rho3 = [driver_gas.density]
P3 = [driver_gas.P]
T3 = [driver_gas.T]
S4 = driver_gas.entropy_mass
## compute unsteady expansion (frozen)
print('Generating points on isentrope P-u curve')
vv = 1/rho3[0]
while u3[-1] < u2[-1]:
vv = vv*1.01
driver_gas.SVX = S4,vv,driver_gas.X
if EQ_EXP:
# required for equilibrium expansion
driver_gas.equilibrate('SV')
a3.append(soundspeed_eq(driver_gas))
else:
# use this for frozen expansion
a3.append(soundspeed_fr(driver_gas))
P3.append(driver_gas.P)
T3.append(driver_gas.T)
rho3.append(driver_gas.density)
u3.append(u3[-1] - 0.5*(P3[-1]-P3[-2])*(1/(rho3[-1]*a3[-1]) + 1./(rho3[-2]*a3[-2])))
## Input limits for finding intersection of polars
# Convert all lists to numpy arrays
P2 = np.asarray(P2); u2 = np.asarray(u2); P3 = np.asarray(P3); u3 = np.asarray(u3);
T2 = np.asarray(T2); a2 = np.asarray(a2); rho2 = np.asarray(rho2);
T3 = np.asarray(T3); a3 = np.asarray(a3); rho3 = np.asarray(rho3);
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
limit_species = 'H2'
i_limit = gas.species_index(limit_species)
gas.TPX = Ts, Ps, q
X_initial = gas.X[i_limit]
gas.equilibrate('UV')
X_final = gas.X[i_limit]
T_final = gas.T
X_gav = 0.5 * (X_initial - X_final) + X_final
T_west = 0.5 * (T_final - Ts) + Ts
for i, X in enumerate(CVout1['speciesX'][i_limit, :]):
if X > X_gav:
t_gav = CVout1['time'][i]
x_gav = t_gav * out['U'][0]
for i, T in enumerate(CVout1['T']):
if T < T_west:
t_west = CVout1['time'][i]
x_west = t_west * out['U'][0]
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
##
# Set freestream velocity .01% above sound speed
U1 = a1*1.0001
mu_min = np.arcsin(a1/U1) # Mach angle
# check to see if flow speed is supersonic
wmax = np.sqrt(2*h0)
# initialize variables for computing PM properties and plotting
rho = []; a = []; P = []; T = []; h = []; mu = []; M = []; Me = []; u = []; ue = [];
v1 = 1/rho2 # lower limit to specific volume in PM fan
v2 = 50*v1 # upper limit to specific volume in PM fan
vstep = 1000
##
# Compute expansion conditions over range from minimum to maximum specific volume.
# 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=vstep):
rho.append(1/v)
x = gas.X # update mole fractions based on last gas state
gas.SVX = s2,v,x
gas.equilibrate('SV') # required for equilibrium expansion
h.append(gas.enthalpy_mass)
u.append(np.sqrt(2*(h0-h[-1]))) # flow speed within expansion
# Need to explicitly upcast to complex, otherwise get NaN:
ue.append(np.real(np.sqrt(2*(np.asarray(h1-h[-1],dtype=complex))))) # ideal axial velocity for RDE model
a.append(soundspeed_eq(gas)) # use this for equilibrium expansion, almost always the case for detonation products
#a.append(soundspeed_fr(gas)) # use this for frozen expansion
Me.append(ue[-1]/a[-1])
M.append(u[-1]/a[-1])
if M[-1] < 1:
# Sometimes the first M value has been observed to be ~0.999 which leads to errors
# in the arcsin and sqrt functions that follow
M[-1] = 1.00001
mu.append(np.arcsin(1/M[-1]))
T.append(gas.T)
P.append(gas.P)
