Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer Page: 48 of 77
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d f
dt =(fVA),+(f VA) 2-(fVA)3+ N (Al -2c)
Since we already know that t here are only two types of links, terminal links to node N f or which we
can use aN t with a positve sign in (38) and incident links with aN / using a negative sign in (38), the
programming is easier and more lucid. I f we were doing more complex geometries then Al -1 would be
more general. Thus, in our notation the aNk are used simply as a matrix location device.
For the f low directions f ixed as in Figure Al .1, the Equation (38) becomes
1dt
df = i (f VA )3 a (f VA )1 + -VjS,
f2 , 1 2,2 2 + +S2 (Al -3)
Vd3 = a32 (f VA )2- a3 (f VA )3 +VS3
or r ear r anged as:
df +a11(fVA)1 +a2(0)-a3(f VA)3 = 1S,
Vdf2 - a (f VA )1 + a2, (f VA )2 +a,, (0) = 2 2 (Al -4)
dt3 + as, (0 ) -a3,2 (f VA )2 + a', (f VA )3 = gS3
The t er ms associat ed wit h aN a are link (j unct ion) t er ms, not t o be conf used wit h t he volume 1, 2 and 3
indices. The aN k indicat e t he posit ion in t he mat r ix of t he f low t er ms. The mat r ix r epr esent at ion can
be writ ten as:
0 0 dfi /dt 1 0 -a (f VA )1 FVS)1
0 * 0 df2 / dt + -a21 a2 0 (f VA )2 VS)2 (Al -5)
0 0 L3 df / dt 0 a32 a33 (f VA) VS )347
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Lucas, D. S. Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer, article, October 1, 2004; [Idaho Falls, Idaho]. (https://digital.library.unt.edu/ark:/67531/metadc889821/m1/48/: accessed April 30, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.