Week 4.2 - Combustion Efficiency Calculation after Preheating

A recuperator is a heat exchanger in which energy from a steady flow of hot combustion products, i.e., flue gases, is transferred to the air supplied to the combustion process. A general flow diagram is shown in the figure below.

Fig. Schematic of the furnace with air preheated by recuperator

A wide variety of recuperators is used in practice, many of which employ radiation heat transfer from the flue gases, as well as convection. An example of a recuperator for an indirect-fired application is illustrated in the figure below.

Fig. Radiant-tube burner with coupled recuperator for indirect firing

1. What is the effect of preheating on the adiabatic flame temperature?
   1. Change pre-heating from 298 to 600K
   2. Explain your results

1.

import cantera as ct
import matplotlib.pyplot as plt

gas = ct.Solution('gri30.cti')


B = ct.Quantity(gas)
B.TPX = 298.15,ct.one_atm,'CH4:1'
B.moles=1
T_pre = []
AFT = []

for T in range(298,600):
	A = ct.Quantity(gas)
	A.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
	A.moles=9.52
	T_pre.append(T)

	M=A+B
	M.equilibrate('HP')
	AFT.append(M.T)

	if (T%10==0):
		plt.plot(T_pre,AFT,'-',color='red')
plt.title('AFT Vs Preheated Inlet Air')
plt.xlabel('Preheated Air (K)')
plt.ylabel('Adaibatic Flame Temperature(K)')
plt.show()

Output:

From the Ablove plot it can be concluded that with the increase in temperature of inlet air the Adiabatic flame temperature also gets increased and which is treated as a big advantage.

2. Does preheating help with fuel saving? If yes, how does combustion efficiency go up as a function of pre-heating temperature? Assume that the furnace exit temperature is 1700K (For this case assume that the combustion products are CO2, H20, and N2).

1. Write the formula for combustion efficiency
2. Plot the effect of pre-heat temeprature on combustion efficiency
3. Is it right or wrong to assume a fixed furnace exit temperature? Explain your answer.

Combustion Efficiency:

`(m_(fuel)*H_(fuel)+m_(air)*H_(air))-Q_(out)-m_(exhaust)*H_(exhaust)=0`

`Q_(out)=(m_(fuel)*H_(fuel)+m_(air)*H_(air))-m_(exhaust)*H_(exhaust)`

also,

`m_(fuel)+m_(air)=m_(exhaust)`

Rearranging we get:

`eta_(combustion)=(Q_(out)/((m_(fuel)*LHV)))*100`

import cantera as ct
import matplotlib.pyplot as plt

gas = ct.Solution('gri30.cti')


B = ct.Quantity(gas)
B.TPX = 298.15,ct.one_atm,'CH4:1'
B.moles=1
T_pre = []
AFT = []

# In the Q calculation we have to calculate the product enthaly and mass of products. So introducing the product object for those calculations.
P = ct.Quantity(gas)
P.TPX = 1700,101325,{'CO2':0.095,'H2O':0.1901,'N2':0.7148}
P.moles = 10.92

h_b = B.h
m_b = B.mass
eff=[]

for T in range(298,600):
	A = ct.Quantity(gas)
	A.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
	A.moles=9.52
	T_pre.append(T)
	h_a = A.h
	m_a = A.mass

	#  Substituted the enthalpy of products and mass of the prodcuts in the Q equation.
	h_p = P.h
	m_p = P.mass
	
	LHV = 50000000

	Q = ((h_a*m_a)+(h_b*m_b)-(h_p*m_p))
	efficiency = Q/(m_b*LHV)
	eff.append(efficiency)
	print(efficiency)

plt.plot(T_pre,eff)
plt.title('AFT Vs Efficiency')
plt.xlabel('Efficiency')
plt.ylabel('Adaibatic Flame Temperature(K)')
plt.show()
plt.show()

Output:

Fuel saving = 1- (efficiency with no preheat/ efficiency with preheat)

At 298 K, efficiency=0.33

At 600 K, efficiency=0.46

fuel saving = 0.2826%

It can be concluded-

• With increase in Adiabatic flame temperature the combustion efficiency also increases.
• There is also fuel savings
• By keeping the exit temperature at constant value we get a control over the process and can get the desired results.