Shockless explosion combustion is a promising concept for implementing pressure gain combustion into a conventional gas turbine cycle. This concept aims for a quasi-homogeneous autoignition that induces a moderate rise in pressure. By this, considerable losses due to entropy generation by inherent shock waves of detonation-based concepts can be avoided. Since the ignition is not triggered by an external source but driven by chemical kinetics only, the homogeneity of the autoignition is very sensitive to local perturbations in equivalence ratio, temperature, and pressure that produce undesired local premature ignition. Therefore, the precise injection of a well-defined fuel profile into an convecting air flow is crucial to ensure a quasi-homogeneous ignition of the entire flammable mixture. The objective of this work is to demonstrate that the injected fuel profile is preserved throughout the entire measurement section. For this, two different control trajectories are investigated. Optical measurement techniques are used to illustrate the effect of turbulent transport and dispersion caused by boundary layer effects on the fuel concentration profile inside the combustor. Results from line-of-sight measurements by tunable diode laser absorption spectroscopy indicate that the transport of the fuel-air mixture is dominated by turbulent diffusion. However, comparisons to numerical calculations reveal the effect of dispersion towards the bounds of the fuel concentration profile. The spatially resolved distributions of the fuel concentration inside the combustor gained from acetone planar laser induced fluorescence replicates a typical velocity distribution of turbulent pipe flow in radial direction visualizing boundary layer effects. Comparing both methods provide deep insights into the transport processes that have an impact on the operation of the shockless explosion combustor.