Dimensional Analysis for Drop Test involving Fluids & Structure 1

[benzflieger]

I need advice on how to properly scale the physical parameters surrounding a scale model drop test I want to perform. Obviously, the way to do this is thru dimensional analysis. My question though, is where to begin….
I this post here, I describe a drop test of a 10000lb cask into a basin of water that I am analyzing using MSC Nastran:

http://www.eng-tips.com/viewthread.cfm?qid=268058

In addition to performing the FE study described in the above post, I want to do some experimental work to validate my results. Essentially I want to run a 1/10 scale physical drop test.

My general approach is to be something like this:
1) Generate an FE model of a "1/10 scale model" scenario to get some "order of magnitude" numbers.
2) Perform a physical drop test of an actual 1/10 scale model and get basin wall stress values from my strain gauges.
3) Determine degree of correlation between scale model FEA and experimental data from 1/10 scale model.
4) Refine FE approach and/or physical experimental approach and re-run as required to gain better agreement…?
5) Run FEA of "full scale" model implementing an lessons learned during FEA of scale model.

A partial listing of the physical parameters that have to be determined to run a scale model test include:
Location & Description Variable Name
-Cask: Diameter, Length, Weight D_cask, L_cask, W_cask
-Basin: Diameter, Height, Wall thickness D_basin, H_basin, T_basin
-Drop Height (this determines the impact velocity) V_impact = sqrt(2 x g x H_drop)

My questions is this: If I fabricate a 1000lb cask whose weight is 1/10 that of the real cask (10,000lb) and drop it, what do my other parameters have to be to get "similar" dynamic fluid (water in the basin) and structure (basin wall) responses?

Real Setup Scale Model
W_cask 10,000 lbs 1,000lb
D_cask 36in ?
L_cask 50in ?

D_basin 84in ?
H_basin 168in ?
T_basin 1/2in ?

V_impact 44ft/sec ?

I know it is not as simple as dividing all the known variables by 10 to generate the unknown variables. I know there are dimensionless parameters like Reynolds number and Froude number that can be use full. I know the origin of the Froude number came out of Froude's research of boat hull drag through the water and his need to determine how best to size his scale boat hull models.

Any advice that can be offered would be helpful. By the way, I am originally posting this in the "Mechanical Engineering Other Topics" Forum, if anyone knows of a more appropriate forum location to post this question please advise.
Thanks in advance for for any help!

 

[electricpete]

The way I look at it, there are three degrees of freedom within your units: mass, distance, time. Everything else can be expressed in terms of these three.

One easy way to generate a dimensionless set is to pick three variables that have independent dimensions (none of their units can be expressed as combo of units of the ohters). Then you can express all the other variables in terms of those first three.


So your variables are something like:
D_cask, L_cask, W_cask
D_basin, H_basin, T_basin
Vimpact
Density of water?
E of water (or something like that)?
Density of steel
E of steel

There are lots of possibilities and some may yield more physical meaning than others. I don't have much insight into your problem. My guess would be use the material properties as your three base variables and express everything else in terms of those.



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[btrueblood]

Caveat: I have never conducted a drop test into water, nor tried to analyse the conditions to determine loads. I know there are researchers who have, and there should be quite a few scholarly articles from a variety of fields where this kind of research has been done. Some suggestions on places to look would include NASA Apollo, Gemini, and Mercury program test reports (all of these used ocean splash-down recovery), geology articles on meteor impacts and simulations, probably a dozen others I can't think of right now...

Have you tried to contact these guys and ask them for pointers to research papers, etc.?

http://www.sandia.gov/vqsec/SON-WD.html

The intent of the full scale drop test is, presumably, to test the integrity of the cask to such treatment. Thus, your subscale test is intended to primarily aid in determining loads on the cask resulting from drops.

The forces acting on the basin are of secondary interest (you don't want to break the container during testing).

I would scale the model cask density, velocity, and/or the fluid density and viscosity, to try and match Reynold's number from subscale to full scale. Here Re = (cask dimension)*(impact velocity)/(density of fluid)/(absolute viscosity of fluid). You might actually test some variations to determine if there are, or might be, any dependence of the load transients on Re.

I don't think the Froude number will be of as much use in correlating forces acting on the cask, but might be of use in correlating forces acting on walls of basin due to wave action; really I'd think you want to measure basin diameter vs. falling body characteristic dimension to correlate those forces...I think.

Let the data collected provide correlation data for modelled/calculated forces on the container walls, but unless you have unlimited funds, I wouldn't try to conduct specific tests to correlate those forces. Building the container wall thicker, or patching cracks in the full scale tank are costs you trade against trying to calculate to the nth degree.

If you do find some links to papers on the subject, it'd be interesting to post them here.

Good luck.

 

[benzflieger]

Thanks btrueblood...
I should have clarified in my OP.
The primary concern for this test is the failure of the 1/2" thick basin wall. Failure in this case would be defined as a fracture, crack, split, etc. that results in 1.5m or more of the water depth leaking out of the basin and into the surrounding soil.

The secondary concern is the dropped cask casing. With the cask, I have the option of adding "impact limiters"

Thanks for the link to Sandia. They might have some helpful info.

Any additional info is appreciated!

 

[amorrison]

See last post of this thread (hope it still works)

http://www.eng-tips.com/viewthread.cfm?qid=96282

also Google sphere impacting water

 

[btrueblood]

Thanks, amorrison, I'd forgotten that one. The google search gives some good hits too...I _was_ coming back to suggest seaplanes, torpedoes, and aerial depth charges as some more places where you might find relevant research...

...but it sounds like your problem is the exact inverse of what I'd assumed. You ARE going to want to model Froude numbers, and examine the effects of basin depth/width relative to impactor size and velocity. You are probably going to have difficulty finding much information on the reaction forces at the container walls, as much research is/was done on natural, open bodies of water (lakes, ocean) as opposed to basins and pools. Hopefully, though, you can derive some information from the literature giving data on splash height, rebound height, etc., and use these as initial conditions for a free-surface model or calculation, to yield wave height estimates at the container wall.

The earlier thread also wanted to know about shock pressures, which I'd tend to discount unless the projectile is hitting the water as some appreciable fraction of the water's sound speed. But that's more of a gut call, not based on anything...sound (sorry could not resist that).

 

[benzflieger]

This afternoon I just did a real quick 1/25 scale (by weight) test. No calcs. just rigged up a quick release mechanism, found something cylindrical and heavy and dropped it into a 55 gallon drum of water from 13ft. Lost 75% of my water and punctured the bottom of the 20ga. steel drum. Good first pass information... and confirmed my suspicion that I should be expecting a big splash.

Hopefully you can see the video I attached here:

http://files.engineering.com/getfil...7-a4d1-b8b9bef2f315&file=383_lb_Cask_Drop.MOV

Now, I need to come up with a more thought out 1/10 scale model like I discuss in earlier posts. I need to start quantifying the stress effects in the tank...

Another source of research I have thought might be the work done by folks who design silos and storage tanks for farms, chemical processing facilities, waste & water treatment plants, etc. They would obviously be most concerned about the integrity of the tank and not the object dropped.