By Brian J. Cantwell

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6 PROPULSIVE EFFICIENCY It is instructive to decompose the overall efficiency into an aerodynamic factor and a thermal factor. Thus the overall efficiency is written as the product of a propulsive and thermal efficiency. 30) If the exhaust is fully expanded so that P e = P 0 and the fuel mass flow is much less than the air mass flow m˙ f « m˙ a the propulsive efficiency reduces to 2U 0 η pr = --------------------- . 31) This is quite a general result and shows the fundamentally aerodynamic nature of the propulsive efficiency.

44) T 1 T ------------- =  ----------- ------------γ M  P A m˙ a a 0 0 0 0 Normalizing the thrust by P 0 A 0 produces a number that compares the thrust to a force equal to the ambient pressure multiplied by the capture area. In order to overcome drag it is essential that this is a number considerably larger than one. 13 2/12/09 Engine notation and T 0 is the temperature of the ambient air. 16)). Thus 1 ⁄ ( f τ f ) is generally a fraction somewhat less than one. 10 ENGINE NOTATION An important part of analyzing the performance of a propulsion system has to do with being able to determine how each component of the engine contributes to the overall thrust and specific impulse.

5 Step 2 - Introduce a burner and add heat to the flow. As the heat is added the mass flow is conserved. 5) implies that f ( M 4 ) must increase and the Mach number downstream of the burner decreases. There is a limit to the amount of heat that can be added to this flow and the limit occurs when f ( M 4 ) attains its maximum value of one. At this point the flow looks like the following. 6 Step 3 - Introduce sufficient heat to bring the exit Mach number to a value slightly greater than one. 7) before unstart Now suppose the temperature at station 4 is increased very slightly.

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