Original Article A theory of Tesla disc turbines Sayantan Sengupta and Abhijit Guha Abstract In the present article, a mathematical theory for the flow field within a Tesla disc turbine has been formulated in the appropriate cylindrical co-ordinate system. The basis of the theory is the Navier–Stokes equations simplified by a systematic order of magnitude analysis. The presented theory can compute three-dimensional variation of the radial velocity, tangential velocity and pressure of the fluid in the flow passages within the rotating discs. Differential equations as well as closed-form analytical relations are derived. The present mathematical theory can predict torque, power output and efficiency over a wide range of rotational speed of the rotor, in good agreement with recently published experimental data. The performance of the turbine is characterized by conceptualizing the variation of load through the non-dimensional ratio of the absolute tangential velocity of the jet and the peripheral speed of the rotor. The mathem- atical model developed here is a simple but effective method of predicting the performance of a Tesla disc turbine along with the three-dimensional flowfield within its range of applicability. A hypothesis is also presented that it may be possible to exploit the effects of intelligently designed and manufactured surface roughness elements to enhance the performance of a Tesla disc turbine. Keywords Tesla turbine, turbine efficiency, power, torque, analytical theory, three-dimensional flowfield Date received: 20 April 2011; accepted: 19 March 2012 Introduction Tesla turbine, a bladeless turbine, was patented by the famous scientist Nikola Tesla (1856–1943) in 1913. 1 Up to now, a major stumbling block in its commercial use has been its low efficiency and certain other operational difficulties. 2 However, there has been a resurgence of research interest in this type of turbines 3 because they have several advantages (as explained below) and hence may be appropriately developed and used in certain niche application areas. In this article, an analytical theory has been developed for predicting the perform- ance of Tesla turbines, which agree well with experi- mental results. The Tesla turbine is also known as disc turbine because the rotor of this turbine is formed by a series of flat, parallel, co-rotating discs, which are closely spaced and attached to a central shaft. 2 The working fluid is injected nearly tangentially to the rotor by means of inlet nozzle. The injected fluid, which passes through the narrow gaps between the discs, approaches spirally towards the exhaust port located at the centre of each disc. The viscous drag force, produced due to the relative velocity between the rotor and the working fluid, causes the rotor to rotate. There is a housing surrounding the rotor, with a small radial and axial clearance. Tesla turbine has several important advantages: it is easy to manufacture, maintain and balance the turbine, and it has high power to weight ratio, low cost, significant reduction in emissions and noise level, a simple configuration which means an inexpensive motor. Tesla turbine can generate power for a variety of working media 3 like Newtonian fluids, non- Newtonian fluids, mixed fluids, particle laden two- phase flows (many aspects of two-phase flow may be found in Guha 4,5 ). This turbine has self-cleaning nature due the centrifugal force field. This makes it possible to operate the turbine in case of non-conventional fuels like biomass which produce solid particles. It also sug- gests that this bladeless turbine can be well suited to Mechanical Engineering Department, Indian Institute of Technology Kharagpur, India Corresponding author: Abhijit Guha, Mechanical Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. Email: a.guha@mech.iitkgp.ernet.in Proc IMechE Part A: J Power and Energy 226(5) 650–663 ! IMechE 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0957650912446402 pia.sagepub.com