# Numerical and Analytical studies of Tesla Turbine

Many analytical and numerical attempts by various investigators were made during mid-nineteenth century to describe behavior of turbulent and laminar flow areas for flow between the tesla turbine’s disks. At times, computational tool capability was very limited that is why most of their studies had to rely on simple flow assumptions. Prof. W. Rice is one of the investigators who by employing different set of formulations has made his great efforts in describing and making a mathematical model of characteristics of operation and summation of parameters of multi-disk turbo machinery. He published an article in 1963 for the selection of quantity of disks of air-based friction compressors & pumps based on an incompressible and steady state flow in single inter-disk space by the determination of surface force and solution of the respective motion equations in tangential and radial coordinates. This study established the higher limit on parameters of performance like efficiency and total non-dimensional pressure rise of the pump by allocating losses due to friction to happen only among the disk spaces (i.e. entry & exit losses, wind age losses, housing and bearing are neglected). As the study continues, several derivations have been performed as for pumps in reverse operation (Multi disk Tesla Turbine) in 1965 having identical flow considerations. It has been derived from the results of study that maximum level of pressure drop and efficiency of turbine is obtained at the inner fluid exit recess and as non-dimensional parameter of flow (Q/ωro 3) increases, the tendency of efficiency decreases. There are some other studies by W. Rice (1968).

Many studies by Hasinger (1963) have elaborated pressure losses of different types which occur at the numerous points of the turbo machines. On the basis of previous studies for maximum attainable efficiency and power by W. Rice and his associates the existing knowledge gap in calculation of accurate performance characteristics of the device was filled by the determination of different frictional losses. The swept path of spiral fluid particle travelling from fluid inlet of rotor to exhaust has been analytically traced out by (Jeffery, 1990). Some other investigators have also achieved the same goal by the use of other tools commercial CFD packages (Jedrzejewski, 2011) and (Piotr, 2009). Various solutions using two dimensional incompressible flow approaches have been proposed by different investigators for solving equations about various flow quantities like Reynolds number, regional shear force, tangential and radial components of velocity, pressure drop as compared with inlet conditions, flow paths of particle, etc. (Waren, 1965). Soo, (1957) has used first and second order approximation to Reynolds number for calculating the axial and radial velocity profiles of incompressible fluid flowing from a stationary and the other rotating disk plates for radially outward and inward flows. Some investigators have also tried to approach analytically by some other means such as by using numerical methods: Breiter and Pohlhausen (1962) presented calculation of outward radial flow between co-rotating disks using finite difference scheme. Boyd and Rice copied the same method for calculating radially inward flow. He modeled inlet region of turbine that grow an asymptotic flow for large Reynolds number.

# Practical Designs and Experimental Studies of Tesla Turbine

N. Tesla is the person who has conducted the experiments and gave his undertakings. He conducted his experiments from 1906 to 1914 on turbine to check and investigate behavior of turbine for several different working conditions. According to him the turbines can be more than 95 % efficient exceeding conventional turbo machines of the day. He wanted to introduce a more reliable and efficient combustion engine in replacement of piston cylinder combustion engine using his technology. In their conversion of fuel to work the best available engines were not able to give more than 27 to 28 percentage efficiency. In 1966, a 6 inch wind turbine was tested by varying different conditions such as supply pressure varying from 6895Pa to 27,579 Pa, angular velocity varying from 4,000rmp to 18,000rpm and design variable such as disk spacing. He came up with observation that steam turbine with specific speed of 0.1 rpm is more efficient and give around 40-45% efficiency if it is compared with single stage turbine of same specific speed that gives efficiency up to 24% maximum. He also established a robust relation between flow rate and torque applied on disk of rotor of Tesla Turbine due to decrease in tangential velocity.

Prof Warren Rice, in 1965, rechecked performance merit stated by tesla. For this he conducted number of experiments. Visco- Geometric properties were replicated under which preceding steps were made. His test results confirm that turbine can be operated at nearly pure impulse to solely reactive mode and the deviation of the results from N. Tesla’s claim of turbine merits at various speed , flow rate and geometry combinations. Adam (1970) tried to verify the research provided by Boyd and Rice (1968). He observed patterns of pressure drops in radial direction from inlet to outlet with partial flow admission for a narrowly separated pair of disks. An analytical model with a good agreement was reached for laminar flow. Pater (1974) made some improvements in the study provided by Adam et al. In his research and study he tried to determine fluid particle streamlines, pressure distribution and various fluid regimes. They described that multiple disk turbo machines may be designed by the combination of kinematic viscosity constant (ν), operating angular speed and flow rate, and if the flow is inside the laminar flow range and ri, ro, and b remaining are kept constant.

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