# 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)
pr.append(p3)
vr.append(1./gas3.density)
print('-------------------------------------------');
fid.write('Zone T = rho'+str(fnsteps+1)+'\n')
fid.write('Variables = "detonation speed (m/s)", "detonation pressure (Pa)", "detonation volume (m3/kg)", "reflected shock pressure (Pa)", "reflected shock volume (m3/kg)"\n')
for i in range(fnsteps):
fid.write(' %14.5e \t %14.5e \t %14.5e \t %14.5e \t %14.5e \n' % (speed[i], ps[i], vs[i], pr[i], vr[i]))
fid.close()
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);
[p3,Ur,gas3] = reflected_eq(gas1,gas,gas3,cj_speed);
v3 = 1./gas.density
print('Reflected shock (equilibrium) computation for ',mech,' with composition ',q)
print(' Reflected wave speed '+str(Ur)+' (m/s)')
print(' Reflected shock pressure '+str(gas3.P)+' (Pa)')
# Bounds for reflected shock speed
Umax = Ur+u2
print(' Maximum reflected shock speed '+str(Umax)+' (m/s)')
print(' Minimum reflected shock speed '+str(Umin)+' (m/s)')
print('Compute shock adiabat and wave curve starting at the CJ state')
step = 10 # approximate desired step size (will not be exactly followed)
npoints = int((Umax-Umin)/step)
p = []; v = []; u3 = [];
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]
V = [1/R[0]]
#T = [gas1.T]
a = [soundspeed_eq(gas1)]
vv = 1/cj_rho[-1]
while u[-1] > 0:
print('CJ Parameters')
print(' UCJ '+str(cj_speed)+' (m/s)')
print(' Pressure '+str(P2)+' (Pa)')
print(' Temperature '+str(T2)+' (K)')
print(' Density '+str(R2)+' (kg/m3)')
print(' Entropy '+str(S2)+' (J/kg-K)')
print(' w2 (wave frame) '+str(w2)+' (m/s)')
print(' u2 (lab frame) '+str(u2)+' (m/s)')
print(' a2 (frozen) '+str(a2_fr)+' (m/s)')
print(' a2 (equilibrium) '+str(a2_eq)+' (m/s)')
print(' gamma2 (frozen) '+str(gamma2_fr)+' (m/s)')
print(' gamma2 (equilibrium) '+str(gamma2_eq)+' (m/s)')
print('--------------------------------------')
#
gas3 = ct.Solution(mech)
p3,UR,gas3 = reflected_eq(gas1,gas,gas3,cj_speed)
print('Reflected CJ shock (equilibrium) computation for '+mech+' with composition '+q)
print(' CJ speed '+str(cj_speed)+' (m/s)')
print(' Reflected wave speed '+str(UR)+' (m/s)')
print('Post-Reflected Shock Parameters')
print(' Pressure '+str(gas3.P)+' (Pa)')
print(' Temperature '+str(gas3.T)+' (K)')
print(' Density '+str(gas3.density)+' (kg/m3)')
print('--------------------------------------');
#
print('Shock computation for '+mech+' with composition '+q)
gas = PostShock_fr(cj_speed,P1,T1,q,mech)
print(' shock speed '+str(cj_speed)+' (m/s)')
print('Postshock State')
print(' Pressure '+str(gas.P)+' (Pa)')
print(' Temperature '+str(gas.T)+' (K)')
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))
print ("Reflected Wave Speed = %.2f m/s" % (UR))
# gas states
print('Incident gas state')
gas1()
print('Post-incident-shock gas state')
gas2()