I indeed found an error I had made in the calculation directly below, but the
discrepancy between the first MFMP revision still exists.
Here is what I believe is the equation Alan would use, neglecting the value of
the delivered volume of total charge to the cell:
mLAH = mtotal / (1 + VRxDR)
where mLAH = Mass of Lithium Aluminum Hydride,
mtotal = TOTAL charge/fuel Mass (0.67 g),
VR = Volume Ratio (Ni Volume) / (LAH Volume) (2.5)
& DR = Density Ratio (Ni Density) / (LAH Density) (2.1545 = 1.06/0.492)
Using this equation, I calculate the mass of LAH at 0.105 g (or 105 mg)
and the Ni mass at 0.67 g – 0.105 g = 0.565 g (or 565 mg),
instead of the mistakes of 124 mg & 546 mg, in the post directly below.
... In the first MFMP Revision, DR = 9.714 (8.908/0.917), so I calculate the
mass of LAH at 0.0265 g
(instead of the mistake 0.0276 g, below), in disagreement with the value of
0.0197 g.
It would be nice if we can resolve this discrepancy.
With this LAH mass, the Ideal Gas Law Maximum Pressure comes out as 8388 psi,
and using the van der Waals equation of state, approx. 1.07 times that, or 8976
psi.
This is using 1.06 ml as the free volume and 1057 C as the temperature.
Mark Jurich
-----Original Message-----
From: Mark Jurich
Sent: Friday, February 13, 2015 6:00 PM
To: vortex-l@eskimo.com
Subject: [Vo]:Re: Dog Bone Project
If one takes the MFMP measured densities along with the volume ratio 2.5
(neglecting the delivered volume value as data), one gets:
mass Li(AlH4) = 124 mg
mass Ni = 0.67 - .124 = 546 mg
This is similar to the way Alan calculated it in the Revision, but I
couldn't recreate his exact value in that revision ( 0.0197 g; I get 0.0276
g), so I may have an error in the above values....
The maximum pressure comes out to be approx. 9480 psi ... If one uses the
van der Waals Equation of State instead of the Ideal Gas Law, the maximum
pressure will be approx. 1.07 times that (10,144 psi).
... Anything over 10,000 psi is not good. Consider the fact that an abrupt
pressure change may cause the Alumina to crack (just like an abrupt
temperature change causes glass to crack). If the pressure rushed up to
such a value, it may be the cause. I believe this data is probably
tabulated somewhere for Alumina, at high temperatures. We need to find a
paper or some values.
Mark Jurich
-----Original Message-----
From: Mark Jurich
Sent: Friday, February 13, 2015 5:33 PM
To: vortex-l@eskimo.com
Subject: Re: [Vo]:Re: Dog Bone Project
Correction (typo) on Mass Ni (Original Message) ... Should be 563.3 mg ...
The Measured Density by MFMP for Li(AlH4) is 0.492 g/cc. If I use that
value instead of 0.74 times 0.917 g/cc (0.74 is theoretical maximum packing
density for identical spheres), which is 0.679 g/cc, I get:
Mass Li(AlH4) = 77.3 mg
Mass Ni = 592.7 mg
Density Ni = 1.509 g/cc
I need to double-check these.
Mark Jurich
-----Original Message-----
From: Mark Jurich
Sent: Friday, February 13, 2015 4:57 PM
To: vortex-l@eskimo.com
Subject: [Vo]:Re: Dog Bone Project
FYI:
I just made a calculation where I assumed the Li(AlH4) Powder density to be
0.74 times 0.917 g/cc. I then calculated the remaining 3 unknowns:
Mass Li(AlH4) = 106.6 mg
Mass Ni = 6282.6 mg
Density Ni = 1.434 g/cc
I assumed the delivered volume was 0.55 cc (0.5 to 0.6 cc)
I then went searching for the Ni Density by the manufacturer of the actual
Ni used, by first trying to identify the manufacturer at the MFMP Site (via
EverNote). I then saw that MFMP have determined the density to be 1.06 g/cc
just a short while ago . This is close...
...More when I find out more.
Mark Jurich
-----Original Message-----
From: AlanG
Sent: Wednesday, February 11, 2015 8:44 AM
To: vortex-l@eskimo.com
Subject: Re: [Vo]:Re: Dog Bone Project
Mark, the powders were already inside the glove box when the scale (also
inside the box) failed, so volume measurements were the only data I had
available. As a result, precise mass measurement was not possible, nor
was determination of exact densities by measurement. The relative
density of the powders was taken from the bulk densities as given in the
respective Wikipedia entries. Unknowns include the packing ratio of each
of the powders. They are both finely divided but not nano scale, so
assuming a similar packing seems reasonable in the absence of other data.
The volumes were calculated from dimensions of the actual components
used, measured with a digital caliper. The space between the filler rod
and the ID of the tube is significant and was included in my
calculation. The possible vacant volume within the powder mass was not
included, nor was the possible absorption of H2 into the nickel, which
we think was minimal given the time scale of the experiment.
Regarding the calculation itself, the mass of the fuel was determined
accurately by weighing the loaded cell after sealing and removal from
the glove box. This was divided by the volume mix ratio, then by the
estimated relative density ratio of the two powders to get the mass of
the LiAlH4 in the cell. The amount of H was then found simply by the
ratio of standard atomic weights. As you correctly pointed out earlier,
the equivalent molar amount must be based on the H2 molecules in the
gas, and that was the final figure used to calculate the pressure.
If I missed something important in my analysis, I'd be happy to know,
and make further corrections.
AlanG
On 2/10/2015 11:30 PM, Mark Jurich wrote:
> New MFMP Charge Analysis regarding the Explosion Run:
>
> http://bit.ly/1z61hEB (5 hours ago)
>
> This is a shocker to me. Here are the changes to the last values (first
> analysis):
>
> Free Volume for Gas: 1.09 ml --> 1.06 ml (not a large change) (Recall that
> Parkhomov estimates 2 ml in his experiment(s))
> Weight Amount of Li(AlH4): 134 mg --> 19.7 mg (!!!!!!!) (Recall
> that Parkhomov/Translation states 100 mg)
>
> With these new values, the calculated pressure become approx. 1500 psi,
> which agrees with my calculation. But this new weight amount of Li(AlH4)
> is totally strange to me. The analysis goes on to state that this
> pressure is in line with Parkhomov's estimates, but as far as I
> understand, using far less Li(AlH4) than Parkhomov. The only value I have
> ever seen stated by Parkhomov is 100 mg, or a factor of 5 times more, by
> weight.
>
> Am I missing something here? This is a tremendous change that I'm having
> a hard time comprehending. I'm looking into the MFMP Calculation further,
> right now.
>
> Thanks,
> Mark Jurich
>
> -----Original Message----- From: Mark Jurich
> Sent: Sunday, February 08, 2015 2:56 AM
> To: vortex-l@eskimo.com
> Subject: [Vo]:Re: Dog Bone Project
>
> I believe there maybe an error in this pressure estimate and that the
> calculated pressure will be exactly half of 19,861 psi (i.e., 9,930.5
> psi).
> Although 0.0141 moles of Hydrogen are released, 0.00706 moles of Hydrogen
> Gas (H2) are released. I don't believe that free H atoms/ions contribute
> to
> the gas pressure in the free volume of the cell, and that the actual gas
> there is H2 Gas.
>
> Please see the following post for the details:
>
> https://www.mail-archive.com/vortex-l@eskimo.com/msg101557.html
>
> Mark Jurich
>
> -----Original Message----- From: Craig Haynie
> Sent: Sunday, February 08, 2015 1:44 AM
> To: vortex-l@eskimo.com
> Subject: Re: [Vo]:Re: Dog Bone Project
>
> Pressure inside the dog bone is calculated to have been near 19,861 psi
> at the time of failure.
>
> https://docs.google.com/document/d/1BWYbi6tBHcjZ4PyQ0BaWn-G1NkdQdkirb-_Qx2HypKs/edit
>
> Craig
>
