Reaction Mechanism Reduction
Objective: -
Write a Reaction Reduction Mechanism code for the GRI 3.0 mechanism,
The code should do the following,
- First, it should run a reference Ignition delay and Max temperature Analysis for the unreduced mechanism for a set of state values (Temperature, Pressure and Equivalence ratio).
- Then, a sensitivity analysis with respect to temperature must be run on all the reactions in the mechanism and must sort the reactions from the most sensitive to least sensitive.
- Then, these sorted reactions should be added to a new mechanism file/object one by one starting from a fixed minimum number of reactions (40).
- Now a graph must be plotted plotting the reduced mechanism's ignition delay and max temperature while having the reference ignition delay and Temperature as a label for reference.
- This graph must have the values of Ignition Delay and Max temperature on the Y-axis, while the number of reactions in the mechanism on the X-axis.
- Now, repeat the same steps for various state values.
State Values Range: -
Temperature - [950 , 1050 , 1150] Kelvin
Pressure - [3 , 4 , 5] bar
Equivalence ratio - [0.5 , 1 , 1.5]
Note: Calculations must be performed with all possible combinations of State Values.
Once the program is complete, justify from the graphs, how many minimum reactions are required in the mechanism to predict accurate ignition delay and max temperature results.
Also in some cases, if the graph is not appearing or the program shows an unexpected error, also explain why this is happening and how it can be prevented.
Solution: -
Understanding Reaction Mechanisms:
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs. It is a theoretical compilation that explains in detail what happens at every stage of a chemical reaction. This mechanism is chosen because it is thermodynamically feasible, and has experimental support in isolated species (Intermediate) or other quantitative and qualitative characteristics of the reaction.
In the current project, we are using GRI 3.0 reaction mechanism which is an optimized mechanism designed to model natural gas combustion, including NO formation and reburn chemistry.
Mechanism Reduction:
Mechanism Reduction is a process where we remove redundant reactions from the mechanism with respect to our problem parameters. This helps us to customize or tune the mechanism to our specific requirements so that we have accurate results pertaining to the problem we are solving. For example, we can reduce a mechanism depending on the specific range of operating conditions we want for the fuel.
Based on the study of hydrocarbons combustion using detailed reaction mechanisms, is an important research area of combustion chemistry. The detailed mechanisms consist of hundreds of chemical species and thousands of reaction steps.
The size of the detailed combustion kinetics mechanisms for surrogates of real fuels makes it impossible for massive design studies with CFD tools.
Types of Mechanisms and their Applications:
1. Detailed:
- Hundreds of species, thousands of reactions for typical Hydrocarbon fuels
- Supposed to work in a wide range of conditions
- But further work is to be implemented with tests
2. Skeletal:
- Tens of species, Thousands of reactions for typical Hydrocarbon fuels
- Derived from the detailed mechanism by removing redundant species and reactions
- Derived for a narrow range of conditions, sometimes for specific problems
- Should be tested at the desired range of conditions
3. Reduced:
- Tens of species and reactions for typical Hydrocarbon fuels
- Derived from Detailed/Skeletal mechanisms by application of Quasi Steady State or Quasi Equilibrium approximations
- Derived for narrow range of conditions, sometimes for specific problem
- Should be tested at the desired range of conditions
4. Global:
- Cannot be directly derived from previous mechanisms, just a simple model
- Can be applied for restricted range of conditions, only for one type of problem
- Must be tested every time before applications
General Strategy for Mechanism Reduction:
The problem and targets for the reduction vary with respect to the combustion processes considered.
1. Perform the initial simulation with the respective conditions (Temperature, Pressure, Composition) pertaining to the specific problem and its targets using the Initial Mechanism. This step will give us the reference curves of the problem, for example the Ignition Delay time for the initial mechanism.
2. Then with the reference data in place, we will slowly reduce the mechanism to fit our problem parameters. This step is achieved by performing the respective sensitivity analysis and sorting the most sensitive reactions in the mechanisms.
3. The sorted mechanisms in the second step are converted into a separate mechanism file and the same simulation is performed from the first step but, this time with the reduced mechanism.
For the current case, we are trying to reduce the mechanism with respect to the reference Maximum Temperature and Ignition Delay time.
Python Program Structure: -
The python code is broken into four parts:
The first part is a File Parser which takes the input parameters i.e. the state values (Temperature, Pressure and Equivalence Ratio) and their range. The data file namely "Reduction_Parameters" contains the upper and lower values of the state parameters provided with the number of values to be considered within their range. This way is efficient as the number of values can be customized easily than providing all the considered values manually.
The second part consists of the initial simulation with respect to the nested loops of the state parameters. This simulation determines the Ignition Delay and the Maximum Temperature of the initial mechanism (325 reactions) under the simulation time of 5 seconds. The obtained values will serve as the reference for the values determined using the reduced mechanisms. To understand more about Ignition Delay, you can refer to this project:https://projects.skill-lync.com/projects/Auto-igniton-using-Cantera-82939
The third part covers the approach for the reduced mechanism which is in this case, a sensitivity analysis with respect to the temperature parameter. Using this approach, we arrange the reactions in order of maximum sensitivity to minimum sensitivity. To understand more about Sensitivity Analysis, you can refer to this project: https://projects.skill-lync.com/projects/Senstivity-Analysis-Assignment-22528
The fourth part implements the actual mechanism reduction. Here, we start with 40 reactions from the re-ordered mechanism and determine the Ignition Delay and the Maximum Temperature. This process is continuously done while adding one reaction at a time to the new reaction mechanism i.e. the simulation for Ignition Delay and the Maximum Temperature is done for a mechanism incrementation of one reaction.
Code:
# Program to find the most efficient Reduced Mechanism for the given range of state values
import os
import numpy as np
import matplotlib.pyplot as plt
import cantera as ct
gas = ct.Solution('gri30.xml')
Dict = {}
for line in open('Reduction_Parameters.txt'):
if '#' not in line:
key = line.split()[0]
value_st = line.split()[2]
value_end = line.split()[3]
step = line.split()[4]
value_st = float(value_st)
value_end = float(value_end)
step = int(step)
all_values = np.linspace(value_st, value_end, step)
Dict[key] = all_values
Temp = []
Press = []
Phi = []
Temp = Dict['Temperature']
Press = Dict['Pressure']
Press = [i*ct.one_atm for i in Press]
Phi = Dict['Equivalence_Ratio']
sim_time = 5 # 5 Seconds
t_step = 0.01
n_time = np.arange(0, sim_time, t_step)
t_len = len(n_time)
case = 1
for tp in Temp:
for p in Press:
for ph in Phi:
initial_state = tp, p, {'CH4':1,'O2':2/ph,'N2':7.52/ph}
# Finding the reference Ignition Delay and Maximum Temperature
gas.TPX = initial_state
r = ct.IdealGasConstPressureReactor(gas, name='R1')
sim = ct.ReactorNet([r])
for i in range(0,gas.n_reactions):
r.add_sensitivity_reaction(i)
# set the tolerances for the solution and the sensitivity co-efficients
sim.rtol = 1.0e-6 # Realtive change in the solution < sim.rtol
sim.atol = 1.0e-15 # Absolute change in the solution < sim.atol
sim.rtol_sensitivity = 1.0e-6 #relative change in sensitivity < sim.rtol_sense
sim.atol_sensitivity = 1.0e-6 #absolute change in sensitivity =400):
Ignition_delay = time
T_old = T_new
max_temp = max(tmp)
for i in range(0,gas.n_reactions): # Sensitivity analysis with respect to temperature
s[ctr,i] = (sim.sensitivity(1, i))
sens = abs(s[:,i])
sens = max(sens)
Smax[i] = np.maximum(Smax[i], sens)
ctr += 1
S = sorted(zip(Smax, gas.reactions()), key=lambda x: -x[0])
print('nCase = ' + str(case) + 'nFor Temperature = ' + str(tp) + ' Kelvin, ' + 'Pressure = ' + str(p) + ' bar, ' + 'Equivalence Ratio = ' + str(ph))
print('nReference Ignition Delay = ', Ignition_delay)
print('Reference Maximum Temperature = ', max_temp)
#Creating a new mechanism and re-run the ignition problem
red_mech = np.arange(40, gas.n_reactions, 1)
T_max = []
ID_max = []
for r_mech in red_mech:
reactions = [r[1] for r in S[:r_mech]]
spec = ct.Species.listFromFile('gri30.cti')
# create the new reduced mechanism
gas2 = ct.Solution(thermo='IdealGas', kinetics='GasKinetics',
species=spec, reactions=reactions)
# Re-run the ignition problem with the reduced mechanism
gas2.TPX = initial_state
r = ct.IdealGasConstPressureReactor(gas2)
sim = ct.ReactorNet([r])
time = 0.0 # Initial Time
# States of Reactor which include all attribiutes of the reactor
states = ct.SolutionArray(gas, extra = ['t_ms','t'])
T_old = tp
tmp = []
Ignition_delay = []
for time in n_time:
sim.advance(time) # Advancing the reactor w.r.t the time step
tmp.append(r.T)
T_new = r.T
if ((T_new - T_old)>=400):
Ignition_delay = time
T_old = T_new
T_max.append(np.max(tmp))
ID_max.append(Ignition_delay)
for n,i in enumerate(ID_max):
if i == []:
ID_max[n] = 0
plt.figure(figsize=(13.0, 7.0))
plt.subplot(2,1,1)
plt.title('Reaction Mechanism Reduction for Case ' + str(case))
plt.plot(red_mech, ID_max, label= 'Reference Ignition Delay = ' + str(Ignition_delay) + 'sec' + 'n Temperature = ' + str(tp) + 'Kelvin' + 'n Pressure = ' + str(p) + 'bar' + 'n Equivalence Ratio = ' + str(ph))
plt.xlabel('Number of Reactions')
plt.ylabel('Ignition Delay [ms]')
plt.legend(loc='best')
plt.subplot(2,1,2)
plt.plot(red_mech, T_max, color = 'red', label= 'Reference Maximum Temperature = ' + str(max_temp) + ' Kelvin' + 'n Temperature = ' + str(tp) + 'Kelvin' + 'n Pressure = ' + str(p) + 'bar' + 'n Equivalence Ratio = ' + str(ph))
plt.xlabel('Number of Reactions')
plt.ylabel('Maximum Temperature [K]')
plt.legend(loc='best')
plt.savefig(' Case '+ str(case) + '.png')
plt.clf()
case += 1 Results and Observation:
The above image shows the plots for Ignition Delay and Maximum Temperature during the reduction process. For the Ignition Delay, we can see that it is increasing from 0 to approximately 0.6 milliseconds from the mechanisms containing 40 to 47 reactions and it stabilizes. This indicates that the state values present in the reactor does not satisfy the fuel's Auto Ignition capability and the mixture here is lean. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 72 reactions.
The bottom plot shows that the Maximum Temperature is increasing in the same range of mechanisms containing from 40 to 47 reactions and it stabilizes. But it is important to understand that the trend observed here is of maximum temperature not the Initial temperature. And the resulting trend is all over the plot and it is hard to understand, the reason for this is explained in the note mentioned at the end of the report. These conclusions here demonstrate that combustion for the current state values is not efficient. The Maximum Temperature plot (bottom) has a trend which stabilises at 2016 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists 163 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 3 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.810 to 0.780 milliseconds from mechanisms containing 40 to 53 reactions and stabilizes at 0.780 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case. As the equivalence ratio is 1, we can say that this mixture is stochiometric and we have efficient combustion. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 67 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2575 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 164 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 3 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 1 to 0.95 milliseconds from mechanisms containing 40 to 53 reactions and stabilizes at 0.95 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1.5 in this case indicating that the mixture here is rich. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 63 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2390 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 245 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 4 bar, and 0.5 respectively. The Ignition Delay plot (top) is increasing from 0 to 0.46 milliseconds from mechanisms containing 40 to 53 reactions and stabilizes at 0.46 milliseconds. This trend shows that combustion for the current state values is inefficient as the Ignition Delay is increasing. For the current case, we have a pressure increase from 3 to 4 bar and equivalence ratio 0.5. From the Auto Ignition Challenge, we have inferred that Ignition Delay is sensitive to pressure but the trend shows an opposite effect. This is due to the decrease in the Equivalence ratio making the mixture lean. The final reduced mechanism for the current state values pertaining to Ignition Delay consists 71 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2017 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 155 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 4 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.580 to 0.560 milliseconds from mechanisms containing 40 to 65 reactions and stabilizes at 0.560 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 65 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2595 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 199 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 4 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 0.710 to 0.680 milliseconds from mechanisms containing 40 to 58 reactions and stabilizes at 0.680 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1.5 in this case indicating that the mixture here is rich. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 58 reactions.
The Maximum Temperature plot (bottom) has a trend which stabilises at 2390 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists 230 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 5 bar, and 0.5 respectively. The Ignition Delay plot (top) is increasing from 0 to 0.37 milliseconds from mechanisms containing 40 to 65 reactions and stabilizes at 0.37 milliseconds. This trend shows that combustion for the current state values is inefficient as the Ignition Delay is increasing. For the current case, we have a pressure increase from 4 to 5 bar and an equivalence ratio of 0.5. From the Auto Ignition Challenge, we have inferred that Ignition Delay is sensitive to pressure but the trend shows an opposite effect. This is due to the decrease in the Equivalence ratio making the mixture lean. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 71 reactions.
The Maximum Temperature plot (bottom) is increasing in the same range of mechanisms containing from 40 to 65 reactions stabilizes at 2018 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 157 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 5 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.450 to 0.440 milliseconds from mechanisms containing 40 to 67 reactions and stabilizes at 0.440 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 67 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2595 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 208 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 950 Kelvin, 5 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 0.540 to 0.520 milliseconds from mechanisms containing 40 to 60 reactions and stabilizes at 0.520 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1.5 in this case indicating that the mixture here is rich. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 60 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2392 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 244 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 3 bar, and 0.5 respectively. The Ignition Delay plot (top) is decreasing from 0.120 to 0.110 milliseconds from mechanisms containing 40 to 49 reactions and stabilizes at 0.110 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. From the Auto Ignition Challenge, we have inferred that Ignition Delay is sensitive to temperature and the trend corroborates it despite having a lean mixture. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 49 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2100 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 180 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 3 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.160 to 0.150 milliseconds from mechanisms containing 40 to 43 reactions and stabilizes at 0.150 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. When again compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 43 reactions.
The Maximum Temperature plot (bottom) has a trend which stabilises at 2618 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 167 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 3 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 0.190 to 0.180 milliseconds from mechanisms containing 40 to 99 reactions and stabilizes at 0.180 milliseconds. We observe the Ignition Delay dropping to zero in the plot many times. The value zero indicates the lack of combustion. This phenomenon is mainly due to the mixture being fuel-rich resulting in combustion instability or Incomplete combustion. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 99 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2464 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 218 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 4 bar, and 0.5 respectively. The Ignition Delay plot (top) is decreasing from 0.090 to 0.080 milliseconds from mechanisms containing 40 to 57 reactions and stabilizes at 0.080 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 57 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2100 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 208 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 4 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.120 to 0.110 milliseconds from mechanisms containing 40 to 44 reactions and stabilizes at 0.110 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 44 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2631 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 164 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 4 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 0.150 to 0.130 milliseconds from mechanisms containing 40 to 63 reactions and stabilizes at 0.130 milliseconds. Similar to case 12, we observe the Ignition Delay dropping to zero in the plot many times. The value zero indicates the lack of combustion. This phenomenon is mainly due to the mixture being fuel-rich resulting in combustion instability or Incomplete combustion. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 63 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2468 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 240 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 5 bar, and 0.5 respectively. The Ignition Delay plot (top) is decreasing from 0.070 to 0.060 milliseconds from mechanisms containing 41 to 83 reactions and stabilizes at 0.060 milliseconds. The Ignition Delay for a mechanism containing 40 reactions is zero due to lack of combustion. This phenomenon is mainly due to the mixture being lean resulting in combustion instability or Incomplete combustion. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 83 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2100 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 147 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 5 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.800 to 0.080 milliseconds from mechanisms containing 40 to 52 reactions and stabilises at 0.080 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. Before reaching to 0.80 milliseconds, the trend starts from 0.1 milliseconds. This is due to new reactions getting added to the mechanism which are endothermic which results in absorbs energy from its surroundings, usually in the form of heat which increases the Ignition Delay. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists 52 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2650 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 158 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1050 Kelvin, 5 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 0.110 to 0.100 milliseconds from mechanisms containing 40 to 65 reactions and stabilizes at 0.100 milliseconds. Before stabilizing, the Ignition Delay goes unstable, this phenomenon is mainly due to the mixture being fuel-rich resulting in combustion instability or Incomplete combustion. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 65 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2470 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 231 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 3 bar, and 0.5 respectively. The Ignition Delay plot (top) is decreasing from 0.070 to 0.020 milliseconds from mechanisms containing 41 to 50 reactions and stabilizes at 0.060 milliseconds. Before reaching 0.70, the trend starts from 0.02 milliseconds. This is due to new reactions getting added to the mechanism which are endothermic in nature which results in absorbing energy from its surroundings, usually in the form of heat which increases the Ignition Delay. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 50 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2186 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 149 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 3 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.270 to 0.03 milliseconds from mechanisms containing 40 to 72 reactions and stabilizes at 0.03 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. Before reaching 0.030 milliseconds, the trend starts from 0.27 milliseconds and keeps decreasing and increasing. This is due to new reactions getting added to the mechanism which is endothermic and exothermic in nature leading to absorbing and releasing energy from its surroundings, usually in the form of heat which results in an increase or a decrease in the Ignition Delay. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 72 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2670 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 257 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 3 bar, and 1.5 respectively. The Ignition Delay plot (top) is increasing and decreasing from 0.042 to 0.042 milliseconds from mechanisms containing 40 to 66 reactions and stabilizing at 0.042 milliseconds. This is due to new reactions getting added to the mechanism which are endothermic and exothermic in nature leading to absorbing and releasing energy from its surroundings, usually in the form of heat which results in an increase or a decrease in the Ignition Delay. The other contributing factor for the unstable Ignition Delay may also be due to the mixture being fuel-rich resulting in combustion instability or Incomplete combustion. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 66 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2540 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 262 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 4 bar, and 0.5 respectively. The Ignition Delay plot (top) is increasing and decreasing from 0.020 to 0.020 milliseconds from mechanisms containing 40 to 57 reactions and stabilizing at 0.020 milliseconds. This is due to new reactions getting added to the mechanism which are endothermic and exothermic in nature leading to absorbing and releasing energy from its surroundings, usually in the form of heat which results in an increase or a decrease in the Ignition Delay. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 57 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2187 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 192 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 4 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.10 to 0.025 milliseconds from mechanisms containing 40 to 57 reactions and stabilizes at 0.03 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. Before reaching 0.025 milliseconds, the trend keeps decreasing and increasing, this is due to new reactions getting added to the mechanism which are endothermic and exothermic in nature leading to absorbing and releasing energy from its surroundings, usually in the form of heat which results in an increase or a decrease in the Ignition Delay. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 57 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2686 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 212 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 4 bar, and 1.5 respectively. The Ignition Delay plot (top) is increasing and decreasing from 0.031 to 0.031 milliseconds from mechanisms containing 40 to 63 reactions and stabilizing at 0.031 milliseconds. This is due to new reactions getting added to the mechanism which are endothermic and exothermic in nature leading to absorbing and releasing energy from its surroundings, usually in the form of heat which results in an increase or a decrease in the Ignition Delay. The other contributing factor for the unstable Ignition Delay may also be due to the mixture being fuel-rich resulting in combustion instability or Incomplete combustion. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 63 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2545 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 261 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 5 bar, and 0.5 respectively. The Ignition Delay plot (top) is increasing and decreasing from 0.015 to 0.014 milliseconds from mechanisms containing 40 to 48 reactions and stabilizing at 0.014 milliseconds. This is due to new reactions getting added to the mechanism which are endothermic and exothermic in nature leading to absorbing and releasing energy from its surroundings, usually in the form of heat which results in an increase or a decrease in the Ignition Delay. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 48 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2189 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 173 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 5 bar, and 1 respectively. The Ignition Delay plot (top) is decreasing from 0.125 to 0.02 milliseconds from mechanisms containing 40 to 68 reactions and stabilizes at 0.02 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. This is also corroborated by high temperature and pressure compared to the previous cases. When again compared to the previous case, the only change in the state values is the Equivalence ratio which is 1 in this case indicating that the mixture here is stoichiometric. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 68 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2696 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 226 reactions.
The state values (Temperature, Pressure, Equivalence Ratio) for the current case are 1150 Kelvin, 5 bar, and 1.5 respectively. The Ignition Delay plot (top) is decreasing from 0.025 to 0.024 milliseconds from mechanisms containing 40 to 69 reactions and stabilizes at 0.024 milliseconds. This trend shows that combustion for the current state values is efficient as the Ignition Delay is decreasing. When compared to the previous case, the only change in the state values is the Equivalence ratio which is 1.5 in this case indicating that the mixture here is rich. The final reduced mechanism for the current state values pertaining to Ignition Delay consists of 69 reactions.
The Maximum Temperature plot (bottom) has a trend that stabilizes at 2548 Kelvin, the reduced mechanism for the current state values pertaining to Maximum Temperature consists of 252 reactions.
The factors that influence Ignition Delay:
We have established for the Auto Ignition challenge that Ignition Delay is sensitive to an increase in Temperature and pressure and it can be corroborated in the above cases. Keeping the former statement in consideration, we can also establish that the Equivalence ratio has a higher contribution to the Ignition Delay which can also be corroborated from the above observations.
The nature of the reaction processes also contributes to the Ignition Delay i.e. the reactions' nature being Endothermic or Exothermic.
The following table shows the Reduced Mechanisms for the above cases pertaining to Ignition Delay and Maximum Temperature:
The average Reduced Mechanism for the range of given state values contains around 60 to 65 reactions.
Note:
1. It is important to understand the trend we observe in the above images. For each step, we are finding the Ignition Delay and the Maximum Temperature for the previous mechanism with the addition of a new reaction. For example, a mechanism consisting of 40 reactions gives a specific value and the next mechanism with 41 reactions gives a new value in which the previous reactions are also present.
2. The Ignition Delay and Maximum temperature trend where it stabilizes is the step where we have the most efficient reduced mechanism i.e. That particular mechanism is safe to be used for that particular state values.
Errors Faced:
During the plotting of the graphs, in some cases, there were instances where the combustion was not occurring. Due to this phenomenon, the Ignition Delay array was taking empty arrays. A piece of code was added to replace those empty values to zero to explain that the combustion was not occurring in that particular reduced mechanism. The occurrence of value 0 in the above Ignition Delay plots indicates the failure of combustion for the state values for that particular mechanism.
For some particular cases, the Ignition Delay trend was constant i.e. it was showing a single value during the whole entire reduction process. To get precise trends, the step size for the simulation time was decreased from 0.01 to 0.001.