Fluids - boundary conditions for rotating sphere

  • Thread starter davcrai
  • Start date
  • #1
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Homework Statement


A sphere under uniform rotation R, in a simple shear flow, given at infinity by
ui = G(x2 + c)deltai1
The centre of sphere is fixed at x2

Boundary conditions are ui = EijkRjxk on sphere,
and ui = G(x2 + c) at infinity


Homework Equations



dij is the kronecker delta
Eijk is the permutation symbol

The Attempt at a Solution



Just trying to understand the boundary condition on the sphere.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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hi davcrai! :smile:

ui = εijkRjxk is the standard formula for rotational velocity …

usually written v = ω x r, which is the same as vi = εijkωjrk :wink:

(in other words, the fluid velocity at the surface of the sphere is the same as the velocity of the surface, as one might expect)
 
  • #3
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Thanks
 

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