FUEL - AIR CYCLES
INTRODUCTION The basic problem in the air-cycle analysis is that it is based on highly simplified approximations. This is why the results obtained from such analysis are much greater than the actual performance. For example, an engine with CR=7 has a thermal efficiency (based on air cycle analysis) equals to 54% while the actual value does not exceed 30%. This is mainly due to the following reasons: 1. 2. 3. 4. 5. 6.
Non-instantaneous burning of the fuel. Non-instantaneous operation of the valves. Over simplifications in using the values of the properties of the working fluids. Incomplete combustion of the fuel. Assuming constant specific heat of the working fluid. Assuming the working fluid to be only air.
Fuel-Air cycle is defined as the theoretical cycle that is based on the actual properties of the cylinder gases. The Fuel-Air cycle takes into account the following: 1.
The actual composition of the cylinder gases (air + fuel + water vapor + residual gases). 2. The variation of the specific heat of these gases with temperature. 3. The incomplete mixing (in-homogeneous) of fuel and air at higher temperatures o (@ above 1600 K). 4. The variations in the number of molecules present in the cylinder as the temperature and pressure change. Besides these, the fuel-air cycle analysis are based on the following assumptions: 1. 2. 3. 4. 5.
No change in the fuel or air chemical composition before combustion. The process is frictionless and adiabatic. Charge is in chemical equilibrium after combustion. Combustion process is instantaneous. Fuel is completely vaporized and perfectly mixed with the air (for SI only).
The basic advantage of the fuel-air cycle analysis is that while the air cycle studies the effect of CR only on other parameters, with fuel-air cycle we can also study the effect of CR, F/A, inlet pressure and temperature, variable specific heat and other factors on engine performance.
VARIABLE SPECIFIC HEAT Specific Heat is defined as the amount of heat required to raise the temperature of water by 1 degree. Generally, all gases, except monatomic gases, show an increase in specific heat at high temperatures as shown below. 3.0 Specific 2.5 Heat 2.0 (kJ/kg-k) 1.5
H2O
1.0
CO2
0.5 0.0 0
500
1000
1500
2000 2500 3000 3500 4000 Temperature (K) This increase, however, does not follow any particular law. It can be divided into two main regimes : For 300 K < T <1500 K CP = a + bT
CV = c + bT
For T >1500 K CP = a + bT + cT
2
2
CV = d + eT + fT o
o
For example : CP @ 0 C = 1.005 and @2000 C = 1.264 kJ/kg-K The basic explanation for this increase in the specific heat with temperature is that as the temperature is raised, larger fraction of the heat input will go to producing motion of the atoms within the molecules. Since temperature is the result of motion of molecules as a whole, the energy which goes into moving the atoms does not contribute to the temperature rise. Hence, more energy will be required to raise the temperature of a unit mass through one degree.
Losses due to variation of specific heat. Pressure
3 3’
2 2’
4 4’ 1 Volume
Since the difference between CP and CV is constant, the value of γ decreases as the temperature increases. With reference to the figure above the effect can be explained a s follows: During the compression stroke : the end-of-combustion pressure and temperature will be lower that with constant specific heat i.e. 2’ instead of 2. During the combustion stroke : because the temperature rise during this process decreases as CP increases and because the end-of-compression temperature (T@2’) is also lower than T@2 the end-of-combustion temperature and pressure will be lower that with constant specific heat i.e. 3’ instead of 3. During the expansion stroke : the natural adiabatic expansion process would have been represented by the line 3-4’, but due to the variable specific heat effect it will follow the path 3-4”. This is because the specific heat decreases as the temperature decreases during the expansion, however, still lower than the ideal cycle temperature T@4. Conclusion: Thus we se that the effect of variable specific heat is to lower the pressure and temperature at point 2 and 3 and hence to deliver less work than the corresponding cycle with constant specific heat.
DISSOCIATION OR CHEMICAL LOSS Dissociation is defined as the disintegration of burnt gases at high temperatures . Disintegration increases with temperatures as shown below. The general effect of dissociation can be explained as follows: as the temperature increases considerable amount of heat will be absorbed by the elements that undergoes dissociation. This heat will be liberated when these elements re-combine as the temperature falls.
Conclusion: Thus we se that the effect of dissociation is a suppression of part of the heat during the combustion process and the liberation of this heat during the expansion process. Though looks similar to that of variation of specific heat, its effect is much smaller that it. The dissociation mainly is of CO2 into CO and O2 : 2CO + O2
2CO2 + Heat
⇔ o
o
This process commences at about 1000 C and by the time it reaches 1500 C it reaches 1%. There is also a very little dissociation of H2O : 2H2 + O2
⇔
2H2O + Heat
Losses due to dissociation. Pressure
3 3’
2 4 4’ 1 Volume With reference to the figure above the effect can be explained a s follows: During the compression stroke : no significant change because the temperature is still below that required for the dissociation to commence. During the combustion stroke : because of the high temperature rise during this process dissociation increases causing the maximum cylinder temperature and pressure to drop. This is represented by the point 3’ instead of 3. During the expansion stroke : the natural adiabatic expansion process would have been represented by the line 3-4’, but due to the re-association effect it will follow the path 3-4”. This is because the re-association process liberates some of this heat hence increases the end-of-expansion temperature and pressure though still below that of ideal cycle.
Conclusion: Thus we se that the effect of dissociation is to lower the pressure and temperature at the beginning of the expansion stroke. This causes the engine to suffer a loss in power and drop in thermal efficiency and increase in specific fuel consumption. Remedy: since the burning of nearly stoichiometric mixture will produce the maximum temperature, dissociation will be maximum at mixtures within stoichiometric. As the mixture becomes lean or rich, the thermal energy produced due to combustion will be low and hence dissociation will be suppressed. This is clearly shown in the following figures.
3000 2800 2600 T C 2400 o
2200 2000 1800 -0.6 -0.4
-0.2 0.0 0.2 0.4 Degree of Richness
0.6
Chemically Correct Mixture BP with no dissociation
Brake Specific Fuel Consumption
11
12
13
14
15 16 17 18 Air – Fuel Ratio
19
20
21
22
COMPARISON OF P-V DIAGRAM BETWEEN AIR STANDARD AND FUEL AIR CYCLES FOR SI ENGINE.
Cycle A B C
P3 (bar) 127.5 100 79.4
T1 (K) 333 333 333
T2 (K) 765 740 653
T3 (K) 6310 4030 2800
T4 (K) 2260 2180 1700
MEP (bar) 21.6 19.0 14.2
η
(%) 57.0 49.4 35.5
A – is for Air-Standard Cycle with constant Specific Heat. B – is for Air-Standard Cycle with variable Specific Heat. C – Fuel-Air cycle. THERMAL EFFICIENCY & FUEL CONSUMPTION. As it was noticed that the air-standard analysis predicts no variation of thermal efficiency with mixture strength. Fuel-air analysis, however, suggests that the thermal efficiency will deteriorate as the mixture supplied is enriched. This can be explained by the increased losses due to dissociation and variable specific heat as the engine temperature is raised due to enrichment of fuel towards the chemically correct mixture. Further, enrichment beyond the chemically correct mixture will result in the supply of unusable excess fuel hence the thermal efficiency will drop rapidly. This implies that the thermal efficiency would increase as the mixture is weakened. This is true up to certain limit beyond which thermal efficiency drops again due to erratic combustion of the fuel. Thus the best thermal efficiency would be near the chemically correct ratio toward the weak side.
Correct Mixture
(14.6) Thermal Efficiency
Specific Fuel Consumption
11
12
13
14
15
16 17 18 19 Air – Fuel Ratio
20
21
22
Specific Fuel Consumption Rich Actual Curve
Weak Mixture
Fuel-Air Theory
Chemically Correct Mixture
Minimum SFC Point
Air-Standard Theory
Maximum MEP Point Mean Effective Pressure This curve is called the Combustion Loop. It is drawn for the engine running at constant engine speed and throttle opening with variable fuel supply. EFFECT OF VARIABLES ON ENGINE PARAMETERS. Since the fuel-air cycle gives us more information about the effect of CR, a/f ratio and many other parameters on the engine’s performance, let us study the effect of these two main factors on the engine’s performance.
Effect of Compression Ratio. The F/A cycle efficiency increases with CR in the same manner as that for airstandard cycle. This is because of the increased scope for expansion work. and also the increased in the end-of-compression pressure and temperature which causes the end-of-combustion pressure and temperature also to rise. 60 55 Thermal 50 Efficiency 45 (%) 40 Compression Ratio
Effect of Air/Fuel Ratio.
Thermal Efficiency (%)
Air-standard Theory Correct Mixture
Actual Curve
Weak
Fuel Air theory
Rich Mixture Strength
From the figure we see that as the mixture is made lean (lesser fuel) the thermal efficiency increases. This is because of the lesser thermal energy released which results in the lowering of the cylinder temperature and pressure hence reducing the specific heat and dissociation losses. This is valid up to certain limit beyond which it again drops down due to erratic burning of the fuel. Correct Mixture Cycle Power
Air-Standard Fuel-Air Actual Curve
Weak
Rich 10% Rich Mixture
Mixture Strength By air-standard cycle theory, engine power is maximum at chemically correct mixture. By air-fuel cycle theory, it peaks at 10% richer mixture beyond which engine power falls rapidly due to erratic, incomplete combustion as well as other losses.
Correct Mixture Peak Cycle Pressure (P3) and Temperature (T3)
Temperature CR Increasing CR Increasing Pressure Weak
Rich 10-15 % Rich Mixture
Mixture Strength For a given compression ratio, the maximum cycle temperature is reached when mixture is slightly rich (about 6% rich) and that for maximum cycle pressure is at about 10% rich. This is because at chemically correct mixture, due to the chemical equilibrium losses, there is still some oxygen present at state point 3, this will cause more fuel to combine with oxygen and burn raising the temperature of the cylinder. Further, this increment in the number of molecules in the cylinder allows for higher peak pressure as the gas law states: P*V = N*R*T. This also helps in increasing the cycle MEP. EXAMPLES 1) A petrol engine of compression ratio 6 uses a fuel of calorific value 44000 kJ/Kg. The air-fuel ratio is 15:1. The temperature and pressure of the charge at the end of o suction stroke are 60 C and 1 bar, respectively. Determine the maximum pressure in the cylinder if the index of compression is 1.32 and the specific heat of the products -5 at constant volume is expressed by the relation CV = 0.71 + 20*10 *T kJ/Kg.K where o “T” is the temperature in K. Compare this value with that for a constant specific heat CV = 0.71 kJ/Kg.K. 2) A diesel engine combustion is assumed to begin at inner dead center and to be at constant pressure. The air-fuel ratio is 28:1, the calorific value of the fuel is 42000 kJ/Kg and the specific heat of the products of combustion at constant volume is -5 expressed by the relation CV = 0.71 + 20*10 *T kJ/Kg.K where “T” is the o temperature in K and “R” for the products = 0.287 kJ/Kg.K. If the compression ratio o is 14:1, and the temperature at the end of compression is 800 K, find at what percentage of the stroke the combustion process is completed. [10.96% Stroke]
