Research Papers: Energy Systems Analysis

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

[+] Author and Article Information
Matthew J. Traum

Engineer Inc,
4832 NW 76th Rd,
Gainesville, FL 32653
e-mail: mtraum@alum.mit.edu

Fatemeh Hadi

Mechanical and Manufacturing
Engineering Department,
Tennessee State University,
3500 John A. Merritt Blvd,
Nashville, TN 37209-1561
e-mail: fhadi@tnstate.edu

Muhammad K. Akbar

Mechanical and Manufacturing
Engineering Department,
Tennessee State University,
3500 John A. Merritt Blvd,
Nashville, TN 37209-1561
e-mail: makbar@tnstate.edu

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received September 11, 2017; final manuscript received September 18, 2017; published online October 17, 2017. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 140(3), 032005 (Oct 17, 2017) (7 pages) Paper No: JERT-17-1488; doi: 10.1115/1.4037967 History: Received September 11, 2017; Revised September 18, 2017

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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Carey, V. P. , 2010, “ Assessment of Tesla Turbine Performance for Small Scale Solar Rankine Combined Heat and Power Systems,” ASME J. Eng. Gas Turbines Power, 132(12), p. 122301. [CrossRef]
Carey, V. P. , 2009, “Assessment of Tesla Turbine Performance for Small Scale Solar Rankine Combined Heat and Power Systems,” ASME Paper No. IMECE2009-10814.
Krishnan, V. G. , Romanin, V. , Carey, V. P. , and Maharbiz, M. M. , 2013, “ Design and Scaling of Microscale Tesla Turbines,” J. Micromech. Microeng., 23(12), p. 125001.
Tesla, N. , 1913, “Turbine,” U.S. Patent No. 1,061,206.
Tahil, W. , 1998, “ Theoretical Analysis of a Disk Turbine,” Tesla Engine Builder’s Association (TEBA) News, Milwaukee, WI, pp. 18–19.
Tahil, W. , 1999, “ Theoretical Analysis of a Disk Turbine (2),” Tesla Engine Builder’s Assoc. (TEBA) News, Milwaukee, WI, pp. 17–18.
Boyd, K. E. , and Rice, W. , 1968, “ Laminar Inward Flow of an Incompressible Fluid Between Rotating Disks, With Full Peripheral Admission,” ASME J. Appl. Mech., 35(2), pp. 229–237. [CrossRef]
Rice, W. , 1965, “ An Analytical and Experimental Investigation of Multiple-Disk Turbines,” ASME J. Eng. Power, 87(1), pp. 29–35. [CrossRef]
Matsch, L. , and Rice, W. , 1968, “ An Asymptotic Solution for Laminar Flow of an Incompressible Fluid Between Rotating Disks,” ASME J. Appl. Mech., 35(1), pp. 155–159. [CrossRef]
Lawn, M. L. , and Rice, W. , 1974, “ Calculated Design Data for the Multiple-Disk Turbine Using Incompressible Fluid,” ASME J. Fluids Eng., 96(3), pp. 252–258. [CrossRef]
Truman, C. R. , Rice, W. , and Jankowski, D. F. , 1978, “ Laminar Throughflow of Varying-Quality Steam Between Corotating Disks,” ASME J. Fluids Eng., 100(2), pp. 194–200. [CrossRef]
Hoya, G. P. , and Guha, A. , 2009, “ Design of a Test Rig and Study of the Performance and Efficiency of a Tesla Disc Turbine,” Proc. Inst. Mech. Eng., Part A, 223(A4), pp. 451–465. [CrossRef]
Guha, A. , and Sengupta, S. , 2014, “ Similitude and Scaling Laws for the Rotating Flow Between Concentric Discs,” Proc. Inst. Mech. Eng., Part A, 228(4), pp. 429–439. [CrossRef]
Deng, Q. , Qi, W. , and Feng, Z. , 2013, “Improvement of a Theoretical Analysis Method for Tesla Turbines,” ASME Paper No. GT2013-95425.
Qi, W. , Deng, Q. , Feng, Z. , and Yuan, Q. , 2016, “Influence of Disc Spacing Distance on the Aerodynamic Performance and Flow Field of Tesla Turbines,” ASME Paper No. GT2016-57971.
Guha, A. , and Sengupta, S. , 2014, “ The Fluid Dynamics of Work Transfer in the Non-Uniform Viscous Rotating Flow Within a Tesla Disc Turbomachine,” Phys. Fluids, 26(3), p. 033601. [CrossRef]
Yang, Z. , Weiss, H. L. , and Traum, M. J. , 2013, “ Gas Turbine Dynamic Dynamometry: A New Energy Engineering Laboratory Module,” American Society for Engineering Education (ASEE) North Midwest Section Conference, Fargo, ND, Oct. 17–18, pp. 1–14.
Usman, M. , Khan, S. , Ali, E. , Maqsood, M. I. , and Nawaz, H. , 2013, “ Modern Improved and Effective Design of Boundary Layer Turbine for Robust Control and Efficient Production of Green Energy,” J. Phys.: Conf. Ser., 439(1), p. 012043.
Rice, W. , 1991, “ Tesla Turbomachinery ,” Fourth International Tesla Symposium, Serbian Academy of Sciences and Arts, Belgrade, Yugoslavia, Sept. 23–25, pp. 1–12.
Gupta, H. E. , and Kodali, S. P. , 2013, “ Design and Operation of Tesla Turbo Machine—A State of the Art Review,” Int. J. Adv. Transp. Phenom., 2(1), pp. 7–14.
Vidhi, R. , Kuravi, S. , Goswami, D. Y. , Stefanakos, E. , and Sabau, A. S. , 2013, “ Organic Fluids in a Supercritical Rankine Cycle for Low Temperature Power Generation,” ASME J. Energy Resour. Technol., 135(4), p. 042002. [CrossRef]
Wong, K. V. , and Tan, N. , 2015, “ Feasibility of Using More Geothermal Energy to Generate Electricity,” ASME J. Energy Resour. Technol., 137(4), p. 041201. [CrossRef]
Güell, B. M. , Sandquist, J. , and Sørum, L. , 2012, “ Gasification of Biomass to Second Generation Biofuels: A Review,” ASME J. Energy Resour. Technol., 135(1), p. 014001. [CrossRef]
Romanin, V. D. , Krishnan, V. G. , Carey, V. P. , and Maharbiz, M. M. , 2012, “Experimental and Analytical Study of Sub-Watt Scale Tesla Turbine Performance,” ASME Paper No. IMECE2012-89675.
Pandey, R. J. , Pudasaini, S. , Dhakal, S. , Uprety, R. B. , and Neopane, H. P. , 2014, “ Design and Computational Analysis of 1 kW Tesla Turbine,” Int. J. Sci. Res. Publ., 4(11), pp. 314–318.
Hasan, A. , and Benzamia, A. , 2014, “ Investigating the Impact of Air Temperature on the Performance of a Tesla Turbine Using CFD Modeling,” Int. J. Eng. Innovation Res., 3(6), pp. 794–802.
Lampart, P. , and Jędrzejewski, L. , 2011, “ Investigation of Aerodynamics of Tesla Bladeless Microturbines,” J. Theor. Appl. Mech., 49(2), pp. 477–499.
Alrabie, M. S. , Altamimi, F. N. , Altarrgemy, M. H. , Hadi, F. , Akbar, M. K. , and Traum, M. J. , 2017, “Method to Design a Hydro Tesla Turbine for Sensitivity to Varying Laminar Reynolds Number Modulated by Changing Working Fluid Viscosity,” ASME Paper No. ES2017-3442.
Choon, T. W. , Rahman, A. A. , Jer, F. S. , and Aik, L. E. , 2011, “ Optimization of Tesla Turbine Using Computational Fluid Dynamics Approach,” IEEE Symposium on Industrial Electronics and Applications (ISIEA), Langkawi, Malaysia, Sept. 25–28, pp. 477–480.
Barbarelli, S. , Florio, G. , and Scornaienchi, N. M. , 2005, “ Performance Analysis of a Low-Power Tangential Flow Turbine With Rotary Channel,” ASME J. Energy Resour. Technol., 127(4), pp. 272–279. [CrossRef]
Derakhshan, S. , and Kasaeian, N. , 2014, “ Optimization, Numerical, and Experimental Study of a Propeller Pump as Turbine,” ASME J. Energy Resour. Technol., 136(1), p. 012005. [CrossRef]
Ho-Yan, B. P. , 2011, “ Tesla Turbine for Pico Hydro Applications,” Guelph Eng. J., 4, pp. 1–8.
White, F. M. , 2011, Fluid Mechanics, 7th ed., McGraw-Hill, New York, p. 382.
Yang, Z. , Weiss, H. L. , and Traum, M. J. , 2013, “ Dynamic Dynamometry to Characterize Disk Turbines for Space-Based Power,” 23rd Annual Wisconsin Space Conference (WSC), Milwaukee, WI, Aug. 15–16, pp. 1–8.
Emran, T. A. , 2011, “ Tesla Turbine Torque Modeling for Construction of a Dynamometer and Turbine,” Master’s thesis, University of North Texas, Denton, TX.
Papamoschou, D. , 1997, “ Mach Wave Elimination in Supersonic Jets,” AIAA J., 35(10), pp. 1604–1611. [CrossRef]
Liu, S. , Yin, H. , Xiong, Y. , and Xiao, X. , 2016, “ A Comparative Analysis of Single Nozzle and Multiple Nozzles Arrangements for Syngas Combustion in Heavy Duty Gas Turbine,” ASME J. Energy Resour. Technol., 139(2), p. 022004. [CrossRef]
Beans, E. W. , 1961, “Performance Characteristics of a Friction Disk Turbine,” Doctoral dissertation, Pennsylvania State University, State College, PA.
Emran, T. A. , Alexander, R. C. , Stallings, C. T. , DeMay, M. A. , and Traum, M. J. , 2010, “Method to Accurately Estimate Tesla Turbine Stall Torque for Dynamometer or Generator Load Selection,” ASME Early Career Technical Conference (ECTC), Atlanta, GA, Oct. 1–2.
Klein, S. A. , and Alvarado, F. L. , 2002, “ Engineering Equation Solver,” F-Chart Software, Madison, WI, accessed Sept. 29, 2017, http://www.fchart.com/ees/
Haar, L. , Gallagher, J. S. , and Kell, G. S. , 1984, NBS/NRC Steam Tables, Hemisphere Publishing, New York.
Zimmerle, D. , and Cirincione, N. , 2011, “Analysis of Performance of Direct Dry Cooling for Organic Rankine Cycle Systems,” ASME Paper No. ES2011-54202.
Giacomel, J. A. , 1987, “Power Translation Device,” U.S. Patent No. 4,655,679.
Fréchette, L. G. , Lee, C. , Arslan, A. , and Liu, Y. C. , 2003, “Design of a Microfabricated Rankine Cycle Steam Turbine for Power Generation,” ASME Paper No. IMECE2003-42082.
Epstein, A. H. , 2004, “ Millimeter-Scale, Micro-Electro-Mechanical Systems Gas Turbine Engines,” ASME J. Eng. Gas Turbines Power, 126(2), pp. 205–226. [CrossRef]
Lee, C. , and Fréchette, L. G. , 2011, “ A Silicon Microturbopump for a Rankine-Cycle Power Generation Microsystem—Part I: Component and System Design,” J. Microelectromech. Syst., 20(1), pp. 312–325. [CrossRef]
McKeathen, J. E. , Reidy, R. F. , Boetcher, S. K. S. , and Traum, M. J. , 2009, “A Cryogenic Rankine Cycle for Space Power Generation,” AIAA Paper No. 2009-4247.


Grahic Jump Location
Fig. 1

Velocity vectors at the inlet and outlet of the Tesla turbine

Grahic Jump Location
Fig. 2

Nozzle orifice schematic

Grahic Jump Location
Fig. 3

Tesla turbine efficiency dependence on the ratio of rotor disk radii and Reynolds number. This result is consistent with plots in Carey [1].

Grahic Jump Location
Fig. 4

Tesla turbine efficiency dependence on nozzle height, h, and mass flow rate, m˙, differs due to the way these parameters impact v-θ,o and v-k,r

Grahic Jump Location
Fig. 5

The derivative of turbine efficiency (dimensionless power) with respect to ξ plotted for laminar Reynolds numbers

Grahic Jump Location
Fig. 6

The derivative of turbine efficiency (dimensionless power) with respect to Rem plotted for 0.1 = ξ and 0.1 < ξ < 0.9 at 0.1 increments



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In