Hydrodynamic Tesla Wheel Flume for Model and Prototype Testing

Spencer Jenkins, Chris Scott, Jacob Strom, Mallory Bond, Harrison Gardner,

Jeffrey Bell, Erica vonBampus, Stephen L. Wood, Ph.D., P.E. Ocean Engineering

Florida Institute of Technology Melbourne, Florida, USA

swood@fit.edu

Abstract—The Ocean Engineering department at Florida

Institute of Technology (Florida Tech) has developed a Hydrodynamic Tesla Wheel Flume that is scheduled to be deployed for testing of models and prototypes. Using flow analysis, the researchers at Florida Tech developed the system to create a steady laminar flow simulating the natural flow of fluid around a moving vehicle/vessel. The following design parameters were implemented: the apparatus must be 1) semi-portable, 2) cost efficient (inexpensive), and most importantly 3) have an effective and accurate laminar flow. The design and implementation met all requirements and the flume is ready for deployment as an efficient and effective alternative to current testing facilities.

Index Terms— flume, hydrodynamic, laminar, fluid, flow, model, prototype testing, Tesla wheel.

I. INTRODUCTION The southeast region of the United States lacks a sizeable

testing flume to study hydrodynamic flows around a body; as a result, universities in this region must ship their designs to the University of Michigan or elsewhere for analysis. Design testing is a crucial facet of any engineering project; however, testing is very difficult when unknown or complicated conditions develop. This is always the case when testing a design that is to perform in open water (ocean) conditions. The present solution to this problem is by using tow tanks; unfortunately tow tanks are expensive and facilities use large amounts of space and energy.

Faced with a lack of appropriate and adequate hydrodynamic testing facilities, the Florida Institute of Technology is developing a self-contained test flume. This flume will be used by the school’s Department of Marine and Environmental Systems (DMES), which includes the Ocean engineering and Naval Architecture programs. The idea behind the flume design is to have a testing apparatus that is manageable in size as opposed to large tow tanks. From these parameters the overall design must be small enough to consider it “semi portable” and large enough to have the required sized for laminar flow.

The approximate size measurements of the initial design were based upon the models that were to be tested. The flume had to contain a steady flow channel that accommodates a 2.13-m (7-ft) model or prototype. The issue was: could the flow be linearized over the 2.13-m (7-ft) distance? An overall

design length of 7.62-m (25-ft) was chosen in order to ensure space for both the flow drive and test flow area, yet still be considered “semi-portable”. The final measurements of the flume are: 7.62-m (25-ft) length, 2.44-m (8-ft) height, and 2.44-m (8-ft) width. The body of the flume is composed of a 6061 aluminum load bearing frame design.

II. BACKGROUND The Tesla turbine, U.S. Patent 1,061,206 -- May 6, 1913

was invented by Nikola Tesla as a means to extract energy from water. The design uses water’s “salient properties of adhesion and viscosity” [1] to create mechanical motion from a moving fluid. The Tesla turbine consists of a chamber that houses a number of round flat disks spaced very close together. These disks are keyed to a shaft, which is geared to an electrical generator. The dimensions, number, and spacing of the disks is determined by the application of the turbine. The turbine is meant to be placed in a quickly moving fluid. The fluid is directed into a valve at the top of the turbine and into the turbine chamber where it circulates several times before being discharged through a valve at the bottom of the turbine. As the water circulates in the chamber, its viscosity surface friction causes the turbine disks, shaft and electrical generator to spin [1]. Figure 2 shows the original application for a patent, filed October 21, 1909, and the Tesla turbine design.

Tesla also patented a system that used this technology that he believed to propel water in a more efficient manner than the

Fig. 1. Flume at Florida Tech

pumps used at the time. This apparatus is US Patent # 1,061,14 "Fluid Propulsion." This pump caused the water being pumped through it to “move in natural paths or streamlines of least resistance” [2]. Like the Tesla turbine it used spinning flat disks. Tesla wrote that skin friction on the disks would cause the water to circulate in the chamber. The fluid was sucked into the chamber at the center of the disks. An outflow was positioned at the top of the chamber and pointed in direction of the flow. He determined that this was the optimal shape and configuration for the pump. Figure 4 shows a working prototype of this design where the casing has been removed to show the disk system.

The Tesla pump has been incorporated into various systems over the last 40 years. For example, the DiscFlo Corporation located in California designs and manufactures pumps which use the Tesla pump. The company founder Max Gurth experimented with the Tesla pump design in 1970 to make it more efficient and useful as a pump. He found that widening the blades from Tesla’s design allowed more fluid into the

pump and increased efficiency. These pumps are used in an extremely wide range of applications with great success. DiscFlo’s patented pumps have exceeded in many situations where other more commonly used pumps have failed. The pumps have had great success in situations where the fluid being pumped needs to be laminar, the fluid is abrasive, contains live organisms, is highly viscous, is air entrained, or has suspended solids in it [3]. These applications are commonly found in the oil and petrochemical, municipal water/ wastewater, food and beverage, and steel manufacturing industries. The pumps consist of a Tesla Turbine with more widely spaced disks that are integrated into the housing of the motor. The Tesla pumps pull fluid into the pump from a pipe mounted to the chamber perpendicular to the disks. The disks have holes in their centers to allow the fluid to travel through the chamber. The flow leaves the chamber through a pipe fitted tangentially to the disks. This arrangement provides a laminar flow.

Working systems can be found at Florida Atlantic University's Harbor Branch Oceanographic Institute in Fort Pierce Florida. In this system a Bio-Fence DiscFlo-pump, by Applied Photosynthetics, pumps sea water without damaging the live organisms where a standard impellor or cavity pump would [3]. With respect to flumes the University of Otago in New Zealand designed and built a flume on the Otago campus. The flume, designed for the school’s athletic program, circulates water at the pace of a swimmer, giving it a range of 0.3-m/s to 5.1-m/s (0.6 to 10-knots), covering novice to Olympic swimmers. The flume is used by canoe and kayak paddlers for workouts. The overall dimensions of this flume are 21-m long, 4-m deep and 4-m wide; it was designed to be large enough to perform hydrodynamic testing on the schools surf skis, paddle boards and rowing shells [4]. The flow is pulled through the flume by large axial flow pumps and then pumped to the other end through pipes under the flume. The flume uses guide vanes to direct and straighten out the flow. To keep the flow laminar the pipes empty into large reservoirs at the ends of the flume [4]. The flume then gets narrower in the testing section to increase the velocity.

Fig. 2. Patent No. 1,061,206 [1]

Fig. 3. Photograph of Tesla Pump Discs [2]

Another flume-like system by Aquabiotech Inc. located in Coaticook, Canada is an artificial river. This artificial river re-circulates water through a 3.66-m (12-ft) testing section. This system (see Fig. 3) was designed for conducting experiments on marine organisms that would be found in a river ecosystem. The testing chamber is meant to be filled with specimens and substrates that would be found in a natural environment such as sand and burrowing organisms. The artificial river is a 487-cm long rectangular box made of acrylic. The box is 50-cm deep and 50-cm wide. The testing velocities range from 5 to 50-cm/sec and are powered by a 0.746-kilowatt (1-hp) pump. The water is pumped through a 30.48-cm (12-in) diameter pipe under the tank and is pumped through a honeycomb block with 6.35-mm (¼-in) diameter cells to even out the flow and prevent fish from swimming into the pump [5]. The tank is also designed to be attached to a chiller to closely control the temperature of the river and to counteract the addition of heat from friction and the pump.

At Florida Tech corrosion tests are being conducted using a Tesla wheel (see Fig. 4). This patented system, originally begun as a senior design project led by Brian Biera, was a way to conduct long term experimentation in moving water. The group, led by ocean engineering professor Dr. Geoffrey Swain, determined that circulating water in a circular tank would be the best way to accomplish this. The original design consisted of a circular tank with a paddlewheel in the center of the tank that spun horizontally, moving water around the edges of the tank [6]. This design created an unsteady flow and was then changed to use a Tesla Pump in place of the paddlewheel. The tesla pump disks were 1.83-m (6-ft) in diameter, constructed of coated plywood. The thickness of the boundary layer was calculated to be 74-mm. From this information the optimal spacing of the disks was determined to 148-mm [6]. Through testing the Tesla Pump was found to create a very laminar and constant flow over long periods of time. The plywood disks eventually failed under the pressure changes due to the changing velocities of the water in the tank and were replaced with disks constructed of a honeycomb core fiberglass composite, holes were also added to the disks which were 63.5-mm in diameter and are as close to center as possible in order to equalize pressure [6]. This design uses a 7.5-hp motor that has successfully powered this Tesla Pump at speeds of 5.1-m/s (10-knots) without any complications or failures for the past

three years. A three phase motor with a detachable controller was used so that the revolutions per minute of the pump could be closely controlled. The three phase motor adjusts its voltage to maintain the RPM set by the controller. The controller also allows a routine to be programmed into the motor to allow the water to be gradually brought up to speed.

III. BASIC THEORY The Reynolds Number is a dimensionless number that

represents the ratio of inertial forces to viscous forces in a liquid [7]. The Reynolds number is fundamental to fluid mechanics. It is used in the calculations for the boundary layer thickness and coefficient of friction, which is needed to optimize the design of the Tesla pump. The Reynolds number is also vital to model testing. Reynolds number similitude is used to accurately test scale models and will have to be used to find the maximum free stream velocity that the flume must be designed to be able to generate. The Reynolds number can be calculated over a surface using Eq. 1.

(1)

Where V is the free stream velocity, L is a representative length, and ν is the kinematic viscosity of the fluid [7]. The Reynolds Number of a rotating disk can be calculated more accurately through Eq. 2.

(2)

Where r is the disks radius, ω is the angular frequency, φ is the swirl factor, and ν is the kinematic viscosity [8].

The boundary layer thickness is the distance off of a surface into a moving fluid to which the effect of the surface is still felt. A boundary layer develops over surfaces along which an inviscid fluid is traveling. At the edge of the surface a no slip condition develops where the velocity of the fluid is zero. The velocity of the fluid then increases exponentially as it moves further away from the surface [7]. There are three main ways to calculate the boundary layer thickness. The first way is the arbitrary method which uses the arbitrary value as seen in

Fig. 3. Aquabiotech’s Flume [5]

Fig. 4. Florida Tech’s Maelstrom

Figure 5. The boundary layer is determined to contain the fluid moving at less than 99% of the free stream velocity using δ=y and U=0.99V.

The second method (Eq. 3) is the displacement thickness method. This method calculates the volume of fluid that is affected by the nonslip condition at the surface boundary. (3)

The third method (Eq. 4) is the Momentum thickness

method. This method works by calculating the momentum of the water that has been affected by the surface it is traveling over, and the liquids effect on the surface.

(4)

The boundary layer over the disks is calculated to

determine the most efficient spacing of the disks and calculated along the length of the tank to avoid boundary layer separation and added turbulence associated with it at high testing speeds. The boundary layer over the Tesla Pump disks was calculated with the equation for a rotating disk (Eq. 5).

(5)

In this equation D is the diameter of the disk, and Re is the Rotational Reynolds Number.

Hydrodynamic drag over a surface is the resistance to motion through a fluid felt by the surface; this is calculated using Eq. 6.

(6) In this equation, Cd is the coefficient of drag, ρ is the

density of the fluid, V is the free stream velocity, and A is the characteristic area of the surface [8]. The drag coefficient for a rotating surface can be found with Eq. 7.

(7)

where Re is the Rotational Reynolds Number [8]. The drag over each side of the disks must be found in order to calculate the torque needed to be generated by the motor which will spin the Tesla pump. This torque is also needed to calculate the cross section of the central shaft needed.

IV. DESIGN The Florida Tech flume consists of three main sections: The

testing channel, the flow return channel, and the flow drive system. The testing channel as previously mentioned is the most important area of the flume in that the flow must be precise in order for precise measurements to be taken. The testing channel can be seen above in Fig. 6 in the top portion of the flume. The channel itself is open allowing for convenient deployment of models or prototypes. The flow return channel is what returns the flow back to the testing channel. The testing channel and flow return are separated by a center divide that allows the flow to move in a cyclical fashion. It is imperative for the flow to be constant, steady, and efficient. With the criteria at hand, it was chosen that the flume would be driven by a Tesla disk drive system.

The initial design for the Tesla drive system called for aluminum disks; however, due to performance requirements, the disks were switched to fiberglass composite construction. The Tesla Drive system is ideal for the flume in that the friction between the rotating disks and the water is used to gradually create a flow. By using this system rather than a pump or paddle wheel design, the flow builds gradually at a steady pace, allowing less turbulence along the flow pattern. Because the flume depends on a laminar flow channel, the smaller amount of flow disturbance means a more defined and accurate testing area.

Once a steady flow is achieved it is still important to direct the flow in order to achieve the goal of a laminar flow in the test channel. To do this flow channels are used at both the entry and exit of the flow channel. This is done to direct the flow in such a way to create a steady column of water.

Fig. 5: Boundary Layer Diagram [9]

Fig. 6. Flume Design

Fig. 7. Flow Channels

V. COMPUTER SIMULATION Testing had to be done to ensure the flow channels (see Fig.

7) would prove effective in constructing a laminar flow. Two programs were used in this effort: Gambit Version 4.3 and Fluent Version 12. Gambit Version 4.3 was used to create a 2-D model of the flume and its internal components such as the center divided and flow channels. Fluent Version 12 illustrates the Computational Fluid Dynamic Calculations or CFD. These programs were used together to simulate the direction of the flow inside the flume.

Using Gambit Version 4.3, the 2-D model of the flume was created using quad and triangular meshing to imitate the boundary conditions. As mentioned, the flume design contains an open-air top for easy access. Unfortunately, the program is limited to closed boundaries; however, this created only minor issues that were easily deciphered during the flow analysis. After the boundary conditions were set up the velocity inlets were made distinct.

Fluent was implemented using the 2-D models from Gambit. The cell conditions were to be defined as being solid and containing fluid. This was consistent with the aluminum design and freshwater that would be used. Two flows of velocities 3.0-m/s and 6.6-m/s were used in the flow analysis. The flume was modeled using upwind momentum equations and second-order pressure calculations. The return channel was modeled using first-order upwind momentum and standard pressure equations. The calculations were carried out to 5,000 iterations each. This ensured accurate results once the flow model was created. The flow model illustrated the particle trajectories and individual velocities. The results can be seen in figures 8-10.

As shown above in Figures 9 and 10, it is evident that a laminar flow was achieved. Both the X and Y velocities show a small eddy formed in the testing area. The small eddy formed on the top is a result of the constraints of the program as the boundary condition was defined as closed. In an open boundary condition the flow would be laminar across the testing area. The model shows that the testing area is large enough to accommodate a wide variety of models and prototypes.

VI. COMPOSITE DISK CONSTRUCTION PROCEDURE The Tesla Pump is constructed of six (6) fiberglass disks

with a 20.3-cm (8-in) gap between each disk. These disks are keyed to a 5.7-cm (2-1/4-in) diameter 6061-T6 aluminum shaft. Each disk is made up of eight (8) foam pre-forms fiberglassed together and finished in resin and Gelcoat. The pre-forms are made using a mold fabricated out of wood. The pre-form mold is divided into a top half and a bottom half where each half is lined with a precut pattern of two ply cloth. This cloth is comprised of 45x45 fiberglass cloth that is backed by a tightly woven polyester cloth. The fiberglass cloth is placed against the mold so that it can later absorb resin during the final construction of the disk. The polyester cloth adheres to the foam inside the pre-form. This polyester cloth is very fibrous allowing for a strong bond between the polyester cloth and the foam and keeps the foam from expanding into the outer layer of fiberglass cloth. After the cloth is placed in each half of the mold and pressed tightly into the corners. The bottom half of the mold is filled with a two part closed cell expanding foam. A computer controlled system monitors the temperature and

Fig. 8. Flow with no control surfaces: X and Y velocity

Fig. 9. X velocity of flume

Fig. 10. Y velocity of flume

mixture of each part of the foam. This system also calculates the exact amount of foam required to fill each mold and meters out that amount so that the technician cannot overfill or under fill the mold. The foam expands and sets up within 10 minutes. Once the foam is cured, the mold is unclamped and the preform is removed from the mold and the next preform can then be made

In order to combine all the pieces into one disk, the sides of the pre-form are wetted out and joined together with a piece of fabric in between them. A mount is made to hold the pie pieces into place; this not only makes sure the pie pieces are in the right spot but also helps to make it easier to flip the disk during the fiberglass phase.

The entire disk (see Fig. 11) is squeezed together by placing a ratchet strap around the outer edge of the disk and tightening allowing all pieces to move into place and allows a perfectly circular hole in the center. The surface of the disk and fiberglass strips of 183-cm (72-in) long and 56-cm (22-in) wide are wetted out and placed across the disk. The disk is flipped and the process is repeated. This whole process is repeated, rotating the disk, until the entire disk is covered. The disk is then perfected by filling the low spots with Bondo. The entire disk is then spray painted to locate low spots on the surface of the disk, which is accomplished by sanding after the paint is dry leaving the only paint in the low spots.

Once the first disk is complete mold construction begins. A flange made of plywood pieces is attached to the edge of the disk along the entire circumference. The plywood pieces are hot glued into place. The wooden flange is then covered in packing tape. One of the sides is then covered with mold release wax. Seven (7) coats of mold release wax are applied,

by covering the disk in wax, waiting 5 to 10 minutes and then removing the wax and waiting 30 minutes between coats. Once the disk is thoroughly waxed, gel coat is sprayed evenly with a 0.24 linear mils thick layer.

After the gel coat starts to cure, the disk is coated in resin and a layer of mat fiberglass is laid down. Once the resin hardens, 3 more layers of fiberglass are added one at a time, with the second being another layer of mat and the final two layers being normal cloth. Once the disk has 4 layers of fiberglass on it, preform beams and resin are applied to provide structural support. The joints of the beams are covered with strips of fiberglass to help prevent hinging. After all of the resin hardens, the mold is popped off the disk. Damaged areas are repaired with Bondo, and the entire process is repeated to make the second mold. Excess fiberglass is cut off around the flange and the molds are then wet sanded and buffed to a high shine.

The molds (see Fig. 12) are then used to make the other 5 disks. Although the molds save a lot of time and ensure better looking disks, making each one a multi-step process. First, the molds need to be coated with 7 layers of mold release wax then coated in a layer of gel coat 24 mils thick. Next, layers of fiberglass cloth are wetted out with resin and laid over the length of each mold so that the cloth fans out just barely overlapping on the outer edge of the mold and completely overlapping in the center of the mold. Next, each preform is wetted out with resin and one strip of cloth coated in resin is placed in between each preform. The pre-forms are arranged in one half of the mold with the other half of the mold placed on top and the flanges are clamped down. The disk is left to cure for 8-12 hours and then popped out of the mold.

VII. DISCUSSION Upon completion, the test flume will become a major asset

on the Florida Institute of Technology Campus. Not only will the university be able to take advantage of the flumes availability but all major institutions will be able to benefit from its semi-portability and mobility. The flume will also open new doors in the area of model testing. Because the model remains stationary as the tests are conducted, there is much more potential for different equipment to be implemented effectively during tests. Students and professors alike will be able to customize their testing apparatus around the steady flow in the way best suited for them.

The actual construction is underway. The frame, center-divide and motor are assembled. The Tesla disks are being constructed and the whole system is expected to be assembled by the conference date at the Florida Institute of Technology Campus. The flume is currently planned to become fully equipped and ready for testing by the end of the 2012.

VIII. CONCLUSION The flume has been designed to test ship models and

underwater vehicles as accurately as possible. It has been designed to re-circulate water to create a laminar flow in the test section. This will allow testing throughout the length of the test section and at different depths in the water column. The flume will be portable so that it can be moved at any time if necessary. The Tesla Pump and tank that have been designed to meet all of the engineering requirements and specifications. It has been designed with appropriate factors of safety and will be

Fig.11. Pre-forms

Fig. 12. Tesla Disk Molds

able to withstand the forces and stresses that develop in the individual members of the flume. The flume will be a major asset to the Department of Marine and Environmental Systems, Ocean Engineering and Florida Institute of Technology as a whole. The flume has the potential to improve research and academics in many fields and majors.

IX. RECOMMENDATIONS The flow through the flume will need be experimented on

and fine-tuned to ensure the most accurate results. It will need to be tested throughout the tank to see if eddies or velocity gradients form. While computer programs such as Fluent are a great tool in designing, they cannot be expected to be perfectly accurate in practice, as there are too many factors to take into account.

Testing apparatuses and scaffolding will also need to be constructed to accommodate experiments and students. As the flume begins to be used in research improvements needing to be made may become evident in different areas and systems. Brackets for instrumentation could be constructed. For instance, the slides required for mounting wave gauges could be installed to allow the monitoring of the free surface elevation possible during testing. A platform needs to be built over the top of the flume to accommodate moving models in and out of the flume and prevent people or debris from falling into the tank.

Finally improvements to the design will undoubtedly be made in the future, as more funding becomes available to future senior design teams. The sheer size of the flume and the

materials that it is constructed of make building the flume more expensive and time consuming than many other senior design projects on campus.

REFERENCES [1] N. Tesla, “Tesla Turbine,” U.S. Patent 1 061 206, Jan. 17, 1911. [2] Nikola Tesla Disk Turbine Pump. RexResearch.[Online].

Available: http://www.rexresearch.com/teslatur/teslatur.htm, [Accessed: Apr. 10, 2012]

[3] DiscFlo Disc Pumps. DiscFlo Corporation. 2011[Online]. Available: http://www.discflo.com/, [Accessed: 10 April. 2012].

[4] Flume. Department of Physical Education, University of Otago, New Zealand. [Online]. Available: http://physed.otago.ac.nz/about/virtual.html, [Accessed: Apr 12, 2012].

[5] AquaBioLab, AquaBioTechInc, Apr. 2011. [Online]. Available: http://www.aquabiolab.com/en/products/flumes_systems/benthicflume.shtml, [Accessed: Apr. 8, 2012].

[6] C. Cawood, “New method for the hydrodynamic evaluation of ship hull coatings.” M.S. Dissertation, Department of Marine and Environmental Systems, Florida Inst. of Technology, Melbourne, Fl, 2009.

[7] B. Munson. Fundamentals of Fluid Mechanics. 6th ed. U.K.: John Wiley and Sons, 2010.

[8] J. Nelka. “Evaluation of a rotating disk apparatus: drag of a disk rotating in a viscous fluid.” Naval Ship Research and Development, 1973.

[9] T. Bruger et al, “eFlow final report”, Florida Institute of Technology: Melbourne, FL, 2011. unpublished