Electrochemical Additive Manufacturing-Based Design of a Heat Sink for Single-Phase Natural Convection Immersion Cooling Application

Data centers are facilities that are centralized and serve as a location for the storage, distribution, and processing of data through networking and computing equipment that is located remotely. They perform an indispensable function in aiding diverse information technology (IT) and digital services, encompassing cloud computing, online applications, and data-intensive operations. Data centers are vital due to their capacity to offer dependable and secure infrastructure for the storage and management of extensive quantities of data. This enables smooth access and processing for individuals, organizations, and businesses.

Global data center electricity use in 2021 was 220–320 TWh [1], or approximately 1.3% of the global electricity demand. Since 2008, heat load per rack has increased rapidly [2]. The total amount of power supplied to the data center is used to power all IT equipment for computing services and to operate a cooling system for removing heat generated by the IT equipment. In addition, data centers utilize electricity for power delivery infrastructures such as uninterruptible power supply and lighting. Figure 1 depicts the division of power consumption in a data center and cooling system. The conventional method of cooling in data centers typically involves the use of air-based cooling systems, such as computer room air conditioning units. These systems use a combination of cool air supply and hot air exhaust to maintain the desired temperature within the data center environment.

The application of liquid cooling in data centers can be classified into two primary categories based on how the coolant interacts with the electronic components: direct and indirect liquid cooling [3]. In direct cooling, the coolant directly contacts the electronics, whereas indirect liquid cooling involves the use of an intermediary heat exchanger, such as a cold plate, to transfer heat from the processor to the coolant. Indirect liquid cooling includes technologies such as cold plates [4,5], heat pipes, and vapor chambers [6]. Conversely, direct liquid cooling encompasses methods like immersion cooling [7], pool boiling [8], submerged jet impingement [9], and spray cooling, among others. Each of these cooling technologies has limitations in terms of heat transmission, as depicted by the heat transfer coefficient shown in Fig. 2. The black bars represent the experimental cooling capacity of the technology studied in literature [10].

Heat sinks are passive components characterized by their thermal conductivity, which enables the extraction of heat from the central processing unit (CPU). This heat is then dissipated throughout the computer system via fins, which offer a large surface area for effective heat dissipation. By facilitating the transfer of heat from the heat-producing components to the cooling medium, such as air, the temperature of both the processor and the heat sink remains low.

Three-dimensional printing technologies, also referred to as additive manufacturing (AM) for metal materials, have been recognized as promising techniques for manufacturing heat transfer devices with enhanced performance. Recent studies in literature have demonstrated intriguing examples where the unique characteristics of AM processes are leveraged to optimize well-known heat transfer enhancement techniques. These techniques include the application of AM for producing pin fins, vortex generators, rough surfaces, offset strip fins, and porous media.

Amongst the AM methods, the one that is distinct from the rest is electrochemical additive manufacturing (ECAM). Contrary to most metal AM methods which utilize expensive metal powder feedstocks, ECAM makes use of a water-based feedstock comprised of widely available and low-cost metal salts. The ECAM feedstock is similar to electroplating chemistries which are used in printed circuit board and semiconductor manufacturing. The key innovation which enables the ECAM process is the printhead, a micro-electrode array composed of millions of individually addressable pixels on the scale of tens of microns. Pairing this micro-electrode array with the metal ion-rich feedstock, ECAM builds parts at the atomic level, allowing for micron-scale feature resolution, complex internal features, high-purity materials, and rapid scalability to support mass manufacturing.

We have employed the principles of triply periodic minimal surface (TPMS) structures in the creation of the heat sink designs. TPMS structures belong to a unique category of minimal surfaces that exhibit translational symmetry in three directions [11]. Consequently, TPMS structures consist of infinite, nonself-intersecting, and periodic surface patterns in three primary directions. They are associated with crystallographic space group symmetry [12]. Different lattice structures, such as gyroid, Schwarz diamond, and Schwartz primitive, are based on TPMS. The practical implementation of these structures closely aligns with metal additive manufacturing techniques. These structures not only offer porosity but also enable fluid permeability through their interconnected patterns, while maintaining a higher surface area to volume ratio.

In this study, we compare heat sinks of gyroid sheet lattice structures for a 1 U data center server. Baobaid et al. showed that under a natural convection flow regime the gyroid sheet TPMS lattice had the best overall performance when compared to the diamond and gyroid solid TPMS lattices [13]. Variables that were studied include the porosity of the lattices, wall thickness, and asymmetry in the unit cell dimensions. We analyzed the impacts of lengthened unit cell dimensions in the flow direction and their results are compared. The lattice heat sink geometries are complex in nature, and their manufacturing is made possible by ECAM technology.

In this study, the lattice-structure heat sink designs were generated using a state-of-the-art software tool, ntopology. This software tool allows for generation of complex lattice structures, including TPMS lattices and general graph unit cell lattices by way of implicit modeling. The solid domain was modeled within the ntopology platform and exported as an stereolithography file type (STL) file. Figure 3 depicts a gyroid heat sink model that was surface meshed in preparation for STL file export.

The STL file was then imported into ansysspaceclaim as faceted geometry, where the boundaries were selected and grouped. Figure 4 depicts the heat sink, or solid domain, and fluid domains modeled within the spaceclaim modeler for preprocessing. The spaceclaim model was then imported into fluent with fluentmeshing using the watertight meshing (WTM) method. The WTM method produces a conformal mesh at the solid–fluid boundary by using a feature called share topology.

The heat sink design parameters were chosen to be representative of a typical 1 U data center server CPU heat sink. The 1 U server design referenced is the Open Compute Project inspired Wiwynn 1 U openEDGE Server [14]. The heat sink design constraints are listed in Table 1. The heat sink length and width were chosen based on current ECAM print capabilities and print bed size constraints. The heater thermal design power and area was chosen to be 250 W, which is that of an Intel Xeon Platinum 8450H Processor.

For this study, the gyroid heat sinks were analyzed based on varying wall thickness, at 0.8 mm and 1.2 mm, as well as 68%, 77%, and 85% porosities at both of those wall thicknesses. The various heat sink designs that were chosen to be analyzed are contained within Table 2. Figure 5 portrays the wall thickness and unit cell design parameters on the gyroid heat sink. For the gyroid with asymmetric unit cell sizes, the unit cell dimensions in the flow direction and lattice height were lengthened to resemble a traditional finned heat sink more closely. A heat sink with asymmetric unit cell size is depicted in Fig. 6.

For the computational fluid dynamics (CFD) study, the conditions which were chosen to be constant across the analyses are engineered fluid material, inlet fluid temperature, heat sink material, and heat sink design volume. The engineering fluid chosen for this study is ElectroCool 110 (EC-110), which is a commonly used dielectric fluid for immersion cooling applications. The fluid properties of EC-110 defined within the CFD are in accordance with the manufacturer's datasheet [15]. With this working fluid, the inlet temperature was set to be 40 °C. The heat sink material chosen is copper; this is, unlike more traditional metallic AM processes, ECAM is capable of printing pure copper, which provides a higher thermal conductivity as compared to other metal alloys.

The CFD model was designed in that there is a solid domain, which is the heat sink, and a fluid domain encompassing that heat sink. The inlet was specified with an arbitrarily small mass flow inlet with 40 °C inlet temperature. The outlet boundary of the fluid domain was specified as a pressure outlet. The flow direction is in the positive y-direction, and gravity is acting in the negative y-direction. This is simply because immersion-cooled data center servers are typically oriented vertically in the immersion tanks [16]. Figure 7 depicts the boundary conditions on the fluid domain within the CFD model. Figure 8 depicts the heat flux boundary condition on the heat sink as well as a cross-sectional view of the volume mesh. The heat flux value applied was 5.71 W/cm². The meshing was performed using the ansysfluent WTM, with polyhedral elements.

Being that this is a natural convection study, the Boussinesq model was used. The energy equation was turned on, and viscous effects were analyzed using the laminar model. Radiation effects were also considered within the CFD model using discrete ordinates. Baobaid et al. [13] showed that under natural convection flow conditions, thermal radiation has significant impacts on the overall heat transfer of gyroid heat sinks. In their study, radiation accounted for approximately 23% of the total heat transfer, and therefore, in this study, we have not considered it to be negligible. The operating density was specified as 820 kg/m³ based on the material datasheet supplied by the fluid manufacturer. The Semi-Implicit Method for Pressure-Linked Equations solver was used with the standard under-relaxation factors of 0.3, 1, 1, 0.7, and 1 for the pressure, density, body forces, momentum, and energy solution controls, respectively.

To validate the CFD model and to ensure convergence, a grid independence study was performed using the gyroid TPMS with 1.2 mm wall thickness and 85% porosity. The minimum edge length was first specified to be at 25% of the heat sink wall thickness and then iterated to smaller element sizes at 20%, 15%, and 10% of the heat sink wall thickness. The CFD model converged consistently for minimum grid edge lengths of 20%, 15%, and 10% of the heat sink wall thickness. Therefore, specifying the grid edge length to be 25% of the heat sink wall thickness provided results within 1 °C, or approximately 1%, of the result when specifying a grid length of 10% of the heat sink wall thickness. Since computational burden increases dramatically as minimum grid edge length decreases, it was chosen to specify a minimum grid edge length of 25% of that of the heat sink wall thickness for all the CFD simulations. Figure 9 displays the max case temperature as a function of the mesh element count in the CFD model. The data point with the red square around it is the max case temperature when specifying a grid size of 25% of the wall thickness.

For the CFD model, fluent designates the fluid domain and solid domain and solves the conservation equations for fluid flow. The governing equations (2)–(6) are listed as follows.

The gyroid heat sink designs were analyzed with the heat flux applied to the heat sink with the boundary conditions as specified within Sec. 3.1. The max case temperature for each of the designs is listed in Table 3. Figure 10 shows the comparison between the nine designs.

From the above figure, we see that thermal performance increased as wall thickness increased from 0.8 mm to 1.2 mm for the heat sink with 68% porosity. Meanwhile, the 0.8 mm and 1.2 mm wall heat sinks exhibit very similar thermal performance at both 77% and 85% porosity. Furthermore, the thermal performance of the asymmetric gyroid heat sink was very similar to that of the 1.2 mm wall thickness heat sink at 68% porosity. By examining the max case temperature data in Table 3 and Fig. 10, it appears that there are likely local minima in the max case temperature curve between 68% and 85% porosity for the 0.8 mm and 1.2 mm wall thickness gyroids. However, for the asymmetric gyroid, it appears that the max case temperature would be minimized at a porosity less than 68%. If we assume that there is an optimal porosity for each of the heat sinks under this model's boundary conditions, then we infer that the optimal porosities for the 0.8 mm and 1.2 mm wall thickness gyroids are likely near 77% for each. Similarly, we can infer that for the 1.2 mm wall thickness, asymmetric gyroid, its optimal porosity is likely less than 68%.

For the given boundary conditions and in the natural convection flow regime as prescribed, the best performing heat sinks are the asymmetric gyroid TPMS with 1.2 mm wall thickness and 68% porosity and the symmetric gyroid with 1.2 mm wall thickness and 77% porosity, with a marginal max case temperature difference between the two. The worst performing design under these conditions is the asymmetric gyroid with 1.2 mm wall thickness and 85% porosity. A midplane temperature contour plot for the 1.2 mm wall thickness, 77% porous heat sink is shown in Fig. 11. Further, a temperature contour plot of the heat sink itself is shown in Fig. 12. A midplane temperature contour plot for the asymmetric gyroid at 85% porosity is shown in Fig. 13, and a temperature contour plot for this heat sink is shown in Fig. 14.

From these temperature results, we believe that the asymmetric gyroid heat sink with the 1.2 mm wall thickness and 85% porosity performs worse than the other designs because of the lack thermal mass and inability to invoke flow in the positive y-direction due to large pores in the flow direction, both hindering heat transfer abilities. However, thermal performance for the asymmetric gyroid at 1.2 mm wall thickness improves significantly as porosity decreases. Meanwhile, the heat sink designs that exhibit better thermal performance by lowering max case temperature likely due so by having more thermal mass in the form of lower porosity and also invoking more flow in the positive y-direction and promoting free convection. Moreover, as porosity decreases, the surface area increases since the volume fraction of solid increases within each unit cell of the structure. Therefore, the thermal performance increase with decreasing porosity is likely due to increase surface area leading to enhanced heat transfer.

To provide a deeper insight into why the designs perform the way they have, it is necessary to examine the fluid flow profiles through each of the heat sinks. Figure 15 contains the velocity contour plots through the midplane for the 1.2 mm wall, 77% porosity heat sink. Likewise, Fig. 16 contains the velocity contour plots through the midplane for the asymmetric gyroid with 1.2 mm wall thickness and 85% porosity.

Examining the velocity profiles of the two designs, it appears that the 1.2 mm wall thickness heat sink at 77% porosity shown in Fig. 15 invokes significantly more flow when compared to the asymmetric gyroid design in Fig. 16. The 1.2 mm wall thickness, 77% porous heat sink also has more thermal mass by having a lower porosity and therefore has greater overall heat transfer area, which aids in invoking fluid flow in the free convection environment.

The various lattice heat sink designs were compared, and the results showed that the best overall heat sink was the asymmetric gyroid TPMS heat sink with 1.2 mm wall thickness and 68% porosity. Moreover, the worst performing heat sink overall was the asymmetric gyroid TPMS heat sink with 1.2 mm wall thickness and 85% porosity. For a given wall thickness, as TPMS structures become less porous, the volume fraction for solid within a unit cell increases, and therefore the surface area increases as well. The improvement in thermal performance as porosity decreased in these designs is due to the increased thermal mass and heat transfer area as the heat sink becomes less porous. These also allow for the heat sink to invoke more fluid flow in the free convection environment, further improving the heat transfer capability of the heat sink. These heat sink designs, once not so easily producible, are now easily manufacturable by AM processes such as ECAM. Future work with this technology will involve experimental validation and testing of ECAM-produced heat sink designs in single-phase immersion cooling applications. The performance of TPMS and other lattice heat sinks would likely improve if used in a forced flow immersion cooling regime, however, some form of ducting would likely be necessary to prevent fluid bypassing the high surface area heat sinks to fully benefit from their complex structures and enhanced heat transfer capabilities.

We would like to acknowledge Fabric8Labs for sponsoring this study. We would also like to acknowledge Yeong-Yan Perng of the ansysfluent team for his contributions in helping to create a functional fluent workflow for analyzing these complex geometries.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$g$ =

gravity

$h$ =

sensible enthalpy

$k$ =

thermal conductivity

$kt$ =

turbulence transport conductivity

$p$ =

pressure

$q″$ =

heat flux

$Sh$ =

volumetric heat generation

$t$ =

time

$T$ =

temperature

$Tcase$ =

max case temperature

$T0$ =

operating temperature

$v$ =

velocity

$β$ =

volumetric expansion coefficient

$λ$ =

TPMS porosity

$μ$ =

dynamic viscosity

$ρ$ =

density

$ρ0$ =

constant density