Introduction

With the surge of modern high-performance gaming and virtual reality, the demand for more powerful computer hardware components has drastically increased in the consumer market. No longer is this high-tech hardware reserved for large corporations, as everyday personal computers (PC) are being fitted with powerful graphics processing units (GPU) in order to cope with the requirements of running high-end games, as well as the advent of virtual reality (Ref 1). This increased demand in performance comes hand in hand with a desire to maintain or reduce the overall size of PCs, leading to a reduction in the GPU footprint. As such, more power is being dissipated as heat over smaller areas, and in tighter confinements. Therefore, efficient cooling and thermal management of these parts has become a significant challenge in recent years (Ref 2).

Heat sinks have been used in PCs for decades, and usually utilize forced convection as the main method of heat transfer, with fans used to generate an airflow over the heat sink. More recently, it has become necessary to use water-cooled heat sinks, as the ability for air to absorb heat may be insufficient (Ref 3). Furthermore, air-cooling systems are less compact than their water-cooled counterparts. Current heat sink manufacturing processes are either material inefficient or costly in terms of change over whenever the heat sink footprint is altered (Ref 4). The latter point is further compounded considering the frequency with which new GPUs are emerging, as heat sinks need to be adapted to new GPU footprints on almost a monthly basis (Ref 5, 6). This can be problematic when restrictive manufacturing processes such as die casting and extrusion are employed. Since these processes rely on a hard-cased pattern, the whole process must be modified to accommodate any change in product design, which offers poor flexibility in a rapidly changing industry and drastically increases the production costs.

Another factor that needs to be accounted for is demand variability, as not all GPUs are sold in the same quantities. High-end GPUs may sell only thousands of units, while lower-end models may sell millions. This inconsistency in demand leads to a variation in the number of heat sinks that must be produced for any one GPU. A challenge thus exists in identifying a heat sink manufacturing process that can accommodate various production volumes (Ref 7) while also remaining flexible to frequent product design changes.

Cold gas dynamic spraying (CGDS) is a well-established metallic coating process and has recently evolved into a novel additive manufacturing (3D printing) technology (Ref 8, 9). Through this technique, metallic powder particles are accelerated to high velocities in an inert supersonic gas stream. Upon impact with the substrate, the particles undergo rapid plastic deformation and bond to the surface to create coatings or simple structures. Recently, this process has been used to produce pin fin heat sinks for compact air–air heat exchangers (Ref 10,11,12). This is accomplished by inserting a wire mesh between the CGDS nozzle and the metallic substrate. In so doing, an array of pyramidal pin fins can be created with geometric parameters dependent on the mesh characteristics and spray parameters.

This process presents many advantages when compared to other competing manufacturing processes, namely limitless variability, low-cost equipment and consumables, and easy adaptability to demand. However, a drawback of the CGDS process is that it can impart high residual stresses to the substrate. If the latter is sensitive to heat and mechanical residual stresses, the use of reduced spray parameters (lower pressure and/or temperature) is required. An unfortunate consequence of this is that a large portion of the powder being sprayed does not deposit on the substrate and is consequently wasted, reducing the process viability. Consequently, in order to mitigate the loss of powder when low spray parameters must be used, the possibility of reclaiming and reusing the un-deposited powder in the manufacturing of subsequent heat sinks should be explored.

This work aims to demonstrate the viability of using CGDS for the manufacturing of copper pin fins for use in GPU heat sinks. More precisely, the work seeks to verify the feasibility of spraying reclaimed copper powder, which is obtained by collecting un-deposited powder particles from previous heat sink spraying runs performed with the as-received copper powder. The reclaimed powder is then re-sprayed and deposited on copper plate substrates (to mimic actual GPUs geometries). From this procedure, it is demonstrated that fully dense copper coatings are achievable with reclaimed powder and that these coatings feature a similar microstructure to those obtained with the as-received powder. An analysis is carried out to demonstrate the economic benefits of powder recycling. Furthermore, the thermal performance of the GPU heat sinks is assessed.

Experimental Procedures

CGDS System

The CGDS system used for the production of all coatings and pin fin arrays in this work was the SST Series EP cold spray system (Centerline Ltd., Windsor, ON, Canada). This system has a maximum stagnation temperature and pressure of 650 °C and 3.4 MPa, respectively. However, due to substrate sensitivity to heat and mechanical residual stresses (which results in excessive bending of the substrate and deteriorate the thermal performance of the cooling system unit), it is required to use reduced spray parameters.

The nozzle used had a 2-mm throat diameter and a 120-mm-long diverging section (UltiLife, Centerline Ltd, Windsor, ON, Canada), with an exit diameter of 6.3 mm. The powder feeder used was the AT-1200 rotary powder feeder (Thermach Inc., Appleton, WI, USA).

Powder and Substrate Material

The feedstock powder used for this work was gas atomized spherical Cu-159 copper powder (Praxair Surface Technologies, Indianapolis, IN, USA). Laser diffraction analysis (Microtrac S3500, Nikkiso, Japan) was performed on the powder to determine the mean particle size, yielding an average particle diameter of 11.43 µm based on volume (MV), 8.05 µm based on the number of particles (MN), and 10.12 µm based on area (MA).

In order to recover the un-deposited powder from the spraying, a reclamation system was built. It consisted of a sheet metal box, which was large enough not to affect the area being sprayed. An opening in the top panel of the box allowed the nozzle to enter and fulfill the desired spray pattern. A detachable side panel allowed for ease of access to the substrate. Finally, a ducting pipe equipped with a 0.5-micron filter was connected to the spray filtering system in order to avoid any backflow toward the gun and to ensure that the maximum amount of un-deposited powder remained in the box.

The substrates used were 3.175-mm-thick C-110 copper plates. Thinner substrates were attempted, but the spraying process caused them to warp beyond prescribed design specifications. Such warping considerably deteriorates the heat transfer performance of the unit due to reduced contact surfaces. The substrate surface was prepared by grit blasting with 1.5–3.0-mm ferrosilicate grit to roughen the surface as it was found that this enhances the bond strength of copper coatings on copper substrates (Ref 13). The final substrate surface roughness (Ra) was 4.97 ± 0.82 µm as obtained using a portable surface roughness gauge (SRG-4000, Phase II Plus, NJ, USA) by taking the average of ten different roughness measurements. The substrates were cleaned after grit blasting using acetone in an ultrasonic bath.

Pin Fin Array Production Procedures

A spray rig was designed and built to hold the substrate and mask in place while spraying the fins. The rig consisted of a steel block with a groove machined into the top surface, into which the substrate could be set. A sheet metal mask was precisely manufactured using wire EDM such that the finned area matches the exact GPU footprint of 49.5 mm by 64 mm. The mesh used for the production of the pin fins was a corrosion-resistant 304 stainless steel woven wire cloth mesh with 4.72 wires/cm (12 wires/in.) in each direction and a 0.584 mm wire diameter. The mesh mask to substrate distance was kept at 2 mm, which was achieved by adding spacers under the mask. The mesh mask was oriented such that the fin arrays once sprayed presented a staggered profile to the flow front. Bolts held the whole setup together so that everything aligns in the same way from one spray trial to the next with minimal variation. An exploded view of the spray rig is shown in Fig. 1.

Fig. 1
figure 1

Spray rig: (1) bolt; (2) mask; (3) wire mesh; (4) spacer; (5) substrate; and (6) holder block

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Using this spray rig, full pin fin array heat sinks could be produced. In order to have lower flow bypass in the heat test rig, and to eliminated potential local variations in fins height, the fins were sprayed above their desired heights and subsequently milled down to the requisite 1.7 mm height of the heat test rig test channel.

The pin fins were produced using reduced spray parameters to avoid substrate damage. The temperatures and pressures used ranged from 200 to 400 °C and 2.06 to 3.45 MPa, respectively. Other spray parameters were determined to ensure the same height fins for each set of parameters.

The copper pin fin arrays and test coatings were annealed after spraying, in order to restore the samples to the near-bulk thermal properties of copper, as seen in the work of Sudharshan et al. (Ref 14). Annealing was done in a Lindberg 4880 W furnace (Lindberg model 51442, Lindberg, WI, USA) at 300 °C for 4 h in air, and the samples were then allowed to cool slowly within the furnace. The samples were then cleaned using acetic acid 5 vol.% to remove any excess copper oxides which may have been formed (Ref 15).

Powder, Coating Morphology, and Fin Characterization

The powder was analyzed both before and after spraying in order to identify the morphological differences between the as-received powder and the reclaimed powder. This was done using a scanning electron microscope (EVO-MA10, Zeiss, UK). Coatings and fins were analyzed using scanning electron microscopy and light microscopy (VHX-2000E, Keyence, Canada). The light microscope has a computer-controlled XY stage and a maximum magnification of 1000 ×. A built-in software allows for autofocus and image stitching, creating fully focused 2D images over large areas. It can also produce 3D imaging by using a focused depth composition function, making it possible to obtain full 3D representations of the finned area. In order to view the particle boundaries, the coatings were etched with a 25 vol.% FeCl3–75 vol.% ethanol solution for a duration of 5 s. Porosity measurements were achieved through analysis of the stitched images on fins or coatings cross sections. An open-source image processing software (ImageJ) was used to transform images into binary form. A built-in process was used to measure the level of porosity for a highlighted area in the fin or coating. Deposition efficiency (DE) was determined by placing a known amount of powder into the powder feeder and running the system continuously over the substrate until no powder remained. This ensured that an exact known amount of powder was projected onto the substrate, and deposition efficiency was determined by taking the ratio of mass added to the substrate and the known mass of powder run through the system. The coatings micro-hardness was measured using a Vickers micro-hardness tester (Struers Duramin-1, Struers Inc., Cleveland, OH, USA) with a 500-g load and a dwell time of 10 s. The distance between indentations was kept above three times the length of the previous indent diagonal, to avoid stress field effects from previous indentations. The reported values are the average of ten micro-hardness tests per sample.

Single Particle Impacts and Powder Velocity Measurements

A study of individual particle impacts was performed to provide qualitative information on the differences between the deposition behavior of as-received particles and reclaimed particles. In order to do so, the feed rate was reduced to its lowest possible setting and the nozzle traverse speed was maximized. For these trials, the substrates were polished to minimize surface roughness and allow clear and unobstructed observation of the impacted particles. The resulting single particle impacts were analyzed using the scanning electron microscope.

The in-flight velocities of the as-received and reclaimed powder particles were also measured, using the ColdSprayMeter (CSM) eVOLUTION (Tecnar Automation Ltd., St-Bruno, Canada). This system uses a continuous 2.4 W (λ = 810 nm) laser and a dual-slit photomask. In-flight particle velocities are calculated by measuring the time difference between the blocking of the two photomasks. For the purposes of this study, velocity measurements were taken at a distance of approximately 10-mm downstream from the CGDS nozzle, as this corresponds to the standoff distance between the nozzle and substrate for the coating deposition tests. Testing was run until a data set of 1000 particles was achieved, and the results are represented in box and whisker plots.

Cost Analysis

Table 1 provides a list of the costs of all consumables, normalized with respect to the hourly cost of labor, associated with each expense, as they are available at the University of Ottawa. The hourly rate of labor was approximated based on typical local rates for manufacturing workshops.

Table 1 Cost of consumables used in the production of pin fin arrays
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The costs for a single set of spray parameters for the production of fins derive most importantly from the time of spray. The required traverse velocity to reach this desired height, given a powder feed rate, was determined iteratively through experimentation and linear interpolation for every set of spray parameters. Thus, given a traverse velocity and spray area dimensions, the time of spray, t, can be given by

$$t = \frac{D}{{V_{\text{T}} }},$$
(1)

where D is the total linear spray distance travelled by the gun (m) and VT is the gun’s traverse velocity (m/s). Using the time of spray as the dependent variable for each spray, it is possible to determine the cost of every single expense depending on the spray parameters. In the case of the copper powder cost, the calculation is:

$${\text{PC}} = t*{\text{PFR}}*C_{\text{Cu}} ,$$
(2)

where PC is the total sprayed powder material cost, PFR is the powder feed rate (g/s), and CCu is the cost of copper per unit mass (cost/g). This cost can be further divided by including the concept of deposition efficiency (DE). The powder cost can be broken up into three categories: (a) the powder that deposits onto the base plate substrate to form the pin fins, (b) the powder that sticks and builds up onto the mask, and (c) the powder that does not deposit. The cost of the powder deposited on the substrate, PCsubstrate, is

$${\text{PC}}_{\text{substrate}} = {\text{PC}}*{\text{DE}}_{\text{substrate}} ,$$
(3)

where DEsubstrate is the deposition efficiency on the substrate, determined experimentally. The cost of the powder that is deposited onto the mask (and ultimately lost), PCmask, is

$${\text{PC}}_{\text{mask}} = {\text{PC}}*{\text{DE}}_{\text{mask}} ,$$
(4)

where DEmask is the deposition efficiency on the mask, also determined experimentally. The cost of the powder that does not deposit, PCun-deposited, is given by:

$${\text{PC}}_{\text{undeposited}} = {\text{PC}} - {\text{PC}}_{\text{substrate}} - {\text{PC}}_{\text{mask}} .$$
(5)

To calculate the gas cost, the gas flow rate used must be known. This can be measured or calculated from gas dynamics principles (Ref 16), taking the gas properties at the converging–diverging nozzle throat. The mass flow rate of gas, \(\dot{m}_{N2}\), is given by:

$$\dot{m}_{N2} = \frac{{P^{*} }}{{RT^{*} }}\sqrt {kRT^{*} } A^{*} ,$$
(6)

where P* and T* are the pressure and temperature at the nozzle throat, A* is the throat diameter, k is the specific heat ratio of nitrogen, and R is the individual gas constant of nitrogen. The pressure at the throat can be determined by

$$P^{*} = \frac{{P_{\text{o}} }}{{\left( {1 + \frac{k - 1}{2}} \right)^{{\frac{k}{k - 1}}} }},$$
(7)

where Po is the stagnation pressure of the gas. The temperature at the throat can similarly be determined by

$$T^{*} = \frac{{T_{\text{o}} }}{{1 + \frac{k - 1}{2}}},$$
(8)

where To is the stagnation temperature of the gas. From this, the cost of gas, GC, is:

$${\text{GC}} = t*\dot{m}_{N2} *C_{N2} ,$$
(9)

where CN2 is the cost per unit mass of nitrogen gas. To estimate the cost of electricity, the electrical consumption of the system was equated to the heat input necessary to heat the gas to the desired temperature. This was done using a simplified version of the first law of thermodynamics (Ref 17),

$$\dot{Q}_{N2} = \dot{m}_{N2} *Cp_{N2} *\left( {T_{2} - T_{1} } \right),$$
(10)

where \(\dot{Q}_{N2}\) is the heat input, CpN2 is the specific heat of nitrogen, and T1 and T2 are the input and output gas temperatures, respectively. To get the total heat consumption, QN2, for the duration of a spray, the heat was converted to kilowatt-hour,

$$Q_{N2} = 2.78*10^{ - 4} *t*\dot{Q}_{N2} ,$$
(11)

to then find the total electricity cost, EC,

$${\text{EC}} = Q_{N2} *C_{\text{electricity}} ,$$
(12)

where Celectricity is the cost of electricity per kilowatt-hour. The cost of the mask was a constant value for all spray parameters, as the characteristics of the masking did not vary. Finally, the labor cost, LC, is given by:

$${\text{LC}} = t*C_{\text{labor}} ,$$
(13)

where Clabor is the hourly cost of labor.

Heat Transfer Test Rig

The heat transfer test rig is illustrated in Fig. 2, which presents an exploded view of the assembly.

Fig. 2
figure 2

Heat transfer test rig: (1) top plate equipped with gasket for sealing, pressure taps, and water in/out; (2) substrate/base plate with pin fin array; (3) bottom plate with insert for the base plate and heater block; (4) heater block equipped with inserts for heating cartridges and thermocouples; (5) and (6) supporting pieces

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The heat transfer test rig was designed to run a flow of water through the pin fin array heat sinks to be tested. The top plate was made of transparent acrylic, for ease of identifying if there are air bubbles present in the system, and inset within this are the water inlet and outlet ports. The top plate seals directly onto the heat sink base plate by a Buna-N nitrile O-ring. The water was supplied to the system with a constant power centrifugal pump (EHEIM universal 300, EHEIM, Germany). Flow rate was measured in the outlet port by a vertical readout flowmeter (8051K39, McMaster-Carr, IL, USA). Nine pressure taps, inserted directly into the top plate, are available to read the pressures through the finned area using a digital pressure transducer (002PD Model 230, Setra, MA, USA). A copper heater block is placed directly under the finned area and is heated by four 120 V heater cartridges (HDC00011, Omega, QC, Canada). The heat output of these cartridges was controlled by a variable transformer power source (2 kW Variable Transformer Variac 2000VA 0–250 V, MASTECH, CA, USA). Two pairs of type T thermocouples (3871K66, McMaster-Carr, IL, USA) placed at the front and back of the heater block read the change in block temperature as the flow passes over the finned area. A silicone-based thermal paste with incorporated conductive particles (ICE Fusion, Cooler Master, Co., Taipei, Taiwan) was added at the interface between the heater block and the pin fin array base plate in order to minimize thermal contact resistance. Two more type T thermocouples were placed within the inlet and outlet water flow ports in order to read the respective water temperatures. The water flowrate was set using a manually adjustable valve placed in the water outlet downstream from the flowmeter. From the heat test rig, it was possible to determine the performance of the CGDS manufactured pin fins. An illustration of the input and output data recorded with the heat test rig is shown in Fig. 3.

Fig. 3
figure 3

Illustration of the heat test rig input and output values

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In this work, two different fin configurations were tested, as well as a bare plate as a baseline. The fin density was kept constant, at 12 fins per inch in each direction; however, the height of fins sprayed before milling down to the requisite height was changed. In so doing, the resulting average fin thickness for each of the two sets of fins was different, and therefore, the size of the flow channel around the fins (net flow area) was also different, as illustrated in Fig. 4. Both sets of fins were tested for heat transfer performance before and after annealing. Table 2 shows the various configurations used in heat testing, where the first letter F designates the finned samples and UF the un-finned plates. The number indicates the height of the as-sprayed fins, 2.0 and 1.8 mm, followed by the designation NA (not annealed) or A (annealed for 4 h in air at 300 °C).

Fig. 4
figure 4

Variation in fin thickness depending on spray height before milling

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Table 2 Sample to be tested in heat test rig
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The thermal performance of the pin fin arrays is evaluated by their thermal conductance, a measure of heat transfer per unit time (power) per unit difference in temperature between the fins and the water. The power transferred by the heater block was measured using the power transmitted to the water, based on the thermocouples placed in the water flow. The sides of the copper heater block were insulated; thus, without losses all the power should be transmitted through the block and into the water. The power transmitted into the water, \(\dot{Q}_{\text{water}}\), was calculated by:

$$\dot{Q}_{\text{water}} = \dot{m}_{\text{water}} *Cp_{\text{water}} *\left( {T_{\text{water,out}} - T_{\text{water,in}} } \right),$$
(14)

where \(\dot{m}_{{\rm water}}\) is the mass flow rate of water through the system, Cpwater is the specific heat of water, and Twater,in and Twater,out are the inlet and outlet water temperatures, respectively.

The pin fin arrays were sprayed to be staggered in relation to the flow direction in order to promote mixing of the fluid, as shown in Fig. 5.

Fig. 5
figure 5

Staggered fin arrangement used for the pin fin arrays showing the direction of the flow around the fin and in red the cross-sectional line where the characteristic flow area is taken

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The reference geometry used for the fin performance calculations is shown in Fig. 6. All dimensions were taken in the plane perpendicular to the incoming flow.

Fig. 6
figure 6

Fin cross section showing reference geometry used for the fin performance calculations where B is the width of the base of the fin, S is the width of the section between fins, H is the height of the fins, ϴ is the angle of the fin, and Aflow is the flow area between fins

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To compare directly between the finned plates and the un-finned plate, the Reynolds number for each configuration was found for comparison on a non-dimensional basis. Using the hydraulic diameter, Dh, to characterize flow channel, the Reynolds number is found by

$$\text{Re} = \frac{{\rho V_{\hbox{max} } D_{\text{h}} }}{\mu },$$
(15)

where ρ is the density of the water, Vmax is the maximum flow velocity, and μ is the viscosity of water. The hydraulic diameter is calculated by

$$D_{h} = \frac{{4A_{\text{flow}} }}{{P_{\text{flow}} }} = \frac{{2A_{{f{\text{low}}}} }}{{S + \frac{H}{\cos \theta } + H\tan \theta }},$$
(16)

where Aflow is the flow area between fins and Pflow is the length of the perimeter of this area. These values are taken with the dimensions at the narrowest junction between fins, which corresponds to the area with the highest flow velocity. The flow area can be found by

$$A_{\text{flow}} = \left( {S + H\tan \theta } \right)H,$$
(17)

and the velocity of the flow is found by

$$V_{ \hbox{max} } = \frac{{\dot{m}_{\text{water}} }}{{A_{\text{flow}} N_{\text{fins,w}} \rho }},$$
(18)

where Nfins,w is the total number of fins along the width of the heat sink. Next, in order to solve the thermal conductance of the fins, it is useful to reduce the heat sink to its equivalent thermal resistance, Req, which is written as

$$\frac{1}{{R_{\text{eq}} }} = \frac{1}{{R_{\text{fin}} }} + \frac{1}{{R_{\text{unfin}} }},$$
(19)

where Rfin represents the resistance contribution of the fins and Run-fin is the resistance of the un-finned area of the base plate. This leads to the calculation of the thermal conductance, UA, which is written as

$${\text{UA}} = \frac{1}{{R_{\text{eq}} }} = hA_{\text{tot}} \eta_{\text{o}} ,$$
(20)

where h is the convection coefficient, ηo is the surface efficiency of the pin fin array, and Atot is the total heat transfer area, divided into the area of the fin surface, Afin, and the un-finned area, Aun-fin, as shown in the following equation:

$$A_{\text{tot}} = A_{\text{fin}} + A_{\text{unfin }} = \frac{{4\left( {B_{\text{s}} - H\tan \theta } \right)H}}{\cos \theta }N_{\text{f}} + \left( {{\text{WL}} - N_{\text{f}} B_{\text{s}}^{2} } \right),$$
(21)

where Bs now denotes the length of the base on the side of the fin, as opposed to the transverse cross section, Nf is the total number of fins, and W and L are the width and length of the area of the base plate covered by fins. Important to note is that the area of the tip of the fin is neglected as it is in direct contact with the acrylic top plate, and therefore, there is no heat transferred to the water across this surface. The surface efficiency is calculated by

$$\eta_{\text{o}} = 1 - \frac{{A_{\text{fin}} \left( {1 - \eta_{\text{f}} } \right)}}{{A_{\text{tot}} }},$$
(22)

where ηf is the efficiency of the individual fins. The fin efficiency is calculated using a relation found in Incropera et al. (Ref 18) for triangular pin fins with a circular base, adapted in the work of Cormier et al. (Ref 19) to suit the pyramidal shape of the fins produced by CGDS. This approximation for fin efficiency was chosen as it is the closest match to the fin geometry seen in this work. For comparison, the fin efficiency for rectangular pin fins was also used and demonstrated very little deviation from the values obtained by the pyramidal pin fin efficiency calculation. Furthermore, this deviation had almost no effect on the final fin conductance calculated. Fin efficiency is therefore calculated with

$$\eta_{\text{f}} = \frac{{2I_{2} \left( {2mH} \right)}}{{mHI_{1} \left( {2mH} \right)}}$$
(23)

and

$$m = \sqrt {\frac{4h}{{k_{\text{Cu}} B_{\text{s}} }}} ,$$
(24)

where I1 and I2 are the first- and second-order modified Bessel functions of the first kind and kCu is the conductivity of copper.

The convection coefficient of the fin array is calculated by

$$h = \frac{{\dot{Q}_{\text{water}} }}{{\Delta T_{\text{lm}} A_{\text{tot}} \eta_{\text{o}} }},$$
(25)

where ∆Tlm is the log-mean temperature difference between the base of the fins and the water. This approximation for temperature difference is generally used for the case of a constant surface temperature with a cross flow (Ref 18) and was used in this case since experimental results showed that it suited the heat transfer regime better than the case of a constant heat flux into a cross flow. It should be noted that the conductivity between the base of the fin and the fin itself could be affected by the presence of residual imbedded grit particles from the grit blasting process; however, this was neglected due to the low frequency of such occurrences. The log-mean temperature difference was calculated using

$$\Delta T_{\text{lm}} = \frac{{\Delta T_{2} - \Delta T_{1} }}{{\ln \frac{{\Delta T_{2} }}{{\Delta T_{1} }}}},$$
(26)

where ∆T1 and ∆T2 represent the difference in temperature between the surface of the base plate and the water at the flow inlet and outlet, respectively. As the thermocouple readings were taken within the heater block, and not at the surface of the base plate, the resulting surface temperature had to be interpolated using the concept of thermal resistance. Knowing the heat flux and the temperature of the block, Tblock, the surface temperature, Ts, is found using

$$T_{\text{s}} = (R_{\text{Cu}} + R_{\text{tc}} )\dot{Q}_{\text{Cu}} + T_{\text{block}} ,$$
(27)

where \(\dot{Q}_{\text{Cu}}\) is the heat transferred through the copper, RCu is the resistance due to the copper block and base plate, and Rtc is the thermal contact resistance between the block and the bottom of the pin fin array base plate. The thermal contact resistance in this work was taken to be 1.0 × 10−5 K m2/W as this was found to be an average value for a copper interface with thermal paste (Ref  20). A sensitivity study showed that slight variation in the value for thermal contact resistance had little effect on the resulting fin conductance.

Results and Discussion

Pin Fin Array Manufacturing and Characterization

Cost Analysis for Parameters Selection

A series of test was carried out, varying the spray process temperature and pressure, to determine the least costly parameters for the production of the as-sprayed 2-mm pyramidal pin fin arrays, before milling. The result of these tests showed that the higher the gas stagnation temperature and pressure used, the cheaper it was to produce fins per unit area, as shown in Fig. 7. Of the various spray parameters considered, it was revealed that the lowest pressure/temperature combination was most expensive, and as such, all costs presented in Fig. 7 are relative to this set of parameters.

Fig. 7
figure 7

Normalized cost associated with producing pin fin array unit at various gas temperatures and pressures

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The factor that had the most drastic impact on the cost of spraying the pin fin array units was the DE. The DE increases with gas temperature, as this increases the carrier gas velocity and therefore the maximum velocity achievable by the particles. Increasing gas pressure also increases DE since higher pressure yields higher gas density, increasing the drag force on the particles in the stream, which allows for greater momentum transfer between the gas and the particles prior to impact. The lower the DE, the more powder was necessary to achieve the desired fin height. Consequently, spraying with reduced parameters took much longer, compounding the gas and labor costs along with the powder cost. The cost of the mask and electricity were mostly negligible. Thus, at 400 °C and 3.45 MPa, the least expensive pin fin arrays could be produced, and these conditions were selected as the preferred parameters for the production of fins and coatings for the remainder of this study.

It is important to note that fins produced at a spray temperature of 500 °C and above were not attempted due to the substrate limitations. To promote heat transfer by the heat sinks being produced, it is necessary to use substrates with minimal thickness. Preliminary trials carried out at 500 °C caused the substrates to warp beyond an acceptable threshold due to high residual stresses. Excessive warping would cause the substrate to lose the desired intimate contact with the underlying GPU to be cooled, resulting in lower heat transfer to the fins.

The list of the parameters used for the production of full pin fin arrays and coatings with powder reclamation is provided in Table 3. The particles were reclaimed from spray runs carried out at 400 °C.

Table 3 CGDS parameters
Full size table

Spraying of Pin Fin Arrays

Full-size samples were produced with fins at a 2 and 1.8 mm height and then milled down to the desired 1.7 mm height, as previously mentioned. The 1.8-mm pin fin arrays were sprayed at 300 °C and 3.45 MPa. An example of the 2- and 1.8-mm fins before and after milling down to 1.7 mm is shown in Fig. 8. The resulting fin geometries are as expected, as shown in Fig. 4, with the 2-mm fins resulting in a wider peak, while the 1.8-mm fins have a narrower peak.

Fig. 8
figure 8

Digital microscope 3D images of: (a) as-sprayed 2-mm pin fins; (b) 2-mm fins milled to 1.7 mm; (c) as-sprayed 1.8-mm pin fin; and (d) 1.8-mm fins milled to 1.7 mm

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The geometry of the fins was then characterized, showing for the 2.0-mm as-sprayed fins a base angle θ = 9° ± 1°, base width B = 1496 ± 27 µm, and fin spacing (at the base) S = 471 ± 31 µm. Then, for the as-sprayed 1.8-mm fins the base angle was θ = 73° ± 1°, the base width was B = 1506 ± 24 µm, and the fin spacing was S = 461 ± 20 µm. One should note that the fin spacing is narrower than the 584 µm wire width from which it is produced. This can be attributed to the spreading effect of the gas stream between the bottom of the mesh and the substrate, but also to the natural funnel produced by the fins as they grow which would cause deviated particles to impact beneath the wire.

Examination of the fin cross sections, as shown in Fig. 9, reveals two distinct structures: a fully dense core with a porous periphery. While the core porosity level is too low to be measured reliably, the porosity of the sides of the fins is found to be approximately 5%. This effect is attributed to the fact that on the edges of the fins, particles experience a lower impact angle and this has been shown to result in increased porosity (Ref 21). An illustration of the changing impact angle through fin growth is provided in Fig. 10(a), showing that the taller the fin, the lower the angle of impact becomes.

Fig. 9
figure 9

Milled pin fin cross section

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Fig. 10
figure 10

Evolving particle impact angle with fin growth with respect to (a) the fins, (b-1) particle to particle impact where the angle of impact causes the particle to ricochet off of a previously deposited particle, and (b-2) particle to particle impact where the angle of impact is high enough to cause the incoming particle to stack on top of a previously deposited particle

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In fact, when closely examining the more porous areas of the fins, one can see what appears to be a columnar growth pattern as shown in Fig. 11. This effect only takes place at extremely low impact angles. When the particles impact at this angle, many of them do not stick and rather ricochet to the side, but those that do adhere are the ones that impact at the small outcroppings formed by previous particles, as illustrated in Fig. 10(b). This would explain the apparent stacking of particles on the periphery of the fins. The porosity this causes may result in a loss of thermal efficiency of the fin, as the thermal conductivity of these voids is much lower than that of the surrounding copper. However, given the high thermal conductivity of copper and size scale of these defects, it is expected that the macroscopic thermal performance of the fin should not be significantly affected.

Fig. 11
figure 11

Columnar growth on the fin periphery

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Powder Recycling

Powder Morphology: As-Received and Reclaimed

Figure 12(a) shows that the as-received powder is composed mostly of spherical particles (with the exception of a few slightly deformed particles) and that smaller particles cluster around the larger ones as satellites. The image of the reclaimed powder (Fig. 12b) reveals that most of the particles have retained little trace of their original spherical shape. The particles become deformed during various steps of the spraying process, such as during feeding or injection into the nozzle, but most importantly, they are deformed by impact on the substrate. Impact might also occur on the mask assembly.

Fig. 12
figure 12

(a) As-received Cu-159 copper powder and (b) reclaimed Cu-159 copper powder

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The reclaimed powder particles show evidence of fracture and plastic deformation. Some particles are still mostly spherical, which indicates that they have experienced minimal deformation during the initial spray process. Other particles are highly deformed: One can observe completely flattened particles which likely experienced high impact velocity, while others have jagged edges, indicating that they fractured under the forces exerted upon them.

By examining the reclaimed particles at higher magnification (Fig. 13), it is possible to see evidence of ductile rupture by the presence of “cup-and-cone” features. This could indicate that metallurgical bonding took place at one time, but that the particles were then shorn from the substrate or underlying coating by either rebound or subsequent impacts (Ref 22).

Fig. 13
figure 13

Cup-and-cone on reclaimed Cu-159 particle

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Single Particle Impacts

An examination of single particle impacts was done to compare the deposition behavior of the as-received particles to that of the reclaimed particles. These tests were done using the previously determined spray parameters of 400 °C and 3.45 MPa. Figure 14 shows the result of a single as-received particle impacted on the substrate. One can see the clear spherical shape of the top of the particle and evidence of jetting on the periphery of the impact zone (Ref 23).

Fig. 14
figure 14

Impact of a single as-received particle

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Figure 15, which shows a reclaimed powder particle that impacted on the substrate, illustrates that the top of the impacted reclaimed powder is severely deformed and has retained very little of its initial spherical shape. Regardless of the shape of the particle, it seems to have experienced localized jetting along its periphery, similar to the as-received particle.

Fig. 15
figure 15

Impact of a single reclaimed particle

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Coatings Comparison

In order to verify the feasibility of depositing reclaimed powder, various coatings were sprayed using: (1) the as-received copper powder, (2) a 50 wt.% as-received–50 wt.% reclaimed powder blend, and (3) 100% reclaimed powder. All three coatings were sprayed using the parameters given in Table 3. The resulting coating porosities and DEs are given in Table 4.

Table 4 DE and porosity of as-received and reclaimed powder blends
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Since the porosity levels of these coatings are comparable, it can be concluded that it is possible to implement powder recycling without any major detriment to the quality of the coatings, and by extension pin fins produced. An important aspect to note is the change in DE between the different powders. The DE for as-received powder was 68% and that of the reclaimed powder is 46%, a considerable reduction. This difference can be attributed to the fact that, in the reclaimed powder, the particles that were the most likely to deposit have already done so, leaving the generally larger and less likely to adhere particles to be reclaimed. The as-sprayed etched coating cross sections in Fig. 16 show that the average particle size appears somewhat larger in the coating made of 100% reclaimed powder.

Fig. 16
figure 16

Images of (etched) coatings produced using as-received and reclaimed powder blends before and after annealing at 300 °C for 4 h

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Another reason the DE may have dropped is due to the fact that the particles have likely been work hardened by their previous impact, and they are now even less likely to bond to the substrate as the critical velocity is potentially larger than in the as-received state (Ref 24). As for the mixed powder, if there was no interaction between the as-received powder and the reclaimed powder, one would expect the DE to be close to the average of their respective DEs, which would give a value near 57%. However, a DE of 64% was recorded. This can be explained by accounting for particle interactions between the two powders, an effect that has been shown to improve DE in feedstock powders featuring blends of hard particles and soft particles (Ref 25). The latter work has shown that the presence of hard particles mixed with an aluminum powder increases the DE of the aluminum. This was determined to be due to both asperity creation and oxide layer removal mechanisms improving the conditions for bonding of aluminum particles. This effect is hypothesized to be present in the mix of reclaimed and as-received particles, where the cold worked, and therefore harder, reclaimed particles act as the hard particles by improving the surface conditions for the bonding of the as-received particles. However, in this case the harder reclaimed particles have the possibility of adhering themselves as well.

The lower DE of the reclaimed powder may cause it to become inefficient to reuse for the spraying of subsequent heat sinks; however, in an industrial setting it would probably not be necessary to use 100% reclaimed powder, but rather the reclaimed powder would likely be mixed into the next batch of as-received powder, such as a 50–50 mix.

The coatings hardness was investigated, with the results presented in Table 5. There was a noticeable reduction in hardness when reclaimed powder was used as opposed to as-received powder. The reason for this is hypothesized to be due to an in situ annealing effect. The powder feed rate when using reclaimed powder (either 100% reclaimed or 50/50 mix) was lower than for the as-received powder when using the same feeder parameters, due to reduced flowability of the reclaimed powder, which stems from the irregular shape of the particles. For this reason, it took longer to spray when using the same powder feeder setting. As such, the CGDS nozzle was over the substrate for a longer time in the reclaimed and mixed powder sprays; thus, the heated gas stream may have induced in situ thermal softening which would have contributed to the lower hardness values in the reclaimed and mixed coatings. In order to improve the feeding of the reclaimed powder, a feeder wheel with larger holes should be employed, and the rotation speed of the feeder wheel increased, allowing to properly supply powder at the prescribed mass-based feed rate in future sprays.

Table 5 Hardness of coatings made with as-received and reclaimed powder
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Another reason for these lower hardness values is believed to be due to a lowering in the cohesion between particles in the reclaimed and mixed coatings (Ref 26). This could again be due to the previous work hardening of the reclaimed particles, causing them to experience less deformation upon a second impact and therefore limiting their potential for metallurgical and mechanical bonding (Ref 24). Another explanation for this lowering in cohesive strength is the presence of an oxide layer on the surface of the reclaimed powder. The reclaimed powder has previously been heated through the spray process, and as such, oxide growth may have taken place. The presence of oxides has been shown to lower the DE and cohesive strength of CGDS coatings (Ref 27).

The coatings were annealed at 300 °C for 4 h in air with the intent of improving the cohesion between particles through sintering (Ref 28), and in so doing improving the coatings conductivity consolidating the particle boundaries (Ref 28, 29). The annealed coating cross sections in Fig. 16 show that the intra-particle boundaries have become much less distinct from the annealing process, improving the conditions for conduction between particles as desired. The results given in Table 5 demonstrate that there is much lower variation in the hardness of the coatings after annealing, indicating that the coatings have now become more uniform. The lowering of the overall hardness, however, is typical of the annealing process, as the work hardening in the coatings that is characteristic of the CGDS process has been relieved (Ref 28).

Particle Velocities

The particle velocity was recorded for both the as-received and reclaimed copper particles. The results, shown in Fig. 17, follow a normal distribution that is typically seen in CGDS particle velocity measurements (Ref 30). The average velocity of the as-received particle was measured to be 538 ± 116 m/s, while the reclaimed particles had an average speed of 487 ± 138 m/s. The reason for this drop in velocity is likely due to the average particle size of the powders. The physical reclamation process makes it more likely for larger particles to be reclaimed, which artificially skews the particle size distribution. These larger particles are known to be more difficult to accelerate, resulting in a lower average velocity (Ref 24). This reduction in mean velocity may also account for the drop in DE of the reclaimed powder (Ref 31).

Fig. 17
figure 17

Box and whisker plots of the as-received and reclaimed powder velocities

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Cost Analysis for Powder Recycling

With powder recycling proving to be possible without drastically changing the microstructural properties of the coatings produced, the economic model was modified to include powder recycling. Figure 18 shows the resulting costs for each set of spray parameters, assuming that all the powder that does not bond to the substrate or mask is reclaimed. These values are normalized with respect to the cost of the most expensive set of spray parameters previously identified without powder recycling. To allow for direct comparison, the total costs without powder reclamation have been added as black dots on the graph for each set of spray parameters. From this, it can be seen that the powder cost no longer dominates the total expense of the pin fin array manufacturing, but rather the gas and labor costs become more important, each of which are directly proportional to the duration of the spray run. A reduction in spray parameters is associated with a reduction in DE, which means that the spray run must be carried out longer to achieve the same desired pin fin height, which explains the trend of increasing costs at lower spray parameters.

Fig. 18
figure 18

Normalized cost associated with producing pin fin arrays with powder recycling at various gas temperatures and pressures compared to cost without powder recycling

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It can also be noted that the powder cost increases at higher spray parameters, which was not the case when there was no powder recycling, as shown previously in Fig. 7. In order to produce the same fin height, each set of spray parameters must deposit the same amount of powder on the substrate. Therefore, the variation in total cost in powder for each set of spray parameters without reclamation is reduced to the cost of un-deposited powder and that of the powder adhering to the mask. With powder recycling, the cost of un-deposited powder is eliminated, but not that of the powder on the mask. As previously stated, DE increases with higher temperatures and pressures, but this also leads to a higher DE on the mask. Consequently, at higher parameters, more powder is lost through adhesion to the mask, which accounts for the relatively higher powder costs at high parameters when powder recycling is introduced. These extra costs are, however, outweighed by the additional savings obtained from the reduced spray time at higher spray parameters. Ultimately, the overall cost is reduced by the utilization of powder recycling, with the lowest cost pin fins being produced at a normalized cost of 0.174 per unit, down from 0.258 per unit, amounting to a 32.5% reduction in production cost. However, in order to further reduce the powder cost, an important avenue to explore in the future would be the reduction in mesh buildup.

Heat Transfer Performance

The thermal performance of the pin fin arrays was calculated from the data acquired through the heat test rig. The resulting conductance values for every fin configuration are shown in Fig. 19. From this, it can be seen that the finned plates, F2.0 and F1.8, largely outperform the un-finned plates, UF, as expected. All plates showed a rise in conductance with increasing Reynolds number, most likely due to increased turbulence and mixing (Ref 17, 32). The annealing process improved the conductance of both finned plates, as F2.0-A and F1.8-A have a higher conductance than their non-annealed counterparts F2.0-NA and F1.8-NA. This is believed to be due to the particle sintering effect engendered by the annealing process, which enhances the conductivity of the particles boundaries, raising the overall fin efficiency.

Fig. 19
figure 19

Thermal conductance before and after annealing, denoted –NA and –A, respectively, of the finned plates F2.0 and F1.8, as well as the bare plate UF

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Conclusions

This work explored the feasibility of powder recycling for cold spray additive manufacturing of pyramidal pin fins for water-cooled graphics processing units with the purpose of reducing the production cost of pin fin array heat sinks. An analysis was done to determine the most cost-effective spray parameters while preventing substrate damage, showing that higher temperature and pressure were key to lowering costs. The reclaimed powder morphology showed that most particles were severely deformed when compared to their as-received counterparts. This, however, did not have a severe impact on the microstructure of coatings deposited with this reclaimed powder. Although the deposition efficiency of the pure reclaimed powder was notably lower than the as-received powder, it was found that mixing 50 wt.% reclaimed powder with 50 wt.% as-received powder results in only a 4% reduction in deposition efficiency in comparison with the as-received powder. Analyzing in-flight particle velocities revealed that the reclaimed powder particles were on average 51 m/s slower than the as-received powder particles, mainly as a result of their large average size. The hardness of the reclaimed coatings was also found to be lower than the as-received, possibly indicating lower cohesion and therefore lower contact between particles. Porosity in all coatings was low, thus demonstrating the viability of powder recycling. These findings suggest that it would be possible to spray pin fin arrays using reclaimed powders with a potential cost reduction of approximately 30%. Finally, the heat transfer performance of the pin fin array heat sinks was tested and found to be far superior to that of a bare plate. Annealing of the fins was also found to slightly improve their heat transfer performance.