Method to Design a Hydro Tesla Turbine for Sensitivity to Varying Laminar Reynolds Number Modulated by Changing Working Fluid Viscosity
Authors: Alrabie Mubarak S. , Altamimi Faisal N. , Altarrgemy Muhammad H. , Hadi Fatemeh , Akbar Muhammad K. , Traum Matthew J. 
Published: August 2017

There has been a recent surge in interest for Tesla turbines used in renewable energy applications such as power extraction from low-quality steam generated from geothermal or concentrated solar sources as well as unfiltered particle-laden biomass combustion products. High interest in these bladeless turbines motives renewed theoretical and experimental study.

Despite this renewed interest, no systematic Tesla turbine design process based in foundational theory has been published in the peer reviewed engineering literature. A design process is thus presented which is flexible, allowing an engineering designer to select and address goals beyond simply maximizing turbine output power. This process is demonstrated by designing a Tesla turbine where Reynolds number can be easily varied while holding all other parameters fixed. Tesla turbines are extremely sensitive to inter-disk spacing. It is therefore desirable to design the experiment to avoid turbine disassembly/reassembly between tests; this assures identical disk spacing and other parameters for all tests. It is also desirable to maintain similar working fluid mass flow rate through the turbine in all tests to minimize influence of losses at the nozzle impacting shaft power output differently across experiments.

Variation in Reynolds number over more than two orders of magnitude is achieved by creating a set of two-component working fluid mixtures of water and corn syrup. Increasing mixture mass fraction of corn syrup achieves increased working fluid viscosity but only small increase in density with a corresponding decrease in working fluid Reynolds number.

The overall design goal is to create a turbine that allows modulating Reynolds number impact on Tesla turbine performance to be evaluated experimentally. The secondary goal is to size the turbine to maximize sensitivity to changes in Reynolds number to make experimental measurement easier.

The presented example design process results in a Tesla turbine with 8-cm-outer-diameter and 4-cm-inner-diameter disks. The turbine will be able to access a range of Reynolds numbers from 0.49 < Rem < 99.50. This range represents a Reynolds number ratio of Rem,max/Rem,min = 202.8, more than two orders of magnitude and spanning the lower part of the laminar range. The turbine’s expected power output will be Ẇ = 0.47 Watts with a delivered torque of 0.024 mN-m at a rotation rate of ωmax = 1197 rev/min.

Combining the analytical equations underpinning the design process with similarity arguments, it is shown that shrinking the Tesla turbine’s physical scale drives the Reynolds number toward 0. The resulting velocity difference between the working fluid and the turbine disks gets driven toward infinity, which makes momentum transfer and the resulting turbine efficiency extremely high. In other words, unlike conventional turbines whose efficiency drops as they are scaled down, the performance of Tesla turbines will increase as they are made smaller.

Finally, it is shown through similarity scaling arguments that the 8-cm-diameter turbine resulting from the design process of this paper and running liquid Ethylene Glycol working fluid can be used to evaluate and approximate the performance of a 3-mm-diameter Tesla turbine powered by products of combustion in air.