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 = []
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_P.append(gas.P / 100000)
plt.plot(P1, PostShock_P, label="phi=%.2f" % (phi / 100))
plt.legend()
plt.xlabel('Initial pressure [bar]')
plt.ylabel('Post shock pressure [bar]')
plt.title('Post shock pressure of hydrogen-air mixture', fontweight='bold')
plt.grid()
plt.savefig('hydrogen_P(P1).png', dpi=1000)
plt.show()
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 = []
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_P.append(gas.P / 100000)
plt.plot(T1, PostShock_P, label="phi=%.2f" % (phi / 100))
plt.legend()
plt.xlabel('Initial temperature [Kelvins]')
plt.ylabel('Post shock pressure [bar]')
plt.title('Post shock pressure of methane-air mixture', fontweight='bold')
plt.grid()
plt.savefig('methane_P(T1).png', dpi=1000)
plt.show()
# 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
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:
PH1[i + 1] = gas.P / ct.one_atm
vH1[i + 1] = 1 / gas.density
i = i + 1
print('Reactant Hugoniot Array Created')
gas = PostShock_eq(U1, P1, T1, q, mech)
veq = 1.0 / gas.density
Peq = gas.P / ct.one_atm
# PRODUCT HUGONIOT
# The method used for finding the product hugoniot is not
# quite as robust as for reactants so some care must be taken
# at large overdrives.
# Get the first point on the product Hugoniot - CV combustion
gas.TPX = T1, P1, q
gas.equilibrate('UV')
Ta = gas.T
Pcv = gas.P / ct.one_atm
va = 1.0 / gas.density
n = np.int((va - 0.4 * vcj) / 0.01)
PH2 = np.zeros(n + 1, float)
vH2 = np.zeros(n + 1, float)
PH2[0] = gas.P / ct.one_atm
vH2[0] = va
i = 0
vb = va
while (i < n):
# First compute upstream state for RDE model, expand detonation products to ambient pressure
# Set freesteam velocity to expansion speed. Accounts for shear across upstream contact
P = np.asarray(P)
if EQ:
gas.SPX = s2,P1,x
gas.equilibrate('SP')
a4 = soundspeed_eq(gas)
U4fun = pchip(P/P1,u)
U4 = U4fun(1)
else:
# alternative state upstream: reactants (need to use frozen shock calculation with this)
#qs = 'C2H4:1.00 O2:3'; %ethylene oxygen
qs = 'O2:1.00,N2:3.76' # combustion air
Ts = 300.
gas.TPX = Ts,P1,qs
a4 = soundspeed_fr(gas)
U4 = u_tp # no shear between bounding gas and reacting layer
##
# states upstream of shock
rho4 = gas.density
P4 = gas.P
T4 = gas.T
s4 = gas.entropy_mass
x4 = gas.X
h4 = gas.enthalpy_mass
gamma4 = a4**2*rho4/P4
beta_min = np.arcsin(a4/U4) # Mach angle
print('State 4 - upstream of oblique shock')
vmin = 0.3 * vcj
vmax = 1.7 * vcj
vinc = .01 * vcj
vsteps = int((vmax - vmin) / vinc)
for v2 in np.linspace(vmin, vmax, num=vsteps):
vR.append(v2)
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
