We present our timesaving joint RANS/LES approach (we originally developed it for numerical simulations of turbulent premixed combustion) to simulate flameless combustion with separate injection of gas fuel and strong exhaust gas recirculation. It is based on successive RANS/LES numerical modeling where part of the information (stationary average fields) is achieved by RANS simulations and part (instantaneous nonstationary image of the process) by LES. The latter is performed using the RANS field of mean dissipation rate to model the sub-grid turbulent viscosity in the context of the Kolmogorov theory of small-scale turbulence. We analyze flameless combustion in the FLOX® combustor where we also simulate non-premixed flame combustion used for preliminary heating of the combustor. Different regimes take place using different systems of air injection. We applied for both regimes the simple assumption of “mixed is burnt”. The main results are the following: 1) RANS simulations demonstrate for used two injection systems respectively more compact flame and distributed flameless combustion. 2)There is agreement between RANS and corresponding LES results: RANS and averaged LES profiles of the velocity and temperature are in reasonable agreement. 3) LES modeling with Kolmogorov independent on time sub-grid viscosity reproduce instantaneous image of the process including the vortex structures. Probably due to using an annular injector system for air the instantaneous field of the temperature demonstrate significant irregularity in the beginning of the burner, which in an animation looks like moving coherent structures. 4) In the joint RANS/LES approach the computer time of the LES sub-problems is much shorter than classic LES modeling due to using time independent subgrid transport coefficients and avoiding long-continued simulations, which are necessary for averaging of instantaneous LES fields. Practically in our simulations time consuming of the LES sub-problem was only several times lager then the RANS one and it makes this approach suitable for industrial applications.