Tesla Turbine - Efficiency and Calculations

Efficiency and Calculations

In Tesla's time, the efficiency of conventional turbines was low because the aerodynamic theory needed for effective blade design did not exist and the low quality of materials available to construct those blades put severe limitations on operating speeds and temperatures. The efficiency of a conventional turbine is related to the pressure difference between the intake and the exhaust. To achieve a higher pressure difference very hot fluids such as superheated steam are used which is why the availability of higher temperature materials allow higher efficiencies. If the turbine uses a gas which is liquid at room temperature then you can use a condenser after the exhaust to increase the pressure difference.

Tesla's design sidestepped the key drawbacks of the bladed turbine. It does suffer from other problems such as shear losses and flow restrictions. Some of Tesla turbine's advantages lie in relatively low flow rate applications or when small applications are called for. The disks need to be as thin as possible at the edges in order not to introduce turbulence as the fluid leaves the disks. This translates to needing to increase the number of disks as the flow rate increases. Maximum efficiency comes in this system when the inter-disk spacing approximates the thickness of the boundary layer, and since boundary layer thickness is dependent on viscosity and pressure, the claim that a single design can be used efficiently for a variety of fuels and fluids is incorrect. A Tesla turbine differs from a conventional turbine only in the mechanism used for transferring energy to the shaft. Various analyses demonstrate the flow rate between the disks must be kept relatively low to maintain efficiency. Reportedly, the efficiency of the Tesla turbine drops with increased load. Under light load, the spiral taken by the fluid moving from the intake to the exhaust is a tight spiral, undergoing many rotations. Under load, the number of rotations drops and the spiral becomes progressively shorter. This will increase the shear losses and also reduce the efficiency because the gas is in contact with the discs for less distance.

Efficiency is a function of power output. A light load makes for high efficiency and a heavy load, which increases the slip in the turbine and lowers the efficiency, though this is not exclusive to Tesla turbines.

The turbine efficiency of the gas Tesla turbine is estimated to be above 60, reaching a maximum of 95 percent. Keep in mind that turbine efficiency is different from the cycle efficiency of the engine using the turbine. Axial turbines which operate today in steam plants or jet engines have efficiencies of about 60 - 70% (Siemens Turbines Data). This is different from the cycle efficiencies of the plant or engine which are between approximately 25% and 42%, and are limited by any irreversibilities to be below the Carnot cycle efficiency. Tesla claimed that a steam version of his device would achieve around 95 percent efficiency. Actual tests of a Tesla Steam Turbine at the Westinghouse works showed a steam rate of 38 pounds per horsepower-hour, corresponding to a turbine efficiency in the range of 20%, while contemporary steam turbines could often achieve turbine efficiencies of well over 50%. The methods and apparatus for the propulsion of fluids and thermodynamic transformation of energy were disclosed in various patents. The thermodynamic efficiency is a measure of how well it performs compared to an isentropic case. It is the ratio of the ideal to the actual work input/output. This can be taken to be the ratio of the ideal change in enthalpy to the real enthalpy for the same change in pressure.

In the 1950s, Warren Rice attempted to re-create Tesla's experiments, but he did not perform these early tests on a pump built strictly in line with the Tesla's patented design (it, among other things, was not a Tesla multiple staged turbine nor did it possess Tesla's nozzle). Rice's experimental single stage system's working fluid was air. Rice's test turbines, as published in early reports, produced an overall measured efficiency of 36% to 41% for a single stage. Higher percentages would be expected if designed as originally proposed by Tesla.

In his final work with the Tesla turbine and published just prior to his retirement, Rice conducted a bulk-parameter analysis of model laminar flow in multiple disk turbines. A very high claim for rotor efficiency (as opposed to overall device efficiency) for this design was published in 1991 entitled "Tesla Turbomachinery". This paper states:

"With proper use of the analytical results, the rotor efficiency using laminar flow can be very high, even above 95%. However, in order to attain high rotor efficiency, the flowrate number must be made small which means high rotor efficiency is achieved at the expense of using a large number of disks and hence a physically larger rotor."

Modern multiple stage bladed turbines typically reach 60% - 70% efficiency, while large steam turbines often show turbine efficiency of over 90% in practice. Volute rotor matched Tesla-type machines of reasonable size with common fluids (steam, gas, and water) would also be expected to show efficiencies in the vicinity of 60% - 70% and possibly higher.