###### Atmospheric Vortex Engine

# Frequently Asked Questions

FAQ INDEXPREVIOUS

### 11. Fluid Dynamics – Advanced Topics

The source of rotation
in convective vortices is amplification of the absolute rotation of ambient air
converging toward the vortex axis in a thin layer. The initial rotation of
the ambient air can be due to convergence of air rotating at the same speed as
the Earth’s surface or to convergence of an air masses rotating relative to the
earth’s surface. Convergence must be limited to a thin layer to significantly
increase rotation. In a convective vortex, convergence takes place in a thin layer near the
earth’s surface where tangential velocity is reduced by friction because at
higher elevations there is no surface friction to reduce tangential velocity
and convergence is inhibited by centrifugal force.

Angular
Momentum (*M
*)
and Circulation (G) are conserved in frictionless
converging
flow. Angular
momentum (*M
*) is the product of
radius (*r*) and tangential velocity (v ) --- (*M* = v *r*). Circulation is
the integral of tangential velocity and path length. For a uniform circular path and
rotation as a solid body, circulation equals
angular momentum multiplied by 2p (G=2pvr).

The absolute tangential velocity (*v*_{s}) of air
stationary relative to the earth surface is:

where *v*_{a}
and *r*_{a} are
the velocity
and radius at the radius of maximum velocity; where *v*_{s}
is the absolute tangential velocity of the earth’s
surface at a distance *r*_{s}
from the axis of rotation, where *N*
is
the number of seconds per day (= 86400), and f
is
the latitude. In the following discussion, the latitude will be taken
to be 30°
so that sin f is 0.5.

Table
11.1 shows the
effect
of circulation on radius of maximum velocity (r_{a})
for
convective vortices
with peak tangential velocities (v_{a})
of 50 m/s. The
radius (r_{s})
in Table 1 is the radius at which air stationary relative to the
earth’s
surface would have the same absolute circulation as the air at the
radius of
peak velocity.

Air stationary relative to the earth’s surface at a radius of 262 km has an absolute tangential velocity of 9.5 m/s relative to the vortex axis. For the 50 km radius hurricane at the bottom of Table 11.1, the air has to converge from a distance of 262 km to produce an eyewall tangential velocity of 50 m/s. For the 1 m radius dust devil at the top of the table, the air has to converge from a distance of 1170 m to produce a peak tangential velocity of 50 m/s. Producing a tangential velocity of 50 m/s from air rotating at the same speed as the earth surface requires the air to converge by a factor of 5.24 in the case of the hurricane and by a factor of 1170 in the case of the dust devil.

Surface
winds, which typically have velocities around 5 m/s, have
little
effect on absolute circulation when the converging air comes from a
location where
the absolute tangential velocity of the earth’s surface is more than
4 m/s
(*r*_{s} > 100
km).
Local wind have a significant effect on circulation when the converging
air
comes from a location where the absolute tangential velocity of the
earth’s
surface in under 1 m/s (*r*_{s} < 10
km).

The circulation of a hurricane results from convergence of air initially rotating at velocities close to the rotation velocity of the earth’s surface. Friction between the air converging towards the base of the vortex and earth’s surface reduces the circulation of the converging air. As a result the converging air would have to come from a radius somewhat higher than 262 km to have a tangential velocity of 50 m/s at a radius of 50 km. The air in the 50 km radius hurricane could have originated at a radius of 500 km and have converged by a factor of approximately 10.

The circulation of dust devils results form convergence in air masses swirling relative to the earth’s surface. The initial swirling action could be the result of the vortex forming within a random eddy or near the boundary between two air streams. Hurricanes always have cyclonic circulation. Dust devils can have cyclonic or anti‑cyclonic circulation. Tornadoes at intermediate size predominantly have cyclonic circulation but occasionally have anti-cyclonic circulation. While the rotation of the earth’s surface plays a major role in large vortices like hurricanes, the earth’s rotation has little effect on small vortices like dust devils.

(Speculative) Like in hurricane, the air in small convective vortices may converge from an initial radius 5 to 20 times the radius of maximum velocity. The air in the 100 m diameter vortex of Table 11.1 could have been air originally at a radius of 1 km rotating at a velocity of 5 m/s or air originally at a radius of 11.7 km rotating at the speed earth’s surface (0.43 m/s). The speed of rotation of the earth’s surface of 0.04 m/s at a radius of 1 km is small relative to a velocity of 5 m/s and would have negligible effect on absolute rotation. The source of rotation in the 100 m radius tornado is more likely to be air originally at a radius of 1 km with a random rotation of 5 m/s than air originally at radius of 11.7 km with a rotation of 0.43 m/s. Convergence ratios of more than 20/1 seem improbable.

In
the absence of energy source the atmosphere would tend to rotate at the
same
speed as the earth’s surface. The vorticity (w)of the earth’s
surface is low and
is maximum at the pole and zero at
the equator. The vorticity of air rotating as a solid body is
circulation divided by enclosed area --- (w=G/pr^{2}). The absolute
vorticity of an air
mass is the sum of the vorticity of the earth's
surface and of the vorticty of the air relative
to the earth's surface. Vorticities significantly higher
than the vorticity of the
earth’s
surface are rare since surface friction tends to attenuate relative
vorticity. Table
11.1 shows the vorticity of air rotating as solid body at the radius of
maximum velocity r_{a}
and at the radius of origin r_{s}.
The only
mechanism
capable of significantly increasing vorticity is convergence in a thin
layer
which requires an energy source. The high tangential velocity of
convective
vortices is always the result of convergence in a relatively thin layer
of air close
to the earth’s surface. In the case of hurricane, of air initially
rotating at
the same speed as the earth’s surface; in the case of dust devils, of
randomly
rotating air masses. Upturning of streamwise (horizontal) vorticity
cannot
produce vertical vorticity. For information vorticity see: http://en.wikipedia.org/wiki/Vorticity

Convergence
does not necessarily produce tight convective vortices; convergence can
be the result of uplift over a broad area. Convergence in
a
thunder storm can produce rotation in large air masses such as rotating
super cells.
The rotation of surface
air resulting
from convergence in super cell enhances the rotation of surface air
producing
air with high rotation whose rotation can be further enhanced by
convergence in
a small diameter vortex. Super cells clouds are not the cause
tornadoes. Convergence in a thin layer is the cause
rotation in both
super cells and tornadoes. Without sustained convergence the rotation
of a large
air mass
is dampened by friction.

The
diameter of convective vortices increases with circulation.. Hurricane
diameter increase during their intensification period indicating that
the
distance from which the air converge increases as the hurricane
intensifies. When the source of the rotationis the earth's rotation,
the
circulation
of the converging air increases as the air's initial distance from the
vortex axis increases.

Friction losses are much lower for
laminar flow
than for turbulent flow. Flow in pipes becomes turbulent when the
Reynolds Number exceed 5000. The Reynolds Number in atmospheric vortex
is much higher than 5000 and therefore the flow should
be turbulent but
centrifugal force inhibits turbulence and keeps the flow
laminar. The smooth thread shape of some waterspouts
shows that flow in a vortex can be laminar. Turbulence is inhibited in
vortex flow because when a particle of fluid moves towards the axis of
rotation its tangential velocity increases to conserve angular momentum
which increases centrifugal force and pushes the particle back towards
its original position.

Table 11.2 shows that friction losses at a velocity of 40 m/s in a
40 m diameter pipe friction losses are 8500 more for turbulent flow
than for laminar flow. The work loss due to friction is 1200 J/kg for
turbulent flow and only 0.14 J/kg for laminar flow. Thermodynamic
calculations show that the work produced when air is raised can be in
the order of 5000 J/kg. For convection work of 5000 J/kg, friction
losses are 24% for turbulent flow and 0.003% for laminar flow. Laminar
flow reduces friction losses to negligible level.

For the same flow, doubling the pipe
diameter
reduces friction loss by a factor of by a factor of 16 for laminar flow
and by a factor of 30 for turbulent flow. Friction loss are inversely
proportional to
the diameter to the 4th power for laminar flow and to the diameter to
the 5th power for turbulent flow.

Friction losses in a vortex would be
slightly
higher than in laminar pipe flow because the flow path is longer and
there
is more shear. Friction loss in vortex flow could be 5 times the
friction losses in laminar pipe flow which is still much less than in
turbulent pipe flow. Friction losses in unconfined flow such
as
cumulus updrafts could be 5 times the friction losses in turbulent pipe
flow. Entrainment further increases friction losses in cumulus
flow.

The Pax Scientific vortex mixer
invented by Jay
Harman demonstrated that using a vortex to circulate the water in a
tank requires much less less energy than alternative methods such as
pumps or agitators. Jay Harman stated that he is convinced
vortices could be used to control atmospheric circulation and to bring
rain to arid or drought ridden regions.

Pax
Scientific vortex
mixer web site

Article on
Jay Harman

References

http://en.wikipedia.org/wiki/Reynolds_number

http://en.wikipedia.org/wiki/Darcy_friction_factor

http://en.wikipedia.org/wiki/Moody_chart

http://en.wikipedia.org/wiki/Colebrook_equation

Thermodynamic analysis permits
calculating the
ideal work (w_{i})
produced when air is
raised reversibly. Ideal work (w_{i})
is capable
of producing an ideal velocity
(v_{i}),
where: w_{i}
= v_{i}^{2}
/ 2.
Energy must be conserved irrepective of the details of the lifting
process. Fig. 11.3 shows how energy is conserved in five steady-state
processes. For each process, the mass flow (M) is uniform
throughout
the length of the pipe.

In case A, the
air is raised in a vertical pipe in an adiabatic, frictionless
(inviscid), steady-state process. The ideal work (w_{i})
results in ideal velocity (v_{i})
at the pipe
outlet. The kinetic energy is mainly produced as the air accelerates in
the bottom of the pipe but the upward velocity also increases as the
density of the rising air decreases in order to produce a
uniform
mass flow. The enthalpy of the air leaving the pipe (h_{2})
is equal to the
enthalpy of the air entering the pipe (h_{1})
minus the increase in its potential energy (gz). The process is
reversible; the
entropy of the air leaving the pipe (s_{2})
is equal to the entropy of the air entering the pipe (s_{1}).

In case B, the flow in the bottom of
the
pipe is
limited by a restriction. The kinetic energy (w_{i})
is produced at the restriction. The cross-sectional area of the
restriction is small relative to the cross-sectional area of the pipe
so that the velocity in the pipe approaches zero. The kinetic energy of
the jet dissipates downstream of the restriction. The enthalpy of the
air leaving the pipe is increased by the kinetic energy dissipated. The
process is irreversible; the entropy of the air leaving the pipe (s_{2})
is greater than the
entropy of the air entering the pipe (s_{1}).

In case C, the kinetic energy of the
air
leaving the
restriction is captured by a turbine and leaves the system as shaft
work. The enthalpy of the air leaving the pipe (h_{2})
is equal to the
enthalpy of the air entering the pipe (h_{1})
minus the increase in its potential energy (gz). The process is
reversible; the
entropy of the air leaving the pipe is equal to the entropy of the air
entering the pipe.

In case D, the cross-sectional area
of
the pipe
increases with height so that the velocity decreases with height. The
kinetic energy is produced as the air enters the pipe and is dissipated
as the velocity decreases. The enthalpy of the air leaving the pipe is
increased by the kinetic
energy dissipated. The process is irreversible; the entropy of the air
leaving the pipe is greater than the entropy of the air entering the
pipe.

In case E, the restriction is
replaced
with a
Venturi. The velocity of the air at the throat of the Venturi can be
greater than ideal velocity (v_{i})
without violating
the law of conservation of energy because the kinetic energy is
converted back to heat resulting the same exit enthalpy as in the
irreversible cases B and D. The enthalpy of the air
leaving the
pipe is increased by the kinetic
energy dissipated. The process is irreversible; the entropy of the air
leaving the pipe is greater than the entropy of the air entering the
pipe. For a given differential pressure the velocity produced in a
Venturi can be greater than the velocity produced in a
restriction or nozzle because the kineitc energy is
recovered.

The
ideal work (w_{i})
reverts to heat
unless it is taken out of the system with a turbine or leaves the
system as exit velocity. In any case the ideal work (w_{i})
is lost unless taken out of the system as shaft work. Producing useful
work requires a shaft to take the work out of the system.

Reference

Venturi
tube Wikipedia

Low
level flow in
tornadoes is characterized
by an
outer region where converging air rotates faster to conserve angular
momentum,
and by an inner region where the air rotates as a solid body
and
where the tangential velocity falls to zero. This
flow
pattern, called a combined Rankine vortex, is illustrated by the solid
lines in
the graph at the bottom of Fig 11.4. The effect of rotation on upward
flow in the annular tube shown in Fig. 11.4 will be used to try to
understand what happens isn a convective vortex. For information on
Rankine vortex
see: http://en.wikipedia.org/wiki/Rankine_vortex

Tangential
velocity in a Rankine vortex is related to radius according to:

where

*v*

_{m}is the maximum tangential velocity

*v*, and

*r*

_{c}is the radius of the annulus of rising air. The inward differential pressure is balanced by centrifugal force except in the boundary layer where friction is significant. In the bottom graph of Fig. 11.4, the solid curves represent the frictionless Rankine vortex and the dotted curve shows the effect of friction in reducing tangential velocity. In order to explain vortical flow is it necessary to understand the contribution of tangential velocity to outward centrifugal force. The radial pressure across a thin shell is: By integration, the radial pressure differential across both the inner and outer parts of the Rankine vortex are: The total radial differential pressure across the two parts of the Rankine vortex is:

For a given DP, the tangential velocity required to balance radial pressure differential is independent of vortex diameter.

The total
radial
differential pressure is the integral of the radial pressure over all
the shell
elements. If the tangential velocity were constant between radius *r*_{a} and *r*_{b }, as
shown by the solid line in the graph at the top
of Fig. 1, the total radial pressure differential pressure
would
be:

*v*

^{2}. A uniform tangential velocity between radius 10 m and 100 m would result in a total radial pressure differential of 2.3 r

*v*

^{2}, 4.6 times the radial pressure differential in the outer part of a Rankine vortex. For a given peak velocity, broadening the peak increases the differential pressure produced by centrifugal force. There is a small decrease in density as the pressure decreases as one moves towards the vortex axis; for purpose of initial discussion the density will be taken to be uniform in the horizontal direction.

Friction
plays an
essential role in the
existence of convective vortices. The slight reduction in velocity
resulting
from friction against the earth’s surface in convergence zone ‘**A**’ of Fig 11.4 reduces centrifugal force
and allows
the air in the layer next to the earth's surface to converge into the
bottom of the annular tube. Increasing
tangential velocity requires energy; the energy is produced
thermodynamically
by the air rising in the annular tube. Tangential velocity increases as
it converges
towards the bottom of the tube to conserve angular momentum.

If
the inner tube were to vanish, the air in zone ‘**C**’
of
the inner tube would be dragged by friction by the air in the
annulus and rotates as a solid body except next to the earth’s surface
where the
air is slowed by friction against the ground. The reduction in axial
pressure
is greatest at a level slightly above the bottom of the tube and tends
pulls
air axially both upward and downward towards level ‘**C**’.
Axial pressure reduction is greatest at level ‘**C**’
near
the bottom of the tube because
the rising air loses angular momentum by friction against the outer
tube or
against the surrounding air and because the vortex diameter is smaller
near the
bottom. Level ‘**C**’ acts like the
rotor of a centrifugal pump. Air is pulled in the eye of the rotor both
from
below and from above. These two axial flows which are small compared to
the
flow in the annulus are added to the annulus flow.

The
reduction in angular momentum by surface friction in zone ‘**B**’
enables some of the converging air to penetrate past the annular
tube and to rise in the inner tube. In dust devils, sand entrained with
the
rising air gets thrown out by centrifugal force once the air is high
enough for
the effect of friction against the bottom surface to diminish and for
the
effect of drag from the rotating annulus to increase centrifugal force.
The
sand is thrown out in a cone which can have sides with a slope of
approximately
30°. In some dust devils a sand filled dark cone is visible above a
clear sand
free space.

The
core is dragged in solid rotation for the whole length of the vortex.
The
stronger axial pressure reduction near the bottom of the vortex tends
to pull
air downward from zone ‘**F**’ towards
zone ‘**C**’. The downward pull is
resisted by the buoyancy of the sinking air because the temperature of
descending air increases as it is compressed. In hurricanes, the air at
the
centre of the eye can be very dry above the 2 km level and
have a
high
relative humidity below the 2 km level indicating that the core air
descends
from high in the troposphere and that air does not descend all the way
to the
bottom of the vortex.

If the outer tube were to vanish, the centrifugal force produced by the air rotating in the annulus could replace the physical outer annular wall and prevent the surrounding air at higher pressure than the air in the annulus from entering the rising air stream in the annulus. The tangential velocity profile in the graph at the top of Fig. 1 shows that the peak velocity can be reduced by friction or by divergence and how the velocity profile can be broadened. The rising air is high entropy air coming from the bottom of the atmosphere while the air surrounding the vortex is low entropy air. The surrounding air stays layered; it rotates but does not rise. At high elevations the radial pressure differential is balanced partly by the centrifugal force in the annulus of rising air and partly by the centrifugal in the non rising surrounding air. The equation in the top graph shows that broadening the tangential velocity profile permits balancing radial pressure differential with lower peak tangential velocities.

** **The
air surrounding the annulus of rising air, zone ‘**D**’,
is
entrained by friction. Angular momentum is transferred from
the rising air to the surrounding air. Centrifugal force in vortex flow
inhibits
turbulence because when a particle of air converges, tangential
velocity
increases to conserve angular momentum and the increased centrifugal
force tends
to push the particle back where it came from. The smooth thread shape
of some
dust devils, waterspouts and tornadoes shows that flow in the tuba can
be
laminar. Friction losses are much lower for laminar flow than for
turbulent
flow. For example the friction loss for air flowing in a horizontal
tube 100 m
in diameter and 10 km long at a velocity of 50 m/s is
670 J/kg for
turbulent flow and 0.03 J/kg for laminar flow. The friction
coefficient
for turbulent flow is 23,000 times the friction coefficient for laminar
flow.
Atmospheric models use a turbulent viscosity approximately 100,000
greater than
the laminar the viscosity of air. ** **

** **Convective
vortices have been simulated with computational fluid dynamics (CFD)
models.
CFD models calculate the time varying properties of a flow field. The
fact that CFD results are able reproduce many of the features observed
in
natural vortices is taken as an indication of the validity of the
model. Testing the effect of a variation can require redefining problem
geometry. It difficult to distinguish whether a change in the flow
field is due
to a change in geometry, a change in initial conditions or a change in
a model
parameter. Traditional fluid mechanics are still used to solve most
fluid mechanics problems.
A CFD model must be supplemented by traditional fluid mechanic
approach. A CFD model matching observations does not necessarily
provide understanding of the role of friction at various point in
the flow field.The above approach based on Fig. 11.4 shows
that
traditional analysis method can throw some light on the role of
friction.

The
pressure under the annular column of rising air depends on the buoyancy
of the rising air. The maximum pressure reduction under the
annulus of rising air is the ideal pressure reduction (DP_{i}),
in the table of FAQ 9.6. The air converging in zone 'A' of the Rankine
vortex turns up as it reaches the annulus diameter because buoyancy of
the rising air is insufficient to draw the converging air any further.

The
central core of the vortex is
entrained in solid body rotation by
friction. The vertical flow in the central core is small and
the
central core plays no role in energy production. Bringing air downward
in the core requires rather than produces energy. The forced rotation
of the core is capable of producing a maximum axial pressure
reduction (DP_{a})
equal to twice the annulus pressure reduction (DP_{i}).

The diameter of the annulus
is the diameter
for which the differential pressure due to centrifugal force in the
outer part of the rankine vortex (DP_{ro}) is equal to the ideal annulus
pressure reduction (DP_{i}).
The ideal annulus pressure recution (DP_{i})
is determined by the thermodynamic properties of the rising air. The
annulus diameter is determined by the circulation of the converging
air. As shown in Table 11.1, diameter increases with circulation. For a
given annulus pressure reduction annulus diameter is
proportional
to circulation.

The fact that observed
annulus pressure
reduction agrees fairly well with ideal process pressurereduction
indicates that frictional losses in a convective are small
irrespective of diameter.

In natural vortices, the source of the rotation is the rotation of the air mass within which the vortex forms which may due to the earth's rotation. In the atmospheric vortex engine (AVE), the rotation is produced by having the air enter a circular arena via tangential entry duct.The circulation is the result of forcing the air to enter a circular area tangentially at a short distance from the vortex axis rather than because the air was initially stationary relative to the earth’s surface at a large distance from the vortex axis. In the natural vortex of Fig. 11.4 and in the AVE of Fig. 11.7, the kinetic energy of the air is derived from the energy produced thermodynamically as the preceding air rises in the vortex.

Natural vortices are rare in spite of the fact that surface air often has sufficient heat content to produce a vortex. An AVE would have additional features to ensure that a vortex can be started, controlled and stopped. A roof with a circular opening is used to force the air to converge. The diameter of the vortex could be 10 to 30% of the roof opening. The lower level of the vortex would is surrounded by a wall to prevent the vortex form being disturbed by the wind until the vortex is well established. Heat can be injected in the center of the station to create a strong updraft to start the vortex. The air can be heated in heat exchangers located upstream of the tangential entries to increase the energy production. The size of the vortex is limited by the amount of air that can flow through the tangential entries; in addition the air flow can be limited with dampers located either in the tangential entries or upstream of the heat exchangers.

The
AVE provides a controlled supply of warm rotating air whose rotation
provides
its own chimney. Should the upper part of the vortex be blown away by a
gust of
wind, the lower part of the vortex re-establishes itself with warm
spinning air from
below. The
upper part of the vortex, which was initially filled with warm spinning
air from the bottom of the atmosphere, fills
with the
cool non spinning air at its base loses its buoyancy and die out. If a
chimney filled with warm flue
gas was
cut in two and the upper part moved horizontally to the side, the upper
half would
quickly fill from the bottom with cools air and the flow in the upper
half would
quickly stop.

Looking at energy conservation in open
systems helps
understand what happens to the energy of convection. Fig.
11.3
panels B, C & D show that provided no work is taken out of the
system and provided that the exit velocity is negligible, the enthalpy
of the air leaving the top of the tube is equal to the enthalpy of the
air entering the tube, minus the increase in its potential energy and
plus the ideal work.

Fig.
11.3 Upward flow in
a vertical tube

Engineers
use the open thermodynamic system shown in Fig. 9.1 to calculate the
maximum quantity of work that can be produced when
a fluid
is transferred from one state to another (or the minimum quantity of
work required to transfer a fluid from one state to another). Ideal
work can only be calculated by assuming: negligible friction loss,
negligible velocity (kinetic energy), and no heat transfer (adiabatic
process). By contrast, the atmospheric science and fluid dynamics try
to determine the properties of the flow field. It is not
readily
apparent that looking at a process with negligible velocity
will
shed light on flow field. Engineers have learned from experience that
the most effective way of understandind energy transformations is to
look at rigorously defined closed or open systems. It is not uncommon
to use both open and close system to gain understanding from different
perspective. The fact that results of thermodynamic anaylysis are
confirmed by observations on real systems has given engineers
confidence in defining thermodynamic systems which are are
not
always obviously related to the real system. Ideal thermodymnamic
systems often bear little relationship to real systems but they are
necessary to understand real systems. Open complex systems can be
understood by looking at simpler closed systems.
Atmospheric scientist have been reluctant to consider closed systems
because the atmosphere is obviously an open system.

Fig.
9.1 Open
Thermodynamic System without additional heat input

Fig. 9.6 shows that the addition of
heat in non
adiabatic process can be accomodated in open system. Ideal system
analysis requires that the velocity be considered negligible in the
adiabatic system of Fig. 9.1 and the non adiabatic system of Fig. 9.6.

Fig.
9.6 Open
Therodynamic System with additional heat input

The open thermodynamic system shown
in the figure
below will be used to examine what happens to ideal work in an
atmospheric vortex. The boundaries of the open thermodynamic system
are the walls of the conduit consisting of the convergence
zone,
the upward flow annular tube, and the divergence zone. Boundaries of
thermodynamic systems can be set arbitrarily as required to facilitate
analysis. The velocity of the air entering and leaving a
vortex
can be made negligible by setting the system boundaries a long way from
the vortex axis.

The ideal work (w_{i})
produced when air is raised is used to produce the tangential velocity (v_{t})
of the spinning air at the red dot under the annular tube; but the fact
that the work of convection is required to produce tangential velocity
does not mean that the work of convection cannot be taken out of the
system. The kinetic energy of the spinning air is restituted
as the
air diverges in the upper part of the vortex.

There is a physics
101experiment where spinning
masses are pulled toward the axis of rotation with a string. The
experiment shows that energy supplied by pulling on the string is
responsible for the increase in the kinetic energy of the rotating
masses and that the energy is restored by the spinning masses pulling
back on the string as the external pull is reduced. The purpose of the
experiment to demonstrate the principle of conservation of
mechanical
energy. The energy required pull the masses in is equal to the energy
produced when the masses move back out. Should the string is cut
instead of gradually let go the mechanical energy would not be
recovered and would somehow revert to heat. A skater pulling his arms
in spins faster; the mechanical energy he supplied is not restored when
he lets his arms out because there is no mechanism for doing
so.

The energy of the spinning air
leaving the vortex
is recovered as the vortex diverges and becomes available to
give
kinetic energy to the air entering the vortex. Therefore it should be
possible to remove energy from the system with peripheral turbines
without significantly attenuating vortex intensity. As explained in FAQ
11.2 friction losses in a laminar vortex are extremely low. Nonetheless
unless there are not machine to remove energy from the system the
mechanical energy dissipates merely because the expansion process is
not constrained as illustrated by the unconstrained piston of FAQ 9.5.

Dissipation
in
unconstrained expansion

A similar argument applies to
vertical velocity.
Upward velocity increases as the air enters the annular tube but the
the upward kinetic energy is recovered when the upward velocity at the
upper end of the vortex. The upward motions stops when the air reaches
its level of neutral buoyancy.The fact that flow in a vortex is laminar
is important for energy recovery because turbulence dissipates energy.

Should removing energy from the
vortex with peripheral turbines
reduce vortex intensity excesively it there are
other alternatives
available namely: injecting air without spin directly in the center of
the vortex via an opening in the center of the arena floor or using a
vertical axis turbine in the center of the arena.

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