Joseph Mooney, winner of the 23rd Annual Sir Bernard Crossland Symposium, on using X-ray tomography and pore network modelling to improve the effectiveness of electronics cooling solutions.

What are heat pipes and why do we need them?

Heat pipes are passive two-phase thermal transfer devices commonly used in a multitude of applications, such as electronics cooling, energy conversion systems, cooling of nuclear reactors and high-performance space applications.

They consist of a hollow enclosed metal capsule lined with an internal porous structure, known as a wick, which is saturated with a working fluid near its saturation pressure.

Figure 1 illustrates a classical heat pipe design along with its key components and operation. When heat is applied to one end, ie, the evaporator, the fluid evaporates from the wick into a hollow vapor channel. A temperature driven vapor pressure between the evaporator and condenser, or heat sink, transports the vapor to the other end.

At the condenser end heat is removed from the fluid forcing it to condense into the wick. The excess of fluid in the wick at the condenser end and the deficiency of fluid at the evaporator end generates a capillary driven flow that transports the working fluid back to the evaporator.

Due to their two-phase characteristics, heat pipes are ideal for transferring heat over long distances with very small temperature drops (typically <5 °C). Moreover, heat pipes can have effective thermal conductivities of order 10² – 10⁴ times superior to those of good heat-conducting materials, such as aluminium, copper or silver.

One of the most commonly used types of heat pipe is a concentric tube, sintered copper powder heat pipe with water as a working fluid(1, 2). It is used because of its thermal characteristics, relative simple design, low manufacturing cost and malleability. 

Figure 1: Fundamental set up of a heat pipe with inclusion of heat and fluid flow

As microelectronics technology evolves, the heat fluxes associated with electronic components are continually increasing, while the space available for heat removal is constantly being reduced.

Heat pipes are conventionally formed and sintered as straight pipes and are then later bent or deformed into shape to fit the application, as seen in figure 2 for a typical electronics application.

It is conventionally understood that the thermal performance of heat pipes can degrade by up to 65% when they are bent. Furthermore, the maximum allowable heat input into these pipes reduces when deformed which can lead to excessive operating temperatures and damage to the electronic components.  

Since heat pipes are opaque and work under vacuum, there is no means of observing the fluid transport within the porous wick structure without compromising its functionality. Hence, existing studies in this area are limited, and they generally only speculate that the increased thermal resistance in deformed heat pipes is due to liquid and vapor flow obstructions. 

Figure 2: Schematic identifying potential problems induced by the employment of heat pipes in space constrained electronics applications

Project objectives 

Our study aims to present a novel, non-destructive, diagnostic tool to the field of heat pips for electronics cooling technologies and present a platform for the development of targeted manufacturing techniques. This will enable engineers to design tailored heat pipes to improve the thermal management of electronic circuits.

Several steps were required to verify our method, which were as follows:

First, we needed to experimentally determine how much of an influence a bend had on the performance of standard heat pipes. We then needed to verify that the non-destructive means of observing the internals of a heat pipe was accurate and did not compromise any data from the bending process.

The next step involved the development of a suitable platform to extract and handle the internal image data obtained. A requirement for this platform was that it should allow us to convert the real image data to a 3D CAD file of the test pipe.

With this information, we could visually inspect the deformation caused by the manufacturing process, ie bending. Before any numerical analysis was performed, an image segmentation model was developed and used to obtain precise information on every individual pore and particle in the wick.

Finally, this data was applied to a thermofluidic model, that used conventional fluid mechanics and heat transfer theory to represent heat pipes. This allowed us to identify and quantify the bottlenecks in our deformed heat pipes.

Quantifying the thermal performance of a deformed heat pipe 

An initial objective of our work was to correlate the experimental thermal resistances of a deformed heat pipe to the thermofluidic data presented by the novel non-destructive observational technique.

Therefore, an experimental apparatus was designed, fabricated and configured to accurately characterise the thermal resistance of a horizontal sintered copper heat pipe in four bend configurations: 0°, 30°, 60° and 90°.

The apparatus featured two radial calorimeters that quantified heat flow from an electrical heat source into the evaporator section of the heat pipe and heat flow from the condenser section of the pipe to a regulated liquid-based cooler.

All bend configurations were run to steady state up to a 15 W heat input through the calorimeter – or when the pipe could not effectively cool the heat source, ie, dry out occurred. The experiment used the combined quantities of heat input and point temperature measurements of the heat pipes’ surface to determine their associated thermal resistances.

Thermal resistance, R_th, characterises how well heat is transported through the pipe as a function of the temperature difference between the evaporator and the condenser ends. It is the ratio of the difference between evaporator and condenser surface temperatures of the heat pipe to the heat inputted into the pipe.

The experimental thermal resistance as a function of bend angle for five heat input values is presented in Figure 3. It was found that as the bend angle was increased from 0 to 90° the thermal resistance of the heat pipe rose by up to ~ 44%.

It was also evident that the increase was non-linear, with a 15 W heat input reporting increments of 6%, 19% and 32%, respectively, for bend angles of 30°, 60° and 90°. Without a detailed analysis, previous studies on deformed heat pipes could not fully explain this non-linear trend in R_th.

Instead, studies have attempted to speculate on what occurs in the bend region by cross sectioning a pipe at the bend site in order to carry out a visual inspection. Any cross section is only representative of one plane in the bend, however, and the wick, more importantly, is often further deformed when the cross section is being made using tools such as pipe or laser cutters. 

Figure 3: Experimental thermal resistance of a 6 mm diameter x 400 mm long (18 W) heat pipe as a function of bend angle

Overcoming Schrödinger’s cat paradox – X-ray tomography and pore network modelling 

Without any accurate means of observing the internals of a heat pipe, researchers in the area of heat pipe design are constrained by a form of Schrödinger’s cat paradox.

They cannot assume what is occurring in the deformed heat pipe by looking at the outside walls and, if they open the pipe, the information relating to the bending process would be considered irrelevant.

We decided to pose the question 'how can we engineer our way out of this paradox?'. Well, if Schrödinger had performed an X-ray or MRI scan of the ‘box’ in question, he would have figured out whether the cat was upright and alive or horizontal and immobile …

X-ray tomography (XRM), as outlined in figure 4, is a non-destructive technique for characterising materials in three dimensions(3). It provides a potential solution to analyse concealed problems, such as defect detection in additive manufacturing(4) or biological samples(5), by enabling non-destructive measurements with fine resolution, i.e., 1- 2000 pixel resolution per image or magnifications down to < 1 μm true spatial resolution.

In our work, each bend configuration that was experimentally tested was also placed inside the XRM and scanned over a range of ± 20 mm from the outer tangent point of the bend. As X-rays were emitted from the source to the detector, some were absorbed by the test specimen, ie the wall or sintered material of the heat pipe.

The X-rays that were not absorbed hit the detector and were represented as greyscale images. The XRM scans produced ~ 2000 sequential images of the test specimen which were used for post-image processing. 

Figure 4: XRM of straight heat pipe with final 3D RAW Data at the bend location

The XRM data was imported into a visual platform (Objects Research System – Dragonfly) that generated a solid 3D file of the heat pipe(6). The pores and particles in the model were separated into defined regions of interest (ROIs).

Figure 5 presents the pore space ROI as a graphed connectivity network (left) and a fluidic network (right). The spheres represent pores and the lattices represent their neighbouring pore connectivity.

These networks contain important pore information such as the individual labels, locations (XYZ), and geometric properties (diameter, porosity (ε ), vapor channel radius (r_v).

The pre-eminent feature of the network analysis is that it can detect pore-to-pore connectivity and present this information as a graph(7), as shown in figure 5. With predefined boundary conditions, for heat input and constant mass flow, a thermofluidic model was developed in MATLAB that utilised these network graphs.

The model looked at the local and global changes in geometry, porosity and permeability. By applying these changes to conventional fluid mechanics theory for heat pipes, the liquid and vapor pressure drops could be quantified. 

Figure 5: Pore Network Modelling process for establishing the liquid pressure drop (P_L1-P_L2) in the wick of a 90° bent heat pipe

Establishing the dominant flow structure in a deformed heat pipe

For normal operation, the capillary limit of a heat pipe must not be exceeded. This limit requires that the (driving) capillary pressure in the wick is greater than the sum of the internal frictional / liquid and vapor pressure drops(8).

If this condition is not met, the rate of evaporation surpasses the rate of capillary back flow to the hot source and the wick dries out. The thermal resistance of a heat pipe is typically reliant on this limit, and any increases in liquid and vapor pressure drop result in an increase in thermal resistance.

The X-ray data and pore network modelling allowed us to extract plots for the liquid and vapor pressure drops in the entire heat pipe post bending. Hagen Poiseuille flow theory was used to model the vapor pressure drop in the vapor channel.

A similar approach was used to analyse the liquid pressure drop in the wick, however it was combined with Darcy’s law and the Lucas-Washburn equation for porous media.

A dimensionless pressure drop term was used to describe the relative percentage increase in the vapor and liquid pressure drops as a function of bend angle. This dimensionless term is a ratio of relative pressure drop in the bend section to a straight section, ie, the vapor (∆P_v^**) and liquid (∆P_L^**) dimensionless pressure drops.

To date, studies that analyse the increase in the thermal resistance of a bent heat pipe have assumed that zero deformation occurs in the wick. This implies that our dimensionless pressure drop terms would theoretically always be unity and that the capillary limit would not be impeded by deformation of the wick. However, this is evidently not the case and our method aims to show this.

Thermofluidic analysis of experimental thermal resistance

Presented in figure 6 and figure 7, respectively, are the XRM images of the bend region of a tested heat pipe, and a corresponding plot for the dimensionless vapor (∆P_v^**) and liquid (∆P_L^**) pressure drops of the heat pipe as a function of bend angle.

From figure 6 it is clear that the wick and vapour channel are both deformed during the bending process. This XRM observational method, alone, offers novel qualitative data for further developing an understanding of the liquid and vapour flows within a heat pipe. 

Figure 6: XRM of experimentally tested heat pipe in all bend configurations

Figure 7: Dimensionless liquid and vapor pressure drop as a function of bend angle

The combined work of pore graphing and OpenPNM, allowed us to model the flow structures in a heat pipe, simulate them in the thermo-fluidic model, and accurately quantify the pressure losses.

Table 1 presents the quantitative results from the XRM and pore network graphing. These include the local change in wick porosity ε, wick permeability K, and vapor channel radius r_v at the bend site. Moreover, a comparison of the vapor pressure drop (∆P_v) and liquid pressure drop (∆P_L) to the maximum capillary pressure limit (i.e. ∆P_cap) of the heat pipe is presented in the table.

From the analysis, we discovered that neither ∆P_v^** or ∆P_L^** remained at unity as the pipe was bent. In the vapor flow, there was a maximum rise in ∆P_v of ~8 Pa, and ∆P_v^** increased by up to 14%. Relative to ∆P_cap, however, this deviation could be considered negligible.

Adversely, in the wick (i.e. liquid flow), the pressure drop increased by ~ 870 Pa for the 90° bend, and ∆P_L^** more than doubled over the range of bend angles from 0 - 90°. Hence, we can conclude that the pressure drop in the wick (∆P_L) was impacted the most relative to the capillary limit (ie, performance) of a bent heat pipe.

From previous wick theory, it has been conventionally assumed that the liquid pressure drop in a wick follows Hagen Poiseuille theory for porous media, and that pressure drop is proportional to the length of the wick, ie, a constant wick geometry is assumed [8].

Our work, however, illustrated that the geometry in a deformed heat pipe is altered. On a more important note, a non-linear trend is evident in the liquid pressure drop (see figure 7), similar to our experimental thermal resistance measurements.

The XRM data has demonstrated that the liquid pressure drop in the bend was significantly altered by a local reduction in wick thickness and porosity, caused by cracking and buckling of the wick, ie, smaller wick and pore space, as shown by the areas within the red circles in figure 5.

These observations imply that novel manufacturing techniques for heat pipes and wicks are essential when fabricating a heat pipe for space-constrained applications.

If not, the performance degradation of a cooling solution is consequential, by a factor of up to ~44%. Nowadays, most electronic cooling solutions comprise heat pipes with multiple bends and deformities. Hence, this figure poses as a lower bound for illustrating the potential degradation in a conventional cooling solution.  

High reflectivity surface finish

It is imperative that the proposed method obtains precise information on every pore, particle and connecting node in the wick. Full 360° scans of the pipes were taken within the XRM, and the heat pipes tested were made from copper with a smooth, high reflectivity surface finish.

As the pipes were bent, the high reflectivity and oblique shape caused image noise that rendered some test samples useless, as seen in figure 8. In order to reduce noise, test samples were coated in matte black paint to maximise absorptivity and minimise any sort of noise created by reflection. If any minor noise was identified, it could be easily removed in post processing.  

Figure 8: A comparison between clean XRM images and a noisy imaged caused by reflection of the X-rays

This work has managed to identify the fluidic bottlenecks associated with today’s heat pipe cooling solutions, which to date have not been accurately reported.

We intend to develop this method further so that it can be applied to any heat pipe configuration, and not just the concentric heat pipes in this study. We will achieve this by training our deep learning image processing models for a multitude of heat pipe designs.

We also need to develop a robust model that will analyse the particle network in the wick, which coincides with the fluidic model. The particle network will obtain axial and radial changes in the local thermal resistances inside a deformed heat pipe.

From a manufacturing standpoint, we are currently investigating how we can improve the wick structure by manufacturing a tailored heat pipe design that is premade as bent.

This will ensure that no unknown deformation occurs post manufacture. Hopefully, this tool will help manufacturers to identify unknown losses in their cooling solutions and improve on any inefficiencies.  

This study presents a novel non-destructive method for observing and analysing the internals of a heat pipe using X-ray tomography and pore network modelling.

The experimental and numerical analyses in this study have shown that a non-linear increase in thermal resistance could be related to a non-linear increase in the liquid pressure drop around the bend of the heat pipe.

An increase in vapor pressure drop, although present, was shown to be negligible in comparison. Hence, to maximise the thermal performance of a heat pipe in today’s heat intensive applications, we conclude that additional manufacturing techniques are desired for the wick of a bent heat pipe. The methods included in this study can be used as a diagnostic tool for the development of these novel manufacturing techniques. 

Author: Joseph Phelim Mooney BE, is a second-year PhD student in Stokes Laboratories, Bernal Institute and his work is funded by the SFI CONNECT Centre (Supervisors: Dr Vanessa Egan and Dr Jeff Punch). He achieved his primary degree in mechanical engineering in 2018 from University of Limerick. His work specialises in microfluidics and heat transfer for the thermal management of passive cooling technologies in 5G applications. His work, however, maintains the versatility to be applicable to a multitude of applications. He recently published work with IEEE titled 'Effect of multiple heat sources and bend angle on the performance of sintered wicked heat pipes' which inspired this investigation on deformed heat pipe structures. 

Acknowledgement

This research is conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number 13/RC/2077 and has been part-funded by the European Regional Development Fund through the SFI Research Centres Programme. 

References

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2) JP Mooney, 'Effect of Multiple Heat Sources and Bend Angle on the Performance of Sintered Wicked Heat Pipes," V. Egan, Ed., ed, 2020.

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