Lecture 6 Turbojet Turbofan Increasing thrust (afterburning) Optimization Cycle selection (mission dependency) Indication of thrust Convergent-divergent nozzles Turbofan Cycle optimization Mixing Increasing thrust (afterburning) Turboprops Problem 3.2

Optimization of the turbojet Specific thrust is strongly dependent on T03 At constant pressure ratio an increase in T03 will cause some increase in SFC Parameter variation is based on Example 3.1 data with polytropic efficiencies

Recall shaft power cycle behavior For a given pressure ratio it is clear that ηcycle increases! Opposite trend

Energy lost in jet increases faster than thrust Energy lost in jet increases faster than thrust. The shaft power cycle does not experience the loss in SFC due to decreasing propulsive efficiency.

High specific thrust is still attractive High T3 => high specific thrust => small engine Reduction in engine size => reduced drag which off-sets this effect In particular for high speed flight

Optimization of the turbojet Same trend in SFC as a function of pressure ratio, when compared with real shaft power cycle Note that if pressure ratios where increased considerably above rc=25, SFC would start to increase again. Which region of pressure ratios does the plot correspond to when you look in the shaft power cycle diagram!

Cycle selection High t3 => expensive alloys, complex (and expensive) cooling High rc => many stages. Ultimately multi-spool configurations Selection of cycle parameters depend on aircraft mission

Cycle selection Business jets: Low cost (by low pressure ratios and cheap turbine material) Fuel consumption less important Range may be important (=>cheap turbojets have been supplanted by cheap turbofans/turboprops)

Lifting engines & long range subsonic Lifting engines (VTOL) Max. thrust per unit weight (compressor pressure ratio set by what could be achieved by one turbine rotor) short life - but run only for short period of time Thrust to weight > 20!!! Modern military engines have around 10. high cost ok (military) Long range subsonic early - high pressure turbojet Today high pressure ratio, high bypass ratio turbofans The XJ99 (vertical engine above) operated at 1360 C, very short combustor (11.5 inch). Counter-rotating shafts allowed the elimination of turbine stators! 9000 lb thrust for a weight around 440 lb (Thrust to weight = 20.5).

Indication of thrust No direct method for measuring engine thrust during flight exists!!! Indirect techniques exist

Theory 6.1 - Indication of thrust P04 and T04 can be measured. Pa is known and the nozzle area is assumed to be fixed (assume choked operation and ηj =100%). The thrust is given by (sea level static): pc

Theory 6.1 - Indication of thrust Continuity, the gas law and the first law give: Which in introduced in the thrust expression yields: Tc

Theory 6.1 - Indication of thrust But p04/p5 is the critical pressure ratio =>

Indication of thrust In sea level static thrust can thus be directly related to the engine pressure ratio (EPR)! When we have ram pressure ratio we have: Thus we have an expression also for in flight thrust estimation

Velocity-Area relation for compressible flow Combining the continuity and momentum equations in differential form for compressible flow gives (Appendix A – Eq. 9): What does this tell us?

Convergent divergent nozzles It can be shown:

So what was this…. ?

Lets undertake some back pressure variations Pe is minutely below Po => small wind. Acceleration in convergent portion and deceleration in divergent There will be some value of Pe at which the flow will just barely go sonic at the throat. If Pe is reduced further the flow in the convergent portion will remain “frozen”

Lets undertake some back pressure variations For values below Pe3 but higher than Pperfectly expanded a shock will stand in the divergent part It will stand exactly in the exit when the pressure behind the normal shock at the design Mach number is equal to Pe For lower pressures the shock will form an oblique shock pattern outside the nozzle which is reduced in strength until the isentropic pressure is attained.

When do we use convergent-divergent nozzles? The critical pressure ratio can be estimated with: For nozzle pressure ratios < 3 the losses incurred are greater in the convergent-divergent nozzles Even at the isentropic condition!!!

Supersonic flight Ram pressure ratio => Exit pressure ratio is increased (EPR) Pressure ratio for high Mach numbers (2-3) is often 10-20 Variable exit/throat area has to be allowed for Divergence angle less than 30°. Exit diameter less than engine diameter to not incur additional drag Noise suppression and thrust reversing will be harder to implement

Thrust reversing On icy, wet or snow covered runways the efficiency of the aircraft brakes may be reduced Reversing the aircraft engine gas stream may allow for efficient braking

Thrust reversing

Thrust reversing

The turbofan engine Improve ηp by reducing the mean jet velocity (in comparison with turbojet) Reduce noise (in comparison with turbojet) Example 3.2 - homework Fan is driven by LP turbine If fan and bypass streams are mixed additional equations are necessary

The turbofan engine

FPR (Fan Pressure Ratio) and specific thrust For military aircraft engines mixers are used Fan exit pressure and turbine exit pressure must be similar for efficient mixing => FPR and EPR are similar EPR sets thrust => FPR sets thrust

Optimization of the turbofan Four available variables: FPR = Fan Pressure Ratio BPR = Bypass Ratio TIT = Turbine inlet temperature (T4) OPR = Overall pressure ratio For a fixed OPR and BPR one obtains: Fig 3.26 We now get OPR,BPR and T4 as well as FPR=F(T4) because we have optima in thrust and SFC. Select globally best SFC => FPR and T4 given for every OPR, BPR. Increased T7 => more energy extraction needed before the optimal velocity is obtained

Optimization of turbofan Perform operation for a “grid” of OPR and BPR. Select the globally best point! Optimization should be computerized Installation losses and weight estimation Life Cycle Cost Engine must complete mission!!! Take-off Top of climb Cruise (most important)

Mixing For afterburning turbofans => only one reheat system. More oxygen is made available (compared to an unmixed core flow) Subsonic transport – small but valuable reduction in SFC An energy balance gives:

Mixing – obtaining p07 A momentum balance gives: M6 (turbine design criteria), T06, P06 are known which gives P6. A6 is obtained from the “X-function”: With p6=p2 we get M2 (p02 is known). mc, Rc, M2, p02 and T02 gives A2 from the X-function. Cc from continuity. mC7+A7P7 is now obtained from the momentum balance. A7=A6+A2 and m =ρC7A7 = (P7/RmT7)C7A7

Mixing T07 is known but both P7 and P07 are unknown. Guess M7 => T7 from T07 and C7 from Mach number definition. Continuity => p7. Check that momentum equation is satisfied. If not improve guess of M7. Pooh….

Increasing thrust Re-design to allow for increased mass flow or increased T3. Temporary increase of thrust (augmentation) Take-off, acceleration from subsonic to supersonic, combat maneuvering Methods for augmentation Liquid injection Afterburning

Liquid injection Spray water methanol (lowers freezing point of water and burns) mixture in compressor during take-off and climb Equivalent drop in compressor temperature => less compressor work => more thrust Secondary effect: thrust increases since mass flow increases Partly outdated method

Afterburning Burn additional fuel in the jet pipe No rotating parts => maximum allowable temperature is higher. Typically around 2000 K Accept penalty in SFC Poor “cycle” (better at high speed – for fixed momentum drag an increase in gross thurst => considerably greater incerease in net thrust) Concordes acceleration from subsonic to supersonic => reduction in fuel consumption in spite of short term increase in fuel flow. For mixed turbofans, provisions for burning even more fuel exist (low inlet temperature and little oxygen consumed in air). Even worse cycle in that case though! Why ?!

Afterburning Speed of sound in the nozzle exit => variable area nozzle required! Aim is to maintain gas generator at same condition => variable area necessary to pass the same mass flow at a much lower density.

Turboprop Jet and propeller deliver combined propulsion Most designs operate with nozzle unchoked and cruise (optimally) around M=0.6. Turboprops have lost market share for commuting and airlines to turbofan-powered aircraft SAAB-Fairchild 340 aircraft.

Common cores Same core High pressure core common to different engines Cut development cost Even from civil to military is possible Same core

Learning goals Be able to explain why an increase in T3 may still be attractive in turbojet cycles, although the SFC is increased Be able to relate this increase to performance gains of turbofan engines by considering the propulsive efficiency and designing for higher BPR Be able suggest suitable engine cycle parameters (pressure ratio and T3 for different missions) Be informed about how the delivered engine thrust is indicated Be familiar with convergent-divergent nozzles, thrust reversing, mixing, thrust augmentation (ways of increasing thrust)