AAE 339 Aerospace Propulsion Summer 2020 Homework Assignment 3 1. Given that an airliner has a range of 6000 miles using 200 tons of JP4 fuel, and its dry weight (with no fuel) is 800 tons. Estimate the range of the aircraft burning (a) the same mass of liquid hydrogen fuel, and (b) the same volume of liquid hydrogen fuel. Use the range formula in Hill, page 152 Eq. 5.19, but note that there should be parentheses around [ln (m1/m2)], so that the range formula is: s = (QR/g) ηo (L/D) [ln (m1/m2)] The dry mass of the aircraft is 800 tons. Assume that the flight speed is varied so that the L/D and the overall efficiency remain the same for the different fuel types. JP4 Density = 800.0 kg/m3 Heating value = 45,000 kJ/kg Liquid Hydrogen Density = 70.8 kg/m3 Heating Value = 120,900 kJ/kg 2. Consider an ideal ramjet engine. Plot the specific thrust, TSFC, and fuel/air ratio as a function of Mach number (range: 0 < M < 7) for the following input data. Tatm = 216.7 K γ = 1.4 Cp = 1005 J/kg-K QR = 42800kJ /kg (a) To4 = Tmax = 1500 K (b) To4 = Tmax = 2000 K (c) To4 = Tmax = 2500 K where To4 = combustor outlet stagnation temperature. 3. A turbojet engine works on an open cycle that is closely related to the Brayton cycle. The main difference is that the air is expanded in the turbine so that the work output exactly matches the compressor work input. Additional expansion is then accomplished in a nozzle to produce a high exhaust velocity jet for thrust. In this assignment, we will analyze the open-cycle turbojet cycle using the procedures given in class for the Brayton cycle. For simplicity, we will study the case of static sea-level thrust, i.e., the jet engine is stationary, which means that the air intake velocity into the engine is negligibly small. You may use these additional assumptions: 1 • • • • Reversible adiabatic processes for the compressor, turbine and nozzle expansion. Combustion is modeled as constant pressure heat-addition. Neglect the mass of fuel added. Potential energy differences are negligible throughout and kinetic energy is negligible everywhere except the nozzle exit. Take air to be a perfect gas with constant specific heats, R=287 J/kg-K and γ =1.4. (1) The intake air at the compressor inlet is at the ambient conditions of 300 K and 0.1 MPa. If the compressor has a pressure ratio of 30, what is the compressor exit temperature? How much work input does the compressor require? (2) The constant pressure heat addition process has an exit temperature of 1500 K. How much heat is added in the burner? (3) The turbine expands the air until the work extracted exactly equals the compressor work input. What is the exit temperature of the turbine? What is the exit pressure? (4) The air from the turbine outlet is then further expanded in a nozzle in a reversible adiabatic expansion down to the ambient pressure of 0.1 MPa. What is the exhaust temperature? Determine the exhaust velocity. Note that there are no work or heat transfers in the ideal nozzle expansion and that kinetic energy is not negligible at the nozzle exit. (5) Determine the nozzle exhaust velocity using the Isentropic Tables (handout). Note that the nozzle inlet temperature is the same as the stagnation temperature because the velocity is negligible at that location. Verify that your answer agrees with that in Part 4. (6) Represent the above turbojet cycle in a T-s diagram. Mark out all the states and processes. (7) Defining the kinetic energy of the exhaust jet as the useful work output of the jet engine, calculate the efficiency of the engine. (8) Speculate on how the efficiency may be improved. You may wish to use some of the insights gained from the Brayton cycle analysis as well as consider the nozzle expansion process. Lecture 9 Introduction to Chapter 5, The Gas Turbine Engine Cycle Rayleigh flow example: Scramjet combustor analysis Performance Parameters • Efficiency • Thrust • Range SCRamjet Combustor example: Suppose the air-force is interested in the use of hydrogen fuel in a scramjet combustor as a mean of high-speed air-breathing propulsion Assume: Complete mixing and combustion Find: Turbojets, Turbofans, Turboprops Turbojet Thrust Single-Stream Air-Breathing Engine T above is ‘net thrust’ For static tests, u = 0, T is ‘gross thrust’ Difference is ‘ram drag’: Fn = Fg – mau If pe ~ pa, and fuel flowrate is neglected Simple Thrust Equation Performance Specific Thrust Thrust Specific Fuel Consumption where kg/N-hr or lb/lbf-hr Ramjets 0.2 2 Turbojets 0.1 1 Turbofans 0.05 0.5 Efficiency Work produced/heat energy supplied In the engine: Fuel energy is converted to mechanical energy with efficiency ht Mechanical energy is converted to useful thrust with efficiency hp Overall Efficiency: ho = useful work done on vehicle energy supplied by fuel Power Mechanical power (work/time) is DKE/time Chemical power is Thrust power is Conservation of Energy Power Fuel Power (chemical energy/time) Thermal Efficiency Jet Power (kinetic energy/time) Propulsion Efficiency Thrust Power (work/time) Power Fuel Power Jet Power Thrust Power Overall Efficiency Thermal Efficiency Jet Power Fuel Power Propulsion Efficiency Thrust Power Jet Power Max when ue=u or Zero Thrust! Overall Efficiency Thrust Power Fuel Power Average ho ~ 0.30 Max when u=ue/2 Turbofan Substitute Energy Balance Specific Thrust Turbofan Efficiencies Aircraft Range How far can an airplane fly, and why? L T D Force balance for an aircraft in steady level flight W Lecture 11 Chapter 5, The Gas Turbine Engine Cycle, cont Performance Parameters - Efficiency, Thrust, Range the Brayton Cycle Engine Design - Goals • Meet required thrust thought flight envelop - aircraft: takeoff, climb, cruise,… - spacecraft: launch, orbit transfer, planetary mission,… • High efficiency - minimize amount of fuel (energy input) required to provide delivered thrust (energy output) • Constraints - materials limitations (max temperature, stress,…) - low emissions: NOx, soot, toxics, … - other: size, lifetime, manufacturability, maintainability Gas Turbine Engines Brayton Cycle Open-Cycle Closed-Cycle Ideal Brayton Cycle 1-2 : Isentropic compression (in a compressor) 2-3 : Constant pressure heat addition 3-4 : Isentropic expansion (in a turbine) 4-1 : Constant pressure heat rejection Closed-Cycle Gas Turbine neglect kinetic and potential energies q1 q2 Closed-Cycle Gas Turbine Treating air as an ideal gas with constant specific heat (‘cold-air-standard’ analysis) with isentropic compression and expansion, and constantpressure heat transfer: Closed-Cycle Gas Turbine T1 cycle = 1 − T2 cycle = 1 − 1  P2     P1   −1  How to improve efficiency? - Increase pressure ratio rp=p2/p1, increase specific heat ratio  For aero-propulsion, pressure ratio is practically limited - weight - compression temperature Pressure Ratio and Temperature Ratio Area under each curve represents specific work, w 1: low pressure ratio, large q, low thermal  2: moderate pressure ratio, less q, higher w than (1) 3: high pressure ratio, least q, high thermal , lower w than (2) Specific Work-Optimized Pressure Ratio   p2   T3  2( −1)   =    p1 opt  T1  Real Brayton Cycle Ideal Real Irreversibilities: - Pressure drop in heat exchanger - More work input to compressor - Less work output from turbine Real Gas Turbine Cycle Diffusion and compression Component Parameters Component Effect Symbol Diffuser Total pressure recovery pd Compressor Efficiency Fan Efficiency/bypass ratio c f, b, Turbine Efficiency t Propeller Efficiency p Shaft Efficiency Combustor Efficiency/total pressure ratio m b, pb Afterburner Efficiency/total pressure ratio ab, pab Primary nozzle Efficiency n Fan nozzle Efficiency Bypass duct Total pressure ratio/split ratio fn pu, s Bypass mixer Total pressure ratio pm Exhaust Pressure ratio pe Real Brayton Cycle - Compressor Process Given: compressor pressure ratio is 20 and compressor efficiency is 0.80, p1=0.1 MPa the ratio of the work required in an isentropic process to that required in the actual process Real Real Brayton Cycle - Compressor Process Given: compressor pressure ratio is 20 and compressor efficiency is 0.80, p1=0.1 MPa Real Real Brayton Cycle - Burner Process Given Real Where 1-rb is the fractional pressure loss in the combustor Real Brayton Cycle - Turbine Process Assume a 5% pressure loss in constant pressure heat rejection, ie, p4/p1 = 1.05 Real Real Brayton Cycle - Turbine Process Assume a 5% pressure loss in constant pressure heat rejection, ie, p4/p1 = 1.05 Real Real Brayton Cycle - Cycle Performance Real Remember this Brayton cycle is ‘closed’ and is only representative of the actual gas turbine cycle Comparisons Carnot Efficiency Ideal Brayton Efficiency Real Brayton Efficiency representing a maximum work, theoretical cycle Lecture 12 Performance of Ramjets, Turbojets, and Turbofans Engine Design Sensitivity to Flight Mach Number Kahn, Mechanics of Jet Propulsion, 2005 Ramjet Engine • Most efficient engine • Simplest air breathing engine • Doesn’t have compressor or turbine • High tolerance to high temperatures • Ideal for very high speed flight X-15 with Ramjet engine https://www.youtube.com/watch?v=c_4UIfHNAZE X-15 The Ultimate Flying Machine Ramjet Engine Diffuser Slows down flow from supersonic to subsonic speeds Adverse pressure gradient can be problem Temperature Increases Pressure Increases Combustor Subsonic constant pressure combustion Nozzle Ideal Expansion to ambient pressure Ramjet Engine Ramjet Advantages: •Low weight •High thrust to weight ratio •No moving parts •Most efficient air breathing engine •Can reach speeds up to Mach 6.0 Turbojet Disadvantages: • Speed must be supersonic • Cannot produce thrust when engine is static • Air must slow down to subsonic speeds for ignition in the burner • As air approaches Mach 6.0, it is too hot to burn SR-71 Blackbird Turbojet/Ramjet Hybrid http://www.youtube.com/watch?v=Ev8Lqm5Ngi8&f eature=related http://www.1000pictures.com/aircraft/special/index.htm Importance of Shock Wave • One way supersonic flow can be compressed • Fluid properties can change almost instantaneously • Shock appears when supersonic flow in pipe is decelerated http://www.physicspost.com Importance of Shock Wave http://www.physicspost.com Ideal Ramjet Engine Ideal Ramjet Thrust and Fuel Consumption Ideal Ramjet Thrust and Fuel Consumption Performance Curves 1000 m/s 0.7 Question: Why does the specific thrust increase with Mach number and then decrease? 0.6 0.42 J-58 Turbo-ramjet Engine Specifications: Model: Pratt & Whitney J-58 Compressor: 9-stage, axial flow, single spool Turbine: two-stage axial flow Thrust: 32,500 lbs. with afterburner Weight: approx. 6,000 lbs. Max. operating altitude: above 80,000 ft. J-58 Engine and Spike J-58 Airflow and Temperature https://www.youtube.com/watch?v=F3ao5S CedIk&t=39s J-58 Engine Testing in Afterburner J-58 Inlet Shocks Realistic Ramjet Cycle Diffusers are prone to irreversibilities: Viscous Effects Shocks Scramjet https://www.youtube.com/watch?v=XV8AfgbGh5M&t=250s
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