Week 4.2 - Combustion Efficiency Calculation after Preheating

AIM -  To learn the effect of preheating on the adiabatic flame temperature.

OBJECTIVE -

1. To observe the effect of preheating on the Adiaabatic flame temperature.
2. To observe the effect of preheating on the combustion efficiency.
3. To observe teh effcet of preheating on fuel consumption.

INTRODUCTION - 

When a hot air gas are passed through a turbine or other energy harvesting unit work is generated and even after that the exhaust gas are hot enough so they can be used to heat the incoming air that is used for combustion. In this way the energy with the exhausted gas can be used to heat the cold incoming air and help in increasing the efficiency as the gas will be already hot when it goes to the furnance and it will result in higher Adiabatic flame temperature and reduced fuel comsumption. We will observe this trend by increasing the tempreature of the preheated air and plot it against the AFT and efficiency of combustion.

CODING APPROCH - 

To write the code for this challenge we will be first importing cantera into our pyhton code then create a gas object under Solutions class . 

then create an object A which is the oxidiser containing oxygen and nitrogen and give the appropiate values for the properites temperature , pressure and mole fractions. note that the temperature of object A will be the preheating temperature and it will be varied to see the desired trends for the AFT and efficeincy. 

also create another object B which is the fuel this is methane and give the STP conditions .  

now the mixture M of both A and B will be used for the combustion using the equilibrate method at constant enthalpy and pressure that is the adiabatic condition which will result in giving the AFT value.

now to calculate the combustion efficeincy we will be keeping the furnance outlet at a fixed temperature of 1700 K. 

to do this a new object will be created by name E and it is set to temperature 1700k and pressure at one atm and the components of this object are CO2 , H2O and N2 

now we will be calculating the effciency by first calcualting the total enthaly of combustion and then we willbe dividing the it by the Lower Heating Value.

`Q sf"(enthalpy-of-combustion)" = sf"Enthalpy of reactants "- sf"Enthalpy of Products"`

formula for calculation of enthalpy of combustion:

`Q_(combustion) = (m_A .h_A + m_B.h_B ) - (m_A+m_B) h_E`

formula for calculation of combustion efficiency:

`eta_(combustion) = Q_(combustion)/(m_B*LHV)`

Now the prehaeting temperature is set ina range form 298 to 600 and using a for loop  the AFT and efficiency can be calculates for each value of preheating temperature .

Lastly the fuel saving is calculated using the formula 

`% sf"saving" = (1 - eta_(298)/(eta_(T-preheating)))*100` 

CODE -

Following is the code used for the analysis for the effect of change of preheating temperature on AFT and efficiency an also fuel saving.

"""
	recopurator challenge

	chemical equation of fuel
	CH4 + 2 (O2 + 3.76 N2) ==> CO2 + 2 H2O +  3.76*2 N2 
"""
import cantera as ct
import matplotlib.pyplot as plt
# creating gas object as instance of Solutions class
gas = ct.Solution("gri30.cti")

T_aft = []
Eta_combustion = []

T_a = range(298,600)

for i in T_a:

	# creating object A as instance of Quantity class under the gas object
	A = ct.Quantity(gas) # A is our oxidiser
	A.TPX = i , ct.one_atm,"O2:1, N2:3.76"
	#A.TPX = 298.15, ct.one_atm, "O2:1, N2:3.76"

	# creating object B similar to A
	B = ct.Quantity(gas) # B is the fuel
	B.TPX = 298.15 ,ct.one_atm,"CH4:1"

	# applying proper molar balance
	A.moles = 9.52
	B.moles = 1

	M = A+B # M is the mixture of A and B
	M.equilibrate("HP")

	T_aft.append(M.T) # adding the temperature to the array

	# creating the plot ot observe the variation on the AFT
	plt.figure(0)
	plt.plot(i,M.T,"o",color = "blue")
	plt.xlabel("Preheating Temperature (K)")
	plt.ylabel("AFT")
	plt.title("variation of AFT due to preheating (K)")
	plt.grid("on")

	E = ct.Quantity(gas) # exhaust at 1700 K 
	E.TPX = 1700,ct.one_atm,"CO2:1,H2O:2,N2:7.52" 
	E.moles = 10.52

	# calcualting the total enthalpy of combustion
	Q_out = -((E.mass)*E.h - A.mass* A.h - B.mass*B.h)
	
	LHV = 5*1e7 #  Lower heating value [J/Kg]

	# efficiency of combustion due to preheating ( in percentage)
	eta_combustion = (Q_out/(B.mass*LHV))*100
	
	Eta_combustion.append(eta_combustion) # adding the values to the array

	# plotting to observe the effect on the efficiency
	plt.figure(1)
	plt.plot(i,eta_combustion,"*",color="red")
	plt.xlabel("Preheating Temperature (K)")
	plt.ylabel("Efficiency of combustion( in %)")
	plt.title("variation in efficiency of combustion due to preheating")
	plt.grid("on")
	

# calculation of fuel saving
percentage_saving=[]

for i in range(1,len(Eta_combustion)):
	# formula for the saving
	saving = (1-(Eta_combustion[1]/Eta_combustion[i]))*100
	
	percentage_saving.append(saving) # addign the values to the array
	
	# plotting the effcet on the fuel saving
	plt.figure(2)
	plt.plot(T_a[i],saving,"o",color="green")
	plt.xlabel("Preheating Temperature (K)")
	plt.ylabel("fuel saving (in %)")
	plt.title("fuel saving due to preheating")
	plt.grid("on")

# to get the output as array 
print("Adiabatic flame temperature = " + str(T_aft))
print("Efficiency of combustion =" + str(Eta_combustion))
print("Percentage saving = " + str(percentage_saving))

# to show the plots
plt.show()

The output for this code is in the from of arrays and plots shown below: 

Arrays:

Adiabatic flame temperature = [2224.5530026633196, 2224.9819736738623, 2225.410768751558, 2225.8393879253936, 2226.267831227001, 2226.696098690577, 2227.12419035288, 2227.5521062532184, 2227.9798464333917, 2228.40741093765, 2228.834799812801, 2229.262013108011, 2229.6890508749284, 2230.115913167598, 2230.5426000424522, 2230.969111558273, 2231.39544777616, 2231.82160875965, 2232.247594574483, 2232.673405288749, 2233.0990409727547, 2233.524501699086, 2233.94978754258, 2234.3748985802436, 2234.7998348913175, 2235.224596281952, 2235.6491833301993, 2236.073595894189, 2236.4978340609487, 2236.9218979195225, 2237.345787561025, 2237.7695030785767, 2238.1930445673174, 2238.616412124366, 2239.039605848801, 2239.462625841689, 2239.885472205977, 2240.3081450465706, 2240.7306444702494, 2241.152970585696, 2241.575123503456, 2241.9971033359075, 2242.4189101972725, 2242.840544203584, 2243.2620054726594, 2243.6832941241423, 2244.1044102793894, 2244.525354061534, 2244.9461255954257, 2245.3667250076455, 2245.787152426495, 2246.2074079819045, 2246.62749180551, 2247.0474040306067, 2247.4671447921246, 2247.8867142265967, 2248.306112472177, 2248.7253396686106, 2249.144395957225, 2249.5632814808982, 2249.9819963840614, 2250.4005408126754, 2250.818914914227, 2251.2371188376806, 2251.6551527335305, 2252.0730167536926, 2252.4907110515846, 2252.9082357820507, 2253.3255911013666, 2253.7427771672205, 2254.15979413871, 2254.576642176315, 2254.9933214418897, 2255.409832098651, 2255.8261743111593, 2256.2423482453055, 2256.658354068309, 2257.0741919486877, 2257.489862056256, 2257.9053645620897, 2258.320699638554, 2258.7358674592483, 2259.150868199024, 2259.5657020339413, 2259.9803691412894, 2260.3948696995462, 2260.809203888383, 2261.22337188864, 2261.637373882317, 2262.0512100525652, 2262.4648805836823, 2262.8783856610667, 2263.291725471242, 2263.704900201825, 2264.1179100415197, 2264.530755180102, 2264.943435808411, 2265.3559521183406, 2265.768304302808, 2266.1804925557567, 2266.592517072159, 2267.0043780479687, 2267.4160756801434, 2267.827610166602, 2268.2389817062444, 2268.6501904989177, 2269.0612367454073, 2269.4721206474283, 2269.8828424076223, 2270.2934022295394, 2270.7038003176103, 2271.114036877163, 2271.5241121143963, 2271.9340262363708, 2272.343779450998, 2272.7533719670223, 2273.162803994031, 2273.572075742377, 2273.9811874237394, 2274.390139248861, 2274.798931431782, 2275.207564185732, 2275.6160377251867, 2276.024352265414, 2276.432508022494, 2276.8405052133044, 2277.2483440554897, 2277.656024767481, 2278.063547568456, 2278.4709126783646, 2278.8781203178837, 2279.28517070843, 2279.6920640721473, 2280.098800631878, 2280.5053806111873, 2280.911804234313, 2281.318071463097, 2281.7241829851396, 2282.1301388166517, 2282.5359391833235, 2282.9415843114148, 2283.347074427754, 2283.7524097597297, 2284.157590535275, 2284.5626169828643, 2284.9674893314987, 2285.372207810701, 2285.7767726504876, 2286.1811840814034, 2286.5854423344554, 2286.9895476411434, 2287.393500233439, 2287.7973003437737, 2288.200948205024, 2288.6044440505198, 2289.0077881140223, 2289.4109806297197, 2289.8140218322005, 2290.21691195648, 2290.6196512379547, 2291.0222399124214, 2291.4246782160435, 2291.8269663853607, 2292.22910465728, 2292.631093269048, 2293.032932458267, 2293.434622462863, 2293.8361635210945, 2294.237555871533, 2294.63879975306, 2295.039895404864, 2295.4408430664107, 2295.8416429774597, 2296.242295378033, 2296.6428005084304, 2297.0431586092036, 2297.4433699211536, 2297.8434346853132, 2298.243353142963, 2298.643125535597, 2299.0427521049187, 2299.442233092858, 2299.841568741518, 2300.240759293218, 2300.6398049904356, 2301.038706075848, 2301.437462792272, 2301.8360753827087, 2302.234544090287, 2302.6328691582917, 2303.0310508301454, 2303.429089349379, 2303.8269849596636, 2304.2247379047644, 2304.62234842856, 2305.019816775023, 2305.417143188208, 2305.814327912258, 2306.21137119138, 2306.6082732698524, 2307.005034392006, 2307.401654802231, 2307.798134744942, 2308.1944744646075, 2308.5906742057127, 2308.9867342127627, 2309.38265473028, 2309.7784360027913, 2310.174078274817, 2310.569581790871, 2310.9649467954555, 2311.3601735330367, 2311.755262248064, 2312.1502131849415, 2312.545026588026, 2312.93970270163, 2313.334241769998, 2313.7286440373096, 2314.1229097476803, 2314.51703914514, 2314.911032473623, 2315.304889976982, 2315.6986118989644, 2316.0921984832075, 2316.485649973237, 2316.8789666124585, 2317.2721486441474, 2317.6651963114455, 2318.0581098573525, 2318.450889524722, 2318.8435355562497, 2319.2360481944747, 2319.628427681764, 2320.02067426023, 2320.412788172026, 2320.804769658948, 2321.196618962618, 2321.5883363245352, 2321.979921986069, 2322.3713761884483, 2322.762699172772, 2323.153891179985, 2323.544952450878, 2323.9358832260864, 2324.3266837460815, 2324.717354251161, 2325.107894981443, 2325.498306176876, 2325.888588077201, 2326.2787409219836, 2326.6687649505698, 2327.058660402121, 2327.4484272229656, 2327.8380661631645, 2328.227577229278, 2328.616960658081, 2329.006216686036, 2329.395345549275, 2329.7843474836136, 2330.1732227245266, 2330.56197150715, 2330.950594066277, 2331.3390906363493, 2331.7274614514517, 2332.115706745311, 2332.5038267512778, 2332.8918217023415, 2333.2796918310996, 2333.667437369826, 2334.055058550201, 2334.442555603808, 2334.829928761631, 2335.2171782543, 2335.60430431203, 2335.991307164623, 2336.3781870414487, 2336.764944171467, 2337.151578783183, 2337.538091104682, 2337.9244813635983, 2338.3107497871147, 2338.696896601966, 2339.0829220344217, 2339.4688263102885, 2339.8546096549094, 2340.240272293147, 2340.6258144493845, 2341.011236347521, 2341.396538210966, 2341.781720262636, 2342.166782724944, 2342.5517258198006, 2342.936549768604, 2343.3212547922467, 2343.7058411110816, 2344.0903089449625, 2344.4746585131975, 2344.85889003456, 2345.243003727292, 2345.626999809088, 2346.0108784970944, 2346.3946400079076]
Efficiency of combustion =[33.873275390443794, 33.907855024933525, 33.942438250409666, 33.977025075596735, 34.01161550927396, 34.046209560274804, 34.08080723748684, 34.115408549851374, 34.15001350636312, 34.184622116069995, 34.219234388072714, 34.2538503315246, 34.288469955631214, 34.32309326965008, 34.357720282890405, 34.39235100471274, 34.42698544452879, 34.46162361180093, 34.49626551604214, 34.5309111668155, 34.565560573734, 34.600213746460284, 34.63487069470624, 34.66953142823279, 34.70419595684954, 34.73886429041455, 34.77353643883396, 34.80821241206177, 34.84289222009947, 34.87757587299581, 34.91226338084645, 34.94695475379371, 34.98165000202624, 35.016349135778746, 35.051052165331676, 35.08575910101093, 35.12046995318755, 35.15518473227752, 35.18990344874129, 35.22462611308364, 35.25935273585331, 35.29408332764271, 35.32881789908764, 35.36355646086701, 35.398299023702485, 35.43304559835823, 35.467796195640624, 35.50255082639794, 35.537309501520085, 35.57207223193822, 35.606839028624584, 35.64160990259208, 35.67638486489407, 35.711163926624046, 35.745947098915295, 35.78073439294069, 35.81552581991228, 35.85032139108112, 35.88512111773687, 35.91992501120758, 35.954733082859306, 35.989545344095895, 36.02436180635865, 36.059182481126065, 36.09400737991345, 36.12883651427274, 36.163669895792125, 36.198507536095796, 36.233349446843626, 36.26819563973088, 36.30304612648788, 36.337900918879804, 36.37276002870632, 36.40762346780129, 36.442491248032475, 36.47736338130129, 36.51223987954243, 36.54712075472366, 36.582006018845405, 36.61689568394061, 36.651789762074266, 36.68668826534327, 36.72159120587603, 36.75649859583223, 36.791410447402434, 36.82632677280797, 36.861247584300436, 36.89617289416155, 36.93110271470276, 36.966037058265, 37.00097593721839, 37.03591936396193, 37.07086735092317, 37.10581991055799, 37.14077705535026, 37.175738797811505, 37.21070515048069, 37.24567612592388, 37.28065173673392, 37.3156319955302, 37.350616914958316, 37.38560650768977, 37.42060078642171, 37.455599763876585, 37.49060345280192, 37.52561186596993, 37.56062501617728, 37.595642916244806, 37.63066557901718, 37.665693017362614, 37.7007252441726, 37.73576227236155, 37.77080411486657, 37.805850784647134, 37.840902294684795, 37.87595865798286, 37.91101988756614, 37.946085996480605, 37.981156997793136, 38.0162329045912, 38.05131372998256, 38.08639948709497, 38.1214901890759, 38.15658584909224, 38.19168648032997, 38.226792095993886, 38.261902709307336, 38.29701833351188, 38.33213898186695, 38.36726466764971, 38.40239540415457, 38.43753120469304, 38.47267208259338, 38.50781805120024, 38.54296912387447, 38.578125313992764, 38.6132866349474, 38.64845310014587, 38.68362472301067, 38.71880151697897, 38.75398349550232, 38.78917067204633, 38.82436306009041, 38.859560673127454, 38.89476352466355, 38.92997162821771, 38.96518499732149, 39.00040364551878, 39.03562758636552, 39.070856833429296, 39.10609140028915, 39.14133130053523, 39.17657654776854, 39.21182715560057, 39.247083137653064, 39.282344507557696, 39.317611278955816, 39.35288346549805, 39.38816108084416, 39.4234441386626, 39.45873265263028, 39.49402663643231, 39.529326103761655, 39.56463106831881, 39.5999415438116, 39.6352575439548, 39.67057908246984, 39.70590617308461, 39.74123882953302, 39.77657706555478, 39.811920894895145, 39.847270331304536, 39.88262538853829, 39.917986080356336, 39.95335242052295, 39.98872442280638, 40.02410210097865, 40.05948546881516, 40.0948745400945, 40.130269328598025, 40.165669848109665, 40.2010761124156, 40.23648813530393, 40.27190593056444, 40.307329511988215, 40.34275889336745, 40.37819408849509, 40.413635111164545, 40.44908197516936, 40.484534694303015, 40.519993282358506, 40.55545775312818, 40.590928120403305, 40.62640439797387, 40.661886599628275, 40.69737473915297, 40.732868830332265, 40.76836888694793, 40.80387492277897, 40.839386951601284, 40.87490498718743, 40.91042904330624, 40.94595913372261, 40.981495272197144, 41.01703747248588, 41.05258574834003, 41.08814011350558, 41.123700581723135, 41.15926716672751, 41.19483988224747, 41.23041874200549, 41.26600375971734, 41.30159494909189, 41.33719232383078, 41.37279589762813, 41.40840568417023, 41.44402169713525, 41.479643950192965, 41.51527245700441, 41.55090723122164, 41.5865482864874, 41.62219563643485, 41.65784929468723, 41.69350927485763, 41.72917559054861, 41.76484825535197, 41.800527282848456, 41.83621268660742, 41.871904480186515, 41.90760267713149, 41.94330729097581, 41.979018335240326, 42.01473582343314, 42.05045976904913, 42.08619018556974, 42.1219270864627, 42.15767048518168, 42.19342039516603, 42.22917682984046, 42.26493980261476, 42.300709326883506, 42.33648541602577, 42.37226808340475, 42.40805734236762, 42.44385320624509, 42.47965568835119, 42.51546480198296, 42.55128056042013, 42.587102976924854, 42.62293206474139, 42.658767837095866, 42.69461030719582, 42.73045948823015, 42.7663153933686, 42.8021780357616, 42.83804742853988, 42.87392358481419, 42.90980651767512, 42.945696240192646, 42.98159276541592, 43.01749610637292, 43.05340627607022, 43.089323287492675, 43.12524715360309, 43.16117788734193, 43.19711550162707, 43.233060009353466, 43.26901142339285, 43.30496975659343, 43.340935021779664, 43.37690723175188, 43.41288639928595, 43.44887253713316, 43.484865658019764, 43.52086577464669, 43.55687289968936, 43.592887045797255, 43.628908225593726, 43.66493645167564, 43.70097173661313, 43.7370140929492, 43.77306353319957, 43.80912006985226, 43.845183715367384, 43.88125448217677, 43.91733238268375, 43.95341742926279, 43.9895096342592, 44.02560900998894, 44.06171556873817, 44.09782932276309, 44.13395028428953, 44.17007846551275, 44.20621387859707, 44.24235653567564, 44.278506448850095, 44.31466363019027, 44.35082809173393, 44.38699984548641, 44.423178903420386, 44.45936527747558, 44.4955589795584]
Percentage saving = [0.0, 0.1018878644515886, 0.20357889046881406, 0.305073671999323, 0.4063728007558054, 0.5074768662259754, 0.6083864556819196, 0.7091021541894227, 0.8096245446175709, 0.9099542076479672, 1.0100917217841898, 1.1100376633608855, 1.2097926065531062, 1.3093571233854684, 1.4087317837411573, 1.5079171553713966, 1.60691380390382, 1.7057222928522076, 1.8043431836248125, 1.9027770355336204, 2.0010244058032423, 2.0990858495794296, 2.196961919938145, 2.2946531678940674, 2.392160142409494, 2.4894833904027913, 2.5866234567571533, 2.6835808843290065, 2.7803562139566584, 2.8769499844686686, 2.9733627326924306, 3.0695949934623434, 3.1656472996283713, 3.261520182064226, 3.3572141696756486, 3.4527297894086706, 3.5480675662579175, 3.6432280232744474, 3.738211681574155, 3.8330190603457215, 3.927650676858563, 4.022107046471001, 4.116388682638162, 4.2104960969197025, 4.304429798987897, 4.39819029663544, 4.491778095783139, 4.585193700487822, 4.678437612949882, 4.7715103335211335, 4.864412360712322, 4.957144191200813, 5.04970631983822, 5.142099239657705, 5.234323441881816, 5.326379415929594, 5.418267649424314, 5.5099886282006905, 5.601542836312323, 5.692930756038872, 5.784152867893544, 5.875209650630198, 5.9661015812507046, 6.056829135011843, 6.147392785432803, 6.237793004302028, 6.328030261684459, 6.418105025928478, 6.508017763672969, 6.597768939854176, 6.687359017712879, 6.776788458801109, 6.866057722989094, 6.955167268472062, 7.044117551777118, 7.132909027769951, 7.221542149661708, 7.310017369015465, 7.398335135753231, 7.486495898162248, 7.574500102901959, 7.6623481950103045, 7.7500406179105035, 7.837577813417306, 7.924960221743859, 8.012188281507838, 8.099262429738063, 8.186183101880795, 8.272950731806173, 8.359565751814591, 8.446028592642929, 8.532339683470823, 8.618499451927008, 8.704508324095562, 8.790366724521848, 8.876075076219026, 8.961633800673985, 9.047043317853431, 9.132304046210093, 9.217416402688706, 9.30238080273197, 9.387197660286638, 9.471867387809452, 9.556390396273107, 9.640767095172043, 9.724997892528464, 9.809083194898138, 9.893023407376278, 9.976818933603193, 10.060470175770265, 10.143977534625447, 10.227341409479262, 10.31056219821027, 10.393640297270911, 10.476576101692958, 10.559370005093305, 10.64202239967942, 10.72453367625501, 10.80690422422551, 10.889134431603587, 10.971224685014624, 11.053175369702195, 11.134986869533536, 11.216659567004895, 11.298193843246862, 11.379590078029956, 11.460848649769705, 11.541969935531993, 11.622954311038603, 11.703802150672093, 11.784513827481359, 11.865089713186737, 11.945530178185049, 12.02583559155499, 12.106006321062146, 12.186042733164214, 12.265945193015904, 12.345714064474189, 12.425349710103372, 12.504852491179964, 12.584222767697783, 12.663460898372914, 12.742567240648661, 12.821542150700516, 12.900385983441065, 12.979099092524793, 13.05768183035305, 13.136134548078948, 13.214457595611961, 13.292651321622984, 13.370716073548927, 13.448652197597688, 13.526460038752575, 13.604139940777316, 13.681692246220567, 13.759117296420765, 13.83641543151053, 13.913586990421589, 13.990632310889184, 14.067551729456628, 14.144345581480088, 14.22101420113303, 14.297557921410576, 14.373977074134336, 14.450271989956642, 14.526442998365063, 14.602490427687053, 14.678414605094082, 14.754215856606168, 14.829894507096409, 14.905450880295124, 14.980885298794366, 15.056198084052141, 15.131389556396812, 15.206460035031299, 15.281409838037508, 15.356239282380335, 15.430948683912238, 15.505538357377091, 15.58000861641463, 15.654359773564597, 15.728592140270791, 15.802706026885371, 15.876701742672772, 15.950579595814052, 16.024339893410822, 16.097982941489352, 16.171509045004594, 16.244918507844332, 16.318211632833012, 16.39138872173599, 16.464450075263215, 16.537395993073446, 16.610226773778113, 16.68294271494514, 16.75554411310308, 16.8280312637448, 16.900404461331455, 16.972663999296344, 17.044810170048784, 17.116843264977867, 17.188763574456324, 17.26057138784428, 17.33226699349307, 17.403850678749034, 17.47532272995709, 17.546683432464715, 17.61793307062549, 17.68907192780279, 17.760100286373635, 17.831018427732094, 17.901826632293126, 17.97252517949619, 18.04311434780883, 18.11359441473026, 18.183965656794953, 18.25422834957632, 18.32438276769003, 18.394429184797858, 18.46436787361092, 18.534199105893446, 18.603923152465985, 18.67354028320921, 18.74305076706706, 18.812454872050466, 18.88175286524063, 18.9509450127925, 19.020031579938102, 19.08901283099007, 19.157889029344922, 19.226660437486366, 19.295327316988896, 19.363889928520816, 19.432348531847754, 19.500703385835926, 19.568954748455436, 19.637102876783498, 19.70514802700779, 19.7730904544296, 19.840930413467184, 19.908668157658948, 19.976303939666472, 20.043838011278105, 20.111270623411727, 20.178602026118185, 20.24583246858439, 20.312962199136376, 20.37999146524252, 20.44692051351663, 20.51374958972113, 20.580478938769854, 20.647108804731573, 20.713639430832707, 20.780071059460546, 20.84640393216619, 20.912638289667573, 20.978774371852673, 21.04481241778229, 21.1107526656931, 21.17659535300063, 21.242340716302255, 21.307988991380167, 21.37354041320424, 21.43899521593493, 21.504353632926374, 21.56961589672911, 21.63478223909301, 21.699852890970185, 21.764828082517905, 21.82970804310136, 21.89449300129642, 21.959183184892773, 22.023778820896467, 22.088280135532766, 22.15268735424909, 22.21700070171758, 22.281220401838077, 22.345346677740764, 22.409379751788972, 22.47331984558184, 22.53716717995715, 22.60092197499398, 22.664584450015447, 22.72815482359133, 22.79163331354088, 22.855020136935355, 22.91831551010072, 22.98151964862043, 23.04463276733787, 23.107655080359134, 23.17058680105555, 23.233428142066348, 23.296179315301213, 23.35884053194296, 23.421412002449994, 23.483893936558943, 23.54628654328724, 23.60859003093555, 23.670804607090435, 23.73293047862687, 23.79496785171066]

Plots :

From the above we can observe that as the preheating temperature increases the AFT value increases, this is due to the energy needed to increasing the temperature of incoming air from STP upto preheating temperature is now saved and not this saved energy can be used to increases temperature upto another higher level.

also the efficiency of combustion and the fuel saving increases due to preheating because with increase in the reactant temperatur the enthalpy of the combustion increases, resulting into increased efficiency.

Here the furnace exhaust temperature is kept constant at about 1700 K it can be varied but then the result will not be able to be compared effectively so it is good if the exahust temperature is kept constant the value may be change to another according to the application of the furnance. Constant value of the furnance will help to compare the efficicncy effectively as now only the preheating temperature varies which will affect in the change of enthalpy of combuation but the Lower heating value for the exhaust gas will be constant and help to get results easily.

CONCLUSION - 

1. As the preheating temperature increase the Adiabatic Flame temperature increases , this is due to the more energy is saved because the incoming air is already heated.
2. As the preheating temperature increases the efficiency of combustion increases form 34 % to 44 % at 600 K of preheating temperature.
3. AS the preheating temperature increases the fuel saving increases upto 20 percent when the preheating temperature is 600K