Basic Mechanical Engineering Chapter 4: Heat Engine PDF

Basic Mechanical Engineering (102001202) Chapter – 4: Heat Engine Prepared by :Prof. Bhavik A Ardeshana Mechatronics Department G H Patel College of Engineering & Technology (A Constituent College of CVM University) Content Introduction Classification o...

Basic Mechanical Engineering (102001202) Chapter – 4: Heat Engine Prepared by :Prof. Bhavik A Ardeshana Mechatronics Department G H Patel College of Engineering & Technology (A Constituent College of CVM University) Content Introduction Classification of Heat Engine Definitions Heat engine cycles Carnot cycle, Rankine cycle, Otto cycle, Diesel cycle Numerical 11-09-2024 Chapter-4 Heat Engine 2 HEAT ENGINE Heat engine is a device which transforms the chemical energy of a fuel into thermal energy and utilizes this thermal energy to perform useful work. Thus, thermal energy is converted to mechanical energy in a heat engine. Generally source of heat is combustion chamber or furnace where combustion of fuel takes place. Heat is continuously supplied to the medium from the combustion chamber for conversion into mechanical work. In addition to the above three elements, there is one cold body, at a lower temperature than the source is known as heat sink. 11-09-2024 Chapter-4 Heat Engine 3 HEAT ENGINE Figure illustrates the basic principle of an elementary heat engine. The working fluid takes heat from heat source and flows to the converting machine E where heat energy converts into mechanical work. After this conversion it is discharged into the sink where it is cooled and comes to the original state. From the heat sink working fluid is supplied to heat source by the pump P, where it is heated again and cycle is repeated. 11-09-2024 Chapter-4 Heat Engine 4 Classification of Heat Engine Heat engine are divided into two broad classes: 1) External Combustion Engine: In this case, combustion of fuel takes place outside the cylinder as in case of steam engines where the heat of combustion is employed to generate steam which is used to move a piston in a cylinder. Other examples of external combustion engine are hot air engines, steam turbine and closed cycle gas turbine. These engines are generally used to drive locomotives, ships, generation of electric power etc. 2) Internal Combustion (IC) Engine: In this case combustion of fuel with oxygen of the air occurs within the cylinder of the engine. The internal combustion engines group includes engines employing mixture of combustible gases and air, known as gas engines, those using lighter liquid fuel or spirit known as petrol engines and those using heavier liquid fuels, known as oil compression ignition or diesel engines. 11-09-2024 Chapter-4 Heat Engine 5 Advantages of Heat Engines The advantages of internal combustion engines are: 1) Grater mechanical efficiency. 2) Lower weight and bulk to output ratio. 3) Lower first cost. 4) Higher overall efficiency. 5) Lesser requirement of water for dissipation of energy through cooling system. The advantage of external combustion engines are: 1) Use of cheaper fuels. 2) High starting torque. 3) Higher weight and bulk to output ratio. 11-09-2024 Chapter-4 Heat Engine 6 DEFINITIONS Working substance When a gas or mixture of gases or a vapour is used in engine for transferring heat, it is known as working fluid or working substance. Working fluids are able to absorb heat, store within them and give up heat when required. During the process of absorbing and giving up heat, its pressure, volume, and temperature changes accordingly. Working fluid is never destroyed or reduced in quantity during the process. Converting machines Any machine, which converts heat energy of the working fluid into mechanical work is called converting machine. Reciprocating machine It is the machine consisting of a hollow cylinder into which a piston reciprocates by the action of a working fluid. 11-09-2024 Chapter-4 Heat Engine 7 DEFINITIONS Rotary machine It is the machine consisting of a wheel, fixed on a shaft, fitted with blades or vanes rotating due to the action of the working fluid upon the blades. Jet machine It is the machine in which the fluid is discharged from the machine in the form of a jet and producing an impact which causes the motion. Cycle It is defined as a series of processes performed in a definite order or sequence so that, after different and definite number of processes, all the concerned substances are returned to their original state and condition. Direct cycle A heat engine, operating on a cycle produces or develops Mechanical energy or work is said to be working on a direct cycle. Reversed cycle If the sequence of operation or processes in direct cycle are reversed it is said to be operating on reversed cycle. 11-09-2024 Chapter-4 Heat Engine 8 Heat engine cycles Following are the various heat engine cycles which will be discussed in detail in this chapter. 1) Carnot cycle 2) Rankine cycle 3) Otto cycle 4) Diesel cycle 11-09-2024 Chapter-4 Heat Engine 9 Carnot Cycle Sadi Carnot in 1824 first proposed the concept of heat engine working on reversible cycle called Carnot cycle. According to Carnot theorem “No cycle can be more efficient than a reversible cycle operating between the same temperature limits.” Carnot cycle is useful to compare the efficiency of any cycle under consideration with the efficiency of any cycle operating between the same two temperatures. A Carnot cycle is a hypothetical cycle consisting four different processes: two reversible isothermal processes and two reversible adiabatic (isentropic) processes. Assumptions made in the working of the Carnot cycle 1) Working fluid is a perfect gas. 2) Piston cylinder arrangement is weightless and does not produce friction during motion. 3) The walls of cylinder and piston are considered as perfectly insulated. 4) Compression and expansion are reversible. 5) The transfer of heat does not change the temperature of sources or sink. 11-09-2024 Chapter-4 Heat Engine 10 Carnot Cycle Figure shows essential elements for a Carnot cycle, P-V and T-S diagrams. This cycle has the highest possible efficiency, and it consists four simple operations as below: 1) Isothermal Expansion (1 – 2) 2) Isentropic Expansion (2 – 3) 3) Isothermal Compression (3 – 4) 4) Isentropic Compression (4 – 1) 11-09-2024 Chapter-4 Heat Engine 11 Carnot Cycle 11-09-2024 Chapter-4 Heat Engine 12 Carnot Cycle Isothermal expansion (1 – 2):- The source of heat (H) is applied to the end of the cylinder and isothermal reversible expansion occurs at temperature T1. During this process 𝑄1 heat is supplied to the system. Adiabatic expansion (2 – 3):- Adiabatic cover (C) is brought in contact with the cylinder head. The cylinder becomes perfect insulator because of non-conducting walls and end. Hence no heat transfer takes place. The fluid expands adiabatically and reversibly. The temperature falls from T1 to T3. Isothermal compression (3 – 4):- Adiabatic cover is removed and sink (S) is applied to the end of the cylinder. The heat, 𝑄2 is transferred reversibly and isothermally at temperature T3 from the system to the sink (S). Adiabatic compression (4 – 1):- Adiabatic cover is brought in contact with cylinder head. This completes the cycle and system is returned to its original state at 1. During the process, the temperature of system is raised from T3 to T1. 11-09-2024 Chapter-4 Heat Engine 13 Efficiency of Carnot cycle Consider 1 kg of working substance Heat supplied during isothermal process (1-2) Heat rejected during isothermal compression (3-4) 11-09-2024 Chapter-4 Heat Engine 14 Efficiency of Carnot cycle During adiabatic expansion (2-3) and adiabatic compression (4-1), the heat transfer from or to the system is zero. Work done, 𝑉2 Let,𝑟 = ratio of expansion for process (1 – 2)= 𝑉1 𝑉4 = ratio of compression for process (3 – 4)= 𝑉3 by substituting the value of 𝑟 in above equation, we get 11-09-2024 Chapter-4 Heat Engine 15 Efficiency of Carnot cycle Thermal efficiency, Where, T1 Maximum temperature of the cycle (K) T3 Minimum temperature of cycle (K) In above equation, if temperature T3 decreases, efficiency increases and it becomes 100% if temperature T3 becomes absolute zero; which is impossible to attain. 11-09-2024 Chapter-4 Heat Engine 16 Limitations of Carnot Gas Cycle 1) The Carnot cycle is hypothetical. 2) The thermal efficiency of Carnot cycle depends upon absolute temperature of heat source T1 and heat sink T3 only, and independent of the working substance. 3) Practically it is not possible to neglect friction between piston and cylinder. It can be minimized but cannot be eliminated. 4) It is impossible to construct cylinder walls which are perfect insulator. Some amount of heat will always be transferred. Hence perfect adiabatic process cannot be achieved. 5) The isothermal and adiabatic processes take place during the same stroke. Therefore the piston has to move very slowly for isothermal process and it has to move very fast during remaining stoke for adiabatic process which is practically not possible. 6) The output obtained per cycle is very small. This work may not be able to overcome the friction of the reciprocating parts. 11-09-2024 Chapter-4 Heat Engine 17 11-09-2024 Chapter-4 Heat Engine 18  Carnot Vapour Cycle In the Carnot vapour cycle, steam or any other vapour is used as working substance in place of a perfect gas. Components and arrangement of Carnot vapour cycle is shown in figure and same is represented on P- V diagram in figure. 11-09-2024 Chapter-4 Heat Engine 19 Carnot Vapour Cycle 11-09-2024 Chapter-4 Heat Engine 20 Carnot Vapour Cycle Process 1-2: This is a isothermal heat addition in the boiler, isothermal process having 𝑇1 = 𝑇2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. This is also constant pressure process. The saturated water at point 1 is isothermally converted into dry saturated steam in a boiler. Process 2-3: This is reversible adiabatic expansion of steam in the turbine. The dry steam at point 2 expands adiabatically in a steam turbine. Turbine develops work 𝑊T. Process 3-4: This is a isothermal heat rejection in the condenser. Condenser converts steam into water at constant pressure and temperature as shown in P-V diagram. Process 4-1: This is reversible adiabatic compression process. steam and water enter into the compressor in which pressure increases from 𝑃2 to 𝑃1. Compressor consumes power 𝑊𝐶. 11-09-2024 Chapter-4 Heat Engine 21 Efficiency of Carnot Vapour Cycle Consider 1 kg of working substance, Work developed by turbine, 𝑊𝑇 = (ℎ2 − ℎ3 ) Work input during compression, 𝑊𝐶 = (ℎ1 − ℎ4 ) Net work developed, 𝑊𝑛𝑒𝑡 = 𝑊𝑇 − 𝑊𝐶 = (ℎ2 − ℎ3 ) − (ℎ1 − ℎ4 ) Heat supplied = (ℎ2 − ℎ1 ) 𝑁𝑒𝑡 𝑤𝑜𝑟𝑘 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 η= 𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 (ℎ2 − ℎ3 ) − (ℎ1 − ℎ4 ) η= (ℎ2 − ℎ1 ) (ℎ2 − ℎ1 ) − (ℎ3 − ℎ4 ) η= (ℎ2 − ℎ1 ) 11-09-2024 Chapter-4 Heat Engine 22 Efficiency of Carnot Vapour Cycle (ℎ2 − ℎ1 ) − (ℎ3 − ℎ4 ) η= (ℎ2 − ℎ1 ) (ℎ3 − ℎ4 ) η=1− (ℎ2 − ℎ1 ) But ℎ3 − ℎ4 =𝑄𝑅 , heat rejected by condenser and ℎ2 − ℎ1 =𝑄𝑠 , heat supplied by boiler. 𝑄𝑅 η=1− 𝑄𝑆 11-09-2024 Chapter-4 Heat Engine 23 Efficiency of Carnot Vapour Cycle 𝑑𝑄𝑟𝑒𝑣 Entropy is defined as ds = ‫𝑇 ׬‬ So, we can write 𝑄𝑅 = 𝑇2 (𝑆3 − 𝑆4 ) and 𝑄𝑆 = 𝑇1 (𝑆2 − 𝑆1 ) 𝑇2 (𝑆3 − 𝑆4 ) η=1− 𝑇1 (𝑆2 − 𝑆1 ) But process (1-2) and (3-4) are isentropic, 𝑆2 = 𝑆3 and 𝑆1 = 𝑆4 𝑇2 η=1− 𝑇1 Where 𝑇1 = Maximum Temperature of cycle 𝑇2 = Minimum Temperature of cycle 11-09-2024 Chapter-4 Heat Engine 24 Limitations 1) Process (4-1) is adiabatic compression of wet vapour, it is very difficult to achieve because the liquid tends to separate out from the vapour. 2) Practically, compression and expansion processes are having irreversibility. This will reduced the actual efficiency than theoretical cycle. 3) To achieve superheating of steam at constant temperature , pressure has to be reduced. It means expansion and heat addition is to be done simultaneously which is practically very difficult. 11-09-2024 Chapter-4 Heat Engine 25 Rankine Cycle It is very difficult to pump mixture of vapour and liquid as in case of Carnot vapour cycle. This difficulty is eliminated in Rankine cycle by complete condensation of vapour on condenser and then pumping the water isentropically to the boiler at the boiler pressure. The Rankine cycle is the ideal cycle for steam power plants. In a steam power plants, the heat energy of the fuel is converted into mechanical energy or power. The ideal Rankine cycle is shown schematically and on P-V, T-s & h-s diagram in Figure. The liquid, vapour and wet regions are also indicated with the help of saturation curve. The main four components of cycle are, 1) Boiler 2) Turbine 3) Condenser 4) Feed Pump 11-09-2024 Chapter-4 Heat Engine 26 Rankine Cycle b 11-09-2024 Chapter-4 Heat Engine 27 Rankine Cycle 11-09-2024 Chapter-4 Heat Engine 28 Rankine Cycle Process 4 – 1: Constant pressure heat addition in the boiler The water is heated at constant pressure 𝑃1 in the boiler until the saturation temperature is reached, (process(4-a)), Saturated water is converted into saturated steam at constant pressure (process(a-b)). During process (process(b-1)), steam is superheated in super heater. Heat supplied is given by 𝑄𝑠 = ℎ1 − ℎ4 Process 1 – 2: Isentropic expansion in the turbine High pressure and high temperature superheated, dry saturated or wet steam generated in the boiler at 𝑃1 and 𝑇1 is supplied to the steam turbine. This steam expands isentropically into steam turbine up to the condenser pressure. Steam turbine develops mechanical work, 𝑊𝑇 due to expansion of steam. Turbine work is given by, 𝑊𝑇 = ℎ1 − ℎ2 11-09-2024 Chapter-4 Heat Engine 29 Rankine Cycle Process 2 – 3: Constant pressure heat rejection in the condenser The exhaust steam from turbine enters into condenser, where it is condensed at constant pressure by circulating cooling water in the tubes. The heat rejected by exhaust steam is 𝑄𝑅. Heat rejected is given by, 𝑄𝑅 = ℎ2 − ℎ3 Process 3 – 4: Isentropic compression in the pump (Pumping Process) The condensed water coming from condenser is pumped to boiler at boiler pressure with the help of feed pump. To do so work, 𝑊𝑃 is supplied to feed pump. Pump work is given by, 𝑊𝑃 = ℎ4 − ℎ3 11-09-2024 Chapter-4 Heat Engine 30 Efficiency of Rankine Cycle Thermal efficiency is given by, 11-09-2024 Chapter-4 Heat Engine 31 Efficiency of Rankine Cycle Net work output 11-09-2024 Chapter-4 Heat Engine 32 Difference between Rankine Cycle and Carnot vapour cycle 1) The exhaust steam from the turbine is not completely condensed in condenser in case of Carnot cycle, while in case of Rankine cycles it is completely condensed. 2) The compressor is used in Carnot cycle to handle mixture of water and steam. In rankine cycle, pump is used in place of compressor, it has to handle only liquid. 3) Superheating of steam is very difficult to achieve in Carnot cycle but there is a possibility of superheating of steam in Rankine cycle. 11-09-2024 Chapter-4 Heat Engine 33 Air Standard Cycles In most of the power developing systems, such as petrol engine, diesel engine and gas turbine, the common working fluid used is air. These devices take in either a mixture of fuel and air as in petrol engine or air and fuel separately and mix them in the combustion chamber as in diesel engine. The mass of fuel used compared with the mass of air is rather small. Therefore the properties of mixture can be approximated to the properties of air. Exact condition existing within the actual engine cylinder are very difficult to determine, but by making certain simplifying assumptions, it is possible to approximate these conditions more or less closely. The approximate engine cycles thus analysed are known as theoretical cycles. The simplest theoretical cycle is called the air-cycle approximation. The air-cycle approximation used for calculating conditions in internal combustion engine is called the air-standard cycle. 11-09-2024 Chapter-4 Heat Engine 34 Air standard efficiency The efficiency of engine in which air is used as working substance is known as air standard efficiency. The air standard efficiency is always greater than the actual efficiency of cycle. Assumptions made for analysis of Air standard cycle: 1) The working fluid is air. 2) In the cycle, all the processes are reversible. 3) The air behaves as an ideal gas and its specific heat is constant at all temperatures. 𝐶𝑃 = 1.005 𝐾𝐽Τ𝐾𝑔 𝐾, 𝐶𝑉 = 0.718 𝐾𝐽Τ𝐾𝑔 𝐾, 𝛾 = 1.4 4) Mass of working fluid remains constant through entire cycle. 5) Heat is supplied from constant high temperature heat reservoir. Some heat is rejected from fluid to a heat sink. 11-09-2024 Chapter-4 Heat Engine 35 Otto Cycle Nicholas-A-Otto, a German engineer developed the first successful engine working on this cycle in 1876. This cycle is also known as Constant volume cycle because heat is supplied and rejected at constant volume. Mainly this cycle is used in petrol and gas engines. Figure shows the Otto cycle plotted on P – V diagram. Adiabatic Compression Process (1 – 2): At pt. 1 cylinder is full of air with volume 𝑉1 , pressure 𝑃1 and temp. 𝑇1 Piston moves from BDC to TDC and an ideal gas (air) is compressed isentropically to state point 2 through compression ratio, 𝑉1 𝑟= 𝑉2 11-09-2024 Chapter-4 Heat Engine 36 Otto Cycle Constant Volume Heat Addition Process (2 – 3): Heat is added at constant volume from an external heat source. 𝑃3 The pressure rises and the ratio 𝑟𝑃 or 𝛼 = is called expansion 𝑃2 ratio or pressure ratio. Adiabatic Expansion Process (3 – 4): The increased high pressure exerts a greater amount of force on the piston and pushes it towards the BDC. Expansion of working fluid takes place isentropically and work done by the system. 𝑉4 The volume ratio is called isentropic expansion ratio. 𝑉3 11-09-2024 Chapter-4 Heat Engine 37 Otto Cycle Constant Volume Heat Rejection Process (4 – 1): Heat is rejected to the external sink at constant volume. This process is so controlled that ultimately the working fluid comes to its initial state 1 and the cycle is repeated. Many petrol and gas engines work on a cycle which is a slight modification of the Otto cycle. This cycle is called constant volume cycle because the heat is supplied to air at constant volume. 11-09-2024 Chapter-4 Heat Engine 38 Air Standard Efficiency of an Otto Cycle Consider a unit mass of air undergoing a cyclic change. Heat supplied during the process 2 – 3, 𝑄𝑆 = 𝐶𝑉 (𝑇3 − 𝑇2 ) Heat rejected during process 4 – 1, 𝑄𝑅 = 𝐶𝑉 (𝑇4 − 𝑇1 ) Work done, 𝑊 = 𝑄𝑆 − 𝑄𝑅 𝑊 = 𝐶𝑉 (𝑇3 − 𝑇2 ) − 𝐶𝑉 (𝑇4 − 𝑇1 ) Thermal efficiency, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑊 η= = (𝑇4 − 𝑇1 ) 𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑄𝑆 η=1− (𝑇3 − T2 ) 𝐶𝑉 (𝑇3 − 𝑇2 ) − 𝐶𝑉 (𝑇4 − 𝑇1 ) η= 𝐶𝑉 (𝑇3 − 𝑇2 ) 11-09-2024 Chapter-4 Heat Engine 39 Air Standard Efficiency of an Otto Cycle For Adiabatic compression process (1 – 2), For Isentropic expansion process (3 – 4), 11-09-2024 Chapter-4 Heat Engine 40 Air Standard Efficiency of an Otto Cycle From above equation, we get, Above expression is known as the air standard efficiency of the Otto cycle. It is clear from the above expression that efficiency increases with the increase in the value of 𝑟 (as γ is constant). 11-09-2024 Chapter-4 Heat Engine 41 Effect of compression ratio on 𝜂 From above equation, we get, Figure shows the variation of air standard efficiency of Otto cycle with compression ratio. 11-09-2024 Chapter-4 Heat Engine 42 Diesel Cycle This cycle was discovered by a German engineer Dr. Rudolph Diesel. Diesel cycle is also known as constant pressure heat addition cycle. The diesel cycle consists of two reversible adiabatic process, a constant pressure process and constant volume process. (p-V) diagram of this cycle is shown in Figure. 11-09-2024 Chapter-4 Heat Engine 43 Diesel Cycle Reversible adiabatic Compression Process (1 – 2) Isentropic (Reversible adiabatic) compression with 𝑉1 𝑟= 𝑉2 Constant Pressure Heat Addition Process (2 – 3) During this process heat is added to air at constant pressure. Due to heat addition volume and temperature 𝑉3 of air increases. Volume ratio is known as cut-off 𝑉2 ratio. Heat supplied, 𝑄𝑆 = 𝑚𝐶𝑃 (𝑇3 − 𝑇2 ) 11-09-2024 Chapter-4 Heat Engine 44 Diesel Cycle Reversible adiabatic Expansion Process (3 – 4): 𝑉4 Isentropic expansion of air = isentropic expansion 𝑉3 ratio. Work is developed during this process. Constant Volume Heat Rejection Process (4 – 1) In this process heat is rejected at constant volume. Hence pressure and temperature of air decreases to initial value. This way cycle is complete. This thermodynamics cycle is called constant pressure cycle because heat is supplied to the air at constant pressure. Heat rejected, 𝑄𝑅 = 𝑚𝐶𝑉 (𝑇4 − 𝑇1 ) 11-09-2024 Chapter-4 Heat Engine 45 Efficiency of Diesel cycle Net work done, 𝑊 = 𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 − 𝐻𝑒𝑎𝑡 𝑟𝑒𝑗𝑒𝑐𝑡𝑑 = 𝑚𝐶𝑃 (𝑇3 − 𝑇2 ) − 𝑚𝐶𝑉 (𝑇4 − 𝑇1 ) Air standard efficiency, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑊 η= = 𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑄𝑆 𝑚𝐶𝑃 (𝑇3 − 𝑇2 ) − 𝑚𝐶𝑉 (𝑇4 − 𝑇1 ) η= 𝑚𝐶𝑃 (𝑇3 − 𝑇2 ) (𝑇4 − 𝑇1 ) η=1− γ(𝑇3 − T2 ) 11-09-2024 Chapter-4 Heat Engine 46 Efficiency of Diesel cycle Let, For process (2-3) For process (3-4): 𝑉1 compression ratio, 𝑟 = 𝑉2 𝑉3 Cut-off ratio, ρ = 𝑉2 𝑉4 Since 𝑃2 = 𝑃3 (from figure) Expansion Ratio, = 𝑉3 For process (1-2): By substituting the value of 𝑇2 from eq. 11-09-2024 Chapter-4 Heat Engine 47 Efficiency of Diesel cycle By substituting the value of 𝑇3 from eq., we get By substituting the values of 𝑇2 , 𝑇3 and 𝑇4 in eq. we get, 11-09-2024 Chapter-4 Heat Engine 48 Efficiency of Diesel cycle It is clear from the above equation that the efficiency of diesel cycle depends upon compression ratio (r), ratio of specific heat (γ), and cut-off ratio ρ. Cut-off ratio ρ is always greater than 1 and γ = 1.4 for air, the quantity in bracket is always greater than one. The efficiency of Diesel cycle is always less than Otto cycle for same compression ratio due to above reason. Heat is added at constant volume in Otto cycle while heat is added at constant pressure in Diesel cycle. From the eq. it is clear that the efficiency of Diesel cycle increases with the increase of compression ratio and with the decreases of cut-off ratio. 11-09-2024 Chapter-4 Heat Engine 49  Thank you 11-09-2024 Chapter-4 Heat Engine 50