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[Fluid dynamics] Normal shock wave problem

  1. Jun 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Air, supplied by a reservoir at 450 kPa, flows through a converging-diverging
    nozzle whose throat area is 12 cm^2. A normal shock stands where A1 = 20 cm^2. (a) Compute
    the pressure, p2, just downstream of this shock. Still farther downstream, where A3 = 30
    cm^2, estimate (b) p3, (c) A3*, and (d) M3.

    (There is no figure given) (We can also assume air as an ideal gas, and isentropic conditions everywhere except at the shock wave)
    2. Relevant equations
    Various isentropic and normal shock relations


    3. The attempt at a solution
    Ok, so I've been stuck on this problem (and this topic) for a while now. I'm sort of struggling with understanding compressible flow in general, so I'm going to go by my current understanding of this stuff to explain what I did so far, please please correct me where I'm wrong!

    a) Since there is a normal shock wave downstream of the throat, the flow must be supersonic past the throat, and therefore the flow should be choked and the throat is in critical state (*) with M=1.

    -So I first need to get p1, static pressure at 1, by use of isentropic relations(and tables):
    A1/A* = function of(M1) = 1.667
    gives M1=1.99

    -And another relation:
    pt/p1 = function of(M1) , where pt is stagnation pressure aka reservoir pressure
    gives p1=58.413 kPa

    -And now, for conditions across the shock:
    M2 = function of(M1) = 0.579

    -Making use of a normal shock wave relation:
    p2/p1 = function of(M1, M2)
    gives p2=260.16kPa

    b)c)d) For these parts, I'm completely lost. I don't know what happens after the shock, particularly what is A2* and A3*? I thought (*) refers to some critical state? I'm also confused about stagnation pressure at each of these states, like state 2 and state 3. Originally, stagnation pressure, pt, was defined as the "reservoir" pressure pretty much before the flow; so what does pt2 and pt3 refer to?

    I'm sorry that I have such a bad understanding of this topic.. my professor and TAs helped pretty much with nothing, as far as completing the homeworks or doing the exams.. It would be a lifesaver if I got some clearer explanation of compressible flows and normal shocks. I feel like this is a pretty typical problem, but I don't have a firm grasp of the material yet!

    Thanks!!!!
     
  2. jcsd
  3. Jun 2, 2013 #2

    SteamKing

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    Science Advisor
    Homework Helper

    The star (*) refers to the state of the gas or one of its properties when M = 1.

    The attachment gives theory and some worked examples:
    http://web.iitd.ac.in/~pmvs/mel7152008/notes-new.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
  4. Jun 4, 2013 #3
    Thanks for the resources! I'll go through that and see what I can learn before I come back for more questions :approve:
     
  5. Jun 5, 2013 #4
    So I'm not sure why I'm not understanding this yet, but I think I need some help..

    I am still stuck on finding the static pressure p3 at point 3. I know that between points 2 and 3, we can assume things are isentropic. I also found the stagnation pressure at point 3, pt3, by using an isentropic relation and using the fact that stagnation pressure at point 2 is equal to pt3.
    But I believe I need the mach number at point 3, M3, to move forward...
    And I can't figure out a way to get M3..
     
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