def eos_derivatives(gas0, gmodel, tol=0.0001):
# Finite difference evaluation, assuming that gas0 is valid state already.
gas1 = GasState(gmodel)
gas1.copy_values(gas0)
p0 = gas0.p; rho0 = gas0.rho; u0 = gas0.u
#
drho = rho0 * tol; gas1.rho = rho0 + drho
gas1.update_thermo_from_rhou()
dpdrho = (gas1.p - p0)/drho
#
gas1.rho = rho0; du = u0 * tol; gas1.u = u0 + du
gas1.update_thermo_from_rhou()
dpdu = (gas1.p - p0)/du
#
return dpdrho, dpdu
# Notes:
# Select t_final to be long enough to reach x_final.
# Select t_inc small enough to capture fast changes near x=0.
#
for j in range(1, nsteps + 1):
# At the start of the step...
rho = gas0.rho
T = gas0.T
p = gas0.p
u = gas0.u
#
# Do the chemical increment.
gas1 = GasState(gmodel) # make the new one as a clone
gas1.copy_values(gas0)
dt_suggest = reactor.update_state(gas1, t_inc, dt_suggest)
gas1.update_thermo_from_rhou()
#
du_chem = gas1.u - u
dp_chem = gas1.p - p
if debug: print("# du_chem=", du_chem, "dp_chem=", dp_chem)
#
# Do the gas-dynamic accommodation after the chemical change.
etot = u + 0.5 * v * v
dfdr, dfdu = eos_derivatives(gas1, gmodel)
if debug: print("# dfdr=", dfdr, "dfdu=", dfdu)
# Linear solve to get the accommodation increments.
# [v, rho, 0.0, 0.0 ] [drho ] [0.0 ]
# [0.0, rho*v, 1.0, 0.0 ] * [dv ] = [-dp_chem ]
# [v*etot, rho*etot+p, 0.0, rho*v] [dp_gda] [-rho*v*du_chem]
# [dfdr, 0.0, -1.0, dfdu ] [du_gda] [0.0 ]
#
from eilmer.gas import GasModel, GasState
gmodel = GasModel("ideal-air-gas-model.lua")
print("gmodel=", gmodel)
print("n_species=", gmodel.n_species, ", n_modes=", gmodel.n_modes)
print("species_names=", gmodel.species_names)
print("mol_masses=", gmodel.mol_masses)
gs = GasState(gmodel)
print("freshly minted gs=", gs)
gs.rho=1.1; gs.p=1.0e5; gs.T=300.0; gs.u=1.44e6; gs.massf=[1.0]
print("after setting some values")
print(" gs.rho=%g p=%g T=%g u=%g massf=%s a=%g k=%g mu=%g" %
(gs.rho, gs.p, gs.T, gs.u, gs.massf, gs.a, gs.k, gs.mu))
gmodel.update_thermo_from_pT(gs) # the way that we do the update in D
gmodel.update_sound_speed(gs) # not necessary from Python but is available
gmodel.update_trans_coeffs(gs)
print("after update thermo from pT")
print(" gs.rho=%g p=%g T=%g u=%g massf=%s a=%g k=%g mu=%g" %
(gs.rho, gs.p, gs.T, gs.u, gs.massf, gs.a, gs.k, gs.mu))
gs.p=3000.0; gs.T=99.0; gs.massf={'air':1.0}
gs.update_thermo_from_rhou() # update another way
gs.update_trans_coeffs()
print("after update thermo from rhou")
print(" gs.rho=%g p=%g T=%g u=%g massf=%s a=%g k=%g mu=%g" %
(gs.rho, gs.p, gs.T, gs.u, gs.massf, gs.a, gs.k, gs.mu))
print("Some derived properties")
print("gs.Cv=%g Cp=%g R=%g enthalpy=%g entropy=%g molecular_mass=%g" %
(gs.Cv, gs.Cp, gs.R, gs.enthalpy, gs.entropy, gs.molecular_mass))
from eilmer.gas import GasModel, GasState, ThermochemicalReactor
gm = GasModel("nitrogen-2sp.lua")
reactor = ThermochemicalReactor(gm, "chem.lua")
gs = GasState(gm)
gs.p = 1.0e5 # Pa
gs.T = 4000.0 # degree K
gs.molef = {'N2': 2 / 3, 'N': 1 / 3}
gs.update_thermo_from_pT()
tFinal = 200.0e-6 # s
t = 0.0
dt = 1.0e-6
dtSuggest = 1.0e-11
print("# Start integration")
f = open("fvreactor.data", 'w')
f.write(
'# 1:t(s) 2:T(K) 3:p(Pa) 4:massf_N2 5:massf_N 6:conc_N2 7:conc_N\n')
f.write("%10.3e %10.3f %10.3e %20.12e %20.12e %20.12e %20.12e\n" %
(t, gs.T, gs.p, gs.massf[0], gs.massf[1], gs.conc[0], gs.conc[1]))
while t <= tFinal:
dtSuggest = reactor.update_state(gs, dt, dtSuggest)
t = t + dt
# dt = dtSuggest # uncomment this to get quicker stepping
gs.update_thermo_from_rhou()
f.write("%10.3e %10.3f %10.3e %20.12e %20.12e %20.12e %20.12e\n" %
(t, gs.T, gs.p, gs.massf[0], gs.massf[1], gs.conc[0], gs.conc[1]))
f.close()
print("# Done.")