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A compression-ignition constant-volume constant-temperature combustion reciprocating internal combustion engine can operate with a first combustion stage and a second combustion stage. The first combustion stage can be configured to occur at about constant-volume, where a quantity of a first heat ad

A compression-ignition constant-volume constant-temperature combustion reciprocating internal combustion engine can operate with a first combustion stage and a second combustion stage. The first combustion stage can be configured to occur at about constant-volume, where a quantity of a first heat addition can be selected to ensure that a first combustion temperature during the first combustion stage does not exceed a threshold temperature at which NOx formation occurs. The second combustion stage can be configured to occur at about a second combustion temperature that remains about constant during the second combustion stage, where the second combustion temperature can be about equal to the first combustion temperature at an end of the first combustion stage, and where a quantity and a rate of a second heat addition delivered to the engine during the second combustion stage can be configured to ensure that the second combustion temperature of the second combustion stage remains about constant during the expansion stroke even as cylinder pressure decreases.

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1. A method for designing a reciprocating internal combustion engine operating on an air cycle, the method comprising: selecting a compression ratio that maximizes internal energy of a working fluid in the engine at an end of a compression stroke;selecting an expansion ratio that minimizes internal

1. A method for designing a reciprocating internal combustion engine operating on an air cycle, the method comprising: selecting a compression ratio that maximizes internal energy of a working fluid in the engine at an end of a compression stroke;selecting an expansion ratio that minimizes internal energy of the working fluid at an end of an expansion stroke;selecting an upper limit combustion temperature for normal engine operation that is below a threshold temperature at which NOx formation occurs; andselecting an amount of heat addition and a rate of heat addition, wherein the amount of heat addition and the rate of heat addition are selected to ensure that the upper limit combustion temperature is not exceeded, and wherein the amount of heat addition and the rate of heat addition are selected to ensure that an upper limit combustion pressure is not exceeded. 2. The method of claim 1, wherein the step of selecting the compression ratio that maximizes internal energy of the working fluid in the engine at the end of the compression stroke comprises selecting the compression ratio to obtain a compression temperature sufficiently high to minimize ignition delay and to ensure fast and complete burning of the fuel. 3. The method of claim 1 further comprising selecting a fuel equivalence ratio to obtain a combustion temperature below the threshold temperature at which NOx formation takes place. 4. The method of claim 1, wherein the step of selecting the expansion ratio that minimizes internal energy of the working fluid at the end of the expansion stroke comprises selecting the expansion ratio that provides high indicated fuel conversion efficiency without excessive friction losses. 5. The method of claim 3, wherein the compression ratio, the fuel equivalence ratio, and the expansion ratio are each selected to minimize specific fuel consumption and emissions. 6. A compression-ignition constant-volume constant-temperature two stage combustion reciprocating internal combustion engine comprising: a first combustion stage configured to occur at about constant-volume, wherein a quantity of a first heat addition is selected to ensure that a first combustion temperature during the first combustion stage does not exceed a threshold temperature at which NOx formation occurs; anda second combustion stage configured to occur at about a second combustion temperature that remains about constant during the second combustion stage, wherein the second combustion temperature is about equal to the first combustion temperature at the end of the first combustion stage, wherein a quantity and a rate of a second heat addition delivered to the engine during the second combustion stage are configured to ensure that the second combustion temperature of the second combustion stage remains about constant during the expansion stroke even as cylinder pressure decreases. 7. The reciprocating internal combustion engine of claim 6, wherein the compression ratio is equal to the expansion ratio, and wherein the compression ratio is between about 16 and 20. 8. The reciprocating internal combustion engine of claim 6, wherein the engine is configured to operate on a four-stroke cycle or a two-stroke cycle. 9. The reciprocating internal combustion engine of claim 6, wherein the first combustion stage is configured to meet a target loading requirement while the engine is operating at a fuel equivalence ratio of about 0.288 or below. 10. The reciprocating internal combustion engine of claim 6, wherein the first combustion temperature is configured to remain below the threshold temperature at which NOx formation occurs during the first combustion stage, and wherein an equivalence ratio calculated during the first combustion temperature is configured to remain below a NOx formation equivalence ratio. 11. The reciprocating internal combustion engine of claim 6, wherein the engine is created by retrofitting an existing four-stroke diesel engine to operate on the constant-volume constant-temperature two-stage combustion process, the retrofitting comprising reducing a cylinder clearance volume of the existing four-stroke diesel engine to obtain a compression ratio of about 18.0. 12. A method for operating a compression-ignition reciprocating internal combustion engine, the method comprising: injecting a first quantity of fuel into a cylinder of the engine during a compression stroke of the engine to produce a first compression-ignition combustion event while a reciprocating piston is at top dead center in the cylinder; andinjecting a second quantity of fuel into the cylinder during an expansion stroke of the engine to produce a second combustion event while the reciprocating piston is descending from top dead center, wherein injecting the second quantity of fuel has a start and an end, wherein injecting the second quantity of fuel is configured to maintain a constant mean cylinder gas temperature between the start and the end of injecting the second quantity of fuel, wherein injecting the second quantity of fuel has an injection rate, and wherein the injection rate increases between the start and the end of injecting the second quantity of fuel to ensure that the mean cylinder gas temperature remains constant despite the reciprocating piston descending in the cylinder during the expansion stroke. 13. The method of claim 12, wherein the mean cylinder gas temperature of the second combustion event is below about 2400 degrees Fahrenheit. 14. The method of claim 13, wherein the start of injecting the second quantity of fuel occurs when the reciprocating piston is at about top dead center. 15. The method of claim 14, wherein the end of injecting the second quantity of fuel occurs when the reciprocating piston has completed about 3% of the expansion stroke, and wherein the second quantity of fuel is equal to about 28% of the first quantity of fuel. 16. The method of claim 14, wherein the end of injecting the second quantity of fuel occurs when the reciprocating piston has completed about 7% of the expansion stroke, and wherein the second quantity of fuel is equal to about 52% of the first quantity of fuel. 17. The method of claim 14, wherein the end of injecting the second quantity of fuel occurs when the reciprocating piston has completed about 14% of the expansion stroke, and wherein the second quantity of fuel is equal to about 72% of the first quantity of fuel. 18. The method of claim 14, wherein the end of injecting the second quantity of fuel occurs when the reciprocating piston has completed about 24% of the expansion stroke, and wherein the second quantity of fuel is equal to about 90% of the first quantity of fuel. 19. The method of claim 14, wherein the end of injecting the second quantity of fuel occurs when the reciprocating piston has completed about 39% of the expansion stroke, and wherein the second quantity of fuel is equal to about 104% of the first quantity of fuel. 20. The method of claim 13, wherein the engine has a compression ratio between about 16 and 20.