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Why Strouhal no. appears in some NS eqns

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Old   July 16, 2006, 19:33
Default Why Strouhal no. appears in some NS eqns
  #1
zonexo
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Hi,

I'm reading a paper by Udaykumar et al. (JCP174,345-380) which is about modelling flow in moving geometries using cartesian cut cell mtd.

The governing NS eqn has the St. term in front of the du/dt for the momentum eqn. May I know how the term come about? Also, if the goemetry becomes stationary, wouldn't St=0, therefore du/dt=0?

Hope someone can shed some light on this. Tks
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Old   July 20, 2006, 14:15
Default Re: Why Strouhal no. appears in some NS eqns
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ag
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The Strouhal number will appear depending on how the governing equations are non-dimensionalized. Some researchers use a frequency to non-dimensionalize the time term, where this frequency has some physical meaning, e.g. the oscillation frequency of a flap or the frequency of an imposed pressure disturbance. If there is no meaningful external frequency then such a non-dimensionalization would be meaningless, and should not be used. So in the case of a fixed geometry, one would not use a frequency in the non-dimensionalization and your last question is moot.
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Old   July 28, 2006, 09:55
Default Re: Why Strouhal no. appears in some NS eqns
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wen long
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ag's comment is excellent.

similar things happen in unsteady boundary layer flow...

Say, when the outer flow is oscillatory or vibrating at a certain frequency, then the non-dimensionalization of the inertial term and the viscous term will give Strouhal number, which means the relative importance between inertial term du/dt and viscous term u_xx, such that the boundary layer thickness can depend on St.

On the other hand, for steady boundary layer, du/dt drops, and the balancing is between convection uu_x and visocus term u_xx which gives Reynold number. Hence in this case boundary layer thickness depends on Re. Re means relative importance between convection term and visocus term.

Further more, conidering wave/open channel flow with viscosity neglected,, NS equation becomes Euler equation, and the balancing terms are inertial term du/dt and convection uu_x, in this case Froud number show up, which means relative importance between convection term and inertial term.

So, finally, what I want to say is St, Re and Fr are just relative importance of any two of the 3 terms: inertial, convection and viscous.

Hope that helps,,,

Wen

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