Lecture P3: Integral Momentum Equation and Engine Efficiency

A copy of the slides as presented in lecture is available here (PDF). We completed the discussion of using the integral momentum equation to calculate engine thrust and then discussed definitions of engine efficiency. We concluded with latter with a description of why engines look the way they do. We did two PRS questions (PRS #1, PRS#2). The first was designed to provide additional practice in applying the integral momentum equation. Note there are two ways to go about solving a problem like this (both are given under the "Answer" button on the PRS question). The objective of the second PRS question was to give you a little practice and familiarity with applying the different definitions of engine efficiency.

Next lecture we will discuss aircraft performance. Please read Chapter IV of the notes.

Mud responses

(8 mud cards, xx students attended class)

1) I am still a little unclear o the PRS question Q10. Why is u dot n = -usin(theta) (and related questions)? (2 students) Because that is the dot product of the vector u and the outward normal unit vector.

2) I don't understand why a higher bypass ratio makes for a more efficienct engine. It seems like it should be the other way around to me? (1 student) The higher the velocity of the exhaust jet relative to the flow around it (which is moving at uo, the flight velocity), the more waste energy is dissipated through viscous forces in the jet. So the most efficient way to convert energy in an exhaust jet into propulsive power is to give a large mass flow of air a small change in velocity.

3) When the engine is travelling at a high Mach number so that it is pulling air from a small starting area to a larger area through the fan, does this cause less surface drag on the engine's outer surface by creating helful streamlines? (1 student) The drag on the outside of the cowl is a function of the flight velocity squared, the density, the surface area, the Reynolds number, and gross behavior of the flow (e.g. separation). Thus to the extent that the flow remains attached (not stalled) the driving factor is the flight velocity in terms of the overall drag. However, there are a variety of smaller effects associited with the flow of air into the inlet and around the outside of the engine. So even for a well-designed inlet, the drag will change as the capture streamtube changes (not counting the effects of velocity changes which come along with this). And certainly, if the flow separates it will cause a potentially large increase in drag and perhaps a large decrease in engine performance (depending on whether the separation impacts the flow outside the engine or the flow going into the engine).

4) No mud (4 students). Good.