Oscillating jet flames in a coflow mimic certain features of turbulent flows in a simplified and controllable way. Our study aims to identify the potential of the HMOM soot model, which is validated in steady laboratory flames to be applied in practical, mostly turbulent flames. The model is found to accurately predict all the measurement parameters in a steady laminar sooting jet flame of ethylene/nitrogen mixture. When applied to an oscillating flame with the same fuel mixture, it was found that, while velocity, temperature, and OH fields are well predicted, the peak soot volume fraction is over predicted and occurs away from the experimentally measured location. The potential for soot model improvement is analysed by correlating the transient gas-phase species, polycyclic aromatic hydrocarbon, and soot formation or destruction behaviour. A need for improved soot nucleation, condensation, and oxidation formulations is identified. It is further found that the soot number density distribution in mixture fraction space is comparable to the transitional turbulent flame regime dominated by Kelvin-Helmholtz rollers.