It is well known that bladeless or Tesla turbomachinery idea was proposed by Nikola Tesla over a century ago, and it has several distinct features, such as reversibility of operation, which includes expander and compressor operations obtained by reversing the rotational speed, provided that the statoric channels are purposely designed.The main objective of this paper is to design a reversible Tesla or bladeless machine with optimal design parameter choice that can operate both in compressor and expander modes. As a consequence of the high losses due to rotor and stator interactions, statorless (volute) configurations are investigated here, showing superior performance in both compressor and expander modes of operation. Numerical study has been conducted for both compressor and expander modes of this machine using air as working fluid. In compressor mode, numerical results have been validated with experimental data, while results for expander mode will be validated in the near future. The numerical results predict peak isentropic efficiencies of 57.5 % and 63.5 %, for the compressor and expander modes of operation excluding assembly losses, respectively, while rotor efficiency is quite high > 90 % at very low mass flow rates. Tests on Tesla machine prototype have shown an experimental isentropic efficiency of maximum 32.4 % when operating in compressor mode. The overall assembly efficiency is reduced, compared to numerical predictions, due to leakage and end wall losses. The CFD simulations could match the experimental results at high pressure ratio and low mass flow, with less than 2 % error on pressure ratio. Through the improvement of the sealing system and the reduction of losses (leakage and end wall friction), it is expected that overall prototype efficiency could improve by at least 10 percentage points.