Review AE 430 Aircraft Propulsion Systems Gustaaf Jacobs

Note Ø Bring Anderson to exam for tables.

Goals Ø Understand analyze gas turbine engines: l Turbojet l Turbofan (turbojet + fanned propeller)! l Ramjet

Analysis Ø Analysis l Energy control volume per engine component • Pressure and temperature changes for ideal engine • With efficiency definitions: pressure and temperature changes for non-ideal engine l Control Volume over complete engine: • Momentum balance=> thrust, propulsion efficiency • Energy balance or thermo analysis: l Brayton cycle: Thermal efficiency

Analysis Ø Detailed component analysis l Inlets • Subsonic flow analysis in 1 D l Pressure recovery estimate • Shock analysis in 1 D inlet (converging-diverging) l l Estimate of losses External deceleration principles • 2 D shock external deceleration l l Oblique shock analysis Estimate spillage and losses

Analysis Ø Combustor l Qualitative idea of combustion physics • Fuel-air ratio (stoichiometric) • Flame speed • Flame holding l Ø Quantitative: pressure loss with 1 D channel flow analysis + heat addition=> not treated due to time restrictions Compressor/Turbine l l Estimate of pressure, temperature recovery with momentum and energy balance Velocity triangles analysis: first order estimate of compressor aerodynamics

Control Volume Analysis: Basic Idea T

Engine Performance Parameters Ø Propulsion efficiency, ratio thrust power to add kinetic energy Ø Thermal efficiency, ratio added kinetic energy to total energy consumption Total efficiency Ø Thrust Specific Fuel Consumption Ø

Thermodynamic cycles Diagram that looks at the change of state variables at various stage of the engine Ø Ideal gas turbine: Brayton cycle Ø Isentropic compression, constant p heat addition, constant p heat rejection Ø First law of thermodynamics analysis gives expression for ηth Ø

Ideal Ramjet Ø Analyze each stage using thermodynamic analysis with energy balance and isentropic relations to find: l l l P, T, p 0, T 0 ve, T/ma f

Ideal Ramjet Ø pt, 0=pt, 7, p 0=p 7 => M 0=M 7 Ø T 7 > T 0 since heat is added during combustion, so v 7>v 0 => Thrust Ø Fuel to air ratio, use first law:

Non-ideal ramjet Ø Non-isentropic compression and expansion: losses lead to lowered total pressure and temperature Ø Define total pressure ratios before and after components to quantify the efficiency: l rc, rn, rd

Non-Ideal turbojet Ø Major difference with ramjet ptotal is not constant like in ramjet but increases and decrease in compressor and turbine. To find these ratios work from front to back through each stage Ø Specific: compressor and turbine power are the same so (first law) Ø

Definition of component efficiencies Ø E. g. diffuser Relates actual total temperature increase to an isentropic temperature increase Ø The isentropic temperature can be related to the total pressure using isentropic relations Ø The total pressure distribution is determined from front to back. Ø Each stage has an effiiciency like this. Ø

Turbofan Ø Example on blackboard.

Detailed analysis of components

Intakes Convert kinetic energy to pressure Ø Subsonic Ø l l l External acceleration or decelleration depends on intake design and speed of aircraft High speed: spillage. Low speed: stall. Diffuser design: prevent stall: use computational (XFOIL, MSES) and experimental validation to design

Supersonic intake 1 D: converging-diverging nozzle Ø Ideal: isentropic decelleration supersonic to throat, subsonic after throat Ø Not possible in practice Ø Shocks in nozzle Ø Possible design: shock close to throat and M~1 at throat Ø Need overspeeding to swallow shock in throat. Ø Kantrowitz-Donaldson: design condition is shock swallowing condition. Ø

Supersonic diffuser Ø 2 -D nozzle l l Use multiple oblique shocks to slow flow down with small losses in total pressure Use oblique shock analysis

Combustor + Compressor Ø Discussed in last classes