Numerical analysis of energy conversion performance in a Tesla turbine: influence of injector design and operating conditions

In this work, a comprehensive three-dimensional numerical analysis of the energy conversion performance of a single-stage Tesla turbine is presented. A turbine with ten rotor discs housed within a cylindrical casing and up to four turbine inlets is considered. The working fluid is modeled as a compressible Newtonian ideal gas, and the simulations are carried out using the SST k-ω turbulence model. The effects of different design and operational parameters on the performance of the Tesla turbine, including inlet pressure, rotational speed, disc thickness, nozzle width, and number of turbine inlets are investigated. The results show that torque decreases almost linearly with increasing rotational speed, while output power exhibits a nonlinear trend peaking at intermediate rotational speeds determined by the inlet pressure. Disc thickness strongly influences performance, where thinner discs enhance viscous shear interaction and improve efficiency, whereas thicker discs increase flow capacity and produce higher power output. Nozzle geometry and inlet configuration also significantly affect turbine behavior. Increasing the nozzle outlet width leads to a higher mass flow rate and output power due to increased flow admission, while smaller widths limit the total flow capacity. Regression fits indicate that the output power decreases by about 188.3 W for every 1 mm reduction in nozzle outlet width, while the mass flow rate decreases by about 8.16 g/s. Among the investigated configurations, the 12 mm four-nozzle configuration achieves the highest power output and mass flow rate, reaching 2.9 kW and 0.25 kg/s, respectively, although with reduced efficiency. In contrast, the highest efficiency is achieved by the 6 mm single-nozzle configuration (48.36%). A Pareto-based analysis identifies the 9 mm double-nozzle configuration as a preferred compromise between power output and efficiency within the investigated operating conditions, achieving 2.4 kW and 35.8% efficiency. These findings provide physical insight into viscous-driven turbomachinery and offer guidance for optimizing Tesla turbine performance through appropriate design and operating conditions.