Bladeless turbine
...
Yeah, it's interesting that Beans' 1961 analytical efficiency was less than his experimental. Also interesting is that Schmidt reported Beans' 1966 efficiency result as twice as his 1961 result, reflecting other experimenters (Rice, Schmidt, Singleton, Huybrechts) results so maybe Beans' 1961 results were flawed. Just now, I discovered Beans' 1966 paper in ttt 1-50.pdf which I believe I sent you a link of. The xerox copies in that pdf are terrible. But I suspect Beans' 1966 paper will indicate flaws in the 1961 experiment.
...
Elliot,
two attachments here and four links below - the last link is pdf photocopies of a Bean article I think.
Biomass Boundary Layer Turbine Power System - final report (pdf)
Tesla Turbo Machinery - Warren Rice
Numerical Simulation of the Flow Field in a Friction-Type Turbine (Tesla Turbine)
Performance Characteristics of a Friction Disc Turbine (pdf)
Marcin Jakubowski
You said that you have access to machining. Can you build the Tesla
turbine and see for yourself? We can crowd-fund materials if you make
a concrete proposal.
This is still an open question - regarding its performance. There
appear to be conflicting messages on efficiency. Have you come to any
further progress on resolving these issues?
Marcin
> A Qualitative Analysis of the Tesla Turbomachine
>
> Glenn A. Barlis
>
> Copyright 2001
>
>
>
>
>
> Introduction
>
>
>
> The Tesla Turbine is a form of centrifugal turbomachine that uses fluid
> viscous shear to effect energy transfer between the fluid and parallel rotor
> disks instead of impulse and reaction transfer between fluid and blades as
> in the typical turbomachine.
>
>
>
> This paper provides a qualitative analysis of the Tesla turbomachine by
> comparing it to the traditional centrifugal compressor/turbine. Contrary to
> the impression of some, the operating mechanism of the Tesla turbomachine is
> well understood and documented in the literature. The fact that there are
> few commercial implementations of the machine and no well defined design
> rules published has led to claims of extraordinary capability of the machine
> or suspicion of conspiracy of technology suppression. The more mundane
> explanation for the lack of commercial implementation of the Tesla machine
> is that there are strong commercial reasons for traditional manufacturers of
> turbomachines to continue to use a well defined design methodology. The
> Tesla machine offers no compelling advantage for established manufacturers
> to switch designs for the majority of applications. The bladed turbomachine
> design has been refined to the point where compressor efficiencies of more
> than 90% are now possible at relatively low cost with modern materials and
> manufacturing techniques.
>
>
>
> The Tesla turbomachine does offer some interesting possibilities for the
> individual experimenter wishing to build a machine. The simplicity of the
> design lends itself to construction with available tools and the machine can
> run with a wide variety of fluids. This paper is written with the individual
> builder in mind. It provides the designer an outline of the technical
> factors to be considered in designing and building a Tesla turbomachine. It
> also offers an explanation of the theory behind the design factors.
>
> Fluid Flow Principles
>
>
>
> First some basic fluid principles will be reviewed to serve as a basis for
> the rest of the discussion. English units of measure will be used
> throughout.
>
>
>
> Fluids have a number of properties that should be understood. Since we are
> using English units we have to distinguish between weight and mass. Weight
> is the gravitational force exerted on a body by the earth. Mass is an
> inherent property of a body. Mass has units of pounds-sec2/ft. The
> acceleration of gravity is represented by (g) and has the value of 32.2 ft/
> sec2. The slug is the unit of mass (m) in the English system and is equal to
> 32.2 pounds weight in standard gravity. We will see the g term in our
> equations since the mass of a body is used in Newton's equation of motion
> but we make measurements by weight. Dividing the weight by g will give us
> mass.
>
>
>
> Specific weight ( g ) is the weight per unit volume. Pounds per cubic foot.
>
>
>
> Density ( r ) is the mass per unit volume. r = g/g
>
>
>
> Specific gravity of a fluid is a ratio of the weight of the fluid to an
> equal volume of water at a standard temperature and pressure. It has no
> dimensions.
>
>
>
> Fluid flow can be laminar defined as the case where the particles move in
> parallel layers. As the velocity increases above some critical value the
> fluid becomes turbulent where the particle motion is no longer steady but
> varies in magnitude and direction. For fluids with relatively low viscosity
> (water, air) the behavior is dominated by inertia forces described by
> pressure. There will be a thin layer near the surface of a body where the
> velocity change is very large as a result of the adhesion and viscosity of
> the fluid. This is called the boundary layer.
>
>
>
> Viscosity (m) is defined as the resistance to flow of a fluid. It is
> expressed as the ratio of the shearing stress (t) or force between adjacent
> layers of the fluid to the rate of change of velocity (V) of the fluid
> perpendicular to the direction of motion.
>
>
>
> m = t / ¶V/¶y
>
>
>
> This is called the absolute viscosity and has units of mass per ft-sec. The
> concept is familiar - molasses has a higher absolute viscosity than water
> for example.
>
>
>
> An equally important characteristic of fluid for turbomachine design is the
> kinematic viscosity (n) defined as the absolute viscosity divided by the
> mass density.
>
>
>
> n = m/r = mg/g
>
>
>
> This is not as intuitive a measure as absolute viscosity. For example, air
> under standard conditions has a higher kinematic viscosity than water due to
> its lower density. In the development of the fluid dynamic equations for
> turbines, the energy transfer is found to be related to the kinematic
> viscosity. If you are thinking in terms of absolute viscosity, your
> intuitive expectation of the operation may not be correct. The kinematic
> viscosity is a critical factor in calculating the disk spacing in a Tesla
> turbomachine.
>
>
>
> The viscosity of a fluid is affected by its temperature. Because of the
> molecular interactions, the viscosity of most liquids decreases with
> temperature, while the viscosity of a gas increases with temperature.
>
>
>
> The Reynolds Number ( NR) is a dimensionless number that is a useful
> descriptor of flow resistance.
>
>
>
> NR = Vd/n
>
>
>
> where V is the fluid velocity and d is some characteristic dimension of the
> passage through which the fluid flows. A large Reynolds Number (> 2500)
> indicates turbulent flow.
>
>
>
> Continuity is the concept that under steady flow conditions the mass of
> fluid passing any point in a system is constant.
>
>
>
> gAV = constant = weight flow in pounds per second
>
>
>
> For liquids the specific weight is essentially constant so
>
>
>
> Q = AV
>
>
>
> where Q is the volume flow rate, A is the cross-section area, and V is the
> fluid velocity.
>
>
>
> Head is a measure of the energy of a unit mass of the fluid and can be
> defined as the height to which a column of fluid must rise to contain the
> same energy as the fluid in a given set of conditions. This is a simple
> intuitive concept as we can think of the energy a pump puts into a liquid as
> the height to which the pump can raise the liquid.
>
>
>
> Potential head is the height of the fluid above some reference plane. It has
> energy because of its position (z). This term is significant when working
> with liquids but is typically ignored as insignificant when work with a gas.
>
>
>
> Velocity head or kinetic head is the energy in the fluid due to its motion.
> The energy is the common expression for kinetic energy
>
>
>
> H = V2/2g
>
>
>
> Pressure head is the energy contained in a fluid due to its pressure.
>
>
>
> H = P/g
>
>
>
> Bernoulli's Theorem says that the total energy in a fluid is a constant,
> neglecting any losses in transmission.
>
>
>
> H = V2/2g + P/g + z
>
>
>
> As a fluid enters a narrow passage in a pipe, for example, the velocity
> increases (continuity equation) and the pressure therefore drops. This is a
> good approximation for liquids at low velocities but the error gets larger
> for high velocities because of the losses due to friction and turbulence.
> These losses increase approximately with the square of velocity and depend
> on factors such as passage roughness, abrupt changes in dimension, length,
> etc.
>
>
>
> A Streamline or Stream tube is a useful visual aid for discussing fluid
> flow. It is an imaginary line or volume where the average velocity of the
> fluid is the same. The streamline could represent the actual particle flow
> for laminar flow. For turbulent flow it represents a time averaged constant
> approximation. These are useful in defining geometrically how the continuity
> equation is satisfied.
>
>
>
> The simplest case is for fluid flowing in a straight pipe of constant cross
> section. The streamlines will be straight lines and, assuming no friction,
> the velocity is the same at all points.
>
>
>
> If a fluid flows radially between two disks, the continuity equation says
> that
>
>
>
> Q = 2pRbVr
>
>
>
> R is the radius, b is the distance between the plates, and Vr is the radial
> velocity at R. For any stream tube
>
>
>
> Q/2p is constant
>
>
>
> so that
>
>
>
> RbVr = constant,
>
>
>
> and if the disks are parallel
>
>
>
> RVr = constant
>
>
>
>
>
> We can also look at the case where the fluid flowing between disks is purely
> rotary, that is it has no radial component but flows tangent to a given
> circumference. It can be shown that in this case
>
>
>
> RVu = constant
>
>
>
> R is the radius and Vu is the tangential velocity. The velocity distribution
> is hyperbolic, the velocity being lower at larger radius.
>
>
>
> In a Tesla turbine the flow has both radial and tangential components. By
> superimposing the two cases we get the resultant velocity
>
>
>
> Vr/Vu = constant.
>
>
>
> This describes a logarithmic spiral; the path of the fluid within the disks
> and also after it leaves the disks. If the disks are not parallel, but
> diverge with radius, the radial component decreases more rapidly and the
> spiral is "tighter" than the log spiral.
>
>
>
>
>
>
>
> Centrifugal Machine Basics
>
>
>
> As mentioned in the introduction, the Tesla turbomachine is a type of
> centrifugal turbomachine. As such, its gross operation can be described by
> the fundamental equations for turbomachinery based on energy and momentum.
> This is a critical point. The basic equations describing the operation of a
> turbomachine are derived from first principles and are independent of the
> actual mechanism by which the fluid interacts with the rotor. The fluid
> mechanics and thermodynamic equations are equally valid for a bladed radial
> turbine, an axial turbine, a mixed flow turbine or a Tesla turbine. The key
> equations and their significance will be described.
>
>
>
> The ideal virtual head (also called fluid head) for a machine can be
> described in terms of three sets of velocities. The ideal head ignores
> turbulence and friction.
>
>
>
> Let u1 = tangential velocity of the fluid at radius 1
>
> u2 = tangential velocity of the fluid at radius 2
>
> v1 = relative velocity of the fluid at radius 1
>
> v2 = relative velocity of the fluid at radius 2
>
> V1 = absolute velocity of the fluid at radius 1
>
> V2 = absolute velocity of the fluid at radius 2
>
>
>
> Then
>
>
>
> H = (u22 – u12 + v22 – v12 + V22 – V12)/2g
>
>
>
> This equation, known as the Euler turbomachine equation, is useful for
> understanding what is happening internally in the machine. The absolute
> velocity is the velocity of the fluid as seen from outside the machine. The
> relative velocity is as seen relative to the rotating component. The
> tangential velocity is normal to a radius. It should be noted that these
> velocities are vector quantities, that is, they have both magnitude and
> direction. The convention used is that a positive sign for the head value
> means the fluid is doing work on the rotor (a turbine) and a negative sign
> means that the rotor is doing work on the fluid (a pump). By doing the
> vector math we can show that the virtual head equation can be simplified to
>
>
>
> H = (u2Vu2 – u1Vu1)/g
>
>
>
> where Vu1 and Vu2 represent the tangential component of the absolute
> velocity. Only the tangential component can produce torque by definition. A
> simplifying assumption that is used for first approximation is that the Vu
> term is zero at the smaller radius ( pure radial flow). This reduces to
>
>
>
> H = (uVu)/g
>
>
>
> We must multiply the head by the flow rate (w) to get the actual energy of
> the system.
>
>
>
> E = wH
>
>
>
> The horsepower (English units) is defined by
>
>
>
> HP = (u2Vu2 – u1Vu1)w/550g
>
>
>
> where w is the fluid flow rate in pounds per second.
>
>
>
> Torque is the product of force times a radius. The tangential component of
> the momentum produces a force on the rotor so the torque can be calculated
> as
>
>
>
> T = (R2Vu2 – R1Vu1)w/g
>
>
>
> Which agrees with the power equation since
>
>
>
> w = u/R and HP = wT/550
>
>
>
> where w is the angular velocity.
>
>
>
> Notice that for a centrifugal machine the equations tell us that we want to
> have the fluid input be at the smaller radius for a pump/compressor and at
> the larger radius for the turbine.
>
>
>
> The above equations are for an ideal machine of any configuration and
> mechanism. They are useful for understanding machine operation and can be
> used for preliminary design using a lot of assumptions. The problem with
> these equations for design and analysis of actual machines is that these are
> component velocities and can not be easily measured. Remember also that
> these are vectors so we need both the magnitude and direction of the fluid
> velocity. In a real machine we can not easily measure these. When designing,
> we can assume some values but these have to be based on experience or first
> principles. If based on experience then we need practical examples with all
> of the other extraneous factors (discussed later) accounted for. An analysis
> based on first principles means working with complicated partial
> differential equations (Navier-Stokes). But for understanding qualitatively
> what is going on, these equations are very helpful.
>
>
>
> Looking at the expanded version of the Euler equation we see that it has
> three components. (This discussion will be presented from the pump point of
> view.)
>
>
>
> (V22 – V12)/2g is the dynamic head or head due to the change in kinetic
> energy of the fluid. In a centrifugal pump this is usually a large part of
> the output energy. Since we typically want static head from a pump, the
> dynamic head has to be transformed into static head by a diffuser mechanism.
> A diffuser operates on the Bernoulli principle by providing an expanding
> area to slow down the fluid and increase its static head.
>
>
>
> The second term (u22 – u12)/2g represents the centrifugal head. This is the
> energy added to the fluid by moving it from a smaller to a larger radius.
>
>
>
> The third term (v22 – v12)/2g called relative head, is the change in the
> kinetic energy due to the change in relative velocity. This results in a
> change in static head within the impeller rotor.
>
>
>
> When working with actual machines, the thermodynamic equations described
> later are much more useful in terms of measuring and evaluating performance.
> For now we will use the above equations to discuss how a turbomachine
> operates and how deviations from the ideal affects performance and design.
>
>
>
>
>
> Conventional Centrifugal Machine Analysis
>
>
>
> The ideal machine described above assumes frictionless, non-turbulent
> continuous flow. In a real machine these assumptions are not true so that
> for a given flow rate the head will be less and the power required for the
> pump higher. The individual effects are difficult to calculate from theory
> and imperical coefficients based on experiments and similarity are used in
> design. Let's look at some of the causes.
>
>
>
> The impeller vanes are optimally designed to transfer momentum between the
> fluid and rotor by impulse and/or reaction. It is the change in momentum of
> the fluid through the machine that produces torque. The blades operate on
> the same principle as an airplane wing, producing a force (lift) as a result
> of deflecting the fluid by impact (impulse) and velocity/direction change
> due to pressure differential around the blade (reaction). When the machine
> operates at other than the design condition (called off-design), the
> efficiency drops off. There are a number of reasons for this.
>
>
>
> Loss of head occurs because of friction. This can occur anywhere within the
> machine where the fluid comes in contact with the parts – input, impeller,
> diffuser and case. Friction losses increase approximately as the square of
> fluid velocity with respect to the machine surface. The machine volume is
> constant so this also means that the friction loss increases with the square
> of the flow rate. The factors that affect the friction loss are the wetted
> area and surface roughness. The wetted area should be kept as small as
> possible and surfaces as smooth as possible.
>
>
>
> Turbulence occurs throughout the machine because the Reynolds Number is
> always well above the critical value for practical flow rates.
>
>
>
> Circulatory flow occurs in the space between the vanes of the impeller
> because a pressure difference occurs across the vane. This flow reduces the
> throughput flow rate and affects the angle at which the fluid leaves the
> impeller. The impeller is a 3 dimensional device so this flow is complex and
> is turbulent. Increasing the number of vanes can reduce the circulatory flow
> but increase wetted area and reduces the total area, thus restricting flow.
>
>
>
> Disk friction is a specific frictional component that adds to the shaft
> power requirement in a pump. It is due to the circulatory flow between the
> impeller rotor and the case. Disk friction is a combination of the fluid
> friction and the power required to "pump" the circulating flow. It goes up
> as a 5th power of rotor diameter and the 3rd power of rotor speed. It can be
> minimized by keeping the gap between rotor and case small and the surfaces
> smooth. For a given peripheral speed, a smaller diameter rotor operating at
> higher RPM has less disk friction than a larger diameter rotor.
>
>
>
> Leakage can occur around the machine elements and this reduces the flow
> capacity of the machine. Wear rings and/or labyrinth seals are used to
> minimize leakage.
>
>
>
> The wear rings, bearings, and other mechanical friction points creates
> mechanical losses that are reflected in the shaft power. These losses are
> relatively invariant with speed.
>
>
>
> It is a starting design assumption that the fluid direction at the small
> radius of the machine is purely radial. This is the inlet of a pump or
> outlet of a turbine. In practice, the fluid tends to have pre-rotation
> because of the vortex created by the shaft and impeller rotor. This results
> in a reduction of head and the impeller speed has to be increased to get to
> the desired head. Guide vanes might be employed to reduce the pre-rotation
> but they introduce friction that can eliminate their advantage. Centrifugal
> rotors have curved input vanes to reduce the pre-rotation effect. They are
> called inducers in a compressor and exducers in a turbine.
>
>
>
> Efficient diffuser design is important to get the desired static head from
> the machine. The velocity head has to be transformed to static head with
> minimal friction and turbulence. This is not easy to do since the fluid is
> going from a lower to higher static pressure region. Separation can occur
> resulting in turbulence and no pressure recovery. A condition called stall
> can occur when the turbulent flow prevents diffusing action. It is easier to
> efficiently convert pressure into kinetic energy using a nozzle because the
> flow from a higher to lower pressure region can be kept less turbulent.
>
>
>
> One of three types of diffuser designs can be used. The simple scroll volute
> has an increasing cross-section area that slows down the fluid. It is
> generally used with pumps. It requires a fairly large diameter around the
> impeller. The annular diffuser use a radial annular space around the rotor,
> The area increases with the radius and slows down the fluid which then goes
> into a collector pipe. The fluid in the diffuser space flows in the spiral
> path described earlier. Annular diffusers can also require a large space but
> are often used in blowers and compressors, sometimes in conjunction with a
> scroll volute. The fluid velocities are typically higher in these machines
> and the annular diffuser lowers the fluid velocity before the collector to
> reduce turbulence and subsequent head loss. The vane diffuser is used to get
> maximum performance in the smallest space. A series of curved vanes are
> spaced around the rotor. The curvature and diverging space between the vanes
> recovers the static pressure. There is an interaction between the diffuser
> vanes and the impeller blades that can introduce turbulent losses. The
> number of diffuser vanes is picked so that it is not a multiple of the rotor
> blades so as to minimize pulsing effects.
>
>
>
> The final condition that will be mentioned is surging. If you plot pressure
> vs. flow for a compressor you will see the pressure increase with flow rate
> up to a maximum and then the pressure starts to drop off with increasing
> flow. The maximum pressure occurs near the flow point where turbulence is a
> minimum. At lower flow rates the turbulence increases as the flow decreases.
> At flow rates beyond the pressure peak both turbulence and friction losses
> increase causing the pressure to drop off. The normal operating point is to
> the right of the pressure peak (higher flow rate). As the flow is reduced it
> will go through the pressure peak and the flow rate will suddenly reverse
> direction and drop to a low flow lower pressure condition. It then builds up
> again only to have the cycle repeat. This is the surge condition and besides
> giving poor performance can lead to equipment damage.
>
>
>
> There are a variety of efficiencies that can be defined. You have to be sure
> that you know the definition when you speak of efficiency. Here are some of
> the more common ones used for pumps.
>
>
>
> Actual measured head
>
> Hydraulic Eff. =
> -------------------------------------------
>
> Head imparted to fluid by
> impeller
>
>
>
> This is less than 100% due to friction and turbulence losses.
>
>
>
> Delivered weight of fluid
>
> Volumetric Eff. =
> -------------------------------------------
>
> Delivered weight plus
> internal leakage
>
>
>
> Mass flow rate times head
>
> We need Fluid HP = --------------------------------
>
> 550
>
>
>
> to define
>
>
>
> Fluid horsepower
>
> Overall Eff. = --------------------------------
>
> Shaft horsepower
>
>
>
> This is less than 100% because of leakage, disk friction, friction and
> turbulence, and mechanical losses.
>
>
>
> Turbines
>
>
>
> The above description concentrated on the pump/compressor operation. Most of
> what was described also applies to turbine operation. By convention the
> sign of the energy equation will be positive for the turbine. Fluid enters
> at the larger radius and exits at the smaller. One difference is that the
> centrifugal energy term creates a pressure gradient in the rotor that
> opposes the inward flow of the fluid instead of aiding outward flow as in
> the case of the pump. A turbine creates shaft power by the momentum change
> of the fluid as it passes through the turbine going from a higher energy
> state to a lower energy state.
>
>
>
> A useful term for classifying turbines is Reaction. This is defined as
>
>
>
> Centrifugal head + Relative
> head
>
> Reaction =
> ----------------------------------------
>
> Total head
>
>
>
> A turbine that has a reaction of zero is called an impulse turbine. In this
> type of turbine the pressure energy of the fluid is converted to kinetic
> energy in a nozzle external to the turbine rotor. There is no further
> kinetic conversion within the rotor so the total head across the rotor is
> just the centrifugal and relative head terms. The case pressure for this
> type of turbine is near ambient. Even though the case pressure is low, good
> seals and close clearances should be used to reduce disk friction and
> leakage losses.
>
>
>
> A turbine that has a reaction other than zero is called a reaction turbine.
> In this design not all of the fluid pressure is converted to kinetic energy
> in the nozzle and some expansion of the fluid (pressure drop) occurs within
> the rotor. This type of turbine has a positive case pressure and must have
> good seals.
>
>
>
> Impulse turbines use a converging/diverging nozzle design to achieve maximum
> kinetic energy. They are usually employed in pairs at opposite ends of a
> diameter to create a pure couple with the rotor and minimize bearing radial
> forces. Impulse turbine designs are popular for steam use because the steam
> pressure from a boiler can be efficiently converted to kinetic energy in a
> nozzle.
>
>
>
> Reaction turbines use a volute and/or nozzle ring (similar to a vane
> diffuser) to direct the fluid into the rotor at the design angle. The
> turbine of low cost turbochargers used in autos typically just use a volute.
> Higher performance units employ a nozzle ring. Gas turbines and many steam
> turbines are designed as reaction turbines. A popular design point is 50%
> reaction; that is, half the expansion takes place in the nozzles and half in
> the rotor.
>
>
>
>
>
> Thermodynamics of Turbomachines
>
>
>
> A very brief discussion of the important concepts of thermodynamics
> applicable to a turbomachine will be given here. A thermodynamics text
> should be consulted for the details and examples of turbomachine
> thermodynamics.
>
>
>
> The first law of thermodynamics is that of the conservation of energy. This
> says that in a closed system (neglecting nuclear reactions) energy is
> neither created nor destroyed. It may be converted into different forms, but
> this is essentially a bookkeeping operation. The steady flow energy equation
> is used for a turbomachine and uses the concept of a control volume. A
> control volume is a boundary drawn around a machine and we account for all
> of the energy that crosses the boundary. For a turbomachine this consists of
> the fluid flows in and out, the shaft work (in or out) and the heat flows in
> and out. The steady flow energy equation is
>
>
>
> Z1 + U12/2g + JH1 + Win +JQin = Z2 + U22/2g + JH2 + Wout +JQout
>
>
>
> In this equation Z is the elevation, U is the fluid velocity, H is the
> enthalpy of the fluid, W is the shaft work, and Q is the heat energy. J is a
> multiplier called Joule's equivalent used to convert heat energy into the
> equivalent mechanical energy. The enthalpy is the measure of internal energy
> and pressure energy in the fluid expressed in BTU/pound. Enthalpy values are
> available in property tables for the fluid. The Z term can be dropped as
> insignificant when working with a gas and the equation can be simplified to
>
>
>
> U12/2g + JH1 + Wnet +JQnet = Z2 + U22/2g + JH2
>
>
>
> This equation alone does not contain everything needed to evaluate the
> turbomachine process. You also need the second law of thermodynamics. This
> can be stated in many ways. The simplest way to think of this is that heat
> does not flow by itself from a lower temperature to a higher temperature.
> You have to do work to make this happen (think of a refrigerator). The
> second law is associated with two key concepts, the availability of energy
> and the concept of reversibility. The availability of energy refers to the
> maximum amount of energy that a given process can convert to work.
> Reversibility refers to the ability to reverse a given thermodynamic
> process. For example of a reversible process, use the shaft work from a
> turbine to drive a compressor to recompress the gas used to drive the
> turbine. There are no pure reversible processes in the real world because of
> all the losses we described earlier. So in this example we would need to add
> shaft work to the system as it would not run by itself as a perpetual motion
> machine. [ Note: These two laws deny the possibility of a perpetual motion
> machine (or over unity machine as they are now called by their proponents
> since perpetual motion is rightly ridiculed). Applying the concept of the
> control volume and careful measurement of all energies is used to debunk
> perpetual motion machines.]
>
>
>
> The second law leads to the concept of entropy. This is a state property of
> a fluid, like enthalpy, that can be found in fluid tables. By using the
> known properties of the fluid entering and leaving the control volume, the
> energy equation can tell us the work and heat changes. By comparing the
> measured values vs. the theoretical available energy the thermodynamic
> efficiency of the process can be calculated.
>
>
>
> Here is an example: (this is taken from "Eshbach's Handbook of Engineering
> Fundamentals").
>
>
>
> A turbine expands air from an initial temperature of 1660 deg Rankine and 5
> atmosphere pressure to 1 atmosphere. The turbine efficiency is 95%.
> Determine the horsepower developed per pound of airflow per second assuming
> isentropic conditions (constant entropy).
>
>
>
> Using standard air tables, the enthalpy and entropy conditions are found at
> the initial condition and for the gas leaving the turbine. The theoretical
> work can be shown to be equal to the enthalpy drop in the fluid. Using the
> energy equation, this is found to be
>
>
>
> W = (H1 - H2)J = (411.82-262.22)778 = 116,388.8 ft-lbs./sec
>
>
>
> HP = W * eff./550 = 201 HP
>
>
>
> Using a similar process you can calculate the efficiency of a machine using
> the measurement of the shaft work, the input pressure and temperature and
> the outlet temperature and pressure. It is important to note that the
> temperatures used here are the absolute temperatures (Rankine) not the
> common Fahrenheit scale. Also the temperatures and pressures are the total
> or stagnation values which take into account the velocity of the fluid. You
> must use care and proper technique in making these measurements to get
> accurate answers.
>
>
>
> One other concept will be briefly mentioned. The turbine is only one
> component of a total energy system. To properly evaluate the whole system
> you need to understand the concept of the thermodynamic cycle. For example,
> the turbine may be the prime mover in a steam generator. This application
> would be based on some variation of the Rankine cycle. If it is part of a
> gas turbine then the operation would be based on the Brayton cycle. Internal
> combustion engines are based on the Otto cycle (gasoline) or Diesel cycle.
> The Carnot cycle is the standard against which other cycles are judged. You
> cannot exceed the efficiency of a Carnot cycle. There are an infinite number
> of possible cycles, but only a few of engineering significance. The concept
> of entropy aids in understanding these cycles. You must have a good
> grounding in cycle concepts to make sense of heat engine applications.
>
>
>
> This brief introduction to thermodynamics is given to provide insight into
> the practical issues needed to test and evaluate turbomachines. Consult an
> engineering thermodynamics text for a more thorough understanding. A good
> understanding of thermodynamics will keep you from chasing will o' the wisp
> ideas that have no sound scientific basis.
>
>
>
> The Tesla Turbomachine
>
>
>
> The only difference between the Tesla turbomachine and the conventional
> bladed turbomachine is the mechanism used in the rotor to effect energy
> transfer. All of the equations and description of operation given above
> apply equally to the Tesla turbomachine. This means that anyone building a
> Tesla machine should follow all of the engineering best practices for
> bearings, seals, diffusers, inlet design, etc. used on conventional
> centrifugal machines. The theory of the centrifugal machine described above
> was well understood when Tesla created his machine. Tesla's patents describe
> the operation of his machine and a careful reading of them will show that
> his description matches what is given above.
>
>
>
> Tesla was an intuitive genius and he attacked the problem of creating a
> better turbomachine by trying to eliminate what was the considered the key
> deficiency of the machines of his time. Efficiencies of turbomachines were
> low because the aerodynamic theory needed to do the proper analysis of flows
> was not available. In addition, the engineering materials of the time put
> severe limitations on operating speeds and temperatures and the
> manufacturing processes were not as advanced as needed. The continued
> development of the knowledge and technologies for the bladed centrifugal
> design in the intervening period has overcome these early deficiencies.
>
>
>
> The brilliance of Tesla's design is that he sidestepped these issues by
> creating a rotor that eliminated or minimized the major problems of the
> bladed centrifugal impeller. The design does have some limitations of its
> own however because of shear losses and flow restrictions.
>
>
>
> As we saw in the analysis of the bladed rotor, the fluid is forced to follow
> the path between the blades. The circulatory flow that results from the
> design reduces flow and creates turbulence. There are also turbulent flow
> issues as the fluid leaves the impeller.
>
>
>
> Tesla design has the fluid flow between two parallel disks in which the gap
> is small enough to limit the flow to boundary layer conditions. If the flow
> rate is limited, the result is laminar flow. The energy transfer takes place
> by the shear forces between fluid and rotor. Tesla described the process as
> utilizing adhesion and viscosity, but this is just a description of the
> fluid boundary layer. Prandtl was developing the theory for boundary layers
> at about the same time that Tesla was developing his turbine. Boundary layer
> theory comprehends both the adhesion and viscous effects and you now often
> hear the Tesla design referred to as a boundary layer machine.
>
>
>
> There are no blades so the fluid is free to take the natural course through
> the rotor (except for the rivets holding the disks together). This is a
> spiral path as described earlier. The shape of the spiral, as we saw,
> depends on the relation between the radial and tangential velocity
> components. A lightly loaded rotor will have a tight spiral and a fluid
> element will take many turns before exiting the rotor. This is because the
> rate of change in radial velocity is small due to the small energy transfer.
> The momentum change in the fluid will be small and this will be a condition
> of high efficiency. As the load increases, the energy transferred increases
> and the rate of change in the fluid radial velocity increases. As a result,
> the fluid will move more rapidly toward the rotor exit. This will shorten
> the spiral path length. The momentum change of the fluid will be greater and
> the efficiency will be less because of increased shear losses. The peak
> turbine power transfer for a machine operated in the impulse mode will occur
> when the entering fluid velocity is two times the rotor peripheral velocity.
> This can be seen when the equation is differentiated because the kinetic
> energy component is related to the square of the velocity.
>
>
>
> One way to think about Tesla's design is as a centrifugal turbomachine with
> an infinite number of infinitely thin blades that automatically adjust to
> the proper shape for the flow conditions. Turbulence and circulatory flow
> seen in the bladed turbine are eliminated since the design forces the fluid
> to operate at laminar flow in the boundary layer. The momentum transfer
> occurs by the mechanism of shear stress between the fluid and the rotor
> surface.
>
>
>
> Theoretical models of the Tesla turbomachine have been developed and provide
> design guidance needed to develop practical machines. The papers describing
> this work are given in the references at the end of this paper. The
> experimental turbomachines described in these papers do not necessarily
> represent the best engineering design and are acknowledged as such. What is
> clear from these papers is that the Tesla design is practical, works as
> described, capable of good efficiency, high power density and may have some
> advantages in certain applications. It is also clear from this work that the
> Tesla machines advantages are found in relatively small size, low flow rate
> applications. Don't expect to see a Boeing airliner or a 100 megawatt
> electrical generator powered by a Tesla Turbine.
>
>
>
> The analysis done by Pohlhausen, and independently by Rice, provides the
> description of operation of the Tesla machine. Here are some of the key
> design considerations.
>
>
>
> The disk gap is a critical parameter in the design. The analysis by Brieter
> and Pohlhausen shows that the optimum gap size to maintain the boundary
> layer is
>
>
>
> D = pi * √(n/w)
>
>
>
> Where D = gap size, n = fluid kinematic viscosity, and w = rotor angular
> velocity.
>
> Here are some representative values of rotor spacing in inches using this
> equation for a rotor running at 10,000 RPM with different fluids.
>
>
>
> Water @ 70 deg F 0.004
>
> Saturated Steam @ 212 deg F 0.017
>
> Air @ 600 deg F 0.027
>
> Air @ 1160 deg F 0.038
>
>
>
> The various analyses show that the flow rate between the disks must be kept
> relatively low for good efficiency. Logically enough, this says that you
> have to increase the number of disks in proportion to the flow rate.
> Hasinger and Kehrt provide a dimensionless parameter that has essential
> machine data.
>
>
>
> A = qd/nri2
>
>
>
> Where q = flow rate, d = disk gap, n = kinematic viscosity, ri = inlet
> radius
>
>
>
> The parameter A should be on the order of 10 to 20 and the outer radius
> should be at least 2.5 times the inlet radius based on a plot of the
> equation from which A is derived. The flow rate for a single disk gap can be
> calculated using the equation and that data used to determine how many disks
> are required for a given flow through the pump or turbine.
>
>
>
> The two equations given above essentially provide all of the information
> that is uniquely needed to design a Tesla machine. All other design
> information needed is the same as for any centrifugal turbomachine.
>
>
>
> For a pump the energy transfer efficiency is poor at the inner radius and
> improves as you move out toward the outer radius. This is a function of the
> difference in fluid tangential velocity and disk speed at the given radius.
> The efficiency would be expected to be worse at the outer radius in a
> turbine for the same reason.
>
>
>
> The theoretical analysis is based on a design that does not incorporate
> rotor spokes or star washers. These act as blades in the region of the pump
> rotor where the efficiency is the poorest and may be expected to contribute
> to the overall output of the Tesla pump at the possible expense of
> cavitation and noise.
>
>
>
> The design of the rotor disk needs to meet several criteria. It should be as
> smooth as possible to maintain the boundary layer. The rotor should be as
> thin as possible to minimize flow disturbance at the edges. On the other
> hand, it must be strong enough to transmit the torque to the shaft and
> maintain its integrity at the operating speed and temperature. The material
> that the rotor is made from must be chosen to meet all of these conditions.
>
>
>
> The fluid condition at inlet and outlet need to be carefully considered for
> the Tesla machine, just as in any turbomachine. Poor diffusion performance
> at either location can reduce the performance significantly. The Tesla rotor
> design is not a cure-all for bad design in the rest of the machine.
>
>
>
> This paper has attempted to meet two needs for those interested in the Tesla
> turbomachine. It has provided the theoretical background of the centrifugal
> turbomachine, of which the Tesla machine is one example. It also has brought
> together some of the key information that is needed to design a Tesla
> machine. Remember that the Tesla machine is a centrifugal turbomachine. It
> is subject to all of the physical laws and design practices of that class of
> machine. It is not magic and it is not going to solve the world's energy
> problems, but it certainly has some interesting possibilities.
>
>
>
>
>
>
>
> References
>
>
>
> Here are the articles and books I used in preparing this paper. Many of
> these are out of print but you may be able to find them in a good university
> library as I did.
>
>
>
> Eshbach's Handbook of Engineering Fundamentals, 4th Edition, Tapley, Byron
> D., Thurman R. Poston (editor), and Ovid W. Eshbach, John Wiley & Sons,
> 1990.
> Book of fundamental engineering data and an excellent summary on
> thermodynamics. You need this if you are designing a Tesla turbine and you
> can only have one book.
>
>
>
> Fundamentals of Hydro and Aerodynamics,
>
> Applied Hydro- and Aeromechanics, Prandtl, L. and O. G. Teitjens,
> McGraw-Hill, 1934
>
> This two volume set is based on Prandtl's lectures and, I believe, was the
> original presentation of his theory in English for engineering use. These
> are now available in paperback from Dover. The first book presents the
> mathematical basis. The second book is aimed at engineering applications and
> has an excellent chapter on experimental methods and apparatus.
>
>
>
> Boundary Layer Theory, Schlichting, Dr. Hermann, McGraw-Hill, 1979.
>
> This book is considered a classic in the field and provides a comprehensive
> treatise on the boundary layer.
>
> Centrifugal Pumps and Blowers, Church, Austin H., John Wiley & Sons, 1944.
>
> This book provides one of the clearest explanations of centrifugal
> turbomachine theory that I have found. The equations and the order of
> representation in this paper were taken from this book.
>
>
>
> The Design of High-Efficiency Turbomachinery and Gas Turbines, 2nd ed.,
> Wilson, David Gordon and Theododios Korakianitis, Prentice-Hall, 1998.
>
> This is one of many in-print books on turbomachines and one of the best at
> providing a clear explanation of the critical issues in designing
> turbomachines.
>
>
>
> "Fluid Propulsion" US Patent 1,061,142 issued 1913, Nikola Tesla
>
> "Turbine" US Patent 1,061,206 issued 1913, Nikola Tesla
>
> These are the two patents by Tesla in which he provides the description of
> his machine. Available on numerous web sites.
>
>
>
> "Laminar Flow Between Two Parallel Rotating Disks", Breiter, Mark C. and
> Karl Pohlhausen, Aeronautical Research Laboratory, Wright-Patterson AFB,
> March, 1962.
>
> This paper provides a mathematical analysis of the Tesla pump operation and
> is the source for the disk gap calculation. Available from 21st Century
> Books.
>
>
>
> "Investigation of a Shear-Force Pump", Hasinger, S. H. and L. G. Kehrt,
> Journal of Engineering for Power, July 1963.
>
> Hasinger and Kehrt were also with the Aeronautical Research Laboratory and
> applied the analysis from Brieter and Pohlhausen to develop a pump design
> that would not have the cavitation problems of conventional pumps. This
> paper has some important design information that applies to Tesla machines.
>
>
>
> Warren Rice of Arizona State University conducted an extensive analysis and
> experiments of the Tesla machine principle for many years. Here are some of
> his papers useful to the Tesla builder.
>
>
>
> "An Analytical and Experimental Investigation of Multiple Disk Pumps and
> Compressors", Rice, Warren, Journal of Engineering for Power, July, 1963.
>
>
>
> "An Analytical and Experimental Investigation of Multiple-Disk Turbines",
> Rice, Warren, Journal of Engineering for Power, January, 1965.
>
>
>
> "Potential Flow Between Two Parallel Circular Disks with Partial Admission",
> Matsch, Lee and Warren Rice, Journal of Applied Mechanics, March, 1967.
>
>
>
> "Experimental Investigation of the Flow Between Corotating Disks", Adams, R.
> and W. Rice, Journal of Applied Mechanics, September, 1970.
>
>
>
> "Flow Regime Definition for Flow Between Corotating Disks", Pater, L.L., E.
> Crowther and W. Rice, Journal of Fluids Engineering, March, 1974.
>
>
>
>
>
> ----
>
> A paper by Hasinger and Kehrt, based on an analysis by Breiter and
> Pohlhausen, provides the following formula for calculating the
> optimum disk spacing:
>
> d = pi* sqrt( nu/omega)
>
> where d = the spacing between the disks
> pi = 3.14159
> nu = kinetic viscosity of the fluid
> omega = angular velocity of the rotor
>
> Notice that the spacing increases with the kinetic viscosity and
> decreases with the angular velocity. Kinetic viscosity increases with
> temperature for gases and decreases with temperature for liquids. The
> fluid conditions and rotor speed at the operating conditions need to be
> determined to specify disk spacing. The actual spacing is a judgement
> call based on the range of speed operation and temperature/density
> changes of the fluid through the rotor.
>
> The table below shows some calculated values of disk spacing for air,
> water, and steam at typical values of temperature and rotor velocity.
> This would be the optimum spacing at the outer diameter of the rotor.
> Steam and air are at 1 atmosphere pressure as would be the case of full
> expansion in a nozzle. For pressures greater than 1 atmosphere divide
> the spacing by the square root of the number of atmospheres (1 atm. =
> 14.7 psi)
>
> Rotor Spacing in Inches
> Rotor RPM Water 70F Sat. Steam 212F Air 600F Air 1160F
> 2000 0.009 0.038 0.060 0.085
> 5000 0.005 0.024 0.038 0.054
> 10000 0.004 0.017 0.027 0.038
> 15000 0.003 0.014 0.022 0.031
> 20000 0.003 0.012 0.019 0.027
> 30000 0.002 0.010 0.016 0.022
> 40000 0.002 0.009 0.014 0.019
> 50000 0.002 0.008 0.012 0.017
>
> Perhaps the most interesting thing in this table is the spacing
> indicated for water. This value is smaller than typically quoted for
> Tesla pumps.
>
>
>
>
--
----
A human being should be able to change a diaper, plan an invasion,
butcher a hog, conn a ship, design a building, write a sonnet, balance
accounts, build a wall, set a bone, comfort the dying, take orders,
give orders, cooperate, act alone, solve equations, analyze a new
problem, pitch manure, program a computer, cook a tasty meal, fight
efficiently, die gallantly. Specialization is for insects.
-- Robert A. Heinlein
...
You said that you have access to machining. Can you build the Tesla
turbine and see for yourself? We can crowd-fund materials if you make
a concrete proposal.
I think its not the best use of my energy right now to try to start that project. Right now I'm focusing on castable refractories for simple rocket stoves or a charcoal making apparatus. Wood chemistry (ie: wood gas, water gas, fischer-tropsch, pyrolysis oil) is a marvelous subject, and so i'm poking around at the very bottom of that ladder. Also, how to mount tensioned mirrors is in second place. starting a turbine (while not yet knowing how to operate a milling machine) is a bit much.
But i think often of being back on the factor e farm and devoting whole day after whole day to working on a project.
This is still an open question - regarding its performance. There
appear to be conflicting messages on efficiency. Have you come to any
further progress on resolving these issues?
nope.
But i agree that once we have steam a turbine will likely show itself. theres all sorts of garage hobbyists better equiped than I who want to see this vision realized.
Also, for those thinking of burning fuel to boil a turbine working fluid, I would want to know more about a solid oxide fuel cell to directly convert steam cracked fuel into electricity.
Josef Davies-Coates
> I think its not the best use of my energy right now to try to start that
> project. Right now I'm focusing on castable refractories for simple rocket
> stoves or a charcoal making apparatus.
Is that like making a rocket stove version of a retort kiln?
Someone was just telling me about retort kilns today and I just saw this:
http://www.instructables.com/id/How-to-Make-some-Charcoal/
They also mentioned using was scraps or corn like this example and
making biochar as a soil conditioner at the same time. Sounds like it
makes sense.
http://www.youtube.com/watch?v=PpozW9039_o
I love to know more about what people know and think about these technologies :)
But I guess I should be asking on open manufacturing rather than here
on solar turbine so I've cc'd there (and the person who was telling me
about retort kilns earlier :) )
Josef.
--
Josef Davies-Coates
07974 88 88 95
http://uniteddiversity.com
Together We Have Everything
...
Is that like making a rocket stove version of a retort kiln?
I guess by rocket stove i just mean a kiln properly designed, with an insulated combustion chamber and a good draft.
Someone was just telling me about retort kilns today and I just saw this:
http://www.instructables.com/id/How-to-Make-some-Charcoal/
Yea, i was thinking of a cylindrical refractory container around a single metal barrel, but then the idea of casting panels makes more sense, so the system could be modular and also easier to carry around and load onto a truck.