Jet Propulsion as a Means of Air Travel - Research Paper Example

Running Head: JET PROPULSION AS A MEANS OF AIR TRAVEL Jet Propulsion as a Means of Air Travel Gp Capt (Ret’d) Noel Moitra VM Ex- Indian Air Force Military Aviation Consultant Jet Propulsion as a Means of Air Travel Table of Contents 1. Abstract 2. Hypothesis 3. Null Hypothesis 4. Delimiting Factors 5. Limiting Factors 6. Charts on the Brayton Cycle 7. Photographs of Turbofan jet engines and explanation 8. The advantage of jet engines for air travel Table of Diagrams/Charts 1. The Ideal Brayton Cycle, T-s Diagram Page-12 2. The Ideal Brayton Cycle, P-v Diagram Page-14 3. Diagram 3: The CFM-56-5B Turbofan Page-15 4. Diagram 4: Cutaway Diagram of a Turbofan jet engine Page-16 Abstract Carnot’s Heat Cycle says that in a heat engine, a gas is reversibly heated and then cooled. A model of the cycle is isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression. This flow, that is both adiabatic and reversible is called an Isentropic Flow. For an isentropic flow of a perfect gas, several relations can be derived to define the pressure, density and temperature along a streamline, which is vital in the aero- and thermodynamics of jet flights, making the jet engine the most widely used mode of the three types of propulsion systems available for aircraft. Though not as efficient as the Turboprop engine at lower speeds, the jetliner fulfils the need to travel from one city to another in the shortest possible time and is the only sensible choice over long distances. This is ideally suited to today’s corporate world that lives at a hectic pace and travels only if it is compelled to, which is more often than not. Thus the jet-engined airliner meets with the requirement of quick travel where cost is not a consideration. Short routes are not viable for these aircraft and Turboprop airliners are most cost-effective there. Piston engines are no longer used for airliners, but are the best engines for small aircraft designed for aerobatics. Hypothesis: The Brayton Thermodynamic Cycle is used in all gas turbine or jet engines. This Cycle is composed of three processes, an isentropic compression, isobaric combustion and an isentropic expansion. In a jet engine, the compression takes place within a compressor, which is the first section exposed to incoming airflow. This compressed air is then sent into annular/can-annular flame tubes or combustion chamber, where fuel is injected into it and the mixture burned. The burnt gases flow through a turbine before expulsion at great force into the atmosphere through an exhaust pipe. The reaction to the exhaust force is the propulsive force which is translated into forward motion, both on the ground during take-off and in the air, an example of Newton’s third law of motion. The flow of the exhaust gases through the turbine causes it to rotate and this rotation is transferred to the compressor using one or two shafts. Van Wylen, Gordon J. and Sonntag, Richard E. Fundamentals of Classical Thermodynamics. and Pilots Notes MiG-21 Bison, Chapter 17, R-25 Turbojet Twin Shaft Engine, Mikoyan and Gurevich, Indian Government Press, Nashik, India, 2000. Using Brayton’s Thermodynamic Cycle, I will show that the Turbofan jet engine of today is the most efficient and cost-effective source of power for medium and long range air travel. Null Hypothesis: The jet engine is unsuitable for short distance flights. Not only will it be inefficient due to the short duration the aircraft travels at its optimal high speed, called Range Speed, but it will also turn out to be a commercial disaster, with huge outgo due to fuel costs. Every flight and landing is a countdown towards its end of life and discard. Turboprop engines, which combine the components of a jet engine and get its turbine to rotate a propeller, are most suitable for short flights, the only limitation being that no portion of the propeller should travel at supersonic speeds which could have serious adverse effects, including fracture of the blade. Essentially, a jet-engined airliner becomes cost-effective at a derivable distance/ period of flight, assuming a given seat occupancy level. Any distance/time beyond this makes the jet engine a revenue earning propulsive system. Today, with 16-18 hour non-stop flights, the earning potential is enormous! Delimiting Factors: Thermodynamic Processes: A system undergoes a thermodynamic process when there is some sort of energetic change within the system, generally associated with changes in pressure, volume, internal energy, temperature, or any sort of heat transfer. Andrew Zimmerman Jones, About.com. In simpler terms, whenever one or more of the properties of a system change, a change in the state of the system occurs. The path of the succession of states through which the system passes is called the thermodynamic process. One example of a thermodynamic process is increasing the temperature of a fluid while maintaining a constant pressure. Another example is increasing the pressure of a confined gas while maintaining a constant temperature. Thermodynamic Systems and Processes, extracted from http://www.tpub.com. Thermodynamic Processes have the following four subcategories: 1. Adiabatic process - a process with no heat (Q) transfer into or out of the system, i.e. there is no energy added or reduced from the system by heating or cooling. An adiabatic process is generally obtained by surrounding the entire system with a strongly insulating material and carrying out the process so quickly that there is no time for a significant heat transfer to take place. Alternatively, the heat transfer into or out of the system typically must happen at such a slow rate that thermal equilibrium is maintained. Tipler, Paul A; Freeman, W.H., Physics for Scientists and Engineers; also Jones, Zimmerman Andrew, in About.com. Guide to Physics, 2006. 2. Isochoric process - a process with no change in volume, in which case the system does no work. Mathematically, δQ = dU, where Q is the heat transferred to the system during the process and U is the change in internal energy. The system needs to be insulated from the environment. Dugdale, Entropy And Its Physical Meaning also physics.about.com. 3. Isobaric process - a process with no change in pressure. physics.about.com. 4. Isothermal process - a process with no change in temperature. This requires the system to be thermally connected to the environment. The word ‘iso’ means ‘equal’. A few more terms need to be understood before we progress further. These are reversibility, irreversibility and enthalpy. Take two ceramic glasses, one with hot water, the other empty. This is the initial stage. Now pour the hot water into the other glass. This pouring is a ‘process taking place’. That glass now has hot water, the first has nothing. Heat (within the water) has been transferred. This is a reversible process as, after it has taken place, it can be reversed. Just return the hot water to the original glass. We will assume no loss of heat or other energy while transferring the water. This causes no change in either the system or its surroundings. Thermodynamically, a process ‘taking place’ refers to its transition from its initial state to its final state. Now change one glass to steel. Heat will be lost to the steel glass. This is an irreversible process i.e. finite changes are made; therefore the system is not at equilibrium. An isenthalpic process (iso-enthalpy) means that enthalpy in the system remains the same. Enthalpy is not any specific form of energy, it is just a defined variable that often simplifies the calculations in the solution of practical thermodynamic problems. I have assumed that the boundaries are impermeable to particles. Derived from http://www.mathpages.com/home/kmath184/kmath184.htm There are different types of jet propulsion, as listed below: 1. The Ramjet: The Ramjet is the most simple jet engine and has no moving parts. The speed of the jet "rams" or forces air into the engine. It is essentially a turbojet in which rotating machinery has been omitted. Its application is restricted by the fact that its compression ratio depends wholly on forward speed. The ramjet develops no static thrust and very little thrust in general below the speed of sound. As a consequence, a ramjet vehicle requires some form of assisted takeoff, such as another aircraft. www.ueet.nasa.gov/ StudentSite/engines also media.nasaexplores.com. 2. The Turboprop Jet Engine A turboprop engine is a jet engine attached to a propeller. The turbine at the back is turned by the hot gases, and this turns a shaft that drives the propeller. www.ueet.nasa.gov/ StudentSite/engines. Some small airliners and transport aircraft are powered by turboprops. The turboprop engine consists of a compressor, combustion chamber, and turbine, the air and gas pressure is used to run the turbine, which then creates power to drive the compressor. Compared with a turbojet engine, the turboprop has better propulsion efficiency at flight speeds below about 300 miles per hour. Modern turboprop engines are equipped with propellers that have a smaller diameter but a larger number of blades for efficient operation at higher flight speeds, up to 400 mph. Jetliners fly much faster. Aerodynamics for Naval Aviators (FAA Handbook) by Federal Aviation Administration, 1998, Aviation Supplies & Academics, Inc., Washington. 3. The Turboshaft Engine A Turboshaft engine is another form of gas-turbine engine that operates much like a turboprop system. It does not drive a propeller. Instead, it provides power for a helicopter rotor. The turboshaft engine is designed so that the speed of the helicopter rotor is independent of the rotating speed of the gas generator. http:// www.ueet.nasa.gov 4. The Turbojet Engine The Turbojet Engine is one in which air taken in from an opening in the front of the engine is compressed to 8 to 12 times its original pressure in the compressor. Fuel is added to the air and burned in a combustion chamber to raise the temperature of the fluid mixture to about 700 to 850° C. The resulting hot air is passed through a turbine, which drives the compressor. If the turbine and compressor are efficient, the pressure at the turbine discharge will be nearly twice the atmospheric pressure, and this excess pressure is sent to the nozzle to produce a high-velocity exhaust of gas which produces thrust. Most military aircraft use turbojets, augmenting thrust by up to 50% using what is called an afterburner, which essentially adds more fuel to the gas just after it exits the turbine into another open-ended burner and reignites the mixture, increasing the energy forced out of the exhaust. GE - Aviation: Engine Education and NASA explores 5-8 Lesson: How Does A Jet Engine Work? also http:// www.geae.com. 5. The Turbofan Jet Engine A turbofan engine has a large fan or low-pressure compressor at the front, which sucks in air. A flow divider splits the compressed air into two streams, one going into the combustion chamber after further compression in a smaller diameter high compression zone like all other jets and the other, the outer layer comprising of up to 80 % or more of total intake flowing around the outside of the engine, cooling the casing and muffling the noise thus making it quieter, and rejoining the burnt fuel-air mixture to increase mass outflow and decrease temperature considerably, giving more thrust at all speeds. The earlier the hot exhaust gases return to ambient temperature, the higher the efficiency. Most of todays jetliners are powered by turbofans. The objective of this sort of bypass system is to increase thrust without increasing fuel consumption. It achieves this by increasing the total air-mass flow and reducing the velocity within the same total energy supply. Bellis Mary, About.com/Inventors-Different Types of Jet Engines. Limiting Factors: The limiting factors are listed below: 1. First Law of Thermodynamics The first law of thermodynamics states that, as a system undergoes a change of state, energy may cross the boundary as either heat or work, and each may be positive or negative. The net change in the energy of the system will be equal to the net energy that crosses the boundary of the system, which may change in the form of internal energy, kinetic energy, or potential energy. The first law of thermodynamics can be summarized in the equation: δ(Q)=d(U)+d(KE)+d(PE)+δ(W) Where: δ(Q)is the heat transferred to the system during the process d(U) is the change in internal energy d(KE)is the change in kinetic energy d(PE)is the change in potential energy δ(W) is the work done by the system during the process In its simplest form, it is also called the law of Conservation of Energy and is taught in basic Physics at the school level. It says: ‘The quantity of energy in the universe is constant. It cannot be created or destroyed, but simply transferred from one state to another’. Thareja BL, Basic Physics for Class X, Vashima Printers, 12th Edition, 1967. 2. Second Law of Thermodynamics: The second law of Thermodynamics states that it impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a cooler body to a hotter body. Clausius says "No machine whose working fluid undergoes a cycle can absorb heat from one system, reject heat to another system and produce no other effect." Kelvin & Planc say the same in different words, i.e. "No engine whose working fluid undergoes a cycle can absorb heat from a single reservoir, deliver an equivalent amount of work, and deliver no other effect." Going further, in any cyclic process the entropy will either increase or remain the same, where Entropy is a measure of the amount of energy which is unavailable to do work. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw. The second law of thermodynamics is also called the law of entropy, as it introduces entropy. It is written as δQ < TdS where δQ is the amount of energy the system gains by heating, T is the temperature of the system, and dS is the change in entropy. For energy to be available there must be a region with high energy level and a region with low energy level. Useful work must be derived from the energy that would flows from the high level to the low level. But it is seen that 100% of the energy cannot be transformed to work Entropy can be produced but never destroyed, the extension of the second law. This is explained by The Engineering Toolbox, available at http://www.engineeringtoolbox.com. We can now leave Thermodynamics and move to our primary focus area of aircraft and their propulsion. Passenger aircraft, or Airliners as they are commonly called, belong to only three categories. These are Piston Engined, like the 4- engined Lockheed Superconstellation of the ‘60s, Turboprop airliners like the ATRs that are in current service and the jet engined, like the Boeing 747. I propose to look at the latter category, with special emphasis on how jet propulsion is used in engines that provide the thrust for aircraft to fly. I will discuss only the Turbofan engine, which I believe is the most efficient and cost-effective engine for airliners. The equation for the first law of thermodynamics is: δ(Q)=d(U)+d(KE)+d(PE)+δ(W) I will show how this equation holds good in the case of a Turbofan engine after understanding what should happen to the airflow into a simple turbojet engine, using the Brayton Cycle. I will refer to the diagrams below, made by Glenn Research Centre at NASA, U.S.A. Chart-1 (Diagram courtesy NASA, U.S.A.) Before we go further, we need to understand Bernoulli’s Theorem. This Theorem says “ In an non-viscous flow of a fluid, the product of its pressure and velocity (pV) is constant. Aerodynamics for Naval Aviators. Thus, when velocity increases, pressure drops and vice versa. According to Scientists at the Glenn Research Center at NASA, in the figure above of a Temperature-Entropy diagram of the Brayton Cycle, free stream conditions exist at station 0 on the chart. In flight, the inlet- which increases in area by design (Diagram 3)- slows the air stream down due to Bernoulli’s Theorem as it reaches the compressor face (station 2 in Chart-1). As the flow slows, it is compressed. Ideally, the compression is isentropic and the static temperature is also increased as shown on the plot. The compressor now compresses (does work on) the gas and increases the pressure and temperature isentropically to its exit (station 3). Theoretically, since the compression is isentropic, a vertical line (station 0 to 3) on the T-s diagram seems appropriate for the process. Actually, the compression is not isentropic and the line is inclined to the right because of the increase in entropy of the flow. The combustion process in the burner occurs at constant pressure (station 3 to 4). An interesting point here is that the fuel is injected along the compressed gas flow. The temperature increase depends on the type of fuel used and the fuel-air ratio. In the next phase, the hot exhaust goes through the power turbine, rotating it. Again, work is done by the turbine, which transfers its rotation to the Compressor using a shaft, (station 4 to 5). Since the turbine and compressor are connected by the same shaft, the work done on the turbine is exactly equal to the work done by the compressor and, ideally, the temperature change is the same. The flow now comes back to free stream pressure (station 5 to 8) isentropically, the nozzle controlling the process. The airflow returns to free stream conditions, completing the cycle. The area under the T-s diagram is proportional to the useful work and thrust generated by the engine. The same source explains the Pressure Volume (p-V) diagram for the ideal Brayton Cycle as shown below: Chart-2 (Diagram courtesy NASA, U.S.A.) As stated earlier, an adiabatic process is a process in which no heat is transferred. This can happen if the process happens so quickly that there is no time to transfer heat, or if the system is totally insulated from its surroundings. Nave,R. http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/adiab.html The Brayton cycle is used to predict the thermodynamic performance of gas turbine engines. A computer program uses it to determine the thrust and fuel flow of an engine design for specified values of component performance. To simplify it further, I will write the next paras in layman language, with reference to Aerodynamics for Naval Aviators. Let us consider an engine fitted on the Airbus A320. This is the CFM 56-5B Turbofan jet engine. Its cover, or cowling, has been taken off, as also its nacelle. Diagram 3: The CFM-56-5B Turbofan What is immediately noticeable is the huge diameter of the engine and the large-bladed first stage fan spaced about 30 cm behind the compressor lip. The blades are aerodynamically designed, using the properties of an aerofoil, so that maximum compression can be achieved. The compressor is rotated by the turbine when the engine is running, as free airflow through it will also rotate it if the engine is dead, this being one property of an aerofoil. Immediately behind the rotary blades are stators, which are fixed gateways to the next stage of the compressor. The fan is normally single stage, followed immediately by the splitter casing, which starts with 2-3 stages of a low-pressure compressor. The high-pressure compressor comes a bit downline. The air to be burnt is compressed further in a smaller diameter high compression zone. Diagram 4. A self explanatory diagram of a Turbofan jet engine The number of compressor stages can be from 4-16, but the average number is kept at 8-10 to keep the engine size down to manageable levels. What is again noticeable is the small size of the exit (exhaust) for the burnt gases. It is possible to make two statements based on the photo: firstly the diameter of the high compression stage is quite small and secondly, a huge amount of air is diverted from entering the core of the engine, the combustion chamber. The ratio of air diverted to air ingested is called the bypass ratio of the engine. Figures vary from a low 0.3 in turbojets to 10-12 for ultrahigh-bypass engines. Jetliners use turbofans that have a bye-pass ratio of 3-4. Encyclopedia Brittanica Online: Byepass Ratio. Most people would have observed that the cowling of a jetliner’s engine bulges outwards from its lip and soon thereafter, tapers at approximately 3-5º towards the exhaust. As the airflow senses the presence of an obstacle ahead through the behaviour of the air particles immediately in front of it, which are slowing down, it starts to slow down itself. This is about 20 cm ahead of the engine. On entering the confines of the engine, it expands in the bulging area and slows down even more. Thus the pressure rises just prior to compression. (Station 2, according to the NASA explanation). The huge fan does work and compresses the inflow with a corresponding increase in temperature (Station 3). There are losses due to friction and dissipation of heat, so the system is not really 100% efficient, nor is it truly isentropic. In other words, the entropy in the flow increases, as entropy is a thermodynamic quantity representing the amount of energy in a system that is no longer available for doing mechanical work. Dugdale. NASA states that the combustion process in the burner occurs at constant pressure from station 3 to station 4. This is not fully true, as the direction and degree of combustion depends on how the fuel is injected into the flame tube. This is proved by the fact that afterburners add fuel to the gases that have not burned fully and retain combustible elements. This time, fuel is injected by a burner ring against the direction of the exhaust. Again, NASA states that the hot exhaust is passed through the power turbine in which work is done by the flow from station 4 to station 5. Because the turbine and compressor are on the same shaft, the work done on the turbine is exactly equal to the work done by the compressor and, ideally, the temperature change is the same. However, matters are rarely ideal and there is a dichotomy here too. Entropy actually increases. (Second Law of Thermodynamics) In the Turbofan engine, the diverted air, having done work in cooling the engine from the high pressure compressor to the flame tubes to the exhaust outer shield, joins up with the 800°C burnt gas flow, bringing the temperature down considerably, while adding almost 60% of mass, since fuel has been added to the burned gas, increasing both its volume and mass. The gases exiting the engine imparts the thrust to the engine, which is attached to the aircraft. This thrust keeps the aircraft in the air. Returning to the first law of thermodynamics: δ(Q)=d(U)+d(KE)+d(PE)+δ(W), we see that the heat transferred to the system during the process by burning compressed air that has been injected with fuel shows up as the change in internal energy, with the aircraft velocity resulting from the Kinetic Energy extracted, the Potential Energy resulting in the aircraft maintaining or changing altitude, all of which have required work to be done at various stages. I have focused on the efficiency of a jet as a propulsive system and proved my point. I have also shown the applicability of the first two laws of Thermodynamics, including Entropy. I will now conclude with the advantages of the jet as a source of propulsion. A jetliner is the most economical and cost-effective mode of travel over long distances, from the airlines’ point of view. The reasons are: 1. Better income from customer-miles. 2. Low cost of engine operation. At height, the ambient temperature drops, going below zero at around 14-15,000 feet (Freezing Altitude) and dropping further at the dry adiabatic lapse rate till it reaches -56.5ºC. ICAO, International Atmospheric Conditions, As the temperature drops, the Specific Fuel Consumption (SFC) of a jet engine drops. SFC is defined as grams of fuel consumed per second per kilonewton of thrust. Aerodynamics for Naval Aviators. 3. Flight is generally at what is called Range Speed, which means that the aircraft is flying at its optimum speed. It generally corresponds at the speed for best SFC. 4. Optimum utilization of the aircraft. 5. Non-stop 16-18 hour flights over 18,000 km. References Cited 1. Carnot, Nicolas Léonard Sadi, died 1832, the proponent of the Heat Cycle, leading to the Second Law of Thermodynamics. 2. Van Wylen, Gordon J. and Sonntag, Richard E. Fundamentals of Classical Thermodynamics. To show that the aircraft moves forward because the thrust is rearwards 3. Pilots Notes MiG-21 Bison, Chapter 17, R-25 Turbojet Twin Shaft Engine, Mikoyan and Gurevich, Indian Government Press, Nashik, India, 2000. To explain how 2 shafts can be used in jets; the first to connect low pressure compressors with low pressure turbines; the second for the high pressure sections. 4. Thermodynamic Systems and Processes, extracted from http://www.tpub.com. To understand thermodynamic processes. 5. Tipler, Paul A; Freeman, W.H., Physics for Scientists and Engineers; also Jones, Zimmerman Andrew, in About.com. Guide to Physics, 2006, also Dugdale, Taylor and Francis Group, London, Entropy And Its Physical Meaning also physics.about.com. For understanding thermodynamic processes and Entropy. 6. http://www.mathpages.com/home/kmath184/kmath184.htm To understand reversibility, irreversibility and enthalpy. 7. www.ueet.nasa.gov/ StudentSite/engines also media.nasaexplores.com. To see how a Ramjet, a turboshaft and a turboprop engine work. 8. Aerodynamics for Naval Aviators, (FAA Handbook) by Federal Aviation Administration, 1998, Aviation Supplies & Academics, Inc., Washington. To describe basic turbine engines and other aerodynamic concepts used. Also, to understand how a turboprop engine works. 9. GE - Aviation: Engine Education and NASA explores 5-8 Lesson: How Does A Jet Engine Work? also http:// www.geae.com. Complete information on jet engines and how they work. 10. Bellis Mary, About.com/Inventors-Different Types of Jet Engines. To see how a turbofan jet achieves increase in thrust. 11. Basic Physics for Class X, Vashima Printers, 12th Edition, 1967. To define the law of Conservation of Energy. 12. Rudolf Clausius (1822-1888) German Scientist famous for his work on Thermodynamics. To understand Entropy 13. Kelvin and Planc: Lord Kelvin, after whom the temperature scale is named and Max Planc, pioneer of Quantum Mechanics To further look at Thermodynamics, mainly Entropy. 14. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw. To understand the definition of the second law of thermodynamics. 15. The Engineering Toolbox, available at http://www.engineeringtoolbox.com To go deeper into Entropy. 16. Brayton Cycle: Glenn Research Centre at NASA, U.S.A. To understand the ideal Brayton Cycles using the T-s and p-V charts. 17. Nave,R. http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/adiab.html To understand further the adiabatic process. 18. Encyclopedia Brittanica Online: Byepass Ratio. To explain byepass ratio. 19. Saucier, Walter J. 2003, Courier Dover Publications, London.ICAO, International Atmospheric Conditions. To describe the International norms of an ideal atmosphere. Read More