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A numerical study was conducted to analyse the performance of different turbulence models and different turbulence intensities and turbulence length scales specified for the boundary condition of the inflow to the internal compression flow field of a typical supersonic inlet. The effect of the back-pressure ratio on the properties of the flow field was also investigated. Computational results obtained by the commercial software FLUENT, which is used to solve the full two-dimensional Reynolds-averaged Navier-Stokes equations, were validated through both graphical and quantitative comparisons with previously published experimental data. The two-equation models that were considered in this study are the RNG k-ε, realisable k-ε, standard k-ε, and SST k-ω turbulence models. The RNG k-ε model had the best performance among the four models and predicted good wall pressure distributions. The best agreement between the predicted results and experimental data was obtained when either the default values of the freestream turbulence intensity and length scale in the FLUENT solver were used, or the empirical formula was used to calculate the two parameters of the freestream turbulence properties. The shock wave pattern varied between the oblique mode and the fully developed normal mode with increasing back-pressure ratio, and the unstart phenomenon occurred when the back-pressure ratio was sufficiently high.