Solar Thermal Cogeneration
[Overview] [Program] [System] [Collector] [Turbine] [Generator] [Controller] [Battery]

Bladeless Turbine


A turbine serves as
one of the STC's major Rankine cycle components.  A turbine can have lower maintenance requirements and better efficiency than a reciprocating engine and its torque/speed character is well-suited to electric generation.  Single-stage radial-flow turbines are generally more efficient than single-stage axial-flow turbines.  Radial-flow is effective in small, low-power applications because the rotor diameter can be small, limiting centrifugal forces and allowing the use of efficient nozzles.  In a cogeneration application multistaging is unnecessary because the waste heat out of the turbine is effectively utilized.  Besides, at small scale, the multistaged axial-flow approach runs into material strength problems.  Bladeless turbines are much easier to design and fabricate than bladed turbines and are more tolerant of wet steam.  For these reasons, single-stage radial-flow bladeless turbines are well suited to the STC application.

The single-stage, radial-flow bladeless turbine, or Tesla Turbine, has a number of closely-spaced flat disks mounted on a shaft, driven by a fluid flowing between them, in spirals concentric with the shaft, toward a center outlet.  The energy transfer does not occur through impingement.  Instead, the fluid's energy is imparted to the disks through the force of adhesion.  When the fluid makes contact with a disk its molecules adhere to the disk and resist departure.  The force of the fluid works against the resistance of the disk and some of the fluid's energy imparts to the disk.  The force of viscosity, or adhesion between layers of fluid molecules, enables more fluid to act on the disk than is able to adhere to it.  The layer of fluid which is able to act on the disk through viscosity is called the boundary layerAs the fluid loses energy it is drawn out by the lower pressure in the turbine outlet.  The main disadvantage of the bladeless turbine is low startup torque. 

Energy, Torque, Efficiency

is expended to create a force.  Force in turn does work by moving something some distance (work = force × distance).  Torque is force at a given radius around an axis of rotation (torque = force × radius).  Torque does work by rotating something some angular distance in radians (work = torque × angular distance).  Power is the rate of work or energy flow (power = torque × angular velocity).  According to Tesla's turbine patent [5] the torque is proportional to the fluid velocity squared, the total rotor surface area, and inversely to the disk spacing. 

The target efficiency for the turbine is 40%, so the turbine must convert 40% of the fluid energy differential (difference between fluid energy in and out of the turbine) into shaft work. The turbine rotor efficiency can be as high as 98% and nozzle efficiency as high as 80% but, according to [4], efficient nozzles have been difficult to achieve when integrated into the turbine.  Still, Tesla demonstrated 38% efficiency for the bladeless turbine, which is very competitive with single-stage bladed turbines.  For comparison, reciprocating steam engines are around 20% efficient and turbo-diesel engines around 40%.  

Experiments with prototype turbines published in peer-review journals indicate a somewhat linear relationship between turbine efficiency and rotor rpm. 
At fixed pressures and varying loads, Singleton [8] reported 21% at 5k rpm, 24% at 7k rpm and 28% at 9k rpm.  Schmidt [7] reported (Beans 1966) 24% at 12k rpm and (Gruber 1960) 32% at 15k rpm (also simulated by Huybrechts). Rice (1965) [6] reported 22.5% at 8k rpm, 24.5% at 10k rpm and 26.5% at 12k rpm.  However, Rice (1965), fig 6 indicates two things:  The efficiency peaks as the rpm varies with load, and the peak increases with pressure.  The data suggests that the compressed air-driven prototype may achieve 40% efficiency at around 130 psia and 19k rpm.

Higher efficiencies in turbines are achieved with multi-staging.  Axial-flow bladed turbines are more suitable for multi-staging than bladeless turbines.  But at smaller scales, the axial flow rotors become too delicate and single-stage bladed designs become most practical.  Tesla noted that the bladeless turbine is light, inexpensive and easy to fabricate and can tolerate wet steam that damages bladed turbines.  More recent research notes [4] that the bladeless turbine is quieter, with a flatter acoustic spectrum.  Also important for the STC is the bladeless turbine's economy and ease of fabrication. 

The turbine's power is proportional to speed, so high speed is necessary.  Higher strength materials are needed to withstand strong centrifugal force, and high-speed bearings are required.  Generator efficiency calls for high speed as well so this is a good match. 

Max-power rpm

The turbine reaches max-power rpm when the rotor velocity is 1/2 the fluid velocity [5].  Below max-power rpm, the turbine is overloaded and the fluid passes with excess slip through the rotor, failing to impart maximum available energy.  The velocity component of power is less than required for max-power.  Above max-power rpm, the turbine is underloaded, and the rotor provides less resistance than needed to draw maximum available energy from the fluid.  The torque component of power is less than required for max-power.  The system may adjust the turbine load to achieve max-power when electrical demand is higher and underload the turbine for more efficiency and lower stress when thermal demand is higher. 

Rotor Geometry

Maximum rotor efficiency requires that a laminar boundary layer is maintained in the fluid passing between the disks (see image below).  Under this condition, adhesion and viscosity are most effective at imparting fluid momentum to the disks.  A boundary layer can be maintained across the entire disk gap when the fluid's boundary layer thickness is one half the gap width.  The boundary layer thickness might be best represented by the momentum thicknessLaminar flow is maintained with smooth bounding surfaces and a limited fluid velocity.  Laminar flow has a low Reynolds number, or ratio of fluid inertial force to viscous force.

Two rotor design formulas arrived at empirically by researchers were published [1]:  To maintain the boundary layer condition the optimum disk gap size is d = pi *(n/w)², where n = fluid kinematic viscosity, and w = rotor angular velocity.  Given a disk inner diameter smaller than 0.4 times the disk outer diameter, D, the volume flow rate per disk gap for maximum efficiency is found in a range of +100%/-50% about q = 4*n*D²/d.  In the table below, n is specified for the given temperature and a pressure of 20 psig:

D (in)

angular velocity
w (ft/s)

n (ft²/s)
gap size
d (in)
flow rate
q (ft³/s)
10000 218
1.7e-4 0.033
30000 654
250 1.4e-4 0.017
30000 654
1.7e-4 0.019
10000 436 250 1.4e-4 0.021
10000 436 400
1.7e-4 0.024
30000 1308
250 1.4e-4 0.012
30000 1308
1.7e-4 0.014

Kinematic viscosity is per unit density so it does not depend on mass, but does depend on temperature.  Volume flow relates to the nozzle area and steam velocity. The design formulas indicate that efficiency for a given rotor diameter requires a relatively small range of volume flow rates and temperatures, while the pre-nozzle pressure, the mass flow rate and the kinetic energy may vary widely.  The rotor diameter might be chosen for optimum efficiency at the lower temperatures of winter.  A larger diameter provides increased shaft torque and is limited by centrifugal stress, while a smaller diameter provides increased shaft speed and is limited by bearing friction.  For a given energy rate, the mass flow rate, temperature/pressure, velocity and the disk diameter are selected according to materials limits, then the volume flow, nozzle area and number of disks are selected according to nozzle criteria below.  The steam velocity should be maximized as torque is proportional to velocity squared, and the rotational speed should be maximized as the generator power is proportional to rotational speed.

turbine cross-section viewThe rotor components should be made from a stainless steel type that has sufficient tensile strength, temperature tolerance and corrosion resistance, such as grade 416. The disk surfaces should be highly polished to minimize friction and turbulence.  Friction causes energy loss to heat and turbulence reduces fluid adhesion to the disk. 

A minimum disk thickness is required to withstand the centrifugal and driving forces on the disks, but the outer disk edge should taper to a point to minimize its deflection of fluid from the nozzle.  The inner disk edge should be tapered toward the outlet to minimize fluid turbulence in the outlet.  At the end of the shaft is a conical shape to help direct the fluid toward the outlet to reduce turbulence.

The end disks should be heavy enough to hold the bolts and nuts that hold the rotor together.  The bolts should be of the hardest steel so that their diameter may be minimized.  The spacer (bolt washer) diameters should also be minimized as they disrupt the fluid flow.  The spacers should be round so as to minimize flow disruption as the flow angle varies with the load.  In applications without a generator to assist startup, more bolts and washers of larger diameter may be needed to increase startup torque.

Rotor Forces

The rotor disks can be attached directly to the shaft or indirectly through an end disk.  Attachment through an end disk eliminates the shaft's interference with the fluid flow and also reduces the number of parts.  This approach requires the end disks and the bolts to bear all the rotor forces.  The bolts are subject to shear force from the tangential fluid stream out of the nozzle, tensile force from the axial fluid flow in the outlet, and shear force in the radial direction from the rotation (centrifugal force).  The shear forces on the bolts may be shared by the washers & disks through static friction maintained through compressive force by the torque on the bolts.  This relief of shear force on the bolts is traded off to a tensile force on the bolts.  Fluid flow in the outlet adds to this tensile force on the bolts, and opposes the compressive force on the washers & disks.  Since steel bolts' shear strength is typically 60% of their tensile strength they should be torqued accordingly. 

The outlet end disk may offload the shear forces on the bolts further according to its own tensile and shear strength.  Direct attachment to the shaft may rely more on mass of the end disks for strength while end disk attachment should rely more on material hardness.

Rotational Loading - Thin Disk - MechengCalculators

Nozzle Design

The nozzle converts the steam's static pressure energy into directed kinetic energy to drive the turbine rotor.  Upstream of the nozzle, the steam is under static pressure, and if superheated then the ideal gas law holds that its energy per volume equals its static pressure (1), or its density times its temperature.  The rotor+condenser maintain a low pressure downstream of the nozzle and the pressure drop (upstream minus downstream) draws the steam through the nozzle.  The nozzle converts the energy in the pressure drop to kinetic energy, governed by the law of conservation of energy, and more specifically by Bernoulli's equation.  The kinetic energy is equal to one half the product of the steam's mass and the square of its velocity. 

A converging nozzle is an orifice with a throat area that narrows from inlet to outlet.  When the inlet pressure is greater than the outlet pressure, the fluid moves from inlet to outlet, and its velocity increases while its pressure decreases as it passes through the narrowing throat.  The fluid's velocity is maximum and its pressure is minimum where the cross-sectional area is minimum. 

If the pressure drop from inlet to outlet in made to increase, the fluid velocity increases until the fluid's sonic velocity is reached.  This is known as the critical flow condition and the critical pressure drop (CPD).  As the pressure drop (inlet press. minus outlet press.) is made to increase beyond the CPD, throat pressure remains at the CPD below the inlet pressure, throat velocity remains fixed at the sonic velocity (2), and mass flow and kinetic energy at the outlet also remain fixed.  The CPD for superheated steam is about 55% of the upstream pressure (3).

The shape of the converging nozzle is convex (trumpet), and narrows from inlet to outlet.  The surface's arc of curvature is circular and to achieve 95% efficiency its radius need only be greater than 1/3 the diameter of the nozzle throat [2].  A value of 3/2 was chosen in [3].  But this efficiency will be reduced when the inlet/outlet pressure drop is less than the CPD because not all of the inlet/outlet pressure drop can be converted to kinetic energy. 

In a diverging nozzle, fluid expands as it passes through a throat that widens from inlet to outlet.  If the initial velocity is below the sonic velocity, the velocity decreases as the fluid expands.  But if the initial velocity is above the sonic velocity, the velocity increases as the fluid expands, drawing energy from the fluid's heat.

converging-diverging nozzleIn a de Laval or converging/diverging nozzle, used in rocket engines, a converging section efficiently raises the fluid velocity to the sonic velocity preceeding a diverging section which efficiently raises it further.  This greatly increases the nozzle's conversion efficiency for general pressure drops, 63% as de Laval found, and was more recently demonstrated at 80%. 

Large scale turbines with large diameter rotors operating at supersonic velocity produce excessive centrifugal forces.  So the design of multistage axial flow turbines has focused on reducing the required rotor speed with supersonic fluid flows.  Smaller scale turbines accommodate supersonic flow with smaller diameter rotors that produce more moderate centrifugal forces.

The nozzle must be operated at its design condition for the supersonic velocity steam to extend past the outlet to reach the rotor, and this condition must be maintained consistently to prevent shock waves from stressing the materials.  The nozzle section lengths affect efficiency.  If they are too long, this increases frictional losses.  If they are too short, turbulence is induced.  Both reduce kinetic energy. 

The nozzle section profiles may be conical, convex or concave.  Conical is simplest to machine.  But in the converging section, convex is most efficient because it least disturbs flow, and thus minimizes turbulence.  In the diverging section, concave is most efficient because it minimizes the average distance in the cross-sectional flow area to the nozzle surface and thus adhesive drag.  It also directs the maximum amount of steam along the nozzle axis and toward the most useful area of the rotor.

For a given throat diameter, the design conditions for different diverging section exit areas may be found with an adjustable diverging section and a temperature measurement at the outlet.  The input/output pressure that provides the lowest temperature at the outlet represents the design condition for a given diverging section area [2].

The rotor speed has to be limited to avoid excessive centrifugal stress and bearing friction.  The sonic velocity varies with temp. and fluid type but 500 m/s is probably it for high temp. steam.  If the rotor diameter is 5", the sonic velocity of this steam equates to a 75k rpm rotor speed, which is probably beyond the stress limits of economic materials.  So the system must be capable of reducing the pressure differential to maintain a safe speed.  In normal operation the turbine is loaded to achieve maximum power rpm which is around half the fluid speed, so in this example around 37k rpm.  

A turbine configuration consisting of a large number of small diameter disks is required for high turbine/generator power output with reduced centrifugal forces, and for high rotor efficiency at laminar flow conditions [4].  This calls for a slot shaped diverging section but not necessarily a slot shaped throat.  The throat should probably be circular to maximize the average distance in the throat cross-sectional area to the throat wall to minimize fluid/wall interaction. 

Through prototyping/testing, the optimum values for nozzle angle and distance to rotor, and diverging section width and height are found to maximize overall turbine efficiency in the key power range.  A perfectly tangential nozzle angle causes excess fluid interaction with the housing, reducing overall turbine efficiency.  Adjusting the angle from tangential to radial (toward the shaft) reduces fluid/housing interaction.

(1) Pressure is force / area and kinetic energy is force * length,  so press = kinen / vol and kinen = press * vol
(2) The sonic velocity is a function of the fluid properties (more). 
(3) The CPD for saturated steam is closer to 58%.

Critical Flow Nozzle
Hypersonic Nozzle Design
Robert Goddard and His Rockets

Nozzle Area

The desired fluid flow rate for a given fluid pressure determines the total nozzle area.  The top nozzle edge should be near the outer rotor radius.  The nozzle width should broaden out smoothly to the rotor edge.  The rates of narrowing and widening of the nozzle contours are selected in a tradeoff between drag and turbulence.  Too long a nozzle presents unnecessary adhesion and friction drag.  Too short a nozzle introduces unnecessary turbulence (1).  Strategies for minimizing turbulence should come from research into fluid flow examples. 

The turbine design should include at least two nozzles placed around the rotor circumference to balance the driving forces, but probably not more than two because this decreases the cross-sectional area of the nozzles which increases drag and lowers efficiency.

The nozzle area is sized to accommodate the desired energy transfer rate. It is associated with the steam volume transfer rate for a given pressure.  If, for example, the desired energy transfer rate is 15 kW, and since the specific enthalpy of steam is about 2700 kJ/kg, the steam mass transfer rate is 5.5 g/s.   Given a pressure of 180 kN/m³, the steam density is about 1000 g/m³, so the volume transfer rate is 0.0055 m³/s.  The required nozzle area is this rate divided by the nozzle velocity which is, given the CPD, about 400 m/s, so the nozzle area is 0.138 cm².  If a circular nozzle, the diameter is 4.2 mm.  If the receiver pipe is 1/2" diameter, the steam flow rate through the pipe is 400 m/s * 0.02139 in²  / 0.19 in² = 45 m/s.  Since the density of water is 1000 times the density of the steam in this example, a water volume transfer rate of 0.0055/1000 m³/s or 5.5 ml/s or 1/3 liter per minute must be supplied to the boiler to maintain this steam transfer rate.

(1) Turbulence reduces order in the fluid molecules' motional direction and ultimately the amount of their energy translated to torque on the rotor shaft. 

Nozzle Fabrication

A nozzle converts static pressure into a directed flow so the shape must minimize impediments to this flow.  Surfaces should be polished, without corners, pockets, edges, dips or bumps so that all surfaces aid in convergence of flow to the desired direction.  The nozzle must be thick and solid to minimize the effect of vibration on the convergence.  

The easiest to fabricate nozzle is a four piece rectangular nozzle with two opposing flat pieces and two opposing curved pieces.  But the sharp angles in rectangular nozzles create flow discontinuities.  The turbine's overall efficiency is highly dependent on nozzle efficiency, which requires minimum flow discontinuities, friction, and adhesion drag, so it's probably best to avoid surface discontinuities altogether.

Another easy to fabricate type of nozzle is an inverted-geometry created by suspending a flow obstructing piece inside a straight cylinder.  To make a converging-diverging nozzle, the obstruction is torpedo shaped.  This piece is easier to machine than the inside surface of a cylinder.  But this type of nozzle is inefficient because for the same effective throat area, the average distance from points in the throat area to the edge is smaller, causing more surface adhesion drag.  Also mechanical stability is reduced and drag is increased by the members that secure the obstructing piece.

The best performance calls for cutting the nozzle shape in the inner surface of a passage through a solid block of metal.  Prototype nozzles can be made of a soft metal like aluminum which can be manipulated into different shapes or pieces soldered together and melted apart, and easily ground smooth for testing.  After testing to find the best nozzle shape for overall turbine efficiency, a permanent stainless steel nozzle can be fabricated.  A lathe can be used to cut a circular nozzle using boring bits or custom-shaped reamers ground from high speed steel.  Using a boring bit, the operator manually creates the nozzle shape by manually adjusting the bit's radial position while while its axial position traverses the block.  A milling machine can be used to cut a slot nozzle using custom-shaped milling cutters.

Machining of Rocket Nozzles
Virtual Machine Shop

Converging/Diverging Nozzle Design Condition

Given a converging/diverging nozzle connecting two large containers, with control over their pressures, for every nozzle there exists a design condition, that is a specific pressure ratio that results in the fluid pressure in the nozzle continuously and gradually dropping from the inlet container pressure at the nozzle inlet to the outlet container's pressure at the nozzle outlet.  For a given nozzle this condition provides maximum kinetic energy by minimizing flow disturbance (turbulence).  The flow is supersonic from the throat out to some maximum distance.  Starting at the design condition, when the outlet container pressure is lowered, the condition becomes overexpanded and turbulence is created at the outlet. And when the outlet container pressure is raised, the condition becomes underexpanded and similar turbulence is created.  The turbulence contains an oblique (not normal) shock wave. The flow velocity is supersonic between the throat and the wave, and subsonic past the wave.  When the outlet pressure is further raised, the turbulent, oblique shock wave recedes into a very thin plane geometry, normal to the flow, coplanar with the outlet. Within this planar wave is a large, sharp pressure/velocity/temperature discontinuity.  The velocity is supersonic from the throat to the wave, and subsonic past the wave.  When the outlet pressure is further raised, the planar wave progresses back toward the throat.  When the shock wave disappears into the throat, pressure/velocity/temperature in the diverging section become continuous again but with peaks/dips at the throat.  In this range of pressure ratios, the diverging section acts to lower the fluid velocity instead of raise it.

Converging/Diverging Nozzle

Fluid Mechanics

Isentropic compressible fluid flow with area change *:
mach <1, area <   =  velocity >, pressure <;  (subsonic converging nozzle)
mach >1, area <   =  velocity <, pressure >;  (supersonic converging nozzle)
mach <1, area >   =  velocity <, pressure >;  (subsonic diverging nozzle)
mach >1, area >   =  velocity >, pressure <;  (supersonic diverging nozzle)


turbineAll surfaces encountered by high-velocity steam should be smoothly contoured and polished.  A minimally-oxidizing material is probably required.  It should also be thick and bolted together tightly to control vibration although the sources should be addressed too.  In a closed-loop steam system the wetted surfaces may be kept relatively free of oxide and pitting by keeping dissolved solids and gases in the water to a minimum.

The figure shows a partial view of a turbine design that eliminates obstructions in the center outlet and is suitable for either horizontal or vertical mounting and multiple nozzles.  Along the entire passageway of the steam from the source to the nozzles there should be sufficient cross-sectional area to minimize steam velocity and friction/turbulence.  There should be just enough clearance between the rotor and the housing to account for the turbulent boundary layer on the housing surface plus rotor thermal & centrifugal expansion.  The rotor end disks should be spaced a significant distance from the housing for a thick cushion of gas to minimize interaction between the housing and the end disks.  But near the rotor's outer radius, the housing should extend as close as 0.4 mm to the rotor ends to minimize fluid leakage (See Seals).  To minimize heat loss, the housing design should minimize total outside surface area and the outside surface should be highly polished, clean and well-insulated.  Also, see Component Interactions.


The optimum outlet design minimizes friction, turbulence and back pressure, and least disrupts the steam flow to the condenser coils.  Flow is disrupted by:  A.) Constrictions which inhibit the volume expansion of the steam out of the rotor.  Making the outlet area smoothly expand to the condenser area (minimum required for condensation) creates the least back pressure.  B.) Discontinuities in the surfaces that disrupt the steam flow to the the condenser.  Smoothly curved surfaces angled to guide the flow toward the condenser are required, with no corners, seams, bumps, pits, notches or edges.  C.) Friction with surfaces.  Friction removes some of the steam's energy by converting it to heat which is absorbed by the outlet material.  The coefficient of friction is minimized with low-oxidation, polished material.  High-temperature materials resist corrosion and keep a polished finish longer.  D.) Adhesion to surfaces.  Steam adhesion on the outlet surfaces is a function of its viscosity.  If the outlet is small in circumference the flow is restricted more by adhesion drag.  E.) A vortex, or angular rotation in the outlet flow, which draws energy, may develop.  An exducer, which is a set of radially oriented vanes parallel to the desired (straight, non-rotating) flow path, may constrain the vortex to produce a net benefit over the extra friction that it introduces [1].


The turbine and generator rotors should be mounted on the same shaft to simplify and economize.  The rotors might be overhung as cantilevers or be placed between bearings.  Cantilever and overall shaft lengths should be minimized.  The bearings should be as close as possible to the rotors and the rotors should be as short as possible, minimizing required shaft diameter and weight.  The shaft should be well-polished at the bearing points.

For horizontal shaft orientation, the bearings should be placed to statically balance and appropriately share the load of the shaft+rotors assembly given the bearings' strengths.  Bearings are specified with a maximum shaft deflection (bend) angle.  A shaft has a certain deflection coefficient which, when multiplied by the cube of the shaft length between bearings and the weight of the radial load between the bearings, gives a deflection.  The arcsine of the deflection/length ratio gives the deflection angle used to match a bearing and a shaft *. describes a tensioned shaft approach that allows low-precision tolerances.  The shaft has threads at both ends and two nuts cinch all of the components together axially with locking collars filling out between components.  The shaft can be made from 4340 steel, or similar, and turned on a lathe using a dial indicator, to remove eccentricities down to 0.005", according to techniques illustrated in
5 Bears - MW54, and 5 Bears - Wren Propjet (3 pages).

Machine 2-shafts (pdf)


Turbine/generators rely on high speed for efficient energy conversionThe goal is to allow bearings of a reasonable cost to serve trouble-free at high operating speeds (10k to 30k rpm) for ten years between rebuilds.  Friction, heat and vibration stress bearings.  Bearings depend on good load distribution and rotational balance to minimize stress and vibration, and good heat distribution and dissipation.

Bearings typically rely on a layer of oil or grease to separate the dynamic and static components.  High speed/temperature bearings usually depend on circulating lubricant for cooling.  Foil bearings eliminate liquid lubricants, but with significant startup friction they are limited to use with smaller, lighter rotors.  Foil bearings are expensive.

Journal/sleeve/plain/fluid bearings consist of a simple sleeve around a shaft that depends on a layer of lubricant for separation. Advantages include almost unlimited speed capability and lifespan, low cost and very low noise.  Disadvantages include high friction on starting until the lubricant is distributed, and the need for lower viscosity lubricant requiring a circulation/cooling system.  High starting friction is an issue in the STC application because the turbine must restart daily.  But with sufficiently hard contact surfaces, adequate lubricant pressure, clean and cool lubricant, journal bearings might hold up for the target ten year service interval.

Ball bearings need less lubricant and starting torque but can be noisy and have a lower speed rating and lifespan than journal bearings.  Since
low-noise/vibration operation is important for the STC, deep-grooved ball bearings are good.  These provide support for axial (thrust) loads in addition to radial loads. Angular contact ball bearings provide radial support and axial support but in a single direction.  Roller bearings provide much more contact surface for applications with high impact loads and are not applicable to the STC.  "Hardened & ground" washers and races reduce noise.

The turbine/generator shaft requires a pair of radial load bearings, one near each end, and a pair of axial load bearings, each handling one of the two directional loads.  A single section of the shaft may be raised in diameter to provide an axial bearing face in both directions.  Tilted-pad journal bearings support both axial and radial loading and appear to be most effective in high-speed use [*|*].  In this case two sections of the shaft are raised to provide tilted bearing faces, one in each direction.

The radial load includes any rotor angular imbalance which should be minimized. 
If the shaft is mounted horizontally, gravity on the rotor presents a radial load on the lower half of the bearings.  If mounted vertically, gravity presents an axial load across the whole bearing surface, so vertical mounting offers a weight distribution advantage.  This advantage is probably significant given the daily startup transient in lubricant flow.

The radial load of the driving steam on the rotor bearings is balanced by the use of two or more nozzles spaced symmetrically around the rotor.  This also distributes temperature more evenly around the housing.  Even distribution of temperature and stress are very important for extending the life of bearings.  Also, resonant frequencies should be considered. 

The vacuum in the turbine exit port may present a significant axial load on the rotor.  Some turbine designs provide an exit port on each side of the rotor to cancel these loads.  For a single exit port turbine the axial load may be balanced with an opposing load created with an axial-flux generator on the turbine shaft.  Balancing axial loads is important to minimize the cost of the bearings. 

Debris contributes greatly to bearing friction and wear.  Good seals are the first line of defense against debris.  A lubricant filter is the second line of defense.  Avoiding contamination during installation and maintenance is very important.

Bearing Selection
Electric motor bearings
Bearing lubrication is essential for reliability

Balanced Driving Forces

Most of the force on the rotor occurs in the vicinity of the nozzle.  Multiple nozzles placed symmetrically around the rotor balance the forces on the shaft bearings and reduce stress on the rotor disks. 

Ideally, a fluid stream moving tangentially to the rotor at its circumference presents a purely tangential/rotational force.  In this case there are no radial forces on the rotor and no forces on the bearings, so only one nozzle is necessary.  But in practice, the fluid stream is positioned inside the rotor's outer diameter and moves in a straight line instead of the circular arc of the rotor. 

With the rotational axis at the x-y plane origin, and a single nozzle at the 1 o'clock position facing the negative x direction, the fluid's force on the rotor has a negative x component (1) and a net negative y component (2).  The stream also interacts with the disk edges, adding a net negative x component (3), and a negative y component (4).  The result is a static lateral force on the bearings, roughly in the 8 o'clock direction, that may be canceled by using two diametrically opposed nozzles.

Since each unit of material in the rotor outer diameter cyclically encounters a nozzle, the stream imposes cyclic dynamic force gradients on the rotor, both radial and tangential.  The variety of force gradients include shear, compressive and tensile.  The peaks of these cyclic dynamic gradients are further reduced by adding more nozzles.  But more than two nozzles is probably not worth it because they decrease the total throat area/circumference ratio of the nozzle set, increasing total nozzle boundary layer drag on the fluid.

(1) On the disk surface, the x force is negative at x>0 and negative at x<0. (5)
(2) On the disk surface, the y force is negative at x>0 and positive at x<0. (5)
(3) On the disk edge, the x force is negative at x>0 and zero at x<0. (5)
(4) On the disk edge, the y force is negative at x>0 and zero at x<0. (5)
(5) Circumferential housing interaction makes x & y forces weaker at x<0.


The rotor housing must be sealed to prevent the steam from going around the the rotor to the outlet, and to prevent the steam from exiting the housing around the shaft.  Water loss from the steam system must be kept to an absolute minimum so that performance is not compromised within the maintenance interval.  The rotor housing may be pressure sealed with labyrinth seals.  This type of seal relies on an open but restricted path of long length to reduce the pressure and leakage of fluid.  It should be made like a wear ring to be replaced on the bearing replacement schedule.

In addition, a shaft mechanical seal must protect the bearing closest to the rotor from steam, water vapor and water, and a small amount of metal oxides from the steam pipes.  This seal must withstand the steam pressure (reduced by the labyrinth seal) and steam temperature and endure high shaft speed and the stress of daily thermal expansion and contraction, minimize the loss of water out of the steam system, and prevent bearing lubricant, or any other contaminants from entering into the steam system when not under pressure.  Other shaft bearing seals must protect against airborne dust and vapors on a high-speed shaft.  Seals must be compatible with bearing lubricant and tolerate flaking metal and oxides from the bearings and lubricant pumping system.

Pumps most often use mechanical seals with the working fluid lubricating the seal.  If leakage is not acceptable, two seals are often used on the same shaft.  Contaminants increase bearing friction, heat and wear, either directly or by reacting with the bearing material, or by destroying lubricant properties.  During servicing, one should completely avoid introducing debris or damaging seals.

Mechanical Shaft Seals
Pusher & Non-Pusher Mechanical Seals
End Face Mechanical Seals
Labyrinth Seals

Bearing Lubricant & Lubricant System

High speed is necessary for turbine/generator efficiency, and minimizing bearing friction/heat is necessary for extended service life.  An oil-based lubricant is typically used to supply a cushion that separates the solid bearing components.  High viscosity grease is used to lubricate lower-speed bearings, and in modern designs the grease is sealed inside the bearing for low maintenance.  High speed bearings require cooling and the lubricant may serve as the coolant, when circulated.  Circulation also allows lubricant filtering, removing bits of bearing material and contaminants, to further extend the life of the bearings.  A very good high temperature lubricant is castor oil.  It has a low viscosity at low temperatures.  Phoenix Navigation sponsors a tesla turbine-builder's club which has highlighted the need for low-viscosity circulating lubrication for high-speed turbines.  It describes a circulation system consisting of an electric pump and filter and recommends this manual (pdf) from bearing company NTN for lubrication techniques.

Bladeless Pump

The bladeless turbine rotor may also serve as a pump rotor (impeller) in the class of efficient radial-flow centrifugal pumps.  The STC system requires various pumps for water, water solutions, and oil at various temperatures and pressures.  The design goals include minimum ingress of air and loss of fluid, high efficiency at variable flow rates, with low vibration and noise, simple construction, inexpensive materials, and reliability over the STC's lifespan with at most two rebuilds. 

The bladeless or shear-force rotor is well-known to handle viscous fluids, and resist cavitation and damage from solid particles [4].  Centrifugal pumps have an inlet in the center and the rotor imparts a radial/tangential momentum to the fluid in the inlet.  This momentum slings the fluid into a channel around the circumference of the rotor, called a volute or diffuser, that feeds the tangential outlet.  Centrifugal pumps are especially efficient in low-flow, high pressure applications.  The bladeless rotor shares the high efficiency of the closed rotors found in some centrifugal pumps.

The gap between the rotor and the housing should be reduced to minimize friction [1].  The path through the gap should be no longer than necessary to minimize fluid recirculation.  Pump efficiency is maintained over time by installing and maintaining wear rings in the gap to maintain the minimum spacing.  Also, the smaller the inter-disk wetted area, the less friction, because friction is proportional to the 5th power of area and the 3rd power of rotor rpm [1].  This implies a smaller diameter rotor running at a higher rpm.

The volute encloses the rotor, captures the fluid out of the rotor, and converts the fluid's rotary kinetic energy to static pressure plus linear kinetic energy directed toward the outlet.  A spiral volute's cross-sectional area increases with angular position around the circumference of the rotor, and is maximum at the outlet.  This maintains a constant fluid velocity and pressure around the volute which maximizes the conversion efficiency at the pump's design flow rate.  However at other rates disturbances and separation can occur *.

Also, while the spiral volute presents balanced lateral forces on the rotor at the design flow rate, it presents an imbalanced lateral force on the rotor at other rates, stressing the bearings and seals.  A circular volute has significantly lower imbalance over a range of flow rates.  A double spiral volute has the very least imbalance across all flow rates *.  A double spiral volute balances lateral forces on the rotor by directing the fluid volume from one side of the rotor into a separate spiral volute channel.  A double spiral volute with two separate discharge nozzles is referred to as dual discharge.  The geometric symmetry makes force balancing easier to achieve with low-tech fabrication but the general need to merge two discharges into one pipe defeats the advantage.

A diffuser reduces turbulent vortices during radial to tangential kinetic energy conversion.  The most effective diffuser vanes are curved, making them complex to machine, but for the STC, easily-machined geometries are preferred, and straight vanes may be worth trying.  Diffusers are typically used with circular volutes but when used with spiral volutes provide maximum efficiency of 90% or greater *.  Diffusers are better suited for high-pressure, low-flow applications.

According to [4], efficient volutes/diffusers have been difficult to achieve with bladeless rotors due to the very small angle of the flow entering the volute from the rotor.  The entering angle should be a function of many parameters including the fluid viscosity, the rotor diameter and inter-disk gap, and the flow rate and total pressure.  The diffuser vanes may be at any angle.  Further research is required to determine the relationship between these parameters, entering angle, diffuser geometry, volute and outlet geometry, and the overall pump efficiency.  The bladeless centrifugal pump design is also suitable as an air fan with low noise, and potentially high efficiency *.

An economic approach to construction is to use plate metal for most pump components including the rotor disks and the housing.  This avoids the need to metalcast complex geometries.  An efficient double spiral volute diffuser pump design might use two flat metal plates sandwiching three curved metal bands:  An outer band to contain the fluid, curved in the spiral volute geometry with a flat face for the discharge nozzle, an inner separator band to form the double spiral, and an inner circular band to form the diffuser, with vanes punched and bent at the optimum angle. 

In designing pumps for efficiency, iterative component-matching is usually necessary due to component interactions affecting the overall efficiency.  The iterations may be performed on prototypes build from convenient materials such as discarded wood and plastic.  If pumping clean water, the pump may be made from aluminum.  Iron and steel are only necessary for pumping abrasives.  Good seals are required to avoid introducing contaminants into the pumpage.

STC - Feedpump
DOE Fundamentals Handbook - Pumps
Hydrodynamics of Pumps
The World of Rotodynamic Pumps
Pumps - Engineering Toolbox


[1] A Qualitative Analysis of the Tesla Turbomachine, Glenn A. Barlis, here (doc) or under files on TheTeslaTurbineList
[2] James Morris, PTBC 2002 Forum Archives
[3] Nozzle Design, Key to Turbine Efficiency -
[4] Tesla Turbo Machinery - Warren Rice, and here (pdf)
[5] Tesla's 1913 turbine patent -
[6]Investigation of Multiple Disk Turbines - Rice, 1965
[7]Biomass Boundary Layer Turbine - Schmidt, 2002
[8]Tesla Turbine Thesis - Singleton, 2000, under files on Tesla Turbine

See also:
Phoenix Navigation's Turbine Builders Club
Numerical Study of a Tesla Turbine, Huybrechts, Berten, Lenclud, under files on TheTeslaTurbineList

Bearing Selection (

The selection of the type of the bearing for a particular application depends upon the various factors such as nature of load, speed, precision, stiffness, misalignment etc. and also the characteristics of different types of bearings.

Guidelines for selecting bearing type are as under:


Copyright (c) 2005-2009 Robert Drury
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
See "GNU Free Documentation License". 

Disclaimer:  This information may contain inaccuracies and is provided
without warranty.  Safety first when working with high temperatures,
pressures, potentials, speeds, energies, various tools and materials.