Question 14.14: Equilibrium Flame Temperature Methane and air enter an adiab...
Equilibrium Flame Temperature
Methane and air enter an adiabatic combustion chamber at 1 atm, 298 K. Do a parametric study of how the adiabatic flame temperature T_{ af } depends on the equivalence ratio Φ. Vary Φ over a range 0.5 through 1.5. Neglect pressure loss and change in ke or pe. Use TESTcalcs with (a) the PG mixture model (complete combustion), (b) IG mixture model (complete combustion), and (c) IGE mixture model (equilibrium combustion) with the following common species in the combustion products: CO _{2}, CO , H _{2} O , OH , O _{2}, N _{2}, NO , NO _{2} .
TEST Analysis
The h-T diagram of Figure 14.34 graphically predicts T_{ eql }<T_{ af }^{ IG }<T_{ af }^{ PG } . To verify this numerically, launch the PG open-steady, non-premixed combustion TESTcalc. On separate tabs, open the corresponding IG combustion TESTcalc and the open-steady equilibrium TESTcalc. In the reaction panel of the PG combustion TESTcalc, select Methane in the fuel block and Theoretical Air from the action menu. The balanced reaction is displayed. In the state panel, evaluate State-1 and State-2 as the fuel and oxidizer state from the known pressure and temperature. Evaluate State-3 for the products partially by entering p1 only. In the device panel, import the fuel, oxidizer, and products’ states, enter Qdot=Wdot_ext=0, and click Super-Calculate. Obtain the adiabatic flame temperature for the theoretical reaction T3 from State-3. Alternatively, you can use the energy equation to enter j3 as =(mdot1*j1+mdot2*j2)/(mdot1+mdot2), which will produce a Qdot of 0 in the I/O panel.
The Super-Calculate operation generates the TEST-code in the I/O panel. Copy the TEST code and switch to the IG TESTcalc tab in your browser. Set up the reaction, paste the TEST code onto the I/O panel, and click the Load button. All the states are updated and the adiabatic flame temperature can be picked up as T3 in State-3. In the reaction panel of the equilibrium TESTcalc, set up the complete reaction as already described. In the composition panel, with the reactants already populated, select the eight species in the products block. In the state panel, enter p1 and T1, select the Reactants radio button, and calculate the state. Select State-2, enter p2=p1 and h2=h1, select the Products radio button, and Calculate. The adiabatic flame temperature is calculated as T2 along with the equilibrium composition of the products mixture.
Copy the temperatures from the three different models (PG, IG, and IGE) into a spreadsheet. Now enter an equivalence ratio (phi), say, 0.8 in the reaction panel of the PG combustion TESTcalc and select Excess/Deficient Air from the action menu. Super-Calculate to update T3. Repeat the same procedure with the IG TESTcalc and the equilibrium TESTcalc. The results are compiled in a spreadsheet and plotted in Figure 14.35.
For equilibrium computations, you can also use the combustion Interactive located in the TEST.Interactives module. Once the Interactive is launched, go to the Known Heat Transfer tab and select the fuel and the desired products. On the Parametric Study box, enter the lower and upper limits of the equivalence ratio Φ, and the number of steps. Click Analyze and the equilibrium temperature variation will be plotted in real time as the computations are performed in the Graphical Results tab (you have to select View Results by Run).
Discussion
The diabatic flame temperature, predicted by the PG model, is consistently much higher than other models. For the theoretical mixture, the predictions from the three models are 2792 K, 2329 K, and 2231 K, respectively. The equilibrium flame temperature is the smallest of the three as can be expected from a graphical interpretation (Fig. 14.34). It is also closest to the actual flame temperature. As the equivalence ratio is increased (rich burning), incomplete combustion becomes increasingly more important, which is captured by the IGE model. For lean combustion (Φ < 1), the flame temperature rapidly decreases (Fig. 14.35), and the discrepancy between the IG and IGE models diminishes, confirming that equilibrium computation assumes important role only at high temperatures. If pure oxygen is used as the oxidizer, a much higher flame temperature will result and the discrepancy between the results of complete combustion and equilibrium combustion will be much larger.
