Week 4 - Combustion Efficiency Calculation after Preheating
AIM :-
I. TO ANALYSE THE EFFECT OF PREHEATING ON ADIABATIC FLAME TEMPERATURE .
II. TO ANALYSE THE EFFECT OF PREHEATING ON COMBUSTION EFFICIENCY OF FUEL.
INTRODUCTION :-
Since We know that In today's world fuel consumption is increasing day by day. It have become must for us to use certain techniques for economical fuel consumption without dealing with expensive installation equipments. So keeping in mind such problem, I have developed a code where I analysed the effect of premixed fuel-mixture in the furnance on the temperature which will help in attaining better efficiency.
Here I have developed program for efficiency of heat recuperator at constant pressure because combustion is taking place in furnance at atmopsheric pressure or ambient condition. The program have been develop in python programming language.
Here also, In the code I calculated the adiabatic flame temperature and combustion efficiency of the fuel in the furnance on the account of preheated air mixed with fuel in the chamber. Here My objective is to analyse the behaviour of adiabatic flame temperature and combustion efficiency so that I can pre-assume the temperature at which I can mix the fuel with preheated air due to which I can attain the maximum efficiency of heat system in order to produce useful work.
THEORY :-
Here My motive is to analyse the combustion process in the furnance which is connected to the recuperator or heat exchanger through which inet air exchanges heat with exhaust air and attains a rise in temperature. The aim was to analyse the efficiency of combustion in the furnance and adiabatic flame temperature during the combustion. In order to adjust the temperature of preheated oxidiser, mixing valve is used which basically mixes fuel with preheated oxidiser and adjusts the temperature of fuel-mixer.
Here I have assumed air-fuel mixture ratio to be '1' or say stoichiometic ratio. Here I could have been adjust the air-fuel mixture ratio but for demonstration purpose I kept the air-fuel mixture to be stoichiometric. Hence chemical equation taken for combustion is stoichiometric equation.
This two things mentioned below were My motivation behind the project which helped me in predicting the temperature at which maximum efficiency of combustion could be attain without dealing with more fuel consumption.
(i) Adiabatic flame temperature.
(ii) Combustion efficiency.
Adiabatic flame temperature is the highest temperature during the combustion when no heat is released form the system or when no heat is lost.
A Recuperator is a special purpose counter-flow energy recovery heat exchanger positioned within the supply and exhaust air streams of an air handling system, or in the exhaust-gases of an industrial process, in order to recover the waste heat. Generally, they are used to extract heat from the exhaust and use it to preheat air entering the combustion system. In this way they use waste energy to heat the air, offsetting some of the fuel, and thereby improves the energy efficiency of the system as a whole.
Here In this project, Object oriented programming method have been used in python programming language software so as to make the programming short and comprehensive. Since python language have very comprehensive coding,user-friendly for end user and have fast result it have been chosen for this project.
Combustion efficiency :-
It basically tells us about that how much percentage of combustion have taken place for burning a particular amount of fuel with respect to standard combustion or calorific value of that fuel.
It could be also explain in another sense as degree of completeness of combustion of a specific fuel.
It's formula is given by:-
`eta_(combustion)= (H(T_(ambient))-H(T_(i ntial)))/((m_f) (L.H.V))` , in terms of mass .
Here, L.H.V stands for lower heating value.
`eta_(combustion)= (H(T_(ambient))-H(T_(i ntial)))/(n (L.H.V))` , in terms of moles .
Here stands for number of moles.
Methane(CH4) have been used as fuel for combustion process and it's lower heating value is 800 KJ per mole and 'Air' have been considered as oxidiser to fuel where it contains nitrogen and oxygen having a ratio of 3.76(nitrogen to oxygen) in terms of moles.
Fixed Furnance exit temperature have been pre-assumed as value of 1700 K.
SOURCE CODE:-
""""
Program to calculate the effect preheated mixture on the adiabatic flame
temperature
"""
import cantera as ct
import matplotlib.pyplot as plt
import numpy as np
gas=ct.Solution('gri30.cti') # to import reaction mechanism data.
T_pre_heat_var= np.linspace(298.15,600,51) # here variable is containing a list of Temperatures from 298.15K to 600K to adjust the preheated temperature.
T_aft=[1700 for _ in range(51)] # variable containing a list of temperature having guess value.
i=0
for i in range(len(T_pre_heat_var)):
A=ct.Quantity(gas)
A.TPX=T_pre_heat_var[i],ct.one_atm,{'O2':0.21,'N2':0.79}
A.moles=200/21 # attribute(moles) of class used to assign the right moles to oxidisers.
print(A.mass_fraction_dict()) # to print mass fractions of given reactants species.
B=ct.Quantity(gas)
B.TPX=298.15,101325,{'Ch4':1}
B.moles=1
M=A + B # Summation of moles of object 'A' and 'B'.
M.equilibrate('HP','auto') # gibbs solver used to solve the reaction at constant pressure.
T_aft[i]=(M.T) # variable containing values of adiabatic flame temperature for variable preheated temperatures.
plt.plot(T_pre_heat_var,T_aft,'*-',color='red')
plt.title('EFFECT OF PREHEATED TEMPERATURE ON COMBUSTION EFFICIENCY')
plt.xlabel('Preheated temperature of air')
plt.ylabel('Adiabatic flame temperature')
plt.show()
print(T_aft)"""
program to calculate combustion effciency of net energy gain of the methane fuel in constant pressure furnance reactor
"""
import matplotlib.pyplot as plt
import cantera as cantera
import numpy as np
CH4_coefficients_h=[ 5.14987613E+00,-1.36709788E-02, 4.91800599E-05,-4.84743026E-08, 1.66693956E-11,-1.02466476E+04,-4.64130376E+00]
O2_coefficients_l=[3.78245636E+00,-2.99673416E-03, 9.84730201E-06,-9.68129509E-09, 3.24372837E-12,-1.06394356E+03, 3.65767573E+00]
N2_coefficients_l=[0.03298677E+02, 0.14082404E-02,-0.03963222E-04,0.05641515E-07,-0.02444854E-10,-0.10208999E+04, 0.03950372E+02]
CO2_coefficients_h=[3.85746029E+00, 4.41437026E-03,-2.21481404E-06, 5.23490188E-10,-4.72084164E-14,-4.87591660E+04, 2.27163806E+00 ]
N2_coefficients_h=[0.02926640E+02, 0.14879768E-02,-0.05684760E-05, 0.10097038E-09,-0.06753351E-13,-0.09227977E+04, 0.05980528E+02]
H2O_coefficients_h=[3.03399249E+00, 2.17691804E-03,-1.64072518E-07,-9.70419870E-11, 1.68200992E-14,-3.00042971E+04, 4.96677010E+00]
def h(coeffs,T):
R=8.314 #j/mol-k
a1=coeffs[0]
a2=coeffs[1]
a3=coeffs[2]
a4=coeffs[3]
a5=coeffs[4]
a6=coeffs[5]
return (a1 + (a2*T)/2 + (a3*pow(T,2))/3 + (a4*pow(T,3))/4 + (a5*pow(T,4))/5 + a6/T)*R*T
T_aft=[2224.224370856459, 2226.812764345683, 2229.3947484381492, 2231.970333756537, 2234.539533849564, 2237.1023655568856, 2239.65884829019, 2242.20900417878, 2244.752857868461, 2247.290436386341, 2249.821769011209, 2252.3468871487516, 2254.865824211467, 2257.3786155028893, 2259.8852981056866, 2262.3859107735693, 2264.8804938267, 2267.369089050333, 2269.8517395966255, 2272.3284898893753, 2274.7993855316945, 2277.2644732311746, 2279.7238007609976, 2282.1774164048634, 2284.625369969316, 2287.0677115313174, 2289.5044919698403, 2291.935762765008, 2294.3615759243226, 2296.781983910874, 2299.1970395734816, 2301.6067960786613, 2304.0113068445066, 2306.410625476223, 2308.804805703461, 2311.1939013192955, 2313.577966120853, 2315.9570538514986, 2318.3312181446377, 2320.7005124688285, 2323.0649900826347, 2325.4247040368127, 2327.7797067372135, 2330.130050745881, 2332.475787845192, 2334.816969447, 2337.1536464549595, 2339.485869220701, 2341.813687501227, 2344.13715041753, 2346.4563064143404]
# Above variable contains list of different values of preheated temperature obtained from cantera method.
T_pre= np.linspace(298.15,600,51) # here T_pre stands for predefined Temperature which contains a list of different values of temperature.
comb_effs=[100 for _ in range(51)] # here comb_effs contains a list of guess values.
LHV=80e+4 #(Joules/mole), here LHV stands for lower heating value of methane per mole.
for i in range(0,len(T_aft)):
# calculating entalphy of the product species:-
h_p_Co2=h(CO2_coefficients_h,T_aft[i])
h_p_H2o=h(H2O_coefficients_h,T_aft[i])
h_p_N2=h(N2_coefficients_h,T_aft[i])
# calculating entalphy of the reactants species :-
h_r_Ch4=h(CH4_coefficients_h,T_pre[i])
h_r_O2=h(O2_coefficients_l,T_pre[i])
h_r_N2=h(N2_coefficients_l,T_pre[i])
# Summation of entalphy of the product
h_r_products= h_p_Co2 + h_p_H2o + h_p_N2
# Summation of entalphy of the reactants
h_r_reactants= h_r_Ch4 + 2*(h_r_O2 + h_r_N2)
# calculating ccombustion efficiency of given fuel "methane" for particular temperature.
comb_effs[i]=((h_r_reactants- h_r_products)/LHV)*100
plt.plot(T_aft,comb_effs,'*-',COLOR='blue')
plt.title('EFFECT OF PREHEATED TEMPERATURE ON COMBUSTION EFFICIENCY')
plt.xlabel('Preheated temperature of air')
plt.ylabel('Combustion efficiency')
plt.show()
RESULT WITH EXPLAINATION:-
From plot, I observe that adiabatic flame temperature is increasing linearly with respect to increase in preheated air(oxidiser) although there is slight increase in adiabatic flame temperature for range of preheated temperature .
By this plot, I get information that Combustion efficiency is also increasing slight curvely with respect to increase in preheated temperature. Here, combustion efficiency is although do not have any significant increase in temperature on account of increase in preheated temperature but still this is something which can bring out impact on curtail of fuel consumption.
We have assumed fixed furnance exit temperature as 1700 K. However this temperature wouldn't reflect in adiabatic flame temperature as it is nothing to deal with combustion efficiency and adiabatic flame temperature because it is just a preassumption which ultimately keep changes when adiabatic flame temperature is calculated. Hence, it is nothing wrong to assume any fixed value of temperature since here it is calculated after each iterations so it do not have any sense.
CONCLUSION :-
1. Adiabatic flame temperature increases linearly with respect to increase in preheated temperature. However, temperature rise may not be too significant.
2. Combustion efficiency also increases with respect to rise in preheated temperature despite having slight increase in percentage value.
3. By considering above both, I can say that preheating of temperature will help in saving the fuel consumption by curtailing the fuel consumption while attaining the high temperature. Hence more efficiency could be attain with same fuel.