Extended analytical model of Tesla turbine with advanced modelling of velocity profile in minichannel between corotating disks with consideration of surface roughness

Consideration of roughness effects in the flow in a minichannel has been a major scientific problem for many decades. Roughness can alter the momentum diffusion, heat transfer conditions or laminar-turbulent transition. These effects are even more pronounced in minichannel flows where the roughness can occupy a large part of the cross-section. Modelling methods applied so far usually fall short in internal flows with high relative roughness. The presented paper pertains to the analytical flow model in Tesla turbine components with consideration of roughness on the rotor walls. The model uses the equivalent sand grain approach to modify dynamic viscosity in the governing equations to achieve a desired downward shift of the dimensionless velocity profile. The model solves two-dimensional equations of continuity, momentum and energy. The semi-empirical function was derived to consider the change in the shape of the radial velocity. The applied model incorporates Euler's turbomachinery equation to determine the influence of roughness on the turbine performance under varied operating conditions. Roughness shortens the streamlines inside the rotor, but the overall turbine's performance is improved. The roughness equal to 10−5 m increased the power generated and isentropic efficiency by factors of 3 and 2.5, respectively, compared to the smooth rotor.