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The aim of this study is to clarify the mixture formation in the combustion chamber of our developed natural gas engine incorporating the sub-chamber injection system, in which natural gas is directly injected into a combustion sub-chamber in order to completely separate rich mixture in the sub-chamber, suitable for ignition, from ultra-lean mixture in the main chamber. Mixture distributions in chambers with and without sub-chamber were numerically simulated at a variety of operating conditions. The commercial software of Fluent 16.0 was used to conduct simulations based on Reynolds averaged Navier-Stokes equations in an axial 2 dimensional numerical domain considering movements of piston. Non-reactive flow in the combustion chamber was simulated before the ignition timing at an engine speed of 2000 rpm. The turbulence model employed here is standard k-ε model. Air-fuel ratio is set with a lean condition of 30.