M = np.asarray(M); rho = np.asarray(rho)
integrand = -1*np.sqrt(M**2-1)/M**2/rho
omega = [theta_det]
for n in range(1,vstep):
omega.append(omega[n-1] +(integrand[n-1] + integrand[n])*(rho[n]-rho[n-1])/2)
##
# compute shock polar
# 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
s = scj * .98
deltas = 0.01 * scj
jmax = 4
PR = np.asarray(PR)
# initialize arrays
Ps_f = np.zeros((len(PR), jmax))
Ps_e = np.copy(Ps_f)
vs_f = np.copy(Ps_f)
vs_e = np.copy(Ps_f)
for j in range(jmax):
for i, pp in enumerate(PR * ct.one_atm):
# frozen (CJ composition)
gas.SPX = s, pp, qcj
Ps_f[i, j] = gas.P / ct.one_atm
vs_f[i, j] = 1 / gas.density
# equilibrium
gas.equilibrate('SP')
Ps_e[i, j] = gas.P / ct.one_atm
vs_e[i, j] = 1 / gas.density
s = s + deltas
print('Isentropes created')
## plot creation
maxP = max(PR)
minP = min(PR)
maxV = max(vR)
minV = min(vR)
