Abstract: A method for determining a heat addition needed to achieve a target/limiting combustion temperature of a working fluid in a thermodynamic cycle in an engine can include determining a third state of the thermodynamic cycle, where the third state is defined by a third internal energy E3Qless and a third volume V3 of the working fluid located in a cylinder of the engine, where an equation of state E3Qless/E2=(V2/V3)k-1 is used to solve for E3Qless when E1, V1, E2, and V2 are known. The method can include determining a target/limiting internal energy E3Limiting that corresponds to a selected target/limiting combustion temperature T3 at the third state by solving E3Limiting=cvT3. The heat addition Q needed to reach the target/limiting internal energy E3Limiting at the third state can then be determined by solving Q=E3Limiting?E3Qless.

Abstract: 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.

Abstract: 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.

Abstract: A method for designing internal combustion engines can include selecting a compression ratio that produces a compression temperature just below the autoignition temperature of a fuel/air mixture, selecting a fuel equivalence ratio that produces a combustion temperature below the threshold temperature at which NOx formation or autoignition of the mixture occurs, and selecting an expansion ratio greater than the compression ratio.