The flow past the needle of a Pelton turbine injector is an axisymmetric wake embedded in a round jet. The wake does not fully relax to yield a uniform velocity jet due to the short distance between injector and the Pelton wheel buckets and this non-uniformity affects the turbine efficiency. To minimize the non-uniformity, it is essential to predict the near wake accurately. While far-field wakes are well described by analytical expressions and also well predicted by CFD codes, the quality of the prediction of axisymmetric near wakes is not known. It is of practical interest to establish the applicability bounds of the Reynolds Averaged Navier-Stokes (RANS) models, which are commonly used in industry, for axisymmetric near wakes, for this specific problem, as well as, in general. Understanding of the near wake is crucial considering various aerospace applications. For example the details of the aerodynamics of the near wake are crucial for stabilization of a flame. The size of recirculation zone affects the rate of production of hot burnt products, and the mixing between the products and reactants is governed by the turbulence in the free shear layers. Wakes from two-dimensional bodies such as a wedge, circular and square cylinder have been extensively studied at different Reynolds number (Re); however, this is not the case with three-dimensional axisymmetric bodies such as spheres, ellipsoids, disks etc. Most common axisymmetric body investigated is a sphere. The flow past sphere is typically characterized in three regions: sub critical, critical and supercritical. In sub critical region, Re<3x105 the boundary layer separation is laminar. Critical region, Re≈3x105, is where the boundary layer transitions to turbulent and then separates resulting in sudden drag reduction. The critical Re may vary depending on flow conditions such as turbulent intensities, sphere surface variations etc. In the supercritical region, Re > 3x105, the boundary layer is turbulent before separation and the drag starts increasing beyond critical drag. Though the geometry and the flow conditions are simple the flow features involved are complex especially laminar to turbulent boundary layer transition and high speed transient vortex shedding. Experimentally it has been observed that the vortex shedding location changes randomly and perhaps rotates. All these features pose a significant challenge for experimental measurements and as well as numerical modeling. Thus most experimental measurements have been done below Re=103. Also the data is measured over the sphere surface, for eg: skin friction, pressure, but almost no data is available in the near wake. Similarly numerical investigations are primarily in subcritical region. DNS has been used for low Re, up to 800. RANS has been used in the subcritical region at Re=104. For higher Re, LES and DES have been used however they are computationally intensive. No numerical work has been reported for an ellipsoid at zero angle of attack. Chevray (1968) has done measurements in the near wake of ellipsoid at Re=2.75x105. Most experimental and numerical investigations of an ellipsoid are at an angle of attack. Given the extensive usage of RANS in the industry due to its economy, the focus of this work is to investigate the applicability of these models for flow prediction in the near wake in the supercritical region. Simulations are performed using commercial code CFX. The code is validated against well-established results for laminar and turbulent boundary layer flow over flat plate. Sufficient agreement has been obtained for laminar flow past sphere, against measured quantities such as separation location, separation bubble length and drag coefficient. The changes in wake structure, as a function of Re, are validated against experimental observations. The wake is steady and axisymmetric up to Re=200, from Re=200 to 270 it remains steady, loses axisymmetry but retains planar symmetry. Beyond Re=290 the wake becomes unsteady due to unstable recirculation bubble which leads to vortex shedding, while still retaining planar symmetry. The formation of typical horseshoe vortices is observed. Before the simulations in the supercritical region the low-Re k- model is validated in the subcritical region at Re=104 against measurements of skin friction, pressure coefficient and average drag coefficient. Very distinct wake fluctuations are observed and low-mode Strouhal number (St) agrees with the past measurements. Vortex sheet fluctuations are observed but the high-mode St calculation is based on crude measurement of the fluctuations. At Re=7.8x104 the trends in the drag, skin friction coefficient and pressure coefficient are in logical direction when compared with data at Re=104. However the near wake velocity data does not match with measurements qualitatively as well as quantitatively. The velocities in the present work are qualitatively justified based on the flow directions in the recirculation bubble. Various RANS models such as k-, k- and Reynolds stress model are used to predict flow past a sphere and an ellipsoid in the supercritical region. The results for sphere are compared against the measurements from Achenbach at Re=1.14x106 and that for ellipsoid are compared against the measurements from Chevray at Re=2.75x106. Four different turbulence models namely: high-Re k-, high-Re k-, low-Re k- and low-Re RSM. All the models over predict skin friction, which is due to simplistic treatment of boundary layer. The boundary layer is treated as fully turbulent as against the experiments where it transitions from laminar to turbulent. The k- model, being high-Re model, did not capture near wall flow and hence predicts an almost steady wake. It over predicts the drag, skin friction and results in delayed separation. However it did show the vortex sheet roll-up and release mechanism prominently which agreed with the experiments by Taneda. In all other models this mechanism is seen but intermittently and the wake is unsteady. Due to highly random wake orientation the low-mode St number is not calculated. RSM model shows certain consistency and St based on that is 0.24. All models show vortex sheet fluctuations with almost equal magnitude and frequency. The high-mode St is about 20 based on this. There is a need to have better understanding both experimentally and numerically about validity of this number. High frequency fluctuations are displayed in the time history of streamwise drag force for all the four models. The St based on this frequency is 4.32. Origin of these fluctuations needs investigation. The RSM model predicts the most accurate skin friction coefficient, pressure coefficient and the drag. For an ellipsoid, two cases are computed, one without blockage (referred to as base case) and another with 25% blockage (referred to as blockage case) to represent the typical blockage due to Pelton injector needle. Same models that were used for sphere are evaluated. Similar to the results for the sphere the maximum drag is predicted by k- model and the least by RSM model. Similarly the skin friction is high and the separation is delayed hence k-w model always predicts a smallest recirculation bubble. The differences in the form drag predictions are a direct result of the differences in upstream stagnation pressures, as there is no significant difference in the pressure curves obtained from different models including the rear stagnation pressure. The form drag is highest in k- model and lowest in RSM and so are the upstream stagnation pressures. The velocities in the near wake are predicted well by all the models. Pressure is predicted accurately before separation at x/D=-0.25. However it is significantly over-predicted after separation. To validate the pressure prediction independent simulation is done for an ellipsoid at an angle of attack of 100. The pressures on the windward and leeward side are in agreement with the measurements by Chesnakes et al. Similar to pressure prediction the turbulent intensity was predicted correctly before separation. After separation the trends agree but the intensities are higher than the measurements by about 10%. The results are not sensitivity to the inlet intensity levels except in the far field. The dissipation of the intensities is under predicted in simulations. The results from blockage case show similar trends as the base case. In the near wake the generation of turbulent kinetic energy is higher and the decay is slower in k- and RSM model compared to k-. This in turn results in higher eddy viscosity and higher velocities in the near wake for these models. Considering overall prediction accuracies RSM model predicts the drag, St and the separation location most accurately. It is important to predict the separation accurately for valid downstream results. For the cases with mild separation such as ellipsoid there is no significant difference in the velocities, however the pressure and drag prediction from RSM are closer to the experiments. The RSM model is more suitable both for sphere and ellipsoid at high Re. Validation of mean velocities and intensities in the near wake are needed to further support the choice of model. (for symbols pl see the original document)