U.S. patent application number 14/404606 was filed with the patent office on 2015-05-28 for mechanism for enhanced energy extraction and cooling pressurized gas.
The applicant listed for this patent is The University of Western Ontario. Invention is credited to Jeliazko Polihronov, Anthony G. Straatman.
Application Number | 20150143819 14/404606 |
Document ID | / |
Family ID | 49672249 |
Filed Date | 2015-05-28 |
United States Patent
Application |
20150143819 |
Kind Code |
A1 |
Polihronov; Jeliazko ; et
al. |
May 28, 2015 |
MECHANISM FOR ENHANCED ENERGY EXTRACTION AND COOLING PRESSURIZED
GAS
Abstract
Systems, methods, and devices relating to a mechanism which can
be used in gas cooling devices, pneumatic motors, turbines and
other pressurized gas devices. A rotatable rotor is provided along
with a number of hollow conduits that radially radiate from an exit
port at the center of the rotor. The pressurized gas is injected
into the mechanism at the inlet port(s). The gas enters the
conduits and travels from the inlet port(s) to the exit port(s). In
doing so, the gas causes the rotor to rotate about its central axis
while the gas cools. This results in a colder gas at the exit
port(s) than at the inlet port(s).
Inventors: |
Polihronov; Jeliazko;
(London, CA) ; Straatman; Anthony G.; (Thorndale,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
The University of Western Ontario |
London |
|
CA |
|
|
Family ID: |
49672249 |
Appl. No.: |
14/404606 |
Filed: |
May 28, 2013 |
PCT Filed: |
May 28, 2013 |
PCT NO: |
PCT/CA2013/050411 |
371 Date: |
November 28, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61652275 |
May 28, 2012 |
|
|
|
Current U.S.
Class: |
62/5 ; 415/1;
415/189 |
Current CPC
Class: |
F01D 9/048 20130101;
F01D 1/34 20130101; F25B 9/04 20130101 |
Class at
Publication: |
62/5 ; 415/1;
415/189 |
International
Class: |
F25B 9/04 20060101
F25B009/04; F01D 9/04 20060101 F01D009/04 |
Claims
1. A mechanism comprising: a rotatable rotor having an axis of
rotation; an exit port; an inlet port, said inlet port being for
receiving pressurized gas; a hollow conduit, said hollow conduit
directly connecting said inlet port to said exit port; wherein a
radial distance between said axis of rotation and said exit port is
less than a radial distance between said axis of rotation and said
inlet port; pressurized gas received at said inlet port passes from
said inlet port to said exit port through said conduit to thereby
cause said rotor to rotate about said axis of rotation; after
passing through said conduit, said pressurized gas at said exit
port is colder than said pressurized gas at said inlet port.
2. A mechanism according to claim 1 wherein said conduit is part of
said rotor.
3. A mechanism according to claim 1 wherein said conduit is mounted
on said rotor.
4. A mechanism according to claim 1 wherein said conduit radially
extends from said exit port to said inlet port.
5. A mechanism according to claim 1 wherein said mechanism is
sealed within an airtight enclosure.
6. A mechanism according to claim 1 wherein said mechanism is used
to decrease a temperature of said pressurized gas.
7. A mechanism according to claim 1 wherein said mechanism lowers a
temperature of said pressurized gas and converts energy extracted
from said pressurized gas into rotational work.
8. A mechanism according to claim 1 wherein a temperature
difference between said pressurized gas at said inlet port and said
pressurized gas at said exit port is up to c.sup.2/c.sub.p where c
is a tangential velocity at an inlet port with a greatest radial
distance from said axis of rotation of said rotor and c.sub.p is an
isobaric heat capacity of said pressurized gas.
9. A mechanism according to claim 1 wherein said pressurized gas is
injected at said inlet port, said pressurized gas being injected at
a direction tangential to said rotor and at right angles to said
axis of rotation.
10. A mechanism according to claim 1 further comprising at least
one other exit port.
11. A mechanism according to claim 10 further comprising at least
one further inlet port and at least one further conduit, said at
least one further conduit connecting said at least one further
inlet port to either said at least one other exit port or said exit
port.
12. A mechanism according to claim 10 further comprising at least
one further inlet port and at least one further conduit, said at
least one further conduit connecting said at least one further
inlet port to said exit port.
13. A mechanism according to claim 1 wherein a rotation of said
rotor is used to pressurize a gas to result in said pressurized
gas.
14. A mechanism according to claim 13 wherein said gas is derived
from pressurized gas exiting through said exit port.
15. A mechanism according to claim 1 wherein a distance between
said axis of rotation and said exit port is at a minimum.
16. A mechanism according to claim 1 wherein an amount of energy
transferred as propulsion to said rotor is up to E.sub.t=Mv.sup.2
where E.sub.t is said amount of energy transferred; M is a mass of
pressurized gas exiting at said exit port; and v is a velocity of
an inlet port with a greatest radial distance from said axis of
rotation of said rotor.
17. A method for cooling a gas, the method comprising: a) providing
a mechanism comprising: a rotatable rotor having an axis of
rotation; an inlet port; an exit port, a radial distance between
said exit port and said axis of rotation being less than a radial
distance between said inlet port and said axis of rotation; a
hollow conduit directly connecting said inlet port to said exit
port; b) providing said pressurized gas to allow said pressurized
gas to enter said inlet port; wherein pressurized gas provided at
said inlet port passes from said inlet port to said exit port
through said conduit to thereby cause said rotor to rotate about
said axis of rotation.
18. A method according to claim 17 wherein a difference in
temperature between said gas at said inlet port and said gas at
said exit port is up to c.sup.2/c.sub.p where c is a tangential
velocity at an inlet port with a greatest radial distance from said
axis of rotation of said rotor and c.sub.p is an isobaric heat
capacity of said pressurized gas.
19. A method according to claim 17 wherein an amount of energy
transferred as propulsion to said rotor is up to E.sub.t=Mv.sup.2
where E.sub.t is said amount of energy transferred; M is a mass of
pressurized gas exiting at said exit port; and v is a tangential
velocity at an inlet port with a greatest radial distance from said
axis of rotation of said rotor.
Description
TECHNICAL FIELD
[0001] The present invention relates to methods and devices
relating to the vortex tube effect and its application in a
mechanism that can be used in various practical applications.
BACKGROUND OF THE INVENTION
[0002] Various physical phenomena have been analyzed and their
practical applications have been found over the years. This
document revisits the concept of angular momentum conservation and
the corresponding propulsion imparted to a reference frame by an
ejected fluid. The focus is on constrained flows within moving
frames, where flow confinement results in a well-defined physical
problem. The thermophysics of the phenomena are examined with a
particular goal in mind--namely, to predict the fluid temperature
as observed in different frames of reference, to predict the
angular propulsion imparted to the rotating reference frame, as
well as describe the underlying physics leading to such
observations. Attention is devoted to the applicability of the
presented physical model to rotational flows, which exhibit radial
temperature separation. A most relevant example is the vortex tube
effect, discovered in 1933 by the French physicist Georges J.
Ranque. The effect has now been studied for nearly 80 years, yet
while a number of models have been proposed, they remain a subject
of debate. The fundamental reason for this is the complexity of
vortex tube flow obscuring the underlying physics, which in its
turn obfuscates any concise understanding of the effect.
Notwithstanding, interest in the vortex tube phenomena remains
high, as demonstrated by a present day literature search in the
Google Scholar database resulting in 4240 references to published
documents discussing the topic of vortex tube airflow.
SUMMARY OF INVENTION
[0003] The present invention provides systems, methods, and devices
relating to a mechanism which can be used in gas cooling devices,
pneumatic motors, turbines and other pressurized gas devices. A
rotatable rotor is provided along with a number of hollow conduits
that radially radiate from an exit port at or near the center of
the rotor. The pressurized gas is provided to the mechanism at the
inlet(s) of the rotor. The gas then enters the conduits and travels
from the inlet(s) of the rotor to the exit port. In doing so, the
gas causes the rotor to rotate about its central axis while the gas
cools. This results in a colder gas at the exit port than at the
outer perimeter of the rotor.
[0004] In one aspect, the present invention provides a mechanism
comprising: [0005] a rotatable rotor having an axis of rotation;
[0006] an exit port; [0007] an inlet port, said inlet port being at
a periphery of said rotor, said inlet port being for receiving
pressurized gas from said periphery of said rotor; [0008] a hollow
conduit, said hollow conduit directly connecting said inlet port to
said exit port; wherein [0009] a radial distance between said axis
of rotation and said exit port is less than a radial distance
between said axis of rotation and said inlet port; [0010]
pressurized gas received at said inlet port passes from a periphery
of said rotor to said exit port through said conduit to thereby
cause said rotor to rotate about said axis of rotation; [0011]
after passing through said conduit, said pressurized gas at said
exit port is colder than said pressurized gas at said periphery of
said rotor.
[0012] In another aspect, the present invention provides a method
for cooling a gas, the method comprising: [0013] a) pressurizing
said gas to produce a pressurized gas; [0014] b) providing a
mechanism comprising: [0015] a rotatable rotor having an axis of
rotation; [0016] an inlet port at a periphery of said rotor; [0017]
an exit port, a radial distance between said exit port and said
axis of rotation being less than a radial distance between said
inlet port and said axis of rotation; [0018] a hollow conduit
directly connecting said inlet port to said exit port; [0019] c)
providing said pressurized gas at a periphery of said rotatable
rotor to allow said pressurized gas to enter said inlet port;
[0020] wherein [0021] pressurized gas provided at said inlet port
passes from the periphery of said rotor to said exit port through
said conduit to thereby cause said rotor to rotate about said axis
of rotation.
BRIEF DESCRIPTION OF THE DRAWINGS
[0022] The embodiments of the present invention will now be
described by reference to the following figures, in which identical
reference numerals in different figures indicate identical elements
and in which:
[0023] FIG. 1 is a schematic diagram used to explain the principles
of the invention;
[0024] FIG. 2 is a partially transparent isometric view of a
mechanism according to one aspect of the invention;
[0025] FIG. 3 is a cross-sectional view of the mechanism of FIG. 2;
and
[0026] FIG. 4 is an exploded view of the mechanism illustrated in
FIG. 2.
DETAILED DESCRIPTION
[0027] The uniform rotation of a straight adiabatic duct about the
vertical symmetry axis of its outlet produces cooling of air at the
rotation center of the device. Air is supplied to the duct inlet by
a pressurized gas tank at room temperature. In this simple
illustration (FIG. 1), the tank is mounted to the duct inlet and
rotates with the duct. As air moves radially inward, it imparts its
kinetic and internal energy as propulsion to the rotating system.
This produces a twofold benefit: elimination of the requirement for
power to sustain rotation; and cooling of air at the exit of
device. Based on these findings it is concluded that the rotation
of this simple device and the accompanying refrigeration of air can
be utilized in providing instantaneous, on-demand refrigeration of
air, and shaft work due to angular propulsion of the rotating
system.
[0028] Thus in one aspect the present invention provides a
rotational device, comprising: [0029] a) a conduit D with length R
and drive means connected to the conduit D to impart rotational
velocity to said conduit D; [0030] b) an air tank, which provides
compressed air to the inlet of duct D [0031] c) a cold exit vent
positioned at a device centre, wherein pre-rotated air, supplied at
device periphery is run through the device and undergoes a sharp
temperature decrease, as this spiral motion of air leads to the
exhaust of cold air via said central exit vent.
[0032] Generally speaking, the systems described herein are
directed to method and device that reproduces and controls the
vortex tube effect. As required, embodiments of the present
invention are disclosed herein. However, the disclosed embodiments
are merely exemplary, and it should be understood that the
invention may be embodied in many various and alternative forms.
The Figures are not to scale and some features may be exaggerated
or minimized to show details of particular elements while related
elements may have been eliminated to prevent obscuring novel
aspects. Therefore, specific structural and functional details
disclosed herein are not to be interpreted as limiting but merely
as a basis for the claims and as a representative basis for
teaching one skilled in the art to variously employ the present
invention.
[0033] For purposes of teaching and not limitation, the illustrated
embodiments are directed to the method and device that that
reproduces and controls the vortex tube effect.
[0034] It should be noted that the analysis of the vortex
phenomenon assumes a priori that a rotating flow can be
discretized. Also examined is the behavior of the phenomenon's
discrete element--a paradigm through which the long-standing
physical phenomenon of temperature separation unravels and becomes
accessible to analysis. The main reasoning in this work follows
along the lines of establishing relative contexts of a stationary
and moving observer, positioned in their corresponding reference
frames, followed by an examination of relative flow motion and the
relevant conservation laws.
[0035] In the physics of fluids, the thermodynamic (or static)
temperature T.sub.S is that which corresponds to thermal
equilibrium and is the same in all frames of reference. The total,
or stagnation, temperature is an effective temperature that
originates from the total (or stagnation) enthalpy
h=hv.sup.2/2
via division by the isobaric heat capacity c.sub.p, and takes the
form
T .ident. T s + v 2 2 c p , ( 1 ) ##EQU00001##
where v is the fluid velocity. Because the total temperature
contains v, it is, consequently, frame-dependent. In a moving frame
F', this temperature becomes
T rel .ident. T s + v ' 2 2 c p , ( 2 ) ##EQU00002##
where v' is the flow velocity relative to the frame. In adiabatic
duct flow, the conservation of energy demands that the total
enthalpy is conserved. Thus, utilizing the connection between total
enthalpy and total temperature, energy conservation can also be
expressed as
T=const (3)
under adiabatic flow conditions.
[0036] Consider the reference frame F', rotating about the z-axis
with constant angular velocity .omega.=const. Energy conservation
in rotating fluid flows has the form
T s + v ' 2 - ( .omega. .times. r ) 2 2 c p = const ( 4 )
##EQU00003##
under adiabatic conditions. Let the rotating frame F' be attached
to a fluid flow system, comprising a tank of compressible fluid
under high pressure and room temperature T.infin., connected to the
inlet of an adiabatic duct, as shown in FIG. 1. The compressed
fluid is allowed to flow through the duct where it gradually
expands, accelerates and exits at the center of the frame. The
velocity addition formula for the system is
v=v'|.omega..times.r (5)
Expressing v' and substituting it into the energy conservation
condition (4) yields
T s + v 2 - 2 v ( .omega. .times. r ) + ( .omega. .times. r ) 2 - (
.omega. .times. r ) 2 2 c p = const . ( 6 ) ##EQU00004##
[0037] Reworking this expression to include the total fluid
temperature T seen in the stationary frame yields
T s + v ( .omega. .times. r ) 2 c p = const . ( 7 )
##EQU00005##
Therefore, the observer in the stationary frame F will report a
temperature difference
.DELTA. T = T ( inlet ) - T ( outlet ) = v inlet ( .omega. .times.
r inlet ) c p - v outlet ( .omega. .times. r outlet ) c p ( 8 )
##EQU00006##
between the high-energy peripheral flow and the low-energy flow at
the rotation center. Since in this particular fluid flow system the
duct is straight,
v'|.omega..times.r
everywhere, and because the flow exits at the rotation center,
r.sub.outlet=0. If we denote the peripheral tip speed of the
duct
.omega..times.r.sub.outlet
as c, then (8) reduces to
.DELTA. T = T ( inlet ) - T ( outlet ) = c 2 c p . ( 9 )
##EQU00007##
[0038] Thermodynamics of the flow is interpreted in F and F' as
follows:
[0039] According to an observer in the moving frame F':
1. Both static and relative total temperatures in the fluid tank
are equal to T.sub..infin.; 2. The tank fluid expands through the
duct and does work to overcome the centrifugal gravitational
potential -(.omega..times.r).sup.2/2; the exiting fluid has lost
internal energy and gained gravitational potential energy; 3. The
fluid accelerates through the duct, due to expansion, and
experiences the deflecting action of the Coriolis force; 4. At the
outlet, the exiting fluid has a higher velocity than at the duct
inlet due to expansion, but has lost internal energy and is
c.sup.2/2c.sub.p cooler than T.sub..infin..
[0040] According to an observer in the stationary frame F:
1. The total temperature in the pressurized fluid tank is
T=T.sub..infin.+c.sup.2/2c.sub.p due to the motion of F'; 2. The
fluid speed at the duct inlet is equal to c and the temperature is
equal to the temperature in the fluid tank
T(inlet)=T.sub..infin.+c.sup.2/2c.sub.p; 3. High-energy fluid
decelerates as it approaches the outlet; that is, while the radial
velocity increases, the tangential velocity goes to zero, resulting
in a substantial net deceleration; 4. At the outlet, the exiting
fluid has low velocity and has also lost internal energy. This
conclusion contradicts the intuition of the stationary observer,
since a high-energy volume of compressible fluid is expected to
exhibit a static temperature rise when brought to rest
adiabatically.
[0041] It is seen that the energy conservation condition (7)
imposes radial dependence in the total temperature known as
temperature separation. It is a physical phenomenon, in which
rotating fluid flow appears heated at the periphery and cooled at
the center of rotation. Therefore, in the case of rotation, cooling
of the ejected fluid is due to conservation of angular momentum and
the corresponding angular propulsion imparted to the rotating
frame. It is this critical element that leads to a clear
understanding of the temperature separation effect in fluids. Since
the energy conservation requirement (4) applies under adiabatic
conditions, it prohibits heat exchange through the duct walls in
the system in FIG. 1. Therefore the cooling of the fluid (9) is a
result of adiabatic expansion, during which the fluid does work on
its surroundings by propelling the moving reference frame.
[0042] Let us now begin to examine the rotating duct system with
the goal of determining the propulsion energy that goes into the
rotation as a result of an ejection of the gas coming from the
tank. For this purpose, consider that the rotating tank and duct
assembly is a system with variable mass. This is the main physical
context within which the following study will be made.
[0043] Let M be the constant composite mass of this system, moving
with angular velocity .omega.=c/r in a circle with radius r. For
generality, consider the position vector R and velocity vector v in
the stationary frame of reference F (which reduce to r and c in the
system shown in FIG. 1). Consider an external torque (e.g.
resistance of the medium) .tau..sub.ext be acting on M at time t.
At some later moment t+.DELTA.t, the composite system ejects mass
.DELTA.M, which moves radially inwards on a radial constraint and
thus the angular momenta L are
L(t)=R.times.Mv
L(t+.DELTA.t)=R.times.(M-.DELTA.M)(v+.DELTA.v).
The rotational equivalent to the second law of Newton
R.times.M{dot over (v)}=.tau..sub.ext-R.times.{dot over (M)}v,
for this constant mass system in F is
.tau..sub.ext=.DELTA.L/.DELTA.t, which leads to the equation of
rotational motion as .DELTA.t.sub..fwdarw.0 where the mass flux
dM/dt is negative, since the mass of the body is decreasing in
time. A tacit assumption is that mass dM, even though moving
initially with velocity v as part of the composite mass M, reaches
zero velocity at the rotation center within a time interval dt.
[0044] For rotating systems with finite size, this is still a
reasonable assumption, since masses dM, each moving with their own
speed within the system, form a continuous radial flow of ejected
mass dM/dt.
[0045] The expression
R.times.{dot over (M)}v
represents rotational thrust, which is maximum in the stationary
frame F, since the velocity of the expelled mass is zero. This
expression has dimension of torque; it is to be attributed to the
third law of Newton, according to which the rotating system
experiences the reaction torque of the radially ejected mass flow
dM/dt.
[0046] The rotational motion produced always corresponds to maximum
thrust when mass is ejected at the center of rotation where its
velocity is zero. Let us consider the case v=const, where the
external resistance of the environment is precisely counterbalanced
by the rotational thrust. In this case, the power delivered to the
rotational system by the thrust torque is since
.tau..sub.ext.omega.={dot over (M)}v.sup.2
since
.tau..sub.ext=R.times.Mv and R.perp.v
which leads to
.tau..sub.ext.omega..sup.12=.tau..sub.ext.omega..
[0047] Then, the thrust energy delivered to the system per expelled
mass M is
E.sub.t=Mv.sup.2.
[0048] The equations of mechanics are sufficient to describe the
concept of the propelled rotational motion. However, one is led to
conclude that the most practically important variable mass systems
will rely on the properties of gas: gases can form continuous flow
and thus produce constant thrust; also, gases are capable of
storing energy, which is reflected by their temperature. For these
reasons, the thermodynamics of rotating variable mass systems is
important, and will be included in this study.
[0049] As it was shown in (9) above, the exiting gas experiences a
drop in total temperature .DELTA.T=c.sup.2/c.sub.p. It was shown,
that according to an observer in F, there is a radial gradient of
the total temperature over the entire radial extent of the system.
The tank at the periphery appears heated (entirely kinetic, not
thermodynamic heating), while the exhaust gas at the center is
cold. Since the total temperature T is defined through the total
(stagnation) enthalpy of the gas, the energy transferred as
propulsion to the rotating system is
E.sub.t=c.sub.pM.DELTA.T=.DELTA.v.sup.2,
the same expression as the one for thrust energy delivery (with v=c
at the duct inlet), calculated above entirely with the equations of
mechanics. Thus, energy was invested into the gas in a twofold
process: (i) energy Mv.sup.2/2 was invested as internal energy and
(ii) kinetic energy Mv.sup.2/2 was invested by setting the system
in rotational motion with angular velocity co. By ejecting itself
from the center of mass of the rotating system, gas with mass M
spends internal energy Mv.sup.2/2 in order to decrease its kinetic
energy by Mv.sup.2/2, thus imparting rotational thrust energy
Mv.sup.2 to the system.
[0050] Thus, rotary propulsion motion producing maximum thrust is
the rotational motion of a system with variable mass, exhausting at
its center. The rotational system can also be characterized as an
angular propulsion engine (APE) that derives thrust torque due to
conservation of angular momentum, i.e.
.tau..sub.ext=.DELTA.L/.DELTA.t. The maximum propulsion energy
attributed to an APE having peripheral speed v by the ejection of
gas at its center is Mv.sup.2--a sum of two equal energy portions,
one of which is due to the deceleration of the expelled gas and the
other to its cooling. The basic rotational system we studied
exhibits a gradient of the total temperature over the entire radial
extent of the system, as witnessed in the stationary reference
frame F. The mechanics of the rotating system has a direct and
precise connection to the cooling of gas explained in the
thermodynamics argument above, and thus further elucidates the
concept of angular propulsion. In addition, the treatment presented
herein shows that the thermophysics of the rotating system is
derived based on existing laws; no special treatment to the mass,
Navier-Stokes or energy transport equations for compressible,
rotating flows is implied. On this basis, it is not surprising that
commercially available computational fluid dynamics solvers are
already capable of predicting the observed cooling effect.
[0051] What are the conditions under which no cooling is observed?
If the reference frame containing the flow is not moving, no
cooling will be observed since the frame is unable to absorb the
flow energy. For a duct at rest, where the exiting flow velocity
has been chosen to be equal to c, no temperature decrease is
observed. Cooling in the stationary frame is produced only when the
duct system is moving and able to absorb the energy of the flow as
thrust or propulsion. The produced temperature separation .DELTA.T
grows with the magnitude of the frame velocity c and is limited by
the speed of sound in the surrounding fluid for practical reasons.
.DELTA.T is always symmetric with respect to the ambient
temperature T.sub..infin. and equal to c.sup.2/c.sub.p. When c is
nearly equal to the speed of sound at sea level (340 m/s),
.DELTA.T=115.2 K. The heating of c.sup.2/2c.sub.p=57.6 K is
entirely dynamic and due to the motion of the duct periphery with
velocity c; the cooling is due to an adiabatic expansion needed to
overcome the centrifugal potential barrier and has magnitude of
c.sup.2/2c.sub.p=57.6 K.
[0052] It is also important to note that compressibility of the
fluid is vital for storing internal energy, which would later be
imparted to the frame upon decompression as well as result in a
reduction of static temperature. In the case of incompressible
fluids, energy is still transferred to the frame due to angular
momentum conservation, however this cannot produce cooling as the
fluid is unable to give up internal energy. The same conclusion is
found in the work of R. Balmer, where water was used as the working
fluid in a vortex tube. Cooling was not achieved in any of the
conducted experiments by Balmer and fluid at the periphery was
reported to have an elevated temperature. This result is consistent
with angular propulsion imparted on the rotating fluid, resulting
in high kinetic energies at the periphery consequently leading to
heating through friction.
[0053] It is also worth noting that the magnitude of AT does not
depend on the radial size of the rotating system, as long as its
peripheral velocity is equal to c in the stationary frame. In
addition, centrifugal and Coriolis forces alone cannot alter the
total temperature of the flow, since no work is subtracted from the
fluid under gravity.
[0054] Flow through the rotating duct shown in FIG. 1 was also
computed using the commercial computational fluid dynamics (CFD)
solver FLUENT to demonstrate that the results of the presented
theoretical model are also obtained by discretely solving the
differential transport equations for mass, momentum and energy.
Simulations were performed with air as an ideal gas using the
3-dimensional, double precision discretization model for
compressible flow. The standard version of the k-.epsilon. model
with wall-functions was used to characterize turbulence effects,
and the second-order upwind discretization scheme was used to model
advection in the transport equations. Since physical scale is not a
factor in the current treatment, the duct was given a length of 15
m and rectangular cross-sectional dimensions 0.3 m.times.0.4 m with
no-slip, adiabatic walls. Smaller or larger ducts will produce the
same effect provided the rotational speed is adjusted to develop
the same pressure gradient across the duct. In all calculations,
the mass flow rate of the air was fixed at 3 kg/s; the highest
rotational speed was selected such that the peripheral velocity of
the duct c remained subsonic. Energy, momentum and mass
conservation were reached in all simulations, with residuals
decreasing smoothly to below 10.sup.-13. Table 1 compares the
theoretical .DELTA.T=.omega..sup.2r.sup.2/c.sub.p (r=15 m) with its
corresponding total temperature difference predicted by FLUENT for
different rotational speeds
TABLE-US-00001 TABLE 1 .DELTA.T for different rotation rates (1),
rod/s 0 2 5 10 15 20 .DELTA.T, CFD [K] 0 0.89 5.53 22.08 49.68 88.3
.DELTA.T, Eq. (9). [K] 0 0.9 5.61 22.42 50.45 89.69
[0055] The CFD predictions approximate the theoretical result to
within 1.5% in all cases. This comparison shows that the numerical
values for AT given by Equation (9) are also obtained using another
well-established method; it should be borne in mind that CFD
utilizes discretization and turbulence modeling and as such
represents an approximation to the physical phenomena described
above.
[0056] While the setup in FIG. 1 is not identical to a vortex tube,
it demonstrates the essential physical characteristics of the
vortex tube flow, namely spiral flow geometry accompanied by radial
pressure and temperature behavior. Therefore, a rotating duct or
conduit can be considered a discrete element of the vortex tube
flow field. It presents a simplification in the description of
vortex tube flow, which allows for a succinct explanation of the
vortex tube phenomenon. For the rotating duct, flow is driven from
the periphery to the center by a pressure gradient that opposes the
centrifugal gravitational field induced by rotation. Energy is
imparted by the expanding fluid to propel the rotating frame via
the interface between the fluid and the solid (i.e. the duct or
conduit wall). In this manner, maximum energy exchange occurs and
the maximum possible temperature separation is observed. In the
case of a vortex tube, flow is driven from the periphery of the
tube to the center by a pressure gradient that opposes the induced
gravitational field, but the expanding fluid can only transfer
energy to the rotating frame (the fluid itself) via fluid friction,
leading to less efficient cooling than that for the confined
flow.
[0057] A key difference between the rotating duct and the vortex
tube is the necessity of a hot fluid outlet in the latter. The hot
outlet is not required in the rotating duct because the compressed
fluid source is rotating with the duct; the only heating that
occurs is due to fluid friction opposing the flow towards the duct
outlet. In a vortex tube, the fluid enters the tube at the
periphery to generate the swirling flow, and to set up the
(centrifugal) gravitational field and the pressure gradient.
Because of the high flow speeds required to set up the required
gravitational field, fluid friction results in significant viscous
dissipation at the periphery, which must be removed to achieve any
cooling effect at the cold outlet (relative to the inlet). If the
hot outlet were closed, the fluid leaving the system would simply
absorb all of the viscous heat and leave the system warmer than it
entered.
[0058] In terms of the magnitude of temperature separation, the
control parameters in either case are the rotational speed of the
fluid and the radius from the center to the periphery, since this
sets up the strength of the centrifugal gravitational field, which
dictates the pressure gradient from the periphery to the center.
This pressure gradient dictates the maximum temperature drop that
can be achieved by expansion of the fluid as it flows towards the
cold outlet.
[0059] When radial flow of a compressible fluid takes place in a
uniformly rotating adiabatic duct, the resulting cooling that is
observed at the centre of rotation is due to adiabatic expansion of
the fluid as well as conservation of angular momentum, which
demands transfer of internal and rotational energy of the moving
mass to the rotational energy of the system. Cooling cannot be
produced in a stationary duct by gravity, as frame motion is
required for an energy transfer to occur. Compressibility is
another required factor for cooling since it reflects the ability
of the fluid to give away internal energy. Of key importance, is
that the confined rotating fluid flow system presented in this work
exhibits the essential physics of the vortex tube flow, namely
radial temperature and pressure gradients as well as velocity
fields and flow geometry. It is therefore plausible to consider
this simplified flow system as a discrete element of vortex tube
flow, which provides a concise understanding of the observed
temperature separation phenomenon.
[0060] The above can be seen as the theoretical basis for one
aspect of the invention. In one implementation, the present
invention provides a mechanism which may be used for rotary motors,
the cooling of gases, and the efficient conversion of gas pressure
into mechanical work.
[0061] Referring to FIG. 2, a partially transparent isometric view
of the mechanism is provided. As can be seen, the partially
transparent view in FIG. 2 is provided to present the internal
workings and components of the mechanism.
[0062] The mechanism 10 in FIG. 2 has four inlet ports 20 through
which a pressurized gas can be provided to the mechanism. A
rotatable rotor 30 is inside the mechanism. The rotor 30 has an
exit port 40 located at its center and four conduits 50 extend
radially from the exit port 40 to the outer perimeter of the rotor.
The conduits 50 are hollow and provide a passageway for pressurized
gas to travel from the outer perimeter of the rotor to the exit
port. In this embodiment of the invention, the conduits are all
straight and do not deviate from the exit port to the outer
perimeter of the rotor.
[0063] Referring to FIG. 3, a side cut-away view of the mechanism
in FIG. 2 is provided. The exit port 40 at the center of the rotor
30 leads to a gas exit shaft 60 through which the pressurized gas
exits the mechanism. To facilitate the rotation of the rotor 30,
the rotor 30 is sandwiched between bearings 70 which allow the
rotor 30 to freely rotate. A driveshaft 80 is coupled to the rotor
30 such that rotation of the rotor 30 similarly rotates the
driveshaft 80. As can be seen, the gas exit shaft 60 is inside the
hollow driveshaft 80. Seals 90 adjacent the bearings 70 and the
driveshaft 80 ensure that an airtight seal is maintained for the
mechanism. Similarly, an enclosure 100 provides an airtight
environment for the mechanism. In this configuration, the
driveshaft 80 is collinear with the rotor's axis of rotation.
[0064] It should be noted that, preferably, there should be minimal
space between the rotor and the upper and lower portions of the
enclosure. However, there should a gap 110 between the outer
perimeter or periphery 120 of the rotor 30 and the inside wall 130
of the enclosure 100. The gap 110 is there to allow the pressurized
gas to travel from the inlet ports to the various conduits.
[0065] In operation, a pressurized gas is provided to the mechanism
by way of the inlet ports. In FIGS. 2-4, the said ports are
oriented such that gas is injected in a direction tangential to the
rotor periphery and in the direction of rotor rotation. This
configuration is preferable as it provides optimal results. The
pressurized gas enters the conduits and travels from the outer
perimeter of the rotor to the exit port at the center of the rotor.
In doing so, the pressurized gas causes the rotor to rotate about
its center and thereby also causes the driveshaft to rotate. While
travelling from the outer perimeter or periphery of the rotor to
the exit port, the temperature of the pressurized gas drops,
thereby providing a cooler gas at the exit port than at the outer
perimeter of the rotor.
[0066] An exploded view of the mechanism in FIGS. 2-3 is
illustrated in FIG. 4 to provide the reader with a more detailed
view of the various parts of the mechanism.
[0067] Regarding the implementation of the mechanism illustrated in
FIGS. 2-4, the four conduits illustrated divide the rotor into four
quadrants. Preferably, these quadrants are of equal size with each
conduit being at 90 degrees from adjacent conduits for the purpose
of mechanical balancing of the rotor.
[0068] It should be noted that while four straight conduits are
shown in the drawings, other configurations are possible. As an
example, a three conduit configuration is possible, with each
conduit being at 120 degrees to its adjacent conduits. Similarly,
more than four conduits may be used.
[0069] Again regarding the spacing of the conduits on the rotor, it
should be noted that while a regular spacing between conduits is
preferable, an uneven spacing between the conduits may also be
used.
[0070] It should be noted that the rotor can be extended axially to
provide space such that radial conduits can be provided in layers,
thereby allowing for any number and configuration of conduits.
Different configurations of such an arrangement is possible. As an
example, differing layers of conduits and rotors may be stacked
above one another with a common exit port at the center of the
driveshaft for the varying rotors.
[0071] The conduits may be formed as a tunnel in the material of a
solid rotor or the conduits may be a hollow tube embedded in the
structure of the rotor. Similarly, the conduits need not be located
within the rotor--placement of the rotor may be above, under, or
inside the rotor as long as the rotor is coupled to the rotor such
that pressurized gas travelling through the conduits will cause the
rotor to rotate. The conduits may have any suitable shape but it
has been found that straight conduits that directly radiate from
the center of the rotor to the rotor's periphery provided the best
results.
[0072] As well, while the figures illustrate straight conduits
which radially radiate from the center of the rotor, straight
conduits which are tangential to the central exit port are also
possible. Such a configuration would still have each conduit
providing a direct passage from the outer perimeter of the rotor to
the exit port. However, for this configuration, the conduits would
be directing the pressurized gas in a direction tangential to the
exit port instead of in a direction that is radial to the exit
port.
[0073] The pressurized gas may be provided to the periphery of the
rotor in any suitable manner. Preferably, if the pressurized gas is
to be injected into the mechanism, the gas is to be injected in a
direction that is tangential to the rotor and at right angles to
the rotor's axis of rotation. Differing angles at which the
pressurized gas may be provided to the mechanism may be used as
long as the gas is not injected in a direction with components that
are opposite to the direction of rotation of the rotor. As well, it
is preferred that the direction of the pressurized gas is not
parallel to the axis of rotation of the rotor.
[0074] It should be noted that the radial distance between the
rotor's axis of rotation and the exit port should be less than the
radial distance between the rotor's axis of rotation and the inlet
port. In the configuration illustrated in FIGS. 2-4, the rotor's
axis of rotation is at the center of the rotor such that the
distance between the rotor's axis of rotation and the exit port is
at a minimum. However, other configurations where the exit port is
not at the center of the rotor are possible. It should further be
noted that, while multiple exit ports are also possible, a single
exit port at the center of the rotor is preferable as this has been
shown to provide the best results.
[0075] For configurations that have multiple exit ports, each of
the various conduits connects one or more of the inlet ports to an
exit port. It should be clear that the various inlet ports and
their associated exit ports need not be on the same plane. It
should also be clear that each inlet port is associated with an
exit port with a conduit directly connecting an inlet port (or
multiple inlet ports) with an exit port.
[0076] It should be noted that in the configuration illustrated in
FIGS. 2-4, the inlet port is located at the periphery of the rotor.
However, other configurations where the inlet port is not at the
periphery of the rotor are possible, as long as the radial distance
from the center of rotation to the inlet port is larger than the
radial distance from the center of rotation to the associated exit
port.
[0077] It should also noted that not all inlet ports need be at the
same radial location. Any configuration is possible provided that
the radial distance from the center of rotation to the inlet port
is larger than the radial distance from the center of rotation to
the associated exit port.
[0078] While FIGS. 2-4 and the discussion above describes multiple
conduits, a configuration using a single inlet port and a single
conduit connecting the inlet port to a single exit port is also
possible.
[0079] Regarding the pressurized gas, this may be any suitable gas
such as compressed air.
[0080] Regarding the use of the mechanism, the mechanism may be
used in any device, motor, engine, or system that involves a
rotating rotor or the cooling of a pressurized gas. As noted above,
the temperature of the pressurized gas at the periphery of the
rotor is higher than the gas exiting at the exit port. Accordingly,
the mechanism may be used in applications that require the cooling
or the lowering of the temperature of a pressurized gas. Similarly,
the rotation of the rotor may be used to turn a shaft that can be
used to do work. The mechanism may therefore be used as part of a
pneumatic engine, turbine or motor.
[0081] In one configuration, the rotation of the rotor may be used
to pressurize gas to be used in the mechanism. As an example, gas
exiting through an exit port may be recycled by being pressurized
using the rotation of the rotor. Once pressurized, the pressurized
gas may then be reintroduced into the system.
[0082] Once the pressurized gas has been introduced into the
system, a pre-rotation may be needed to start the system. This may
take the form of manually rotating the rotor. Once the rotor starts
rotating, the pressurized gas in the system can continue the
rotor's rotation.
[0083] To better understand the principles behind the invention,
the following references are provided. These references are hereby
incorporated by reference. [0084] G. J. Ranque, "Experiments on
expansion in a vortex with simultaneous exhaust of hot and cold
air", J. Phys. Radium, vol. 4, p. 112S, 1933. [0085] Y. Xue, M.
Arjomandi and R. Kelso, "A critical review of temperature
separation in a vortex tube", Exper. Therm. Fluid Sci., vol. 34, p.
1367, 2010. [0086] E. A. Baskharone, "Principles of Turbomachinery
in air-breathing engines", Cambridge University Press, Jul. 31,
2006. [0087] M. G. Rose, "From Rothalpy to Losses", Lecture Notes,
Swiss Federal Institute of Technology LSM Zurich 2002. [0088] R.
Resnick and D. Halliday, "Physics I", p. 307, Wiley, 1966. [0089]
R. T. Balmer, "Pressure-driven Ranque-Hilsch Temperature Separation
in Liquids", J. Fluid Engn., vol. 110, p. 161, 1988.
[0090] A person understanding this invention may now conceive of
alternative structures and embodiments or variations of the above
all of which are intended to fall within the scope of the invention
as defined in the claims that follow.
* * * * *