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Variable Cross-Section area layer height and volume #128

Open GoogleCodeExporter opened 9 years ago

GoogleCodeExporter commented 9 years ago 
See the attached case.  A 10x10x10 compartment with a fast t^2 fire where I 
define variable cross-sectional areas as:

0, 100
2, 200
4, 300
6, 200

I run the case and the t=0 layer height is 4.8 m when I would expect 10 m.  At 
the end of the case the layer height is 4.4 m.  The layer volume is reported as 
1000 m^3.  However it should be (10-6)*200+(6-4.4)*300 = 1280 m^3.

The manual is not very explicit on this feature.  I assume that the 
cross-sectional area is maintained constant from 0 to 2, 2 to 4, 4 to 6, and 6 
to 10.  If instead it is a linear interpolation then I would expect a volume of 
(10-6)*200+(6-4.4)*0.5*(300+(300+(200-300)*(4.4-4)/(6-4)) = 1184 m^3

If I change it to a 30x30 compartment then the initial layer is 10 m.  It 
doesn't make sense why that should change the initial layer height when I 
override the width and depth with a custom cross-sectional area.  At the end of 
that simulation the layer height is near 0 and the volume is 2100 m^3, but the 
volume of my cross sections is only 2000 m^2.

Original issue reported on code.google.com by drjfloyd on 23 Feb 2015 at 6:12

Attachments:

GoogleCodeExporter commented 9 years ago 
Forgot to note I used 6.3.0.1445

Original comment by drjfloyd on 23 Feb 2015 at 6:30

GoogleCodeExporter commented 9 years ago 
Clearly a bug here.  There at least two things going on.  1. We initialize the 
minimum and maximum layer volumes before we account for variable 
cross-sectional area which causes the odd issue with a 10 m x 10 m x 10 m 
specified input.

It also looks like the calculation of layer volume which just interpolates the 
calculated volume as a function of height isn't working right for the 30 m x 30 
m x 30 m specified input variant.

CFAST does interpolate between the cross-sectional area data points, so I get 
the full volume to be (2-0)*(200+100)/2 + (4-2)*(300+200)/2 + (6-4)*(200+300)/2 
+ (10-6)*200 = 2100 m^3

Original comment by cfastdev@gmail.com on 26 Feb 2015 at 6:45

GoogleCodeExporter commented 9 years ago 
In addition to fixing the bugs, I think additional explanation regarding the 
interpolaion in the User's Guide would help.

Original comment by drjfloyd on 26 Feb 2015 at 6:48

GoogleCodeExporter commented 9 years ago 
I agree.  We'll add discussion to the guides.  How do you see it being used? At 
the moment, we have an inconsistent input, I think. Consider the following 
simple case: 10 m x 10 m x 10 m compartment; area at the floor is 100 m^2; area 
at the ceiling is 0 m^2.  If you assume the structure is a pyramid, the total 
volume is 333.33... m^3. If you assume the structure is an A-frame (which it 
turns out is what CFAST currently assumes), the total volume is 500 m^3. There 
are an infinite number of other possibilities.

I'm inclined to change the input to volume as a function of height rather than 
area since that's what we're actually using in the code. Since we determine the 
upper layer volume from the ODEs, we calculate the layer height by 
interpolating a volume as a function of height curve calculated from the area 
as a function of height inputs. The problem is that the area inputs do not map 
to a single unique set of volumes.

Thoughts?

Original comment by rpea...@gmail.com on 26 Feb 2015 at 8:25

GoogleCodeExporter commented 9 years ago 
I guess the A-frame makes sense if the use case in mind was a vaulted ceiling.  
I agree that doesn't really address all the possibilities.

The scenario that started this was I had a 4 story atrium (width was close to 
height so I wasn't very concerned about shaft effects) where each floor had a 
slightly different area open to the atrium. I wanted to get the correct volume 
for smoke filling as the layer dropped to the floor.

In this case being able to specify volumes would be perfect.  I guess you would 
use the compartment dx,dy,dz for estimating surface area for heat transfer and 
then let the user specify i pairs of z and vol  where vol = the volume between 
z_i and z_i-1 (z_0 is the floor)? In this case there would be a presumption of 
constant area over each interval.

Original comment by drjfloyd on 26 Feb 2015 at 8:59

GoogleCodeExporter commented 9 years ago 
Our thinking has evolved a bit as we try different test cases in the updated 
code. Here's a draft of updated documentation for the variable area inputs. 
I've tried to explain how things are handled in the code in the bullets at the 
end (which is the style we use throughout the user's guide). Is there more that 
you would like to see explained / Is this still confusing / ... thoughts?

Original comment by rpea...@gmail.com on 13 Mar 2015 at 3:49

Attachments:

GoogleCodeExporter commented 9 years ago 
I think that is the right level of detail. It is clear to me how CFAST 
processes the inputs, the relation to the original compartment definition,and 
how the areas are used during a calculaiton.

Original comment by drjfloyd on 13 Mar 2015 at 7:27