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I Conservation of Angular Momentum on a rotating disc

  1. Oct 21, 2018 #1
    I have a disc that is rotating due to air being blown at its outer radius. The incoming relative velocity of the air is high, therefore the effect of friction supersedes the effect of conservation of angular momentum. The tangential portion of this velocity decreases due to the friction as it travels (swirls) towards the inner radius of the disc. When the tangential velocity reaches its minimum, the tangential velocity then begins to increase due to the conservation of angular momentum.

    How does tangential velocity increase due to conservation of angular momentum and not just stay at its minimum value?

    Thank you.
     
  2. jcsd
  3. Oct 22, 2018 #2

    sophiecentaur

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    You cannot 'supersede' that conservation. Momentum is Transferred. Are you asking where, on the disc, most of the transfer takes place?
     
  4. Oct 22, 2018 #3

    CWatters

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    I think a photo or diagram would help.
     
  5. Oct 22, 2018 #4
    The supersede part makes sense to me when considering the angular momentum of the entire system. But could you explain how momentum transfers in this scenario? My understanding is that the momentum from the air flow transfers to the disc via friction, thus slowing down the flow to a minimum value while the disc gains rotational speed. But I do not understand how flow could then increase due to conservation of angular momentum. I feel like flow would remain at this minimum value until it exits the disc.
     
  6. Oct 22, 2018 #5
    I am sorry I should have included this in the main message. When I say disc I am referring to the discs within a tesla turbine. I have attached an image of the discs, the air enters at the outer radius r2 and exits the turbine through the central exit at r1.

    The specific paper that I am referencing is "A theory of Tesla disc turbines" by Sayantan Sengupta and Abhijit Guha. My question derives from the statement:
    "For a high value of gamma=Vtheta/(angular velocity*r2), the relative tangential velocity is high, therefore the effect of friction may supersede the effect of conservation of angular momentum. This is why, when gamma is high, tangential velocity initially decreases from the inlet (r2) up to a certain value of r/r2 at which it attains its minimum value. At lower values of r/r2, it increases again as the effect of the angular momentum conservation starts to dominate."
     

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  7. Oct 23, 2018 #6

    sophiecentaur

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    This concept is basically flawed. If it appears to you that angular momentum is not conserved then you need to approach the problem differently. The disc is not isolated and neither is the gas around it so you can't look for or apply conservation. There will be a velocity profile of gas with distance from the disc surface, Whenever there is a difference in velocity between the disc surface and the gas flow, momentum will be transferred.
     
  8. Oct 23, 2018 #7

    anorlunda

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    As I read it, that passage discusses whether friction or momentum is dominant in different regions. It does not imply that momentum is not conserved. A passage like that is difficult to interpret in any language. It should be accompanied by equations and curves to make the point.
     
  9. Oct 23, 2018 #8

    sophiecentaur

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    But they are two different quantities. How can one dominate the other? The brakes on a car will produce a Force which, when applied for a certain time (the Impulse) will change the Momentum of the car. The only difference here is that it's angular momentum being discussed, rather than linear momentum. The interaction between the gas and the turbine will be due to transfer of momentum by friction. I think this has to be true because there are no obstructions (blades) in the axial direction so the only transfer can be through lateral forces over the surfaces of the discs - that can only be a frictional effect as friction is the only force on the disc surfaces..
    Any vortices formed in between the discs will involve angular momentum and that can transfer to the discs by friction. So I think your question could be modified to ask when the transfer is greater or less by straight tangential force from free flowing gas or by a tangential couples from the gas vortices. Presumably the vortices will increase as the angular velocity of the discs increases.
     
  10. Oct 23, 2018 #9

    kuruman

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    If air is being blown at the outer radius, there is an external torque acting on the disk. If an external torque is acting on the disk, its angular momentum is not conserved.
     
  11. Oct 23, 2018 #10

    sophiecentaur

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    And who would expect it to be? The angular momentum of the whole system is what is conserved. The disc is not isolated so conservation of the disc's angular momentum is not a meaningful concept. This is my point. The disc accelerates because it gains angular momentum, transferred from the moving gas.
     
  12. Oct 23, 2018 #11

    jbriggs444

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    It might have been more clear if the author had distinguished between the tangential force on the gas due to friction versus the tangential force on the gas due to Coriolis. It is the use of the term "angular momentum" (and especially to its non-conservation) to refer to the same effect as Coriolis which is off-putting to me.
     
  13. Oct 24, 2018 #12
    If I were to blow a finite amount of air into the turbine and no more, and then say that my control volume contains the discs and the finite amount of air, could I apply the conservation of momentum to that cv?

    I believe that in this cv, the air transfers its momentum to the discs via shear force, which retards the air flow until it reaches a minimum point. At the minimum point there is no more momentum transfer since there is no longer a gradient between the flow and the disc. From this point on there are no momentum transfers.
     
  14. Oct 24, 2018 #13
    In your opinion, does it make sense that the flow velocity could increase due to a dominate momentum?

    I am starting to think that the author is considering flow velocity to increase after its minimum value due to the increase in pressure at this minimum point, when the flow slows down to its minimum it will have a build up of pressure so then the flow will want to travel towards the center (if it has a lesser pressure at the center than the minimum point).
     
  15. Oct 24, 2018 #14
    Is there a possibility that these vortices could somehow cause the fluid to speed up near minimum fluid speed (aka maximum disc speed) or would the tangential force from free flowing gas and tangential couple from gas vortices create the same outcome that is speeding up the rotation of the disc? The concept of vorticity in a turbine like this is quite challenging to think about.
     
  16. Oct 24, 2018 #15

    anorlunda

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    I said it poorly. I should have said that the passage does not suggest that momentum is not conserved.
     
  17. Oct 25, 2018 #16

    sophiecentaur

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    Any motion involving gases in containers cannot be analysed in terms of momentum conservation because there is always an external force due to the container walls. Some momentum will always be transferred out of the container. The wording is poorly chosen and the OP has latched onto the conservation idea and associated it with a different quantity. I think that starting from scratch would be a good idea with this problem, with the right terms used.
     
  18. Oct 25, 2018 #17

    jbriggs444

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    In this case it is even worse. We have external transfers of angular momentum from the gas entering the system, from the gas leaving the system and from the torque produced by the turbine.
     
  19. Oct 25, 2018 #18

    sophiecentaur

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    Also , the only interaction between the gas and the sides of the disc has to be frictional because the walls are smooth / flat.
     
  20. Oct 25, 2018 #19
    What if we disregard the solid walls and the flow on the outside of the two discs and are just looking at the flow in between the rotating discs, nowhere else. In this case the concept of conservation could be applied to the discs and fluid, correct?

    Now the model is simplified to exclude any friction via bearings, container walls, and more and only include flow through a microchannel that is rotating and the discs. I believe in this case conservation of momentum is applicable to the system albeit a rather simplified model but atleast a starting point.
     
  21. Oct 26, 2018 #20

    sophiecentaur

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    It's reasonable to say that some or most of the net momentum of the incoming gas will be transferred to the disc but I would say that the turbulence which provides coupling of that aspect of the angular momentum between gas and disc is bound to be lossy and that some angular momentum has to be lost. The other coupling, between the linear momentum of the gas and angular momentum of the disc is also relevant. I think your original question is basically about the relative amounts of each. But each involves friction - there is no other mechanism to make the disc spin and that's why I questioned your original dichotomy. You are right to try to apply the momentum conservation principle, as with any collision problem. You need to include the momentum of the exit gas too, because the mass flow rate in and out must be the same - apart from any slight effect of pressure change with speed.
     
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