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We are thinking of similar things... just a hair different details... mainly along the limits of what current science would allow ... and the best current tech available... vs I think you were thinking of more average real world devices.
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I'm not so sure we are thinking of similar things. HHO has a very specific meaning these days. It has essentially nothing to do with the science of water electrolysis and the various means to obtain good round trip efficiencies in, for example, going from electricity-to-H2-to-fuel-cell-to-electric-motor-to-car-wheels. Real scientists ask, "Does it makes sense to go from solar energy to electricity to H2 through a fuel cell back to get electricity again, through a motor and to the ground?" "Does it make more sense or less sense to start with methane, and reform it into H2?" "Does it make more sense or less to simply charge batteries with PV, and avoid all the losses of fooling with H2?" These are questions to which scientists and engineers can provide supported answers and informed opinions (and some of the answers are complex).
There are no scientists and engineers involved with "HHO*," in any meaningful sense. The term "HHO" (in the context of this thread) has the meaning that Dennis Lee (the guy the FTC sued, and probably the largest promoter of HHO units and perpetual motion machines) and similar folks have given it:
An onboard electrolyser, powered by the car's alternator, the output of which is fed into the intake airstream, with the supposed goal of improving fuel efficiency. These units, to work, would have to work by magic, and have never been demonstrated to work. When Lee's unit (a "better" unit than most) was tested by arguably the most prominent, highly-respected guy in the automotive combustion field, the results were just as the science would predict: no effect at all. Even the negative effect of the energy loss was too small to measure: turning on an HHO unit is like turning on the headlights: 140 watts is too small to measure in an engine that can produce 100,000 watts or more.
(One unit was advertised as using almost no water -- you filled the tank monthly or some such. Of course, if it is not using water, it is doing nothing at all -- a stunningly obvious point missed by customers.)
The web is chock full of demonstrations of oxyhydrogen burning with a bang, as "proof" that these units work. Some of the people offering this as proof might be sincere, but completely uninformed. The issue is not that "HHO" units make a burnable gas -- of course they can. The issue is that the gas they make is produced with a huge (percentage) loss in energy. It is a smokescreen: "See, there's the bang... it works!"
Ironically, if an HHO unit were made that had significant output (20 liters per minute,for example) then the losses would be measurable (and a 200 amp alternator would be smoking). As it is, the units are placebos, so some people are convinced they are getting better mileage.
In this case, we are not replacing a car's engine with a combined cycle/ cogeneration gas turbine that can operate at 60% efficiency. We are using the existing car's engine. (You seem to be thinking about a highly efficient source of electric energy that is somehow onboard the car.) The car's engine produces an electrical output at no more than 20% efficiency (even if the car is the best of the best, a Prius with a high efficiency alternator.) If the HHO unit were 100% efficient, it would produce an output energy (in the form of H2) of 1/5 the the input energy (gasoline). In other words, for each ounce of gasoline burned, you get back 1/5 of an ounce energy equivalent in H2. Clearly, even with an impossibly efficient HHO unit, you operate at a net loss. To break even on an energy balance, you would need 500% efficiency at the HHO unit.
I think you are answering a different question: "If we wanted to make a perpetual motion machine, using electrolyzed H2 in the process, and using the highest conversion rates demonstrated in heat engines, then what efficiency would be required for the electrolysis step?" That is not the question that applies to HHO units as used in an attempt to improve fuel efficiency. These people are not considering replacing their engines.
To make me believe that
lower than 500% HHO unit efficiencies could reach break even, you would have to show me a production car that produces electricity from its alternator at better than 20% efficiency (from gasoline to electricity).
500% is a convenient round number, but as I wrote above 666% is more realist very best case.
Obviously, efficiencies over 100% are impossible. These HHO units do not operate in the endothermic region, and do not have a COP of remotely close to 1.2. (This can only occur with steam electrolysis -- and then only under certain conditions.) They are not heat pumps, and if they were, the typical car engine would have a difficult time making productive use of low grade heat: engineers have worked for decades on just making use of the abundant waste heat from engines, with only the most minor successes.)
But obviously, breaking even is not the goal. The goal is a large increment in fuel efficiency (50% gains, 100% gains 200% gains -- you name it, it's been advertised) Dennis Lee used to advertise 100 mpg from a Honda Accord, and his site provided all sorts of creative and outlandish explanations for how that might be possible.
*The people who make welding units use the term oxyhydrogen.
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While I agree with the differences ... I wouldn't go so far as saying 'has nothing at all'
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I'm sticking to my story here. By "nothing at all" I mean nothing meaningful. Results of a study in which injection amounts are more than 2 orders of magnitude greater and in which the H2 is supplied for free energetically have no bearing on the physics of HHO applications. Yes, a study on dress making and a study on electrolysis have something in common (physics affect both), but it is reasonable to say, less literally, that one has nothing to do with the other.
Do you realize what microscopic quantities of H2 we are talking about? A 2 liter engine might produce 100 kW, and use 25 kg of fuel per hour, or 417 grams per minute. The .06 grams of H2 that a 1 lpm HHO unit produces has the energy of .15 gram of gasoline. .15/417 is a very small percentage: .035%