VPM Technical Discussion

Sat Mar 8 03:01:04 PST 2014

Thanks Robert, for the quick response on a weekend.

As you said the other day about the pressure of small bubble is far higher
than larger bubble...I have confirmed with what you said myself........(1)

Let me start with this by proving that smaller the bubble ...greater the
pressure.

Considering the pressure of bubble (which drives vpm)

Pressure inside bubble = Ambient pressure + Pressure due to Surface Tension

(I learnt as a physics student in my schooling that pressure inside bubble
is greater than outside pressure)

-> Pressure inside bubble = Ambient pressure + (Skin constant/Radius of
bubble)

(Here clearly smaller the radius, greater is the pressure inside a bubble,
which proves the first fact (1) )

I'm sure we have ambient pressure data during ascent or descent.
Skin constant = 2*Gamma (where Gamma is the surface tension of water i.e
0.073N/m)

Next,  As you asked, as far as my knowledge about VPM is concerned, we put
a single bubble in each compartment to simulate the actual bubble formation.

Next, Regarding the radius of the bubble,we will have to initialize it at
the surface                (this one point I read from Eric Baker's
research paper)...
It is actually initialized this way at the surface.
Every compartment has it's own pressure(we use this as pressure inside
bubble at surface) i.e they are at equlibrium.

Next we use the formula P inside = Pambient + (2*gamma)/r.....where we
solve this equation for every compartment to find the initial radius(r)
Technically speaking since we have different pressures in different
compartments initially, we will simulate initial values for all
compartments.

No-bubble Growth Equation:

So this is all about "Controlling the supersaturated state"

So here compartmental pressure (called Tissue tension) is critical.
Let this value be called PTC.

         So Pressure inside compartment < pressure inside the bubble
This helps maintain No-growth because whenever Pressure inside compartment
goes above Pressure of bubble, diffused gases go inside the bubble,
expanding it.

So to avoid this we control pressure of compartment by the below

PTC < Pressure inside bubble   (theoritically this is possible to be at
Equilibrium)

->    PTC < Ambient pressure + (S/r)

-> PTC-Pa < S/r    (This term PTC-Pa  shows the supersaturation and upper
bound on their difference)

This was the term I was talking about in my previous mail.
The above equation for No-Growth helps maintain our Compartmental pressures.

Now THIS is the whole point,
As you implemented supersaturation using half life times and getting
Maximum Compartmental Pressure,
 I will reverse map this to the M-values that are possible while
decompression/ascent. This helps us in formulating the deco table for
finding the acceptable ascents with an upperbound based on the pressures
that we get from the No-bubble growth equation.

So, technically you dealt with Compartments completely in assessing height
of ascent possible, I want to use bubble as a parameter for that decision
to be taken in VPM.

As I am going through various papers I'm improving my understanding,
I'm sure I will better and clear on this very soon.
I think I answered most of your questions, I will be more elaborate on the
backtracking part and mapping it(as I am currently understanding that),
very soon and will let you know.

I'm working only on this project as part of GSOC 2014, and only with
subsurface.
I'm trying hard to get to know things better. I am confident that I would
make through with your guidance and help.
Let us fix a meeting on IRC, if you are free sometime.

Thanks a lot or the guidance and let me know your suggestions,

Regards,
Gopichand.

On Sat, Mar 8, 2014 at 4:30 AM, Robert C. Helling <helling at atdotde.de>wrote:

>
> On 07 Mar 2014, at 23:27, Gopichand Paturi <gopichandpaturi at gmail.com>
> wrote:
>
> Gopichand,
>
> > I have been waiting for you on IRC to let you know my progress.
> > Well, As I go through VPM, I'm developing keen interest to implement it,
> given the background of deco algorithm that you implemented.
> >
> > I have gone through the permeability and other related concepts of
> surface tension very recently, as you discussed with me on irc.
> >
> > Also, As far I see it, VPM is critically about the handling of bubbles
> in each compartment. I'm yet to know more detailed description of some
> constants like Regeneration time and 'S'(Skin constant). Let me know your
> idea,how to get these values for a specific bubble in a compartment.
> >
> > I found out after detailed study on VPM is that handling the No Bubble
> Growth equation is critical step in the implementation of VPM.
> > Especially finding the radius of bubble is most important for finding
> supersaturated state.
> >
>
> Great. Can you explain the "No Bubble Growth" equation to me? How is it
> derived?
>
> > I have plans to put proper documentation and complete explanation of
> these algorithms into place in subsurface also as part of implementing it.
> > (I will mention this in GSOC application)
> >
> > Because doing so, I strongly believe would help extending it to new
> algorithms like RGBM etc, which helps subsurface in the future (I'm
> interested to work on the same after this summer).
> >
>
> As far as I know, RGBM is not published. You have to buy a license to be
> told the details. If that is the case this is not compatible with open
> source.
>
>
> > I also want to know how to maintain the track of continous compression
> details of bubble during descent.
> > As this is a continous function depending on Pa-PTC. I want to know how
> to implement these type of values.
>
> I have to admit I don't know what you are talking about.
>
> Let me ask a very naive question: Are we going to track one bubble per
> compartment? And if yes, how is its initial size determined? Or do we have
> to simulate a whole range of initial sizes?
>
> How does the backtracking part of the algorithm work? What exactly is the
> condition for success? How is that derived?
>
> >
> > Do you actually trigger the above actions by your code running a
> continous loop checking for changes in the descent/ascent depth for a
>  constant time interval?
>
> Except for "constant", yes.
>
> > Or Is it that we are not implementing a dive planner.So running this
> algorithm on predefined depths and changes would be far easier(i feel) .
> >
>
> Both.
>
> Sorry for not being very responsive at the moment. The more concrete your
> questions are the easier it is for me to answer them.
>
> Best
> Robert
>
> --
>
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> Robert C. Helling     Elite Master Course Theoretical and Mathematical
> Physics
>                       Scientific Coordinator
>                       Ludwig Maximilians Universitaet Muenchen, Dept.
> Physik
> print "Just another   Phone: +49 89 2180-4523  Theresienstr. 39, rm. B339
>     stupid .sig\n";   http://www.atdotde.de
>
>
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