def test_one_phase_dP_dz_acceleration_example():
# This requires thermo!
from thermo import Stream, Vm_to_rho
from fluids import one_phase_dP, one_phase_dP_acceleration
import numpy as np
from scipy.integrate import odeint
from numpy.testing import assert_allclose
P0 = 1E5
s = Stream(['nitrogen', 'methane'], T=300, P=P0, zs=[0.5, 0.5], m=1)
rho0 = s.rho
D = 0.1
def dP_dz(P, L, acc=False):
s.flash(P=float(P), Hm=s.Hm)
dPf = one_phase_dP(m=s.m, rho=s.rhog, mu=s.rhog, D=D, roughness=0, L=1)
if acc:
G = 4.0*s.m/(np.pi*D*D)
der = s.VolumeGasMixture.property_derivative_P(P=s.P, T=s.T, zs=s.zs, ws=s.ws)
der = 1/Vm_to_rho(der, s.MW)
factor = G*G*der
dP = dPf/(1.0 + factor)
return -dP
return -dPf
ls = np.linspace(0, .01)
dP_noacc = odeint(dP_dz, s.P, ls, args=(False,))[-1]
s.flash(P=float(P0), Hm=s.Hm) # Reset the stream object
profile = odeint(dP_dz, s.P, ls, args=(True,))
dP_acc = profile[-1]
s.flash(P=dP_acc, Hm=s.Hm)
rho1 = s.rho
dP_acc_numerical = dP_noacc - dP_acc
dP_acc_basic = one_phase_dP_acceleration(m=s.m, D=D, rho_o=rho1, rho_i=rho0)
assert_allclose(dP_acc_basic, dP_acc_numerical, rtol=1E-4)
def test_one_phase_dP_dz_acceleration_example():
# This requires thermo!
from thermo import Stream, Vm_to_rho
from fluids import one_phase_dP, one_phase_dP_acceleration
import numpy as np
from scipy.integrate import odeint
from fluids.numerics import assert_close
P0 = 1E5
s = Stream(['nitrogen', 'methane'], T=300, P=P0, zs=[0.5, 0.5], m=1)
rho0 = s.rho
D = 0.1
def dP_dz(P, L, acc=False):
s.flash(P=float(P), Hm=s.Hm)
dPf = one_phase_dP(m=s.m,
rho=s.rhog,
mu=s.rhog,
D=D,
roughness=0,
L=1.0)
if acc:
G = 4.0 * s.m / (pi * D * D)
der = s.VolumeGasMixture.property_derivative_P(P=s.P,
T=s.T,
zs=s.zs,
ws=s.ws)
der = 1 / Vm_to_rho(der, s.MW)
factor = G * G * der
dP = dPf / (1.0 + factor)
return -dP
return -dPf
ls = linspace(0, .01)
dP_noacc = odeint(dP_dz, s.P, ls, args=(False, ))[-1]
s.flash(P=float(P0), Hm=s.Hm) # Reset the stream object
profile = odeint(dP_dz, s.P, ls, args=(True, ))
dP_acc = profile[-1]
s.flash(P=dP_acc, Hm=s.Hm)
rho1 = s.rho
dP_acc_numerical = dP_noacc - dP_acc
dP_acc_basic = one_phase_dP_acceleration(m=s.m,
D=D,
rho_o=rho1,
rho_i=rho0)
assert_close(dP_acc_basic, dP_acc_numerical, rtol=1E-4)
def Analysis(L, OD, N2, H2, H2O, CO2, CO, m):
"""Conditions"""
comp = [
'nitrogen', 'hydrogen', 'water', 'carbon dioxide', 'carbon monoxide'
]
zs = [N2, H2, H2O, CO2, CO]
for i in range(0, len(zs)):
if zs[i] == 0:
if i == 0:
comp.remove('nitrogen')
elif i == 1:
comp.remove('hydrogen')
elif i == 2:
comp.remove('water')
elif i == 3:
comp.remove('carbon dioxide')
else:
comp.remove('carbon monoxide')
zs = np.array(zs)
zeros = len(zs) - np.count_nonzero(zs > 0)
delete = np.arange(0, zeros)
for i in delete:
zs = np.delete(zs, np.where(zs == 0))
Pavg = 0.859826 #atm
Pavg_pa = 87121.86945 #Pa
R = 0.08206 #L*atm/mol/K
sigma = 5.67e-8
Tavg = 681.15 #K
Ti = 293.15 #K
def Moody_fff(Re, eps):
if Re < 2100:
return 16 / Re
else:
y = -np.log10(eps / 3.7 - 4.52 / Re * np.log10(7 / Re + eps / 7))
y = -np.log10(eps / 3.7 + 5.02 * y / Re)
y = -np.log10(eps / 3.7 + 5.02 * y / Re)
y = -np.log10(eps / 3.7 + 5.02 * y / Re)
return 1 / (16 * y**2)
def Nusselt(Re, Pr):
if Re < 2100:
return 3.66
else:
return 0.023 * Re**0.8 * Pr**0.4
Feed = Stream(comp, zs=zs, T=Tavg, P=Pavg_pa, m=m)
mixture = Mixture(comp, zs=zs, T=Tavg, P=Pavg_pa)
"""Gas Properties"""
Cp = Feed.Cp #J/kg/K
MW = Feed.MW #g/mol
mu = Feed.mu #Pa*s or kg/m/s
Pr = Feed.Pr
k = Feed.k #W/m/k
rho = Feed.rho #kg/m3
"""Tubing Properties"""
Cp1 = 511 #J/kg/C # at 427 C
rho1 = 8440 #kg/m3
k1 = 15.7 #W/m/C at 427 C
epsilon = 0.8 #emissivity
"""System"""
OD *= .0254 #m
thick = 0.035 * .0254 #m
ID = (OD - 2 * thick) #m
CSA_i = np.pi * ID**2 / 4 #m2
SA_i = np.pi * ID * L
"""Flud Analysis"""
E = 0.000196721
v = m / rho / CSA_i
Re = rho * v * ID / mu
fff = Moody_fff(Re, E)
dP = 4 * fff * rho * (L / ID) * (v**2 / 2) #Pa
Nu = Nusselt(Re, Pr)
h = Nu * k / ID
h_fc = 25 #W/m2/K
Rthermal = (1 / h / np.pi / ID / L) + np.log(OD / ID) / 2 / np.pi / L / k1
U = 1 / Rthermal / SA_i #W/m2/K
"""Solution"""
n = 1000 #number of tubing node
x = np.linspace(0, L, n)
dx = L / n
Tw = 1073.15 #K
Tcsa = Tw - (Tw - Ti) * np.exp(-np.pi * ID * x * h / m / Cp)
Tg = np.linspace(Ti, Tw, n)
for i in range(0, n):
def res(T):
Tgi = T[0]
Tti = T[1]
eq1 = np.pi * OD * dx * sigma * epsilon * (
Tw**4 - Tti**4) + h_fc * np.pi * OD * dx * (
Tw - Tti) - np.pi * ID * dx * U * (Tti - Tgi)
eq2 = np.pi * ID * dx * U * (Tti - Tgi) - m * Cp * (Tgi -
Tg[i - 1])
return [eq1, eq2]
if i == 0:
inletT = lambda Tt0: np.pi * OD * dx * sigma * epsilon * (
1073.15**4 - Tt0**4) + h_fc * np.pi * OD * dx * (
Tw - Tt0) - np.pi * ID * dx * U * (Tt0 - Tg[i])
inletTt = fsolve(inletT, 600)
Tt = np.linspace(inletTt[0], Tw, n)
else:
sol = fsolve(res, [Tg[i - 1], Tt[i - 1]])
Tg[i] = sol[0]
Tt[i] = sol[1]
plt.clf()
plt.plot(x, Tg - 273.15, color='blue', label='Gas T')
plt.plot(x, Tt - 273.15, color='red', label='Tube T')
plt.plot(x,
Tcsa - 273.15,
color='orange',
label='Constant Surface T Assumption')
plt.axis([0, L, 0, 850])
plt.xlabel('Distance (m)')
plt.ylabel('Temperature (C)')
plt.legend(loc='lower right')
plt.show()
print('----- Gas Properites -----')
print('Cp = {:.3f} J/kg/K'.format(Cp))
print('MW = {:.3f} g/mol'.format(MW))
print(' μ = {:.3e} kg/m/s'.format(mu))
print('Pr = {:.3f}'.format(Pr))
print(' k = {:.3f} W/m/K'.format(k))
print(' ρ = {:.3f} kg/m3'.format(rho))
print(' h = {:.3f} W/m2/K'.format(h))
print('ΔP = {:.3f} Pa'.format(dP))
print('--------------------------')
if Tg[-1] > (795 + 273.15):
L795 = np.interp(795 + 273.15, Tg, x)
print('T = 795 C after {:.1f} m'.format(L795))
else:
print('T = {:.2f} C after {:.1f} m'.format(Tg[-1] - 273.15, L))