U.S. patent application number 10/278480 was filed with the patent office on 2004-06-03 for thermal management system.
Invention is credited to Crutchfield, Paul.
Application Number | 20040104011 10/278480 |
Document ID | / |
Family ID | 32392351 |
Filed Date | 2004-06-03 |
United States Patent
Application |
20040104011 |
Kind Code |
A1 |
Crutchfield, Paul |
June 3, 2004 |
Thermal management system
Abstract
The present invention includes use of suitable inert, or
non-reactive, gas, or gases, having suitably small molecules (such
as helium or neon) in a heat pipe to enhance the surface tension
(capillarity) of the heat pipe working fluid, thus improving the
design and performance of almost any heat pipe. A region in the
vapor space adjacent to the curved liquid surface contributes about
5-10% to the total surface tension, and is described as the
Crutchfield Transition Region. The invention takes advantage of the
kinetic theory of capillarity based on penetrations of the liquid
surface by the overbearing gas and vapor molecules until a
collision between liquid and gaseous molecules occurs. Smaller
molecules such as helium penetrate further. A spread loss (or gain)
of the particle flux frames a pressure change.
Inventors: |
Crutchfield, Paul; (Duluth,
GA) |
Correspondence
Address: |
TROUTMAN SANDERS LLP
BANK OF AMERICA PLAZA, SUITE 5200
600 PEACHTREE STREET , NE
ATLANTA
GA
30308-2216
US
|
Family ID: |
32392351 |
Appl. No.: |
10/278480 |
Filed: |
October 23, 2002 |
Current U.S.
Class: |
165/104.26 ;
165/104.21 |
Current CPC
Class: |
F28D 15/02 20130101 |
Class at
Publication: |
165/104.26 ;
165/104.21 |
International
Class: |
F28D 015/00 |
Claims
What is claimed is:
1. In a heat pipe having a container, a transfer device, and a
working fluid, the improvement comprising the addition of a gas in
the container having suitably small molecules to enhance the
surface tension of the working fluid.
2. The improved heat pipe of claim 1, wherein the gas and the
working fluid have a mean free path greater than that between air
and water.
3. The improved heat pipe of claim 1, wherein the gas has a
particle diameter less than that of water.
4. The improved heat pipe of claim 1, wherein the working fluid is
capable of hydrogen bonding.
5. The improved heat pipe of claim 1, wherein the working fluid is
polar.
6. The improved heat pipe of claim 1, wherein the gas is an inert
gas.
7. The improved heat pipe of claim 1, wherein the gas is
helium.
8. The improved heat pipe of claim 1, wherein the gas is neon.
9. The improved heat pipe of claim 1, wherein the transfer device
is a wick.
10. The improved heat pipe of claim 1, wherein the transfer device
is a porous material.
11. The improved heat pipe of claim 1, wherein effective collision
diameter for molecules of the working fluid and molecules of the
gas is less than approximately 3.04 .ANG..
12. In a heat pipe having a container, a transfer device, and a
working fluid, the improvement comprising the addition of a gas in
the container wherein the gas and the working fluid have a mean
free path greater than that between air and water.
13. The improved heat pipe of claim 12, wherein the gas is an inert
gas.
14. The improved heat pipe of claim 12, wherein the effective
collision diameter for molecules of the working fluid and molecules
of the gas is less than approximately 3.04 .ANG..
15. The improved heat pipe of claim 12, wherein the gas has
particle diameter of less than 3.88 .ANG..
16. The improved heat pipe of claim 12, wherein the gas has
particle diameter of less than 3.72 .ANG..
17. The improved heat pipe of claim 12, wherein the gas has
particle diameter of less than 2.18 .ANG..
Description
BACKGROUND OF THE INVENTION
[0001] 1 Field of the Invention
[0002] The present invention generally relates to a thermodynamic
system that takes advantage of the kinetic theory of capillarity,
including a vapor-side component of capillarity. More specifically,
the present invention is a thermal management system including a
heat pipe having a helium atmosphere, the heat pipe utilizing a
vapor-side component of capillarity.
[0003] 2. Description of the Related Art
[0004] Conventional wisdom holds that the rise of water in a thin
capillary tube is understood as a mismatch of intermolecular forces
at the interface of the water surface and the overbearing
atmosphere. The mismatch produces a state of tension at the surface
such that for a hemispheric surface of the water in a capillary
tube, the lifting force, .sigma. in Newtons per meter (N/m), acting
on the circumference of the hemisphere, will lift the
water--ignoring air density above the surface in the
tube--according to the following relationship:
2.pi..sigma.R=.DELTA..rho.gH.pi.R.sup.2, (1)
[0005] where .DELTA.p is the difference in water density and the
surrounding gas,
[0006] H is height of rise of the column of water,
[0007] g is the gravity constant, and
[0008] .sigma. is the surface tension in N/m.
[0009] A review of units shows "Newtons"="Newtons", or
"force"="counter force". Division by the capillary tube
cross-sectional area, .pi.R.sup.2, leaves the unit force per unit
area, or pressure. The force of surface tension produces a step
change in pressure across the meniscus surface equal to the drop in
pressure produced by the rise of water in the tube.
[0010] In the case of non-circular surfaces, the sum of orthogonal
curvatures, 1/R.sub.1+1/R.sub.2 must be used instead of 2/R as
encountered in a circular tube. The wetting angle between the water
surface and the tube surface must also be considered.
[0011] Many have written about the capillary rise phenomena,
including Newton, Gauss, Laplace, Gay-Lussac, Poisson and Maxwell.
Further, the value of the surface tension of water has been
thoroughly measured from the freezing temperature to the critical
temperature, as partially shown in Table 1. Table 1 provides
calculations of the three components of surface tension in
10.degree. C. steps under atmospheric air. The temperature and
density components in the vapor state are lumped by means of the
Clausius-Clayperon factor.
1TABLE SUFACE TENSION COMPONENTS, WATER IN AIR ATMOSPHERE, N/M
10.sup.3 Steam Table Temp Liq. Density Liq., T Vapor Eff. Molecular
Derived Radii, (C.degree.) Component.sup.1 Comp.sup.2 Comp.sup.3
.sigma. TOTAL.sup.4 Radii, .ANG..sup.5 .ANG..sup.6 0 54.32 18.03
3.15 75.50 1.86 1.926 10 57.78 13.32 3.30 74.40 1.84 1.926 20 59.84
9.59 3.44 72.87 1.86 1.927 30 60.75 6.87 3.58 71.20 1.89 1.928 40
60.81 4.96 3.71 69.48 1.92 1.931 50 60.29 3.65 3.83 67.77 1.94
1.933 60 59.38 2.77 3.91 66.06 1.95 1.937 70 58.21 2.19 3.96 64.36
1.95 1.940 80 56.93 1.82 3.94 62.69 1.93 1.944 90 55.34 1.61 3.83
60.78 1.90 1.949 100 53.75 1.59 3,57 58.91 1.81 1.953 .sup.1Derived
using density term of Equation (3) below. .sup.2Derived using
temperature term of Equation (3) below. .sup.3Derived using
Equations (3) and (5) below. .sup.4Total values of surface tensions
(sum of components) obtained from Tables On Thermophysical
Properties Of Liquids And Gases, Second Edition, by N.B. Vargaflik,
Hemisphere Publishing Corp., Washington, London. .sup.5Effective
Molecular Radii are collision radii of liquid molecules that would
produce necessary components of surface tension to agree with
experimental results. .sup.6Steam Table Derived Molecular Radii are
obtained by determining radius of a sphere taking up the volume
allocated to individual molecules from Avogadro's number. (Included
as an indicator of the reasonableness of "Effective Molecular
Radii").
[0012] Although the value of the surface tension of water has been
measured, few have analytically quantified the values of surface
tension over any range of temperatures. This is understandable, as
those of the past had neither modern computers nor a suitable
Equation of State for water, the equation itself a product of
modern computers.
[0013] It proves to be beneficial to provide a kinetic approach to
surface tension, and to use such an approach to provide a new and
non-obvious enlianced thermal management system. It is to the
provision of such a system that the present invention is primarily
directed.
BRIEF SUMMARY OF THE INVENTION
[0014] The present invention is an application of a kinetic theory
to explain the capillarity (surface tension) phenomenon, and will
be discussed in examples using water as the working medium,
although any element or mixture in its liquid state may be
suitable, especially those exhibiting a relatively high surface
tension, polarity, or a capability of hydrogen bonding. It is
assumed the overbearing air and water vapor molecular penetrations
into the water surface produce an expansion, or compression, of the
liquid across a transition zone at a curved interface because of
the focusing effect of the curved surface. A fallout of the theory
is a discovery of a pressure change contribution across a vapor
transition zone, usually about one order of magnitude less than the
liquid transition contribution, this region hereby being defined as
the "Crutchfield Transition Region."
[0015] In the vapor region remote from the liquid surface,
constituent molecules develop a "mean free path" between
collisions. This concept leads to pressure against a smooth
container wall. Hitherto it stops short of consideration of a
curved, partially penetrable liquid surface. Such curves and
penetrations generally require no consideration in the case of a
flat liquid surface. However, for a curved surface, molecules
departing the surface experience either a compression or an
expansion, hence either a rise or fall in temperature and pressure
when joining their new surroundings. A Clausius-Clayperon
relationship facilitates analysis of this situation.
[0016] Accordingly, there are four components of the surface
tension--a pressure one and a temperature one in the liquid
transition zone, and a pressure one and a temperature one in the
Crutchfield Transition Zone, the latter two amenable to coupling
using the Clausius-Clayperon formula. Utilizing known data and an
Equation of State, surface tension components of water from the
freezing temperature to the critical temperature were calculated,
with good results except near the critical temperature (where the
basic assumptions are invalid). Results in Table 1 are shown for
water under a standard atmosphere, 0.degree. to 100.degree. C.
[0017] An experiment illustrates an increase in the capillary rise
of water under a helium atmosphere (as opposed to air) attributable
to the thicker transition zones effected by the relatively smaller
helium atoms.
BRIEF DESCRIPTION OF THE FIGURES
[0018] FIG. 1 is a cross section of a heat pipe according to the
present invention.
[0019] FIGS. 2a-c are examples of cycloids referenced herein.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0020] A Kinetic Approach To Surface Tension
[0021] A compressed gas exerts pressure on the walls of a container
by means of the rebounds of myriad molecules of the contained gas
against the walls. The same occurs against an underlying liquid
surface, for example, water. However, some degree of penetration
.DELTA..sub.PENETRATION into the water should take place, depending
upon the size and shape of the involved molecules of both the water
and the gas. Though it is easier to measure a capillary rise, it is
simpler to analyze effects on spherical droplets where the sphere's
surface produces a focusing effect.
[0022] Consider the normal direction from a differential area,
.DELTA.S, on the surface of a spherical drop of water in an air
atmosphere. Unless the sphere is in motion with respect to its
environment, non-radial molecular bombardments (and recoils) will
cancel each other's non-radial forces. There will be a mean free
distance that molecules will penetrate to, or emanate from, inside
.DELTA.S. The operative distance (similar to the development of
viscosity theory), taking all directions into account, would be
one-third a mean free path in the radial direction -.delta.r. The
focusing effect of the spherical surface drives the radial flux of
water (and air) molecules according to the relationship:
.PHI.=.PHI..sub.0(R/r).sup.2 (2)
[0023] where .PHI..sub.0 is the flux at the surface, and
[0024] where r=R.
[0025] Vapor Component of Surface Tension
[0026] A hitherto neglected phenomenon in the capillary arena is
the region in the vapor area immediately surrounding the sphere
which also extends to one-third a mean free path radially,
.DELTA.r--orders of magnitude greater than that in the liquid.
[0027] Since pressure of water may be defined by a function of
density and temperature, the differential relationship follows:
dP=.differential.P/.differential.T
dt+.differential.P/.differential..rho.d- .rho. (3)
[0028] Keenan, Keyes, Hill and Moore in their STEAM TABLES,
Thermodynamic Properties of Water Including Vapors Liquid, and
Solid Phases, Keenan, Keyes, Hill and Moore, John Wiley & Sons,
have provided an Equation of State for addressing Equation (3)
above. The density is inversely proportional to r.sup.2 in both the
liquid and vapor regions, to wit:
d.rho.=(-)(2/R).rho..sub.0dr (4)
[0029] where dr is one-third a mean free path in either region.
[0030] Assuming the region extending to a distance .DELTA.R in the
vapor region is saturated, the Clausius-Clayperon relationship
would apply, to wit:
dP=(h.sub.fg/v.sub.fg)dT/T (5)
[0031] where h.sub.fg and v.sub.fg are the enthalpy and volume
differences between the saturated liquid and saturated vapor.
[0032] Solving equations (3) and (5) provides a multiplying factor
to apply to the partial derivative with respect to density,
yielding the total derivative, dP/d.rho., in the vapor region. The
value of .DELTA.R is calculated from known viscosities of saturated
vapor. The change in temperature in the liquid region is obtained
by multiplying the change in the vapor region by .delta.r/.DELTA.R,
the respective one-third mean free paths.
[0033] Referring back to Table 1, inasmuch as the radius of a
helium molecule (atom) is about 40% that of nitrogen and oxygen,
the one-third a mean free path in both regions should be
considerably greater than those of water-under-air. In an
experiment, the water rise in a capillary tube in air was marked.
The air was then released, and commercial grade helium was
substituted therefore. The water rose about 30% higher in the same
capillary tube, as predicted.
[0034] Effect of Helium Gas Coverage Versus Air
[0035] The "dr" in the various differentials is linearly
proportional to the relevant capillarity component. The governing
characteristic is the penetration distance of the overbearing gas
molecules before the first collision beyond the interfacial
surface, or since the last collision in the Crutchfield Region. The
sizes of the colliding molecules are a primary factor. (A similar
relationship is encountered in nuclear reactor theory). In fact,
the specific factor is the "collision diameter"--the sum of the
radii of the colliding particles--the smaller the better. Helium is
very attractive as one of the colliders. It is small, inert and,
for many purposes, light.
[0036] A proof-of-principle experiment in a helium atmosphere
provided results indicating that the decreased collision diameter
between the helium and water molecules versus that between air and
water produced the desired results.
[0037] As described above, this kinetic theory of capillarity
proposes two transition zones at the interface between the liquid
water and the overriding air/water vapor mixture. One zone is in
the liquid of thickness .delta. the other is in the air/vapor
mixture of thickness A. The thickness .delta. is established by the
mean penetration of the air/vapor molecules into the liquid and is
1/3 the mean free path (MFP). The thickness .DELTA. is, likewise,
1/3--MFP in the air/vapor mixture. Both are determined by the fluid
densities and the "effective" liquid and gas molecule radii.
(Molecular velocity considerations are subsumed in the term
"effective".) In the gas region, treating the mixture as
homogeneous, the collision diameter would be the sum of the equal
"effective" radii.
[0038] Rohsenow and Choi in their Heat, Mass and Momentum Transfer,
Prentice-Hall, 1961 (Table 20.1, p.493), provide molecular
diameters in .ANG. for several gases at 15.degree. C. They list
3.72 .ANG. as the diameter of the air molecule. Calculations by the
applicant yielded 3.88 .ANG. as the effective diameter of the
liquid molecules at 15.degree. C. This combination would yield a
collision diameter of about 3.80 .ANG. for saturated air molecules
impinging on the water surface.
[0039] Rohsenow and Choi set forth 2.18 .ANG. as the molecular
diameter of helium at 15.degree., and at atmospheric pressure,
about 2.20 .ANG.. It should be expected that the effective
collision diameter for such molecules impinging on liquid water to
be (3.88 .ANG.+2.20.ANG.)/2, or 3.04 .ANG.. Since .delta. is
inversely proportional to the square of the collision diameter,
.delta. under the helium atmosphere should be greater than that in
air by the square of the ratio 3.80/3.04, or about 1.56. The
.DELTA.s should be related by the square of the ratio 3.80/2.20, or
about 2.98.
[0040] Because of this expansion of the transition zone in a helium
atmosphere, one should expect a significant increase in the surface
tension of water in such circumstances.
[0041] An overbearing atmosphere of, for example, neon, another
inert gas, with a molecular diameter of 2.59 .ANG. according to
Rohsenow and Choi, would also provide a greater capillary rise than
an air atmosphere. A reduction in the collision diameter will
provide an enhanced capillary rise, mutatis mutandis.
[0042] High Altitude Effects
[0043] In the rarer atmosphere at high altitudes where the pressure
is considerably reduced, the one-third mean free path in the vapor
region, .DELTA.R, increases. For P halved, .DELTA.R would be
approximately doubled, at least to a first order effect. Since the
pressure change across the transition zone is proportional to the
product of P and .DELTA.R, the pressure difference across .DELTA.R
should not change significantly, except for very small radii of
curvature of the liquid surface.
[0044] At 0.degree. C. and sea level pressure, .DELTA.R is
approximately 3 centimicrons. At about an 18,000 feet altitude, 5.5
km, the pressure is halved. Assuming 0.degree. C. at 5.5 km--a hot
day at ground level--.DELTA.R would double. A million-molecule
spherical water droplet would have a radius of slightly less than 3
centimicrons. The focusing effect of the droplet would increase the
particle density--both air and water vapor--nine-fold at the liquid
surface, raising the droplet temperature to about 34.degree. C.
[0045] A million-molecule droplet in a 10.degree. C. ambient
environment would be at a temperature of about +23.degree. C. Such
droplets hitherto have been labeled "supersaturated".
[0046] These considerations point to the possible formation of
clouds and fog particles in the form of collections of "Hot Air
Balloons." A cloud consisting of solid liquid balls would defy the
law of gravity. However, surface tension phenomena afford the
existence of such "hollow" constructs. The quenching of a volume of
saturated air, creating a volume of super saturation, could effect
such constructs, inter alia. The thickness of the liquid skin would
depend primarily upon surface tension and the ambient atmospheric
pressure, and weakly upon the balloon radius. An assumption is that
the greater total force acting outward on the smaller inner liquid
skin area equals the lesser total force acting inward on the outer
surface of the liquid skin. Too large a balloon radius would deny
enough heat to lighten the air-steam interior; too small, not
enough lift to offset the liquid weight. Other factors to consider
are the comparative molecular weights of water and air, and the
energy balances, particularly between the heat of condensation
going to liquid and the heating of the interior of the balloon.
[0047] It is further interesting to note that the vapor
contribution to surface tension suggests a possibility of "vapor
wakes" behind ships or submarines. The theories regarding ocean
waves have not addressed a Crutchfield Transition Zone, of course.
Capillary phenomena generally are meaningful only at small,
uninteresting dimensions. The prevailing theories have the parcels
of water at the surface in deep ocean waters move essentially in
circles, with the phase relationship producing various wave
motions. One such curve is a cycloid, a curve described by a point
on the circumference of a circle which rolls along a fixed straight
line. At its lowest point the curvature of a cycloid is infinite,
compressing the air above. A curtate cycloid is one described by a
point just inside the circumference of the rolling circle. The
curvature at the low point is not infinite, but can be large. There
could be cumulative or resonant effects producing a wind shear.
Winds make waves. It follows that waves can make winds. FIGS. 1a-c
show various cycloids. FIG. 1a exhibits a curve described by a
point on the circumference of a circle which rolls along a fixed
straight line where x=a(.PHI.-b sin .PHI.) and y=a(1-cos .PHI.).
The area of one arch=3.pi.a.sup.2. The length of the arc of one
arch=8a. FIGS. 1b and 1c exhibit proloate and curtate cycloids.
Here, a curve is described by a point on a circle at a distance b
from the center of the circle of radius a which rolls along a fixed
straight line, where x=a.PHI.-b sin .PHI. and y=a-b cos .PHI..
[0048] Heat Pipes
[0049] A system of thermal management utilizing the kinetic theory
of capillarity is the heat pipe 10, as shown in FIG. 2. A heat pipe
10 is a vapor-liquid phase-change device that transfers heat from a
hot reservoir to a cold reservoir using capillary forces generated
by a transfer device, preferably a wick 12 or porous material, and
a working fluid 14. A heat pipe typically comprises a container 16,
lined with the wick 12, which provides the capillary driving force
to return the condensate to the evaporator.
[0050] The container isolates the working fluid from the ambient.
It is leak-proof, maintains the pressure differential across its
walls, and enables the transfer of heat from and into the working
fluid.
[0051] The container is filled with the working fluid near its
saturation temperature. The working fluid has both a liquid phase
and a vapor phase which is the desired range of operating
temperatures. When one portion of the container is exposed to a
relatively higher temperature, it functions as an evaporator
section 18. The working fluid is vaporized in the evaporator
section and flows in the vapor phase to the relatively lower
temperature section of the envelope which becomes a condenser
section 22. The working fluid is condensed in the condenser section
and then returns in the liquid phase in a short time from the
higher temperature section of the envelope to the lower temperature
section as a consequence of the phase change of the working
fluid.
[0052] Because it operates on the principle of phase change rather
than on the principles of conduction or convection, a heat pipe is
capable of transferring heat at a much higher rate than
conventional heat transfer systems.
[0053] In heat pipes using a wick, the quantity of working fluid is
selected so that no surplus liquid phase is provided at the desired
operating temperature. As a result there is only modest
interference between the liquid phase and the vapor phase.
[0054] If a heat pipe container is generally tubular in shape and
is disposed substantially horizontally, the liquid phase of the
working fluid will return to the high temperature of the heat pipe
in either direction under the action of gravity so that heat
transfer is bidirectional and does not require a capillary wick to
return the working fluid to the evaporative section, thus
permitting a more inexpensive heat pipe to be used.
[0055] In heat pipe design, a high value of surface tension is
desirable in order to enable the heat pipe to operate against
gravity and to generate a high capillary driving force. In addition
to high surface tension, it is necessary for the working fluid to
immerse the wick and the container material i.e. contact angle
should be zero or very small. The vapor pressure over the operating
temperature range must be sufficiently great to avoid high vapor
velocities, which tend to setup large temperature gradient and
cause flow instabilities.
[0056] In one embodiment of the present invention, water is used as
the working fluid in environments of between 0.degree. and
100.degree. C., while a gas 24, such as helium, is supplied as an
atmosphere in the heat pipe. Other atmospheres would be beneficial,
including those with a particle diameter less than that of water,
approximately 3.72-3.88 .ANG. at 15.degree. C. Other gasses,
preferably inert, can be used other than helium.
[0057] Other working fluids are more practical than water in
different temperature ranges. In such environments, heat pipes have
an effective thermal conductivity many thousands of times that of
copper. The heat transfer or transport capacity of a heat pipe is
specified by its "Axial Power Rating (APR)". It is the energy
moving axially along the pipe. The larger the heat pipe diameter,
greater is the APR. Similarly, the longer the heat pipe, the
smaller the APR. Heat pipes can be built in almost any size and
shape.
[0058] The present invention comprises the use of suitable inert,
or non-reactive, gas, or gases, having suitably small molecules
(such as helium or neon) in a heat pipe to enhance the surface
tension (capillarity) of the heat pipe working fluid, thus
improving the design and performance of almost any heat pipe.
[0059] Although the present invention has been described with
respect to particular embodiments, it will be apparent to those
skilled in the art that modifications to the method of the present
invention can be made which are within the scope and spirit of the
present invention and its equivalents.
* * * * *