Zinn Due 10 ZI Og Problem Set 5 Ramjets and Turbojets Homework solutions sholJlrl be nerlt on web page i nrl Inoir 8l1v oresented SAA fnrm t re uifp rr ntc For the following problems please include a sketch of the flow system and indicate clearly your choice of control surface Also indicate on your figure your definitions of forces Always indicate any assumptions you make If you use any results or equations from the class notes or text in you solutions please note and reference them but you better be sure they are applicable to the problem at hand Try to solve the problem algebraically first Only use numbers values in the final steps of your solution 1 Ideal Ramjet Consider a ramjet used as the propulsion source for a missile The missile is designed to operate at an altitude where the ambient temperature is 250 K and the pressure is 40 kPa The ramjet operates on JP 8 fuel and can withstand a maximum temperature of 2100 K Assume the flow through the ramjet and around the missile is ideal inviscid variable area inlets and nozzles no shocks etc and that air is a thermally and calorically perfect gas with a molecular weight of 28 8 and a specific heat c p of 1200 J kg K a What is the maximum speed u that the missile could achieve in level flight b What would the velocity be of the gas exiting the nozzle i e ue at this maximum operating flight speed 2 Ideal Ramjet V5 Turbojet Performance Text problem 5 8 You are to assume that both engines are ideal no aerodynamic losses means the components are reversible Also note you are to assume constant gas properties cp y etc throughout the engine Do not assume the mass of added fuel is negligible This means the answers in the back are not the same that you will get though they may be close a As asked in the book compare the engine s TSFC give answers in kg kN s b IN ADDITION compare the specific thrusts of the two engines 3 Turbine Cooling with Bleed Air Consider modifying a turbojet as shown in the figure below Some of the air from the compressor exhaust is diverted to the turbine to cool the turbine blades This bleed air air bled from the compressor is injected into the turbine blades flows through small passages in the blades the exits the blades and joins with the main flow exiting the turbine The amount of air bled from the compressor is given by the bleed ratio b which is defined by b 0 ri lb ri la By cooling the turbine blades the maximum temperature in the engine can be increased i e the maximum temperature is now a function of the bleed ratio T max T max b The goal is to increase the engine thrust by operating at a higher fuel air ratio 6 The analysis of such an engine is complicated if one was to completely account for all the processes involved in reintroducing the air through the holes in the turbine blades to the main in a flow For simplicity Turbojet with bleed thermodynamics analysis you could air cooling assume the bleed air returns to the main air flow not in the turbine but just at the turbine exhaust In other words the turbine exhaust mixes with the bleed air to produce a new exhaust stream see modified schematic below You could also assume that the bleed air has the same stagnation temperature it had when it exited the compressor T03 T 03 Q J a Derive an equation that describes the stagnation temperature at the exit of the turbine after bleed reinjection T 06 based on the combustor exhaust temperature which you can assume to be equal to T max the compressor exit temperature T 03 b f the fuel air ratio the power required to run the compressor per unit mass flowrate entering the compressor and the specific heat of the gas cpt For simplicity you can assume that the gas is calorically perfect 1 1 I I 1 I I I I I C I 10 V Simplified schematic of turbojet with bleed air mixing with turbine exhaust b Derive an equation that describes the stagnation pressure at the exit of the turbine after bleed reinjection Po6 as a function of b f P05 T 031T05 T061T 05 P03 P05 and Yl where P03 is the stagnation of the bleed air before it mixes with the turbine exhaust You may assume that the mixing of the bleed air and turbine exhaust occurs reversibly