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In this paper a new method for burned mass fraction - pressure relation, x-p  relation, for two-zone model combustion calculation is developed. The main  application of the two-zone model is obtaining laminar burning velocity, SL,  by using a pressure history from a closed vessel combustion experiment. The  linear x-p relation by Lewis and Von Elbe is still widely used. For linear  x-p relation, the end pressure is necessary as input data for the description  of the combustion process. In this paper a new x-p relation is presented on  the basis of mass and energy conservation during the combustion. In order to  correctly represent pressure evolution, the model proposed in this paper  needs several input parameters. They were obtained from different sources,  like the PREMIX software (with GRIMECH 3.0 mechanism) and GASEQ software, as  well as thermodynamic tables. The error analysis is presented in regard to  the input parameters. The proposed model is validated against the experiment  by Dahoe and Goey, and compared with linear x-p relation from Lewis and Von  Elbe. The proposed two zone model shows sufficient accuracy when describing  the combustion process in a closed vessel without knowing the end pressure in  advance, i.e. both peak pressure and combustion rates can be sufficiently  correctly captured

Closed vessel combustion modelling by using pressure-time evolution function derived from two-zonal approach