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Work done on turbine: EW,t = (m ̇a + m ̇f )(h04 − h05) (4) Heat added to system during combustion: Qin = (m ̇a + m ̇f )h04 − m ̇ah03 (5) Heat rejected from the system in the gas stream: Qout = (m ̇a + m ̇f )h06 − m ̇ah00 (6) The work done by the gas on the turbine is in a turbo jet only used to drive the com- pressor and various auxiliaries. The energy left in the gas stream after the turbine and how that is converted to propulsive force is what is of interest in this context. Using conservation of energy, assuming that the change in potential energy due to elevation is negligible and assuming conservation of mass (neglecting fuel flow since m ̇ air >> m ̇ fuel) qout + 12(V62 − V02) = qin + (eW,c − eW,t) (7) Using the thrust equation from the previous section, eq 1, the kinetic energy term can be written as V62 −V02 =(V6 −V0)(V6 +V0)=(V6 +V0)Fn (8) m ̇ Substituting back into eq 7, and assuming eW,in − eW,out = 0, since in the ideal case no work is done by the shaft, gives an expression for thrust Fn = Vm ̇ [(qin − qout)] (9) avg Define the over all efficiency of the engine, the ratio of work done by the exiting stream to the rate of heat added ηo=FnV0= V0 (1−qout) (10) m ̇qin Vavg qin Propulsive efficiency, eq 2 can be rewritten as ηp = V0/Vavg, thus overall efficiency can be stated as a product of propulsive and thermal efficiency, ηo = ηpηth, where thermal efficiency is defined as ηth =1−qout =1−h06−h00 (11) qin h04 − h03 Both heat in and heat out are constant pressure processes, approximating constant specific heat Cp = Cp,avg, equation 11 becomes C(T −T ) T00T06 −1 p 06 00 T00 ηth=1−Cp(T04−T03)=1−T03T04 −1 (12) T03 9PDF Image | Design and construction of a simple turbojet engine
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