The reduction of full and part load emissions and the increase of the turndown ratio are important goals for gas turbine combustor development. Combustion techniques, which generate lower $NOx$ emissions than unstaged premixed combustion in the full load range, and which have the potential of reducing minimum load while complying with emission legislation, are of high technical interest. Therefore, axial-staged combustion systems have been designed, either with or without expansion in a turbine stage between both stages. In its simpler form without intermediate expansion stage, a flow of hot combustion products is generated in the first stage of the premixed combustor, which interacts with the jets of premixed gas injected into the second stage. The level of $NOx$ formation during combustion of the premixed jets in the hot cross flow determines the advantage of axially staged combustion regarding full load $NOx$ emission reduction. Employing large-eddy simulation in openfoam, a tool has been developed, which allows to investigate staged combustion systems including not only temperature distribution but also $NOx$ emissions under engine conditions. To be able to compute $NOx$ formation correctly, the combustion process has to be captured with sufficient level of accuracy. This is achieved by the partially stirred reactor model. It is combined with a newly developed $NOx$ model, which is a combination of a tabulation technique for the $NOx$ source term based on mixture fraction and progress variable and a partial equilibrium approach. The $NOx$ model is successfully validated with generic burner stabilized flame data and with measurements from a large-scale reacting jet in cross flow experiment. The new $NOx$ model is finally used to compute a reacting jet in cross flow under engine conditions to investigate the $NOx$ formation of staged combustion in detail. The comparison between the atmospheric and the pressurized configuration gives valuable insight in the $NOx$ formation process. It can be shown that the $NOx$ formation within a reacting jet in cross flow configuration is reduced and not only diluted.

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