GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC Lorenzo Talluri1, Olivier Dumont2, Giampaolo Manfrida1, Vincent Lemort2 and Daniele Fiaschi1 Department of Industrial Engineering (DIEF) University of Florence Florence, Italy [email protected] 1 Thermodynamics laboratory, Aerospace and Mechanical Engineering Department, University of Lige, Alle de la Dcouverte 17, Belgium 2

Table of contents Tesla turbine 2D model Geometry assessment Rotor channel width/inlet diameter ratio Rotor outlet/inlet diameter ratio & Throat/width ratio Fluid dynamics assessment Assessment of correct geometry Efficiency versus Power and Expansion Ratio Conclusions GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 2

Tesla turbine Multiple parallel flat rigid disks The disks are arranged coaxially in order to maintain a very small gap between them. The radial-inflow admission of the working fluid is from one or more tangential nozzles, providing a strong tangential component. Admission to plenum chamber The working fluid moves from the inlet to the outlet radius due to the difference in pressure determined by friction and by the exchange of

momentum, and exits from openings made on the disks and/or shaft at the inner radius. Plenum chamber Fluid Trajectory inside the rotor Nozzles Rotor Fluid discharged axial direction GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 3

2D model The model hypothesizes the fluid as real and compressible with steady and viscous flow. GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 4 Geometry Assessment GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 5 Rotor channel width/inlet diameter ratio Total-to-total efficiency of the turbine vs. channel width, at fixed 100C total inlet temperature and total inlet

pressure corresponding to a 10 K super heating level. Loci of best efficiency, The quadratic interpolated equation for the determination of the non-dimensional rotor channel width B, which allows achieving the highest efficiency vs. rotor outer diameter D2 B = 0.0021 D22 0.0017 D2 +0.0006 GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 6 Rotor outlet/inlet diameter ratio & Throat/width ratio When the optimal non-dimensional channel width correlation is applied, the best value for practically every turbine size is always in the range 0.3 0.4

Total-to-total efficiency increases linearly with decreasing TWR. => low TWRs imply higher velocities at the throat, which are beneficial for rotor efficiency. The power output shows an opposite behaviour, steadily increasing with increasing TWR. T WR= TW H s Z stat 2 r 2 b ndisk GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 7 Fluid dynamics assessment Increasing throat Mach number allows an

improvement of both efficiency and power. The tangential velocity ratio is one of the most important parameters for Tesla turbine optimization. The right matching of rotor inlet tangential velocity and peripheral speed is of paramount importance to achieve a high efficiency. 2 = 2 GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 8 Assessment of

correct geometry Considering different working fluids, the obtained geometry as a function of rotor outer diameter results to be optimized within similar ranges of the main design parameters: 0.3 < R< 0.4, TW = 0.02, Ma = 1 = 1. Fluid R1233zd(E) R245fa R1234yf n-Hexane Non-dimensional rotor channel width (B) GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC

9 Assessment of correct geometry When constrained rotational velocity applications are considered, high expander efficiencies are directly related to a proper selection of the rotor diameter. => Expansion ratio and efficiency are maximised when approaches unity GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC

10 Efficiency versus Power and Expansion Ratio 3.5 < < 5.5 0.005 < P < 35 kW > 60% for all fluids GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 11 Geometric sizing guidelines are proposed to achieve high performance of Tesla turbine working with 4 different fluids. The most critical parameters for achieving good turbine performance are found to be the rotor inlet tangential velocity ratio , the non-dimensional rotor channel width B and the rotor outlet/inlet diameter ratio R. Proper design expansion ratios for the Tesla turbine are determined between 3.5 and 5.5.

Hydrocarbon fluids are suitable for micro power generation. Specifically, n-Hexane achieves high efficiency at lowpressure levels. Nonetheless, if a high power per unit volume is required, organic refrigerants appear to be a good choice, as the power output per channel is definitely higher when compared to hydrocarbons. GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC 12 GEOMETRY AND PERFORMANCE ASSESSMENT OF TESLA TURBINES FOR ORC Lorenzo Talluri1, Olivier Dumont2, Giampaolo Manfrida1, Vincent Lemort2 and Daniele Fiaschi1 Department of Industrial Engineering (DIEF) University of Florence Florence, Italy [email protected]

1 Thermodynamics laboratory, Aerospace and Mechanical Engineering Department, University of Lige, Alle de la Dcouverte 17, Belgium 2