AP3456 – 3-1 - Basic Theory and Principles of Propulsion CHAPTER 1 - BASIC THEORY AND PRINCIPLES OF PROPULSION Introduction 1. When an aircraft is travelling through air in straight and level flight and at a constant true airspeed (TAS), the engines must produce a total thrust equal to the drag on the aircraft as shown in Fig 1. If the engine thrust exceeds the drag, the aircraft will accelerate, and if the drag exceeds the thrust, the aircraft will slow down. 3-1 Fig 1 Arrangement of Thrust and Drag Forces 2. Although a variety of engine types are available for aircraft propulsion, the thrust force must always come from air or gas reaction forces normally acting on the engine or propeller surfaces. 3. The two common methods of aircraft propulsion are: a. The propeller engine powered by piston or gas turbine. b. The jet engine. Rotary wing aircraft are powered by turboshaft engines which produce shaft power to drive a gearbox and work on similar principles to gas turbine propeller engines (turboprops), except that all the available energy is absorbed by the turbine, with no residual jet thrust. Turboshaft engines are considered in Volume 3, Chapter 16. The Propeller Engine 4. With a propeller engine, the engine power produced drives a shaft which is connected to a propeller usually via a gearbox. The propeller cuts through the air accelerating it rearwards. The blade of a propeller behaves in the same way as the aerofoil of an aircraft; the air speeds up over the leading face of the propeller blade causing a reduced pressure with a corresponding increase of pressure on the rearward face (see Fig 2). This leads to a net pressure force over the propeller (where Force = Pressure × Area), thus providing thrust. For example: Net pressure of 40 kPa (Pa = N/m2); Blade area of 1 m2, Thrust = 40 kPa × 1 m2 = 40 kN With gas turbine powered propeller engines, a small amount of thrust is produced by the jet exhaust which will augment the thrust produced by the propeller. Revised May 10 Page 1 of 8 AP3456 – 3-1 - Basic Theory and Principles of Propulsion 3-1 Fig 2 Propeller Thrust Direction of Flight Slipstream Velocity Vj Relative Air Flow Va Net Force Direction (Axial Component) of Propeller 5. An alternative method of calculating the thrust produced by a propeller is provided by Newton’s laws of motion which give: Force = Mass × Acceleration ∴ Thrust = Mass flow rate of air through Propeller × Increase in velocity of the air = M × (Vj – Va) Where M = Mass flow rate of the air Vj = Velocity of slipstream Va = Velocity of the aircraft (TAS) This will give the same result as that given by the sum of pressure forces. In the case of the propeller, the air mass flow will be large, and the increase in velocity given to the air will be fairly small. The Jet Engine 6. In all cases of the jet engine, a high velocity exhaust gas is produced, the velocity of which, relative to the engine, is considerably greater than the TAS. Thrust is produced according to the equation in para 5 i.e.: Thrust = M × (Vj – Va) where Vj is now the velocity of the gas stream at the propelling nozzle (see Fig 3). This represents a simplified version of the full thrust equation as the majority of thrust produced is a result of the momentum change of the gas stream. 3-1 Fig 3 Jet Thrust - Relative Velocities a j Revised May 10 Page 2 of 8 AP3456 – 3-1 - Basic Theory and Principles of Propulsion 7. In the rocket engine (Fig 4) the gases which leave the engine are the products of the combustion of the rocket propellants carried; therefore no intake velocity term Va is required: The simplified version of the equation giving the thrust produced thus becomes: Thrust = Mass flow rate of propellant × Vj 3-1 Fig 4 Rocket Engines Solid Propellant Rocket Liquid Propulsion Rocket The Turbofan (By-pass) Engine 8. The Turbofan or by-pass engine (Fig 5) powers the vast majority of modern aircraft, and is likely to do so for the foreseeable future. It can be seen as the link between the Turbopropeller and the Turbojet engine. The thrust from a by-pass engine is derived from the mass air flow from the 'fan' plus the mass air flow from the core engine and can be exhausted separately or mixed prior to entering the jet pipe. 3-1 Fig 5 Turbofan Thrust 9. The thrust for a mixing turbofan engine can be treated in the same way as a simple turbojet, as the mass flows are mixed prior to entering a common exhaust and propelling nozzle. However, where the by-pass air flow is exhausted separately the simplified thrust calculation becomes: Thrust = Mass flow rate of air through fan duct × (Vjb – Va) + Mass flow rate of air through core engine × (Vje – Va) = Mfan × (Vjb – Va) + Mcore × (Vje – Va) The ratio Mfan/Mcore is called the by-pass ratio and is quoted for both mixing and non-mixing turbofans. Engines with by-pass ratios of less than 1.5 are termed low by-pass ratio engines, while those with ratios above 1.5 are considered high by-pass. Engine Efficiency 10. As the engine thrust propels the aircraft, propulsive power is being developed in proportion to the airspeed, i.e.:Propulsive power = Engine thrust × TAS Revised May 10 Page 3 of 8 AP3456 – 3-1 - Basic Theory and Principles of Propulsion The power developed must be sufficient to overcome aircraft drag with an adequate margin to increase aircraft velocity as required. Fuel is consumed during combustion thus releasing energy to generate power. (1 kg of kerosine produces 43 MJ of energy.) The overall efficiency (ηο) of the engine as a propulsive powerplant is defined as: Propulsive power developed ηo = Fuel power consumed Thermal and Propulsive Efficiency of Gas Turbines 11. In the conversion of fuel power into propulsive power it is convenient to consider the conversion taking place in two stages: a. The conversion of fuel power into gas power. b. The conversion of gas power into propulsive power. The airbreathing engine burns fuel to produce useful gas kinetic energy. Some of this energy is lost in the form of heat in the jet efflux, by kinetic heating, conduction to engine components, and friction. The ratio of the gas energy produced in the engine to the heat energy released by the fuel in unit time, determines the THERMAL efficiency (ηth ) of the engine, i.e.: Rate of increase in KE of gas stream ηth = Rate of energy release from fuel 12. Of the gas kinetic energy produced, some is converted into propulsive power, whilst the remainder is discharged to atmosphere in the form of wasted kinetic energy. The ratio of the propulsive power to the rate of increase in kinetic energy of the gas stream determines the PROPULSIVE efficiency (ηp ) of the engine, i.e.: Propulsive power developed ηp = Rate of increase in KE of gas stream 13. An examination of the expressions derived for the thermal, propulsive and overall efficiencies shows that the following relationship exists: ηο = ηth × ηp 14. Fig 6 shows a typical breakdown of the total fuel power produced from burning kerosine at a rate of 1.4 kg/s to produce a power potential of 60 MW. By calculating the efficiencies of the above example viz: ηth = 15/60 = 25% ηp = 12/15 = 80% ηο = 12/60 = 20% It can be seen that the biggest single loss is through waste heat, the majority of which (75%) is lost without being converted to useful kinetic energy. A further loss (5%) is experienced by failing to convert all the remaining kinetic energy to useful propulsive power. Revised May 10 Page 4 of 8 AP3456 – 3-1 - Basic Theory and Principles of Propulsion 3-1 Fig 6 Representation of Energy Efficiency 15. The generation of thrust as shown in Fig 7, M × (Vje – Va), is always accompanied by the rejection 2 of power in the form of wasted kinetic energy (kinetic energy = ½ × M × (Vje – Va) ) with a consequent effect on the propulsive efficiency (ηp). 3-1 Fig 7 Gas Turbine Thrust - Absolute Velocity For a given thrust, this wasted kinetic energy can be reduced by choosing a high value of air mass flow rate (M) and a low value of (Vje – Va), since kinetic energy is proportional to the square of the velocity. This result is shown in Fig 8. 3-1 Fig 8 Variation in KE Loss with Mass Flow Rate at Constant Thrust y g r e n E c i t e n i K d e t s a W Air Mass Flow Therefore, provided that the thermal efficiency remains constant, engines with a large mass flow and relatively low increase in gas velocity will be more efficient (see Fig 9). Revised May 10 Page 5 of 8 AP3456 – 3-1 - Basic Theory and Principles of Propulsion 3-1 Fig 9 Comparison of Propulsive Efficiencies r) le el an p pf ro ro P P d e t nc e 80 a -J v o d rb (A u T % y s c s n a e p i y s c i B s f f 60 h a p T E ig y B u n H r b o - w i n o o s - l a L P u - -F r p o n o o b a p r r -F P u T o 40 rb u T 20 0 200 400 600 800 Airspeed (kt) 16.