BACKGROUND OF INVENTION In researching the present invention, I discovered many patents that took advantage of waste heat to increase mechanical work and engine efficiency. Most of these patents selected water as the injected liquid. None of the other patents, however, made use of superheated injected liquids. The liquid entering a relatively low pressure cylinder when compared with the liquid's saturation pressure at the injected temperature is indeed superheated for an instant after being injected. The physical calculations of temperature and pressure show that the temperature of the injected liquid if water is the selected substance needs to be within a fairly close proximity to the critical temperature in order to increase pressure of the mixture. Water has such a high latent heat of vaporization that it can easily over cool the compressed gas and result in a decrease of pressure. No engine will be as efficient as it is without injecting water, if both temperature and pressure decrease before the power stroke begins expansion. Typically, in engine patents that I reviewed, ambient water was converted to steam using waste heat of combustion gasses. Each, typically, also used internal combustion from an Otto or Diesel cycle to generate the heat. The present invention does not use internal combustion for its heat source. A ‘carrier gas’ is heated outside the engine, via solar, a typical water heater, or exhaust recovery heat. A liquid is also pre-heated externally or by purchasing/renting an insulated, pressurized container of the hot liquid. The present invention is somewhat more like a battery powered motor than an internal combustion engine. Some combination of liquid and carrier gas should permit the use of ambient heating of the carrier gas while supplying a pressurized, stored ‘thermos’ of liquid heated to near its critical temperature as the only energy input necessary. Presently, the demonstrated RAKH Cycle Engine prefered configuration uses argon carrier gas with hot water as the injected liquid.
References Cited
U.S. Patent Documents
770468 September, 1904 Lake 60/674
917317 April, 1909 Lake 60/674
924100 June, 1909 Nichols 123/191
1032236 July, 1912 Patten 60/650
1739255 December, 1929 Niven 123/193
1926463 September, 1933 Stoddard 60/650
2062013 November, 1936 Opolo 123/193
2791881 June, 1954 Denker 60/619
3006146 October, 1961 Jackson 60/649
3867816 February, 1975 Barrett 60/682
3,964,263 Jun. 22, 1976 Tibbs 60/712
4,270,351 Jun. 2, 1981 Kuhns 60/517
4,322,950 Apr. 6, 1982 Jepsen 60/712
4,326,388 Apr. 27, 1982 McFee 62/324.6
4,402,193 Sep. 6, 1983 McFee 62/304
4,553,397 Nov. 19, 1985 Wilensky 60/649
4,691,523 Sep. 8, 1987 Rosado 60/649
5,035,115 Jul. 30, 1991 Ptasinski 60/712
5,983,640 Nov. 16, 1999 Czaja 60/674
SUMMARY OF THE INVENTION The engine and its thermodynamic cycle, which is described herein, will be called the RAKH CYCLE ENGINE. The said engine cycle involves a gas or mixture of gasses that are herein referred to as the ‘carrier gas’ and a superheated liquid, which vaporizes but does not burn. The purpose of the carrier gas is to bring thermal energy into a volume where compression is used to concentrate thermal energy at a higher temperature. A liquid is then injected. In an engine cycle, the liquid must be superheated above its saturation temperature corresponding to the pressure that the carrier gas attains at its maximum compression. The carrier gas must be much hotter than the injected liquid in order to force heat to be transferred into the injected liquid rapidly. Heat that is transferred from the carrier gas will cool the carrier gas resulting in a lower temperature and pressure. Transfer of the heat from the carrier gas into the liquid, on the other hand, will greatly increase the volume of the injected liquid, through converting it into a vapor. The temperature of the liquid will increase while the temperature of the carrier gas will decrease. The decrease of temperature is moderated by further compression of the carrier gas due to displacement from the vapor produced forcing the carrier gas into a smaller volume. All of the experimental results, which I have derived by calculation, have always resulted in a lower temperature from the end of event one up through to the end of mixture temperature equalization in event three. This theoretical observation may prove false in practice however, for real liquids that are injected at pressures above their critical point into a carrier gas that is also compressed to a point that is above the critical pressure of the liquid. Some real gasses and liquids exhibit an overall increase in pressure upon vaporization of the liquid in the mixture. The compression phase end temperature of the carrier gas before liquid injection decreases after temperature equalization of the mixture. The present invention may also use substances injected above their critical temperature and pressure. Those superheated substances are still considered as liquids for. The best choice of carrier gas would not condense at the peak cycle pressure. The purpose of the carrier gas is to carry heat into the cycle, which is transferred to a liquid injected at a later point in the cycle after the carrier gas is compressed. Calculations are very difficult because of changing gamma values for the liquid and carrier gas. The preferred implementation uses Argon as the carrier gas and water as the injected liquid. The gamma value for Argon is nearly constant at varying temperatures. FIGS. 1 through 3 illustrate the prefered implementation of a closed four-cycle, piston driven RAKH Cycle Engine.
The first event of the RAKH CYCLE is adiabatic compression of a carrier gas to increase its temperature via input of mechanical energy similar to a diesel cycle compressing air to a temperature hot enough to ignite fuel via adiabatic compression. The purpose of this compression in the RAKH cycle, however, is to concentrate the thermal heat via an increase in temperature to force rapid transfer of energy to the liquid injected in event two.
The second event in this thermodynamic cycle is the injection of liquid into a nearly constant volume of the gas at the end of the first event. If the cycle is used in an engine, the liquid will be heated to some sufficient temperature, such that part of the liquid flashes into the gasseous phase due to the excess thermal energy of the liquid enthalpy beyond that of the liquid at its saturation temperature for the pressure in the cylinder (or turbine) arrived at by the mixture.
Event three in the cycle is equalization of temperature prior to the rapid expansion event, which follows. This third event happens very fast within the same constant volume (shown in FIG. 4) and includes the transfer of thermal energy from the carrier gas to the injected liquid, which had not yet completely flashed to a gas. If there is a sufficient temperature difference to allow heat to transfer from the carrier gas to the liquid at its saturation temperature and pressure, further vaporization will occur. Complete vaporization is not required for this event. The mixture's pressure may go down during this event. Pressure and or the temperature may be above the critical point for the liquid at the point of injection or after the temperature equalization of event three. In an engine, the sum of partial pressures must exceed the pressure at the end of event 1 or the engine will not run with out power input to the cycle. Power to volume is low in any case. The fourth event is adiabatic expansion of the mixture. This adiabatic expansion will typically be back down to the original volume found at the beginning of event one. A turbine engine application may have the advantage over the piston engine since the final volume of a piston engine is geometrically constrained to equal event one's starting volume. Values at each point of expansion that are shown in Listings 1 through 6 were calculated as if the liquid had been injected at those points as though they were the end points of the compression. The physical path to the end compression point makes no difference on theoretical adiabatic end pressure and temperature. Listings 1 to 6 are listings of the theoretical results using a computer program.
The fifth event, is the exhausting of the mixture. The exhaust mixture should be captured into a condenser designed to handle separation of the mixture into its separate components to increase efficiency. The RAKH Cycle, however, does not require a condenser, but does assume a continuous supply of carrier gas and liquid from some source at a constant temperature and pressure. Burning a little oxygen in a predominantly hydrogen carrier gas would provide adequate hot hydrogen carrier gas having a little superheated steam mixed in with it.
Event six is the induction of the carrier gas, which brings the cycle back to the initial conditions of event one whenever the cycle is running in a steady state. This sequence of six events will be repeated as a continuous thermodynamic cycle, which will be referred to as the RAKH CYCLE without regard for which starting point is arbitrarily picked for event 1. FIG. 5 is a typical engine Pressure Volume (PV) diagram showing pressure during through each event in the cycle.
Engines using this cycle are RAKH Cycle Engines. Refrigeration machines using this cycle with appropriate working substances selected for refrigeration, are referred to as RAKH refrigerators.
The selection of the carrier gas and liquid are major variables impacting the cycle efficiencies. Ability for the combination to produce power, is a very narrow margin between operable and non-operability for a RAKH Cycle Engine. The variability of gamma for the real gasses is what allows the cycle to work below the critical point. The gamma value is the ratio of the specific heat at constant pressure to the specific heat at constant volume. For a small adiabatic change of volume, the change of pressure is dependent upon gamma in the relationship: P2=P1 times (V1/V2) raised to the gamma power where P1 is the starting pressure, V1 represents the starting volume, and V2 is the final volume. This is also frequently referred to as the compression ratio. If gamma is 2 and the compression ratio is 10 then the adiabatic final pressure will be P1 times 100 (10 squared) and not simply P1 times 10 as might have otherwise been expected. I selected carrier gasses that had a very nearly constant gamma for ease of calculation in the illustrated computer listings. Hydrogen may be the best bet for a carrier gas for efficiency in heating previously mentioned and because it is fairly easy to separate from the hydrogen-steam mixture.
BRIEF DESCRIPTION OF THE DRAWINGS FIGS. 1-3 Show the complete essential elements of the preferred implementation of a closed cycle RAKH Cycle Engine.
FIG. 1 Illustrates the carrier gas storage and heating system elements which deliver engine induction carrier gas to the heat converting mechanical work engine.
FIG. 2 shows a compact, high volume W9 piston type implementation of a RAKH Cycle Engine.
FIG. 3 illustrates the exhaust recovery system that returns dry carrier gas back to the carrier gas storage and heating system of FIG. 1.
FIGS. 4-6 show the thermodynamic sequence of Pressure, Temperature, and Volume at initial conditions, compression, and superheated liquid injection for a piston. FIG. 4 shows mass, and initial P, V, and T, at the beginning of compression. FIG. 5 shows P, V, and T, at TDC after maximum compression and; FIG. 6 at Top Dead Center (TDC) after liquid injection, at the start of the power stroke using the 4-stroke RAKH cycle engine described in FIGS. 1-3 and the set of initial conditions selected in the last computer printout listing, listing 6.
Listings 1-6 are computer program listings which show power and efficiency variations and the thermodynamic conditions of the RAKH Cycle Engine Run at uniform incremental points of the cycle under variations of compression ratio, initial carrier gas induction temperatures, and liquid injection quantities for water injected near the critical temperature at 704 degrees F.
COMPUTER LISTINGS
Listing 1 is a computer printout for 8:1 compression at 1200 deg. F. starting gas temperature.
Argon @ STP = 39.948 grams for 22.4 liters
Cp = .133; Cv = .075165; gamma = 1.769441
T2 = 7760.784 deg. F. & P2 = 2813.341 psia; Head Vol. = 62.5 cc;
CR = 8:1; free Ambient = 300 deg. F.
Argon Pres/Temp compensated mass in grams = 1.37449
Thermal energy per power cycle to heat Argon = .2049907 BTUs
Assumed free feed Water heat = 268 BTUs per pound
Thermal energy per power cycle to heat Water = 7.598673E−02 BTUs
Mechanical work done to compress the Argon is −928.0307 ft-lbs
************************* Event 2 **********************************
At TDC, inject .06 grams of superheated Water at 704 deg. F.
% Mole mass Argon = 95.81733% % Mole mass H2O = 4.18267%
********************************************************************
Since the injected Water is superheated, some flashes to vapor;
Volume .06 grams of Saturated vapor at 2784.7 psia = .390925 cc
So, Argon is further compressed and now occupies only 62.10907 cc
The cylinder pressure however, decreases to 2784.7 psia
as a result of all the Water converting to saturated vapor
and the carrier gas temperature changes to 7638.407
Equalizing temperatures, the vapor's temperature goes up to meet
Argon's decreasing temperature at 5692.219 deg. F.
8:1 Compression of Argon starting @ 1200 deg. F. & 71 psia
Calculating partial volumes of .06 grains Water vapor & 1.37449 grams Argon
yields 4.551353 & 57.94865 cc respectively after equalizing temperatures.
Sums of the partial volumes must equal the cylinder volume of 62.5 at TDC.
Angle Temp. F. PSIA Cyl Vol Steam Argon
90 5692.219 2983.976 62.5 4.5513 SUP 57.94865
80 5415.021 2657.699 66.60092 4.9205 SUP 61.68034
70 4747.316 1959.702 78.80437 5.9693 SUP 72.83501
60 3973.675 1307.761 98.53674 7.6205 SUP 90.91614
50 3265.964 851.2669 124.8817 9.8463 SUP 115.0354
40 2691.061 564.1493 156.6411 12.607 SUP 144.0338
30 2241.762 387.6474 192.4153 15.710 SUP 176.7049
20 1897.452 278.4525 230.6973 19.435 SUP 211.2621
10 1624.841 208.0506 269.9732 22.626 SUP 247.347
0 1416.888 163.8102 308.8161 28.522 SUP 280.2934
−10 1254.789 132.4055 345.9635 32.056 SUP 313.9067
−20 1131.672 110.5387 380.3672 33.588 SUP 346.7791
−30 1035.548 93.85143 411.2137 31.029 SUP 380.1843
−40 963.3055 82.05675 437.9155 25.810 SUP 412.1045
−50 908.7077 74.63467 460.0805 22.649 SUP 437.4312
−60 868.5814 69.51414 477.4703 20.515 SUP 456.955
−70 841.2895 66.18478 489.955 19.153 SUP 470.801
−80 827.2404 64.29819 497.4729 18.418 SUP 479.0547
−90 820.8011 63.6814 499.9999 18.153 SUP 481.8467
Exhaust pressure of the binary mixture is 63.6814 psia at 820.8011 degrees F.
Work done is 947.6757 ft-lbs;
Estimated W-9 Horsepower @ 3600 RPM = 9.644 hp
Estimated heat for Argon = 55.3475 BTU/sec and for liquid = 20.51642 BTU/sec
Theoretical Efficiency = 8.983552%
COMPUTER LISTINGS
Listing 2 is a computer printout for 8:1 compression at 1400 deg. F. starting gas temperature.
Argon @ STP = 39.948 grams for 22.4 liters
Cp = .133; Cv = .075165; gamma = 1.769441
T2 = 8751.396 deg. F. & P2 = 2813.341 psia; Head Vol. = 62.5 cc; CR = 8:1;
free Ambient = 300 deg. F.
Argon Pres/Temp compensated mass in grams = 1.22667
Thermal energy per power cycle to heat Argon = .2235992 BTUs
Free feed Water heat = 268 BTUs per pound
Thermal energy per power cycle to heat Water = 7.598673E−02 BTUs
Mechanical work done to compress the Argon is −928.0307 ft-lbs
************************* Event 2 **********************************
At TDC, inject .06 grams of superheated Water at 704 deg. F.
% Mole mass Argon = 95.3368% % Mole mass H2O = 4.663202%
********************************************************************
Since the injected Water is superheated, some flashes to vapor;
Volume .06 grams of Saturated vapor at 2784.7 psia = .3909251 cc
So, Argon is further compressed and now occupies only 62.10907 cc
The cylinder pressure however, decreases to 2784.7 psia
as a result of all the Water converting to saturated vapor
and the carrier gas temperature changes to 8614.273
Equalizing temperatures, the vapor's temperature goes up to meet
Argon's decreasing temperature at 6153.344 deg. F.
8:1 Compression of Argon starting @ 1400 deg. F. & 71 psia
Calculating partial volumes of .06 grams Water vapor & 1.22667 grams Argon
yields 4.858467 & 57.64153 cc respectively after equalizing temperatures.
Sums of the partial volumes must equal the cylinder volume of 62.5 at TDC.
Crank Angle Temp. F. PSIA Cyl Vol Steam Argon
90 6153.344 2999.854 62.5 4.8584 SUP 57.64153
80 5862.012 2672.399 66.60092 5.2606 SUP 61.34026
70 5153.316 1971.232 78.80437 6.3964 SUP 72.40793
60 4326.985 1315.87 98.53674 8.1837 SUP 90.35295
50 3575.412 856.8443 124.8817 10.600 SUP 114.2809
40 2964.404 568.0646 156.6411 13.612 SUP 143.0291
30 2475.762 390.3107 192.4153 16.938 SUP 175.4763
20 2105.5 280.4383 230.6973 20.979 SUP 209.7177
10 1816.841 209.6149 269.9732 24.602 SUP 245.3707
0 1590.476 165.1332 308.8161 30.892 SUP 277.9238
−10 1414.789 133.8045 345.9635 34.761 SUP 311.2022
−20 1279.843 111.3988 380.3672 36.596 SUP 343.7709
−30 1175.548 94.80654 411.2137 34.345 SUP 376.8687
−40 1095.426 82.59328 437.9155 28.434 SUP 409.4808
−50 1035.117 74.75674 460.0805 24.783 SUP 435.2975
−60 992.4648 69.61333 477.4703 22.471 SUP 454.9989
−70 962.9454 66.27042 489.955 20.988 SUP 468.9663
−80 945.4143 64.37533 497.4729 20.152 SUP 477.3203
−90 938.8011 63.75652 499.9999 19.869 SUP 480.1304
Exhaust pressure of the binary mixture is 63.75652 psia at 938.801 degrees F.
Work done is 953.8967 ft-lbs;
Estimated W-9 Horsepower @ 3600 RPM = 12.697 hp
Estimated heat for Argon = 60.37178 BTU/sec and for liquid = 20.51642 BTU/sec
Theoretical Efficiency = 11.09368%
COMPUTER LISTINGS
Listing 3 is a computer printout for 10:1 compression at 1200 deg. F. starting gas temperature.
Argon @ STP = 39.948 grams for 22.4 liters
Cp = .133 Cv = .075165 gamma= 1.769441
T2 = 9300.61 deg. F. & P2 = 2764.002 psia; Head Vol. = 50 cc; CR = 10:1;
free Ambient = 300 deg. F.
Argon Pres/Temp compensated mass in grams = .9098739
Thermal energy per power cycle to heat Argon = .1356981 BTUs
Free feed Water heat = 268 BTUs per pound
Thermal energy per power cycle to heat Water = 6.332228E-02 BTUs
Mechanical work done to compress the Argon is -758.6626 ft-lbs
************************* Event 2 **********************************
At TDC, inject .05 grams of superheated Water at 704 deg. F.
% Mole mass Argon = 94.79099% % Mole mass H2O = 5.209018%
********************************************************************
Since the injected Water is superheated, some flashes to vapor;
Volume .05 grams of Saturated vapor at 2732.787 psia = .3402922 cc
So, Argon is further compressed and now occupies only 49.65971 cc
The cylinder pressure however, decreases to 2732.787 psia
as a result of all the Water converting to saturated vapor
and the carrier gas temperature changes to 9141.189
Equalizing temperatures, the vapor's temperature goes up to meet
Argon's decreasing temperature at 6281.403 deg. F.
10:1 Compression of Argon starting @ 1200 deg. F. & 47 psia
Calculating partial volumes of .05 grams Water vapor & .9098739 grams Argon
yields 4.185383 & 45.81462 cc respectively after equalizing temperatures.
Sums of the partial volumes must equal the cylinder volume of 50 at TDC.
Angle Temp. F. PSIA Cyl Vol Steam Argon
90 6281.403 2961.447 50 4.1853 SUP 45.8146
80 5912.367 2556.354 54.21809 4.6300 SUP 49.5880
70 5050.044 1754.167 66.77021 5.8883 SUP 60.8818
60 4106.926 1084.716 87.06635 7.8927 SUP 79.1735
50 3294.834 663.436 114.1641 10.626 SUP 103.5371
40 2663.506 419.4027 146.8309 13.996 SUP 132.8349
30 2186.437 278.9729 183.6271 18.161 SUP 165.4661
20 1825.887 195.0003 223.0029 22.377 SUP 200.6253
10 1545.998 144.5772 263.401 29.013 SUP 234.3875
0 1334.585 110.1319 303.3537 31.682 SUP 271.6711
−10 1173.009 85.30632 341.5625 25.712 SUP 315.8498
−20 1050.427 69.7062 376.9491 19.498 SUP 357.4505
−30 956.1718 59.6932 408.6769 15.727 SUP 392.9495
−40 884.814 52.40205 436.1416 13.106 SUP 423.0352
−50 830.8615 47.46509 458.9399 11.402 SUP 447.5375
−60 794.1226 44.09988 476.8266 10.295 SUP 466.5308
−70 768.5775 41.89244 489.6679 9.5812 SUP 480.0866
−80 753.5972 40.63806 497.4006 9.1804 SUP 488.2202
−90 749.0366 40.22953 499.9999 9.0537 SUP 490.9461
Exhaust pressure of the binary mixture is 40.2295 psia at 749.0366 degrees F.
Work done is 778.1189 ft-lbs,
Estimated W-9 Horsepower @ 3600 RPM = 9.551 hp
Estimated heat for Argon = 36.6385 BTU/sec and for liquid = 17.0970 BTU/sec
Theoretical Efficiency = 12.5612%
COMPUTER LISTINGS
Listing 4 is a computer printout for 10:1 compression at 1400 deg. F. starting gas temperature.
Argon @ STP = 39.948 grams for 22.4 liters
Cp = .133; Cv = .075165; gamma= 1.769441
T2 = 10476.78 deg. F. & P2 = 2764.002 psia; Head Vol. = 50 cc; CR = 10:1;
free Ambient = 300 deg. F.
Argon Pres/Temp compensated mass in grams = .8120207
Thermal energy per power cycle to heat Argon = .1480163 BTUs
Free feed Water heat = 268 BTUs per pound
Thermal energy per power cycle to heat Water = 6.332228E−02 BTUs
Mechanical work done to compress the Argon is −758.6626 ft-lbs
************************* Event 2 **********************************
At TDC, inject .05 grams of superheated Water at 704 deg. F.
% Mole mass Argon = 94.19968% % Mole mass H2O = 5.800325%
********************************************************************
Since the injected Water is superheated, some flashes to vapor;
Volume .05 grams of Saturated vapor at 2732.787 psia = .3402922 cc
So, Argon is further compressed and now occupies only 49.65971 cc
The cylinder pressure however, decreases to 2732.787 psia
as a result of all the Water converting to saturated vapor
and the carrier gas temperature changes to 10298.16
Equalizing temperatures, the vapor's temperature goes up to meet
Argon's decreasing temperature at 6727.823 deg. F.
10:1 Compression of Argon starting @ 1400 deg. F. & 47 psia
Calculating partial volumes of .05 grams Water vapor & .8120207 grams Argon
yields 4.432171 & 45.56783 cc respectively after equalizing temperatures.
Sums of the partial volumes must equal the cylinder volume of 50 at TDC.
Angle Temp. F. PSIA Cyl Vol Steam Argon
90 6727.823 2977.473 50 4.4321 SUP 45.5678
80 6338.564 2570.751 54.21809 4.9082 SUP 49.3098
70 5432.52 1764.889 66.77021 6.2589 SUP 60.5112
60 4438.989 1092.14 87.06635 8.4068 SUP 78.6595
50 3582.834 668.1401 114.1641 11.363 SUP 102.8006
40 2915.923 422.6461 146.8309 15.036 SUP 131.794
30 2400.371 281.1099 183.6271 19.452 SUP 164.1748
20 2020.208 196.4961 223.0029 23.954 SUP 199.0484
10 1719.998 145.9168 263.401 31.284 SUP 232.1168
0 1492.543 111.1008 303.3537 34.328 SUP 269.025
−10 1317.009 85.7609 341.5625 28.119 SUP 313.4429
−20 1182.627 69.81921 376.9491 21.228 SUP 355.7203
−30 1080.743 59.76393 408.6769 17.135 SUP 391.5417
−40 1002.673 52.79094 436.1416 14.416 SUP 421.7255
−50 944.4111 47.52547 458.9399 12.440 SUP 446.4995
−60 902.3192 44.14756 476.8266 11.216 SUP 465.6096
−70 873.3138 41.93295 489.6679 10.429 SUP 479.238
−80 857.5972 40.67531 497.4006 9.9988 SUP 487.4018
−90 851.0366 40.26515 499.9999 9.8487 SUP 490.1512
Exhaust pressure of the binary mixture is 40.2651 psia at 851.0366 degrees F.
Work done is 783.384 ft-lbs;
Estimated W-9 Horsepower @ 3600 RPM = 12.1361 hp
Estimated heat for Argon = 39.96441 BTU/sec and for liquid = 17.0970 BTU/sec
Theoretical Efficiency = 15.03015%
COMPUTER LISTINGS
Listing 5 is a computer printout for 12:1 compression at 1200 deg. F. starting gas temperature.
Argon @ STP = 39.948 grams for 22.4 liters
Cp = .133 Cv = .075165 gamma= 1.769441
T2 = 10770.53 deg. F. & P2 = 2760.743 psia; Head Vol. = 41.6667 cc; CR = 12:1;
free Ambient = 300 deg. F.
Argon Pres/Temp compensated mass in grams = .6582066
Thermal energy per power cycle to heat Argon = 9.816456E−02 BTUs
Free feed Water heat = 268 BTUs per pound
Thermal energy per power cycle to heat Water = 4.432559E−02 BTUs
Mechanical work done to compress the Argon is −648.5344 ft-lbs
************************* Event 2 **********************************
At TDC, inject .035 grams of superheated Water at 704 deg. F.
% Mole mass Argon = 94.951% % Mole mass H2O = 5.048999%
********************************************************************
Since the injected Water is superheated, some flashes to vapor;
Volume .035 grams of Saturated vapor at 2734.399 psia = .2378876 cc
So, Argon is further compressed and now occupies only 41.42878 cc
The cylinder pressure however, decreases to 2734.399 psia
as a result of all the Water converting to saturated vapor
and the carrier gas temperature changes to 10615.93
Equalizing temperatures, the vapor's temperature goes up to meet
Argon's decreasing temperature at 7199.492 deg. F.
12:1 Compression of Argon starting @ 1200 deg. F. & 34 psia
Calculating partial volumes of .035 grams Water vapor & .6582066 grams Argon
yields 3.331799 & 38.33487 cc respectively after equalizing temperatures.
Sums of the partial volumes must equal the cylinder volume of 41.6667 at TDC.
Angle Temp. F. PSIA Cyl Vol Steam Argon
90 7199.492 2954.399 41.66667 3.3317 SUP 38.33487
80 6693.274 2474.644 45.96288 3.7609 SUP 42.20195
70 5581.69 1590.765 58.74744 4.9866 SUP 53.76077
60 4434.087 923.742 79.41944 6.9565 SUP 72.46288
50 3495.073 539.0018 107.019 9.6969 SUP 97.32202
40 2790.533 329.7793 140.2907 13.082 SUP 127.2083
30 2267.495 214.0209 177.7684 16.943 SUP 160.8246
20 1881.981 148.6708 217.8733 23.112 SUP 194.7608
10 1588.337 106.9171 259.0196 25.766 SUP 233.2534
0 1365.485 78.10737 299.7121 18.435 SUP 281.2764
−10 1198.119 61.58424 338.6284 13.282 SUP 325.3464
−20 1069.991 50.85831 374.6704 10.164 SUP 364.5055
−30 972.6651 43.53189 406.9858 8.1669 SUP 398.8188
−40 899.26 38.05911 434.9591 6.7535 SUP 428.2055
−50 843.4289 34.49232 458.1796 5.8702 SUP 452.3094
−60 805.2305 32.01327 476.3975 5.2878 SUP 471.1096
−70 778.4795 30.39824 489.4766 4.9135 SUP 484.5631
−80 764.2328 29.48538 497.3525 4.7102 SUP 492.6423
−90 758.4092 29.18753 499.9999 4.6399 SUP 495.36
Exhaust pressure of the binary mixture is 29.1875 psia at 758.4092 degrees F.
Work done is 666.9431 ft-lbs;
Estimated W-9 Horsepower @ 3600 RPM = 9.0370 hp
Estimated heat for Argon = 26.50443 BTU/sec
Estimated heat for injected liquid = 11.96791 BTU/sec
Theoretical Efficiency = 16.59994%
COMPUTER LISTINGS
Listing 6 is a computer printout for 12:1 compression at 1400 deg. F. starting gas temperature.
Argon @ STP = 39.948 grams for 22.4 liters
Cp = .133 Cv = .075165 gamma= 1.769441
T2 = 12123.84 deg. F. & P2 = 2760.743 psia; Head Vol. = 41.6667 cc; CR = 12:1;
free Ambient = 300 deg. F.
Argon Pres/Temp compensated mass in grams = .5874192
Thermal energy per power cycle to heat Argon = .1070757 BTUs
Free feed Water heat = 268 BTUs per pound
Thermal energy per power cycle to heat Water = 4.432559E−02 BTUs
Mechanical work done to compress the Argon is −648.5344 ft-lbs
************************* Event 2 **********************************
At TDC, inject .035 grams of superheated Water at 704 deg. F.
% Mole mass Argon = 94.37678% % Mole mass H2O = 5.62322%
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Since the injected Water is superheated, some flashes to vapor;
Volume .035 grams of Saturated vapor at 2734.399 psia = .2378876 cc
So, Argon is further compressed and now occupies only 41.42878 cc
The cylinder pressure however, decreases to 2734.399 psia
as a result of all the Water converting to saturated vapor
and the carrier gas temperature changes to 11950.6
Equalizing temperatures, the vapor's temperature goes up to meet
Argon's decreasing temperature at 7714.418 deg. F.
12:1 Compression of Argon starting @ 1400 deg. F. & 34 psia
Calculating partial volumes of .035 grams Water vapor & .5874192 grams Argon
yields 3.532375 & 38.13429 cc respectively after equalizing temperatures.
Sums of the partial volumes must equal the cylinder volume of 41.6667 at TDC.
Angle Temp. F. PSIA Cyl Vol Steam Argon
90 7714.418 2969.924 41.66667 3.5323 SUP 38.1342
80 7173.274 2488.044 45.96288 3.9886 SUP 41.9742
70 6005.69 1600.18 58.74744 5.3040 SUP 53.4433
60 4794.087 929.7141 79.41944 7.4253 SUP 71.9941
50 3802.525 542.8007 107.019 10.385 SUP 96.6333
40 3053.34 332.2596 140.2907 14.051 SUP 126.2389
30 2489.76 215.678 177.7684 18.227 SUP 159.541
20 2079.981 149.9546 217.8733 24.869 SUP 193.0038
10 1766.371 107.7979 259.0196 27.897 SUP 231.1217
0 1527.485 78.36844 299.7121 20.123 SUP 279.5889
−10 1344.46 61.65889 338.6284 14.465 SUP 324.1626
−20 1205.932 50.90034 374.6704 11.079 SUP 363.5905
−30 1098.773 43.55795 406.9858 8.8979 SUP 398.0878
−40 1019.412 38.42031 434.9591 7.4608 SUP 427.4982
−50 959.3326 34.51474 458.1796 6.4075 SUP 451.7721
−60 915.2305 32.03089 476.3975 5.7622 SUP 470.6352
−70 886.4795 30.41343 489.4766 5.3566 SUP 484.12
−80 868.9189 29.49901 497.3525 5.1273 SUP 492.2252
−90 864.4092 29.20099 499.9999 5.0581 SUP 494.9417
Exhaust pressure of the binary mixture is 29.2010 psia at 864.4092 degrees F.
Work done is 671.0901 ft-lbs,
Estimated W-9 Horsepower @ 3600 RPM = 11.073 hp
Estimated heat for Argon = 28.9104 BTU/sec and for liquid = 11.9679 BTU/sec
Theoretical Efficiency = 19.14237%
DETAILED DESCRIPTION The RAKH Cycle Engine utilizes a novel thermodynamic cycle, which is described here in detail. FIG. 1 shows an insulated storage tank (1) that is initially full of the selected carrier gas. Argon is used as the preferred carrier gas because of its calculation friendly nature of maintaining a nearly constant specific heat. The carrier gas is nearly free of any liquid water when it exits the storage tank because of the ceramic fuel filter (8), which passes gas through it but not water, similar to a common ceramic gasoline fuel filter that allows gasoline to pass through but not water. The carrier gas will pass through the ceramic with negligible back pressure. Excess water can be drained from the storage tank through manual operated valve (9) and may be collected or discarded on exiting through the drain tube after the valve. The carrier gas is drawn though the heater (3) by the intake stroke of the RAKH Engine (see FIG. 2). The heater is warmed by the boron burner (4), which is continuously fed oxygen from tank (6) through the thermostatically controlled regulator valve (7), controlled by thermostat (5). Thermostat (5) is also contains a high voltage spark plug, which sparks during startup only. There is no exit from the burner except through orifices in the boron feeder assembly (11), which plugs the exit automatically with slow draining boria (the glassy solid product of the combustion of boron in oxygen). The close-up particulars of the boron feeder assembly are shown the adjacent drawing detail, which shows the oxygen orifice entering at the right side below and exiting through a little tungsten tube (14), which is bent toward the boron filament at its upper end. This tungsten tube serves to help blow away the glassy boria protective coating formed on the surface of the boron. The intense heat at the tip would melt most other metal tubes that could be used but tungsten is the least likely to melt in this application. A plug of boria should be left in the upper end of the boron feeder assembly. Electrical heating coils (13) will help warm this boria plug which will begin to drain out the boria drain tube (12). Boria (15) flowing out slowly is the only thing that impedes the oxygen. Otherwise, oxygen would exit through the same tube (12). The boria also seals the boron filament entering the burner. The boron feeder assembly (11) boron entry hole diameter must be slightly larger than the largest diameter of the solid boron filament being forced into the boron feeder assembly. There will be virtually no possibility for extrusion since boron is nearly as hard as diamond. FIG. 1 is presented only to show a viable hot gas delivery system, which produces none of the so called greenhouse waste gasses of current carbon fuel based engines. Boron burns to form the solid waste boria and has no exhaust gas!
FIG. 2. shows a compact diesel type engine converted to a RAKH Cycle Engine. The RAKH Cycle Engine intakes a hot carrier gas rather than air through intake port (C) via intake valve (I). Like in a diesel, the carrier gas is then compressed adiabatically, requiring work input from a typical diesel Crankshaft Flywheel (not shown on FIG. 2). At a point very near Top Dead Center for the piston, FIG. 4 shows the thermodynamic results of injecting superheated water (water heated to a point above the saturation temperature with respect to its pressure environment after being injected into the cylinder). FIG. 4 uses the conditions assumed in the listing of FIG. 6. Water stored in pressure vessel (M) flows through high pressure delivery line (L) into injection channel (K) surrounding the inlet of electronically heated and electronically controlled plunger (B) of injector (D) which is like a diesel injector but it injects a superheated liquid, namely water in these illustrated Figures. The water cannot burn, of course, but conditions are so hot in the cylinder that it seems to explode into steam from its own excess enthalpy at the pressure of its new environment within the cylinder and a rapid heating from the adiabatically heated carrier gas. The mixture of steam and the carrier gas have more pressure than the carrier gas did alone, which cause net work output from piston (P) down connecting rod (F) forcing crankshaft connected at crank offset throw (J) to exert a rotational torque on crankshaft (G) with more average force due to pressure increased during the power stroke than that required to compress the carrier gas. Like other 4 stroke engines, the power stroke is followed by the exhaust stroke, which forces the exhaust mixture out through valve (E) and on out Exhaust port (A) to the condenser/dryer system illustrated in FIG. 3.
FIG. 3 Illustrates the Condenser System, which saves the carrier gas and removes the small volume of vapor in the mixture caused by injecting the superheated liquid. Steam in the preferred implementation presented here. Wet mixture (W) enters the Condenser tank (T) where it is immediately cooled by the spray injection (I) that is pumped into the condenser by continuous centrifugal pump (R), which pumps water from the condenser through water cooled radiator (G). Cooling water (C) comes from virtually any large source of cooling water. Engine induction continually pulls carrier gas (V) out of the condenser through two ceramic disks with high pressure water trapped between those two ceramic disks (similar to the ceramic filter described in FIG. 1). Any water vapor trying to leave the condenser with carrier gas (V) is cooled and trapped in the water between the two ceramic disks. The trapped water is continuously heated by the addition of steam and its volume continuously increases until pressure relief valve (P) releases water back into the condenser hydraulic gear pump (M) continuously pumps water from pressurized hot water tank (B) through water cooled radiator (H) or through bypass line (U) depending on the temperature controlled thermostatic valves (K) and (L). Valve (K) opens when the temperature increases and valve (L) remains open when the temperature is low. The valves are both open at a selectable preset equilibrium temperature so both valves are never closed at the same time. After exiting the throat of the condenser past the pressure relief valve (P), a sleeved (S) U-tube routes the flow back into the throat of the condenser between the two ceramic disks (D) back into tank (B) and into the base of collector dish (Q), which is normally submerged. Another ceramic disk (D) blocks the exit of water via the throat at the upper end of pressurized tank (B). Valve J is a pressure relief valve set to release at a pressure that is only half of the pressure setpoint that opens pressure relief valve (P). If any carrier gas gets transported into tank (B) then it should eventually be released with a small amount of steam back into the condenser. A little steam in the dried carrier gas shouldn't affect operation of the RAKH Cycle Engine. The drawing shows release into the dry gas side rather than back into the condenser to simplify drawing the vent line.
Eventually the liquid at the bottom of the condenser would overflow so a float controller (F) sends a signal to open drain line valve (E) draining to a low pressure air vented overflow tank, not shown on the drawing. Steam trapped between the ceramic disks continually heats tank (B) and preheats the carrier gas a little bit after the spray injection (I) has cooled it for a slight added efficiency bonus in capturing and recycling the carrier gas with a closed cycle.
FIG. 4 shows the theoretical thermodynamic conditions of Pressure, Volume, and Temperature for a single cylinder after the induction stroke at Bottom Dead Center (BDC) for 1 piston given the particular RAKH Cycle Engine configuration and initial conditions selected for computer listing number 6, which follows.
FIG. 5 shows the theoretical thermodynamic conditions of Pressure, Volume, and Temperature after the compression stroke at Top Dead Center (TDC) from the initial state in FIG. 4.
FIG. 6 shows the same piston position at TDC as in FIG. 5 an instant later after the water is injected, showing the final P, V, and T for the mixture.
Listings 1 and 2 computer printouts are for an 8 to 1 compression ratio RAKH Cycle Engine with 0.06 grams of water injected at 704 degrees F.
Listings 3 and 4 computer printouts are for a 10 to 1 compression ratio RAKH Cycle Engine with 0.05 grams of water injected at 704 degrees F.
Listings 5 and 6 computer printouts are for a 12 to 1 compression ratio RAKH Cycle Engine with 0.035 grams of water injected at 704 degrees F.
Listing 1 has 1200 degree F. initial Argon carrier gas temperature and 71 psia intake pressure.
Listing 2 has 1400 degree F. initial Argon carrier gas temperature and 71 psia intake pressure.
Listing 3 has 1200 degree F. initial Argon carrier gas temperature and 47 psia intake pressure.
Listing 4 has 1400 degree F. initial Argon carrier gas temperature and 47 psia intake pressure.
Listing 5 has 1200 degree F. initial Argon carrier gas temperature and 34 psia intake pressure.
Listing 6 has 1400 degree F. initial Argon carrier gas temperature and 34 psia intake pressure.
At TDC for each of these listings, the maximum pressure is close to 3000 psia
