Abstract The present experimental-cum-numerical work reports three different types of transitions (Type I, Type II, and Type III) observed in the flame topology of non-premixed methane/air and biogas/air coflow flames as the co-annular air Reynolds number (Rea) is varied from zero to maximum limit or till flame blows off/blows out for a given range of fuel Reynolds number (Ref). Type I transition represents the transformation from burner lip-attached flame to lifted flame and then backward propagation towards the burner exit plane as Rea is increased. In Type II transition, the burner lip-attached flame lifts off from the burner exit, stabilizes at a new location, and then extinguishes as Rea is increased. In Type III transition, the burner lip-attached flame directly extinguishes as Rea is increased. RANS-Based 3D numerical simulations are performed to simulate these three types of transitions (Type I, Type II, and Type III) using GRI 2.11 detailed reaction mechanism. Flow turbulence is modeled by employing the standard k−ɛ turbulent model. Flamelet-Generated Manifold (FGM) approach is used as the turbulent-combustion model. To validate the numerical method/models, the numerical temperature profiles have been compared against the experimental temperature measurements as a part of the present work. The numerical results are employed to gain further insights to understand flame–flow interactions.