References
----------
.. [1] A. Cavallini, J. R. Smith and R. Zecchin, A dimensionless correlation
for heat transfer in forced convection condensation, 6th International
Heat Transfer Conference., Tokyo, Japan (1974) 309-313.
.. [2] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
.. [3] Balcılar, Muhammet, Ahmet Selim Dalkılıç, Berna Bolat, and Somchai
Wongwises. "Investigation of Empirical Correlations on the Determination
of Condensation Heat Transfer Characteristics during Downward Annular
Flow of R134a inside a Vertical Smooth Tube Using Artificial
Intelligence Algorithms." Journal of Mechanical Science and Technology
25, no. 10 (October 12, 2011): 2683-2701. doi:10.1007/s12206-011-0618-2.
'''
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
Vl = m * (1 - x) / (rhol * pi / 4 * D**2)
Vg = m * x / (rhog * pi / 4 * D**2)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mul)
Reg = Reynolds(V=Vg, D=D, rho=rhog, mu=mug)
'''The following was coded, and may be used instead of the above lines,
to check that the definitions of parameters here provide the same results
as those defined in [1]_.
G = m/(pi/4*D**2)
Re = G*D/mul
Rel = Re*(1-x)
Reg = Re*x/(mug/mul)'''
Reeq = Reg * (mug / mul) * (rhol / rhog)**0.5 + Rel
Nul = 0.05 * Reeq**0.8 * Prl**0.33
return Nul * kl / D # confirmed to be with respect to the liquid