Jet Engine. Figure 1 Jet engine

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1 Jet Engne Prof. Dr. Mustafa Cavcar Anadolu Unversty, School of Cvl Avaton Esksehr, urkey GROSS HRUS INAKE MOMENUM DRAG NE HRUS Fgure 1 Jet engne he thrust for a turboet engne can be derved from Newton s second law whch mples that the force equals to the tme rate of change of momentum: F = d( mv ) dt where mv s the momentum. he net thrust of a et engne s the dfference between the outgong exhaust gas momentum flow and ncomng ar momentum flow. Outgong exhaust gas momentum s usually referred the gross thrust, and ncomng ar momentum flow s called momentum drag or ram drag. Snce m & = dm / dt s the mass flow rate of the ar passng through the engne, then the gross thrust g = mv & + A ( p pam ) where V = exhaust gas velocty, A = area of et nozzle, p = statc pressure at the et nozzle dscharge, and = atmospherc pressure. pam he ncomng ar momentum flow (momentum drag) = m& V Prof. Dr. Mustafa Cavcar,

2 where V s the ncomng ar velocty. herefore, the net thrust Net thrust = Gross thrust - Momentum drag = [ mv & + A ( p p )] = m& ( V V ) + A ( p am mv & p ) am Factors Affectng Jet hrust Ar Velocty Incomng ar velocty affects the thrust n two dfferent and opposte ways. When the arcraft s statc, as when an engne s beng run up pror to take-off at the end of a runway, momentum drag s equal to zero, because V = 0. However, as the arcraft commences to move, the velocty of the ar enterng the engne also begns to ncrease because of the speed of the arcraft. herefore, the dfference between V and V Fgure 2 Jet engne thrust versus arspeed [1]. wll become less as arspeed, or V, ncreases. On the other hand, as the arcraft gans speed down a runway, the movement of the arcraft relatve to the outsde ar causes ar to be rammed nto the engne nlet duct. hs compresson of ar n an nlet duct arsng from forward moton s called ram pressure or ram effect. he ram effect both ncreases the ar mass flow to the engne and the ntake pressure, and consequently, ncreases the thrust. Fgure 2 shows how the thrust vares wth arspeed consderng both velocty dfference varaton and ram effects. However, ram pressure rse s not sgnfcant at lower speeds, thus t cannot offset the effect of ( V V ) dfference and the thrust decreases as the arcraft speeds up durng take-off. hrust decrease due to arspeed ncrease durng take-off s more sgnfcant for the turbofan engnes as shown n Fgure 3. Because the pure et and Prof. Dr. Mustafa Cavcar,

3 the lower by-pass rato engnes have less arflow per unt of thrust, they suffer less momentum drag as speed ncreases. Fgure 3 ake-off thrust varaton for varous engnes [2]. Ar emperature he thrust generated by a et engne s nversely proportonal wth the ambent ar temperature, thus the thrust decreases as the ar temperature ncreases. However, ths also means an ncrease of thrust when the temperature decreases, so that an engne may generate hgher thrust than ts desgn ratng at lower ambent ar temperatures. Hgher thrust above the desgn ratng can harm the engne. For ths reason, engnes are restrcted Fgure 4 hrust versus ar temperature for a flat to a maxmum thrust. hs rated engne. thrust restrcton s called flat ratng, and engnes wth restrcted maxmum take-off thrust are called flat rated. At a gven pressure alttude, temperature has no nfluence on engne takeoff thrust, below the so-called reference temperature ( ref ) or flat ratng Prof. Dr. Mustafa Cavcar,

4 temperature. Above ths reference temperature, engne thrust s lmted by the Exhaust Gas emperature (EG). he consequence s that the avalable thrust decreases as the temperature ncreases [3]. hrust versus temperature for a flat rated engne s shown n Fgure 4. Alttude he effect of alttude on thrust s a functon of densty. As the alttude ncreases, the pressure and densty decreases so does the thrust, but as the temperature decreases, the thrust ncreases. However, the pressure and densty of the outsde ar decreases faster than the temperature, so an engne actually produces less thrust as the alttude s ncreased [1]. Because Fgure 5 hrust versus alttude. temperature stays constant n the stratosphere whle pressure and densty are decreasng as the alttude ncreases, thrust wll drop off more rapdly n the stratosphere as shown n Fgure 5. Combned Effects of Velocty and Alttude Fgure 6 hrust versus Mach number for P&WC J15D-4C urbofan engne [4]. Fgure 6 shows the maxmum cruse thrust varaton of J15D-4C turbofan engne wth the Mach number for varous alttudes. Snce true arspeed s proportonal Prof. Dr. Mustafa Cavcar,

5 wth the Mach number at a gven pressure alttude, then these varatons wll be smlar for thrust versus arspeed case. As shown n the fgure, thrust decrease to the velocty ncrease s more sgnfcant at lower alttudes. As the alttude ncreases, the thrust varaton due to arspeed flattens, and even a slght ncrease occurs at hgher arspeeds. References [1] Unted echnologes Pratt & Whtney, he Arcraft Gas urbne Engne and Its Operaton, P&W Oper. Instr. 200, [2] R.S. Shevell, Fundamentals of Flght, Prentce Hall, Englewood Clffs, [3] Arbus Industre, Gettng to Grps wth Arcraft Performance, Blagnac, [4] Unted echnologes Pratt & Whtney Canada, J15D-4C Fact Sheet, Longueul, Prof. Dr. Mustafa Cavcar,