gas1.TPX = T1,P1,q
rho1 = gas1.density
# Find CJ speed
cj_speed = CJspeed(P1, T1, q, mech)
# CJ state
gas = PostShock_eq(cj_speed,P1, T1, q, mech)
print('CJ computation for '+mech+' with composition ',q)
P2 = gas.P
T2 = gas.T
q2 = gas.X
rho2 = gas.density
w2 = rho1/rho2*cj_speed
u2= cj_speed-w2
Umin = soundspeed_eq(gas)
print('CJ speed '+str(cj_speed)+' (m/s)');
print('CJ State');
print(' Pressure '+str(P2)+' (Pa)');
print(' Particle velocity '+str(u2)+' (m/s)');
# reflected shock from CJ detonation
gas3 = ct.Solution(mech);
[p3,Ur,gas3] = reflected_eq(gas1,gas,gas3,cj_speed);
v3 = 1./gas.density
print('Reflected shock (equilibrium) computation for ',mech,' with composition ',q)
print(' Reflected wave speed '+str(Ur)+' (m/s)')
print(' Reflected shock pressure '+str(gas3.P)+' (Pa)')
# Bounds for reflected shock speed
Umax = Ur+u2
print(' Maximum reflected shock speed '+str(Umax)+' (m/s)')
# SET TYPE OF EXPANSION COMPUTATION
# Frozen: EQ = false Equilibrium EQ = true
EQ = False
##
# set the initial state and compute properties
P1 = 100000.
T1 = 300.
q = 'O2:0.2095 N2:0.7808 CO2:0.0004 Ar:0.0093'
mech = 'airNASA9ions.cti'
gas = ct.Solution(mech)
gas.TPX = T1, P1, q
if EQ:
# use this for equilibrium expansion
gas.equilibrate('TP')
a1 = soundspeed_eq(gas)
else:
# use this for frozen expansion
a1 = soundspeed_fr(gas)
x1 = gas.X
rho1 = gas.density
v1 = 1 / rho1
s1 = gas.entropy_mass
h1 = gas.enthalpy_mass
##
# Set freestream velocity .01% above sound speed
U = a1 * 1.0001
mu_min = np.arcsin(a1 / U) # Mach angle
# check to see if flow speed is supersonic
if U < a1:
# Find CJ speed
cj_speed = CJspeed(P1, T1, q, mech)
# Evaluate gas state
gas = PostShock_eq(cj_speed,P1, T1, q, mech)
# Evaluate properties of gas object
T2 = gas.T
P2 = gas.P
R2 = gas.density
V2 = 1/R2
S2 = gas.entropy_mass
w2 = gas1.density*cj_speed/R2
u2 = cj_speed - w2
x2 = gas.X
a2_eq = soundspeed_eq(gas)
a2_fr = soundspeed_fr(gas)
gamma2_fr = a2_fr**2*R2/P2
gamma2_eq = a2_eq**2*R2/P2
# Print out
set_printoptions(precision=4)
print('CJ computation for '+mech+' with composition '+q)
print('CJ Parameters')
print(' UCJ '+str(cj_speed)+' (m/s)')
print(' Pressure '+str(P2)+' (Pa)')
print(' Temperature '+str(T2)+' (K)')
print(' Density '+str(R2)+' (kg/m3)')
print(' Entropy '+str(S2)+' (J/kg-K)')
print(' w2 (wave frame) '+str(w2)+' (m/s)')
print(' u2 (lab frame) '+str(u2)+' (m/s)')
# mech = Cantera mechanism File name
# calculate composition based on percentage of propane
HC_comp = propane_comp
O_comp = (100 - HC_comp) * 0.21
N2_comp = (100 - HC_comp) * 0.79
# initial pressures and temperatures
P1 = initpress[IC] * 1000
T1 = inittemp[IC]
q = {'C3H8': HC_comp, 'O2': O_comp, 'N2': N2_comp}
mech = 'gri30.cti'
# make solution and initialize to starting conditions, store density
gas_initial = ct.Solution(mech)
gas_initial.TPX = T1, P1, q
rho_1 = gas_initial.density
csound = soundspeed_eq(gas_initial)
# compute CJ speed, print, and add to speed array
[cj_speed, R2, plot_data] = CJspeed(P1,
T1,
q,
mech,
fullOutput=True)
# compute equilibrium CJ state parameters
gas = PostShock_eq(cj_speed, P1, T1, q, mech)
ae = soundspeed_eq(gas)
af = soundspeed_fr(gas)
rho_2 = gas.density
gammae = ae**2 * rho_2 / gas.P
gammaf = af**2 * rho_2 / gas.P
w2 = cj_speed * rho_1 / rho_2
a3 = [soundspeed_fr(driver_gas)]
u3 = [0]
elif CASE_DRIVER=='uv':
## Set initial state for driven section - combustion driver shock tube
# using constant volume state approximation for reacting driver, use equilibrium expansion
EQ_EXP = True
P_driver_fill = P1; T_driver_fill = T1;
q4 = 'C2H2:1.0 O2:2.5'
driver_mech = 'gri30_highT.cti'
driver_gas = ct.Solution(driver_mech)
driver_gas.TPX = T_driver_fill,P_driver_fill,q4
driver_gas.equilibrate('UV')
P4 = driver_gas.P
T4 = driver_gas.T
a3 = [soundspeed_eq(driver_gas)]
u3 = [0]
elif CASE_DRIVER=='cj':
## Detonation driver with CJ wave moving away from diaphragm
EQ_EXP = True
P_driver_fill = P1; T_driver_fill = T1;
q4 = 'C2H2:1.0 O2:2.5'
driver_mech = 'gri30_highT.cti'
driver_gas = ct.Solution(driver_mech)
driver_gas.TPX = T_driver_fill,P_driver_fill,q4
rho4 = driver_gas.density
cj_speed = CJspeed(P_driver_fill, T_driver_fill, q4, driver_mech)
driver_gas = PostShock_eq(cj_speed,P_driver_fill, T_driver_fill, q4, driver_mech)
P4 = driver_gas.P
T4 = driver_gas.T
# User can adjust the increment and endpoint to get a smooth output curve and reliable integral.
# Could also try a logarithmic range for some cases.
for v in np.linspace(v1,v2,num=1000):
rho.append(1/v)
x = gas.X # update mole fractions based on last gas state
# workaround to avoid unsized object error when only one species in a .cti file
# (flagged to be fixed in future Cantera version)
if gas.n_species > 1:
gas.SVX = s1,1/rho[-1],x
else:
gas.SV = s1,1/rho[-1]
if EQ:
# required for equilibrium expansion
gas.equilibrate('SV')
a.append(soundspeed_eq(gas))
else:
# use this for frozen expansion
a.append(soundspeed_fr(gas))
h.append(gas.enthalpy_mass)
u.append(np.sqrt(2*(h0-h[-1])))
M.append(u[-1]/a[-1])
mu.append(np.arcsin(1/M[-1]))
T.append(gas.T)
P.append(gas.P)
# convert lists to Numpy arrays to allow vectorized operations
M = np.asarray(M); rho = np.asarray(rho); P = np.asarray(P)
print('Case '+str(i+1)+' Fuel concentration: '+str(x[ifuel]*100)+'%')
print('Molefractions')
print(' fuel ('+fuel+'): '+str(x[ifuel]))
print(' oxidizer ('+oxidizer+'): '+ str(x[ioxidizer]))
print(' diluent ('+diluent+'): '+ str(x[idiluent]))
print(' Phi = '+str(phi[-1]))
gas.TPX = T1,P1,x
init_rho = gas.density
init_af = soundspeed_fr(gas)
# Constant Pressure Explosion State
gas.equilibrate('HP')
hp_rho.append(gas.density)
hp_exp.append(init_rho/hp_rho[-1])
hp_T.append(gas.T)
hp_ae.append(soundspeed_eq(gas))
# Constant Volume Explosion State
gas.TPX = T1,P1,x
gas.equilibrate('UV')
uv_P.append(gas.P)
uv_T.append(gas.T)
uv_ae.append(soundspeed_eq(gas))
# CJ speed
gas.TPX = T1,P1,x
Ucj.append(CJspeed(P1, T1, x, mech))
# vN state
gas1 = PostShock_fr(Ucj[-1], P1, T1, x, mech)
vn_T.append(gas1.T)
Tc = 300;
Pc = 1e6;
for helium in range(1,21):
q = 'O2:1 H2:2.001 He:'+str(helium)
gas.TPX = Tc,Pc,q
print('Computing chamber conditions and isentropic quasi 1-d flow for '+q+' using '+mech)
# compute equilibrium properties for constant pressure burn
gas.equilibrate('HP')
qc = gas.X
# Isentropic expansion from stagnation state to low pressure
Tt = gas.T
St = gas.entropy_mass
Ht = gas.enthalpy_mass
Pt = gas.P
Rt = gas.density
ct = soundspeed_eq(gas)
gammat_eq = ct**2*Rt/Pt
print('Total pressure '+str(Pt)+' (Pa)')
print('Total temperature '+str(Tt)+' (K)')
print('Total density '+str(Rt)+' (kg/m3)')
print('Total entropy '+str(St)+' (J/kg-K)')
print('Total sound speed (equilibrium) '+str(ct)+' (m/s)')
print('gamma2 (equilibrium) '+str(gammat_eq)+' (m/s)')
# ambient pressure for impulse computation
Pa = 0.0
print('Computing isentropic expansion')
pp = Pt
P = []; R = []; T = []; c = []; M = [];
h_eq = []; u_eq = []; Isp_eq = [];
h_fr = []; u_fr = []; Isp_fr = [];
# stoichiometric H2-air detonation at nominal atmospheric conditions
P1 = 100000.
T1 = 295
q = 'H2:2 O2:1 N2:3.76'
mech = 'Mevel2017.cti'
gas_initial = ct.Solution(mech)
gas_initial.TPX = T1, P1, q
rho_1 = gas_initial.density
# compute CJ speed
[cj_speed, R2, plot_data] = CJspeed(P1, T1, q, mech, fullOutput=True)
# compute equilibrium CJ state parameters
gas = PostShock_eq(cj_speed, P1, T1, q, mech)
ae = soundspeed_eq(gas)
af = soundspeed_fr(gas)
rho_2 = gas.density
gammae = ae**2 * rho_2 / gas.P
gammaf = af**2 * rho_2 / gas.P
w2 = cj_speed * rho_1 / rho_2
u2 = cj_speed - w2
print('CJ computation for ' + mech + ' with composition ' + q)
print('Initial conditions: P1 = %.3e Pa & T1 = %.2f K' % (P1, T1))
print('CJ Speed %.1f m/s' % cj_speed)
print('CJ State')
print(' Pressure %.3e Pa' % gas.P)
print(' Temperature %.1f K' % gas.T)
print(' Density %.3f kg/m3' % gas.density)
print(' Entropy %.3e J/K' % gas.entropy_mass)
print(' w2 (wave frame) %.1f m/s' % w2)
print(' Density '+str(rho1)+' (kg/m3)')
print(' Sound speed (frozen) '+str(a1_fr)+' (m/s)')
print(' Enthalpy '+str(h1)+' (J/kg)')
print(' Entropy '+str(s1)+' (J/kg K)')
print(' gamma (frozen) '+str(gamma1_fr)+' ')
##
# Find CJ speed
U_CJ = CJspeed(P1, T1, q, mech)
# Evaluate CJ gas state
gas = PostShock_eq(U_CJ,P1, T1, q, mech)
x2 = gas.X
P2 = gas.P
T2 = gas.T
rho2 = gas.density
a2_eq = soundspeed_eq(gas)
s2 = gas.entropy_mass
h2 = gas.enthalpy_mass
w2 = rho1*U_CJ/rho2
u2 = U_CJ-w2
gamma2_eq = a2_eq**2*rho2/P2
print('State 2 - CJ ')
print(' CJ speed '+str(U_CJ)+' (m/s)')
print(' Pressure '+str(P2)+' (Pa)')
print(' Temperature '+str(T2)+' (K)')
print(' Density '+str(rho2)+' (kg/m3)')
print(' Enthalpy '+str(h2)+' (J/kg)')
print(' Entropy '+str(s2)+' (J/kg K)')
print(' w2 (wave frame) '+str(w2)+' (m/s)')
print(' u2 (lab frame) '+str(u2)+' (m/s)')
gas.equilibrate('SV')
P.append(gas.P)
R.append(gas.density)
T.append(gas.T)
# species
X = gas.X
xH.append(X[iH])
xO.append(X[iO])
xOH.append(X[iOH])
xH2.append(X[iH2])
xO2.append(X[iO2])
xH2O.append(X[iH2O])
# gamma computed from Gruneisen coefficient
grun_eq.append(gruneisen_eq(gas))
grun_fr.append(gruneisen_fr(gas))
a_eq.append(soundspeed_eq(gas))
a_fr.append(soundspeed_fr(gas))
# logarithmic slope of isentropes in P-V coordinates
kappa_fr.append(a_fr[-1]**2*R[-1]/P[-1])
kappa_eq.append(a_eq[-1]**2*R[-1]/P[-1])
# logarithmic slope of isentropes in T-V coordinates
# equilibrium
gas.SV = S2,1.01*V
gas.equilibrate('SV')
T_2 = gas.T
gas.SV = S2,0.99*V
gas.equilibrate('SV')
T_1 = gas.T
tvdvdt_eq.append(-V*(T_2-T_1)/(0.02*V)/T[-1])
# frozen
gas.SVX = S2,V*1.01,X2
print(' Density ' + str(rho1) + ' (kg/m3)')
print(' Sound speed (frozen) ' + str(a1_fr) + ' (m/s)')
print(' Enthalpy ' + str(h1) + ' (J/kg)')
print(' Entropy ' + str(s1) + ' (J/kg K)')
print(' gamma (frozen) ' + str(gamma1_fr) + ' ')
##
# Find CJ speed
U_CJ = CJspeed(P1, T1, q, mech)
# Evaluate CJ gas state
gas = PostShock_eq(U_CJ, P1, T1, q, mech)
x2 = gas.X
P2 = gas.P
T2 = gas.T
rho2 = gas.density
a2_eq = soundspeed_eq(gas)
s2 = gas.entropy_mass
h2 = gas.enthalpy_mass
w2 = rho1 * U_CJ / rho2
u2 = U_CJ - w2
gamma2_eq = a2_eq**2 * rho2 / P2
print('State 2 - CJ ')
print(' CJ speed ' + str(U_CJ) + ' (m/s)')
print(' Pressure ' + str(P2) + ' (Pa)')
print(' Temperature ' + str(T2) + ' (K)')
print(' Density ' + str(rho2) + ' (kg/m3)')
print(' Enthalpy ' + str(h2) + ' (J/kg)')
print(' Entropy ' + str(s2) + ' (J/kg K)')
print(' w2 (wave frame) ' + str(w2) + ' (m/s)')
print(' u2 (lab frame) ' + str(u2) + ' (m/s)')
print('Computing CJ state and isentrope for ' + q + ' using ' + mech)
# compute CJ speed
cj_speed = CJspeed(P1, T1, q, mech)
# compute equilibrium CJ state
gas = PostShock_eq(cj_speed, P1, T1, q, mech)
T2 = gas.T
P2 = gas.P
D2 = gas.density
V2 = 1. / D2
S2 = gas.entropy_mass
w2 = D1 * cj_speed / D2
u2 = cj_speed - w2
a2_eq = soundspeed_eq(gas)
a2_fr = soundspeed_fr(gas)
gamma2_fr = a2_fr * a2_fr * D2 / P2
gamma2_eq = a2_eq * a2_eq * D2 / P2
print('CJ speed = %.2f (m/s)' % (cj_speed))
print('CJ State')
print(' Pressure %.2f (Pa) ' % (P2))
print(' Temperature %.2f (K) ' % (T2))
print(' Density %.3f (kg/m3) ' % (D2))
print(' Entropy %.3f (J/kg-K) ' % (S2))
print(' w2 (frozen) %.2f (m/s)' % (w2))
print(' u2 (frozen) %.2f (m/s)' % (u2))
print(' a2 (frozen) %.2f (m/s)' % (a2_fr))
print(' a2 (equilibrium) %.2f (m/s)' % (a2_eq))
print(' gamma2 (frozen) %.4f ' % (gamma2_fr))
PRpa = (P1 - r1**2 * U1**2 * (v2 - v1))
PR.append(PRpa / ct.one_atm) # Pressure in atmospheres
print('Rayleigh Line Array Created')
## Compute product Hugoniot
# Use CV combust as initial state
gas.TPX = T1, P1, q
gas.equilibrate('UV')
Ta = gas.T
va = 1 / gas.density
PH2 = [gas.P / ct.one_atm]
vH2 = [va]
Grun = [gruneisen_eq(gas)]
gamma = [(soundspeed_eq(gas))**2 / (vH2[0] * gas.P)]
denom = [1 + Grun[0] * (vH2[0] - v1) / (2 * vH2[0])]
i = 0
vb = va
while vb > vmin:
i = i + 1
vb = va - i * .01
# use new volume and previous temperature to find next state
fval = fsolve(hug_eq, Ta, args=(vb, h1, P1, v1, gas))
gas.TD = fval, 1 / vb
PH2.append(gas.P / ct.one_atm)
vH2.append(vb)
Grun.append(gruneisen_eq(gas))
gamma.append((soundspeed_eq(gas))**2 / (vH2[-1] * gas.P))
# User can adjust the increment and endpoint to get a smooth output curve and reliable integral.
# Could also try a logarithmic range for some cases.
for v in np.linspace(v1, v2, num=1000):
rho.append(1 / v)
x = gas.X # update mole fractions based on last gas state
# workaround to avoid unsized object error when only one species in a .cti file
# (flagged to be fixed in future Cantera version)
if gas.n_species > 1:
gas.SVX = s1, 1 / rho[-1], x
else:
gas.SV = s1, 1 / rho[-1]
if EQ:
# required for equilibrium expansion
gas.equilibrate('SV')
a.append(soundspeed_eq(gas))
else:
# use this for frozen expansion
a.append(soundspeed_fr(gas))
h.append(gas.enthalpy_mass)
u.append(np.sqrt(2 * (h0 - h[-1])))
M.append(u[-1] / a[-1])
mu.append(np.arcsin(1 / M[-1]))
T.append(gas.T)
P.append(gas.P)
# convert lists to Numpy arrays to allow vectorized operations
M = np.asarray(M)
rho = np.asarray(rho)
P = np.asarray(P)
print(' Pressure '+str(P1)+' (Pa)')
print(' Temperature '+str(T1)+' (K)')
print(' Density '+str(rho1)+' (kg/m3)')
print(' gamma2 (based on frozen sound speed) '+str(gamma1_fr)+' (m/s)')
print(' Specific heat at constant pressure '+str(gas1.cp_mass)+' (J/kg K)')
if transport:
print(' viscosity '+str(mu1)+' (kg/m s)')
print(' viscosity (kinematic)'+str(nu1)+' (m2/s)')
print(' thermal conductivity '+str(kcond1)+' (W/m K)')
print(' thermal diffusivity '+str(kdiff1)+' (m2/s)')
print(' Prandtl number '+str(Pr))
## Postshock (Frozen)
gas2 = PostShock_fr(speed,P1,T1,q,mech)
af2 = soundspeed_fr(gas2)
ae2 = soundspeed_eq(gas2)
P2 = gas2.P
T2 = gas2.T
S2 = gas2.entropy_mass
rho2 = gas2.density
gamma2_fr = af2**2*rho2/P2
gamma2_eq = ae2**2*rho2/P2
w2 = rho1*speed/rho2
u2 = speed - w2
if transport:
mu = gas2.viscosity
nu = mu/rho2
kcond = gas2.thermal_conductivity
kdiff = kcond/(rho2*gas2.cp_mass)
Pr = mu*gas2.cp_mass/kcond
