A Practical Design Approach of the Tesla Turbine for Hydro Power Applications

In the global push for harnessing energy in a vast number of scenarios, the Tesla Turbine stands out as a potential niche device in various small-scale applications. This device can be fabricated rapidly, using locally available materials and conventional manufacturing operations. Despite these advantages, several technological challenges have held back the development of the Tesla Turbine. Besides, modern bladed turbines have a much broader range of applications. Another issue is that this turbine’s most recent experiments were focused on numerical tests or findings from the computational simulation. Very few studies that were conducted resulted in low-efficiency ratings. For advanced applications such as particulate flow, biomedical, and some modern machining methods that use abrasive particle-rich fluids, Tesla turbines can also be used as it is not sensitive to mixed fluids compared to conventional bladed turbines. Moreover, the construction cost of a Tesla turbine is meager compared to bladed turbines. Thus, the cost-to-performance ratio is higher than that of conventional turbines, which the authors believe could pose much interest for both further research and development.


Introduction
The Tesla turbine is a unique bladeless, centripetal flow turbine eponymously invented by Nikola Tesla [1] in 1913.It is constructed of flat parallel co-rotating disks, spaced along a shaft.A highvelocity flow of fluid between the disks results in a momentum exchange between the fluid and the disks resulting in output torque and power.The rotor flow can be either laminar or turbulent [2], depending on the fluid velocity with specific advantages and disadvantages in each case.Most of the studies have had a specific limited application as the objective, concerning size and speed and the operating fluid's nature.However, some of the research has tried to establish the generalized performance of the Tesla turbine.Despite this, the development of the field is still mainly in a primitive stage.Studies on the Tesla Turbine vastly lack compared to other types of conventional turbines.As of this study's time on a particular day, a quick Scopus search of 'Tesla Turbine' (Abstract-Keywords-Title) yields only about 140 articles, compared to over 240,000 for a search query with only 'turbine.'Because of the design's low cost and simplicity, the turbine design has essential implications in renewable energy [3,4], energy recovery plants [5,6,7] and even in bio-medical engineering [8].
IOP Publishing doi:10.1088/1757-899X/1305/1/012004 2 The turbine's low-cost and efficiency-related features have drawn particular attention from the research communities worldwide in recent times, where harnessing energy in various conditions has become a priority globally.For example, the authors see the tremendous potential of the Tesla turbine in dealing with various types of waste energy.Examples of such waste energy include gas from vehicle exhaust pipes and waste heat from industrial settings [5,6,7].An attempt has been made in the article to present results from a comprehensive literature review related to Tesla's turbine.Useful information related to working principles, formulas, notable research activities, prospective applications, and selected design parameters that can improve a Tesla turbine's performance is presented in the subsequent sections.

Brief History
The boundary layer theory was presented first in 1904 at the Third International Congress of Mathematicians by Ludwig Prandtl [9].In 1913 Nikola Tesla, who was also the inventor of alternating current [10], patented a bladeless turbine [1], which had parallel disks instead of blades in a single shaft which later on named as Tesla turbine, which worked by Prandtl's boundary layer theory.The turbine works by using fluid properties such as viscosity.Fluid enters the parallel disk gaps with high velocity.Due to the viscosity, fluid particles stick to the disk's surfaces and cause the disks to revolve within its axis.

Basic Components
The Tesla Turbine configuration could be rapidly built from readily available materials using components such as parallel disks, nozzle, shaft, spacer, housing, and bearings as "Fig" .Besides, the manufacturing cost is relatively low compared to a conventional turbine having intricate blade design.It is interesting to note that the Tesla turbine can also be used as a reverse flow pump [11] by coupling a motor with the main shaft, which is advantageous.

Working Principle
Tesla turbine follows the law of boundary layer theory [12].According to this theory, molecules that are immediately adjacent to the surface, adhere to the surface as the fluid transits past each disk surface.Those molecules that follow the surface, adhere to it and are slowed down in their contact with the molecules stuck to it.These molecules in results slow down the flow, which is just above them.As these molecules move away from these surfaces, the chances of their interference with the object surface are reduced.Meanwhile, due to the viscous forces, the molecules of the fluid resist separation.These viscous forces become dominant over the inertial forces.This will provide a pulling force that is transferred or moved to the disk, which causes the disk to revolve in the direction of the fluid [12].The turbine comprises flat parallel disks with rough surfaces on both sides.Small gaps are maintained between two disks to circulate the fluid particles.Each disk has one or multiple exhaust holes.The 1305 (2024) 012004 IOP Publishing doi:10.1088/1757-899X/1305/1/0120043 disks are fixed with the central shaft, and disk spacers are placed between the disks to maintain gaps.The central shaft is set to the housing through bearings.Single or multiple inlet nozzles are placed tangentially, and the exhaust ports are located perpendicular to the disks as shown in "Fig.2".Fluid enters the turbine radially and exits in the axial direction.Fluid particles enter the turbine chamber through nozzles having high velocities and low pressure "Fig.2".The fluid particles then start to lose their kinetic energy and exit through the exhaust, as shown in "Fig.2".Even though its kinetic energy decreases, the relative velocity difference between fluid and rotating plate can go up.This spiraling feature makes the Tesla turbine more efficient.As per the no-slip condition [13], the viscous working fluid particles stick to the solid surfaces of the disks and exert drag forces to rotate them. According to Rice [14], Tesla turbines can achieve up to 90% efficiency theoretically.Ho-Yan [15] and Lawn and Rice [16] claimed over 70% efficiency. Deam et al [17] argued that at tiny scales (sub-cm diameters), viscous turbines can beat the performance of standard-bladed turbines and might give 40% efficiency. Hoya and Guha [18] and Guha and Smiley [19] analyzed medium to large Tesla turbines and claimed 25% efficiency, however, they indicated that alternative nozzle styles can improve the efficiency.Although derived for mesoscale and macro-scale turbines, these studies provide a basis for the verification of small turbine designs. Jacobson, Stuart, Epstein, and Alan [20], Herrault et al. [21], Peirs et al [22], and Razak et al. [23] reported systems that can operate between 100,000 to 1 million revolutions per minute. Turbine Designs with power densities of 5 mW/cm3 to 30 W/cm3 were offered by many researchers including Krishnan et al. [4], Beans [24] and Ho-Ya  [15].In general, critical issues like power density are not explained well enough, and therefore the turbine efficiency is very low.As turbine structures become smaller, resistance forces increase.So new approaches to accurately estimate friction are necessary. Kandlikar et al. [25] have modified the normal Moody diagram where the value of relative surface roughness is over 0.05, arguing that depending on this value the flow constriction varies. Croce et al. [26] used a machine approach to model conical roughness components. Gamrat et al. [27] provided a detailed outline of previous studies and also said that the Poiseuille range will increase with surface roughness.

2.5 Patents
There are a lot of patents following Tesla's design.Mclean and William [28], and Possell and Clarence [29], used this design for their gas-turbine power plant designs.Then there was Rafferty, Edson, Kletschka, and Harold [30] who designed a pump similar to the design of the Tesla turbine which was estimated to be able to be used as a heat pump.Shanahan and John [31] patented a rotary engine.Conrad et al. [32] designed a turbine that would transmit motive force between a fluid and a plurality of spaced-apart rotatable members.Palumbo and John [33] designed a turbocharger depicted from Tesla's design.Milind, Darrell, Bhoodev, and Bart [34] filed high-efficiency fluid movers motivated by the Tesla turbine.Leininger et al. [35] mapped a system and method for continuous solids slurry depressurization following the design boundaries of the Tesla turbine.These are a few of the patents among many others only from the US.With proper investigation, these designs could prove to be very important to enrich the turbine technology.

Applications
According to Rice [2], the Tesla turbine will be best suited for applications involving high angular velocities, low torque, and low mass flow rates.Razak et al. [23] and Carey [36] demonstrated different scaled turbines for micro-hydro power applications.Deam et al. [17] argued that at small scales (sub-cm diameters), viscous turbines outperform conventional bladed turbines and can provide around 40% efficiency.Besides, it is not sensitive to particulate flow as Rafferty, Edson, Kletschka and Harold [30] patented this as a heat pump.Krishnan et al. [4] also discussed that this turbine has excellent performance characteristics.It should be noted that the Tesla turbine is supposed to work with viscous fluid, and the performance may vary with fluid viscosity according to Rice [14] and Leininger et al. [35].A Tesla turbine can be applied in diversified applications and some of the promising applications are listed below.
 Could be used as a pumping device [1,3,11,37,38,39,40] instead of conventional centrifugal pumps due to its lower manufacturing cost and smaller form factor.  As an efficient motor with low wear and friction [41,42,43], because the Tesla turbine is not sensitive to particle-rich fluid [30]. Power generation sectors such as gas turbines or reusing waste heat [5,6,7]. As thermal regenerative devices [44,45] utilizing the waste heat of aerospace and nuclear power plants. Bio-medical applications [8].For example, the heart pumps because of the turbine does not affect the blood cells due to its unique working principle of boundary layer effect rather than conventional reaction and impulse turbine. As a pump for a high vacuum application [11] such as electronic devices. High and low-temperature operations [38,39,45,46] such as scientific studies conducted in arctic and volcanic regions. Environmentally friendly devices [3,4] such as small hydro turbines where a fixed dam is not needed. In conventional pumps, fans, compressors, generators, blowers, transmissions, various hydraulic and pneumatic systems [1,41,42,47]. Desalinization of water and hydrogen generation as a fluid transferring device [11] for example efficiently producing hydrogen from seawater. Fluid transferring applications [48] such as pressure pumps, air coolers for electronics, and particle mixed fluid transfer in advanced machining equipment. Ultra-small profile heat engines [49] because of the simple construction Tesla turbine designs can be scaled down easily compared to conventional turbines.

Design Parameters
The performance of the Tesla turbine is affected by several parameters, including the width of the disks, the number of the disks, the gap between the disks, the inlet pressure, etc.A preliminary investigation and publication of the parameters by Choon et al. [50] can be considered for design as shown.

Amount of Fluid
According to Tsegaw et al [51], the amount of fluid between the disk gaps depends on the distance between two adjacent disks (b), kinematic viscosity ( and the disk's outer radius (r 0 ).This helps to understand how the disks divide the total amount of liquid/gas.The amount of fluid between the parallel disks (q) is - Where A is a dimensionless parameter.According to Hasinger and Kehrt [52], A can be taken from the imperial range, 10 ≤ A < 20.Q is the fluid flow rate.

Number of Disk Gaps
Using the total fluid flow rate and the amount of fluid between the disks, the theoretical number of disk gaps can be determined from the following equation.

Number of Disks
The number of disks of the turbine can be determined from the following expression.

Flow Velocity
The fluid stores potential energy as it is raised by a pump to the reservoir.This potential energy converts into kinetic energy when it comes down due to the gravitational force.The fluid flows inside the turbine nozzle with a high velocity called flow velocity.The kinetic energy of the fluid converts into mechanical energy when the disks start rotating at an angular velocity, as shown in "Fig.3".The flow velocity can be determined from the following basic fluid mechanics formula, Where a is the inner area of the pipe.

Design Analysis Using a Morphological Matrix
The Morphological Matrix has been shown by many engineering designers to be a useful tool to generate concept designs [53].Using 9 design features by 5 options, the authors have discussed one suitable final concept design, suitable for fabrication using locally available resources in Bangladesh, to showcase and discuss "TABLE 1".This chosen concept design was further refined via rapid prototyping and testing in a lab scenario.The experimental setup and results are detailed in the following subsections.

Disk Material and Geometry
For the disk material, we chose aluminum alloy (B1 in "TABLE 1") because it was easily sourced from scrap 3.5-inch mechanical hard drives at a very low cost as shown in "Fig.5".The hard drive disk (HDD) pallet's tensile strength, hardness, and yield strength are almost or over two times that of aluminum 6061.Another advantage is old hard drive disks (HDD) are easily feasible and the constructions of the pallets are consistent across almost all well-known manufacturers.It was easily machined by a vertical drill.For disk geometry, we chose the 3rd option (C3 in "TABLE 1") because of its simplicity of the design as shown in "Fig.5".

Nozzle
For the nozzle, we chose the 1 st option (D1 in "TABLE 1") as shown in "Fig.6" because of the housing design we chose and the design was simple and easily replicable in conventional machines.

Case and Exhaust Geometry
We chose option 1 (G1 in "TABLE 1") for case geometry as shown in "Fig.7" because in this design it is possible to change the flow angle of the fluid as it passes through the disks.So, one can easily optimize the flow angle in one's specific application.For exhaust geometry, we chose option 2 (H2 in "TABLE 1") shown in "Fig.7" as it has the most surface area to release low-velocity fluid.

Analysis of Turbine Power
The viscous fluid particles stick to the solid disks and help them to move with the fluid.The outlets in the center take the fluid out.The no-slip condition of fluid produces torque T on the turbine shaft.According to Swithenbank [54], the turbine's theoretical power can be determined using Equations ( 5) to (10).
The Tangential Velocity of a specific point of a rotating disk increases with the distance from the center.Tangential velocity is maximum at the outermost point of the disk.So, the tangential velocity V 

V   r0 
Where ,  is the angular velocity and r 0 is the outer disk radius.

Circulation
Circulation refers to the fluid-induced movement of blades tangential to the velocity vectors of the disk.This helps to identify the amount of generated surface torque on the disk.So, it increases with higher RPM.Therefore,  it can be expressed as,    9

Surface Torque
The amount of theoretical surface torque depends on the fluid viscosity ( and the distance between two adjacent disks (h).So, surface torque T,     r0 2 -r 2 )/2h  Where r i is the inner radius of the disk .

Disk Torque
Each disk has two surfaces on both sides.So, the disk torque T D ,   

Disk Power
With this generated disk torque, the disk power PD can be calculated.
PD   TD 

Turbine Power
The turbine power (P T ) can be obtained from the following equation.
  

Design Analysis through an Experimental Investigation
Analysis was done following the steps of the workflow below in "Fig.8. Workflow of the Design and Experimentation Process".The process was an open loop system and the result and discussion were the outcome.

Analysis with the Number of Disks
Initially, disk number was theoretically analyzed using Equations ( 1) to (3).A palate from the hard drive disk was taken, and the outer radius of the disk was measured.A constant disk gap of 0.5 mm was taken into consideration during analysis.To determine the amount of fluid between two parallel disks gap using Equation ( 1) where kinematic viscosity of water is taken at 25oC and the value of the dimensionless number was taken 19, which is close to 20 to minimize the number of disks and increase the amount of fluid per disk gap.The model was analyzed using three flow rates.Later, the flow velocities of the fluid for those flow rates were determined using Equation ( 4), where the inner pipe area was constant.The number of gaps and the number of disks were determined using Equation ( 1) and ( 3) respectively and analyzed as shown in "TABLE 2".

Fabrication of the Model Turbine
In collaboration, precise fabrication was done using CNC lathe and CNC milling machines at the Bangladesh Council of Scientific and Industrial Research (BCSIR).So, no expenses were incurred for fabrication.It was important to place the nozzles inside the main housing in the exact position, which is also possible using conventional machines operated manually.The CNC lathe machine was used for cutting the shaft and drilling the holes in the nozzles.The materials used for different parts of the model turbine are listed in "TABLE 3".

Experimental Setup
The experimental setup, illustrated in "Figure 9", investigates the performance of the model Tesla turbine inside a lab at Ahsanullah University of Science & Technology (AUST).Different components to regulate the flow of water for the experimental investigation.The control valve regulates the water flow rate which can be determined by a digital flow rate sensor.Then the fluid goes straight through the nozzles and into the rotor.The nozzle angle could be adjusted freely at any moment due to its flexible design feature.The rotor shaft was paired with a laser tachometer which gave the rpm readings.The shaft was directly connected to a Brake Dynamometer which gave the torque measurements at different flow rates and nozzle angles.Initially, water at a high flow rate was provided to overcome the static inertia.A leather belt was attached to the shaft to create tension for the brake dynamometer.The exhaust water was then again stored in a tank which again supplied the water into the main tank using a high-pressure pump.

Performance Analysis
From the flow rate data, the optimal disk number and turbine power were determined.The turbine was fabricated based on the optimal disk number for a certain flow rate.However, the performance of the turbine was analyzed by changing the flow rates.The angular velocity of the disks was measured using a laser tachometer and converted into.Tangential disk velocity was determined using Equation (5).Using this velocity, the circulation can be determined from Equation (6).As mentioned by Swithenbank [54], the Surface torque of a disk can be determined using Equation (7) where the viscosity of water is taken at 25 o C. As each disk had two surfaces on both sides, the disk torque of a disk would be twice the surface torque as per Equation ( 8).This disk torque was required to identify the disk power from Equation (9).By using disk torque and several disks, the turbine power could be determined from Equation (10).An overall analysis has been shown in "TABLE 5" with and without load conditions.

Return on Investment (ROI)
In hydro power applications, the calculation of Return on Investment (ROI) holds significant importance.This practice serves as a vital metric for comparing various power plant technologies with their predecessors, while also determining the timeframe required for the power plant to recoup its initial investment.In our experimental study, we focused on computing ROI concerning flow rate and the unit cost of household electricity in Bangladesh, estimated at approximately 8 BDT per kilowatthour (KWh).An overall analysis has been shown in "TABLE 6".Using a variable fluid flow rate, the angular velocity of the disk in RPM was measured.This turbine was designed for a specific flow rate of 0.000667 m3/s.As shown in "Fig.11" the RPM increased with the increment of the flow rate.However, after reaching the optimal flow rate, the incremental rate of RPM got lower with an increasing flow rate.

Figure 11: Variation of RPM with Flow rate
The Fluid flow rate had a similar impact on turbine power.Initially, it increased with an increasing flow rate.After reaching the designed flow rate, the increment rate slightly decreased for load and noload conditions as shown in "Figure 12".The limited display of test outcomes is attributed to setup losses.Predominantly, joint leakage and erratic pressure gauge readings were observed across the majority of trials as a consequence.Presented herein are the results from iterations closely approximating an optimal configuration within the laboratory setup, characterized by minimal to negligible leakage losses.Further enhancements in results can be anticipated through refinement of the laboratory apparatus.

Limitations of the Experimental Investigation
The performance of the actual turbine was relatively lower than the theoretical one because of various losses, which resulted from structural geometry and lab facility.The turbine housing was made of 3 separate parts and no additional O-ring was used for better sealing.Also, there were alignment issues with the two bearings because of the smaller bearing size.This resulted in fluid loss and kinetic energy

Conclusion
Tesla turbine can be used as a turbine, pump, or even a compressor that is bespoke to specific situations to harvest renewable energy, transfer materials, or pump fluids in rural areas where compactness is required.It ought to be seen that, as an unconventional way of rotating movement of this sort, the Tesla turbine can keep running under broad range of applied fluid technologies.The rotor is modular and can be varied in terms of the disk number to meet the input flow rates and reduce manufacturing costs.Disk gap can be varied to optimize for the particulate type flow or higher density fluids such as highly concentrated particle-laden flow.This will increase the momentum transfer in order to reach desired power densities.In that way, no external filters will be needed.Disk surface roughness can also be increased to achieve higher friction for low-viscosity fluids such as air and gas.With a simple construction method that was used in this research, it can be easily replicated in areas with limited resources, using readily available local materials.Also, there are design options such as disk geometry, and nozzle geometry to explore.Disk surface finish will play an important part in the performance.Cost-effective composite materials can also be used for housing and side panels.Furthermore, in this experiment, the calculation of Return on Investment (ROI)serves as a benchmark for assessing the performance of the current design.This baseline ROI provides a foundational reference point for further enhancements and refinements in the design.

Acknowledgement
We express our gratitude to Rupesh Chandra Roy (Former Director of PDC, BCSIR) and Engr.Muhammad Ali Zinnah (Senior engineer) for giving us the opportunity to do the collaborative fabrication under the Bangladesh Council of Scientific and Industrial Research (BCSIR) with their high-tech tools and machines.We are also thankful to Shihab Hasan Sarwar for providing us with plastic 3D printing support for preliminary analysis and to the fluid lab assistant Mr. Kishor.

Figure 1 :
Figure 1: Exploded view of a Tesla Turbine

Figure 2 :
Figure 2: Entry and Exhaust Path of working fluid 2.4 Notable Research Activities Conducted in the Past Apart from experimentation investigations, various computational analyses have been conducted in the past to assess the performance of Tesla turbines.With the advent of high-speed computing facilities, simulation studies have been used to get a deeper understanding of different types of Tesla turbines.Some of the notable research works are listed below.

Figure 4 :
Figure 4: Main housing material mounted on a milling machine

Figure 7 :
Figure 7: Housing and Exhaust Side Panel

Figure 8 :
Figure 8: Workflow of the Design and Experimentation Process

Figure 9 :
Figure 9: Experimental Setup for the Performance Analysis of Model Tesla Turbine

Figure 12 :
Figure 12: Variation of Turbine Power with Flow rate

Table 1 :
Morphological Matrix 4.1 Housing MaterialPolyamide 6 or PA 6 grade cast nylon (A1 in Table1) for main housing and side panels as shown in "Fig" because of their availability, feasibility, cost, and work hours in Bangladesh.Nylon is cheap and strong enough material for moderate flow rates and it is very easily machinable with conventional machines such as milling.However, it should be noted that nylon shouldn't be used in any hightemperature applications because nylon has a melting temperature of 230 o C.

Table 2 :
Disk Number Analysis for Different Flow Rate

Table 3 :
Material Used for the Different Parts of the Model Turbine

Table 4 :
Material Cost

Table 5 :
Performance Analysis of the Turbine

Table 6 :
Return of Investment (ROI) Analysis IOP Publishing doi:10.1088/1757-899X/1305/1/01200414 loss.A proper turbine mounting setup was missing in the lab facility, which resulted in noise and vibration during experimentation.