def calc_cjtemperature(self):
# Calculation for the Chapman-Jouget speeds
cj_speed_mps = self.calc_cjspeed()
if self.ps_eq is False:
# Post shock (equilibrium) pressure to be determined
self.ps_eq = PostShock_eq(U1=cj_speed_mps, P1=self.P1, T1=self.T1, q=self.q, mech=self.mech)
cj_temperature_k = self.ps_eq.T
return cj_temperature_k
##
# SET TYPE OF EXPANSION COMPUTATION
# Frozen: EQ = False Equilibrium: EQ = True
EQ = True
##
# set the initial state and compute properties
P1 = 100000.; T1 = 300.
q = 'O2:1 N2:3.76 H2:2'
mech = 'Mevel2017.cti'
gas = ct.Solution(mech)
# Find CJ speed
cj_speed = CJspeed(P1, T1, q, mech)
# Evaluate gas state
gas = PostShock_eq(cj_speed,P1, T1, q, mech)
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
##
Ucj.append(CJspeed(P1, T1, x, mech))
# vN state
gas1 = PostShock_fr(Ucj[-1], P1, T1, x, mech)
vn_T.append(gas1.T)
vn_P.append(gas1.P)
vn_rho.append(gas1.density)
vn_af.append(soundspeed_fr(gas1))
# ZND Structure
ZNDout = zndsolve(gas1,gas,Ucj[-1],advanced_output=True)
ind_len_ZND.append(ZNDout['ind_len_ZND'])
exo_len_ZND.append(ZNDout['exo_len_ZND'])
# CJ state
gas1 = PostShock_eq(Ucj[-1],P1, T1,x,mech)
cj_T.append(gas1.T)
cj_P.append(gas1.P)
cj_rho.append(gas1.density)
cj_af.append(soundspeed_fr(gas1))
# Reflected CJ state
[ref_P[i],Uref[i],gas2] = reflected_eq(gas,gas1,gas2,Ucj[-1])
# State 3 - Plateau at end of Taylor wave
# print('Generating points on isentrope and computing Taylor wave velocity')
w2 = gas.density*Ucj[-1]/cj_rho[-1]
S2 = gas1.entropy_mass
u2 = Ucj[-1] - w2
u = [u2]
P = [gas1.P]
R = [gas1.density]
plt.xlabel('Initial temperature [Kelvins]')
plt.ylabel('CJ speed [m/s]')
plt.title('Cj detonation speed of methane-air mixture', fontweight='bold')
plt.grid()
plt.savefig('methane_cjspeed(T1).png', dpi=1000)
plt.show()
for phi in range(50, 175, 25):
T1 = []
X = 'O2:2, N2:7.52, CH4:' + str(phi / 100)
PostShock_T = []
for T in range(250, 2500, 250):
gas.TPX = T, P1, X
T1.append(T)
U = CJspeed(P1, T, X, mech)
gas = PostShock_eq(U, P1, T, X, mech)
PostShock_T.append(gas.T)
plt.plot(T1, PostShock_T, label="phi=%.2f" % (phi / 100))
plt.legend()
plt.xlabel('Initial temperature [Kelvins]')
plt.ylabel('Post shock temperature [K]')
plt.title('Post shock temerature of methane-air mixture', fontweight='bold')
plt.grid()
plt.savefig('methane_T(T1).png', dpi=1000)
plt.show()
for phi in range(50, 175, 25):
T1 = []
X = 'O2:2, N2:7.52, CH4:' + str(phi / 100)
PostShock_P = []
# set maximum normal speed
wmax = US
# initialize variables for plotting
rho2 = []; w1 = []; w2 = []; u2 = []; vt = []; a2 = []; P2 = []; beta = []; theta = [];
##
# compute shock jump conditions over range from minimum to maximum normal
# speeds. Adjust the increment to get a smooth output curve.
step = 5 # approximate desired step size (will not be exactly followed)
npoints = int((wmax-wmin)/step)
for w in np.linspace(wmin,wmax,num=npoints):
if EQ:
# equilibrium state
gas = PostShock_eq(w, Ps, Ts, xs, mech)
a2.append(soundspeed_eq(gas))
else:
# for non-reactive or cold upstream state, use frozen shock calculation
gas = PostShock_fr(w, Ps, Ts, qs, mech)
a2.append(soundspeed_fr(gas))
rho2.append(gas.density)
ratio = rhos/rho2[-1]
w1.append(w)
w2.append(w*ratio)
P2.append(gas.P)
beta.append(np.arcsin(w/US))
vt.append(US*np.cos(beta[-1]))
theta.append(beta[-1] - np.arctan(w2[-1]/np.sqrt(US**2-w**2)))
u2.append(np.sqrt(w2[-1]**2 + vt[-1]**2))
# set initial state, composition, and gas object
P1 = 100000
T1 = 300
q = 'H2:0.31 N2O:0.69'
mech = 'Mevel2015.cti'
gas1 = ct.Solution(mech)
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);
q = 'H2:2 O2:1 N2:3.76'
mech = 'Mevel2017.cti'
## compute initial state
gas1 = ct.Solution(mech)
gas1.TPX = T1, P1, q
h1 = gas1.enthalpy_mass
r1 = gas1.density
v1 = 1 / r1
## compute CJ speed
cj_speed = CJspeed(P1, T1, q, mech)
print('CJ speed ' + str(cj_speed))
## compute CJ state
gas = PostShock_eq(cj_speed, P1, T1, q, mech)
vcj = 1 / gas.density
pcj = gas.P
Pcj = pcj / ct.one_atm
tcj = gas.T
scj = gas.entropy_mass
qcj = gas.X
U1 = cj_speed
## Compute RAYLEIGH Line
vR = []
PR = []
vmin = 0.3 * vcj
vmax = 1.7 * vcj
vinc = .01 * vcj
### 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'] exo_len_ZND[i] = ZNDout['exo_len_ZND'] Tf_ZND[i] = ZNDout['T'][-1] ##Calculate CJstate Properties### gas = PostShock_eq(cj_speed[i],P1[i], T1,x, mech) T2[i] = gas.T P2[i] = gas.P rho2[i] = gas.density #Approximate the effective activation energy using finite differences Ta = Ts[i]*(1.02) gas.TPX = Ta,Ps[i],x CVout1 = cvsolve(gas,t_end=1e-4) taua = CVout1['ind_time'] Tb = Ts[i]*(0.98) gas.TPX = Tb,Ps[i],x CVout2 = cvsolve(gas,t_end=1e-4) taub = CVout2['ind_time'] #Approximate effective activation energy for CV explosion if taua == 0 and taub == 0:
P1 = 100000 T1 = 500 q = 'H2:2 O2:1 ' mech = 'gri30.xml' fname = '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 equilibrium post shock state for given speed gas = PostShock_eq(cj_speed, P1, T1, q, mech) 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
ind_time_CV[i] = CVout['ind_time']
### ZND Detonation Data ###
gas.TPX = T1,P1,x
gas = PostShock_fr(cj_speed*overdrive[i], P1, T1, x, mech)
# Solve znd detonation ODEs
ZNDout = zndsolve(gas,gas1,cj_speed*overdrive[i],advanced_output=True)
exo_time_ZND[i] = ZNDout['exo_time_ZND']
exo_len_ZND[i] = ZNDout['exo_len_ZND']
ind_time_ZND[i] = ZNDout['ind_time_ZND']
ind_len_ZND[i] = ZNDout['ind_len_ZND']
Tf_ZND[i] = ZNDout['T'][-1]
### Calculate CJ state properties ###
gas = PostShock_eq(cj_speed*overdrive[i], P1, T1, x, mech);
T2[i] = gas.T
P2[i] = gas.P
rho2[i] = gas.density
# Approximate the effective activation energy using finite differences
factor = 0.02
Ta = Ts[i]*(1.0+factor)
gas.TPX = Ta,Ps[i],x
CVout1 = cvsolve(gas)
taua = CVout1['ind_time']
Tb = Ts[i]*(1.0-factor)
gas.TPX = Tb,Ps[i],x
CVout2 = cvsolve(gas)
taub = CVout2['ind_time']
# Approximate effective activation energy for CV explosion
fname = 'h2air'
od = 1
gbound = 1.4
makePlot = True
# EDIT VALUES ABOVE THIS LINE
##############################
gas1 = ct.Solution(mech)
gas1.TPX = T1, P1, q
h1 = gas1.enthalpy_mass
r1 = gas1.density
v1 = 1.0 / gas1.density
#Get CJ Point
cj_speed = CJspeed(P1, T1, q, mech)
gas = PostShock_eq(cj_speed, P1, T1, q, mech)
vcj = 1.0 / gas.density
Pcj = gas.P / ct.one_atm
print('CJ Point Found')
U1 = od * cj_speed
#Find Postshock specific volume for U1
gas = PostShock_fr(U1, P1, T1, q, mech)
vsj = 1.0 / gas.density
Psj = gas.P / ct.one_atm
#Find Gamma
gas = PostShock_fr(gbound * cj_speed, P1, T1, q, mech)
g = gas.cp_mass / gas.cv_mass
q = 'O2:0.2095 N2:0.7808 CO2:0.0004 Ar:0.0093'
mech = 'airNASA9ions.cti'
fname = 'Air'
U1 = 3500.
plt_num = 1
# EDIT VALUES ABOVE THIS LINE
##############################
# set initial state
gas1 = ct.Solution(mech)
gas1.TPX = T1, P1, q
h1 = gas1.enthalpy_mass
r1 = gas1.density
v1 = 1.0 / gas1.density
#Get equilibrium postshock state
gas = PostShock_eq(U1, P1, T1, q, mech)
v_ps = 1.0 / gas.density
P_ps = gas.P / ct.one_atm
# RAYLEIGH LINE,
minv = 0.9 * v_ps
maxv = 1.00 * v1
stepv = 0.01 * v1
n = np.int((maxv - minv) / stepv)
vR = np.zeros(n, float)
PR = np.zeros(n, float)
i = 0
v2 = maxv
while (i < n):
vR[i] = v2
print('Layer detonation computation for '+mech+' with composition '+q)
print('State 1 - Initial state of reacting layer')
print(' Pressure '+str(P1)+' (Pa)')
print(' Temperature '+str(T1)+' (K)')
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)')
gamma1_fr = a1_fr * a1_fr * D1 / P1
print('Initial State:')
print(' Composition ' + q)
print(' Pressure %.2f (Pa) ' % (P1))
print(' Temperature %.2f (K) ' % (T1))
print(' Density %.3f (kg/m3) ' % (D1))
print(' a1 (frozen) %.2f (m/s)' % (a1_fr))
print(' gamma1 (frozen) %.4f ' % (gamma1_fr))
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')
## Evaluate initial state
rho1 = driven_gas.density
a1 = soundspeed_fr(driven_gas)
## Evaluate post-shock state (frozen) for a range of shock speeds
print('Generating points on shock P-u curve')
Ustart = a1*1.01; Ustop = 8*a1; Ustep = 25
nsteps = int((Ustop-Ustart)/Ustep)
a2 = []; P2 = []; T2 = []; rho2 = []; u2 = []; Us = []
for U in np.linspace(Ustart,Ustop,num=nsteps):
if CASE_DRIVEN=='frozen':
shocked_gas = PostShock_fr(U, P1, T1, q1, driven_mech)
elif CASE_DRIVEN=='equilibrium':
shocked_gas = PostShock_eq(U, P1, T1, q1, driven_mech)
a2.append(soundspeed_fr(shocked_gas))
P2.append(shocked_gas.P)
T2.append(shocked_gas.T)
rho2.append(shocked_gas.density)
w2 = rho1*U/shocked_gas.density
u2.append(U - w2)
Us.append(U)
if CASE_DRIVER=='gas':
## Set initial state for driver section - pressurized gas and no reaction
# for nonreacting driver, use frozen expansion
EQ_EXP = False
P_driver = 3e6; T_driver = 300.;
q4 = 'He:1.0'
driver_mech = 'Mevel2017.cti'
# create gas objects for other states
gas2 = ct.Solution(mech)
gas3 = ct.Solution(mech)
# compute minimum incident wave speed
fig_num = 0;
cj_speed = CJspeed(P1, T1, q, mech)
# incident wave must be greater than or equal to cj_speed for
# equilibrium computations
UI = 1.2*cj_speed
print('Incident shock speed UI = %.2f m/s' % (UI))
# compute postshock gas state object gas2
gas2 = PostShock_eq(UI, P1, T1, q, mech);
P2 = gas2.P/ct.one_atm;
print ('Equilibrium Post-Incident-Shock State')
print ('T2 = %.2f K, P2 = %.2f atm' % (gas2.T,P2))
# compute reflected shock post-shock state gas3
[p3,UR,gas3]= reflected_eq(gas1,gas2,gas3,UI);
# Outputs:
# p3 - pressure behind reflected wave
# UR = Reflected shock speed relative to reflecting surface
# gas3 = gas object with properties of postshock state
P3 = gas3.P/ct.one_atm
print ('Equilibrium Post-Reflected-Shock State')
print ('T3 = %.2f K, P3 = %.2f atm' % (gas3.T,P3))
plt.xlabel('Initial pressure [bar]')
plt.ylabel('CJ speed [m/s]')
plt.title('Cj detonation speed of hydrogen-air mixture', fontweight='bold')
plt.grid()
plt.savefig('hydrogen_cjspeed(P1).png', dpi=1000)
plt.show()
for phi in range(50, 175, 25):
P1 = []
X = 'O2:0.5, N2:1.88, H2:' + str(phi / 100)
PostShock_T = []
for P in range(100000, 1250000, 250000):
gas.TPX = T1, P, X
P1.append(P / 100000)
U = CJspeed(P, T1, X, mech)
gas = PostShock_eq(U, P, T1, X, mech)
PostShock_T.append(gas.T)
plt.plot(P1, PostShock_T, label="phi=%.2f" % (phi / 100))
plt.legend()
plt.xlabel('Initial pressure [bar]')
plt.ylabel('Post shock temperature [K]')
plt.title('Post shock temerature of hydrogen-air mixture', fontweight='bold')
plt.grid()
plt.savefig('hydrogen_T(P1).png', dpi=1000)
plt.show()
for phi in range(50, 175, 25):
P1 = []
X = 'O2:0.5, N2:1.88, H2:' + str(phi / 100)
PostShock_P = []
gas1.TPX = T1, P1, q ## Evaluate initial state R1 = gas1.density c1_fr = soundspeed_fr(gas1) cp1 = gas1.cp_mass w1 = gas1.mean_molecular_weight gamma1_fr = c1_fr**2 * R1 / P1 ## Set shock speed cj_speed = CJspeed(P1, T1, q, mech) Us = cj_speed ## Evaluate gas state # q = 'O2:1. N2:3.76' gas = PostShock_eq(Us, 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 * Us / R2 u2 = Us - w2 x2 = gas.X c2_eq = soundspeed_eq(gas) c2_fr = soundspeed_fr(gas) gamma2_fr = c2_fr**2 * R2 / P2 gamma2_eq = c2_eq**2 * R2 / P2
for rho1 in np.linspace(start,stop,num=nsteps):
gas1.SVX = s0,1/rho1,x0
P1 = gas1.P
T1 = gas1.T
print('Density '+str(rho1)+' (kg/m^3)')
fid.write('# Initial conditions\n')
fid.write('# Temperature (K) %4.1f\n' % T1)
fid.write('# Pressure (Pa) %2.1f\n' % P1)
fid.write('# Density (kg/m^3) %1.4e\n' % rho1)
# Find CJ speed
cj_speed = CJspeed(P1, T1, q, mech)
print('CJspeed '+str(cj_speed)+' (m/s)');
gas = PostShock_eq(cj_speed,P1, T1, q, mech)
P2 = gas.P
# Evaluate overdriven detonations and reflected shocks
fstart = 1.; fstop = 1.5; fstep = 0.05
fnsteps = int((fstop-fstart)/fstep)
speed = []; vs = []; ps = []; pr = []; vr = []
for f in np.linspace(fstart,fstop,num=fnsteps):
u_shock = f*cj_speed
speed.append(u_shock)
print(' Detonation Speed '+str(speed[-1])+' (m/s)')
gas = PostShock_eq(u_shock,P1, T1, q, mech)
# Evaluate properties of gas object
vs.append(1./gas.density)
ps.append(gas.P)
[p3,UR,gas3] = reflected_eq(gas1,gas,gas3,u_shock)
print(' Specific heat at constant pressure '+str(gas2.cp_mass)+' (J/kg K)')
print(' Expansion ratio '+str(rho1/rho2)+' (kg/m3)')
print(' Entropy '+str(S2)+' (J/kg-K)')
print(' Sound speed (frozen) '+str(af2)+' (m/s)')
print(' Sound speed (equilibrium) '+str(ae2)+' (m/s)')
print(' gamma2 (based on frozen sound speed) '+str(gamma2_fr)+' (m/s)')
print(' gamma2 (based on equilibrium sound speed) '+str(gamma2_eq)+' (m/s)')
if transport:
print(' viscosity '+str(mu)+' (kg/m s)')
print(' viscosity (kinematic)'+str(nu)+' (m2/s)')
print(' thermal conductivity '+str(kcond)+' (W/m K)')
print(' thermal diffusivity '+str(kdiff)+' (m2/s)')
print(' Prandtl number '+str(Pr))
## Postshock (Equilibrium)
gas3 = PostShock_eq(speed,P1,T1,q,mech)
af3 = soundspeed_fr(gas3)
ae3 = soundspeed_eq(gas3)
P3 = gas3.P
T3 = gas3.T
rho3 = gas3.density
S3 = gas3.entropy_mass
gamma3_fr = af3**2*rho3/P3
gamma3_eq = ae3**2*rho3/P3
w3 = rho1*speed/rho3
u3 = speed - w3
if transport:
mu = gas3.viscosity
nu = mu/rho3
kcond = gas3.thermal_conductivity
kdiff = kcond/(rho3*gas3.cp_mass)
