A numerical method for studying the flow field of an under-expanded axis-symmetric jet created by a converging-diverging nozzle and impinging on a flat plate is presented. The calculation domain of interest is a region that contains all the features of the jet that leaves the nozzle and impinges onto the plate. Axial symmetry of the domain allows a reduced 2- dimensional model to be used. FLUENT software is utilized to solve the continuity, momentum and energy equations using a coupled implicit scheme. The ideal-gas law is used to determine the gas density along with a k- ε turbulence model with a special modification to account for compressibility effects. In addition, the temperature dependency of viscosity has been taken into consideration. A number of different modeling techniques are investigated including different approximations to account for the flow inside the nozzle. Performance of non-equilibrium wall functions for near-wall turbulence treatment is compared with standard wall functions and multi-block structured rectangular grids as well as triangular grids are implemented and compared. Modifications necessary to apply the method to the 3-dimensional case are discussed. The plate is far enough from the nozzle exit so that a set of expansion and compression waves form. A discussion of these waves and other features of the flow field such as a recirculation region close to the plate are presented. The flow is found to be extremely complex due to the interactions of the shock waves in the free jet and those created due to the existence of a barrier. The numerical model is evaluated by comparison with an existing Shadowgraph image and with previous simplified numerical results.
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