def ShahCondensation_Average(x_min,x_max,Ref,G,D,p,TsatL,TsatV):
it_2=my_counter_2.next()
#print it_2
if G<0:
G=3
else:
pass
# ********************************
# Necessary Properties
# Calculated outside the quadrature integration for speed
# ********************************
mu_f = PropsSI('V', 'T', TsatL, 'Q', 0, Ref) #kg/m-s
cp_f = PropsSI('C', 'T', TsatL, 'Q', 0, Ref)#*1000 #J/kg-K
k_f = PropsSI('L', 'T', TsatV, 'Q', 0, Ref)#*1000 #W/m-K
Pr_f = cp_f * mu_f / k_f #[-]
Pstar = p / PropsSI(Ref,'Pcrit')
if it_2==357:
h_L = 0.023 * (G*D/mu_f)**(0.8) * Pr_f**(0.4) * k_f / D #[W/m^2-K]
else:
h_L = 0.023 * (G*D/mu_f)**(0.8) * Pr_f**(0.4) * k_f / D #[W/m^2-K]
def ShahCondensation(x,Ref,G,D,p):
return h_L * ((1 - x)**(0.8) + (3.8 * x**(0.76) * (1 - x)**(0.04)) / (Pstar**(0.38)) )
if not x_min==x_max:
#A proper range is given
return quad(ShahCondensation,x_min,x_max,args=(Ref,G,D,p))[0]/(x_max-x_min)
else:
#A single value is given
return ShahCondensation(x_min,Ref,G,D,p)
def ShahCondensation_Average(x_min, x_max, Ref, G, D, p, TsatL, TsatV):
it_2 = my_counter_2.next()
#print it_2
if G < 0:
G = 3
else:
pass
# ********************************
# Necessary Properties
# Calculated outside the quadrature integration for speed
# ********************************
mu_f = PropsSI('V', 'T', TsatL, 'Q', 0, Ref) #kg/m-s
cp_f = PropsSI('C', 'T', TsatL, 'Q', 0, Ref) #*1000 #J/kg-K
k_f = PropsSI('L', 'T', TsatV, 'Q', 0, Ref) #*1000 #W/m-K
Pr_f = cp_f * mu_f / k_f #[-]
Pstar = p / PropsSI(Ref, 'Pcrit')
if it_2 == 357:
h_L = 0.023 * (G * D / mu_f)**(0.8) * Pr_f**(0.4) * k_f / D #[W/m^2-K]
else:
h_L = 0.023 * (G * D / mu_f)**(0.8) * Pr_f**(0.4) * k_f / D #[W/m^2-K]
def ShahCondensation(x, Ref, G, D, p):
return h_L * ((1 - x)**(0.8) + (3.8 * x**(0.76) * (1 - x)**(0.04)) /
(Pstar**(0.38)))
if not x_min == x_max:
#A proper range is given
return quad(ShahCondensation, x_min, x_max,
args=(Ref, G, D, p))[0] / (x_max - x_min)
else:
#A single value is given
return ShahCondensation(x_min, Ref, G, D, p)
def MultiDimNewtRaph(f,
x0,
dx=1e-6,
args=(),
ytol=1e-4,
w=1.0,
JustOneStep=False):
"""
A Newton-Raphson solver where the Jacobian is always re-evaluated rather than
re-using the information as in the fsolve method of scipy.optimize
"""
x = np.array(x0)
error = 999
J = np.zeros((len(x), len(x)))
error_list = []
iteration_list = []
#If a float is passed in for dx, convert to a numpy-like list the same shape
#as x
if isinstance(dx, float):
dx = dx * np.ones_like(x)
r0 = array(f(x, *args))
while abs(error) > ytol:
#Build the Jacobian matrix by columns
for i in range(len(x)):
epsilon = np.zeros_like(x)
epsilon[i] = dx[i]
J[:, i] = (array(f(x + epsilon, *args)) - r0) / epsilon[i]
v = np.dot(-inv(J), r0)
x = x + w * v
#Calculate the residual vector at the new step
r0 = f(x, *args)
error = np.max(np.abs(r0))
iteration = my_counter_2.next()
error_list.append(error)
iteration_list.append(iteration)
#print error
#Just do one step and stop
if JustOneStep == True:
return x
error_convergence = np.array(error_list)
iteration_convergence = np.array(iteration_list)
print '---MultiDimNewtRaph---'
print iteration_convergence
print error_convergence
matplotlib.rc('text', usetex=True)
plt.rc('font', family='serif')
fig = figure(figsize=(8, 6))
ax = fig.add_subplot(1, 1, 1)
plot(iteration_convergence,
error_convergence,
'bs-',
linewidth=2.0,
markersize=10,
markerfacecolor="blue",
markeredgewidth=2,
markeredgecolor="black")
plt.axhline(y=1e-5, color='r', ls='dashed', linewidth=2.5)
xlabel('Iteration [-] ', fontsize=18)
ylabel(r'$|Resid|$', fontsize=18)
title('Overall Cycle Convergence', fontsize=18)
plt.yscale('log')
plt.minorticks_off()
for tickx in ax.xaxis.get_major_ticks():
tickx.label.set_fontsize(20)
for ticky in ax.yaxis.get_major_ticks():
ticky.label.set_fontsize(20)
show()
fig.savefig('MultiDimNewtRaph.png', dpi=300)
return x
def MultiDimNewtRaph(f,x0,dx=1e-6,args=(),ytol=1e-4,w=1.0,JustOneStep=False):
"""
A Newton-Raphson solver where the Jacobian is always re-evaluated rather than
re-using the information as in the fsolve method of scipy.optimize
"""
x=np.array(x0)
error=999
J=np.zeros((len(x),len(x)))
error_list=[]
iteration_list = []
#If a float is passed in for dx, convert to a numpy-like list the same shape
#as x
if isinstance(dx,float):
dx=dx*np.ones_like(x)
r0=array(f(x,*args))
while abs(error)>ytol:
#Build the Jacobian matrix by columns
for i in range(len(x)):
epsilon=np.zeros_like(x)
epsilon[i]=dx[i]
J[:,i]=(array(f(x+epsilon,*args))-r0)/epsilon[i]
v=np.dot(-inv(J),r0)
x=x+w*v
#Calculate the residual vector at the new step
r0=f(x,*args)
error = np.max(np.abs(r0))
iteration=my_counter_2.next()
error_list.append(error)
iteration_list.append(iteration)
#print error
#Just do one step and stop
if JustOneStep==True:
return x
error_convergence = np.array(error_list)
iteration_convergence = np.array(iteration_list)
print '---MultiDimNewtRaph---'
print iteration_convergence
print error_convergence
matplotlib.rc('text', usetex=True)
plt.rc('font', family='serif')
fig=figure(figsize=(8,6))
ax=fig.add_subplot(1,1,1)
plot(iteration_convergence, error_convergence,'bs-',linewidth=2.0,markersize = 10,markerfacecolor="blue", markeredgewidth=2, markeredgecolor="black")
plt.axhline(y=1e-5,color='r',ls='dashed', linewidth=2.5)
xlabel('Iteration [-] ',fontsize=18)
ylabel(r'$|Resid|$',fontsize=18)
title('Overall Cycle Convergence',fontsize=18)
plt.yscale('log')
plt.minorticks_off()
for tickx in ax.xaxis.get_major_ticks():
tickx.label.set_fontsize(20)
for ticky in ax.yaxis.get_major_ticks():
ticky.label.set_fontsize(20)
show()
fig.savefig('MultiDimNewtRaph.png',dpi=300)
return x