def hFit(a,T):
"""
a = [a1 ... a6]
T is numpy array
Returns h and dh/dT (where by h, H/RT is meant)
"""
h = a[0] + a[1]*T/2 + a[2]*T**2/3 + a[3]*T**3/4 + a[4]*T**4/5 + a[5]/T
dhdT = a[1]/2 + a[2]*2*T/3 + a[3]*3*T**2/4 + a[4]*4*T**3/5 - a[5]/T**2
return h,dhdT
def sFit(a,T):
"""
a = [a1 ... a7]
T is numpy array
Returns s and ds/dT (where by s, S/R is meant)
"""
s = a[0]*np.log(T) + a[1]*T + a[2]*T**2/2 + a[3]*T**3/3 + a[4]*T**4/4 + a[6]
dsdT = a[0]/T + a[1] + a[2]*T + a[3]*T**2 + a[4]*T**3
return s,dsdT
def coeffImport(species):
"""
Takes a Cantera species object
"""
midT = species.thermo.coeffs[0]
minT = species.thermo.min_temp
maxT = species.thermo.max_temp
highCoeffs = species.thermo.coeffs[1:8]
lowCoeffs = species.thermo.coeffs[8:15]
return minT,midT,maxT,lowCoeffs,highCoeffs
def continuity(mech,absTol=1e-5):
"""
Takes a string representing Cantera mechanism, e.g. 'gri30.cti'
absTol is the absolute tolerance used when checking for C0 and C1
continuity. Can vary the default value if desired.
Absolute rather than relative tolerance used to avoid division by zero
since some species (e.g. Ar) have zero slope for all T.
"""
print('Mechanism file '+mech)
gas = ct.Solution(mech)
ns = gas.n_species
ne= gas.n_elements
nr = gas.n_reactions
"""
Compute gas standard state properties for each species
"""
T0 = 298.15
P0 = 101325.
gas.TP = T0, P0
R = ct.gas_constant # universal gas constant
w = np.zeros(ns)
hs = np.zeros(ns)
cps = np.zeros(ns)
ss = np.zeros(ns)
deltahf = np.zeros(ns)
for k in range(gas.n_species):
w[k]=gas.molecular_weights[k] # molecular weight of the ith species
hs[k] = gas.standard_enthalpies_RT[k] #specific enthalpy of the ith species
deltahf[k] = 1E-6*hs[k]*R*gas.T # heat of formation (kJ/mol)
cps[k] = gas.standard_cp_R[k] # heat capacity of the ith species
ss[k] = gas.standard_entropies_R[k] # entropy of the ith species
print('Number of elements = '+str(ne))
print('Number of species = '+str(ns))
print('Number of reactions = '+str(nr))
S = ct.Species.listFromFile(mech) # list of species objects
nCoeffs = int((S[0].thermo.n_coeffs-1)/2) # number of coefficients per polynomial, i.e. identifies NASA-7 vs. NASA-9s
globalMinT = gas.min_temp
globalMaxT = gas.max_temp
print('NASA-'+str(nCoeffs)+' polynomials')
print('Range of valid temperatures for all fits:')
print('Max(Min. T) for all species = '+str(globalMinT)+' K')
print('Min(Max. T) for all species = '+str(globalMaxT)+' K')
print("Absolute error tolerance for C0 and C1 {:.2e}".format(absTol))
print('\n')
f = open("BadSpecies.txt","w+")
print('Species\tCp C0\tCp C1\th C0\th C1\ts C0\ts C1\tMin T\tMid T\tMax T\tW\tCp/R\tS/R\tH/RT\tDeltaHf')
cpjumpmax = 0.
ibad = 0
for i,species in enumerate(S):
minT,midT,maxT,lowCoeffs,highCoeffs = coeffImport(species)
# Polynomial class takes coefficients in ascending powers of x
lowPolyCp = P(lowCoeffs[0:5])
highPolyCp = P(highCoeffs[0:5])
# Check for continuity
cpjump = abs(lowPolyCp(midT)-highPolyCp(midT))
if cpjump > cpjumpmax:
cpjumpmax = cpjump
spmax = species
cpc0 = cpjump < absTol
if not cpc0:
f.write('{0:18} {1:10.2f} {2:10.2f} {3:10.2f} \n'.format(species.name,minT,midT,maxT))
ibad = ibad + 1
cpc1 = abs(lowPolyCp.deriv()(midT)-highPolyCp.deriv()(midT)) < absTol
hc0 = abs(hFit(lowCoeffs[0:6],midT)[0]-hFit(highCoeffs[0:6],midT)[0]) < absTol
hc1 = abs(hFit(lowCoeffs[0:6],midT)[1]-hFit(highCoeffs[0:6],midT)[1]) < absTol
sc0 = abs(sFit(lowCoeffs[0:7],midT)[0]-sFit(highCoeffs[0:7],midT)[0]) < absTol
sc1 = abs(sFit(lowCoeffs[0:7],midT)[1]-sFit(highCoeffs[0:7],midT)[1]) < absTol
print(species.name+'\t'+str(cpc0)+'\t'+str(cpc1)+'\t'+str(hc0)+'\t'+str(hc1)+'\t'+str(sc0)+'\t'+ \
str(sc1)+'\t'+str(minT)+'\t'+str(midT)+'\t'+str(maxT)+'\t{:.2f}'.format(w[i])+'\t{:.2f}'.format(cps[i])+ \
'\t{:.2f}'.format(ss[i])+'\t{:7.2f}'.format(hs[i])+'\t{:7.2f}'.format(deltahf[i]))
print('\n'"Wrote {:d} species to BadSpecies.txt file".format(ibad))
print('\n'+spmax.name+" has the maximum Cp/R jump of {:.2e}".format(cpjumpmax))
jumps(spmax)
plotter(spmax)
plt.show()
f.close()
return
def plotter(species):
"""
Takes a Cantera species object
"""
minT,midT,maxT,lowCoeffs,highCoeffs = coeffImport(species)
lowPolyCp = P(lowCoeffs[0:5])
highPolyCp = P(highCoeffs[0:5])
lowTrange = np.linspace(minT,midT)
highTrange = np.linspace(midT,maxT)
plt.figure()
plt.plot(lowTrange,lowPolyCp(lowTrange),label='Low')
plt.plot(highTrange,highPolyCp(highTrange),label='High')
plt.legend()
plt.title(r'$C_p$ fits for '+species.name)
plt.xlabel('T [K]')
plt.ylabel(r'$C_p$/R')
plt.figure()
plt.plot(lowTrange,hFit(lowCoeffs[0:6],lowTrange)[0],label='Low')
plt.plot(highTrange,hFit(highCoeffs[0:6],highTrange)[0],label='High')
plt.legend()
plt.title(r'h fits for '+species.name)
plt.xlabel('T [K]')
plt.ylabel('h/RT')
plt.figure()
plt.plot(lowTrange,sFit(lowCoeffs[0:7],lowTrange)[0],label='Low')
plt.plot(highTrange,sFit(highCoeffs[0:7],highTrange)[0],label='High')
plt.legend()
plt.title(r's fits for '+species.name)
plt.xlabel('T [K]')
plt.ylabel('s/R')
return
def jumps(species):
"""
Takes a cantera species object
"""
minT,midT,maxT,lowCoeffs,highCoeffs = coeffImport(species)
lowPolyCp = P(lowCoeffs[0:5])
highPolyCp = P(highCoeffs[0:5])
lowTrange = np.linspace(minT,midT)
highTrange = np.linspace(midT,maxT)
CpJump = lowPolyCp(midT)-highPolyCp(midT)
CpTJump = lowPolyCp.deriv()(midT)-highPolyCp.deriv()(midT)
HJump = hFit(lowCoeffs[0:6],midT)[0]-hFit(highCoeffs[0:6],midT)[0]
HTJump = hFit(lowCoeffs[0:6],midT)[1]-hFit(highCoeffs[0:6],midT)[1]
SJump = sFit(lowCoeffs[0:7],midT)[0]-sFit(highCoeffs[0:7],midT)[0]
STJump = sFit(lowCoeffs[0:7],midT)[1]-sFit(highCoeffs[0:7],midT)[1]
print('\n')
print(species.name+" discontinuities at {:.2f} K".format(midT))
print("Cp/R {:.2e}".format(CpJump))
print("Cp'/R {:.2e}".format(CpTJump))
print("H/RT {:.2e}".format(HJump))
print("H/RT' {:.2e}".format(HTJump))
print("S/R {:.2e}".format(SJump))
print("S'/R {:.2e}".format(STJump))
Tzero = 298.15
R = ct.gas_constant
Cp = R*lowPolyCp(Tzero)/1000.
H = R*Tzero*hFit(lowCoeffs[0:6],Tzero)[0]/1.E06
S = R*sFit(lowCoeffs[0:7],Tzero)[0]/1000.
print('\n')
print("Minimum temperature {:.2f} K".format(minT))
print("Midpoint temperature {:.2f} K".format(midT))
print("Maximum temperature {:.2f} K".format(maxT))
print('\n'+species.name+" properties at {:.2f} K".format(Tzero))
print("Cp {:.3f} J/mol-K {:.3f} cal/mol-K".format(Cp, Cp/4.184))
print("H {:.3f} kJ/mol {:.3f} cal/K".format(H,H/4.184))
print("S {:.3f} J/mol-K {:.3f} cal/mol-K".format(S,S/4.184))
return
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mylist=("Iphone","Pixel","Samsung")
for i in mylist:
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mylist=["iPhone","Pixel","Samsung"]
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