Continuity equation question

  1. Clausius2

    Clausius2 1,479
    Science Advisor
    Gold Member

    Hi guys. I am solving the axisymmetric free jet of an incompressible fluid. But I have troubles at r=0. Continuty equation can be written in cylindrical coordinates as:

    1/r*d(rv)/dr + du/dz=0

    v=radial velocity (v=0 at r=0)
    u=axial velocity.
    hz=delta(z)
    hr=delta(r)

    What happens at r=0?. I have to obtain a finite difference scheme in order to integrate the problem, so I have created a grid that has "i" index for "z" coordinate and "j" index for "r" coordinate. j=1 corresponds to the simmetry axe.

    for j>1 I have no problem because r>0. But in r=0 there is a singularity point. How can I deal with this?. As you can see I know v(i,1)=0
     
  2. jcsd
  3. 1/r*d(vr)/dr+du/dz=0 =>

    1/r*(v+r*dv/dr)+du/dz = v/r + dv/dr +du/dz

    at r=0, v=0 ->

    dv/dr + du/dz = 0

    does this help?
     
    Last edited: Jul 23, 2004
  4. Clausius2

    Clausius2 1,479
    Science Advisor
    Gold Member

    Hey, thanks for your reply.

    But it does not help me so much. At r=0, v=0, and it is undetermined. I have had time to investigate and it is dealed by expanding du/dr it in Taylor Series.
     
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