Understanding Limits on Fin Aspect Ratios in Counterflow ... - Classes

Brian K. Paul Department of Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331

Patrick Kwon Ramkumar Subramanian Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

Understanding Limits on Fin Aspect Ratios in Counterflow Microchannel Arrays Produced by Diffusion Bonding This paper investigates the manufacturability limits of fin aspect ratios within two-fluid counter-flow microchannel arrays based on the stress state between laminae during diffusion bonding. In prior papers, it has been shown that the diffusion bonding of two-fluid systems by microlamination can result in regions of the device that do not directly transmit bonding pressure and, consequently, result in unbonded regions leading to device leakage. A finite element model is used to analyze the stress state between laminae during diffusion bonding. The stress state is used to determine the critical stress necessary for diffusion bonding to occur in areas not receiving direct bonding pressure. Model results are compared with experimental results over a wide range of counter-flow geometries. It has been found generally that a compressive stress state must exist in every part of the geometry in order to produce leak-free bonds. Implications of this finding on the design of two-fluid microchannel arrays are discussed. 关DOI: 10.1115/1.2280672兴 Keywords: microlamination, microchannel, aspect ratio, counterflow, crossflow, heat exchanger

1

Introduction

Over the last ten years, there has been a growing interest in the use of low-cost, engineering materials to fabricate micro energy and chemical systems 共MECS兲. MECS are multi-scale fluidic devices, which rely on embedded micro-scale features to process bulk fluids for portable and distributed energy and chemical systems applications. MECS are expected to provide a number of important functions, where a premium is placed on mobility, compactness, or point application. Examples include miniature refrigerators for high-speed electronics 关1兴, portable power packs based on combustion 关2兴, and miniature chemical reactors for on-site waste processing 关3兴. One major advantage of MECS devices over same-sized conventional devices is that they have greater surface area available for heat transfer, reaction, separations, etc. This large surface area to volume ratio accounts for the high rates of heat and mass transfer within MECS devices 关4–6兴. Friedrich and Kang 关7兴 used the term surface area density to quantify this attribute of MECS devices defined as the amount of surface area per unit volume of device. High aspect ratio 共AR兲 microchannels can have very high surface area densities in excess of 5000 m2 / m3 where AR is defined as the ratio of channel width to channel height. System miniaturization is provided by the reduction in residence time 共and consequent reduction in channel length兲 needed by fluid molecules flowing through microchannel reactors and heat exchanagers. Further, the high AR microchannels within MECS devices tend to have low pressure drops when compared with other high surface area density structures 共e.g., carbon foams兲. In fact, the characteristic reduction in channel length causes MECS devices to have no theoretical increase in pressure drop over conventional systems. Overall, MECS devices provide the opportunity to Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received April 7, 2005; final manuscript received March 7, 2006. Review conducted by K. Rajurkar.

greatly reduce the size and weight of energy and chemical system applications while providing the opportunity for enhanced process control for novel material synthesis. Many MECS devices have been produced using a fabrication approach known as microlamination. Microlamination involves the patterning and bonding of thin layers of material called laminae 关8兴. Laminae can be metal shims or polymer films having the desired mechanical, thermal and chemical properties important to the device function. The patterning step usually involves the machining, molding or forming of discrete laminae from foils and films. Subsequently the laminae are registered to each other and bonded together to create a monolithic stack. Microlamination techniques have been used to fabricate MECS devices for advanced climate control 关9兴, solvent separation 关10兴, microcombustion 关11兴, fuel processing 关12兴, high-temperature catalysis 关13兴, fluid compression 关14兴, and microdialysis 关15兴 among others. Several research institutions and industrial companies have developed microlamination approaches for producing MECS devices 关15,16兴. In all, systems of microchannel arrays have been constructed in a wide array of materials including copper, stainless steel, titanium, nickel, intermetallics and various polymers with features as small as 5 ␮m. Figure 1 shows the general approach to microlamination for a 2 ⫻ 4 microchannel array. In the case of heat transfer, the function of a typical microchannel heat exchanger is to transmit the heat from one fluid stream into a second fluid stream. Several different approaches can be used to accomplish this task. The most efficient heat transfer methods tend to interleave the two fluids in an alternating succession of cross-flow or counter-flow channels. In particular, counterflow channels are known to provide better temperature distributions along the length of heat exchangers when compared to coflow heat exchangers 关17兴. Most MECS applications make use of counterflow microchannel arrays. Whereas, in the case of single fluid flow, microchannels with relatively high AR’s have been fabricated successfully even in hard-to-produce materials 关18兴, the aspect ratio is generally constrained in two-fluid micro-scale heat exchangers because of the more complex geometry 关19兴. This re-

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Fig. 3 Top view of a counter-flow microchannel array comprised of microchannel and fin laminae. The necked-regions of the device are highlighted in gray.

Fig. 1 Microlamination scheme used to fabricate a dual microchannel array. Arrows show direction of flow.

search investigates the necessary bonding conditions and consequent limits on fin aspect ratios within two-fluid MECS devices.

2

Problem Definition

For this investigation, the case of a two-fluid, counter-flow, microchannel array was investigated though it is expected that the conclusions of this work will apply to other types of two-fluid microchannel arrays. The prototypical counter-flow device is comprised of alternating layers of microchannels, which allow the two fluids to flow in opposite directions separated by fins. A concept of the through-cut lamina design for a microlaminated counter-flow

microchannel array is shown in Fig. 2. It is assumed that once the laminae are stacked they are diffusion bonded according to Fig. 2. The plan view of the resulting monolith comprised of microchannels and fins is shown in Fig. 3. In order to diffusion bond the laminae, a uniform bonding pressure is applied on the stack at an elevated temperature. The pressure is transmitted uniformly through the device except at the neck of the microchannels where each individual microchannel interfaces with fluid headers 共the gray regions where the crosssection AA is in Fig. 3兲. The lack of transmitted bonding pressure in these regions can cause the laminae to remain unbonded. In many cases, unbonded regions are observed in the cross section of counterflow microchannel arrays at points A and B shown in Fig. 4, resulting in leakage within the device and mixing of the two fluids. Figure 5共A兲 shows a region within a counterflow microchannel device where pressure was directly transmitted through all of the laminae. Joints between laminae exhibit excellent bonding. Figure 5共B兲 shows a region where pressure was not transmitted directly between adjacent laminae because of the counter-flow design 关19兴. Figure 5共B兲 exhibits unbonded regions.

Fig. 4 Cross-section of a microchannel neck at cross-section AA in Fig. 3

Fig. 2 An exploded view of the two-fluid counter flow microchannel array investigated in this study

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Fig. 5 Cross-section of a diffusion-bonded counter-flow microchannel heat exchanger showing sections through which the bonding pressure: „A… Was transmitted; and „B… was not transmitted. Cross-section „B… resulted in leakage between the two fluids.

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Fig. 7 Specific critical dimensions of the test article used in this study

Fig. 6 Geometry of the test coupon studied in this paper and verified by leakage testing

By experience, the width of the neck has to be constrained to a dimension where bonding will occur. The limit on the width of the channel at which bonding takes place depends on the thickness of adjacent fin laminae. In other words, as the thickness of the fin laminae above and below the neck of the microchannels increases, the neck can be made wider. The ratio of the channel span in the necked region to the fin lamina thickness is defined as the fin aspect ratio. It is expected that for a given set of bonding conditions 共time, temperature, bonding pressure兲, there exists a bonding pressure 共stress in the direction of stacking兲 limit that all areas of the laminae must receive in order to bond. This minimum pressure will ultimately constrain the fin aspect ratio for any given twofluid microchannel device.

3

8共A兲 and 8共B兲 show the out-of-plane stress 共S33兲 distribution on the counterflow model for h = 152.4 ␮m and a = 1.70 mm. Figure 8共A兲 on the left is a zoomed in view of one of the channels of the same model. Figures 9共A兲 and 9共B兲 are S33 stress contour plots for the test coupon for the same h = 152.4 ␮m but different channel spans. Under the same conditions 共h = 152.4 ␮m and a = 1.70 mm兲, the out of plane stresses 共pressure between the laminae兲 throughout the two devices were found to be within ±4%. These conditions were verified across a wide range of neck widths and fin thicknesses validating the geometry of the test coupon used in this study. Because the temperature and pressure conditions were constant throughout the diffusion bonding cycle, a simple linear elastic model was found to be adequate. As the model is always under compression, the analysis was performed on a 6 h thick 3D deformable model instead of six separate layers each with thickness h, in order to reduce contact nonlinearity problems. Two rigid three-dimensional discrete plates are used on the top and bottom to apply the bonding pressure. The model was a linearly elastic isotropic model with the following material properties: E = 124,800 N / mm2, ␯ = 0.2235. These values were chosen as the elastic properties of 304 stainless steel at the bonding temperature of the laminae 共900 ° C兲. Contact was defined between the rigid plates and a set of the deformable plates representing the heat exchanger. Load was applied in three steps to prevent numerical singularity: 共1兲 The deformable body was constrained in the Z direction. Then the top and bottom rigid plates were moved towards the body of the heat exchanger by a very small distance 共1 ⫻ 10−8 mm兲 to establish the contact between the nodes. 共2兲 After removing the Z direction constraint on the deformable body, the bottom rigid plate was constrained in all six degrees of freedom.

Theoretical Analysis

An analytical approach to modeling this phenomenon has been attempted based on simple elastic beam theory 关19兴. However, no general analysis of the stress conditions between laminae was performed. Here a finite element model is used to analyze the effect of lamina thickness and necked width 共span兲 on the pressure distributed through the necked region of the sample. An understanding of the pressure limits necessary for bonding to occur in this area will allow designers to formulate the appropriate channel geometry for ensuring sound bond joints. To simplify the analysis, a test coupon geometry was developed 共Fig. 6兲 to approximate the conditions of the necked region shown in Figs. 3 and 4. Critical dimensions of the test coupon are given in Fig. 7 along with definitions of the lamina thickness, h, and the span of the neck, a. The purpose of the test geometry was to simplify the fabrication of test coupons needed to experimentally verify the findings of the model. To validate the geometry of the test coupon, FEA was performed on the geometry in Figs. 6 and 7 as well as the geometry of the two-fluid counterflow microchannel array in Fig. 2. Results of the validation are shown in Figs. 8 and 9. The contours in Figs. Journal of Manufacturing Science and Engineering

After removing the displacement boundary condition in Step 1 on the top rigid plate, a pressure of 5.86 MPa was applied on the top rigid plate. The load was applied in steps of 100 to prevent numerical singularity and negative eigenvalue. An eight-noded brick element with reduced integration 共C3D8R兲 was used for all laminae with the models. For the rigid plates, 3D rigid elements were used.

4

Experimental Approach

The fabrication procedure for making the test specimens 共Fig. 6兲 consisted of a microlamination procedure involving laser machining and diffusion bonding. This procedure is reported in more detail in 关19兴. First, laminae were patterned from blanks of 304 NOVEMBER 2006, Vol. 128 / 979

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Fig. 8 „A… Zoom in view of S33 stress contours for one of the microchannels. „B… S33 stress contours from FEA on counterflow microchannel model.

stainless steel shim stock of various thicknesses 共76.2, 152.4, 203.2, 254, and 508 ␮m兲 using a 532 nm Nd:YAG laser installed on a laser micromachining system. Overall size of the laminae was 25.4⫻ 25.4 mm. Critical dimensions of the first and third laminae are shown in Fig. 7. Efforts were made to remove laser burrs by abrasion after laser machining. Laminae were cleaned with acetone, methanol, and deionized water for degrease and rinse and put into an alignment fixture to be bonded in a vacuum hot press. The base of the hot press fixture is made of graphite with tungsten pins for facilitating the edge alignment of the laminae. All laminae were diffusion bonded in the vacuum hot press at 900 ° C and 5.86 MPa for 2 h. Preliminarily, a set of test coupons were developed to verify the existence of the bonding problem under study. Laminae thicknesses for preliminary coupons were 254 and 508 ␮m. Metallography was conducted on these coupons to verify bonding conditions. In all cases, metallography specimens were prepared by molding in epoxy and then cross sectioning by metallographic saw and polishing. Once the process was verified, additional test specimen were produced in the remaining thicknesses. To speed up testing, the bonds of these devices were evaluated by means of a leakage test in which the open header was pressurized by air to several atmospheres and held under water to look for air leakage. The experimental approach is reported in greater detail in 关19兴. 980 / Vol. 128, NOVEMBER 2006

5

Results

To begin the experimentation, three specimens with a lamina thickness of 508 ␮m and neck spans of 2.54, 3.175, and 5.08 mm were diffusion bonded at the conditions described previously. Metallography of the specimens revealed that the specimens with 2.54 and 3.175 mm spans were bonded in the necked region, whereas small gaps between laminae were detected for the specimen with the 5.08 mm span. Figures 10共A兲–10共C兲 represents the micrographs of the 508 ␮m thick specimens. Specimens were prepared by molding in epoxy and then cross sectioning by metallographic saw and polishing. Similarly, three specimens with lamina thickness of 254 ␮m and neck spans of 1.524, 2.54, and 5.08 mm were diffusion bonded. Metallography of these specimens showed that specimens comprised of 5.08 and 2.54 mm were not bonded in the necked region, whereas the specimen with the 1.524 mm span did not have any gaps. Micrographs of these specimens are shown in Figs. 10共D兲–10共F兲. These micrographs confirm that the leakage problem occurs above and below the necked region of the microchannels. Further experiments were performed by fabricating and leakage testing specimens consisting of 76.2, 152.4, and 203.2 ␮m thick laminae. A summary of results gleaned from both metallography and leakage tests are shown in Fig. 11 关19兴 along with a line indicating the approximate boundary at which stress Transactions of the ASME

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Fig. 11 Mild stress variations at the neck region on Case 7

4, 8, 11, and 13, all were very close to the leakage limit and, consequently, had results approaching a no stress condition. As shown in Fig. 12, the stress distribution on Case 8 was not uniform throughout the neck region. There is a slight variation in the stresses showing some nodes being in tension while other nodes being in compression. For example, the variation in stress for case 10 ranges from −0.05 to 0.15 MPa. The “bonded/not bonded“ column for each case was obtained from the experimental data in Fig. 11. If the test case did not have corresponding experimental data, the column was marked “not tested.” These FEA simulations were performed to determine where the compression to tension boundary was within the plot.

6

Fig. 9 „A… S33 stress countours on test coupon with h = 0.1524 mm and a = 1.70 mm. „B… S33 stress countours on test coupon with h = 0.1524 mm, and a = 1.30 mm.

conditions transition from compression to tension using finite element modeling. The line is a curve fit for five FEA conditions where the out-of-plane nodal stress conditions were near zero. In an effort to compare experimental results with modeling results, Table 1 shows the finite element results for several corresponding experimental results 共the table also contains additional FEA results used to determine where the transition from compression to tension occurred at various lamina thicknesses兲. In this table, the critical stress is defined as the out-of-plane nodal stresses 共S33兲 above and below the necked regions in Fig. 6. These values were obtained by averaging all the nodal out-ofplane stress on this bridge. As readily observed, some patterns emerge by comparing theoretical and experimental results from Table 1. All compressive stresses yielded a bonded device. For most cases, the value of the critical stress is uniform throughout the necked region. However, the cases 8, 11, and 13, the stress distribution was not uniform like in the other cases. Similarly, if the necked region was strictly tensile, the device leaked. Cases 1,

Fig. 10 „A…–„C… Micrographs of test specimens consisting of 508 ␮m thick laminae: „A… 5.08 mm span „50Ã …; „B… 3.175 mm span „50Ã …, and „C… 2.54 mm span „50Ã …. „D…–„F… Micrographs of test specimens consisting of 254 ␮m thick laminae: „D… 5.08 mm span „50Ã …; „E… 2.54 mm span „50Ã …, and „F… 1.524 mm span „50Ã ….

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Discussion

As shown, variations in stress are centered around the neckedregion of the channels. From the FEA model we can predict that when the value of the S33 critical stress reaches 0.2 MPa of tension, then leakage takes place. Also when there are a few nodes in the bridge region in tension and a few in compression, and when the value of the tensile stress on these nodes does not exceed ±0.2 MPa then it appears that the layers are just bonded. In any event, it is safe to say that the layers will be bonded together when the stresses present in the necked region are purely compressive. In other words, when the channels become wide enough compared to the thickness of the laminae, the stresses near the center of the neck become tensile. When that happens, no matter how much bonding pressure is applied, the laminae above and below the neck will not bond. One significant finding from this study is that as the size scale of microchannel devices decreases, the allowable fin aspect ratio of the device increases. Figure 13 shows the same data presented in Fig. 11 with the y-axis divided through by the lamina thickness to yield the aspect ratio of the channels. This graph shows that in general, the fin aspect ratio never exceeded more than about 10:1 in the necked region of the devices made. The line demarks the leakage versus bonding region and is simply a curve fit of the data points of bonded geometries closest to the critical bonding pressure at each lamina thickness. This line indicates that as the thickness of the fins decrease, higher fin aspect ratios can be achieved. This is counter-intuitive but consistent with prior findings 关19兴. According to this graph, fin aspect ratios of greater than 20:1 共high aspect ratio兲 are possible with fin thicknesses less than 1.36 ␮m. Under these bonding conditions, the only concerns would be that any fin deflection 共elastic or plastic兲 incurred during processing would not exceed the adjacent microchannel heights resulting in the fins bonding to one another. To avoid this, the channel laminae would have to be thicker than the fin laminae, suggesting that while higher fin aspect ratios are possible, it does not necessarily translate directly into higher channel aspect ratios 共our primary concern兲. The results of the FE simulation show that simple elastic FE models with a set of lamina thickness and channel span can be NOVEMBER 2006, Vol. 128 / 981

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Table 1 The geometrical specifications of all Test coupons and the results of FE simulations for critical stresses FE simulation case

Lamina thickness, h 共mm兲

Channel span, a 共mm兲

Aspect ratio, a / h

Leakage/ bonded

Critical stress 共MPa兲

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.005 0.0762 0.1524 0.1524 0.1524 0.1524 0.2032 0.2032 0.2032 0.2032 0.254 0.254 0.508 0.508

0.025 0.75 0.50 1.30 1.70 2.50 1.0 1.5 2.2 3.5 1.8 2.6 3.1 5.1

15 9.84 3.28 8.53 11.15 16.4 4.92 7.38 10.83 17.22 7.09 10.24 6.1 10.04

Bonded Bonded Bonded Bonded Leakage Leakage Bonded Bonded Leakage Leakage Bonded Leakage Bonded Leakage

−0.005 −0.17 −0.45 −0.05 +0.43 +0.44 −0.30 −0.07 to +0.1 +0.45 +0.39 −0.05 to +0.15 +0.36 −0.026 to +0.15 +0.30

used to determine the interfacial stress between the lamina. Neither the complex creep behavior nor the diffusion behavior of the lamina was necessary to predict the integrity of the diffusion bonded laminate.

7

Conclusions

An investigation on the limits of fin aspect ratios for counterflow heat exchangers was carried out in this study. Following are the conclusions of this study: 1. The fins in two-fluid microchannel heat exchangers have a certain aspect ratio limit for a given thickness of the lamina, beyond which poor bonding will occur within the device resulting in leakage and mixing of the two fluids in the device. 2. For a given set of bonding conditions, the width of the channel can be interpreted as a function of the thickness of the

lamina with the key bonding characteristic being that only compressive out of plane stresses exist in the critical necked region. It is expected that the laminae may just bond even if a tensile stress up to a maximum of 0.15 MPa exists in a few places in the critical necked region, provided that at all other places of the necked region the out-of plane stress is purely compressive. 3. Fin aspect ratios in the necked regions of counterflow devices were found up to 10:1 aspect ratio. However, it was also found that the allowable fin aspect ratio generally decreases with increasing fin thickness. This finding is counterintuitive but has been verified by the FE model developed in this study. It is expected that higher aspect ratios can be accommodated at smaller scales with high aspect ratio 共greater than 20兲 fins possible at lamina thicknesses less than 1.36 ␮m for this set of bonding conditions. This does not

Fig. 12 A plot of the experimental results showing the conditions under which bonding did and did not occur. Bonding conditions for all of these samples were 5.86 MPA at 900° C for two hours. The boundary line shows the rough conditions under which the modeled stress was near zero.

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Fig. 13 A plot of the experimental results showing the aspect ratios under which bonding did and did not occur. Bonding conditions for all of these samples were 5.86 MPA at 900° C for two hours. The boundary line shows the rough conditions under which the modeled stress was near zero.

necessarily translate into increases in channel aspect ratios limited by the amount of fin warpage incurred during diffusion bonding. 4. Finally, this study shows that a simple elastic model is adequate for determining the stress conditions during diffusion bonding of a counter-flow microchannel array.

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