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Wake drag of moving/stationary flat plates: Not identical?

  1. Dec 28, 2015 #1
    Hi All!

    See the picture.
    A-Consider a flat plate physically moving perpendicularly through the air.

    B-Consider this same flat plate sitting perpendicularly and stationary now in a wind tunnel where air is made to flow.
    Accordingly if airspeeds, areas etc are similar, the 2 situations should produce the exact same results.

    However, I am interested in comparing only the rear wake drag in the two situations.

    In situation A, if I understand correctly, main cause of the rear wake drag comes mostly from the the air being displaced ahead by the moving plate thus creating and leaving a rarified partial vacuum area behind the plate which wants to suck air from top/bottom side of the plate which results in the negative drag pressure i.e. wake drag on the plate.

    Now, in situation B, the air coming from the front is similarly hitting the front of the plate and similarly basically not easily allowed to pass behind the plate. BUT!, in situation B there is still ambient air behind the plate, i.e. there is no rarified air or partial vacuum behind the plate because the plate in sitiation B hasnt physically displaced any air mass, right?

    I thought perhaps too much about this issue which may have led to this very unintelligent question, still I would love to have clarification.

    So, are the wake drags of A and B yet exactly equal? If so, may you explain how the -identical-to-A- wakedrag of B is caused?


    Attached Files:

  2. jcsd
  3. Dec 28, 2015 #2
    Just imagine what you would see if you were moving along with the same velocity as the plate. It is exactly the same thing you would see if both you and the plate were stationary in a wind tunnel.
  4. Dec 28, 2015 #3


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    Also, be careful with the term "rarefied". It has a very specific meaning in the context of fluid mechanics and typically denotes a region of fluid where the mean free path is large enough that the continuum assumption breaks down.
  5. Dec 28, 2015 #4
    Sorry, perhaps the word rarefied was not adequate, what I mainly meant was that the air flow directly behind the moving plate seemed different than behind the stationary plate.

    Ok, lets see, I am moving with the moving plate, lets say I am at the center of the plate area and looking now downstream towards the center of the wake. What I see is that the air particles are moving away from me further downstream, where--directly behind the plate- there is a zone of lower pressure created by the plate as it has scooped out the air. In other words, immediately behind the plate and at the center of the wake there are less air particles than far far downstream.

    I am now sitting at the center of the stationary plate in the windtunnel, The windtunnel is still Off, I look at the space where the wake will be created and I see stationary airparticles at ambient pressure. The fan of the windtunnel starts, those air particles immediately behind the plate at the center of the wake are still
    stationary(?), as the plate itself hasn't scooped out any air. And, well, you see, that is where my problem lies.

    Attempt at understanding
    The only way I can imagine how the air particles in the center of the wake directly behind the stationary plate are affected is by the interaction of escaping airstreams coming from the front and out from the plate side edges. We could see that the viscosity of these edge air streams are affecting the air directly behind the plate. Sure, but this viscosity effect also exist in the moving plate scenario A in addition to the displaced air effect and thus is not an adequate explanation In my humble opinion? Thanks
  6. Dec 28, 2015 #5


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    The two situations are identical. What @Chestermiller was attempting to have you do is imagine the plate moving me through the air. You are looking at it from the side like your picture shows. Now imagine while it moves, you are moving the same rate still looking at it.
  7. Dec 28, 2015 #6
    (Of course I realize that the two wakes of the two situations ought to be identical somehow, but how? )

    I have considered and imagined several frames of reference. But still I dont understand how the air in the wakes would be similar. I outlined my thinking in the earlier posts.
  8. Dec 28, 2015 #7


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    Well both instances must start from rest, correct? In both cases then there will initially be no pressure difference between the front and the back. Now, whether it is the air that starts moving or the plate, that fact doesn't change, yet in at least one instance according to your line of reasoning, a low-pressure region develops behind the plate. It must be that this low pressure region develops due to the motion, and the motion in the two situations are identical except for a simple Galilean transformation. So they start from the same condition and end with the same free stream condition so the fields should be the same.

    (Apologies if this isn't clear. I'm sneaking typing while my wife shops.)
  9. Dec 28, 2015 #8
    Your words are clear. Obviously though, the subject is more clear to you than it is to me, a fact which may make you bypass some things that may be regarded as straightforward to you but not to me:). Happy shopping btw, (hope its not too heavy on the wallet hehe).

    In both cases then there will initially be no pressure difference between the front and the back. Good.

    Now, whether it is the air that starts moving or the plate, that fact doesn't change, What exact fact were you referring to here? what fact doesn't change do you mean? the fact of "no pressure difference"?

    yet in at least one instance according to your line of reasoning, a low-pressure region develops behind the plate Do you agree that there is a low pressure behind?

    It must be that this low pressure region develops due to the motion, and the motion in the two situations are identical except for a simple Galilean transformation. Yes and perhaps here I can come closer to the heart of the understanding issue. If I put it this way:

    My question concerns specifically the flow immediately behind the stationary plate.
    My reasoning is that as the wind tunnel fan starts, this same airflow will for the most part not be able to get behind the plate, thus my "erroneous" reasoning implies that the space with its air mass behind the plate can thus not be affected in anyway i.e. no motion of the air behind the plate and no low pressure behind the plate. If my point is not clear I will make a drawing of another better example.
  10. Dec 28, 2015 #9
    I disagree with the description of the moving & stationary plate cases. In both cases, air is being forced from the leading face of the plate off the sides. There is no vacuum formed on the back side, air doesn't jump from the edges to move behind the plate, but swirls form based properties of the air flow at the edges, these are either carried away by the flowing air or stay in place as the plate moves away. The effect looks the same for both moving plate & stationary plate in wind tunnel.
  11. Dec 28, 2015 #10
    Hi leviterande,

    Here's a thought experiment for you.

    You're in a tunnel. You're sitting on a cart, and the flat plate is mounted facing forward on a vertical pole affixed to the cart. The cart can move forward with a velocity V, and the ride is so smooth that you can't even feel the cart moving. The walls and floor of the tunnel are so smooth that you can't tell visually whether the cart is moving forward or not. There is a fan ahead of you in the tunnel that is capable of blowing air at a uniform velocity V toward you. The fan is either far enough away or is transparent, so that you can't see it.

    Situation 1: The cart is moving forward with velocity V, but the fan is not blowing
    Situation 2: The cart is stationary, and the fan is blowing air toward you with velocity V.

    In both situations, the velocity of the air relative to the cart is V, and the velocity of the cart relative to the air is V (in the other direction).

    I submit that there is no experiment you can do to prove that you are experiencing Situation 1 (and not Situation 2), or vice versa. If you can think of one, please describe it. The air velocities that you measure from your frame of reference on the cart will be exactly the same, the streamlines will be exactly the same, and the pressures at various locations (including behind the plate) will be exactly the same.

    Last edited: Dec 29, 2015
  12. Dec 29, 2015 #11
    I appreciate your replies. I understand that the 2 situations should be the same, -a fact you have made clear- I just dont grasp yet the how; how the two wakes are identical. it seems my exact question wasnt clear.

    My current understanding of negative pressure drag

    Besides the eddies behind the 2 plates creating drag I imagined there is another source of drag existing only in the moving plate:
    We take the wind tunnel wall as the frame of reference. As the plate physically moves forward, the air in the space behind it must accelerate trying to catch up/fill up the momentarily hole/vacuum that the plate created behind. Since obviously air cannot accelerate instantly, and since the plate is constantly moving, there will be a low pressure zone behind the moving plate where the air behind tries to fill up the void. How wrong Am I in this thinking ?
  13. Dec 29, 2015 #12
    This is exactly the same thing that happens with the wind blowing past the stationary plate.
  14. Jan 1, 2016 #13
    I feel that what I wanted to know, the issue in question, seems -despite what I wrote- to not have came out clear.
    I understand that the situations should be the same but I want to understand how, how the air directly behind is the same for the 2 situations.
    To illustrate my point even further look at the picture below, replace the flat plate with a C- shaped plate, i.e. the flat plate now has sides on top and bottom. For simplicity's sake lets assume from now that all flows are 2D.
    The moving C plate has a low pressure air behind it as described earlier.
    Now, how will this low pressure form behind the stationary plate? The air from the fan of the wind tunnel can barely get around and behind the C plate?

    Attached Files:

  15. Jan 1, 2016 #14
    I don't see how you can say that. The air in the stationary C plate picture is also blowing around the outside of the plate, and circles around in back and down.

    I would like to see what you think the streamlines look like for the stationary C plate case. Can you please prepare a sketch of what you think the streamlines look like. (I know what they look like, but I'd like to give you a chance to work it out).

    Last edited: Jan 1, 2016
  16. Jan 2, 2016 #15
    My final comment on this: Unless the moving plate is moving at the speed of sound, there will not be a low pressure region behind the plate. If you put Pitou tubes on the front, back and side edges of the plate, the static pressure will be the same for all three locations. This also is the case for the wind tunnel plate.

    However, at supersonic speeds, funny things start to happen. That is why rocket nozzles get larger in the direction of flow, this forces the exhaust to increase speed.
  17. Jan 2, 2016 #16
    This is definitely not correct. If this were the case, then there would be uniform pressure at the cylinder surface in both viscous and inviscid fluid flow past a cylinder. We know that that is not the case.
  18. Jan 3, 2016 #17


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    If viscosity was nonexistent then you'd be onto something. Since fluids do have viscosity, however, this is not correct. There will be a massive low pressure region behind the plate.
  19. Jan 4, 2016 #18


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    The Galilean invariance argument applies for constant velocities (two inertial frames): A plate that has moved at constant speed for a while has the same flow as a plate in a wind tunnel which has run at constant speed for a while.

    However, in the transition phase, when either the plate or the air is accelerating, there is no equivalence and the flow might look different. For example, in the frame of the accelerating plate you have an inertial force field, which isn't there in the frame of the plate in the wind tunnel.
    Last edited: Jan 4, 2016
  20. Jan 7, 2016 #19
    Indeed, in accelerating frames things get different. However I am luckily only talking about constant speeds:)(at least I think I am thus far hehe)

    I feel that my exact point was probably not clear so I am going to use an extreme example (possibly inappropriate but should show the point ) that I originally wanted to use at first but due to some reasons I didn't. Ok, lets assume that the flat plate and it´s two cases still occur in the same single wind tunnel. This flat plate however is so big that it fits exactly the cross section of the tunnel. The flat plate in other words is free to glide back and forth on air tight bearings through the tubular wind tunnel. Air from front/behind of the plate cant get past the plate. The wind tunnel is very long but is opened at both ends. In front of the plate we have the same fan.

    Case A
    Fan is off, plate is physically moving in a direction towards the fan.
    There will be positive pressure ahead acting on the front of the plate
    Furthermore, there will ALSO be negative pressure behind acting on the rear of the plate

    Case B
    Fan is on, Plate is stationary.
    There will be positive pressure ahead acting on the front of the plate
    Here however, the way I see it, we don´t have negative pressure behind acting on the rear of the plate. The air behind is not affected by the stream coming from the fan.

    I appreciate your patience
  21. Jan 7, 2016 #20
    There is a stationary plate version of Case A that gives the exact same pressure distribution, but does not involve a fan. Can you figure out what that is?
  22. Jan 7, 2016 #21


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    Here again the Galilean equivalence used in wind tunnels stops being applicable. The idea of a wind tunnel is that you have only two objects relevant for the flow:
    - The test body (here the plate)
    - The airmass
    Galilean invariance tells you that it doesn't matter which of the two is moving.

    In your scenario the boundaries of the tunnel become relevant for the flow, as a third object. There is no Galilean Transformation that makes the two cases equivalent, with that third object involved.
  23. Jan 7, 2016 #22
    Case A is a bicycle tire pump. The air in front of the plate gets hot because it is being compressed, the air behind the plate is atmospheric, no change in temperature and it is not in a vacuum. The air just follows along with the back of the plate.
  24. Jan 7, 2016 #23
    Hi A.T.,

    Did you see my post #20? The actually is a Galilean Transformation that works for Case A, but it doesn't involve a fan.

  25. Jan 7, 2016 #24
    One more item, for a flat plate, the air will not curl around the edges. In both cases the air is forced to move parallel to the plate, once it reaches the edge, it continues in a straight line, due to the change in momentum caused by the flat plate changing the direction of flow. Other shapes (cylinder, square, sphere, etc) will have different flows.

    Flat plate moving or stationary with air moving against it will have the same flow patterns, no negative pressure behind it.
  26. Jan 7, 2016 #25
    Please provide a diagram of what you think the streamline pattern looks like for air blowing past a stationary flat plate (illustrating what you said above).
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