Extending “Assessment of Tesla Turbine Performance” Model for Sensitivity-Focused Experimental Design

Abstract

The analytical model of Carey is extended and clarified for modeling Tesla turbine performance. The extended model retains differentiability, making it useful for rapid evaluation of engineering design decisions. Several clarifications are provided including a quantitative limitation on the model’s Reynolds number range; a derivation for output shaft torque and power that shows a match to the axial Euler Turbine Equation; eliminating the possibility of tangential disk velocity exceeding inlet working fluid velocity; and introducing a geometric nozzle height parameter. While nozzle geometry is limited to a slot providing identical flow velocity to each channel, variable nozzle height enables this velocity to be controlled by the turbine designer as the flow need not be choked. To illustrate the utility of this improvement, a numerical study of turbine performance with respect to variable nozzle height is provided. Since the extended model is differentiable, power sensitivity to design parameters can be quickly evaluated—a feature important when the main design goal is maximizing measurement sensitivity. The derivatives indicate two important results. First, the derivative of power with respect to Reynolds number for a turbine in the practical design range remains nearly constant over the whole laminar operating range. So, for a given working fluid mass flow rate, Tesla turbine power output is equally sensitive to variation in working fluid physical properties. Second, turbine power sensitivity increases as wetted disk area decreases; there is a design trade-off here between maximizing power output and maximizing power sensitivity.