Although BRANCh and OPNBRanch have their uses, they are often inadequate for describing the variations in branch impedance with operating conditions. For example, the branch might be a Helmholtz resonator whose impedance changes significantly with frequency. Further, BRANCh and OPNBRanch are wholly inadequate when branches involve thermoacoustic components. The TBRANch segment addresses these inadequacies by allowing DELTAE to integrate its way down a side branch and then return to the trunk and integrate there as before.
As an example, consider the modification shown in Figure V.1 to the basic ``beer cooler" (heat-driven thermoacoustic refrigerator) shown in Figure I.7. We might want to investigate whether performance would improve by adding the side branch so that the entire volume velocity required by the prime-mover stack would no longer have to flow through the refrigerator stack and much of the resonator dissipation would show up at ambient temperature instead of at the cold heat exchanger.
Modified "beer cooler."
DELTAE uses the TBRANch segment for cases like this. When it encounters a TBRANch, DELTAE treats subsequent segments as the sequential members of the branch, until it reaches a HARDEnd or SOFTEnd. It then ``returns to the trunk," treating the rest of the segments as trunk members. So the sequence of segments for the example of Figure IV.1 might be as follows:
TITLE BEGIN 0 ENDCAP 1 HXFRST 2 STKSLAB 3 HXLAST 4 TBRANCH 5 ISOCONE 6 ISODUCT 7 COMPLIANCE 8 HARDEND 9 HXFRST 10 STKSLAB 11 HXLAST 12 ISODUCT 13 COMPLIAN 14 HARDEND 15
Segments 5 through 9 comprise the side branch; the others comprise the trunk.
The method of computation is as follows. At a branch, the branch impedance (complex) is a pair of guesses, that DELTAE adjusts in its usual way to get the complex impedance at the next 'END to come out right. (If asked to do so, DELTAE should pair select both of these guess and target pairs as part of a default set. If not, you should enable them.) The guessed branch impedance determines how the (complex) volume velocity splits up at the branch. TBRANCHed models tend to have guess and target vectors of high dimension, since every 'END contributes two targets (and a few more targets are almost always needed for temperatures, heats, etc.). Stacks and heat exchangers can also be used in branches, and, of course, branches can have subbranches of their own.
TBRANch has a companion segment type, TEE, that takes the filename of another valid DELTAE input file as its only parameter. When DELTAE encounters a TEE, it loads the named file into the model, and replaces the BEGIN segment of the branch file with a TBRANch segment. It tries to guess starting values for the complex branch impedance, and then adjusts the addresses in any sameas declarations and free target-type segments occurring in the branch (or after the branch point) by the number of segments in the branch. Once the file has been read in, the TEE segment disappears-the .out file and (d)isplayed segments will be the composite model.
When rewriting our previous example to use a TEE segment, the model has the form
TITLE BEGIN 0 ENDCAP 1 HXFRST 2 STKSLAB 3 HXLAST 4 TEE 5 branch.in HXFRST 6 STKSLAB 7 HXLAST 8 ISODUCT 9 COMPLIAN 10 HARDEND 11
where we have omitted the parameters of all but the TEE segment. The file branch.in is a valid DELTAE input file, which we have run and debugged separately. This input file looks like this:
TITLE BEGIN 0 ISOCONE 1 ISODUCT 2 COMPLIANCE 3 HARDEND 4
The file may have any name (e.g., branch.in, branch.out, branch.tee), but it must be specified with the complete suffix.
The two models above will combine to produce the same model of our first example. This approach is recommended, especially for nontrivial branches containing stacks, etc., so that the two simpler submodels can be evaluated first. The impedance that DELTAE chooses for the TBRANch may need immediate attention; guess and target vectors, free targets, and sameas references should also be checked carefully. Special modes (see below) that link length parameters across the branch point will not be handled properly, and must be redone with new segment numbers.
The multiply-connected duct network of Figure I.3 can also be handled by DELTAE, through use of TBRANch and UNION. The UNION segment is used to tell DELTAE to ``connect" a TBRANch's SOFTEnd (or HARDEnd) back to the trunk at the location of the UNION segment. The branch's' SOFTEnd impedance targets are no longer used; instead, the two real input variables (b and c) of the UNION segment should always be active targets. It does not matter what the initial values of these parameters are; as soon as DELTAE processes the segment, it copies in the current values of the complex pressure at the SOFTEnd referenced by the number in parameter a of the UNION segment. These values are compared to the local complex pressure result, at this UNION, in the trunk, and iteration should drive the model until their difference is zero. As before, the guessed branch impedance determines how the (complex) volume velocity splits up at the TBRANch. Volume velocities are summed at the UNION. (The UNION segment is somewhat similar to the freetargets of the previous section, except that it grabs two results simultaneously, from fixed locations within the referenced segment. Also, the `target' values are not specified by the user, since they move dynamically depending on what is happening at the attached 'End segment.)
This feature of DELTAE is largely untested by us, and it is currently somewhat inadequate. Eventually, we hope to let DELTAE also guess how to split enthalpy flow at a TBRANCH to force temperatures at the SOFTEnd of the branch and at the UNION to be equal. In the meantime, if you need such a capability, try using a FREEtarget to keep temperatures equal at the UNION.