LECTURE NOTES ON AEROSPACE PROPULSION

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LECTURE NOTES ON AEROSPACE PROPULSION I III B. Tech I semester (JNTUH-R13) Mr. K. BHARADWAJAN Associate Professor Mr. CH. SATYA SANDEEP Assistant Professor Mr. S. SRIKRISHNAN Assistant Professor DEPARTMENT OF AERONAUTICAL ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING DUNDIGAL, HYDERABAD - 500 043 I. Introduction to Propulsion A. Goal: Create a Force to Propel a Vehicle Two options: 1. Take mass stored in a vehicle and throw it backwards (rocket propulsion). Use the reaction force to propel the vehicle. expand Propellant - burn - through nozzle (kinetic (chem. (thermal energy & energy) energy) momentum) Q1 (PDF) 2. Seize mass from the surroundings and set the mass in motion backwards. Use the reaction force to propel vehicle (air-breathing propulsion). Continuously: a) Draw in air. b) Compress it. c) Add fuel and burn (convert chemical energy to thermal energy). d) Expand through a turbine to drive compressor (extract work). e.1) Then expand in a nozzle to convert thermal energy to kinetic energy & momentum (turbojet). e.2) Or expand in a second turbine (extract work), use this to drive a shaft for a fan (turbofan), or a propeller (turboshaft). The fan or propeller impart k.e. & mom. to the air. Remember: Overall goal: take at V (flight speed), throw it out at V + DV o o Q2 (PDF) 1 of 3 04/08/09 6:06 PM Figure 1.1 Schematics of typical military gas turbine engine: J57 turbojet with afterburning. Figure 1.2 A typical high bypass-ratio turbofan (Adapted from Pratt & Whitney). For more examples of real world powerplants, refer to Hill, P. and C. Peterson. Thermodynamics of Propulsion. 2nd Ed. Addison-Wesley, 1991. B. Performance Parameters The two performance parameters of greatest interest for a propulsion system are the force it produces (thrust, T), and the overall efficiency with which it uses energy to produce this force (h ). We overall will begin by looking at the production of thrust using the integral form of the momentum theorem. In the second lecture we will discuss the efficiency of propulsion systems. 2 of 3 04/08/09 6:06 PM C. Propulsion is a systems endeavor There are a multitude of other factors which a propulsion engineer must take into account when designing a device including weight, cost, manufacturability, safety, environmental effects, etc. Thus propulsion is truly a systems endeavor, requiring knowledge of a variety of disciplines: Fluids + thermo + structures + dynamics + controls + chemistry + acoustics + … We will focus mostly on these two disciplines in the Unified propulsion lectures. Previous Unified Propulsion Next 3 of 3 04/08/09 6:06 PM II. Integral Momentum Theorem We can learn a great deal about the overall behavior of propulsion systems using the integral form of the momentum equation. The equation is the same as that used in fluid mechanics. A. An Expression of Newton's 2nd Law (e.g. = d/dt (mv)) 1. Consider two coordinate systems: a) Inertial (labeled with subscript “I” in diagram at right) b) Fixed to vehicle (labeled with subscript “V” in diagram at right). Moves with velocity relative to the inertial coordinate system. All velocities relative to the vehicle- fixed coordinate frame are denoted 2. Newton’s second law for a control volume of fixed mass or All external forces on Force due to change in Change in control volume inertia for accelerating momentum of mass (pressure forces, shear vehicle in c.v. forces, body forces) To explain the above equation further, consider Figure 2.1 Figure 2.1 Falling blocks. 1 of 5 04/08/09 6:06 PM The falling block labeled (a) has a control volume fixed to it. In this case, the first term on the right hand side of the above equation is nonzero since the control volume is accelerating relative to an inertial reference frame. The second term is zero because the block is not accelerating relative to a coordinate system fixed to the control volume. The opposite is true for the falling block labeled (b), which is falling within a fixed control volume. The first term of the above equation is zero in this case because the control volume is not accelerating relative to an inertial reference frame. The second term is nonzero because the block is moving relative to a coordinate system fixed to the control volume. The mathematical result of both cases is as follows, (a) (b) As expected, the result is the same for both. The integral momentum equation reduces to a familiar form, . To continue, the equation can be rewritten as follows, From conservation of mass, so 2 of 5 04/08/09 6:06 PM NOTE: This is a vector equation. 3. Considering only the components in the x-direction Then, by the divergence theorem, where is outward unit normal vector. so where the forces acting on the control volume may be composed of pressure forces, body forces, and skin friction Q6 (PDF) 4. For steady flow, with no acceleration of the vehicle then This is the form we will use most frequently in this class. Q8 (PDF) B. Application of the Integral Momentum Equation to Rockets 3 of 5 04/08/09 6:06 PM Figure 2.2 Control volume for application of momentum theorem to a rocket. Static thrust for a rocket engine C. Application of the Momentum Equation to an Aircraft Engine Figure 2.3 Control volume for application of the momentum theorem to a gas turbine engine. So we have: 4 of 5 04/08/09 6:06 PM Everything that relates to flow through the engine is conventionally called thrust. Everything that relates to the flow on the outside of the engine is conventionally call drag. Therefore, gathering only those terms that relate to the fluid that passes through the engine, we have: Q3 (PDF) Q9 (PDF) Q10 (PDF) The thrust is largely composed of the net change in momentum of the air entering and leaving the engine, with a typically small adjustment for the differences in pressure between the inlet and the exit. We could have arrived at the same equation by considering only the streamtube that passes through the engine as shown below: Figure 2.4 Control volume for flow through engine. Homework P1 (PDF) Homework P2 (PDF) Homework P3 (PDF) Previous Unified Propulsion Next 5 of 5 04/08/09 6:06 PM III. Efficiencies of A/C Engines In the first lecture we arrived at general expressions that related the thrust of a propulsion system to the net changes in momentum, pressure forces, etc. Now we will look at how efficiently the propulsion system converts one form of energy to another on its way to producing thrust. A. Overall Efficiency Thus B. Thermal and Propulsive Efficiency It is often convenient to break the overall efficiency into two parts: thermal efficiency and propulsive efficiency where such that hoverall = hthermal × hprop 1 of 7 04/08/09 6:08 PM The thermal efficiency in this expression is the same as that which we used extensively in Thermodynamics during Fall term. For an ideal Brayton cycle it is a function of the temperature ratio across the compressor. Note that we can use our expression for thrust to rewrite the equation for propulsive efficiency in a more convenient form Then C. Implications of propulsive efficiency for engine design If we consider our expressions for thrust and propulsive efficiency together and we see that as but and as and Also note that for The balance between propulsive efficiency and specific thrust ( thrust per unit mass flow) is shown in Figure 3.1. 2 of 7 04/08/09 6:08 PM Figure 3.1 Propulsive efficiency and specific thrust as a function of exhaust velocity. For fighter aircraft (e.g., the F-22 Raptor) that need high thrust/weight and fly at high speed, it is typical to employ engines with smaller inlet areas and higher thrust per unit mass flow and However, transport aircraft (e.g., the Boeing 777-200) that require higher efficiency and fly at lower speeds usually employ engines with relatively larger inlet areas and lower thrust per unit mass flow and At low flight velocities, the highest propulsive efficiency is typically obtained with a propeller or an unducted fan. A propeller gives a relatively small impulse (Du) to a relatively large mass flow. 3 of 7 04/08/09 6:08 PM Figure 3.2 An advanced, contour-rotating, unducted fan concept. Copyright Rolls-Royce plc. Reproduced with the kind permission of Rolls-Royce plc. Figure 3.3 Propulsive efficiency comparison for various gas turbine engine configurations. Copyright Rolls-Royce plc. Reproduced with the kind permission of Rolls-Royce plc. Q13 (PDF) D. Other expressions for efficiency Sometimes the overall efficiency of aircraft engines is expressed in alternative parameters: specific impulse, I, and thrust specific fuel consumption, TSFC or just SFC. Both of these parameters have dimensions. Specific Impulse (I or I ): sp (units of seconds) Specific Fuel Consumption (SFC or TSFC): 4 of 7 04/08/09 6:08 PM (lbm/hr/lbf or kg/s/N) E. Trends in thermal and propulsive efficiency Figure 3.4 Trends in aircraft engine efficiency (after Pratt & Whitney). Trends in thermal efficiency are driven by increasing compression ratios and corresponding increases in turbine inlet temperature as shown in Figures 3.5 and 3.6. Whereas trends in propulsive efficiency are due to generally higher bypass ratio engines. 5 of 7 04/08/09 6:08 PM Figure 3.5 Pressure ratio trends for commercial transport engines (Epstein, 1998). Figure 3.6 Trends in turbine inlet temperature (Koff, 1991). 6 of 7 04/08/09 6:08 PM Figure 3.7 Trends in engine bypass ratio (Epstein, 1998). Previous Unified Propulsion Next 7 of 7 04/08/09 6:08 PM IV. Aircraft Performance In this lecture we will make the connections between aircraft performance and propulsion system performance. For a vehicle in steady, level flight, the thrust force is equal to the drag force, and lift is equal to weight. Any thrust available in excess of that required to overcome the drag can be applied to accelerate the vehicle (increasing kinetic energy) or to cause the vehicle to climb (increasing potential energy). Figure 4.1 Force balance for aircraft in steady level flight. Q14 (PDF) A. Vehicle Drag Recall from fluids that drag takes the form shown below, being composed of a part termed parasitic drag that increases with the square of the flight velocity, and a part called induced drag, or drag due to lift, that decreases in proportion to the inverse of the flight velocity. Figure 4.2 Components of vehicle drag. 1 of 10 04/08/09 6:09 PM where and Thus or The minimum drag is a condition of interest. We can see that for a given weight, it occurs at the condition of maximum lift-to-drag ratio We can find a relationship for the maximum lift-to-drag ratio by setting from which we find that and and 2 of 10 04/08/09 6:09 PM B. Power Required Now we can look at the propulsion system requirements to maintain steady level flight since Thus the power required (for steady level flight) takes the form Figure 4.3 Typical power required curve for an aircraft. The velocity for minimum power is obtained by taking the derivative of the equation for P req with respect to V and setting it equal to zero. As we will see shortly, maximum endurance (time aloft) occurs when the minimum power is used to maintain steady level flight. Maximum range (distance traveled) is obtained when the aircraft is flown at the most aerodynamically efficient condition (maximum C /C ). L D Homework P4 (PDF) 3 of 10 04/08/09 6:09 PM To see the implications of excess power, visit NASA Glenn - GO C. Aircraft Range, the Breguet Range Equation Again, for steady, level flight, The weight of the aircraft changes in response to the fuel burned or applying the initial conditions, at t = 0 W = W \ const. = ln W initial initial the time the aircraft has flown corresponds to the amount of fuel burned, therefore then multiplying by the flight velocity we arrive at the Breguet Range Equation which applies for situations where Isp and flight velocity are constant over the flight. 4 of 10 04/08/09 6:09 PM

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