Can anyone explain to me for 2D supersonic flow through a nozzle, ie M= 2, 4, 6 ,8 how the boundary layer will effect the exit mach number? Are there scale factors which may be used to correlate the result from one exit Mach number to the next?

(1). I can only guess that you are talking about the supersonic nozzle with the exit Me=2,4,6,8. (2). With the nozzle contour properly designed,that is, shock free condition, the pressure on the boundary layer will be smooth and continuous from the nozzle throat to the nozzle exit. (3). The inviscid supersonic flow field can be obtained from 2-D MOC exact numerical method. (4). Depending upon the upstream condition, the boundary layer can be either laminar or turbulent. And the conventional boundary layer theory can be used to obtain the solution. Since each nozzle will have different exit height ( and length), one needs to compute the boundary layer separately. (5). If the conventional inviscid-viscous concept is applicable under the condition given, the boundary layer displacement effect can be included to account for the blockage. (6). If the condition for the nozzle is such that it is viscous everywhere, then you may have to solve the Navier-Stokes equations instead of the boundary layer equation. (7). Contact people at wind tunnel facilities, because 2-D nozzle is commonly used there, including nozzle with flexible walls.(these are symmetric nozzles)

The effective exit area will be decreased due to the boundary layer thickness at the end..i.e. less A/A*..it can be corrected by calculating the actual exit area.

What I am trying to understand regarding 2-D supersonic flow using MOC, is the following.

Given Me=# Solve MOC to obtain Ae/At. Calc. the B.Layer to determine its effect on exit mach number. Due to BL thickness, get new Ae/At, hence new Me.

Now, can this result of the b.l. growth be scaled to other MOC 2d supersonic nozzles, or is each result independant of the next?

For example;

[Ae/At(Me1)]/ [Ae/At(Me2)] = [b.l. (me1)/b.l.(me2)]

Is this proportionality valid based on different exit mach number solutions, for MOC?

(1). It does not matter whether it is right or wrong. (2). In either way, you must prove that it is the case. (3). So, you can assume that it is right in the first place. In this way, you will have a place to start. Then try to prove that it is always right. (4). I think, it is a good exercise.