Hackney: As if the burner on the tank never fires?
Don't take the temperature numbers in that picture too literally- it's a piece of marketing hype from one of the smaller vendors, but I posted it for clarity of how the output needs to be plumbed. They're a bit optimistic on the drainwater temp if the shower head output is actually 40C, the drain will be a few degrees less, but the concept is clear. The actual temp out of potable side of the HX depends on the flow and the size- the taller-fatter ones will actually exceed 80F at 2.5gpm balance-flow configurations.
For reference, the 4" x 4' in my basement delivers a delta-T of ~30F during the cold water months at whatever uncalibrated gusher-head flow my shower is running, but it's probably more than 2.5, less than 3.5gpm, and I can shower 24/365 without the boiler modulating any higher than ~55-60KBTU/hr. (YMMV) and that's even with sub-40F incoming water. Since it's not running as a priority zone, it'll sneak up to ~70KBTU/hr output with all zones calling for heat while somebody is in the shower, and I have the hydro-air zone set up to kick off when the water temp drops to ~110F to be sure that the shower literally never runs cold (all heat is pulling from the same buffer tank, single temp, but the DHW is isolated with an internal HX in the buffer.)
The BTU input rate of the burner on an 80 gallon tank is pretty substantial (but unstated.) If he's not pulling the ungodly 15gpm continuously, burner-on counts for a lot. In third party Canadian testing at 2.5 gpm flows, when plumbed as in the above diagram, it takes about an hour for the shower head temp to drop below 37C (body temperature) with standard-burner 40 gallon gas-fired tanks with ~8C incoming water, and goes literally forever with higher BTU burners. (If you want test data much of it is available online with a google search, and not too hard to find. googling on "drainwater" in combination with "NRCAN" gets you a bunch of the very-abbreviated overviews, and some of the characterization test descriptions.)
With ~2x the tank ~2x the burner, assuming the sidesprays aren't running a 100% duty cycle so maybe it's only 4x the average flow (rather than ~8x) it won't run for the hour with only an 75-80K burner behind it, but, with the burner firing it'll still go a LOT further that it can without the BTU feedback of the HX. If it's ~4-5 gpm for most of the showering period, but 15-16gpm for a few minutes at the end, that's totally tank-able with the HX (and totally NOT without it.) At 8x the flow continuously it needs more burner, but the price and performance of the HX is still better than adding a third tankless.
Ballvalve: The center pipe is a smooth bore copper drain, and it counts on a vertical orientation and the surface tension of the greywater to spread as a thin film clinging to the interior of the pipe, which is does. So called "gravity film" heat exchangers like this have been around for about 30 years now, and they've since been improved both performance & anticipated longevity (~30-50 years before hitting only 75% of day-1 efficiency.)
At current gas prices most people won't have them long enough to pay off, but with gusher showers like that the payback is pretty quick- like the first time your wife goes into the shower shortly after you, and doesn't come back screaming. (Have you priced divorce lawyers?
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