pfr.py (Source)

# -*- coding: utf-8 -*-
"""
This example solves a plug-flow reactor problem of hydrogen-oxygen combustion.
The PFR is computed by two approaches: The simulation of a Lagrangian fluid
particle, and the simulation of a chain of reactors.
"""

import cantera as ct
import numpy as np

#######################################################################
# Input Parameters
#######################################################################

T_0 = 1500.0  # inlet temperature [K]
pressure = ct.one_atm  # constant pressure [Pa]
composition_0 = 'H2:2, O2:1, AR:0.1'
length = 1.5e-7  # *approximate* PFR length [m]
u_0 = .006  # inflow velocity [m/s]
area = 1.e-4  # cross-sectional area [m**2]

# input file containing the reaction mechanism
reaction_mechanism = 'h2o2.xml'

# Resolution: The PFR will be simulated by 'n_steps' time steps or by a chain
# of 'n_steps' stirred reactors.
n_steps = 2000
#####################################################################


#####################################################################
# Method 1: Lagrangian Particle Simulation
#####################################################################
# A Lagrangian particle is considered which travels through the PFR. Its
# state change is computed by upwind time stepping. The PFR result is produced
# by transforming the temporal resolution into spatial locations.
# The spatial discretization is therefore not provided a priori but is instead
# a result of the transformation.

# import the gas model and set the initial conditions
gas1 = ct.Solution(reaction_mechanism)
gas1.TPX = T_0, pressure, composition_0
mass_flow_rate1 = u_0 * gas1.density * area

# create a new reactor
r1 = ct.IdealGasConstPressureReactor(gas1)
# create a reactor network for performing time integration
sim1 = ct.ReactorNet([r1])

# approximate a time step to achieve a similar resolution as in the next method
t_total = length / u_0
dt = t_total / n_steps
# define time, space, and other information vectors
t1 = (np.arange(n_steps) + 1) * dt
z1 = np.zeros_like(t1)
u1 = np.zeros_like(t1)
states1 = ct.SolutionArray(r1.thermo)
for n1, t_i in enumerate(t1):
    # perform time integration
    sim1.advance(t_i)
    # compute velocity and transform into space
    u1[n1] = mass_flow_rate1 / area / r1.thermo.density
    z1[n1] = z1[n1 - 1] + u1[n1] * dt
    states1.append(r1.thermo.state)
#####################################################################


#####################################################################
# Method 2: Chain of Reactors
#####################################################################
# The plug flow reactor is represented by a linear chain of zero-dimensional
# reactors. The gas at the inlet to the first one has the specified inlet
# composition, and for all others the inlet composition is fixed at the
# composition of the reactor immediately upstream. Since in a PFR model there
# is no diffusion, the upstream reactors are not affected by any downstream
# reactors, and therefore the problem may be solved by simply marching from
# the first to last reactor, integrating each one to steady state.
# (This approach is anologous to the one presented in 'surf_pfr.py', which
# additionally includes surface chemistry)


# import the gas model and set the initial conditions
gas2 = ct.Solution(reaction_mechanism)
gas2.TPX = T_0, pressure, composition_0
mass_flow_rate2 = u_0 * gas2.density * area
dz = length / n_steps
r_vol = area * dz

# create a new reactor
r2 = ct.IdealGasReactor(gas2)
r2.volume = r_vol

# create a reservoir to represent the reactor immediately upstream. Note
# that the gas object is set already to the state of the upstream reactor
upstream = ct.Reservoir(gas2, name='upstream')

# create a reservoir for the reactor to exhaust into. The composition of
# this reservoir is irrelevant.
downstream = ct.Reservoir(gas2, name='downstream')

# The mass flow rate into the reactor will be fixed by using a
# MassFlowController object.
m = ct.MassFlowController(upstream, r2, mdot=mass_flow_rate2)

# We need an outlet to the downstream reservoir. This will determine the
# pressure in the reactor. The value of K will only affect the transient
# pressure difference.
v = ct.PressureController(r2, downstream, master=m, K=1e-5)

sim2 = ct.ReactorNet([r2])

# define time, space, and other information vectors
z2 = (np.arange(n_steps) + 1) * dz
t_r2 = np.zeros_like(z2)  # residence time in each reactor
u2 = np.zeros_like(z2)
t2 = np.zeros_like(z2)
states2 = ct.SolutionArray(r2.thermo)
# iterate through the PFR cells
for n in range(n_steps):
    # Set the state of the reservoir to match that of the previous reactor
    gas2.TDY = r2.thermo.TDY
    upstream.syncState()
    # integrate the reactor forward in time until steady state is reached
    sim2.reinitialize()
    sim2.advance_to_steady_state()
    # compute velocity and transform into time
    u2[n] = mass_flow_rate2 / area / r2.thermo.density
    t_r2[n] = r2.mass / mass_flow_rate2  # residence time in this reactor
    t2[n] = np.sum(t_r2)
    # write output data
    states2.append(r2.thermo.state)

#####################################################################


#####################################################################
# Compare Results in matplotlib
#####################################################################

import matplotlib.pyplot as plt

plt.figure()
plt.plot(z1, states1.T, label='Lagrangian Particle')
plt.plot(z2, states2.T, label='Reactor Chain')
plt.xlabel('$z$ [m]')
plt.ylabel('$T$ [K]')
plt.legend(loc=0)
plt.show()
plt.savefig('pfr_T_z.png')

plt.figure()
plt.plot(t1, states1.X[:, gas1.species_index('H2')], label='Lagrangian Particle')
plt.plot(t2, states2.X[:, gas2.species_index('H2')], label='Reactor Chain')
plt.xlabel('$t$ [s]')
plt.ylabel('$X_{H_2}$ [-]')
plt.legend(loc=0)
plt.show()
plt.savefig('pfr_XH2_t.png')