Pattern identification and Froude Number
Hi,
Reynolds number and Froude number are the two dimensionless parameters for judging the dynamic similarity. Therefore, both could be employed to quantify the regime transition. In gassolid twophase systems, the value of Fr=Umf^2/dp.g has been employed to evaluate the flow patterns( <1: uniform, >1 aggregative ). Questions: 1) who can tell me the physical meaning of Fr. ? 2) what is, how to choose, the character velocity in Fr. ? Are there some books or references introducing this in details ? 3) some examples of Fr applying for the flow pattern identification in single phase flow and/or in multiphase flows? Many thanks ! Jie Li 
Re: Pattern identification and Froude Number
I have no idea about your multiphase flow. But I am working with plumes, which Fr plays an important part.Froude number is the ratio of inertia force to gravity force. If Fr < 1, the plume is buoyancy controlled, if Fr >1, then the initial momentum plays important effects. Then it is called jet. The typical value for fires is around 1.52.0. My text book is An Introduction to Fire Dynamics by Drysdale. page 154, simple introduction. Tingguang

Re: Pattern identification and Froude Number
Many thanks. I am interested in knowing that Fr.is also employed in the fire research.
I am still wondering how you set the velocity value in Froude number in your field since, as you know, the flow velocity has always a distribution. It seems that in some cases the mean velocity is employed as those in the dimensionless process of NS equation. but in some other cases the squared sum of fluctuation velocity is applied to characterize the dissipation. Could you be kind enough to highlight that ? 
Re: Pattern identification and Froude Number
It is a good question, which I have to ask my advisor for the answer. The velocity has the same physical unit as SQRT(gravity*length). So the later is used as the characteristic velocity for dimensional analysis. In fact, the length can is related to the heat release rate of the fire, so froude number is a dimensionless heat release rate Q* (Dimensionless Energy rate). If you know, froude number is similar to dimensionless energy, then what you said about Fr is reasonable. For fire research, we focus on central line velocity and central line Fr number, so no need to characterize the velocity. Hope that can meet your need. Tingguang

Similitude
No one characteristic velocity is correct. To have complete dynamic similitude you need the whole distribution of velocities. People pick a velocity which BEST describes their problem. ie. for Reynold's Numbers the Mean velocity may be a good indication of the Large Scale Motions and the Root Mean square velocity may be a good indication of the small scale motion. (Depends on what you want to look at...) or in the case of a froude number a wave speed can be used.
To determine the one you need I would first suggest reading papers regarding your application to see how others define it. This is a good way because you will want in the end to compare your results with theirs. If your the first to define it pick one that is easy for others to use experimentally and accurately describes the problem at hand.... Happy Characterizing..... 
Re: Similitude
From our discussion it seems clear that there is no a uniuqe defination for Froude number. It changes with the purpose of application.(now I myself know that there are 3 types of defination.)
Many thanks for Tingguang's kind assistance and Joe's suggestion. But I have to define a Froude number myself as there is no such an exact parameter available in this field. Because I wish to characterize the energy dissipations due to particleparticle collision and the particlefluid interaction in gassolid twophase flows which is appearently in microscale, it would be wise to choose a microscale quantity, such asthe root mean square velocity of the particles, as the characteristic velocity. Best regards, Jie 
Re: Pattern identification and Froude Number
you may find that your undergraduate fluid mechincs book has good discussions on the use of Fr. I recall than mine used it a lot for open channel flow. I think you use it similarly to the mach number for compressible flows

Re: Pattern identification and Froude Number
Could you introduce one? I have checked those books witten by G. Batchlor ( Introduce of fluid Mechanics) and by Bird et al. (Transport phenomena) But there are limitted information on Fr.
For the single flow phase it is the ratio of inertia force to gravity FORCE. But in granular flow, it was employed as ratio of particle kinetic ENERGY to potential energy. Are you working in sigle phase system of channel flows or mulitiphase flow? How do you use it? for what purpose ? Thanks anyways ! Best Jie 
Re: Pattern identification and Froude Number
try the book by Munson and Okiishi. for the most part the Froude number is use in free surface liquid flows, but I can see how it'd be usefull for your purposes. From my knowledge your definiton of Fr is the one I'm familiar with although the first one you defined is probably equivalent. As i said in my previous post the Froude number is equivalant to the Mach number to some extent. the text I quoted above will explain that more. you'll probably have to make a lot of your conclusion by analogy because your area is not as widely studied

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