# Tune dt for quicker solving of ODEs. For these parameters, Case 1 has a much longer timescale
# than the other cases.
if i == 0:
t_end = 1e-3
dt = 1e-5
else:
t_end = 5e-5
dt = 1e-7
# Approximate the effective activation energy using finite differences
gas = PostShock_fr(Ucj[-1], P1, T1, x, mech)
Ts = gas.T; Ps = gas.P
Ta = Ts*(1.02)
gas.TPX = Ta,Ps,x
CVout1 = cvsolve(gas,t_end=t_end,max_step=dt)
Tb = Ts*(0.98)
gas.TPX = Tb,Ps,x
CVout2 = cvsolve(gas,t_end=t_end,max_step=dt)
# Approximate effective activation energy for CV explosion
taua = CVout1['ind_time']
taub = CVout2['ind_time']
if taua==0 and taub==0:
theta_effective_CV.append(0)
else:
theta_effective_CV.append(1/Ts*((np.log(taua)-np.log(taub))/((1/Ta)-(1/Tb))))
print('--------------------------------------');
###############################
step = 5; start = 10; stop = 60
nsteps = int((stop-start)/step)
for compression_ratio in np.linspace(start,stop,num=nsteps):
gas.SVX = s1,1/(compression_ratio*rho1),q
T2.append(gas.T)
P2.append(gas.P)
rho2.append(gas.density)
print('Compressed State')
print(' Pressure '+str(P2[-1])+' (Pa)')
print(' Temperature '+str(T2[-1])+' (K)')
print(' Density '+str(rho2[-1])+' (kg/m3)')
# Compute constant-volume explosion
# need to set final time sufficiently long for low temperature cases
CVout = cvsolve(gas,t_end=50.,max_step=1)
t_ind.append(CVout['ind_time'])
t_pulse.append(CVout['exo_time'])
print(' Induction time = '+str(t_ind[-1])+' (s)')
print(' Pulse time = '+str(t_pulse[-1])+' (s)')
if file:
y = (T2[-1], P2[-1]/1e6, t_ind[-1], t_pulse[-1])
fid.write('%1.4g \t %6.2f \t %3.2e \t %3.2e\n' % y)
if file:
fid.close()
P2 = np.asarray(P2); T2 = np.asarray(T2)
# plot induction time vs reciprocal temperature
u_cj = cj_speed * gas1.density / gas.density
# Find frozen post shock state for given speed
gas = PostShock_fr(cj_speed, P1, T1, q, mech)
# Solve ZND ODEs, make ZND plots
out = zndsolve(gas, gas1, cj_speed, t_end=1e-3, advanced_output=True)
# Find CV parameters including effective activation energy
gas.TPX = T1, P1, q
gas = PostShock_fr(cj_speed, P1, T1, q, mech)
Ts = gas.T
Ps = gas.P
Ta = Ts * 1.02
gas.TPX = Ta, Ps, q
CVout1 = cvsolve(gas)
Tb = Ts * 0.98
gas.TPX = Tb, Ps, q
CVout2 = cvsolve(gas)
# Approximate effective activation energy for CV explosion
taua = CVout1['ind_time']
taub = CVout2['ind_time']
if taua == 0 and taub == 0:
theta_effective_CV = 0
else:
theta_effective_CV = 1 / Ts * ((np.log(taua) - np.log(taub)) / ((1 / Ta) -
(1 / Tb)))
# Find Gavrikov induction length based on 50% limiting species consumption,
# fuel for lean mixtures, oxygen for rich mixtures
# Westbrook time based on 50% temperature rise
for i in range(npoints):
P1[i] = Po*(0.1 +1.1/npoints*(i))
P = P1[i]
print('%i : P1 = %.2f atm' % (i+1,P/ct.one_atm))
gas.TPX = T1,P1[i],x
### Constant Volume Explosion Data ###
# FIND POST SHOCK STATE FOR GIVEN SPEED
cj_speed[i] = CJspeed(P1[i], T1, x, mech)
gas = PostShock_fr(cj_speed[i], P1[i], T1, x, mech)
Ts[i] = gas.T #frozen shock temperature
Ps[i] = gas.P #frozen shock pressure
# SOLVE CONSTANT VOLUME EXPLOSION ODES
CVout = cvsolve(gas,t_end=1e-4)
exo_time_CV[i] = CVout['exo_time']
ind_time_CV[i] = CVout['ind_time']
### ZND Detonation Data ###
# FIND POST SHOCK STATE FOR GIVEN SPEED
gas1.TPX = T1,P1[i],x
gas = PostShock_fr(cj_speed[i], P1[i], T1, x, mech)
Ts[i] = gas.T #frozen shock temperature
Ps[i] = gas.P #frozen shock pressure
# SOLVE ZND DETONATION ODES
ZNDout = zndsolve(gas,gas1,cj_speed[i],advanced_output=True)
ind_time_ZND[i] = ZNDout['ind_time_ZND']
ind_len_ZND[i] = ZNDout['ind_len_ZND']
exo_time_ZND[i] = ZNDout['exo_time_ZND']
P1 = 100000
T1 = 300
U1 = 2000
q = 'H2:2 O2:1 N2:3.76'
mech = 'Mevel2017.cti'
file_name = 'h2air'
# Set up gas object
gas1 = ct.Solution(mech)
gas1.TPX = T1, P1, q
# Find post shock state for given speed
gas = PostShock_fr(U1, P1, T1, q, mech)
# Solve constant volume explosion ODEs, make CV plots
CVout = cvsolve(gas)
cv_plot(CVout)
print('Reaction zone pulse time (exothermic time) = ' + str(CVout['exo_time']))
print('Reaction zone induction time = ' + str(CVout['ind_time']))
############################################################
# CREATE OUTPUT TEXT FILE
############################################################
fid = open(file_name + '_' + str(U1) + '.txt', 'w')
d = datetime.date.today().strftime("%B %d, %Y")
P = P1 / ct.one_atm
fid.write('# CV: EXPLOSION STRUCTURE CALCULATION\n')
mech = 'Mevel2017.cti'
file_name = 'h2air'
# Find CJ speed and related data, make CJ diagnostic plots
cj_speed,R2,plot_data = CJspeed(P1,T1,q,mech,fullOutput=True)
CJspeed_plot(plot_data,cj_speed)
# Set up gas object
gas1 = ct.Solution(mech)
gas1.TPX = T1,P1,q
# Find post shock state for given speed
gas = PostShock_fr(cj_speed, P1, T1, q, mech)
# Solve constant volume explosion ODEs, make cv plots
CVout = cvsolve(gas,t_end=1e-6,max_step=1e-8)
cv_plot(CVout)
print('Reaction zone pulse time (exothermic time) = '+str(CVout['exo_time']))
print('Reaction zone induction time = '+str(CVout['ind_time']))
############################################################
# CREATE OUTPUT TEXT FILE
############################################################
fid = open(file_name+'_'+str(cj_speed)+'.txt','w')
d = datetime.date.today().strftime("%B %d, %Y")
P = P1/ct.one_atm
R.append(gas1.density)
V.append(1 / R[-1])
a.append(soundspeed_eq(gas1))
u.append(u[-1] + 0.5 * (P[-1] - P[-2]) * (1 / (R[-1] * a[-1]) + 1 /
(R[-2] * a[-2])))
# estimate plateau conditions (state 3) by interpolating to find the u = 0 state.
P3.append(P[-1] + u[-1] * (P[-2] - P[-1]) / (u[-2] - u[-1]))
# Approximate the effective activation energy using finite differences
gas = PostShock_fr(Ucj[-1], P1, T1, x, mech)
Ts = gas.T
Ps = gas.P
Ta = Ts * (1.02)
gas.TPX = Ta, Ps, x
CVout1 = cvsolve(gas, t_end=5e-5)
Tb = Ts * (0.98)
gas.TPX = Tb, Ps, x
CVout2 = cvsolve(gas, t_end=5e-5)
# Approximate effective activation energy for CV explosion
taua = CVout1['ind_time']
taub = CVout2['ind_time']
if taua == 0 and taub == 0:
theta_effective_CV.append(0)
else:
theta_effective_CV.append(1 / Ts * ((np.log(taua) - np.log(taub)) /
((1 / Ta) - (1 / Tb))))
print('--------------------------------------')
###############################
