How do I calculate adiabatic compression of a mixture?

Interesting concept!

PV=NRT can tell you the temperature that would be reached by dry air. Then introduce sufficient liquid water to bring the temperature back down to 600K through heat of vaporization. This will give you a first approximation...

"The input is ambient temperature air and water, and the output is ambient temperature air and distilled water, thermodynamically "perfect"."

The input is ambient temperature air, water, and the energy required to compress the air/water mixture. The output is at least a little above ambient temperature air, plus water vapor, plus possibly liquid water, including whatever impurities were in the water to start with (in a still, there is a means of separating the impurities from the water vapor - In this device the water and its impurities are not separated, so the output is NOT distilled water), and the output energy. Most devices, like turbines and steam engines, that convert the energy of hot air/water mixtures into motion will leave a significant portion of the water in vapor form, which means that the energy used to vaporize that water is wasted.

"Experiments in 1930 proved that a compressed air-water mixture, which minimizes the heat lost from the system, when fed to a "steam engine" expander, is a more efficient means of power transmission than an electric generator and motor."

The strength of permanent magnets has increased vastly since the '30s, leading to significant improvement in the efficiencies of generators and alternators. I'm not aware of similar improvements in steam engines, so the results of the 1930 experiments may or may not still be valid.

Referring to my 1982 copy of Mark's Handbook for Mechanical Engineers, Eigth Edition:

"There was a time when water was injected into the suction of air compressors to reduce the discharge temperature; when the speed of machinery was increased and the clearance volume reduced, the practice was abandoned as hazardous. The temperature drop was substantial."

It goes on to say that "this scheme is still applied in chemical processes to wash out unsaturated gums and suppress the discharge temperature of exothermic gases." So there has to be a body of knowledge out there regarding this type of process.

Marks has a formula for estimating power requirement for compressing air, but no formulas for water-air mixtures. There is a statement that valve loss correction factor is 6 percent for each set of valves air travels through.

Interesting concept, what kind of compressor are you hoping to use? Is there one that can tolerate large quantities of liquid? How about the expander?

I anticipate a piston compressor and expander, which is what was used in 1930. Follow the logic here: One has a cylinder and piston. There is air and water in the cylinder. Push the piston to compress the air, which heats up. Some of the water boils, so there is a mixture of air and steam at some total pressure equal to the steam pressure (a function of temperature for staturated steam) and the air pressure. the air being cooler than it would be if compressed dry. When the gasses expand, the piston does work equal to the work put in, less friction and slight heat loss (poor insulation), so the end result is the same as the beginning, a cylinder full of air with some water, at or slightly less than the temperature it started at. No heat is lost through heat of vaporization, since one starts and ends with saturated air and liquid water. (OK, in a desert...) Obviously, the steam condenses as the mixture cools while it does work. Steam engines waste heat by exhausting gasseous water, but this scheme does not.

If the compressed gasses are stored separately, and the compression and expansion take place in different cylinders, the energy transmission and storage is still efficient. (US Patent Number 5,832,728)

The problem is, calculating what goes on is tricky. If you simply compress the air adiabatically, at say, a compression ratio of 30-1, and then inject water to cool it, one gets different answers than if you compress the air to a given temperature (600K for ease of calcuation -- roughly 300 C, which is comfortably less than the temperature at which steel loses strength) and then isothermally compress it while the water boils. One is also compressing the steam. There ought to be a simple way to simply calculate the total enthalpy in the storage tank vs. the enthalpy in the intake air and water, but then, how does one figure the ratio of air and water? I imagine I coud work up some sort of spreadsheet and optimize by a kind of Monte Carlo approach, but surely some of you working engineers out there know how to do this computation with elegant simplicity.

By the way, my citing 80 kw-hr storage is based on the x-prize requirement of 200 miles at 100 miles per gasoline equivalent. One must use xprize-supplied fuel (not a wind turbine) so I suppose using an electrically driven compressor. The compression ratio of the compressor should equal the expansion ratio of the expander, except the expander will have variable injection (hence variable expansion ratio) to accomodate different load conditions. Under low loads (overexpansion), the exhaust will be cool for free air conditioning. If at maximum injection, underexpansion, the exhaust will be warm for "free" heat; clearly efficiency suffers, but there is a requirement for 0 to 60 in 12 seconds. An advantage of air is that one can get very high power for a short time without destroying the batteries, and the air tanks should last as long as the rest of the vehicle, not requiring periodic recycling or disposal as toxic waste. Another advantage is that air tanks can be refilled quickly, at a gas station, not needing hours to recharge. Unfortunately, 80 kW-hr stored intanks may take up 80 cubic feet or more, which won't fit in my Prius.

For a hybrid vehicle, simply use the engine that came with the car, but use one cylinder for the compressor (downhill) and expander (uphill). Of course, that requires that the one cylinder has variable valve timing and air injection. Overall efficiency is limited by the IC engine.

For the xprize, the efficiency is limited by the efficiency of the electric motor driving the compressor, off -vehicle. If overall system efficiency exceeds 50 per cent, 100 MPGe (miles per gellon equivalent) should be feasible. Depending on the source of the electricity, the sytem can be totally pollution-free.

"If you simply compress the air adiabatically, at say, a compression ratio of 30-1, and then inject water to cool it, one gets different answers than if you compress the air to a given temperature (600K for ease of calcuation -- roughly 300 C, which is comfortably less than the temperature at which steel loses strength) and then isothermally compress it while the water boils. One is also compressing the steam."

This difference could be quite large, as you would be putting more energy into the compression of the gas if you don't cool it during compression. The average pressure against which you inject the water will also be greater for this case, but that is a relatively small effect.

Which illustrates that any answer will depend on the profile of the water injection. To first order, injecting the water at the start will minimise the amount you need for a given final temperature**. Probably the optimum (for minimum water volume) would be to inject it so that it always just evaporates during injection. But don't forget that water/steam is a wonderful catalyst for oxidation - particularly at high temperatures.
**Minimum water volume <=> minimum energy stored...

Fyz

I would suppose a simple carburettor at the air intake would provide fine droplets of water mixed in the air. As the air is compressed, the water droplets are supposed to boil to steam. Problem: at some point the air pressure may be higher than the steam pressure at that temperature, and the droplets won't boil! Considering that, at 238 deg C, saturated steam has a pressure of 31 bar, I probably won't have that problem and need not go much higher in temp.

High air pressure will stop the water boiling - but that's not a problem as such - you are concerned with evaporation. Bubble formation (boiling) will tend to improve the mixing and so speed this up, but that should not be important if the droplets are small enough (sorry, I can't give numbers on this).

So long as the temperature eventually reaches your target, the presence of modest amounts of excess water in the compression chamber won't significantly affect the thermodynamic efficiency. The potential problems would be that droplets in the mix will increase turbulence losses (like driving through rain), and that droplets on the surfaces would provide "seed" points for damaging chemical reactions. However, if you want to saturate the mixture with steam, it will not be possible to avoid the second, because the chamber surfaces will always be cooler than the gas during the compression cycle.

My inclination would be to present no more water than you actually need. Also, it's worth remembering that steam and mixed-steam engines do not exceed the efficiencies of a Carnot cycle, and reducing the peak temperature will lower both the energy you can convert and the maximum operating efficiency.

Two final notes for now:
a) whenever the temperature exceeds the critical temperature of water (~374^OC), the water will boil irrespective of the gas pressure.
b) make certain you understand the risks involved in this sort of work, and that you take adequate precautions (err on the overcautious side if anything). For example: high pressures and temperatures and water make for interesting effects if ever there is a leak (steam jets make wonderful cutters - they put most lasers to shame).

It will never work. Just buy a system at Walmart. Done. Take a vacation.

very fuzzily i remember that you must take into account the entrophy term of the energy balance for the REAL work done on compressed gas. the solution comes from solving simutaneous 2nd order diferential equations .. i did it for a mixture of three gases in 1984 in school.. my advise is find a thermo book and look a look up work to compress non ideal gas, behavior etc..

work done in multiple steps if theoretically more effeicient that work done in single steps. as is seen in the asian high rpm engines small displacement engines vs the old school not so big 3 high displ low rpm like we have always done solution

i am lost regarding the last statement regarding input and output

Welcome fellow XPrize competitor!

I'm here to steal all your secrets. Actually, this sounds really interesting, although 600K seems very hot if you are to avoid heat loss. Ordinarily, if you wanted to store 80 kW in a minimum volume, compressed air would be one of the last places to look, but steam would have much higher energy. There'd have to be a prime mover, and I assume this would not be onboard, given the 80kWh storage capacity. It would be great to see a fundamentally different approach to propelling a vehicle.

I'd have to say your technology would be about 30 years more advanced than mine: I am emulating the 1903 Lohner-Porsche gasoline-hybrid.

The input is ambient temperature air and water, and the output is ambient temperature air and distilled water, thermodynamically "perfect".

This may be oversimplifying things a bit. Viewed as a system, a compressed-air-powered car has the characteristic you describe: ambient temp air goes into the compressor, and ambient (or even lower) temp air comes out the tailpipe.

But interesting, anyway. Too bad the Stanley Steamer name has been taken by a carpet cleaning company!

Good luck, and I hope to see you on the race course!

to my point !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

if it requires computer solutions to simutaneous differential equations i do not want to participate. accuracy is one thing, learning a painful lesson on how complex reality is is quite another, where do i sign up for the easy!

i read once a long time ago an article written by Igor Sekorsky about how he drove 60 miles on one gallon of gas in the 50s! i think i am going to enter the challenge! ( speeding up and then turning it off and coasting!)

the author does have a good point however -- the internet sux at capturing information before it was born -- DOW chem and other companies have brightened up to look at expired intellectual property and determine if there is a fit with todays solutions and a possible improvements

i saw an interview on TV with Peter Diamandis, the X- founder, what a neat guy - very few people (male ha ha) i would like to hang out with for a day , but he would be on the top of the list

ideas, a dream, people, passion, progress.....................

keep computing -- remember .......you can sail across the ocean on air power! just like Columbus!