Yanwei
School of Aerospace, Mechanical and Manufacturing Engineering
Part C Learning Guide INTRODUCTION TO AIRCRAFT
Lecture 5 A
Introduction to Aircraft Propulsion II
March 2013
Introduction to Aircraft
1
School of Aerospace, Mechanical and Manufacturing Engineering
Lecture 5A: Introduction to Aircraft Propulsion II
Introduction
History of Gas Turbines Since we are talking about turbines, there is an intimate relationship with turbo-machinery, hence the first important aspect to the history of gas turbines in the invention of the modern centrifugal pump by Appold in 1851. Then in 1902 Renault patented the centrifugal supercharger. This marks the application of turbo-machinery to engines. In 1908 Lorin proposed the forerunner of the motorjet (we will see this shortly), where air flow from behind the propeller was directed to a combustion chamber to produce jet thrust at the rear of an aircraft. Next in 1917 Morize (in France) proposes and Harris (in England) patents the motorjet. In a motorjet a conventional engine is used to drive a compressor which pumps compressed air into a combustion chamber, where fuel is added and then burnt to produce jet thrust at the rear of the aircraft. Finally, as we saw in Week 2 (History of Aviation), in 1930 Sir Frank Whittle patents the centrifugal flow turbojet. The design of Whittle is a direct evolution of the previous turbomachinery developments, and their application to aircraft. In it, he uses a Centrifugal compressor to achieve the compression ratio that Otto knew we needed inside an engine to make it more efficient. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
2
School of Aerospace, Mechanical and Manufacturing Engineering
Jet Propulsion Concept To understand the basic physics behind jet propulsion consider an enclosed cylinder. The “fluid” inside the cylinder is at a higher pressure than the “fluid” outside the cylinder. That is, P1 > P0. The pressure difference is balanced by the stress within the pressure vessel. No think what would happen if I instantly cut this cylinder in half. The pressure on the inside would cause the “fluid” within the pressure vessel to push out against the outside pressure, over the area of the cylinder. However, these two pressures are not equal, and the resultant is that the fluid will flow out with a velocity v, and from Newton’s Third Law, we know this excess pressure over the area, will gives us a force, which will be equal and opposite to the thrust of the cylinder, which will accelerate it. That is,
F A F AP = A A F = AP = A( P − P0 ) 1 P=
Now if we had some way to pump fluid at the original pressure into the pressure vessel we could sustain this thrust. This principle can be applied to a “jet ski” or a “jet aircraft”. The simplest example is that of a balloon. Definition Why do we use the term “Turbojet” when talking about the quintessential “jet engine” used on aircraft? Why the prefix “turbo”? This relates to turbo machinery. In turbo-machinery two things are possible, rotational energy can be converted into fluid energy, or conversely fluid energy can be converted into rotational energy. Why “jet”? Simple, we are utilizing the jet propulsion concept, where a fluid is forcefully propelled from a nozzle as we saw before. Hence we have a fluid “jet”. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
3
School of Aerospace, Mechanical and Manufacturing Engineering
Types of Gas Turbines Turbojets: There are two general subcategories of turbojets. These are: 1. Centrifugal flow turbojets, where the gas flows radially outwards relative to the line of the thrust, and 2. Axial flow turbojets, where the gas flows straight through the engine along the line of the thrust. There are advantages and disadvantages of both. The first practical design was centrifugal, while all large modern designs are axial. For axial flow turbo get there are again two typical configurations: 1. Single spool 2. Double spool Here a spool refers to a coupled compressor turbine pair on a common shaft. So for a double spool engine, the outer shaft (turned by the high pressure turbine, and driving the high pressure compressor) is hollow, with the low pressure spool located concentrically in it. Turboprops: Here the “prop” refers to the fact that the turbine is used to drive a propeller. In a turboprop a mechanism to convert high rpm of engine shaft into lower rpm of propeller is required. There are efficiency benefits associated with the use of turboprops; however, there use reintroduces the limitations of propeller (maximum speed), and the main motivation for Whittle to suggesting the use of gas turbines. Different types of internal configuration can be used. These can be identical to the variations in turbojet configurations. More importantly, there are two categories of turboprop, Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
4
School of Aerospace, Mechanical and Manufacturing Engineering
1. Free power turbine: Where there the propeller is driven by an independent turbine (this can be an inner spool, but is more commonly a reverse flow engine where the propeller is at the “back” of the engine relative to the airflow (this does not mean it has to be a pusher prop). 2. Direct drive turbine, where the propeller is driven from a compress/turbine spool (the lowest pressure spool in a multispool engine). Turboshaft: Here the “shaft” refers to the driveshaft driven by a turbine. This also requires mechanical gearing, and can have the same configurations as a turboprop engine (essentially a turboprop engine is a turboshaft engine where the shaft is used to drive a propeller). The main applications of turboshaft engines are in: Helicopters Power Generators (power plants) Naval vessels Hovercraft Tanks And the F-35B uses a turboshaft to drive the lift fan Turbofan: The advent of a bypass ratio to improve efficiency of turbojet engines has led to the development of the turbofan, where a turbine is used to drive a fan. The bypass ratio (BPR) is defined as the ratio of the mass of air that by passes the core of the engine to the mass of air that passes through the core of the engibe. That is,
BPR = Air Bypassed/Air Core, or BPR = Air Bypassed:
Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
5
School of Aerospace, Mechanical and Manufacturing Engineering
Air Core, where air core = 1. A turbofan can be described as having either a high or low bypass ratio. An arbitrary value of 2.5 is typically used to distinguish between these. A turbofan can be also be triple spool, where both the single and double spool engines are typically configured like direct drive turboshaft engines, turning a fan, and triple spool engines are effectively free power turbines, where the lowest pressure turbine is driving the fan (but without the need for reduction gearing).
Thrust
Turbojet We learnt about the jet propulsion concept, and this is applicable in certain circumstances to jet engines. However, we have neglected Newton’s Second Law, which we kind of lied to you about in high school.
F = ma = m dv dmv dp = = dt dt dt
That is, we used a simplified version of Newton’s Second Law. What you know now is that the force is directly proportion to the rate of change of the momentum. This becomes essential when you look at rockets propulsion. We can apply this “concept” quiet simply to the propeller. The propeller gives momentum the air, increasing its speed a little, which intern results in a thrust. What is important here is that the air already has some initial momentum because of the speed of the aircraft through it. That is, relative to the aircraft, the air is moving towards it. This then gives
F= dp d d = ( p f − pi ) = (mv − mu ) dt dt dt
But we assume that neither v or u is changing (for an aircraft in straight and level flight), so this then becomes
F= d & (mv − mu ) = dm (v − u ) = m(v − u ) dt dt
What changes overtime is the mass of air. This quantity, ṁ is simple the mass of air per second, or technically the air mass flow rate, ṁa. For a turbojet, we then combine the momentum component and the pressure component to give
& F = ma (v − u ) + A(Pe − P0 )
Lecture 5 A
Introduction to Aircraft Propulsion II
March 2013
Introduction to Aircraft
6
School of Aerospace, Mechanical and Manufacturing Engineering
The main thing to note here is that for subsonic flight, the pressure term will be zero. That is, the air leaves the engine at atmospheric pressure. We have more than air in the exhaust, we add fuel. What about that? Under the assumption that we add the fuel in at a very low velocity (uf = 0), then,
& & & & F = ma (v − u ) + m f (v − 0 ) = (ma + m f )(v − u )
Now we introduce a new term, the fuel air ratio, f=mf/ma; that is, the mass flow rate of the fuel divided by the mass flow rate of the air. Now we get the final form of the thrust equation for a subsonic turbojet,
& F = ma [(1 + f )v − u ]
Turbofan Well for a turbofan, and a turboprop, there is not just the air that goes through the core of the engine, there is the stuff that goes around the outside. Repeating the above momentum derivation above we come to the full form of the thrust equation for a turbofan at subsonic speeds,
& & F = F=mac(vc − u)+mah [(l + f)vh − u]
We can now also define the bypass ratio as, BPR=ṁac/ṁah For a turbofan the hot thrust accounts for about 20% of the total thrust, while for a turboprop the hot thrust accounts for about 10% of the total thrust. Propulsive Efficiency The efficiency is a measure of the power used to the total power (used + wasted). Power is wasted in terms of kinetic energy given to the exhaust gases. With some nice mathematics we can take the kinetic energies and propulsive power (thrust × velocity), and come up with a propulsive efficiency ηp = 2u/(v+u) What you need to understand here is that an engine will only have 100% efficiency if v=u, which means the speed of the air after the engine is the same as the speed of the air as it approaches the engine. That then means the v-u=0, so there is no thrust. That is, to have maximum thrust, will typically involve lower efficiency. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
7
School of Aerospace, Mechanical and Manufacturing Engineering
More importantly, if ṁa is small, (v-u) will need to be large to achieve a suitable thrust value. This means the propulsive efficiency will be low. However, the same thrust can be achieved with a large ṁa and a small (v-u). The advantage of this is that the propulsive efficiency will be high. This is the important difference between turbojets, turbofans, and turboprops.
Thermodynamics
The Brayton Cycle The Brayton cycle is also referred to as a continuous cycle, because all of the processes are happening at the same time (unlike in a 4 stroke engine). This is not the reason it is called an open cycle! All real engines are open cycles in the real world, and simple because working fluid enters and leaves, unlike our sealed cylinder or balloon (they are closed cycles). Pilots Note: There is some confusion regarding this at CASA!
Here we see that the stages are; 1 to 2 intake; 2 to 3 inlet; 3 to 4 compressor; 4 to 5 combustion; 5 to 6 turbine (power); 6 to 7 nozzle (exhaust); 7 to 1 exhaust
1 to 2 is an isobaric intake 2 to 4 is an isentropic compression 4 to 5 is an isobaric combustion 5 to7 is an isentropic expansion 7 to 2 is an isobaric heat rejection We say that heat energy is added in the combustion process, and rejected in the exhaust. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
8
School of Aerospace, Mechanical and Manufacturing Engineering
The area X34Y is the work required to compress the air. The area Z65Y is equal to the area X34Y The area 176Z is the energy left for propulsion etc (the thrust power and also the wasted power)
Lecture 5 A
Introduction to Aircraft Propulsion II
March 2013
Introduction to Aircraft
9
Part C Learning Guide INTRODUCTION TO AIRCRAFT
Lecture 5 A
Introduction to Aircraft Propulsion II
March 2013
Introduction to Aircraft
1
School of Aerospace, Mechanical and Manufacturing Engineering
Lecture 5A: Introduction to Aircraft Propulsion II
Introduction
History of Gas Turbines Since we are talking about turbines, there is an intimate relationship with turbo-machinery, hence the first important aspect to the history of gas turbines in the invention of the modern centrifugal pump by Appold in 1851. Then in 1902 Renault patented the centrifugal supercharger. This marks the application of turbo-machinery to engines. In 1908 Lorin proposed the forerunner of the motorjet (we will see this shortly), where air flow from behind the propeller was directed to a combustion chamber to produce jet thrust at the rear of an aircraft. Next in 1917 Morize (in France) proposes and Harris (in England) patents the motorjet. In a motorjet a conventional engine is used to drive a compressor which pumps compressed air into a combustion chamber, where fuel is added and then burnt to produce jet thrust at the rear of the aircraft. Finally, as we saw in Week 2 (History of Aviation), in 1930 Sir Frank Whittle patents the centrifugal flow turbojet. The design of Whittle is a direct evolution of the previous turbomachinery developments, and their application to aircraft. In it, he uses a Centrifugal compressor to achieve the compression ratio that Otto knew we needed inside an engine to make it more efficient. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
2
School of Aerospace, Mechanical and Manufacturing Engineering
Jet Propulsion Concept To understand the basic physics behind jet propulsion consider an enclosed cylinder. The “fluid” inside the cylinder is at a higher pressure than the “fluid” outside the cylinder. That is, P1 > P0. The pressure difference is balanced by the stress within the pressure vessel. No think what would happen if I instantly cut this cylinder in half. The pressure on the inside would cause the “fluid” within the pressure vessel to push out against the outside pressure, over the area of the cylinder. However, these two pressures are not equal, and the resultant is that the fluid will flow out with a velocity v, and from Newton’s Third Law, we know this excess pressure over the area, will gives us a force, which will be equal and opposite to the thrust of the cylinder, which will accelerate it. That is,
F A F AP = A A F = AP = A( P − P0 ) 1 P=
Now if we had some way to pump fluid at the original pressure into the pressure vessel we could sustain this thrust. This principle can be applied to a “jet ski” or a “jet aircraft”. The simplest example is that of a balloon. Definition Why do we use the term “Turbojet” when talking about the quintessential “jet engine” used on aircraft? Why the prefix “turbo”? This relates to turbo machinery. In turbo-machinery two things are possible, rotational energy can be converted into fluid energy, or conversely fluid energy can be converted into rotational energy. Why “jet”? Simple, we are utilizing the jet propulsion concept, where a fluid is forcefully propelled from a nozzle as we saw before. Hence we have a fluid “jet”. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
3
School of Aerospace, Mechanical and Manufacturing Engineering
Types of Gas Turbines Turbojets: There are two general subcategories of turbojets. These are: 1. Centrifugal flow turbojets, where the gas flows radially outwards relative to the line of the thrust, and 2. Axial flow turbojets, where the gas flows straight through the engine along the line of the thrust. There are advantages and disadvantages of both. The first practical design was centrifugal, while all large modern designs are axial. For axial flow turbo get there are again two typical configurations: 1. Single spool 2. Double spool Here a spool refers to a coupled compressor turbine pair on a common shaft. So for a double spool engine, the outer shaft (turned by the high pressure turbine, and driving the high pressure compressor) is hollow, with the low pressure spool located concentrically in it. Turboprops: Here the “prop” refers to the fact that the turbine is used to drive a propeller. In a turboprop a mechanism to convert high rpm of engine shaft into lower rpm of propeller is required. There are efficiency benefits associated with the use of turboprops; however, there use reintroduces the limitations of propeller (maximum speed), and the main motivation for Whittle to suggesting the use of gas turbines. Different types of internal configuration can be used. These can be identical to the variations in turbojet configurations. More importantly, there are two categories of turboprop, Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
4
School of Aerospace, Mechanical and Manufacturing Engineering
1. Free power turbine: Where there the propeller is driven by an independent turbine (this can be an inner spool, but is more commonly a reverse flow engine where the propeller is at the “back” of the engine relative to the airflow (this does not mean it has to be a pusher prop). 2. Direct drive turbine, where the propeller is driven from a compress/turbine spool (the lowest pressure spool in a multispool engine). Turboshaft: Here the “shaft” refers to the driveshaft driven by a turbine. This also requires mechanical gearing, and can have the same configurations as a turboprop engine (essentially a turboprop engine is a turboshaft engine where the shaft is used to drive a propeller). The main applications of turboshaft engines are in: Helicopters Power Generators (power plants) Naval vessels Hovercraft Tanks And the F-35B uses a turboshaft to drive the lift fan Turbofan: The advent of a bypass ratio to improve efficiency of turbojet engines has led to the development of the turbofan, where a turbine is used to drive a fan. The bypass ratio (BPR) is defined as the ratio of the mass of air that by passes the core of the engine to the mass of air that passes through the core of the engibe. That is,
BPR = Air Bypassed/Air Core, or BPR = Air Bypassed:
Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
5
School of Aerospace, Mechanical and Manufacturing Engineering
Air Core, where air core = 1. A turbofan can be described as having either a high or low bypass ratio. An arbitrary value of 2.5 is typically used to distinguish between these. A turbofan can be also be triple spool, where both the single and double spool engines are typically configured like direct drive turboshaft engines, turning a fan, and triple spool engines are effectively free power turbines, where the lowest pressure turbine is driving the fan (but without the need for reduction gearing).
Thrust
Turbojet We learnt about the jet propulsion concept, and this is applicable in certain circumstances to jet engines. However, we have neglected Newton’s Second Law, which we kind of lied to you about in high school.
F = ma = m dv dmv dp = = dt dt dt
That is, we used a simplified version of Newton’s Second Law. What you know now is that the force is directly proportion to the rate of change of the momentum. This becomes essential when you look at rockets propulsion. We can apply this “concept” quiet simply to the propeller. The propeller gives momentum the air, increasing its speed a little, which intern results in a thrust. What is important here is that the air already has some initial momentum because of the speed of the aircraft through it. That is, relative to the aircraft, the air is moving towards it. This then gives
F= dp d d = ( p f − pi ) = (mv − mu ) dt dt dt
But we assume that neither v or u is changing (for an aircraft in straight and level flight), so this then becomes
F= d & (mv − mu ) = dm (v − u ) = m(v − u ) dt dt
What changes overtime is the mass of air. This quantity, ṁ is simple the mass of air per second, or technically the air mass flow rate, ṁa. For a turbojet, we then combine the momentum component and the pressure component to give
& F = ma (v − u ) + A(Pe − P0 )
Lecture 5 A
Introduction to Aircraft Propulsion II
March 2013
Introduction to Aircraft
6
School of Aerospace, Mechanical and Manufacturing Engineering
The main thing to note here is that for subsonic flight, the pressure term will be zero. That is, the air leaves the engine at atmospheric pressure. We have more than air in the exhaust, we add fuel. What about that? Under the assumption that we add the fuel in at a very low velocity (uf = 0), then,
& & & & F = ma (v − u ) + m f (v − 0 ) = (ma + m f )(v − u )
Now we introduce a new term, the fuel air ratio, f=mf/ma; that is, the mass flow rate of the fuel divided by the mass flow rate of the air. Now we get the final form of the thrust equation for a subsonic turbojet,
& F = ma [(1 + f )v − u ]
Turbofan Well for a turbofan, and a turboprop, there is not just the air that goes through the core of the engine, there is the stuff that goes around the outside. Repeating the above momentum derivation above we come to the full form of the thrust equation for a turbofan at subsonic speeds,
& & F = F=mac(vc − u)+mah [(l + f)vh − u]
We can now also define the bypass ratio as, BPR=ṁac/ṁah For a turbofan the hot thrust accounts for about 20% of the total thrust, while for a turboprop the hot thrust accounts for about 10% of the total thrust. Propulsive Efficiency The efficiency is a measure of the power used to the total power (used + wasted). Power is wasted in terms of kinetic energy given to the exhaust gases. With some nice mathematics we can take the kinetic energies and propulsive power (thrust × velocity), and come up with a propulsive efficiency ηp = 2u/(v+u) What you need to understand here is that an engine will only have 100% efficiency if v=u, which means the speed of the air after the engine is the same as the speed of the air as it approaches the engine. That then means the v-u=0, so there is no thrust. That is, to have maximum thrust, will typically involve lower efficiency. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
7
School of Aerospace, Mechanical and Manufacturing Engineering
More importantly, if ṁa is small, (v-u) will need to be large to achieve a suitable thrust value. This means the propulsive efficiency will be low. However, the same thrust can be achieved with a large ṁa and a small (v-u). The advantage of this is that the propulsive efficiency will be high. This is the important difference between turbojets, turbofans, and turboprops.
Thermodynamics
The Brayton Cycle The Brayton cycle is also referred to as a continuous cycle, because all of the processes are happening at the same time (unlike in a 4 stroke engine). This is not the reason it is called an open cycle! All real engines are open cycles in the real world, and simple because working fluid enters and leaves, unlike our sealed cylinder or balloon (they are closed cycles). Pilots Note: There is some confusion regarding this at CASA!
Here we see that the stages are; 1 to 2 intake; 2 to 3 inlet; 3 to 4 compressor; 4 to 5 combustion; 5 to 6 turbine (power); 6 to 7 nozzle (exhaust); 7 to 1 exhaust
1 to 2 is an isobaric intake 2 to 4 is an isentropic compression 4 to 5 is an isobaric combustion 5 to7 is an isentropic expansion 7 to 2 is an isobaric heat rejection We say that heat energy is added in the combustion process, and rejected in the exhaust. Lecture 5 A Introduction to Aircraft Propulsion II March 2013
Introduction to Aircraft
8
School of Aerospace, Mechanical and Manufacturing Engineering
The area X34Y is the work required to compress the air. The area Z65Y is equal to the area X34Y The area 176Z is the energy left for propulsion etc (the thrust power and also the wasted power)
Lecture 5 A
Introduction to Aircraft Propulsion II
March 2013
Introduction to Aircraft
9