THE POLYTROPIC COMPEX CYCLE MACHINE
By : Rudolph N. J. Draaisma
(latest revision date:
11 May, 2008
)
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First of all, the below is NOT about any invention, nothing that can be patented, but pure thermo theory only.
THE POLYTROPIC COMPEX cycle theory is the basis for a polytropic technology, to achieve refrigeration without condensing and evaporating a medium. Moreover, the drive energy is far lower than in conventional technology. A further development as a steam cycle, even gives a method to convert heat energy into mechanical power at very high efficiency rates.
Similar innovations on the subject normally consist of designs, in which heat exchange is done from gas-to-solid, f.ex. a gas column in resonance (sound), or by using gas-to-gas heat exchangers. This gives a bad heat transfer and the need of excessive heat exchange areas, which prohibits the commercial use of these innovations. In the polytropic COMPEX cycle machine, these limitations are eliminated through the per-design probability for it.
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In the COMPEX design (COMPression-EXpansion), see illustration on the left, a liquid is brought into intensive contact with an alternately compressing and expanding gas, giving optimal heat transfer between the two media.
This alternating heat transfer causes a to isotherm shifted polytropic compression and expansion. The gas creates temperature differences and the liquid acts as an energy carrier. Heat exchange with the environment is then done from liquid-to-solid.This gives a good heat transfer with moderate heat transfer areas, which keeps the size of the design within marketing restraints. |
The thermodynamics, see figure on the right above, are quite similar to the (inverted) Sterling process. The main difference is though, that internal exchanges of heat occur spontaneously by virtue of probabilty, that the design creates (in the Sterling, these exchanges are forced about externally, creating efficiency-depleting irreversibilities)
The theory is easy but doing it is not (the scheme above is not a valid design concept - it will not work that way, cause I tried it out). However, there is an other way. I have long tried to find a way to inverse the cycle (the arrows go clockwise instead), in order to convert heat directly into mechanical power on the shaft. Even if it could be done, the small work area DW, of such great advantage in a cooling machine, would be equally of disadvantage for an energy converter, as the machine size would become too large.
During the last years I became aware of the experiments done by nobody less than James Watt, around 250 years ago, showing a quite different way. It finally brought me on an idea, still being the compex-cycle, but now using saturated and wet steam as active medium.
Because wet steam contains mixed water droplets, it will compress in a polytropic manner, just as shown above and thus the steam will not get superheated during compression, requiring much less compression work than expected isentropic work. Watt showed that the expansion of saturated steam is quite different from that of inert gases and I call it "supertropic expansion", doing far more work than the expected isentropic expansion would. To close the cycle, an amount of heat, equal to the difference between compression and expansion work, must be applied from an external source and in the ideal case, this heat fully appears as mechanical output power on the shaft of the compex machine. It follows from the following calculations:
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I have secured that there is only one solution to the block of equations, which is imperative to give it credibility.
The minuscule water droplets (molecules), that whirl around in the steam after expansion, have such a perfect heat exchange with the steam, that they absorb enough compression heat to nearly keep the same increasing temperature as the compressing steam, equal to the saturation temperature of momentary pressure, but without evaporating.
This drives the compression process polytropically towards isotherm, as shown by n2 = 1.07
Remarkable is the large amount of expansion work, considering that isentropic expansion would give a specific enthalpy change DHx of appr. 390 kJ/kg (Mollier diagram), where it is calculated here to be 738 kJ/kg.
If we force DHx to be 390 kJ/kg in the calculation (replace the integral with DHx = 390), we get n = 1.13 at x = 0.87, as the latter is found in the Mollier diagram also - the formulas are thus correct. (see also PH-diagram below)
All gases have a specific k = Cp/Cv for adiabatic change of condition and for saturated steam we thus get k = 1.13 (similar to hydro-carbon gases)
When heat is applied during expansion, or cooled off during compression, Cp/Cv changes to n < k and becomes n = 1 for isotherm change of condition. The compression work becomes less and the expansion work becomes more than when n = k
n > k supertrope
n = k isentrope (adiabatic)
n < k polytrope
n = 1 isotherm |
My explanation for the supertropic expansion of saturated steam (and all other saturated vapors) is, that at each incremental decrease of pressure, previous formed water droplets re-evaporate, doing additional expansion work, by which they liquefy again, evaporate again and so on continuously. This is the basic process; the detailed process on the molecular level, even more when also the piston action (slugging) is considered, is of course far more complicated.
In the general PH-diagram on the left (valid for all vapors) we see the process as calculated above. Expansion from point 1 to point 3 with enthalpy H3, by which the gas part goes saturated from 1 to 2 and the resulting liquid part at the end of expansion is in point 5.
Mind that this liquefaction is totally different fom condensation. Condensation occurs coagulated on colder surfaces, by cooling off heat. Not so here, where liquid water molecules pop-up evenly divided everywhere in the expanding volume, due to the decrease of internal energy as a result of doing work - no heat is cooled off..
During compression, the gas part rerverts saturated to point 1 and the liquid part goes saturated to point 4, so the end condition becomes in point 6, with enthalpy H6. The heat applied to close the cycle from point 6 to 1, is H1-H6 and appears on the shaft as mechanical work - hence 100% heat to mechanical work conversion (ideal case).
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| This is consistent with the results of James Watt's experiments, as follows: |
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".....The efficiency to be secured by the expansion of steam had long been known to Watt, as early as 1769. The patent was issued on July 17, 1782. Watt specified a cut-off at one quarter stroke as usually best. The sketch on the left shows this progressive variation of pressure as expansion proceeds.
Steam entering the cylinder is admitted until one-fourth the stroke has been made, when the steam valve is closed, and the remainder of the stroke is performed without further addition of steam. The variation of steam pressure is approximately inversely proportional to the variation of its volume. The pressure is always nearly equal to the product of the initial pressure and volume divided by the volume at the given instant...."
 In symbolics: P2 = (P1•V1)/V2, which is isotherm behavior! On the other hand, saturated and wet steam cannot expand isothermally, while doing work - this causes the supertropic character, as calculated above and shown here on the right.
The red curve shows fully isotherm expansion and the blue, dashed curve, the actual expansion from the calculation above - very consistent with Watt's observations!
Read the full report here
http://www.history.rochester.edu/steam/thurston/1878/Chapter3.html
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Steam technology developed further on basis of full cylinder loads and without condenser in vehicles (locomotives), in order to keep the cylinder sizes down. The later internal combustion engine took over from the steam piston in vehicles and the steam turbine in power stations for the generation of electricity (in most today's steam turbines the steam is not expanded, but its heat energy is converted to kinetic energy in venturi tubes).
Thus the expansive power of steam was never further investigated after Watt and supertropic expansion of saturated and wet steam was never discovered. I claim to be the first one to have done it now, 250 years after Watt experimented with it. (see also this testimonial )
I have worked things out more extensively with computer modeling, showing quite some interesting results. I have the design data caculations ready for building a test-stand, to see what really happens with steam under various conditions, as well as dimensioning calculations for a first experimental machine.
I hope that some developer will hire me as a contracted consulting engineer, to turn this concept into a commercial product (no claims on intellectual property from my side). If you are such a possible developer, please contact me.
Rudolph N.J. Draaisma B.Sc. Tech
 CONSULTING ENGINEER
Energy conversion and recovery systems
CAD drawings &Techn. calculations (MathCad)
Techn descriptions & illustrations
Translations, Documentations
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www.draaisma.net/alternative_engineering/
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