Code Manual for CONTAIN 2.0 - Federation of American Scientists

where
,=W
Ipgu+wi
Note that when all slip ratios are one, the effective flow density, pfl, reduces to the sum of the gas
and debris densities, which is equivalent to the heavy-gas no slip assumption. Also, as s. tends
toward infinity, pfltends toward p~ as one would physically expect.
From the above equations one can write the atmosphere fluid, or gas, flow rate, W~, and the debris
field mass flow rate for each field, W~, in terms of the total combined debris and gas flow rate, Wij,
Wgij = % w..
‘f’ “
Wdijn = % w., (6-10)
,,
SnPfl 1’
where W~,ij is the mass flow rate of gas, and W~,ij,nis the mass flow rate of debris in field n.
Physically, we knOW that the sum of W~,ijand W~jj,~over all fields must be equal to the total mass
flow rate, Wij. It can be shown from the above two equations that this is true.
Gas and debris mass and energy conservation equations are shown in the following sections based
on the expressions derived above. Note that the variable ~ defined in Equation (6-8) turns out to be
important for evaluating the effect of flow on the distribution of gases and debris. A different value
of ~ is calculated for each cell depending upon the amount of debris in each field in the cell and the
slip parameter in each field in the cell.
6.2.2 Gas Mass Conservation
The net gas flow term in the gas mass conservation equation for cell i is written in terms of the gas
flOW rate W~,jiinto cell i, and W~jj out of cell i
x
w flow,i,k = N
ji
[“1
W~j,ejim~j,~ _
2
k
‘g,j,k
~ Wgijeij
[ ij 1
N
2
k
m. g,l,k
‘g,i,k
1
(6-8)
(6-9)
(6-11)
O 69 6/30/97