# Why Strouhal no. appears in some NS eqns

 Register Blogs Members List Search Today's Posts Mark Forums Read

 July 16, 2006, 19:33 Why Strouhal no. appears in some NS eqns #1 zonexo Guest   Posts: n/a Sponsored Links 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

 July 20, 2006, 14:15 Re: Why Strouhal no. appears in some NS eqns #2 ag Guest   Posts: n/a 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.

 July 28, 2006, 09:55 Re: Why Strouhal no. appears in some NS eqns #3 wen long Guest   Posts: n/a 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

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post DaiG Main CFD Forum 1 August 2, 2011 15:06 quarkz Main CFD Forum 2 November 18, 2010 09:21 soggy316 FLUENT 0 February 17, 2010 06:15 vasilis Main CFD Forum 4 October 7, 2008 02:56 J. Held Main CFD Forum 0 March 26, 1999 05:10