UNIT II GAS POWER CYCLES AIR STANDARD CYCLES Air standard cycles are used for comparison of thermal efficiencies of I.C engines. Engines working with air standard cycles are known as air standard engines. Air is used, as the working fluid and the efficiency calculated to these engines are known as air standard efficiencies. ASSUMPTIONS The assumptions made are, (i) Air is the working fluid, assumed to be a perfect gas. (ii) Effect of calorific values of fuels is neglected by using hot and cold body contacts with the engine cylinder head for addition and rejection of heat respectively. (iii) Frictionless. (iv)no heat is either gained or lost during the cycle except during the contact of hot body and cold body with the cylinder head. IMPORTANT TERMINOLOGIES USED IN AIR STANDARD CYCLES (i) Bore It is diameter of the cylinder measured internally and is denoted by D. (ii) Stroke Stroke is defined as the displacement of the piston from its Top Dead Centre to the Bottom Dead Centre and is denoted by L (iii) Clearance volume It is the minimum volume of a gas inside the cylinder when the piston is at Top Dead Centre (T.D.C) and is denoted by V c (iv) Swept or stroke volume It is the volume of a cylinder when the piston is moving from T.D.C to B.D.C and is denoted by (v) Cylinder volume It is the volume of a gas inside the cylinder when the piston is at Bottom Dead Centre (B.D.C) and is denoted by V. (vi) Compression ratio It is defined as the ratio of cylinder volume to the clearance volume and is denoted by γ. (vii) Air standard efficiency It is defined as the ratio of work done by the engine to the heat supplied. It is also known as ideal efficiency of the cycle. It is denoted by η
(viii) Mean effective pressure It is defined as the average pressure required for developing same power as that of the same engine operating under different pressures under same operating conditions. It can be calculated from P-V diagram. It is also defined as the ratio of work output to the stroke volume. OTTO CYCLE / CONSTANT VOLUME CYCLE Otto cycle was invented by German scientist Nichloas Otto in 1876. In this cycle he proposed constant volume heat addition and rejection instead of isothermal heat addition and rejection used in Carnot cycle. All petrol, Spark ignition (S.I.) and gas engines are working under this cycle. Figure 1.2 P-v and T-s diagram of Otto Cycle 1-2 Adiabatic / Isentropic compression 2-3 Heat addition at constant volume 3-4 Adiabatic / Isentropic Expansion 4-1 Heat rejection at constant volume Isentropic compression process 1-2 Air is compressed isentropically from state 1 to state 2. During this process pressure, temperature of air increases and volume decreases. Constant volume heat addition process 2-3 Heat is added at constant volume from state 2 to state 3. During this process temperature, pressure increases and volume remains constant.
Isentropic expansion process 3-4 Air is expanded isentropically from state 3 to state 4. During the process pressure, temperature decreases and volume increases. Constant volume heat rejection process 4 1 Heat is rejected from the air at constant volume from state 4 to state 1. During the process pressure, temperature decreases and volume remains constant. In this cycle combustion takes place fully at constant volume process, so this cycle is also called as constant volume cycle.
From the above equation, air standard efficiency of Otto cycle increases with increase in compression ratio and vice-versa. Compression ratio is maintained 7 10 for better performance in engines operating under this cycle. If it increases more than 10 knocking will take place due to this life of the cylinder is reduced. Expression for mean effective pressure Mean effective pressure is the average pressure in Newton s per unit area which acts on the piston throughout the cycle. It is given by the breadth of rectangle whose length is equal to the swept volume. Work done = force x distance moved = pressure x area x length = P x A x L = pressure x Volume
DIESEL CYCLE / CONSTANT PRESSURE CYCLE Diesel cycle was invented by Rudolph Diesel in 1892. All Diesel, Compression Ignition (C.I.) engines are working under this cycle.
Figure 1.3 P-v and T-s diagram of Diesel Cycle 1-2 Adiabatic / Isentropic compression 2-3 Constant pressure heat addition 3-4 Adiabatic / Isentropic expansion 4-1 Constant volume heat rejection Isentropic Compression Process 1-2 Air is compressed isentropically from state 1 to state 2. During this process pressure, temperature of air increases and volume decreases. Heat addition Process 2-3 Heat is added at constant pressure from state 2 to state 3. During this process temperature, volume increases and pressure remains constant. Expansion Process 3-4 Air is expanded isentropically from state 3 to state 4. During the process pressure, temperature decreases and volume increases. Heat rejection process 4 1 Heat is rejected from the air at constant volume from state 4 to state 1. During the process pressure, temperature decreases and volume remains constant. In this cycle combustion takes place fully at constant pressure process, so this cycle is also called as constant pressure cycle. Expression for air standard efficiency
Expression for Mean Effective Pressure DUAL CYCLE / LIMITED PRESSURE CYCLE Figure 1.4 P-v and T-s diagram of Dual Cycle
1-2 Isentropic Compression 2-3 Constant Volume Heat addition 3-4 Constant Pressure Heating 4-5 Isentropic Expansion 5-1 Constant Volume Cooling Isentropic Compression Process 1-2 Air is compressed isentropically from state 1 to state 2. During this process pressure, temperature of air increases and volume decreases. Heat addition Process 2-3 Heat is added at constant volume from state 2 to state 3. During this process temperature, pressure increases and volume remains constant. Heat addition Process 3-4 Heat is added at constant pressure from state 3 to state 4. During this process temperature, volume increases and pressure remains constant. Expansion Process 4-5 Air is expanded isentropically from state 4 to state 5. During the process pressure, temperature decreases and volume increases. Heat rejection process 5-1 Heat is rejected from the air at constant volume from state 5 to state 1. During the process pressure, temperature decreases and volume remains constant. In this cycle combustion takes place partially at constant volume and partially at constant pressure, so this cycle is called as Dual cycle. Expression for air standard efficiency
Pressure ratio (rp): It is the ratio of the final pressure to the initial pressure during constant volume combustion. Expression for mean effective pressure
COMPARISON OF OTTO, DIESEL AND DUAL CYCLES The important variable factors which are used as the basis for comparison of the cycles are compression ratio, peak pressure, heat addition, heat rejection and the network. In order to compare the performance of the Otto, Diesel and Dual combustion cycles, some of the variable factors must be fixed. In this section, a comparison of these three cycles is made for the same compression ratio, same heat addition, constant maximum pressure and temperature, same heat rejection and network output. This analysis will show which cycle is more efficient for a given set of operating conditions. Case 1: Same Compression Ratio and Heat Addition The Otto cycle 1-2-3-4-1, the Diesel cycle 1-2-3'-4'-1 and the Dual cycle 1-2-2-3 -4-1 are shown in p-v and T-s diagram in Fig.4.7.1 (a) and (b) respectively for the same compression ratio and heat input. From the T-s diagram, it can be seen that Area 5-2-3-6 = Area 5-2-3'-6 = Area 5-2-2"- 3"-6" as this area represents the heat input which is the same for all cycles. All the cycles start from the same initial state point 1 and the air is compressed from state 1 to 2 as the compression ratio is same. It is seen from the T-s diagram for the same heat input, the heat rejection in Otto cycle (area 5-1-4-6) is minimum and heat rejection in Diesel cycle (5-1-4'-6') is maximum. Consequently, Otto cycle has the highest work output and efficiency. Diesel cycle has the least efficiency and Dual cycle having the efficiency between the two. One more observation can be made i.e., Otto cycle allows the working medium to expand more whereas Diesel cycle is least in this respect. The reason is heat is added before expansion in the case of Otto cycle and the last portion of heat supplied to the fluid has a relatively short expansion in case of the Diesel cycle. Case 2: Same Compression Ratio and Heat Rejection
Efficiency of Otto cycle is given by [Figs.4.7.2 (a) and (b)], Where, Qs is the heat supplied in the Otto cycle and is equal to the area under the curve 2-3 on the T-s diagram [Fig.4.7.2 (b)]. The efficiency of the Diesel cycle is given by, Where Q s is heat supplied in the Diesel cycle and is equal to the area under the curve 2-3' on the T-s diagram [Fig.4.7.2. (b)]. From the T-s diagram in Fig.4.7.2, it is clear that Qs > Q s i.e., heat supplied in the Otto cycle is more than that of the Diesel cycle. Hence, it is evident that, the efficiency of the Otto cycle is greater than the efficiency of the Diesel cycle for agiven compression ratio and heat rejection. THEORETICAL AND ACTUAL CYCLES FOUR STROKE PETROL ENGINE
Fig. 1.12 (a) and (b) shows the actual p-v diagram and theoretical p-v diagram of four stroke Petrol engine. The line 5-1 represents the suction stroke in which the charge enters into the cylinder. The suction of mixture is possible only if the pressure inside the cylinder is below atmospheric pressure. That s the reason line 5-1 lies below the atmospheric pressure line. The burnt gases can be pushed out only if the pressure of the exhaust gas is above atmospheric pressure. This is represented by the line 1-5. The area in between the process 5-1 and 1-5 in the indicator diagram gives pumping loss of the engine. The compression stroke is shown by the line 1-2 which shows that the inlet valve closes (IVC) a little beyond 1. At the end of this stroke, there is an increase in pressure inside the engine cylinder. Before the end of compression stroke, the charge is ignited (IGN) with the help of spark plug. Thus, the pressure and temperature of the cylinder increase. But the volume remains constant as shown by line 2-3. Expansion is shown by the line 3-4. The exhaust valve opens (EVO) little before 4. The burnt gases are exhausted to atmosphere. It has been found practically, that the actual pressure rise in such an engine is only half of the theoretical value. The corners are rounded off because both inlet and exhaust valves do not open and close suddenly. THEORETICAL AND ACTUAL CYCLES FOUR STROKE DIESEL ENGINE Fig. 1.13 (a) and (b) shows the actual p-v diagram and theoretical p-v diagram of four stroke Diesel engine. The line 5-1 represents the suction stroke in which the air enters into the cylinder. The suction of mixture is possible only if the pressure inside the cylinder is below atmospheric pressure. That s the reason line 5-1 lies below the atmospheric pressure line. The burnt gases can be pushed out only if the pressure of the exhaust gas is above atmospheric pressure. This is represented by the line 1-5. The air is compressed adiabatically in the cylinder during 1-2 process which takes place after inlet valve closed. Before the end of compression stroke, fuel is injected through the fuel injector (FVO). The fuel is ignited due to the temperature of highly compressed air inside the cylinder. The combustion takes place at constant pressure as shown in line 2-3. Actually, combustion at constant pressure is not possible as the fuel will not burn completely as it is introduced into the cylinder. Then the charge is expanded adiabatically is shown by the line 3-4. The exhaust valve opens (EVO) little before 4. The burnt gases are exhausted to atmosphere.
Theoretically, the compression and expansion are followed adiabatically. But in actual cycle it is not so. Because of heat and pressure losses are involved. THEORETICAL AND ACTUAL CYCLES FOR TWO STROKE PETROL ENGINE Fig. 1.14 (a) and (b) shows the actual p-v diagram and theoretical p-v diagram of two strokepetrol engine. The suction stroke is carried out from transfer ports open (TPO) and transfer port close (TPC). During half of the suction stroke, exhaust port is also opened. Now, the volume of air fuel mixture is entered into the cylinder. This happens as the piston moves from TDC to BDC. During second half of the suction stroke (i.e. BDC to TPC), the air and fuel mixture is compressed and burnt gases pushed out. A little beyond TPC, the exhaust port closes (EPC) at 1. These processes are represented in theoretical cycle as 1-5-6 and 6-5-1. Now, the air fuel mixture is compressed isentropically in the cylinder. This is shown by line 1-2. A little before the end of compression, the charge is ignited (IGN) with the help of spark plug as shown in the above diagram. Combustion of air fuel mixture increases the pressure and temperature of the products of combustion. During this process, volume remains constant. This represented by the line 2-3. The expansion process is shown by line 3-4. The end of the expansion stroke, exhaust port opens (EPO) at 4 and burnt gases are pushed out to the atmosphere. During this, the pressure falls suddenly to the atmospheric pressure. As the piston is moving towards BDC, the volume of burnt gases increases from 4 to 5. At 5, transfer port opens (TPO) and the suction starts. THEORETICAL AND ACTUAL CYCLES FOR TWO STROKE DIESEL ENGINE Fig. 1.15 (a) and (b) shows the actual p-v diagram and theoretical p-v diagram of two stroke Diesel engine
The suction stroke is carried out from transfer ports open (TPO) and transfer port close (TPC). During half of the suction stroke, exhaust port is also opened. Now, the volume of air is entered into the cylinder. This happens as the piston moves from TDC to BDC. During second half of the suction stroke (i.e. BDC to TPC), the air is compressed and burnt gases pushed out. A little beyond TPC, the exhaust port closes (EPC) at 1. These processes are represented in theoretical cycle as 1-5-6 and 6-5-1. Now, the air is compressed isentropically in the cylinder. This is shown by line 1-2. A little before the end of compression, the fuel is admitted into the cylinder by means of fuel injector (INJ).Combustion of fuel increases the pressure and temperature of the products of combustion. During this process, pressure remains constant. This represented by the line 2-3. The expansion process is shown by line 3-4. The end of the expansion stroke, exhaust port opens (EPO) at 4 and burnt gases are pushed out to the atmosphere. During this, the pressure falls suddenly to the atmospheric pressure. As the piston is moving towards BDC, the volume of burnt gases increases from 4 to 5. At 5, transfer port opens (TPO) and the suction starts. APPLICATION OF IC ENGINES Internal combustion engines are most commonly used for mobile propulsion in vehicles and portable machinery. In mobile equipment, internal combustion is advantageous since it can provide high power-to-weight ratios together with excellent fuel energy density. Generally using fossil fuel (mainly petroleum), these engines have appeared in transport in almost all vehicles (automobiles, trucks, motorcycles, boats, and in a wide variety of aircraft and locomotives). Where very high power-to-weight ratios are required, internal combustion engines appear in the form of gas turbines. These applications include jet aircraft, helicopters, large ships and electric generators.