U.S. patent application number 16/421950 was filed with the patent office on 2019-11-28 for permeable membrane microchannel heat sinks and methods of making.
The applicant listed for this patent is Purdue Research Foundation. Invention is credited to Ivel Lee Collins, Suresh V. Garimella, Liang Pan, Justin A. Weibel.
Application Number | 20190360759 16/421950 |
Document ID | / |
Family ID | 68614370 |
Filed Date | 2019-11-28 |
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United States Patent
Application |
20190360759 |
Kind Code |
A1 |
Collins; Ivel Lee ; et
al. |
November 28, 2019 |
PERMEABLE MEMBRANE MICROCHANNEL HEAT SINKS AND METHODS OF
MAKING
Abstract
Permeable membrane microchannel heat sinks and methods of
producing such a heat sink, wherein such a heat sink includes a
base and at least first and second microchannels defined by at
least one porous and permeable membrane that is on the base and
defines primary heat exchange surfaces of the heat sink. The
membrane has opposing faces exposed to the first and second
microchannels, and a fluid flowing through the heat sink flows from
the first microchannel to the second microchannel through pores in
the membrane.
Inventors: |
Collins; Ivel Lee; (West
Lafayette, IN) ; Weibel; Justin A.; (West Lafayette,
IN) ; Pan; Liang; (West Lafayette, IN) ;
Garimella; Suresh V.; (West Lafayette, IN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Purdue Research Foundation |
West Lafayette |
IN |
US |
|
|
Family ID: |
68614370 |
Appl. No.: |
16/421950 |
Filed: |
May 24, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62676494 |
May 25, 2018 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B22F 3/1055 20130101;
B33Y 80/00 20141201; F28D 2015/0225 20130101; F28D 15/02 20130101;
F28F 3/12 20130101; F28F 2260/02 20130101; H01L 23/473 20130101;
B22F 5/10 20130101 |
International
Class: |
F28D 15/02 20060101
F28D015/02; F28F 3/12 20060101 F28F003/12 |
Claims
1. A heat sink comprising a base and at least first and second
microchannels defined by at least one porous and permeable membrane
that is on the base and defines primary heat exchange surfaces of
the heat sink, the membrane having opposing faces exposed to the
first and second microchannels, and an entirety of a fluid flowing
through the first microchannel flows from the first microchannel to
the second microchannel through pores in the membrane
therebetween.
2. The heat sink of claim 1, wherein the membrane has a nonlinear
horizontal profile.
3. The heat sink of claim 2, wherein the nonlinear horizontal
profile of the membrane approximates a sine wave.
4. The heat sink of claim 1, wherein the membrane has a nonlinear
vertical profile.
5. The heat sink of claim 4, wherein the membrane is not
perpendicular to the base.
6. The heat sink of claim 1, further comprising at least one fluid
inlet fluidically connected to at least the first microchannel and
at least one fluid outlet fluidically connected to at least the
second microchannel.
7. The heat sink of claim 6, wherein the inlet is fluidically
connected to only the first microchannel.
8. The heat sink of claim 6, wherein the inlet is fluidically
connected to the first microchannel and at least another
microchannel of the heat sink.
9. The heat sink of claim 6, wherein the outlet is fluidically
connected to only the second microchannel.
10. The heat sink of claim 6, wherein the outlet is fluidically
connected to the second microchannel and at least another
microchannel of the heat sink.
11. The heat sink of claim 1, wherein the first and second
microchannels define flowpaths that are parallel to each other.
12. The heat sink of claim 1, wherein the first and second
microchannels and the membrane are disposed in a single tier on the
base and the membrane is contiguous with and projects away from the
base.
13. The heat sink of claim 1, further comprising an electronic
device in thermal contact with the base of the heat sink, and the
fluid is flowing through the heat sink to absorb and transfer heat
from the source by conductive heat transfer from the source to the
membrane and then convective heat transfer from the membrane to the
fluid.
14. A method of fabricating the heat sink of claim 1, the method
comprising an additive manufacturing technology.
15. The method of claim 14, wherein the additive manufacturing
technology comprises direct metal laser sintering.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Provisional
Application No. 62/676,494, filed May 25, 2018, the contents of
which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] The present invention generally relates to heat transfer
devices and methods. The invention particularly relates to
permeable membrane microchannel (PMM) heat sinks having complex and
thin porous internal structures capable of exhibiting relatively
low pressure drops, and methods of producing such heat sinks.
[0003] The pursuit for higher power and more compact electronics in
aerospace, automotive, and other applications requires
complimentary thermal management technologies that can effectively
remove large amounts of heat within a small envelope. Microchannel
heat sinks are known in the art as capable of high-heat-flux
cooling with low thermal resistance, and therefore suitable for
removing dense heat loads from high-power electronic devices.
Microchannel heat sinks have been extensively studied for a range
of working fluids in both single- and two-phase operation. A
nonlimiting example of a microchannel heat sink is schematically
represented in FIG. 1 as comprising headers to distribute fluid
flow among multiple parallel microchannels. While straight channels
having a rectangular cross section are common, other
cross-sectional shapes (e.g., circular, triangular, trapezoidal)
have been investigated. Non-linear channels have also been
investigated both numerically and experimentally, for example, wavy
channels that can increase heat transfer at the cost of a higher
pressure drop. Indeed, the high pressure drop associated with flow
through the small channels in microchannel heat sinks is a primary
drawback, and numerous design concepts have been proposed to
address this issue.
[0004] A well-recognized and effective method of reducing the
pressure drop across a microchannel heat sink is through the
addition of a separate manifold layer to shorten the flow length
through individual microchannels. A nonlimiting example of a
manifold microchannel (MMC) heat sink is schematically represented
in FIG. 2 as comprising a heat transfer layer that contains
multiple parallel microchannels and a separate manifold layer for
distributing fluid flow among the microchannels. Experimental
studies have shown that MMC heat sinks are capable of dissipating
heat fluxes in excess of 1 kW/cm.sup.2. The geometry of MMC heat
sinks has been optimized for several different performance
objectives, with the optimized designs improving surface
temperature uniformity and reducing the thermal resistance of the
heat sink at a fixed pumping power compared to a standard
microchannel heat sink without a manifold.
[0005] Aside from the addition of a manifold, attempts have been
made to improve the performance of microchannel heat sinks by
incorporating porous features. The use of a porous medium that
simply occupies the entire microchannel cross-section has been
shown to provide excellent heat transfer performance, albeit at the
cost of a drastically increased pumping power requirements.
Numerical investigations of porous media within microchannels have
found that a porous layer on the walls of a microchannel offer a
desirable balance between increased thermal performance and higher
pressure drop. In addition, simulations to assess the performance
of a straight microchannel design utilizing porous fins between the
channels instead of conventional solid walls have indicated a
slight increase in thermal resistance that was offset by a
significant reduction in pressure drop. This decrease in pressure
drop has been attributed to the effectively non-zero `slip` fluid
velocity at the wall of the porous fin. Other research has
considered wavy channels. In addition to the pressure drop
reduction offered by the porous fins, wavy channels are capable of
reducing the thermal resistance as a result of a longer effective
flow length, mixing due to vortices, and forced permeation of a
portion of the fluid through the fins. However, while these
numerical modeling efforts indicated the potential improvement that
these increasingly complex designs may offer, fabrication of such
heat sinks via conventional subtractive manufacturing techniques
(e.g., micromachining, anisotropic chemical etching) is difficult
if not impossible. The complexity of structures with internal
porosity have been limited to features that can be produced by
sintering particles in a mold.
[0006] More recently, advances in additive manufacturing (AM)
technologies have enabled the fabrication of more complex geometry
than previously possible with subtractive manufacturing. However,
there has been little focus to date on leveraging these fabrication
capabilities to enhance the performance of microchannel heat sinks
for electronics cooling. Work that has studied microscale heat
exchangers made by additive manufacturing, specifically powder bed
fusion processes, frequently highlights issues associated with
material properties and high surface roughness. I. L. Collins, J.
A. Weibel, L. Pan, and S. V. Garimella, "Evaluation of Additively
Manufactured Microchannel Heat Sinks," IEEE Trans. Compon. Packag.
Manuf. Technol. (2018), demonstrated AM fabrication of straight
microchannel and manifold microchannel heat sinks in an aluminum
alloy having channel hydraulic diameters of 500 .mu.m and a
monolithic construction. The pressure drop was well-predicted by
conventional hydrodynamic theory, albeit with a roughness-induced
early transition to turbulence at low Reynolds numbers (Re<800).
The thermal performance was over-predicted, attributed to
uncertainty in the thermal conductivity of the material.
[0007] Others have experimentally tested additively manufactured
wavy microchannels having numerically optimized designs, with
results indicating that wall roughness introduced by AM processes
assisted in augmenting the heat transfer, while also contributing
to an increase in pressure drop. Designs optimized for minimum
pressure drop were hampered by this roughness and did not meet the
performance expectations, but designs that strived for both
pressure drop reduction and heat transfer augmentation via the
optimization scheme yielded improved performance compared to the
baseline wavy channels having rectangular cross-sections. Pin fin
heat exchangers have also been studied experimentally, with results
indicating that the geometric print fidelity and surface roughness
had large effects on performance. Accurate production of
sharp-edged solid features below 0.5 mm has been difficult or
impossible.
[0008] Research on the fabrication of additively produced porous
media, primarily non-stochastic lattice structures, has been
conducted. These structures have been produced with powder bed
fusion processes in several available metals with porosities of
about 30 to about 90%. In addition to heat exchangers, these
structures have been considered desirable for filtration
applications. Literature regarding the intentional introduction of
stochastic porosity within parts fabricated with powder bed fusion
processes is relatively rare, as this is generally an undesired
result and significant efforts are commonly made to eliminate
porosity in nominally solid parts. Nevertheless, stochastic
porosities of up to about 45% have been reported in aluminum and
titanium alloys. Porosities are generally induced by varying the
process parameters, including hatch spacing (the distance between
adjacent laser passes) and the scanning speed.
[0009] While the study of additively manufactured microscale heat
exchangers is relatively new, there have been a few demonstrations
that exhibit the novel and complex heat exchanger designs that this
fabrication approach enables. As an example, topological
optimization has been used to generate heat sink geometries for an
air-cooled jet impingement application that was then produced using
powder bed fusion in an aluminum alloy. The additively produced
design was compared to several conventional designs, achieving an
improved coefficient of performance even when compared to heat
sinks made of a higher thermal conductivity material. Others have
utilized an electrochemical fabrication additive process to produce
a prototype hybrid heat sink that incorporates both jet impingement
and microchannel flows. Simulations have been reported indicating
the superiority of the design compared with other microchannel
concepts, with the designed geometry addressing several concerns
normally associated with jet arrays such as wall jet formation,
cross-flow, and even flow distribution.
BRIEF DESCRIPTION OF THE INVENTION
[0010] The present invention provides permeable membrane
microchannel (PMM) heat sinks and methods of producing such heat
sink, wherein the heat sinks have complex and thin porous internal
structures capable of exhibiting relatively low pressure drops. The
heat sinks are capable of exploiting the capabilities of direct
metal laser sintering (DMLS) to produce the complex and thin porous
features to mitigate pressure drops commonly associated with the
use of porous materials for heat exchange.
[0011] According to one aspect of the invention, a permeable
membrane microchannel (PMM) heat sink includes a base and at least
first and second microchannels defined by at least one porous and
permeable membrane that is on the base and defines primary heat
exchange surfaces of the heat sink. The membrane has opposing faces
exposed to the first and second microchannels, and a fluid flowing
through the heat sink flows from the first microchannel to the
second microchannel through pores in the membrane.
[0012] According to another aspect of the invention, a method of
fabricating a permeable membrane microchannel heat sink includes an
additive manufacturing technology.
[0013] Other aspects of the invention include methods of removing
dense heat loads from high-power electronic devices using a
permeable membrane microchannel heat sink comprising the elements
described above, and high-power electronic devices equipped with a
permeable membrane microchannel heat sink comprising the elements
described above.
[0014] Technical aspects of the heat sinks described above
preferably include the ability to incorporate complex, non-linear
structures having internal porosity to enhance heat transfer and
reduce pressure drop as compared to a manifold microchannel heat
sink. Such heat sinks preferably utilize one or more porous walls
as their primary heat transfer surface(s) and are capable of
increasing the amount of surface area available for heat transfer
while not requiring an increase in the volume of the heat sink, for
example, as would result if the heat sinks required the use of
manifolds to route fluid to their heat transfer surface(s). Heat
sinks with these characteristics can be advantageous for reducing
the temperature rise of heat-generating surfaces and/or allowing
higher performances by increasing the amount of heat that can be
removed in a wide variety of applications that would benefit from
compact removal of large heat loads, including but not limited to
power electronics, radars, high-performance computing electronics,
portable electronics, avionics, and automotive systems.
[0015] Other aspects and advantages of this invention will be
appreciated from the following detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1 schematically represents a perspective view of a
microchannel heat sink comprising headers to distribute fluid flow
among multiple parallel microchannels.
[0017] FIG. 2 schematically represents a perspective view of a
manifold microchannel (MMC) heat sink comprising a heat transfer
layer that contains multiple parallel microchannels and a separate
manifold layer for distributing fluid flow among the
microchannels.
[0018] FIGS. 3, 4, 5, and 6 schematically represent, respectively,
a perspective view of a manifold microchannel heat sink, a top view
of a highlighted schematic unit cell of the heat sink of FIG. 3, a
perspective view of a permeable membrane microchannel (PMM) heat
sink in accordance with a nonlimiting embodiment of the invention,
and a top view of a highlighted schematic unit cell of the heat
sink of FIG. 5.
[0019] FIG. 7 schematically represents a surface portion of a
permeable membrane microchannel heat sink in accordance with a
nonlimiting embodiment of the invention, and FIG. 8 is an image
showing a fabricated specimen of the heat sink of FIG. 7.
[0020] FIG. 9 is an image showing a front view of a .mu.CT-based 3D
reconstruction of a nominally 400 .mu.m thick permeable membrane,
and FIG. 10 is an image showing an image slice through a fin of the
3D reconstruction of FIG. 9.
[0021] FIGS. 11 and 12 are contour plots comparing, respectively,
the ratio of the pressure drop, .DELTA.P.sub.PMM/.DELTA.P.sub.MMC,
and the thermal resistance,
.DELTA.R.sub.th,PMM/.DELTA.R.sub.th,MMC, of the permeable membrane
microchannel heat sink of FIG. 5 and the manifold microchannel heat
sink of FIG. 3 at a fixed pumping power of 0.018 W.
[0022] FIGS. 13, 15, and 17 schematically represent perspective
fragmentary views of, respectively, a manifold microchannel heat
sink, a first permeable membrane microchannel heat sink in
accordance with a nonlimiting embodiment of the invention, and a
second permeable membrane microchannel heat sink in accordance with
a nonlimiting embodiment of the invention, and FIGS. 14, 16, and 18
are images of specimens of the heat sinks of, respectively, FIGS.
13, 15, and 17 fabricated in aluminum alloy AlSi.sub.10Mg via
direct metal laser sintering (DMLS).
[0023] FIG. 19 is a graph plotting a comparison of measured
pressure drop as a function of flow rate for the manifold
microchannel heat sink of FIG. 14 and the permeable membrane
microchannel heat sink of FIG. 18 (+0.172 kPa error bars are not
shown).
[0024] FIG. 20 is a graph plotting a comparison of the performance
of the manifold microchannel heat sink of FIG. 14 and permeable
membrane microchannel heat sink of FIG. 18 while subjected to
different pumping powers that allowed for a comparison of the heat
sinks at approximately equal pressure drops.
DETAILED DESCRIPTION OF THE INVENTION
[0025] The following describes the development, fabrication, and
evaluation of heat sinks that incorporate complex non-linear
three-dimensional (3D) structures comprising one or more porous
walls (membranes) as their primary heat transfer surface(s),
whereby the heat sinks contain internal porosity that creates fluid
flow paths through the membranes to increase the area available for
heat transfer, and the membranes are sufficiently thin to reduce
pressure drop in comparison to a manifold microchannel heat sink.
The internal porosity-containing heat sinks, referred to herein as
permeable membrane microchannel (PMM) heat sinks, were fabricated
using direct metal laser sintering (DMLS) of an aluminum alloy
(AlSi.sub.10Mg), though it should be understood that heat sinks
formed by other fabrication techniques and materials are also
within the scope of the present invention.
[0026] Investigations discussed below benchmarked PMM heat sinks
against a manifold microchannel (MMC) heat sink both experimentally
and by using a reduced-order model to explore the relative
performance trends between these designs. The investigations
evidenced that the inclusion of a porous membrane in the PMM heat
sinks as the primary heat transfer surface(s) enabled the heat
sinks to meet the same heat transfer capability as the MMC heat
sink, but with a reduced total volume as compared to the MMC heat
sink by eliminating the need for a separate manifold layer to route
fluid to their heat transfer surfaces. Both the porosity of the
membranes and their complex shapes serve to increase the surface
area available for fluid flow and heat transfer, allowing for
potential benefits in both hydraulic and thermal performance.
[0027] Nomenclature Used in the Following Discussion: [0028] A Area
[0029] C Coefficient in Eq. (2) [0030] D.sub.H Hydraulic diameter
[0031] D.sub.p Particle diameter [0032] f.sub.F Fanning friction
factor [0033] G Mass flux [0034] h Heat transfer coefficient [0035]
K.sub..infin. Incremental pressure drop number [0036] k Thermal
conductivity [0037] L Length [0038] Nu Nusselt number, hD/k.sub.1
[0039] Pr Prandtl number, c.sub.p.mu./k.sub.1 [0040] .DELTA.P
Pressure drop [0041] Q.sub.in Power input [0042] R Thermal
resistance [0043] Re Reynolds number, GD/.mu. [0044] T Temperature
[0045] t.sub.wall Wall/membrane thickness [0046] u.sub.sup
Superficial velocity [0047] x.sup.+ Dimensionless entry length
[0048] Greek Symbols Used in the Following Discussion: [0049]
.kappa. Permeability [0050] .alpha. Aspect ratio [0051] .mu.
Dynamic viscosity [0052] .rho. Density [0053] .phi. Porosity
[0054] Subscripts Used in the Following Discussion: [0055] app
Apparent, accounting for developing flow [0056] base Evaluated at
the heat sink base [0057] ch Channel [0058] dev Developing flow
[0059] eff Effective [0060] l Evaluated for the fluid [0061] m
Evaluated at mean fluid temperature [0062] s Evaluated for the
solid material [0063] sf Solid-fluid interface [0064] tot Total
[0065] w Evaluated at interfacial temperature
[0066] As the hydraulic diameter of a channel decreases, there is a
proportional increase in internal convective heat transfer
coefficient between a fluid flowing through the channel and the
walls of the channel. This scaling is the fundamental premise for
using microscale channels (microchannels) in heat sinks.
Microchannel geometries can be directly fabricated, or
alternatively, this effect can be achieved using an open-celled
microporous media in which the effective hydraulic diameter reduces
to the pore size. As a heat transfer surface, porous media can
generally achieve smaller hydraulic diameters and higher internal
surface area-to-volume ratios than directly fabricated straight
microchannels, though at the cost of a significantly higher
pressure drop. To minimize this pressure drop penalty,
investigations leading to the present invention developed,
fabricated, and evaluated porous membranes whose wall thicknesses
were minimized to reduce the flow length through their narrow pore
paths, and whose frontal areas were augmented to reduce the flow
rate through any one pore path.
[0067] As previously discussed, a common design goal of heat sinks
is to reduce the pressure drop, which is particularly a challenge
for microchannel heat sinks that leverage very small channels for
heat exchange. As noted in reference to FIG. 2, manifold
microchannel heat sinks use a manifold layer to reduce the
effective flow length through their microchannels. Because manifold
microchannel heat sinks are well accepted as exhibiting low
pressure drops, a manifold microchannel heat sink design was
utilized as a benchmark for the investigations leading to the
present invention.
[0068] FIGS. 3 and 4 represent, respectively, a fragmentary
perspective view and a top-down unit cell schematic view of a
manifold microchannel (MMC) heat sink 10 having the selected
design. The heat sink 10 comprised a heat transfer layer 12 of
straight microchannels 14 beneath a separate manifold layer 16 with
inlet and outlet channels 18A and 18B that are larger than the
microchannels 14 and distribute the flow across the entire bank of
microchannels 14. For the purpose of dissipating heat from a source
(not shown), for example, an electronic device, the heat transfer
layer 12 is placed in thermal contact with the source and a working
fluid flows through the heat sink 10 by traveling along the
manifold inlet channel 18A in the manifold layer 16, down into the
microchannel layer 12 within the heat transfer layer 12, across a
short flow length in the microchannels 14, and then exits via the
smaller outlet channel 18B in the manifold layer 16.
[0069] FIGS. 5 and 6 represent, respectively, a fragmentary
perspective view and a top-down unit cell schematic view of a
nonlimiting embodiment of a permeable membrane microchannel (PMM)
heat sink 20 within the scope of the invention. The PMM heat sink
20 comprises microchannels 22 defined and separated by a bank of
thin porous and permeable walls or "membranes" 24 that define the
primary heat exchange surfaces of the heat sink 20, which includes
the walls of pores (not shown) within the membranes 24. As such,
the permeable membranes 24 are deemed to be permeable if permeable
to a working fluid used to absorb and conduct thermal energy from
the heat sink 20. The microchannels 22 and membranes 24 are
represented as disposed in a single tier or layer on a base 26 of
the heat sink 20, with the membranes 24 being contiguous with and
projecting away from the base 26.
[0070] For the purpose of dissipating heat from a source (not
shown), for example, an electronic device, the base 26 of the heat
sink 20 is placed in thermal contact with the source and the
working fluid flows through the heat sink 20 to absorb and transfer
heat from the source by conductive heat transfer from the source to
the membranes 24 and then convective heat transfer from the
membranes 24 to the working fluid. The fluid enters the heat sink
20 through inlets 28 associated with some but not all (alternating
in FIGS. 5 and 6) of the microchannels 22, designated as inlet
microchannels 22A. Though a single inlet microchannel 22A is shown
associated with each inlet 28, in some embodiments multiple inlet
microchannels 22A may be fluidically connected to each inlet 28.
Solid endcaps 30 prevent a direct exit of the fluid from the heat
sink 20 through the inlet microchannels 22A, and instead all of the
fluid flowing through the heat sink 20 must pass from each inlet
microchannel 22A to one of the remaining microchannels 22,
designated as the outlet microchannels 22B, through the thin
permeable membranes 24 that separates the microchannels 22A and 22B
before the fluid exits the heat sink 20 through outlets 32
associated with the outlet microchannels 22B. Though a single
outlet microchannel 22B is shown associated with each outlet 32, in
some embodiments multiple outlet microchannels 22B may be
fluidically connected to each outlet 32.
[0071] As the primary heat exchange surfaces of the heat sink 20,
the permeable membranes 24 act as fins that conduct heat from the
base 26 and transfer the absorbed heat to the fluid passing through
the pores within the membranes 24. The membranes 24 have nonlinear
horizontal profiles (approximating a sine wave) and nonlinear
vertical profiles (not perpendicular to the base 26), which have
the effect of increasing the surface area of the face of each
membrane 24 (i.e., the surfaces of each membrane 24 exposed to one
of the microchannels 22) as compared to a flat membrane sheet, so
as to reduce the pressure drop and increase the heat exchange area.
Though the membranes 24 are nonlinear, they effectively define
flowpaths through the microchannels 22 that may be generally
described as parallel, as evident from FIGS. 5 and 6. The specific
profiles of the membranes 24 that were evaluated were heuristically
chosen for the investigations. However, the shapes of the membranes
24 offer a design variable that is only limited by the capabilities
of the process used to fabricate PMM heat sinks within the scope of
the invention.
[0072] Because subtractive and other conventional machining
processes are not able to readily produce the complex geometry with
permeable membranes 24 shown in FIG. 5, additive manufacturing
techniques were used to fabricate PMM heat sinks that were
evaluated. For production of microchannel heat sinks, accurate
fabrication of sub-millimeter features in a
high-thermal-conductivity metal was desired. Direct metal laser
sintering (DMLS) is a commercially mature, widely available
technology that is suitable for producing microchannel heat sinks
with features on the order of hundreds of micrometers. DMLS is a
powder bed fusion technology that uses a laser to selectively fuse
a thin layer of metal powder to create a cross-section of the
desired component. After fusion, another thin layer of powder is
deposited on top of the fused layer, and the process is repeated
until the desired component is completed. In this way, the
component is built up layer by layer. Based on previous work and
the literature, a microchannel width of about 500 .mu.m is near the
lower limit of what can be commercially fabricated by DMLS because,
though laser spot sizes of 50-100 .mu.m are common, there is a
significant heat-affected zone. Therefore, the membrane pores in
the PMM heat sinks were not directly printed, but rather the
material was rendered porous during the powder fusion process to
achieve these small features. As previously noted, the PMM heat
sinks were fabricated from AlSi.sub.10Mg, an aluminum alloy with a
nominal thermal conductivity k.sub.s of about 110 W/m-K, though a
number of alloys are available for use with DMLS.
[0073] To evaluate the relative performance of nonlimiting
embodiments of PMM heat sinks of this invention to the MMC heat
sink 10 represented in FIGS. 3 and 4, a reduced-order model was
developed. The model was used to study performance trends of PMM
heat sinks as a function of the membrane characteristics and
provide an assessment of PMM heat sink designs relative to the MMC
heat sink 10.
[0074] The pressure drops across the heat sinks were assumed to
occur primarily across the smallest hydraulic diameter features
used for heat exchange (viz., the microchannels 14 in the MMC heat
sink 10 and the porous membrane 24 in the PMM heat sink 20) and the
outlet channels of the heat sinks. The pressure drops at the inlets
of each heat sink were presumed to be lower than in the outlets due
to pressure recovery by fluid discharge from the inlets and, in the
MMC heat sink 10, the smaller hydraulic diameter of the outlets.
For the outlet channel pressure drop in both the MMC and PMM heat
sinks, a conservative estimate was to assume that all of the flow
must travel along the entire outlet channel length:
.DELTA. P ch = 2 f F , app L ch G ch 2 .rho. l D H ( 1 )
##EQU00001##
[0075] where f.sub.F,app is the apparent Fanning friction factor
from Ref. T. M. Harms, M. J. Kazmierczak, and F. M. Gerner,
"Developing convective heat transfer in deep rectangular
microchannels," Int. J. Heat Fluid Flow, vol. 20, no. 2, pp.
149-157 (April 1999), which accounts for developing flow effects
and is given by
f F , app = ( 1 Re ) ( .mu. w .mu. m ) 0.58 ( 16 C ) + K .infin. 4
x + , x + .gtoreq. 0.1 ( 2 ) f F , app = ( 1 Re ) 11.3 ( x + ) -
0.202 .alpha. - 0.094 , 0.02 .ltoreq. x + < 0.1 ( 3 ) f F , app
= ( 1 Re ) 5.26 ( x + ) - 0.434 .alpha. - 0.010 ( 4 )
##EQU00002##
where:
x + = L ch D H Re ##EQU00003##
is the dimensionless entry length,
C = 2 3 + ( 11 24 ) .alpha. ( 2 - .alpha. ) ##EQU00004##
is a correction factor for friction factors in rectangular
channels, and K.sub..infin.=-0.906.alpha..sup.2+1.693.alpha.+0.649
is the incremental pressure drop number that accounts for the
developing region.
[0076] The pressure drop in the microchannels 14 for the MMC heat
sink 10 can be calculated using Equation (1) using the fractional
flow rate that goes through any one microchannel 14 and the
effective flow length between the inlet and outlet. It is important
to account for the developing flow effects in the heat transfer
layer 12 containing the microchannels 14, even for reduced-order
fidelity, as the entire flow length can be developing.
[0077] The pressure drop across the membrane in a PMM heat sink can
be calculated using Darcy's Law
.DELTA. P wall = u sup .mu. l t wall .kappa. ( 5 ) ##EQU00005##
[0078] whu.sub.sup={dot over (V)}/A ere is the superficial velocity
within the porous medium.
[0079] The permeability K of the membrane was estimated using the
Carman-Kozeny equation
K = D p 2 .phi. 3 150 ( 1 - .phi. ) 2 ( 6 ) ##EQU00006##
[0080] It was assumed that all heat transfer to the fluid occurs
within the heat transfer layer 12 in the MMC heat sink 10 and with
the membranes in the PMM heat sinks. For the microchannels, the
Nusselt number was calculated assuming hydrodynamically and
thermally developing flow as
Nu dev = 1.86 ( RePrD H L ) 1 3 ( .mu. l .mu. wall ) 0.14 ( 7 )
##EQU00007##
[0081] The heat transfer surface areas of the microchannels 12 and
22 were trivially calculated from the given channel geometry. For
the membrane 24, the Nusselt number was obtained from a
particle-diameter-dependent correlation developed in K. K. Bodla,
J. Y. Murthy, and S. V. Garimella, "Direct Simulation of Thermal
Transport Through Sintered Wick Microstructures," J. Heat Transf.,
vol. 134, no. 1, p. 012602 (2012), as
Nu sf = h sf D p k l = 2.081 + 0.296 ( Re D p 0.6 Pr 1 3 ) 1.2 ( 8
) ##EQU00008##
[0082] where the particle diameter was taken as the powder
? = 1 ? ? indicates text missing or illegible when filed
##EQU00009##
clump size in the fabricated membrane 24. The internal solid-fluid
interfacial area of the membrane 24 was estimated as
A sf = 6 ( 1 - .phi. ) V tot D p ( 9 ) ##EQU00010##
[0083] The fin efficiency of the microchannel membranes 24 can be
calculated using the nominal thermal conductivity of the solid
printed aluminum. For the porous membranes 24, the effective
thermal conductivity, k.sub.eff, was calculated in accordance with
the effective medium theory model, and is given as
k eff = 1 4 ( ( 3 .phi. - 1 ) k s + ( 3 ( 1 - .phi. ) - 1 ) k l + (
( 3 .phi. - 1 ) k s + ( 3 ( 1 - .phi. ) - 1 ) k l ) 2 + 8 k l k s )
( 10 ) ##EQU00011##
[0084] To compare nonlimiting embodiments of PMM heat sinks of this
invention to the MMC heat sink 10 represented in FIGS. 3 and 4, the
total pressure drop was calculated from the sum of the two
component drops for each.
[0085] The convective thermal resistance was calculated as using
the heat transfer coefficient and the nominal heat transfer surface
area for each.
[0086] A flow loop identical to that described in I. L. Collins, J.
A. Weibel, L. Pan, and S. V. Garimella, "Evaluation of Additively
Manufactured Microchannel Heat Sinks," IEEE Trans. Compon. Packag.
Manuf. Technol. (2018), was used to experimentally characterize the
thermal and hydraulic performance of the heat sinks. The flow loop
used deionized water as the working fluid and imposed controlled,
constant boundary conditions to the heat sinks and enabled
measurement of the flow rate, fluid temperature, heat sink
temperature, pressure drop, and power input. The key components are
briefly summarized here.
[0087] The system was closed and a gear pump was used to circulate
the working fluid. The flow rate was measured and the fluid
filtered and preheated before entering a test section that held the
heat sink. A 200 W ceramic heater provided adjustable heat input to
the heat sink being tested. After exiting the heat sink, the fluid
was cooled back to ambient temperature and returned to a flexible
reservoir that maintained ambient pressure.
[0088] The test section, which secured the heat sink and heater
together, positioned thermocouples for temperature measurements and
contained pressure taps to measure the pressure drop, was modified
slightly compared to I. L. Collins, J. A. Weibel, L. Pan, and S. V.
Garimella, "Evaluation of Additively Manufactured Microchannel Heat
Sinks," IEEE Trans. Compon. Packag. Manuf. Technol. (2018). Due to
the lack of an incorporated lid on the heat sinks due to
fabrication constraints and a desire to visualize the heat transfer
features, a silicone rubber gasket was used to seal the interface
between the heat sink and the component routing the flow into the
part. The inlet temperature of the working fluid was maintained at
30.degree. C.
[0089] Prior to testing, the heat sinks were cleaned with
compressed air and inserted in the test section. The experimental
heat loss was measured by assembling the test section and applying
power without the presence of the working fluid. After reaching a
steady temperature at each power, the base heat sink temperature
was recorded. A best-fit line, assuming a zero intercept, was
fitted to these measurements to yield an empirical correlation and
allow for conservative estimation of the temperature-dependent heat
loss based on the base temperature of the heat sink. The range of
heat loss in this study was 2.8% to 4.1%.
[0090] To characterize the hydraulic performance of the heat sinks,
the flow rate through the unheated test section was varied over the
range from about 50 mL/min to about 500 mL/min in 50 mL/min
increments. After achieving steady conditions at each flow rate,
the pressure drop across the heat sink was measured. The measured
pressure drop was then used to identify the flow rates needed to
achieve a comparison of the thermal performance between the two
heat sink sinks at a constant pumping power. Two nominal pumping
powers of 0.008 W and 0.018 W were chosen for the thermal
performance characterization.
[0091] At each of the pumping powers, the heat input power to the
heat sink was incremented from 0 W to 200 W in steps of 20 W. At
each step, the system was allowed to reach steady state and then
data were recorded for 60 s. A single time-averaged value was
reported for each measurement. The thermal performance was
characterized by the total thermal resistance of the heat sinks
R tot = T base - ? Q in ? indicates text missing or illegible when
filed ( 11 ) ##EQU00012##
which can be calculated directly from the measured temperatures at
the center of the heat sink base and the fluid inlet temperature,
as well as the loss-adjusted heat input.
[0092] For a given heat sink geometry and flow rate, the thermal
resistance was expected to be constant with power input during
single-phase operation; changes in heat flux translated to
proportional changes in the streamwise temperature gradient within
the fluid and the local temperature difference between the
convection surface and the bulk fluid. Due to the near-constant
values of thermal resistance measured across the range of power
inputs, the thermal resistance was reported as an arithmetic mean
of all test points from 0 W to 200 W for a given heat sink and flow
rate.
[0093] The sensor uncertainties specified by the manufacturers are
listed in Table 1 below.
TABLE-US-00001 TABLE 1 Uncertainty in measured and calculated
values. Measured Value Uncertainty Pressure drop .+-.0.172 kPa
Volumetric flow rate .+-.5 mL/min Temperature .+-.1.0.degree. C.
Voltage .+-.<1% Calculated Value Mean Uncertainty (Range)
R.sub.tot 3.1% (1.1-12.9%)
[0094] The uncertainty in calculated thermal resistance is also
listed, and was determined using a sequential perturbation method.
The uncertainty in thermal resistance was highest at lower flow
rates due to the smaller temperature difference between the heat
sink base and the working fluid.
[0095] An MMC heat sink configured as shown in FIGS. 3 and 4 was
used as the benchmark for comparison against nonlimiting
embodiments of PMM heat sinks of this invention. The MMC heat sink
was held fixed, using the minimum possible feature sizes based on
the fabrication limits for the geometry. The manifold layer (16 in
FIGS. 3 and 4) was 1.5 mm tall and had 1.0 mm-thick solid wall
features, with inlet and outlet channel widths of 1.5 and 0.5 mm,
respectively. These channel widths were in accordance with several
design optimizations performed in the literature that have
indicated the ideal single-phase inlet-to-outlet width ratio is
3:1. The effective flow length, from inlet to outlet through the
microchannels (14 in FIGS. 3 and 4), was thus 2.00 mm. The total
footprint of the heat transfer layer (12 in FIGS. 3 and 4) was 15.0
mm.times.15.5 mm and was covered by sixteen rectangular
microchannels of 0.5 mm width and 2.0 mm height, spaced by 0.5
mm-wide solid walls (fins). The base thickness between the bottom
of the heat sink and the bottom of its heat transfer layer was 1.0
mm Though thinner widths are possible based on the fabrication
limits, this thickness was chosen to eliminate any potential for
leakage. A 250 .mu.m deep, 1000 .mu.m wide groove ran from one edge
of the heat sink to the center, allowing for placement of a
thermocouple to measure the base temperature.
[0096] A PMM heat sink configured as shown in FIGS. 5 and 6 was
fabricated to have membranes (24 in FIGS. 5 and 6) that were 2.0 mm
tall and covered a 15.0 mm.times.15.5 mm footprint, identical to
the heat transfer layer envelope in the MMC heat sink (note that
the PMM heat sink was more compact compared to the MMC heat sink if
considering the manifold layer of the latter). The membranes (fins)
were nominally 400 .mu.m thick, the thinnest width successfully
fabricated at the process parameter set used for the PMM heat sink.
The permeable membranes had a curved profile in the horizontal
plane, with an amplitude of 0.5 mm and a wavelength of 25% of the
channel length. The vertical profile (normal to the heat sink base
26 in FIGS. 5 and 6) was that of a triangular chevron with an
amplitude equal to the width of the membrane. The inlet and outlet
channels (28 and 32 in FIGS. 5 and 6) had widths of 0.6 mm. The
solid endcaps (30 in FIGS. 5 and 6) at the ends of the
microchannels (22A in FIGS. 5 and 6) were 0.5 mm thick. The base
thickness was identical to the manifold design and also contained a
thermocouple groove.
[0097] In the PMM heat sink, the membrane pore characteristics and
thickness that can be successfully fabricated with the additive
process are unknown. The following describes an evaluation of the
range of membrane characteristics that can be fabricated via
additive manufacturing, inputs a range of membrane characteristics
into the reduced-order model to identify the design space in which
the PMM heat sink is predicted to perform well, and describes the
experimental evaluation of a PMM heat sink design that was
predicted to provide improved performance compared to the MMC heat
sink.
[0098] Direct metal laser sintering fabrication processing
parameter sets for achieving induced porosity in AlSi.sub.10Mg are
not commonly available. A set of process-tuning sample cubes was
designed and fabricated to determine the membrane thickness that
could be achieved at different bulk sample porosities. To this end,
ten samples were fabricated in collaboration with a commercial
vendor (EOS M280; GPI Prototype & Manufacturing Services), each
with different laser and scanning parameters. The geometry of the
sample cubes and a photograph of one fabricated part are shown in
FIGS. 7 and 8. The sample cube had a solid base layer, a porous
core layer in the center, and a solid top layer. The porous core
layer was used to assess the nominal bulk porosity that was
achieved at the given processing parameters. A series of six
membranes (fins) of differing widths between 150 and 500 .mu.m were
built on the solid top surface. These fins have the same chevron
profile as the heat sink, while the height of the fins was 1.0 mm
and the wavelength was 5.0 mm. Across the set of ten samples cubes,
porosities between 12-23% were achieved, as determined based on
mass and volume measurements. The thinnest fins below 300 .mu.m in
width failed to build on all samples. The 300 .mu.m-wide fins were
successfully built when the bulk porosity was low (<-18%) and
the 400 .mu.m and 500 .mu.m fins were successfully constructed on
all samples (as can be seen for the 23% porosity sample in FIG.
8.
[0099] In addition to optical inspection, .mu.CT scanning (Bruker
Scyscan 1272) was used to non-destructively examine the morphology
of the permeable membranes. FIG. 9 shows a 3D reconstruction of a 3
mm-long section of the nominally 400 .mu.m thick membrane from the
sample cube shown in FIG. 8. From the reconstruction, it was found
that the effective thickness of the membrane was below that of the
nominal geometry specified during printing, approximately 300
.mu.m. This was due to the fact that, when fabricating porous
features, the standard laser-scanning dimensional offsets that
compensate for the heat-affected zone and melt pool size during
printing of solid features were not accurate (such offsets were
disabled entirely during printing of these porous parts).
Additionally, while the powder used to fabricate the samples has a
mean particle diameter of 45 .mu.m, the membrane exhibited larger
clumps of solid material and pores. The solid clump sizes were
approximately 250 .mu.m in diameter (the membrane was only 1-2
clump diameters thick), with membrane pores ranging between 150-400
.mu.m in diameter. These measured clump sizes and pore diameters
were used as inputs to the reduced-order model to evaluate the
viability of the permeable membrane microchannel design compared to
the benchmark manifold microchannel design, for a range of membrane
porosities and thicknesses.
[0100] The performance of the PMM heat sink was evaluated relative
to the MMC heat sink 10 based on the pressure drop ratio,
.DELTA.P.sub.PMM/.DELTA.P.sub.MMC, and the convective thermal
resistance ratio, .DELTA.R.sub.th,PMM/.DELTA.R.sub.th,MMC. The
performance ratios were compared at a constant pumping power of
0.018 W. While various performance factors could be used to assess
the heat sinks, comparison of the thermal resistance at a constant
pumping power is common. However, for a fair comparison it is
important to ensure that the two heat sinks also had the same order
of pressure drop at this pumping power, such that they would use
similar pumping technologies.
[0101] FIGS. 11 and 12 plot contours of the pressure drop ratio
(FIG. 11) and thermal resistance ratio (FIG. 12) for ranges of
membrane thickness and porosity that encompass and expand upon
those achieved in the fabrication of the samples cubes. FIG. 11
shows that the pressure drop over a majority of the viable
parameter range studied was within a half-order of magnitude, and
that the pressure ratio improved (i.e., is reduced) as the membrane
becomes thinner and more porous. Conversely, FIG. 12 shows that as
the membrane becomes thicker and less porous, the relative thermal
resistance of the PMM heat sink improved. Thicker and less porous
membranes increase the interfacial area and the fin efficiency,
leading to low thermal resistance at the cost of a higher pressure
drop. For a membrane with an effective thickness of 300 .mu.m and a
porosity of 23% (within the range demonstrated for the fabricated
sample cubes of FIG. 8), the model predicted a 35% reduction in the
pressure drop and a 28% reduction in the convective thermal
resistance for the PMM heat sink compared to the MMC heat sink.
This membrane width and porosity were used to fabricate and
experimentally characterize a PMM heat sink as discussed below.
[0102] MMC and PMM heat sinks were commercially fabricated using
the same aluminum alloy (AlSi.sub.10Mg) and AM process (DMLS) as
discussed above. The fabricated heat sinks are schematically
represented in FIGS. 13 and 17, and images of the fabricated heat
sinks are shown in FIGS. 14 and 18. The MMC heat sink of FIG. 14
was fabricated to have microchannels that were 500 .mu.m wide and
2000 .mu.m deep, whereas the PMM heat sink of FIG. 18 was
fabricated to have membranes that were 400 .mu.m thick,
microchannels that were 600 .mu.m wide, and two inlets per inlet
microchannel. An additional PMM heat sink that was prepared but not
evaluated during this phase of the investigation is schematically
represented in FIG. 15 and shown in FIG. 16. The PMM heat sink of
FIGS. 15 and 16 corresponds to the PMM heat sink 20 of FIGS. 5 and
6, characterized by permeable membranes that were 400 .mu.m thick,
microchannels that were 1200 .mu.m wide, and a single inlet per
inlet microchannel.
[0103] The measured pressure drops of the heat sinks of FIGS. 14
and 18 are shown in FIG. 19 as a function of total flow rate. As
predicted by the reduced-order model, the pressure drop of the PMM
heat sink (FIG. 14) was lower than the MMC heat sink (FIG. 18). The
pressure drop reduction was between 20-70%, with higher reductions
being achieved at higher flow rates. The magnitude of the pressure
drop was very low for both heat sinks, on the order of less than 4
kPa at 500 mL/min as compared to more typical pressure drop ranges
of from tens to hundreds of kPa.
[0104] The pressure drop data from the adiabatic hydraulic testing
are shown (open symbols) as a function of pumping power in FIG. 20
for both heat sinks. The pressure drop data measured during the
thermal testing are superimposed as filled symbols. The thermal
test points were chosen to enable comparison of the MMC and PMM
thermal resistances at both constant pumping power (about 0.008 W
and about 0.018 W) and pressure drop (about 2.5 kPa). The measured
values of thermal resistance are annotated in FIG. 20 next to the
corresponding pressure drop data point. At a pumping power of 0.008
W, the thermal resistance of the PMM heat sink (FIG. 18) was 10%
lower than the MMC heat sink (FIG. 14) and the pressure drop was
lower by 26%. At the higher nominal pumping power of 0.018 W, the
reduction in thermal resistance was 17% and the reduction in
pressure drop was 28%. At a constant pressure drop of 2.5 kPa, the
thermal resistance of the PMM heat sink was lower by 25% compared
to the MMC heat sink. From these data, it was shown that the same
thermal resistance can be achieved with the PMM heat sink at a 56%
lower pressure drop. The PMM heat sink was unequivocally
demonstrated to provide improved performance over the MMC heat sink
benchmark.
[0105] The reduced-order model predictions and the experimental
results compared favorably at the higher nominal pumping power of
0.018 W. The model predicted a pressure drop reduction of 35% and a
decrease in convective thermal resistance of 28%. The experimental
data indicated decreases of 28% in the pressure drop and 17% in the
total thermal resistance. The difference in the thermal resistances
can be attributed to the additional thermal resistances due to
conduction through the solid base and the caloric temperature rise
in the fluid, which were fixed between the PMM and MMC heat
sinks.
[0106] In conclusion, the investigations discussed above
demonstrated the performances of certain PMM heat sink designs that
were experimentally characterized and benchmarked against a
high-performance MMC heat sink design. A reduced-order model was
used to assess the relative pressure drop and thermal resistance
between the PMM and MMC heat sinks at a constant pumping power for
a range of membrane thicknesses and porosities. Experimental
characterizations of the heat sink designs showed that PMM heat
sink designs can offer a reduced thermal resistance at a constant
pressure drop or pumping power. The PMM heat sink designs also
demonstrated the ability of additive manufacturing to produce
complex geometries incorporating locally porous features, otherwise
unobtainable via conventional manufacture, to achieve heat sink
performance enhancement.
[0107] While the invention has been described in terms of
particular embodiments and investigations, it should be apparent
that alternatives could be adopted by one skilled in the art. For
example, a PMM heat sink could differ in appearance and
construction from the embodiments described herein and shown in the
drawings, functions of certain components of the PMM heat sinks
could be performed by components of different construction but
capable of a similar (though not necessarily equivalent) function,
and various materials could be substituted for those noted. As
such, it should be understood that the above detailed description
is intended to describe the particular embodiments represented in
the drawings and certain but not necessarily all features and
aspects thereof, and to identify certain but not necessarily all
alternatives to the represented embodiments and described features
and aspects. As a nonlimiting example, the invention encompasses
additional or alternative embodiments in which one or more features
or aspects of a particular embodiment could be eliminated or two or
more features or aspects of different embodiments could be
combined. Accordingly, it should be understood that the invention
is not necessarily limited to any embodiment described herein or
illustrated in the drawings, and the phraseology and terminology
employed above are for the purpose of describing the illustrated
embodiments and investigations and do not necessarily serve as
limitations to the scope of the invention. Therefore, the scope of
the invention is to be limited only by the following claims.
* * * * *