A tunnel fire is a dangerous accident, which may lead to serious injuries and deaths. This work studies the flow of combustion products during naturally ventilated tunnel fires, i.e., without a mechanical ventilation system. In such an event, two stratified layers with opposing velocity directions are formed. The safety of tunnel users is compromised if the smoke, initially flowing in the upper layer, contaminates the lower one, which has been found to happen abruptly at a distance xc from the fire. This is caused by the cooling of the jet leading to a large enough decrease in momentum for the smoke to be entrained by the lower layer. Natural ventilation may be an effective and inexpensive smoke control strategy if the fire-to-portal distance is shorter than xc. However, there is a lack of research to predict under which conditions this occurs and how xc is influenced by factors such as natural wind. An open-source Computational Fluid Dynamics (CFD) code, fireFoam, was used to conduct Large Eddy Simulations (LES) of naturally ventilated tunnel fires. The numerical model was validated by performing a simulation of a large-scale tunnel fire test. Additionally, 7 fire scenarios with varying wind velocities were simulated. The contamination distance xc was found to decrease for higher wind velocities. Furthermore, a simple semi-analytical model was employed to obtain quick estimates of xc, by calculating ceiling jet properties using balance equations and empirical correlations. Model coefficients were calculated using the CFD results.