Abstract:
Provided is a combustion chamber for producing a pressurized gas having a wall structure defining an interior chamber, an explosion chamber disposed within the interior chamber, an annular chamber connected to the explosion chamber, a first reflecting surface for reflecting a pressure wave within the interior chamber, a second reflecting surface for reflecting the pressure wave within the interior chamber, at least one inlet for introducing a first gas into the interior chamber, and at least one outlet from the interior chamber for drawing off a pressurized gas from the interior chamber.

Description:
This application is a Divisional application of U.S. Ser. No. 09/305,481, filed on May 6, 1999, now U.S. Pat. No. 6,167,693, which is a Divisional application of U.S. Ser. No. 08/840,476, filed on Apr. 21, 1997, now U.S. Pat. No. 5,983,624, the complete disclosures of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a high pressure gas cycle for use in an engine. The invention also relates to an electrical power generating plant. 
     2. Background of Related Art 
     The Otto cycle shown diagrammatically in FIG. 1 [Prior Art], with pressure as the ordinate and volume as the abscissa, is a cycle that closely represents the explosion and compression stages of a gasoline automobile engine. In the Otto cycle, the air is drawn in at atmospheric pressure, shown at  1 , then compressed isentropically to a high pressure with fuel mixed in the air, shown at  2 . The fuel air mixture explodes at a theoretically constant volume to form a combustion gas having an increased pressure, shown at  3 . The combustion gas expands isentropically back to the original inlet volume, shown at  4 , where the combustion gas is then discharged. As shown in FIG. 1, the combustion gas discharges at a pressure above atmosphere, shown at  4 , and then the pressure drops to atmosphere as it exhausts from the engine, not shown. The energy that could be available by expanding from exhaust pressure to atmospheric pressure, represented by the difference between  4  and  1  shown in FIG. 1, is wasted. 
     The theoretical efficiency of the Otto Cycle is defined by the relationship 1−(V 2 /V 1 ) (K−1)  where V 1 /V 2  is the ratio of the volume before compression to the volume after compression, commonly called the compression ratio. K=ratio of specific heat at constant pressure to specific heat at constant volume=C p /C v . 
     Another cycle commonly used in automobile engines is the Diesel cycle. The pressure vs. volume diagram for a Diesel cycle is shown in FIG. 2 [Prior Art]. In a Diesel cycle, air is drawn in at atmospheric pressure, shown at  5 , and then the air is compressed, shown at  6 . The fuel is injected after the air is compressed and burns at somewhere near constant pressure to form a combustion gas, shown at  7 . The combustion gas expands isentropically back to the original inlet volume, shown at  8 , where the combustion gas is then discharged. As shown in FIG. 2, the combustion gas discharges at a pressure above atmosphere, shown at  8 , and then the pressure drops to atmosphere as it exhausts from the engine, not shown. The energy that could be available by expanding from exhaust pressure to atmospheric pressure, represented by the difference between  8  and  5  shown in FIG. 5, is wasted. 
     The advantage of the Diesel cycle compared to the Otto cycle is that the compression ratio can be made much higher than that for the Otto Cycle, because the fuel is not mixed in the air, and therefore the rise during compression in temperature will not ignite the fuel until after the fuel is injected at the high pressure. In general, this increase in compression ratio for the Diesel Cycle enables the Diesel cycle to achieve higher efficiencies than are possible with the Otto Cycle. 
     The compression ratio for the Otto Cycle is usually limited to about 10 to 1, corresponding to a pressure ratio of about 25 to 1. The reason for this is that at higher ratios the fuel air mixture becomes so hot that the explosion occurs before the mixture is fully compressed. This preignition or detonation actually decreases the power output. 
     In the Diesel engine the fuel injection occurs after compression, and only air is being compressed during the compression cycle. Therefore, typical compression ratios are 23 to 1, corresponding to pressure ratios of 82 to 1. This is the basic reason why the Diesel cycle is more efficient than the Otto cycle. 
     A further cycle is the Brayton or Joule cycle, as shown in FIG. 3 [Prior Art]. In the Brayton cycle, air is drawn into a compressor at atmospheric pressure, shown at  9 , and then compressed to a high pressure, shown at  10 . Fuel is injected into the compressed air in the combustor, where it burns at nearly a constant pressure (except for friction losses in the combustor) to form a combustion gas, shown at  11 . The combustion gas expands isentropically back to atmospheric pressure, shown at  12 . In this case, the expansion to atmospheric pressure is advantageous, and the theoretical efficiency is like the Otto cycle above in that the theoretical efficiency is equal to 1−(V 2 /V 1 ) (K−1)  where V 1 /V 2  is again the volume ratio of specific volume at atmospheric pressure divided by the specific volume at the pressure at which burning starts. The Brayton cycle is the cycle commonly used in gas turbines, and is limited in efficiency by the fact that the temperature of the gas entering the turbine is nearly the same as the combustion temperature. Therefore the combustion temperatures possible in a gas turbine system are usually limited to approximately 2300 to 2600° F. However, the Brayton cycle does have an advantage over the Otto cycle in that complete expansion back to essentially atmosphere is achieved. 
     A disadvantage of the Brayton cycle is that as pressure ratios or compression ratios are increased the temperature leaving the compressor and entering the combustor becomes higher. Therefore, less fuel energy can be added because of the temperature limit of the turbine. For this reason, although efficiency can be increased by increasing the pressure ratio in a gas turbine cycle, the output gradually decreases as higher pressure ratios are used. Therefore, it is common practice to limit the pressure ratio in industrial gas turbines to about 10 to 20 atmospheres. 
     Table 1 shows typical theoretical performance calculations for the Brayton cycle, based on air standard data and constant mass flow through the cycle. 
     
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                   
                 A 
                 B 
                 C 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                  1 
                 PS/P1 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
               
               
                  2 
                 T1 
                 520 
                 520 
                 520 
                 520 
                 520 
                 520 
                 520 
                 520 
               
               
                  3 
                 T3 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
               
               
                  4 
                 P1/J 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
               
               
                  5 
                 V1 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
               
               
                  6 
                 EFF COMP 
                 1 
                 0.9 
                 0.85 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                  7 
                 COOL FACT 
                 1 
                 1 
                 1 
                 0.9 
                 0.8 
                 0.7 
                 0.6 
                 0.5 
               
               
                  8 
                 N/(N − 1) CO 
                 3.463 
                 3.1167 
                 2.94366 
                 3.463 
                 3.895875 
                 4.452429 
                 6.1945 
                 6.2334 
               
               
                  9 
                 (N − 1)/N CO 
                 0.288757 
                 0.320852 
                 0.339726 
                 0.288767 
                 0.256682 
                 0.224597 
                 0.192511 
                 0.160428 
               
               
                 10 
                 N COMP 
                 1.406009 
                 1.472434 
                 1.514522 
                 1.406009 
                 1.345319 
                 1.289651 
                 1.238407 
                 1.19108 
               
               
                 11 
                 EFF TURB 
                 1 
                 0.9 
                 0.85 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                 12 
                 N/(N − 1) TU 
                 3.463 
                 3.847778 
                 4.074118 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
               
               
                 13 
                 (N − 1)N TU 
                 0.288767 
                 0.25989 
                 0.245452 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
               
               
                 14 
                 N TURB 
                 1,406009 
                 1.351151 
                 1.325297 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
               
               
                 15 
                 W IN 
                 212.1196 
                 251.5701 
                 276.9102 
                 235.6885 
                 221.0261 
                 207.4814 
                 194.9616 
                 183.3819 
               
               
                 16 
                 V1/V2 
                 11.76285 
                 10.52493 
                 9.858518 
                 11.76285 
                 13.14636 
                 14.6926 
                 16.4207 
                 18.35205 
               
               
                 17 
                 T2/T1 
                 2.72043 
                 3.0404 
                 3.245924 
                 2.72043 
                 2.434134 
                 2.177968 
                 1.94876 
                 1.743674 
               
               
                 18 
                 T2 
                 1414.624 
                 1581.008 
                 1687.88 
                 1414.624 
                 1265.75 
                 1132.543 
                 1013.355 
                 906.7106 
               
               
                 19 
                 HEAT IN 
                 330.8437 
                 291.3941 
                 266.0545 
                 330.8437 
                 366.1417 
                 397.725 
                 425.9845 
                 451.2699 
               
               
                 20 
                 V3 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
               
               
                 21 
                 W EXPAN 
                 421.3532 
                 395.5742 
                 381.6844 
                 395.5742 
                 395.5742 
                 395.5742 
                 395.5742 
                 395.5742 
               
               
                 22 
                 NET WORK 
                 209.2335 
                 144.0041 
                 104.7742 
                 15.6857 
                 174.6481 
                 188.0928 
                 200.6127 
                 212.1923 
               
               
                 23 
                 EFF. 
                 0.632424 
                 0.49419 
                 0.393807 
                 0.483267 
                 0.478723 
                 0.472922 
                 0.470939 
                 0.470212 
               
               
                   
               
             
          
           
               
                   
                 A 
                 J 
                 K 
                 L 
                 M 
                 N 
                 O 
                 P 
               
               
                   
               
               
                  1 
                 P2/P1 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
               
               
                  2 
                 T1 
                 520 
                 520 
                 520 
                 520 
                 520 
                 520 
                 520 
               
               
                  3 
                 T3 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
                 2810 
               
               
                  4 
                 P1/J 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
               
               
                  5 
                 V1 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
                 13.089 
               
               
                  6 
                 EFF COMP 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                  7 
                 COOL FACT 
                 0.4 
                 0.3 
                 0.2 
                 0.1 
                 0.05 
                 0.04 
                 0.03 
               
               
                  8 
                 N/(N − 1) CO 
                 7.79175 
                 10.389 
                 15.5835 
                 31.167 
                 62.334 
                 77.9175 
                 103.89 
               
               
                  9 
                 (N − 1)/N CO 
                 0.128341 
                 0.096256 
                 0.06417 
                 0.032085 
                 0.016043 
                 0.012834 
                 0.009626 
               
               
                 10 
                 N COMP 
                 1.147237 
                 1.106508 
                 1.068571 
                 1.033149 
                 1.016304 
                 1.013001 
                 1.009719 
               
               
                 11 
                 EFF TURB 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                 12 
                 N/(N − 1) TU 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
               
               
                 13 
                 (N − 1)N TU 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
               
               
                 14 
                 N TURB 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
               
               
                 15 
                 W IN 
                 172.6651 
                 162.7406 
                 153.5437 
                 145.0155 
                 140.9852 
                 140.197 
                 139.4146 
               
               
                 16 
                 V1/V2 
                 20.51057 
                 22.92296 
                 25.6191 
                 28.63234 
                 30.26937 
                 30.60784 
                 30.9501 
               
               
                 17 
                 T2/T1 
                 1.560171 
                 1.39598 
                 1.249068 
                 1.117617 
                 1.057174 
                 1.045484 
                 1.033922 
               
               
                 18 
                 T2 
                 811.289 
                 725.9096 
                 649.6154 
                 581.1609 
                 549.7306 
                 543.6515 
                 537.6396 
               
               
                 19 
                 HEAT IN 
                 473.8944 
                 494.1378 
                 512.2509 
                 528.4577 
                 535.9099 
                 537.3512 
                 538.7766 
               
               
                 20 
                 V3 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
                 2.210342 
               
               
                 21 
                 W EXPAN 
                 395.5742 
                 395.5742 
                 395.5742 
                 395.5742 
                 395.5742 
                 395.5742 
                 395.5742 
               
               
                 22 
                 NET WORK 
                 222.9091 
                 232.8337 
                 242.0305 
                 250.5587 
                 254.589 
                 255.3772 
                 256.1596 
               
               
                 23 
                 EFF. 
                 0.470377 
                 0.471192 
                 0.472484 
                 0.474132 
                 0.47509 
                 0.475252 
                 0.475447 
               
               
                   
               
             
          
         
       
     
     In Table 1 the following definitions are used: 
     P 2 /P1 is the pressure ratio 
     T 1 =air inlet temperature in ° R (degrees Rankin) 
     T 3 =combustion temperature in ° R 
     P 1 /J=inlet pressure in lbs/ft 2 /778.2 
     V 1 =inlet specific volume in ft 3 /lb. 
     EFF COMP is polytropic compression efficiency 
     COOL FACT is a factor that is multiplied by (N−1)/N, where (N−1)/N=(k−1)/K/comp EFF., and (K−1)/K=0.2888. This factor shows a new value of (N−1)/N that simulates continuous intercooling during the compression process. Actual intercooling is a step-by-step process, but this simulation shows the approximate effect of intercooling. 
     (N−1)/N CO=(K−1)/K/EFF COMP×COOL FACT 
     N Comp. is the polytropic exponent used in the equation for work 
     EFF TURB is the polytropic efficiency of the turbine 
     (N−1)/N TU=(k−1)/K×EFF TURB 
     WIN=Compressor work in Btu/lb 
     V 1 /V 2 =Compression ratio 
     T 2 /T 1 =Ratio compressor discharge temperature/inlet temperature 
     T 2 =Compressor discharge temperature ° R 
     Heat IN=Heat Input from T 2  to T 3 , assuming specific heat=0.2371 Btu/lb° F. 
     V 3 =Specific volume at turbine inlet in cu.ft./lb 
     W EXPAN=Turbine work output in Btu/lb 
     NET WORK=W EXPAN-WIN 
     EFF=NETWORK/HEAT IN=cycle efficiency 
     In column C, the Brayton cycle efficiency is listed as 0.494. This is higher than the actual efficiency of a gas turbine because leakage losses, cooling air losses, pressure drop in the combustor, and losses due to kinetic energy of the gases leaving the turbine column D, where efficiencies of 85% are used for compressor and turbine, were excluded. 
     It would be advantageous if one could combine the constant volume or explosion cycle as shown in the Otto cycle at the high pressure end, and at the same time expand the volume all the way to atmospheric pressure at the exhaust end, as shown FIG.  4 . FIG. 4 is a theoretical complete expansion cycle. 
     An almost complete expansion cycle was made by Sargent, in which the air inlet to the engine is throttled to take in less air volume and thereby allow for an increase in volume in the exhaust. However, this Sargent cycle was not a success in a reciprocating engine because of the high mechanical friction losses. 
     Thus, there is a need for a complete expansion cycle that is suitable for use in a reciprocating engine, which substantially avoids wasting energy due to exhaust pressures that are greater than atmospheric pressure. 
     There is also a need for an improved combustion chamber that is capable of supplying compressed gas to a turbine blade at temperatures significantly below the combustion temperature of the fuel being burned. 
     There is a further need for an improved apparatus for supplying a compressed gas having significantly reduced friction losses. 
     Electrical power plants utilizing turbine engines to drive electrical generators produce large amounts of combustion gasses which contain carbon dioxide and byproducts such as nitrogen oxides. Furthermore, the exhaust gas from conventional turbine engines usually has a temperature of about 700° F. to about 1240° F. Typically a Rankine cycle system is used to recovery valuable energy from the exhaust gas. However, efficient low temperature vapor turbines usually cannot be used because the exhaust temperature from a conventional turbine engine is too high. Exhaust temperatures from conventional turbine engines usually require the use of an expensive steam turbine to recover the energy. 
     Thus, there is a need for an electrical generating power plant comprising more efficient turbines to reduce the quantity of combustion gasses produced, and for turbine engines having exhaust temperature suitable for use in driving low temperature vapor turbines. 
     SUMMARY OF THE INVENTION 
     It is an objective of the present invention to provide a substantially complete expansion cycle that is suitable for use in a gas turbine engine, that substantially avoids wasting energy due to exhaust pressures that are greater than atmospheric pressure. 
     Another objective of the present invention is to provide an engine that utilizes a substantially complete expansion cycle, which substantially avoids wasting energy due to exhaust pressures that are greater than atmospheric pressure. 
     A further objective of the present invention is to provide an improved combustion chamber that is capable of producing a pressurized gas for driving a turbine blade at a temperature significantly below the combustion temperature of the fuel being burned in the combustion chamber. 
     Another objective of the present invention is to provide an improved combustion chamber for producing a pressurized gas, which has significantly reduced friction losses. 
     A further objective of the present invention is to provide a method for forming a pressurized gas, which can be converted to mechanical energy in an engine. 
     Another objective of the present invention is to provide an electrical generating power plant comprising more efficient turbines to reduce the quantity of combustion gasses produced. 
     A further objective is to provide an electrical generating power plant comprising a turbine engine an efficient low temperature vapor turbine driven by the exhaust from said turbine engine. 
     The above objectives and other objectives are surprisingly achieved by the following. 
     Provided is a novel combustion chamber for producing a pressurized gas comprising: 
     a wall structure defining an interior chamber; 
     a first reflecting surface for reflecting a pressure wave within said interior chamber; 
     a second reflecting surface for reflecting said pressure wave within said interior chamber, wherein said first and second reflecting surfaces being constructed and arranged to resonate said pressure wave in said interior chamber; 
     at least one first inlet for introducing a first gas into said interior chamber; and 
     at least one outlet from said interior chamber for drawing off a pressurized gas from said interior chamber. 
     Also provided is a novel turbine engine comprising: 
     at least one combustion chamber; 
     at least one compressor constructed and arranged to provide a compressed gas to said at least one combustion chamber; and 
     at least one turbine blade constructed and arranged to be driven by a pressurized gas formed in said combustion chamber; wherein said combustion chamber comprises: 
     a wall structure defining an interior chamber; 
     a first reflecting surface for reflecting a pressure wave within said interior chamber; 
     a second reflecting surface for reflecting said pressure wave within said interior chamber, wherein said first and second reflecting surfaces being constructed and arranged to resonate said pressure wave in said interior chamber; 
     at least one first inlet for introducing a first gas into said interior chamber; 
     at least one second inlet for introducing said compressed gas into said interior chamber, said second inlet being connected to said at least one compressor; and 
     at least one outlet from said interior chamber for drawing off said pressurized gas from said chamber and being constructed and arranged to supply said pressurized gas to said at least one turbine blade. 
     The present invention also provides a novel electrical generating power plant comprising: 
     at least one turbine engine; 
     at least one electrical generator connected to said turbine engine; wherein said turbine engine comprises: 
     at least one combustion chamber; 
     at least one compressor constructed and arranged to provide a compressed gas to said at least one combustion chamber; and 
     at least one turbine blade constructed and arranged to be driven by a pressurized gas formed in said combustion chamber; wherein said combustion chamber comprises: 
     a wall structure defining an interior chamber; 
     a first reflecting surface for reflecting a pressure wave within said interior chamber; 
     a second reflecting surface for reflecting said pressure wave within said interior chamber, wherein said first and second reflecting surfaces being constructed and arranged to resonate said pressure wave in said interior chamber; 
     at least one first inlet for introducing a first gas into said interior chamber; 
     at least one second inlet for introducing said compressed gas into said interior chamber, said second inlet being connected to said at least one compressor; and 
     at least one outlet from said interior chamber for drawing off said pressurized gas from said chamber and being constructed and arranged to supply said pressurized gas to said turbine blade. 
     Also provided is a novel method of forming a pressurized gas having a temperature lower than a combustion temperature of a. combustible gas used to form said pressurized gas comprising the steps of: 
     introducing a combustible gas into a combustion chamber having first and second reflecting surfaces that are constructed and arranged to provide a resonating pressure wave reflecting between said first and second reflecting surfaces, said combustible gas being introduced into said combustible chamber at a frequency such that said resonating pressure wave ignites said combustible gas to thereby form a resonating pressure wave; 
     introducing a second gas into said combustion chamber at a location and frequency such that said pressure wave compresses and combines with said second gas to form a pressurized gas having a temperature lower than a combustion temperature of said combustible gas; and 
     withdrawing said pressurized gas from said combustion chamber. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 [Prior Art] illustrates a graph of the pressure vs. volume for an Otto cycle engine. 
     FIG. 2 [Prior Art] illustrates a graph of the pressure vs. volume for a Diesel cycle engine. 
     FIG. 3 [Prior Art] illustrates a graph of the pressure vs. volume for a Brayton cycle engine. 
     FIG. 4 illustrates a graph of the pressure vs. volume for a theoretical complete expansion cycle. 
     FIG. 5 illustrates a schematic diagram of an engine utilizing a high pressure cycle according to the present invention. 
     FIG. 6 illustrates a diagram of a resonating pressure wave in a combustion chamber having a length that is one-half of the wavelength of the pressure wave. 
     FIG. 7 illustrates a diagram of a resonating pressure wave in a combustion chamber having a length that is one wavelength of the pressure wave. 
     FIG. 8 illustrates a graph of the pressure vs. volume for a high pressure turbine cycle according to the present invention. 
     FIG. 9 is a cross-sectional view of a rotary distributor valve according to the present invention. 
     FIG. 10 is a cross-sectional view of a rotary distributor valve according to the present invention. 
     FIG. 11 illustrates a schematic diagram of an engine utilizing a high pressure cycle according to the present invention. 
     FIG. 12 illustrates a schematic diagram of an engine utilizing a high pressure cycle according to the present invention. 
     FIG. 13 illustrates a schematic diagram of an engine utilizing a high pressure cycle according to the present invention. 
     FIG. 14 illustrates a schematic diagram of an engine utilizing a high pressure cycle according to the present invention. 
     FIG. 15 illustrates a schematic diagram of an engine utilizing a high pressure cycle according to the present invention. 
     FIG. 16 illustrates a schematic diagram of a power plant according to the present invention. 
     FIG. 17 illustrates a cut-away view of six high pressure cycles shown in FIG. 5 arranged circumferentially around the rotor blades. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The present invention will be further explained with reference to the attached drawings. The present invention provides a combustion chamber for producing a pressurized gas, which has significantly reduced friction losses. Furthermore, the pressurized gas introduced into the combustion chamber can be provided at a temperature which is significantly lower than the combustion temperature of the fuel being burned in the combustion chamber. Moreover, the combustion chamber utilizes detonation of a combustible gas to provide improved burning efficiency and reduced byproducts such as nitrogen oxides. 
     The improved combustion chamber according to the present invention will be explained with reference to a turbine engine. However, it will be understood by one skilled in the art that the pressurized gas produced by the combustion chamber can be converted to mechanical energy using other means besides a turbine blade. For example, the pressurized gas can be used to drive a reciprocating piston. The pressurized gas could also be used for jet propulsion. 
     The present invention demonstrates that unexpectedly it is possible to attain the advantages of an explosion cycle at high pressures, and also to achieve substantially complete expansion of the exhaust, thereby greatly improving the cycle efficiency of an engine. A combustion chamber can be provided that is capable of supplying pressurized gas to a turbine blade at temperatures significantly below the combustion temperature of the fuel being burned. By producing a pressurized gas having a temperature below combustion temperatures, the following advantages can be attained: 
     (1) significantly greater pressure ratios can be utilized in the turbine while not exceeding the temperature limits of the turbine blades; 
     (2) greater amounts of fuel can be burned while not exceeding the temperature limits of the turbine blades; 
     (3) net power output of the turbine can be greatly increased; and 
     (4) at the higher pressure ratios achieved by the combustion chamber according to the present invention, specific volumes are lower, thereby permitting shorter turbine blades, that are stronger and easier to cool compared with longer turbine blades. 
     FIG. 5 illustrates a cross-sectional view of an embodiment of the high pressure cycle according to the present invention which is used in a turbine engine. On the left end of the shaft shown at  30  is the last stage of a series of axial flow compressor blades, the last blade being shown at  32 . Air is compressed by the compressor blades and discharged from the compressor, shown at  34 . After leaving the air compressor, the compressed air enters a chamber which is divided into two sections by a divider plate, shown at  35 . In an upper section, shown generally at  36 , fuel is introduced into the chamber through a fuel inlet, shown at  38 , and mixes with the air. In the lower section, shown generally at  40 , the air remains substantially free-of fuel. The air/fuel mixture is discharged through the inlet of a valve, shown at  42 , into a combustion chamber. The combustion chamber, shown at  47 , comprises an explosion chamber, shown generally at  48 , and a compression chamber, shown generally at  52 . Any valve that is suitable for controlling the flow of a compressed gas into the combustion chamber can be utilized. Preferably, the valve is capable of synchronizing the flow of gas into the combustion chamber with a resonating pressure wave therein, whereby the valve is open when the combustion chamber pressure is lower than average and closed when the combustion chamber pressure is greater than average. A non-limiting preferred example of a valve is a distributor rotary valve, examples of which are illustrated in FIGS. 9 or  10 , described below. Based on the disclosure provided herein, one skilled in the art will be able to select the desired valve for the desired application. 
     As shown in FIG. 5, as the rotary valve rotates it alternately opens the valve to the lower air compression chamber, shown at  44 , and the valve to the upper explosion chamber, shown at  46 . The air/fuel mixture enters the explosion chamber shown at  48  and is ignited by a high pressure wave compressing the mixture, or alternatively by an igniting device, shown at  50 , such as a spark plug. The explosion of the air/fuel mixture starts a pressure wave down the channel of the explosion chamber and curves around until it compresses air previously introduced through the open valve  44  (now closed) against the lower valve plate shown at  54 . The general area where the air is compressed in the combustion chamber is shown generally at  52 . The pressure wave is then reflected back the direction it came and the pressure wave compresses a new air/fuel mixture to create another explosion in the explosion chamber  48 . Thus, there is a continuous alternating cycle between explosions creating a pressure wave which compresses air in the air compression chamber and reflections of the pressure wave that compress the air/fuel mixture to cause the explosions. Preferably, the frequency of the explosions is controlled to provide a resonating pressure wave in the tube. This means that the pressure in the tube alternates between the following two stages: 
     (A) high pressure in the compression chamber  48  and low pressure in the compressor chamber  52  during the explosion stage; and 
     (B) low pressure in the compression chamber  48  and high pressure in the compressor chamber  52  during the compressing of the air (compression stage). 
     Examples of means for adjusting the frequency of explosions in the combustion chamber include; 
     (1) adjusting the length of the tube; 
     (2) adjusting the frequency of the air/fuel mixture entering the combustion chamber; 
     (3) adjusting the temperature of gas contained within combustion chamber; 
     (4) adjusting the amount of air/fuel mixture being supplied to the combustion chamber; 
     (5) adjusting the speed of the rotary valve; and 
     (6) adjusting the relative flow areas, shown at  44  and  46  in the Figures. 
     The combustion chamber can be adjusted to be a length that provides the desired resonant frequency. For example, if the length of the tube is one-half of the pressure wave length and the frequency of explosions resonate, then the pressure at somewhere near the middle of the wave travel remains practically constant (about an average of the combustion chamber pressure), but is significantly higher than the inlet pressure coming from the air compressor. Examples of suitable combustion chamber lengths for providing a resonating pressure wave include, but are not limited, to the following combustion chamber lengths shown in FIGS. 6 and 7. 
     FIG. 6 illustrates a combustion chamber having a length that is one-half of the wave length of the pressure wave. Between the points E 1  and E 2  in the combustion chamber, the pressure variation is significantly less than elsewhere in the combustion chamber, such as at the first reflecting surface R 1  or at the second reflecting surface R 2 . At R 1  and R 2 , the pressure varies from P 1  to P 3 . Between the points E 1  and E 2 , the pressure varies significantly less than between P 1  to P 3 . Thus, the gas flow taken from the combustion chamber between the points E 1  and E 2  will fluctuate significantly less than the gas flow taken elsewhere from the combustion chamber. Preferably, the gas flow taken from the combustion chamber is at substantially the average combustion chamber pressure, shown at P 2 . 
     FIG. 7 illustrates a combustion chamber having a length that is one wave length of the pressure wave. Between the points E 3  and E 4  or the points E 5  and E 6  in the combustion chamber, the pressure variation is significantly less than elsewhere in the combustion chamber, such as at the first reflecting surface R 1  or at the second reflecting surface R 2 . At R 1  and R 2 , the pressure varies from P 1  to P 3 . Between the points E 3  and E 4  or between E 5  and E 6 , the pressure varies significantly less than between P 1  to P 3 . Thus, the gas flow taken from the combustion chamber between the points E 3  and E 4  or between the points E 5  and E 6  will fluctuate significantly less than the gas flow taken elsewhere from the combustion chamber. Preferably, the gas flow taken from the combustion chamber is at substantially the average combustion chamber pressure, shown at P 2 . 
     The resonating pressure waves shown in FIGS. 6 and 7 represent a combustion chamber having a constant temperature throughout the length of the combustion chamber. However, when a combustion chamber is used where an air/fuel mixture is injected into the combustion chamber at or near the first reflecting surface R 1  and air is injected into the combustion chamber at or near the second reflecting surface R 2 , the temperature will be significantly higher near the first reflecting surface where combustion is occurring than at the second reflecting surface. Since the compression wave travels faster as the temperature is increased, the resonating pressure waves shown in FIGS. 6 and 7 will be skewed away from first reflecting surface R 1 . Thus, the part of the combustion chamber defined between E 1  and E 2  will be farther from the first reflecting surface R 1  and closer to the second reflecting surface R 2  than shown in FIG.  6 . Similarly, the parts of the combustion chamber defined between E 3  and E 4 , and between E 5  and E 6 , will be farther from the first reflecting surface R 1  and closer to the second reflecting surface R 2  than shown in FIG.  7 . Based on the disclosure provided herein, one skilled in the art will easily be able to determine the location in the combustion chamber that provides a substantially constant gas flow pressure. 
     As shown in FIG. 5, the outlet from the compression chamber, shown at  56 , is farther away from the inlet for the air/fuel mixture than it is from the inlet for the air. As explained above, since the temperature of the exploding air/fuel mixture is much higher than that of the air in the air compression chamber, the velocity of the pressure wave corresponding to acoustic velocity in the gas is much higher in the hotter explosion chamber than in the colder compression chamber. Typically, the acoustic velocity is proportional to the square root of the absolute temperature. Therefore, the point at which the pressure remains constant in the system with proper tuning will be closer to the air compression chamber portion than it is to the explosion chamber portion of the combustion chamber. The hot exploding air/fuel mixture forms a hot combustion gas that mixes with the cooler air compression gases to form a pressurized gas having a temperature somewhere between the explosion temperature (or combustion temperature of the fuel/air mixture) and the air compression temperature. The pressurized gas then flows out of the combustion chamber through turbine nozzles to drive the turbine blades. The result of this system is that the pressure of the pressurized gas contacting the turbine blades can be considerably higher than the pressure of the compressed air formed by the air compressor. In particular, the exploding air/fuel mixture forms a pressure wave that acts as a piston to further compress the compressed air introduced into the compression chamber portion of the combustion chamber to form a mixture of twice compressed air and combustion gasses, referred to as pressurized gas. The pressurized gas can be withdrawn from the combustion chamber at a pressure significantly higher than the pressure of the compressed air entering the combustion chamber. Furthermore, the temperature of the pressurized gas leaving the combustion chamber is significantly less than the air/fuel mixture explosion temperature (or combustion temperature of the air/fuel mixture). Thus, more air/fuel mixture can be burned in the combustion chamber according to the present invention while not exceeding the temperature limit of the turbine blades, compared to conventional combustion chambers. 
     FIG. 8 illustrates a pressure volume diagram that is applicable to the high pressure cycle described above. The air enters at a first pressure and volume, shown at  70 , and is compressed isentropically to a second pressure and volume, shown at  72 . At this point, approximately one-half of the air is mixed with fuel and explodes to a high pressure, shown at  74 . The pressure wave formed expands isentropically and the pressure decreases to a lower pressure and greater volume, shown at  76 . 
     The energy of expansion is approximately equal to the energy required to compress the air from the pressure and volume shown at  72  to the pressure and volume shown at  78 . This results in an intermediate pressure corresponding to the pressure shown at  80  and  76 . 
     When the hot gas mixes at the pressure and volume shown at  76 , with the air at the pressure and volume shown at  78 , they end up at a specific pressure and volume shown at  80 . From the pressure and volume of the gases shown at  80 , the gasses expand to approximately atmospheric pressure, shown at  82 , and eventually reduce in specific volume back to the volume shown at  70 , external to the system. The temperature at the pressure and volume shown at  74  can be much higher than the temperature of the gas that enters the gas turbine because after expansion from the volume shown at  74  to the volume shown at  76 , and mixing with the compressed air shown at  80 , the temperature of the gas is much lower. Therefore, the effective explosion temperature (or combustion temperature of the fuel/air mixture) is significantly higher than the temperature of the pressurized gas that contacts the turbine blades. This then makes use of the potential of operating the combustion system at much higher combustion temperatures than is currently possible with a turbine operating on the Brayton Cycle, because the temperature of the pressurized gas contacting the turbine blades is lower than the combustion temperature. 
     The rotary valve illustrated in FIG. 9 has  3  holes, shown at  43 . The rotary valve illustrated in FIG. 10 has 5 holes, shown at  45 . The circles represent the location of the holes in the stationary plate with one hole representing the inlet to the combustion chamber and the other hole representing the inlet to the air compression chamber. 
     Preferably, the rotary valve has holes aligned whereby the valve  46  is open when the valve  44  is closed, and the valve  44  is open when the valve  46  is closed. For example, if the valve  46  and the valve  44  are placed in line with the central axis of the rotary valve, as shown in FIG. 5, the rotary valve should have an odd number of holes so that valves  46  and  44  are not open at the same time. 
     Since the explosion can reach a very high temperature, it may be necessary to cool the walls of the chamber. For example, in FIG. 5, a cooling jacket is shown at  51 , that can be used to cool the explosion chamber portion of the combustion chamber. Optionally, water-cooled walls can be used for the entire combustion chamber if desired. 
     The combustion chamber shown in FIG. 5 utilizes a mixture of fuel/air. FIG. 11 illustrates a cross-sectional view of a turbine engine similar to that shown in FIG. 5, with the following modifications. In the turbine shown in FIG. 11, fuel is not introduced into the air chamber preceding the combustion chamber. Instead, air is introduced to combustion chamber  47 ′ through the valve shown at  46 ′. Fuel is introduced into the combustion chamber through the fuel inlet shown at  100 . The fuel mixes with the air in the explosion chamber portion of the combustion chamber, shown generally at  48 ′. 
     When using the combustion chamber shown in FIG. 11, the fuel injection should alternate in tune with the air inlet valve to the chamber. The fuel injection can be timed with an injection pump, if liquid fuel, or with a valve, if gaseous fuel, so that the fuel enters at approximately the same time as the air enters through valve  46 . 
     FIG. 11 shows an optional annular space around the explosion chamber, shown at  102 . This annular air space allows the compressed air in the air compression chamber to help cool the wall of the explosion chamber. However, since the explosion temperature can be high, further cooling of the explosion chamber wall may be desired. 
     As shown in FIG. 11, the pressure wave travels to the end of the explosion chamber, turns, and travels toward the air compression chamber, shown generally at  52 ′. The spherical end, shown at  104 , may cause a reflection of the pressure wave and disrupt the single frequency resonating pressure wave in the combustion chamber. This undesirable reflection could be avoided, for example, by using the U tube design shown in FIGS. 5 or  12 , or a straight tube as the combustion chamber. FIG. 12 illustrates an annular space, shown at  110  around the combustion chamber. The two curves at the right hand end of the tube serve to deflect the pressure wave smoothly without an intermediate reflection, such as shown in FIG.  12 . 
     The pressurized gas outlet, shown at  58 , to the turbine, shown at  60 , is closer to the air compression chamber  52 ′ than the explosion chamber  48 ′. As discussed previously, the high temperature exploding air/fuel mixture compression wave has a higher acoustic velocity, and therefore in the same time travels farther than the lower temperature compression wave in the air compression chamber. Therefore, the outlet to the turbine should not be at one-half the total length of the chamber but should be closer to the air compression end, when a substantially constant pressure is desired and when using a combustion chamber having a length equal to one-half wavelength of the pressure wave. 
     Although it is possible to have the fuel injected separately into the explosion chamber, usually it is more desirable to have the fuel mixed with the air prior to introducing the air and fuel to the explosion chamber. Therefore in FIG. 5, the fuel inlet  38  connects to the mixing chamber  36  and a divider plate  35  separates the air/fuel mixture from the air prior to entering the explosion chamber. This scheme is usually more desirable than having the fuel injected directly into the explosion chamber for the following reasons: 
     (1) The air/fuel mixture is usually more uniformly mixed compared to fuel injection because the air/fuel mixture has time to mix thoroughly before the explosion occurs. 
     (2) The ignition of the air/fuel mixture can be more easily generated by the pressure wave itself than when using fuel injection. Ignition via the pressure wave usually provides a more substantially constant volume explosion than is possible when using a spark plug to ignite the fuel. Constant volume explosion improves the theoretical efficiency of the explosion chamber system. 
     (3) By having the air/fuel thoroughly mixed before the explosion, the explosion temperatures can be more uniform than when using a flame propagation created by a spark plug. This is desirable because the variation of temperature will be considerably less than that when flame propagation occurs. This has the effect of reducing formation of nitrogen oxides and other undesirable combustion by-products. 
     A problem with mixing the fuel and air prior to entering the explosion chamber may be that the air temperature leaving the compressor could be too high, which can lead to undesirable combustion in the mixing chamber. This could be prevented by intercooling the air going through the air compressor so that the temperature of the air leaving the air compressor is low enough that detonation will not occur in the mixing chamber. 
     In the Otto Cycle used in automobile engines, where fuel and air are mixed before compression, the limiting value of compression ratio is approximately 8:1 to 10:1, corresponding to a pressure ratio of approximately 25 to 1, to avoid detonation. By intercooling air as it passes through the compressor, it is possible to limit the temperature of the air entering the mixing chamber to avoid detonation. This makes it possible to use higher pressure ratios than are normally possible with the Otto Cycle used in the automobile engine. If the mixture is then ignited by the pressure wave returning from the compression end of the combustion chamber, the explosion occurs throughout the mixture and can reach a higher pressure than is possible if it occurs by flame propagation. In other words, by intercooling the air compressor significantly higher pressure ratios can be used while mixing the air and fuel before introducing them into the explosion chamber. 
     The present invention provides a remarkable advantage because use of the detonation characteristics of fuel are utilized, rather than attempting to suppress the detonation characteristics as is usually done in conventional automobile engines. 
     In FIG. 8, the temperature of the combustion gas at point  74  can be much higher than the temperature of the pressurized gas that enters the gas turbines because after expansion from  74  to  76 , the combustion gas is mixed with the compressed gas at  78  to form a pressurized gas. The temperature of the pressurized gas is less than the temperature of the combustion gas. Therefore, the effective burning temperature can be much higher than the temperature of the pressurized gas that enters the gas turbine. This then makes use of the potential of operating the system at much higher temperatures than is currently possible with a gas turbine operating on the Brayton Cycle. 
     Performance values for the high pressure cycle according to the present invention are shown in the following Table 2. Table 3 illustrates the equations used for determining the performance values shown in Table 2. The calculations are based on what is considered to be the air standard cycle with constant mass flow through the system, and no addition of mass for the fuel, constant specific heats throughout the cycle and other possible operating conditions. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                   
                 A 
                 B 
                 C 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
                 J 
                 K 
                 L 
                 M 
                 N 
               
               
                   
               
               
                 1 
                 P2/P1 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
                 32 
               
               
                 2 
                 T1 
                 520 
                 520 
                 400 
                 460 
                 460 
                 460 
                 460 
                 460 
                 460 
                 460 
                 460 
                 520 
                 520 
               
               
                 3 
                 P1/J 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
               
               
                 4 
                 T3 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
                 4000 
               
               
                 5 
                 EFF. COMP. 
                 1 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                 6 
                 COOL FACT. 
                 1 
                 1 
                 1 
                 1 
                 0.9 
                 0.8 
                 0.7 
                 0.6 
                 0.5 
                 0.4 
                 0.3 
                 1 
                 1 
               
               
                 7 
                 N/(N − 1) CO 
                 3.463 
                 3.1167 
                 3.1167 
                 3.1167 
                 3.463 
                 3.895875 
                 4.452529 
                 5.1945 
                 6.2334 
                 7.79175 
                 10.389 
                 3.1167 
                 3.1167 
               
               
                 8 
                 (N − 1)/N CO 
                 0.288766965 
                 0.320852 
                 0.320852 
                 0.320852 
                 0.288767 
                 0.256682 
                 0.224597 
                 0.192511 
                 0.160426 
                 0.128341 
                 0.096256 
                 0.320852 
                 0.320852 
               
               
                 9 
                 N COMP 
                 1.406008932 
                 1.472434 
                 1.472434 
                 1.472434 
                 1.406009 
                 1.345319 
                 1.289651 
                 1.238407 
                 1.19108 
                 1.147237 
                 1.106508 
                 1.472434 
                 1.472434 
               
               
                 10 
                 EFF TURB 
                 1 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                 11 
                 N/(N − 1) TU 
                 3.463 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
                 3.847778 
               
               
                 12 
                 (N − 1)/N TU 
                 0.288766985 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
                 0.25989 
               
               
                 13 
                 N TURB 
                 1.406008932 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
                 1.351151 
               
               
                 14 
                 T2/T1 
                 2.720430224 
                 3.0404 
                 3.0404 
                 3.0404 
                 2.72043 
                 2.434134 
                 2.177988 
                 1.94676 
                 1.743674 
                 1.660171 
                 1.39598 
                 3.0404 
                 3.0404 
               
               
                 15 
                 T2 
                 1414.623716 
                 1581.008 
                 1216.16 
                 1398.584 
                 1251.398 
                 1119.702 
                 1001.885 
                 986.4297 
                 802.0901 
                 717.6788 
                 642.1508 
                 1581.008 
                 1581.008 
               
               
                 16 
                 P3/P2 
                 2.827607054 
                 2.530032 
                 3.289041 
                 2.860036 
                 3.198425 
                 3.67238 
                 3.992553 
                 4.462146 
                 4.986971 
                 5.573524 
                 6.229066 
                 2.555332 
                 2.783035 
               
               
                 17 
                 P3/P1 
                 90.48342574 
                 80.96102 
                 105.2493 
                 91.52115 
                 102.2856 
                 114.3162 
                 127.7617 
                 142.7887 
                 159.5831 
                 178.3528 
                 199.3301 
                 81.77063 
                 89.05712 
               
               
                 18 
                 V1/V2 
                 11.76284535 
                 10.52493 
                 10.52493 
                 10.52493 
                 11.76285 
                 13.14636 
                 14.6926 
                 16.4207 
                 18.35205 
                 20.51057 
                 22.92296 
                 10.62493 
                 10.52493 
               
               
                 19 
                 V1 
                 13.089 
                 13.089 
                 10.06846 
                 11.57873 
                 11.57873 
                 11.57873 
                 11.57873 
                 11.57873 
                 11.57873 
                 11.57873 
                 11.57873 
                 13.089 
                 13.089 
               
               
                 20 
                 V2 
                 1.112740975 
                 1.243618 
                 0.95663 
                 1.100124 
                 0.984348 
                 0.880756 
                 0.788066 
                 0.70513 
                 0.630923 
                 0.564525 
                 0.505115 
                 1.243618 
                 1.243618 
               
               
                 21 
                 X = V3/V2 
                 0.5 
                 0.509 
                 0.573 
                 0.543 
                 0.588 
                 0.587 
                 0.603 
                 0.617 
                 0.628 
                 0.638 
                 0.646 
                 0.5 
                 0.436 
               
               
                 22 
                 (1 − X)/X 
                 1 
                 0.964637 
                 0.745201 
                 0.841621 
                 0.760583 
                 0.703578 
                 0.658375 
                 0.620746 
                 0.592357 
                 0.567398 
                 0.547988 
                 1 
                 1.293578 
               
               
                 23 
                 V3 
                 0.556370488 
                 0.633002 
                 0.548149 
                 0.597367 
                 0.55911 
                 0.517004 
                 0.475204 
                 0.435065 
                 0.39622 
                 0.360167 
                 0.326304 
                 0.621809 
                 0.542218 
               
               
                 24 
                 P4/P2 
                 2.088337068 
                 1.908258 
                 2.553583 
                 2.186671 
                 2.475192 
                 2.797871 
                 3.162952 
                 3.578572 
                 4.040154 
                 4.56475 
                 5.153344 
                 1.911016 
                 1.944272 
               
               
                 25 
                 P4/P3 
                 0.738552785 
                 0.754243 
                 0.776473 
                 0.764561 
                 0.774362 
                 0.783195 
                 0.792213 
                 0.801538 
                 0.810142 
                 0.819014 
                 0.827306 
                 0.747854 
                 0.698616 
               
               
                 26 
                 P4/P1 
                 66.8267861 
                 61.06424 
                 81.72331 
                 69.97348 
                 79.20614 
                 89.53187 
                 101.2145 
                 114.4503 
                 129.2849 
                 146.0734 
                 164.907 
                 61.15251 
                 62.21671 
               
               
                 27 
                 P4 
                 982.3537557 
                 897.6444 
                 1201.333 
                 1028.61 
                 1164.33 
                 1316.118 
                 1487.853 
                 1682.419 
                 1900.489 
                 2147.279 
                 2424.133 
                 898.9419 
                 914.5857 
               
               
                 28 
                 T4/T2 
                 1.236967851 
                 1.205189 
                 1.310986 
                 1.253515 
                 1.299195 
                 1.345996 
                 1.394526 
                 1.444912 
                 1.498876 
                 1.55039 
                 1.605652 
                 1.205872 
                 1.211694 
               
               
                 29 
                 T4C 
                 1749.844058 
                 1905.382 
                 1594.369 
                 1753.145 
                 1625.81 
                 1507.114 
                 1397.128 
                 1295.262 
                 1200.469 
                 1112.682 
                 1031.071 
                 1908.177 
                 1915.698 
               
               
                 30 
                 T4/T3 EXPLO 
                 0.916196417 
                 0.921776 
                 0.929541 
                 0.9254 
                 0.928811 
                 0.931858 
                 0.934944 
                 0.938108 
                 0.941008 
                 0.943971 
                 0.946721 
                 0.919514 
                 0.901604 
               
               
                 31 
                 T4E 
                 3664.785666 
                 3687.102 
                 3718.164 
                 3701.699 
                 3715.242 
                 3727.431 
                 3739.776 
                 3752.434 
                 3764.025 
                 3775.883 
                 3788.884 
                 3714.836 
                 3967.06 
               
               
                 32 
                 T4 
                 2707.314862 
                 2812.277 
                 2611.304 
                 2811.156 
                 2812.607 
                 2810.44 
                 2809.744 
                 2811.337 
                 2810.382 
                 2811.804 
                 2811.326 
                 2810.507 
                 2810.092 
               
               
                 33 
                 V4 
                 1.019738658 
                 1.159236 
                 0.86589 
                 1.011235 
                 0.893822 
                 0.790128 
                 0.698755 
                 0.618296 
                 0.547165 
                 0.484523 
                 0.429114 
                 1.158834 
                 1.136879 
               
               
                 34 
                 HEAT IN 
                 217.9472207 
                 207.5916 
                 268.9407 
                 238.1591 
                 263.2193 
                 285.0579 
                 304.8078 
                 322.8526 
                 338.5973 
                 353.0888 
                 365.7222 
                 207.293 
                 207.223 
               
               
                 35 
                 T5/T4 
                 0.297178567 
                 0.343472 
                 0.31842 
                 0.331528 
                 0.321019 
                 0.310957 
                 0.301201 
                 0.291733 
                 0.282837 
                 0.27381 
                 0.285315 
                 0.343343 
                 0.341807 
               
               
                 36 
                 T5 
                 804.5505359 
                 885.8385 
                 895.1744 
                 931.9758 
                 902.901 
                 873.9255 
                 846.2989 
                 820.1596 
                 794.3183 
                 769.8996 
                 745.8858 
                 964.968 
                 960.5091 
               
               
                 37 
                 HEAT OUT 
                 67.46693206 
                 105.732 
                 117.4058 
                 111.9055 
                 105.0118 
                 98.14172 
                 91.59146 
                 85.39383 
                 79.26687 
                 73.47719 
                 67.78352 
                 105.5019 
                 104.4447 
               
               
                 38 
                 WORK 
                 150.4802886 
                 101.8596 
                 151.5348 
                 126.2537 
                 158.2075 
                 186.9182 
                 213.2163 
                 237.4588 
                 259.3304 
                 279.5916 
                 297.9386 
                 101.7911 
                 102.7783 
               
               
                 39 
                 EFF. 
                 0.690443715 
                 0.490673 
                 0.563451 
                 0.530123 
                 0.601048 
                 0.655713 
                 0.699511 
                 0.735502 
                 0.765898 
                 0.79189 
                 0.814658 
                 0.491049 
                 0.495979 
               
               
                 40 
                 V5 
                 20.25135188 
                 24.31365 
                 22.53245 
                 23.45678 
                 22.72693 
                 21.99759 
                 21.3022 
                 20.64425 
                 19.9938 
                 19.37915 
                 18.7747 
                 24.28922 
                 24.17699 
               
               
                 41 
                 WORK COM 
                 150.8664994 
                 170.8533 
                 131.4256 
                 151.1395 
                 148.2876 
                 145.3359 
                 142.3185 
                 139.2844 
                 136.1977 
                 133.1392 
                 130.1056 
                 170.8533 
                 170.8533 
               
               
                 42 
                 WORK EXP 
                 320.8768874 
                 324.003 
                 336.2501 
                 329.7661 
                 335.123 
                 339.8275 
                 344.5533 
                 349.4198 
                 353.787 
                 358.3217 
                 362.4518 
                 323.8628 
                 324.5722 
               
               
                 43 
                 WORK EXH 
                 19.48231334 
                 30.53217 
                 33.90328 
                 32.31491 
                 30.32422 
                 2834034 
                 28.44881 
                 24.65911 
                 22.88982 
                 21.21793 
                 19.57376 
                 30.46572 
                 30.16044 
               
               
                 44 
                 NET WORK 
                 150.5280747 
                 122.6175 
                 170.9212 
                 146.3117 
                 158.5112 
                 166.1512 
                 175.788 
                 185.4963 
                 194.6994 
                 203.9646 
                 212.7725 
                 122.5435 
                 123.5585 
               
               
                 45 
                 EFF. BY WORK 
                 0.69066297 
                 0.690667 
                 0.635535 
                 0.614344 
                 0.594604 
                 0.582868 
                 0.576711 
                 0.574554 
                 0.575018 
                 0.577691 
                 0.581787 
                 0.591161 
                 0.596259 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                   
                 A 
                 B 
                 C 
                 D 
                 E 
               
               
                   
               
               
                 1 
                 P2/P1 
                 32 
                 32 
                 32 
                 32 
               
               
                 2 
                 T1 
                 520 
                 520 
                 400 
                 460 
               
               
                 3 
                 P1/J 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
               
               
                 4 
                 T3 
                 4000 
                 4000 
                 4000 
                 4000 
               
               
                 5 
                 EFF. COMP. 
                 1 
                 0.9 
                 0.9 
                 0.9 
               
               
                 6 
                 COOL FACT. 
                 1 
                 1 
                 1 
                 1 
               
               
                 7 
                 N/(N − 1) CO 
                 = 3.463*B5/B6 
                 = 3.463*C5/C6 
                 = 3.463*D5/D6 
                 = 3.463*E5/E6 
               
               
                 8 
                 (N − 1)/N CO 
                 = 1/B7 
                 = 1/C7 
                 = 1/D7 
                 = 1/E7 
               
               
                 9 
                 N COMP 
                 = 1/(B7 − 1) + 1 
                 = 1/(C7 − 1) + 1 
                 = 1/(D7 − 1) + 1 
                 = 1/(E7 − 1) + 1 
               
               
                 10 
                 EFF TURB 
                 1 
                 0.9 
                 0.9 
                 0.9 
               
               
                 11 
                 N/(N − 1)TU 
                 = 3.463/B10 
                 = 3.463/C10 
                 = 3.463/D10 
                 = 3.463/E10 
               
               
                 12 
                 (N − 1)/N TU 
                 = 1/B11 
                 = 1/C11 
                 = 1/D11 
                 = 1/E11 
               
               
                 13 
                 N TURB 
                 = 1/(B11 − 1) + 1 
                 = 1/(C11 − 1) + 1 
                 = 1/(D11 − 1) + 1 
                 = 1/(E11 − 1) + 1 
               
               
                 14 
                 T2/T1 
                 = B1{circumflex over ( )}B8 
                 = C1{circumflex over ( )}C8 
                 = D1{circumflex over ( )}D8 
                 = E1{circumflex over ( )}E8 
               
               
                 15 
                 T2 
                 = B2{circumflex over ( )}B14 
                 = C2{circumflex over ( )}C14 
                 = D2{circumflex over ( )}D14 
                 = E2{circumflex over ( )}E14 
               
               
                 16 
                 P3/P2 
                 = B4/B15 
                 = C4/C15 
                 = D4/D15 
                 = E4/E15 
               
               
                 17 
                 P3/P1 
                 = B16*B1 
                 = C16*C1 
                 = D16*D1 
                 = E16*E1 
               
               
                 18 
                 V1/V2 
                 = B1{circumflex over ( )}(1/B9) 
                 = C1{circumflex over ( )}(1/C9) 
                 = D1{circumflex over ( )}(1/D9) 
                 = E1{circumflex over ( )}(1/E9) 
               
               
                 19 
                 V1 
                 = 13.089*B2/520 
                 = 13.089*C2/520 
                 = 13.089*D2/520 
                 = 13.089*E2/520 
               
               
                 20 
                 V2 
                 = B19/B18 
                 = C19/C18 
                 = D19/D18 
                 = E19/E18 
               
               
                 21 
                 X = V3/V2 
                 0.5 
                 0.509 
                 0.573 
                 0.543 
               
               
                 22 
                 (1 − X)/X 
                 = (1 − B21)/B21 
                 = (1 − C21)/C21 
                 = (1 − D21)/D21 
                 = (1 − E21)/E21 
               
               
                 23 
                 V3 
                 = B20*B21 
                 = C20*C21 
                 = D20*D21 
                 = E20*E21 
               
               
                 24 
                 P4/P2 
                 = ((B16 + B22)/ 
                 = ((C16 + C22)/(C22 + C 
                 = ((D16 + D22)/(D22 + D 
                 = ((E16 + E22)/(E22 + E 
               
               
                   
                   
                 (B22 + B16{circumflex over ( )}0.711233)){circumflex over ( )}3.463 
               
               
                 25 
                 P4/P3 
                 = B24/B16 
                 = C24/C16 
                 = D24/D16 
                 = E24/E16 
               
               
                 26 
                 P4/P1 
                 = B1*B24 
                 = C1*C24 
                 = D1*D24 
                 = E1*E24 
               
               
                 27 
                 P4 
                 = B26*14.7 
                 = C26*14.7 
                 = D26*14.7 
                 = E26*14.7 
               
               
                 28 
                 T4/T2 
                 = B24{circumflex over ( )}0.2888 
                 = C24{circumflex over ( )}0.2888 
                 = D24{circumflex over ( )}0.2888 
                 = E24{circumflex over ( )}0.2888 
               
               
                 29 
                 T4C 
                 = B28*B15 
                 = C28*C15 
                 = D28*D15 
                 = E28*E15 
               
               
                 30 
                 T4/T3 EXPLO 
                 = B25{circumflex over ( )}0.2888 
                 = C25{circumflex over ( )}0.2888 
                 = D25{circumflex over ( )}0.2888 
                 = E25{circumflex over ( )}0.2888 
               
               
                 31 
                 T4E 
                 = B4*B30 
                 = C4*C30 
                 = D4*D30 
                 = E4*E30 
               
               
                 32 
                 T4 
                 = B31*B21 + B29*(1 − B21) 
                 = C31*C21 + C29*(1 − C2 
                 = D31*D21 + D29*(1 − 
                 = E31*E21 + E29*(1 − 
               
               
                   
                   
                   
                   
                 D2 
                 E2 
               
               
                 33 
                 V4 
                 = 54.282 B32/B27/144 
                 = 54.282 C32/C27/144 
                 = 54.282 D32/D27/144 
                 = 54.282 E32/E27/144 
               
               
                 34 
                 HEAT IN 
                 = (B4 − B15)*0.1688*B21 
                 = (C4 − C15)*0.1688*C2 
                 = (D4 − D15)*0.1688*D2 
                 = (E4 − E15)*0.1688*E2 
               
               
                 35 
                 T5/T4 
                 = 1/(B1*B24) B12 
                 = 1/(C1*C24) C12 
                 = 1/(D1*D24) D12 
                 = 1/(E1*E24) E12 
               
               
                 36 
                 T5 
                 = B32*B35 
                 = C32*C35 
                 = D32*D35 
                 = E32*E35 
               
               
                 37 
                 HEAT OUT 
                 = 0.2371*(B36 − B2) 
                 = 0.2371*(C36 − C2) 
                 = 0.2371*(D36 − D2) 
                 = 0.2371*(E36 − E2) 
               
               
                 38 
                 WORK 
                 = B34 − B37 
                 = C34 − C37 
                 = D34 − D37 
                 = E34 − E37 
               
               
                 39 
                 EFF 
                 = B38/B34 
                 = C38/C34 
                 = D38/D34 
                 = E38/E34 
               
               
                 40 
                 V5 
                 = 53.282*B36/14.7/144 
                 = 53.282*C36/14.7/14 
                 = 53.282*D36/14.7/14 
                 = 53.282*E36/14.7/14 
               
               
                 41 
                 WORK COM 
                 = 2.7201*B19/(B9 − 1)/B5*(B1{circumflex over ( )}B8-1) 
                 = 2.7201*C19/(C9 − 1)/C 
                 = 2.7201*D19/(D9 − 1)/D 
                 = 2.7201*E19/(E9 − 1)/E 
               
               
                 42 
                 WORK EXP 
                 = B27*B33*B10/5.40417/ 
                 = C27*C33*C10/5.404 
                 = D27*D33*D10/5.404 
                 = E27*E33*E10/5.404 
               
               
                   
                   
                 (B13 − 1)*(1 − 1/B26{circumflex over ( )}B12) 
               
               
                 43 
                 WORK EXH 
                 = 2.7201*(B40-B19) 
                 = 2.7201*(C40 − C19) 
                 = 2.7201*(D40 − D19) 
                 = 2.7201*(E40 − E19) 
               
               
                 44 
                 NET WORK 
                 = B42 − B41 − B43 
                 = C42 − C41 − C43 
                 = D42 − D41 − D43 
                 = E42 − E41 − E43 
               
               
                 45 
                 EFF. BY WORK 
                 = B44/B34 
                 = C44/C34 
                 = D44/D34 
                 = E44/E34 
               
               
                   
               
             
          
           
               
                   
                 A 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 1 
                 P2/P1 
                 32 
                 32 
                 32 
                 32 
               
               
                 2 
                 T1 
                 460 
                 460 
                 460 
                 460 
               
               
                 3 
                 P1/J 
                 2.7201 
                 2.7201 
                 2.7201 
                 2.7201 
               
               
                 4 
                 T3 
                 4000 
                 4000 
                 4000 
                 4000 
               
               
                 5 
                 EFF. COMP. 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                 6 
                 COOL FACT. 
                 0.9 
                 0.8 
                 0.7 
                 0.6 
               
               
                 7 
                 N/(N − 1) CO 
                 = 3.463*F5/F6 
                 = 3.463*G5/G6 
                 = 3.463*H5/H6 
                 = 3.463*I5/I6 
               
               
                 8 
                 (N − 1)/N CO 
                 = 1/F7 
                 = 1/G7 
                 = 1/H7 
                 = 1/I7 
               
               
                 9 
                 N COMP 
                 = 1/(F7 − 1) + 1 
                 = 1/(G7 − 1) + 1 
                 = 1/(H7 − 1) + 1 
                 = 1/(I7 − 1) + 1 
               
               
                 10 
                 EFF TURB 
                 0.9 
                 0.9 
                 0.9 
                 0.9 
               
               
                 11 
                 N/(N − 1)TU 
                 = 3.463/F10 
                 = 3.463/G10 
                 = 3.463/H10 
                 = 3.463/I10 
               
               
                 12 
                 (N − 1)/N TU 
                 = 1/F11 
                 = 1/G11 
                 = 1/H11 
                 = 1/I11 
               
               
                 13 
                 N TURB 
                 = 1/(F11-1) + 1 
                 = 1/(G11 − 1) + 1 
                 = 1/(H11 − 1) + 1 
                 = 1/(I11 − 1) + 1 
               
               
                 14 
                 T2/T1 
                 = F1{circumflex over ( )}F8 
                 = G1{circumflex over ( )}G8 
                 = H1{circumflex over ( )}H8 
                 = I1{circumflex over ( )}I8 
               
               
                 15 
                 T2 
                 = F2{circumflex over ( )}F14 
                 = G2{circumflex over ( )}G14 
                 = H2{circumflex over ( )}H14 
                 = I2{circumflex over ( )}I14 
               
               
                 16 
                 P3/P2 
                 = F4/F15 
                 = G4/G15 
                 = H4/H15 
                 = I4/I15 
               
               
                 17 
                 P3/P1 
                 = F16*F1 
                 = G16*G1 
                 = H16*H1 
                 = I16*I1 
               
               
                 18 
                 V1/V2 
                 = F1{circumflex over ( )}(1/F9) 
                 = G1{circumflex over ( )}(1/G9) 
                 = H1{circumflex over ( )}(1/H9) 
                 = I1{circumflex over ( )}(1/I9) 
               
               
                 19 
                 V1 
                 = 13.089*F2/520 
                 = 13.089*G2/520 
                 = 13.089*H2/520 
                 = 13.089*I2/520 
               
               
                 20 
                 V2 
                 = F19/F18 
                 = G19/G18 
                 = H19/H18 
                 = I19/I18 
               
               
                 21 
                 X = V3/V2 
                 0.568 
                 0.587 
                 0.603 
                 0.617 
               
               
                 22 
                 (1 − X)/X 
                 = (1 − F21)/F21 
                 = (1 − G21)/G21 
                 = (1 − H21)/H21 
                 = (1 − I21)/I21 
               
               
                 23 
                 V3 
                 = F20*F21 
                 = G20*G21 
                 = H20*H21 
                 = I20*I21 
               
               
                 24 
                 P4/P2 
                 = ((F16 + F22)/(F22 + F1 
                 = ((G16 + G22)/(G22 + G 
                 = ((H16 + H22)/(H22 + H 
                 = ((I16 + I22)/(I22 + I 
               
               
                 25 
                 P4/P3 
                 = F24/F16 
                 = G24/G16 
                 = H24/H16 
                 = I24/I16 
               
               
                 26 
                 P4/P1 
                 = F1*F24 
                 = G1*G24 
                 = H1*H24 
                 = I1*I24 
               
               
                 27 
                 P4 
                 = F26*14.7 
                 = G26*14.7 
                 = H26*14.7 
                 = I26*14.7 
               
               
                 28 
                 T4/T2 
                 = F24{circumflex over ( )}0.2888 
                 = G24{circumflex over ( )}0.2888 
                 = H24{circumflex over ( )}0.2888 
                 = I24{circumflex over ( )}0.2888 
               
               
                 29 
                 T4C 
                 = F28*F15 
                 = G28*G15 
                 = H28*H15 
                 = I28*I15 
               
               
                 30 
                 T4/T3 EXPLO 
                 = F25{circumflex over ( )}0.2888 
                 = G25{circumflex over ( )}0.2888 
                 = H25{circumflex over ( )}0.2888 
                 = I25{circumflex over ( )}0.2888 
               
               
                 31 
                 T4E 
                 = F4*F30 
                 = G4*G30 
                 = H4*H30 
                 = I4*I30 
               
               
                 32 
                 T4 
                 = F31*F21 + F29*(1 − F2 
                 = G31*G21 + G29*(1 − G2 
                 = H31*H21 + H29*(1 − H2 
                 = I31*I21 + I29*(1 − I2 
               
               
                 33 
                 V4 
                 = 53.282{circumflex over ( )}F32/F27/144 
                 = 53.282{circumflex over ( )}G32/G27/144 
                 = 53.282{circumflex over ( )}H32/H27/144 
                 = 53.282{circumflex over ( )}I32/I27/144 
               
               
                 34 
                 HEAT IN 
                 = (F4 − F15)*0.1688*F2 
                 = (G4 − G15)*0.1688*G2 
                 = (H4 − H15)*0.1688*H2 
                 = (I4 − I15)*0.1688*I2 
               
               
                 35 
                 T5/T4 
                 = 1/(F1*F24){circumflex over ( )}F12 
                 = 1/(G1*G24){circumflex over ( )}G12 
                 = 1/(H1*H24){circumflex over ( )}H12 
                 = 1/(I1*I24){circumflex over ( )}I12 
               
               
                 36 
                 T5 
                 = F32*F35 
                 = G32*G35 
                 = H32*H35 
                 = I32*I35 
               
               
                 37 
                 HEAT OUT 
                 = 0.2371*(F36 − F2) 
                 = 0.2371*(G36 − G2) 
                 = 0.2371*(H36 − H2) 
                 = 0.2371*(I36 − I2) 
               
               
                 38 
                 WORK 
                 = F34 − F37 
                 = G34 − G37 
                 = H34 − H37 
                 = I34 − I37 
               
               
                 39 
                 EFF 
                 = F38/F34 
                 = G38/G34 
                 = H38/H34 
                 = I38/I34 
               
               
                 40 
                 V5 
                 = 53.282*F36/14.7/144 
                 = 53.282*G36/14.7/14 
                 = 53.282*H36/14.7/14 
                 = 53.282*I36/14.7/14 
               
               
                 41 
                 WORK COM 
                 = 2.7201*F19/(F9 − 1)/F 
                 = 2.7201*G19/(G9 − 1)/G 
                 = 2.7201*H19/(H9 − 1)/H 
                 = 2.7201*I19/(I9 − 1)/I 
               
               
                 42 
                 WORK EXP 
                 = F27*F33*F10/5.4041 
                 = G27*G33*G10/5.404 
                 = H27*H33*H10/5.404 
                 = I27*I33*I10/5.404 
               
               
                 43 
                 WORK EXH 
                 = 2.7201*(F40 − F19) 
                 = 2.7201*(G40 − G19) 
                 = 2.7201*(H40 − H19) 
                 = 2.7201*(I40 − I19) 
               
               
                 44 
                 NET WORK 
                 = F42 − F41 − F43 
                 = G42 − G41 − G43 
                 = H42 − H41 − H43 
                 = I42 − I41 − I43 
               
               
                 45 
                 EFF. BY WORK 
                 = F44/F34 
                 = G44/G34 
                 = H44/H34 
                 = I44/I34 
               
               
                   
               
             
          
         
       
     
     In Table 2: 
     Row  1  shows the pressure ratio of 32 through the air compressor. 
     Row  2  shows the inlet temperature in degrees Rankine. 
     Row  3  shows the value of 14.7 psia×144/778.2. T 3  is the peak temperature reached in the explosion in degrees Rankine, and should be achievable. Actually, if stoichiometric combustion is achieved, then the values for T 3  should be higher than 4000° R. 
     Row  5  shows compressor polytropic efficiency. 
     Row  6  shows a cooling factor which represents intercooling with the number 1 being the case with no intercooling in the compressor. 
     Row  7  represents the value of N/(N−1) where N is the equivalent ratio of specific heat at constant pressure to the specific heat at constant volume when compression is polytropic rather than isentropic, and the value shown is the value that occurs with the polytropic efficiency and cooling factor shown. 
     Row  8  is the inverse of Row  7 . 
     Row  9  is the ratio of specific heats and the equivalent value shown for the actual polytropic exponent, or the exponent as affected by continual process intercooling. 
     Row  10  shows polytropic efficiency of expansion in the turbine. 
     Rows  11 ,  12  and  13  correspond to Row  7 ,  8  and  9 , but as calculated for the expansion curve for the turbine. 
     Row  14  is the ratio of compressor discharge temperature to compressor inlet temperature. 
     Row  15  is the compressor discharge temperature in degrees Rankine. 
     Row  16  is the ratio for the pressure at the peak of the explosion to the pressure at the outlet from the compressor. 
     Row  17  shows the ratio of peak pressure in the explosion to atmospheric inlet pressure. Note that the values of P 3 /P 1  go as high as 199 in column L. Currently diesel engine peak cylinder pressures reach approximately this same value. 
     Row  18  V 1 /V 2  is the ratio of inlet volume to the volume after compression in the compressor. V 1  is the specific volume of air at the corresponding pressure P 1  and T 1 . This is stated in cubic feet per pound. V 2  is the specific volume after compressing in the compressor. 
     Row  21  X is the ratio of the volume of air entering the explosion chamber to the volume of air entering the compression chamber end of the chamber. 
     Row  23  V 3  is the specific volume of the gas at peak explosion pressure. 
     Row  24  P 4 /P 2  is the ratio of the pressure after expansion from the peak explosion pressure to the pressure leaving the compressor. 
     Row  25  P 4 /P 3  is the ratio of the pressure of the mixture leaving the combustion chamber to the peak pressure of the explosion. 
     Row  26  P 4 /P 1  is the expansion ratio passing through the turbine after combustion. 
     Row  27  P 4  is the pressure at turbine inlet in lbs/square inch absolute. 
     Row  28  T 4 /T 2  is the ratio of turbine inlet temperature to compressor discharge temperature. 
     Row  29  T 4 C is the temperature in the compressor end of explosion chamber in degrees Rankine. 
     Row  30  T 4 /T 3  is the ratio of the temperature laving the explosion chamber to the temperature at the peak of explosion. 
     Row  31  T 4 E is the temperature of the exploding gas mixture before it mixes with the air in the opposite end of the chamber. 
     Row  32  T 4  is the temperature of the mixture leaving the combustion chamber and entering the turbine. 
     In these calculations, the value of X has been adjusted whereby the value of T 4  is approximately 2810° R (2350° F.) which is a usable modern turbine inlet temperature. 
     Row  33  V 4  is the specific volume of the gas mixture as it leaves the chamber. 
     Row  34  the heat in is the heat input from the fuel heating the air or air fuel mixture from a temperature of T 2  to a temperature of T 3 . 
     Row  35  T 5 /T 4  is the ratio of turbine exhaust temperature to turbine inlet temperature. 
     Row  36  T 5  is the exhaust temperature from the system in degrees Rankine. 
     Row  37  the heat out represents the specific heat at constant pressure times the quantity (T 5 -T 1 ). 
     Row  38  the work output is in BTU&#39;s per pound, and is calculated from the difference between the heat input and the heat output. This work output is correct for the theoretical condition as shown in column B. 
     Row  39  the cycle efficiency equals the quantity item  34 -item  37  divided by item  34 . The efficiency calculation is correct for the theoretical case shown in column B. The efficiency is an approximation and may be slightly lower due to intercooling and inefficiency in the compression and expansion in this cycle. 
     Row  40  V 5  is the specific volume of the gas at exhaust. 
     Row  41  the work of compression is calculated by the compression formula at the value of N shown on Row  9 . 
     Row  42  the work of expansion is the work output from the turbine as calculated based on the N value shown on item  13 . 
     Row  43  the work from the exhaust represents theoretical work that is lost as the volume at the exhaust shrinks to the volume at the inlet temperature. 
     Row  44  the net work equals the work of expansion item  42 —item  41 —item  43 . 
     Row  45  the efficiency is simply the net work divided by item  34 , the heat input. 
     The efficiencies shown in Table 2 do not take fully into account other losses that should be accounted for in an actual turbine, and therefore the efficiencies may be slightly lower than those shown above. Despite these additional losses not shown in the Table 2, the remarkable increase in efficiency shown in Table 2 compared to Table 1 is very significant and startling. For example, in comparing column c in Table 2 with column c in Table 1, the increase in efficiency is almost 20%. This difference is even more accentuated when using an intercooled system. For example comparing column j in Table 2 with column j in Table 1, the increase in efficiency is 22%. 
     The turbine and compressor polytropic efficiencies of 0.9 are rather typical of what is attained in gas turbines today. 
     The efficiency of the explosion process was not calculated and was assumed to be 100%. The following important factors should be noted regarding the explosion process. 
     1. There will be less heat loss from the combustion chamber according to the present invention than what occurs in a Diesel engine cylinder. The reason for this is that with a gas piston in the explosion chamber the walls can be much hotter than the walls in a diesel engine cylinder where lubrication is required. Therefore, the radiation or convection heat loss should be much less in the high pressure cycle according to the present invention than in a Diesel cycle. 
     2. There should be a very low friction loss in the present invention because compression is achieved using a compression wave instead of a piston. Furthermore, if the average velocity in the explosion chamber is at most about 200 feet per second, then friction loss becomes negligible. 
     3. The efficiency of a traveling pressure wave is very high. For example, a tidal wave or tsunami can travel thousands of miles across the ocean with very little diminution of energy. 
     4. When a detonation type of explosion is made to occur, as in the present invention, the explosion should be very close to constant volume. 
     In Table 2, columns D and E show the considerable improvement in efficiency and output compared to column C, which is made possible by refrigerating the inlet air to 400° R or 460° R. 
     Refrigerating the inlet air to the compressor, as shown on columns F through L, makes possible liquid injection intercooling. This liquid injection intercooling is made possible because refrigerating the inlet air removes the moisture from the air stream, and makes it possible to inject water and evaporate it within the compressor, thereby performing effective intercooling with very little losses. 
     In columns C through L, the percentage of air in the explosion process has been adjusted to allow the turbine inlet temperature, T 4 , to be approximately 2810° R which is a usable turbine inlet temperature in modern day turbines. Note that in both Table 1 and 2, the various degrees of intercooling maintain fairly constant cycle efficiency, but the net work output increases very greatly with more intercooling. Therefore, liquid injection intercooling and inlet refrigeration become very important factors in increasing the power output of a given size turbine. 
     Columns M and N show the effect of increasing the explosion temperature closer to the stoichiometric value when compared to column C. This demonstrates that the efficiency will increase with higher explosion temperatures at the same turbine inlet temperature by virtue of the fact that the X value or ratio of V 3 /V 2  is adjusted to produce the same turbine temperature. 
     The peak pressure values shown on line  17  appear to be quite high. However, it should be noted that current peak pressure ratios on diesel engines are as high as 200. Therefore, these high peak pressures should be reasonably achievable. 
     An important factor in comparing Table 2 with Table 1 is that the gas volume introduced into the turbine shown on line  20  in the Brayton Cycle versus V 4  on line  33  on table 2 shows that the volume of the gas entering the turbine is much less in Table 2 than it is in Table 1. For example, on column J which is an intercooled case, the volume entering the turbine in Table 2 is 0.547 cubic feet per lb whereas the volume of V 3  on column J for the Brayton Cycle is 2.210 cubic feet per lb. This is a ratio of 4 to 1. The significance of this is that the turbine blades in the high pressure cycle according to the present invention can be approximately one-fourth of the length of turbine blades for the Brayton Cycle. A short blade length means that the turbine blade stresses are significantly lower and they will be significantly easier to cool than the longer blades for the Brayton Cycle. This in turn means that higher turbine inlet temperatures could be used, which is an important practical advantage. 
     An important factor in the high pressure cycle according to. the present invention is that exhaust temperatures can be much lower than those generally achievable in the Brayton Cycle turbines in use today. For example, in column J line  36 , the exhaust temperature from the cycle is 794° R or 334° F. 
     Typical exhaust temperatures from modern gas turbines range from 700° F. to 1240° F. In contrast, an exhaust temperature from a turbine engine according to the present invention is significantly lower, on the order of about 300° F. to about 500° F. 
     Vapor turbine cycles typically operate efficiently in the range of from 800 to 160° F. inlet temperature. Thus, the exhaust from the turbine engine according to the present invention can be used directly to drive a vapor turbine cycle. 
     In general, high exhaust temperatures correspond to low compressor pressure ratios, and low exhaust temperatures occur with higher pressure ratios. However, in the turbine engine according to the present invention, the exhaust pressure can also be adjusted by adjusting the amount of air being compressed in the air compression chamber. In general, the more air being mixed with and compressed by the combustion gas compression wave, the lower the exhaust temperature. 
     Because of the great demand for higher efficiency gas turbine cycles, it is today increasingly common practice to use a combined cycle in which the exhaust gas is used to heat a Rankine cycle system, and produce additional power and increased efficiency. Typically those cycles utilizing exhaust gas temperatures of 1100° F. require that a steam turbine cycle be used to recover the exhaust energy. This is very expensive, and high pressure steam turbines are usually not efficient. Also, high pressure steam turbines cannot economically use condensing temperatures very close to atmospheric temperature because the volume expansion ratio through such a steam turbine is extremely high. 
     However, if the exhaust temperature from the gas turbine is as low as 334° F., then this heat can be conveniently used in a low temperature vapor turbine cycle, using a working fluid such as isobutane. This cycle attains a significantly higher turbine efficiency than a steam turbine, and also permits utilizing condensing temperatures very close to atmospheric temperatures. This also has the significance that the heat of condensation of the water vapor in the exhaust can be recovered. Therefore, the overall cycle efficiency can be significantly higher than that for other combined cycles in use today. 
     In gas turbine cycles in use today, it is common practice to use cooling air supplied by the compressor to be injected into the first stage turbine disk and out through holes in the turbine blades, thereby cooling the blades so that higher inlet temperatures can be used. FIG. 13 illustrates diagrammatically how this can be accomplished using the high pressure cycle according to the present invention. In order to provide air at sufficiently high pressure to force its way through the cooling passages in the turbine blades, the blade cooling air supply line, shown at  11 , is located where the combustion chamber pressure varies greatly, such as near an inlet to the compression chamber. As shown in FIG. 7, the blade cooling air supply line can be located in the combustion chamber where the combustion chamber pressure approaches P 3 , such as between the points E 4  and ES, the points R 1  and E 3 , or the points R 2  and E 6 . A check valve can also be installed in the line to prevent backflow into the combustion chamber. The pulsating pressure at these locations can be high enough so that pulses of cooling air are sent to the turbine blades. As pointed out above, the turbine blades can be much shorter, and therefore much easier to cool than the long turbine blades required for the Brayton Cycle system. Therefore the amount of cooling air required to cool the blades can be greatly reduced compared to a conventional gas turbine, both because less cooling air is required, and because with intercooling of the compressor, the air coming from the compression chamber is colder than it is from the ordinary gas turbine compressor discharge. 
     FIG. 14 shows an alternative blade cooling system in which steam is used to cool the turbine blades. This has several potential advantages. Steam has a higher heat transfer coefficient than air, and therefore for a given temperature in the cooling line the cooling becomes more effective. As shown in FIG. 14, steam cooling can be supplied by having the water jacket around the explosion chamber be fed with a high pressure pump, shown at  130 , that keeps the water pressure above the boiling point. The high pressure water can then be expanded through a throttle valve, shown at  132 , part of it will flash into steam in the high pressure flash tank shown at  134 , and this steam can then be sent through the line shown at  136  to cool the turbine blades. The water at the bottom of the flash tank can be returned to the inlet of the high pressure pump using the line shown at  138 . An additional water supply pump, shown at  140 , can feed make up water into the water return line  138 . This system is potentially more efficient than the system using air to cool the turbine blades because the heat loss from the explosion chamber is used directly to generate the steam that cools the turbine blades. 
     Although the steam cooling system described above may be very attractive, it may also be possible to eliminate use of a water jacket on the explosion chamber simply by increasing the heat transfer from the outside of the explosion chamber walls. As shown in FIG. 15, the incoming air surrounds the explosion chamber in the air chamber shown at  150 . The fins, shown at  152 , on the combustion wall transmit much more heat to the air than would be the case if the wall were smooth. By calculation, it appears that this scheme of cooling the walls may be more efficient, and also less costly than using water jackets either for direct cooling or for providing steam cooling to the blades. 
     Preliminary estimates of the potential size of the combustion chambers required for a high pressure cycle can be made by assuming a mass flow of air into the system and assuming conditions of operation as shown on column J of Table 2. 
     Assuming a flow of 385 pounds per second at conditions specified on column J. The net output of the turbine is then 194.7 BTUs per pound of air. The turbine output equals pounds per second times BTUs per pound times kilowatts per BTUs per second. The output would then be 385 times 194.7 times 1.055 equals 79,000 kilowatts. 
     The volume flow to the combustor equals 385 times 0.6309 cubic feet per pound at the compressor outlet or equals 242.9 cubic feet per second. At what might be considered a reasonable velocity of 200 feet per second the flow area would be 242.9/200, which equals 1.214 square feet. 
     If six combustors  300  are used, as shown in FIG. 17 the area for each equals {fraction (1.214/6=0.2024)} square feet or the diameter of the chamber equals 6.09 inches. This appears to be a reasonable size for a turbine of this capacity. 
     The lengths of the combustors can be estimated by assuming a frequency of explosions and a mean acoustic velocity of the ignited gas and of the compressed gas in the compressor section. A mean temperature in the explosion end might be 3880° R and the acoustic velocity might be approximately 3005 feet per second. If the distributor valve having three holes is rotated at a rotating speed of 1800 RPM, then the wave period would be {fraction (1/90)} of a second. At a period of {fraction (1/90)} of a second, one quarter wave length would be {fraction (1/90×3005/4)}=8.35 feet. 
     In the compression end, assuming the mean temperature would be approximately 981° R, the acoustic velocity should be approximately 1511 feet per second. One quarter wave length would then be 4.20 feet. Based on these calculations, the total length of the combustion chamber should then be (8.35+4.20)=12.55 feet. 
     These sample calculations indicate that the size of the combustor for the high pressure cycle can be very reasonable, and can be fitted around the circumference of a turbine producing an output of about 79 megawatts. 
     Although the location in the combustion chamber where the gas mixture leaves to enter the turbine should be at a constant pressure, it is very likely that the pressure may not be exactly constant, and some pulsations in the pressure may occur. This may be undesirable if more than one combustor is used and all combustors fire in unison. Therefore, in order to minimize the pressure pulsation effect on the turbine inlet nozzles and blades the explosions in the separate combustion chambers should be synchronized so that they are out of phase, such as by having one-half of the combustion chambers being out of phase with the other half. Another solution for minimizing these pulsations at the turbine inlet would be to use slightly different lengths for the combustion chambers and slightly different frequencies of explosions. Either of these methods should assure that undesirable turbine blade vibrations can be avoided. 
     While a combustion chamber having two gas inlets has been described, it will be understood by one skilled in the art that the present invention can be practiced using one gas inlet. When using one gas inlet as opposed to two or more gas inlets, less gas may be pressurized in the air compression portion of the combustion chamber and the temperature of the pressurized gas leaving the combustion chamber will be higher. Thus, a combustion chamber having at least two gas inlets is preferred because more gas is compressed in the air compression chamber portion of the combustion chamber and the temperature of the pressurized gas leaving the combustion chamber will be significantly lower. 
     While the location of the gas outlet in the combustion chamber has been described as being located where the combustion chamber pressure is substantially constant, it will be understood by one skilled in the art that the gas outlet can be located elsewhere if desired. For example, if a substantially constant pressure is not required for the desired application, the gas outlet can be located in the combustion chamber where the combustion chamber pressure varies significantly. If maximum pressure is the goal, the gas outlet can be located near one of the reflecting surfaces, or other area in the combustion chamber where the combustion chamber pressure peaks (such as between E 4  and E 5 , R 1  and E 3 , or R 2  and E 6 , in FIG.  7 ). In such applications, it may be desirable to use a check valve to prevent backflow into the combustion chamber. However, for most applications a constant gas pressure is desired. 
     While a U-shaped combustion chamber has been described above, it is understood by one skilled in the art that the shape of the combustion can be adjusted as desired. For example, the combustion chamber can be substantially straight or a combination of U-shapes. If desired, the combustion chamber can have a circular shape or a spiral shape that surrounds the turbine. The main concern is that the combustion chamber be constructed and arranged to provide at least one resonating pressure wave therein. Furthermore, the combustion chamber can have varying dimensions along the length thereof. For example, the volume per set length of the combustion chamber located near a reflecting surface can be greater than the volume per set length of the combustion chamber elsewhere, as shown in FIG.  11 . In general, the greater the volume per set length of combustion chamber the lower the pressure of the gas contained therein. Preferably, the side walls of the combustion chamber, in the direction of the pressure wave travels, have substantially a round tube shape, as used in the Example. However, the side walls of the combustion chamber can also have as square, triangular, hexagonal, elliptical, or other shapes. Based on the disclosure provided herein, one skilled in the art will be able to select the desired dimensions of the combustion chamber to provide the desired resonating pressure wave and pressurized gas. 
     The high pressure cycle according to the present invention provides many important advantages over previously used gas turbine cycles as listed here. 
     1. The high pressure cycle can obtain higher thermal efficiencies than any cycle heretofore presented. This is important for saving fuel in an energy hungry world that is gradually depleting all available sources of fossil fuel. 
     2. The high pressure cycle has a higher efficiency and emits less carbon dioxide into the atmosphere. This is recognized today as an important factor in affecting the climate of the world, and is now considered so important that predictions are being made that a carbon tax will be imposed for all of the carbon dioxide emitted from a power plant into the atmosphere. 
     3. The use of detonation to ignite the air/fuel mixture provides improved burning with significantly reduced production of undesirable nitrogen oxides and other combustion by-products. 
     4. Refrigerating the inlet to a gas turbine removes the moisture from the air and thereby permits liquid injection intercooling, which in turn permits higher efficiency and higher capacity to be attained. 
     5. Refrigerating the inlet to the gas turbine greatly increases the output power for a given size turbine. This means a great deal in reducing the cost per kilowatt power output. 
     6. Liquid injection intercooling makes premixing of the fuel with the air possible, and assures that detonation in the combustion chamber is possible. This in turn assures more uniform combustion and less generation of nitrogen. oxides in the combustion process. 
     7. In the high pressure cycle, the specific volume of the gas entering the turbine is much lower than that entering typical gas turbine blades. Therefore, the turbine blades can be shorter, easier to cool, and will be subject to less stress by nature of the blades being shorter. 
     8. Better blade cooling because of the shorter blades makes higher turbine inlet temperatures possible, which in turn increases potential turbine efficiency. 
     9. The higher efficiency of the high pressure cycle assures lower exhaust temperatures, which in turn assures higher overall efficiencies for combined cycles, because lower expansion ratios for the Rankine cycle can be used. 
     10. In the combined cycle, the use of a steam turbine can be avoided, and it is possible to use isobutane as the working fluid in the Rankine cycle which is run from the exhaust of the gas turbine. This permits condensing at much lower exhaust temperatures than can be used in a steam cycle, and in turn permits recovery of water from the exhaust. Recovery of water becomes more and more important as water becomes a scarce commodity throughout the world. 
     The present invention also provides an improved electrical power generating plant comprising at least one of the novel turbines described herein above driving an electrical generator. Any conventional electrical generator can be used to convert the mechanical energy of the turbine to electrical power. The power plant utilizing the improved turbine engines is capable of producing significantly less carbon dioxide and undesirable combustion by-products such as nitrogen oxides. 
     Preferably, the improved power plant further contains a Rankine cycle to utilize the energy contained in the exhaust gas of the turbine engine. The turbine engines according to the present invention can be driven to provide exhaust gasses having a temperature suitable for use in low temperature vapor turbine cycle, such as isobutane. Examples of other suitable low temperature vapor turbine cycles include propane, propylene, or other hydrocarbons, as well as fluorocarbons, and chlorofluorocarbons, of which there are many compounds commercially available. A low temperature vapor cycle typically operates at a temperature of about 400° F. or less. 
     The exhaust from a turbine engine according to the present invention is sufficiently low enough for directly driving a low temperature vapor cycle. This is a remarkable improvement because low temperature vapor turbine cycles are significantly more efficient and less expensive than high temperature vapor turbine cycles, such as steam. 
     FIG. 16 illustrates an example of power plant according to the present invention. Air enters the system through the air inlet saturation cooler shown at  201 . An air inlet fan shown at  202  can be used to draw the air into the system. The air can then be cooled by passing through the air inlet refrigeration coils shown at  203 . The cooled air can be compressed using the compressor shown at  204 . The air can also be intercooled in the compressor so as to control the temperature of the compressed air leaving the compressor down to a temperature where fuel can be injected into or mixed with the compressed air without causing combustion prior to entering the combustion chamber. The compressed air can be further compressed and combusted by using the resonating combustion chamber shown at  205 . This combustion chamber can be any one or combination of combustion chambers described herein above. After being compressed and combusted, the air can be used to drive a turbine, shown at  206 . The turbine can be used to drive an electrical generator shown at  207 . 
     The air inlet refrigeration coils can be refrigerated, for example, by using the low stage refrigerant compressor shown at  208 , the high stage refrigerant compressor shown at  209 , and the refrigerant condenser shown at  210 . 
     The exhaust from the turbine in the present invention can surprisingly be made low enough to drive a low temperature vapor cycle. As shown in FIG. 16, the exhaust from the turbine is used to vaporize isobutane in the isobutane superheater shown at  211 . The superheated isobutane can be used to drive the low pressure vapor turbine engine shown at  217 . The low pressure vapor turbine engine can be used to drive an electrical generator shown at  218 . The exhaust from the low pressure vapor turbine engine can be heated in the liquid heater shown at  213  and then transferred to the liquid heater and boiler shown at  212 . Hot gas leaving the isobutane superheater  211  is passed through the liquid heater and boiler  212 . The heated isobutane from the liquid heater and boiler  212  can be used to drive a high pressure vapor turbine shown at  215 . The high pressure turbine can be used to drive an electrical generator shown at  216 . 
     Exhaust from the liquid heater and boiler can be expelled through the exhaust stack with the induced draft fan shown at  214 . 
     Isobutane usually exhausts from turbine  217  at temperatures well above the saturation or condensing temperature. Therefore, this isobutane exhaust can be used in the liquid heater  219 , which preheats liquid isobutane coming from boiler feed pump  220  before it enters gas heated heater and boiler  212 . 
     After leaving the liquid heater  213  the isobutane condenses to liquid in condensor  219  and the liquid then flows to pump  220 , from whence it is pumped into liquid heater  213  to be preheated before entering boiler  212 . 
     The air condenser  219  is cooled by air drawn over the condenser coils  219  by the induced draft fan  222 . 
     Before passing through condensor coils  219 , the air is cooled to nearly the wet bulb temperature by passing the air through air saturator  221 . The saturator  221  is cooled by water sprayed over the opening of the saturator surfaces. The water flows down through the surfaces countercurrent to the air flow, and evaporates into the air, thereby cooling the air to nearly the wet bulb temperature. 
     Since the wet bulb temperature may be as high as 20 to 30° Fahrenheit below the ambient dry bulb temperature, the cooled air condenses the isobutane in condensor  219  to a much lower temperature than would be possible if ambient air was circulated over the condenser coils. 
     The lower condensing temperature achieved increases power output from isobutane turbine  217 , and thereby increases power cycle efficiency. 
     The invention will be further explained using the following non-limiting examples. 
     EXAMPLE 
     A combustion chamber was formed using a 4 inch diameter tube having a length of approximately 20 feet. The inlet air was controlled by a rotary valve which alternately opened and closed the supply of air from an air compression system. 
     At the opposite end of the tube was an air compressor check valve, which allowed air to enter when the pressure wave was less than the average pressure in the combustion chamber and automatically close when the pressure wave was greater than the average pressure in the combustion chamber. The exhaust outlet from the combustion chamber was approximately at the middle of the tube. High frequency pressure transducers were installed at both ends of the tube, and also at the middle where the exhaust left through a throttling valve. The pressures were recorded on a high speed oscillograph with pressure plotted against time. 
     By adjusting the frequency of the rotary inlet valve and fuel flow, the explosions of the fuel/air mixture could be made to resonate. By actual measurements, the explosion pressure varied up and down, and the pressure at the opposite air inlet end also varied with the explosion pressure transmitted from the explosion at the fuel air mixture inlet end. The pressure at the exhaust near the middle of the chamber was substantially constant when the timing of the pressure wave was controlled to resonate so that the length of the chamber was approximately one-half the wave length of the explosion wave. 
     By experimenting and adjusting the frequency of the wave so that it resonated, the pressure ratio between the exhaust pressure and the inlet pressure was 1.04. A pressure ratio of 1.04 in a combustion process provides a significant increase in the efficiency of a gas turbine cycle, compared to one which had constant pressure combustion or somewhat less than constant pressure combustion due to friction in the combustion chamber causing a pressure drop between the inlet and the outlet to the turbine nozzles. 
     One of the critical problems in the experimental chamber was that the air inlet check valve could not be made to survive the high frequencies used in the explosion chamber. 
     However, in the design proposed above, the inlet distributor valve controls the flow both to the explosion chamber and to the air compression chamber. This can be accomplished as shown in FIGS. 9 and 10 by using a distributor valve with either three or five holes in it, so that the inlet hole to the explosion chamber opens alternately with the inlet hole to the air compression chamber. By using a return channel, the whole system is in effect folded so that the inlet to the explosion chamber and the inlet to the air compression chamber are both at the same end, and therefore can be controlled by a distributor valve motor that is operated at the correct frequency to cause resonating explosions. 
     While the present invention has been described in detail and with reference to specific embodiments, it is apparent to one of ordinary skill in the art that various changes and modifications can be made therein without departing from the scope and spirit of the claimed invention.