Converging Jet Impingement for Enhanced Liquid Cooling

Jet impingement cooling is a widely studied technique to achieve high heat transfer coefficients for a variety of applications. Industrial drying, aerospace turbine cooling, and electronic thermal management include those systems which can take advantage of the increased cooling rates. Compared to traditional cooling schemes such as cold plates, heat sinks, and two-phase boiling, jet impingement offers a simplified means to limit the intensity of hot spots generated by localized heat loads [1]. With respect to power electronics devices, those of which are dedicated to the transmission and transformation of high voltage, internal device locations input thermal energy into the surrounding architecture via electrical switching losses. If not properly maintained, these hot spots can cause premature device malfunction through mechanical and electrical failure modes [2]. Thus, it is of vital importance that we continue to improve our thermal management capabilities so that power electronic systems in electric vehicles, hybrid-electric aircraft, and energy management can operate more efficiently and at higher power loads.

Studies show that up to 55% of the failures in power electronic systems can be directly attributed to thermal characteristics [3]. Other failure modes, such as shock, vibration, contamination, dust, and humidity are primarily categorized as external factors. In other words, these failure modes are caused by the environment in which the system has been introduced. On the contrary, the thermal considerations caused by switching losses are mostly internal. Delamination, wirebond failure, interconnect detachment, thermal runaway, and substrate cracking include a few ways a power electronics module might failure under thermal stresses [4]. Managing the heat loads is a challenge that must be taken seriously. Without sufficient cooling, a mean temperature increase of 20 °C can lead to failure 1000 h sooner [5]. For silicon carbide (SiC) electronics, a junction temperature of 175 °C is used as the thermal threshold. This junction temperature can be found as a direct function of the thermal resistance between the switching loss generator and the active cooling medium. In this network, it has been shown that the presence of a thermal interface material can increase the thermal resistance by 30–40% [6]. Conventional cooling techniques like cold plates rely on this thermal interface to transfer heat from the power electronics to coolant through conduction. Jet impingement replaces this interface with direct convection-based cooling, thereby reducing overall thermal resistance. The benefits of jet impingement have been extensively studied analytically, numerically, and experimentally. Throughout the literature, it is the consensus that the increase in heat transfer is attributed to the reduced thickness of the thermal boundary layer on the target surface. With respect to hot spot management, the location of jet contact, or the stagnation point, can reach heat fluxes up to 2000 W/cm² [7], compared with 250 W/cm² one might see with cold plates [8].

The typical arrangements of jet impingement can be categorized as steady, axisymmetric jets. Steady, meaning constant nozzle velocity with respect to time. Axisymmetric meaning the jet is radially symmetric about the centerline of the nozzle. Figure 1 provides a more detailed schematic of standard jet impingement methodology. After the fluid impinges onto the target surface, the wall jet region forms. In this region, the fluid can be characterized as crossflow over a flat plate with respect to the boundary layer thickness. At the initiation of this region, one might see a secondary peak in the Nusselt value, typically 0.75–3 nozzle diameters from the jet centerline [9].

Recently, there has been increased motivation throughout the literature to obtain higher heat transfer values from a jet impingement cooling scheme. Turbulence generation is a key factor in the performance of cooling jets. Nonsteady and stochastic in nature, turbulent eddies provide additional methods to disrupt the thermal boundary layer on the target surface. Studies show that introducing turbulence into a jet cooler can increase heat transfer by 30–50% compared to traditional jets [10]. Pulsating, oscillating, and swirling jets have been implemented for this purpose. The impingement angle of a steady jet has also been studied, with a wealth of literature showing the effects on heat transfer, wall jet formation, and fountain region interactions. For this study, the impingement of multiple jets is of interest. Key geometric parameters include the nozzle diameter (D), the distance between nozzles (S), the nozzle-to-target distance (H), and jet inclination angle (θ). Table 1 gives a survey of literature that examined the effects of multiple impinging jets with a focus on converging inclination angles.

Bentarzi et al. [11] found a maximum stagnation pressure with 60 deg converging jets to occur at 8D (80 mm) from the symmetry line due to jet deflection. This resulted in two Nusselt number peaks with a value of 20–42 depending on Reynold's number. One peak occurred at the stagnation point followed radially by the high-velocity wall jet region. Additionally, it was found that the jet Reynolds number had a minor effect on the stagnation pressure coefficient in the tested range. This means for a given setup, the location of maximum heat transfer remains unchanged at varying flowrate. Zheng et al. [12] examined three coplanar converging jets. Being in an unconfined configuration, the jets were allowed to diffuse into the fluid pool without an impingement wall. This allowed the study of jet velocity profiles, where the combined jets were observed to preserve a velocity core until 12D from the jet exit. Moreover, the jet velocity did not alter the jets' interactions with respect to merged behavior. A key conclusion from this study is the knowledge that converging jets will merge in an unconfined setting, or with a sufficiently large height value. Zhang et al. [13] examined the pressure coefficient of converging jets compared to parallel jets. They found that a reduced angle of inclination of 60 deg will create a larger stagnation pressure by three times compared to a parallel jet, which can be defined as 90 deg inclination. Although this study did not include heat transfer analysis, one can deduct an increased heat transfer due to higher coefficient of stagnation pressure as is commonly seen in steady jet impingement research. Finally, Adbel-Fattah et al. [14] studied turbulent twin jet flow with slightly divergent inclination angles. While different than the previous references looking at converging jets, this study continued to confirm the finding that the jet Reynold's number has little effect on the location of maximum stagnation pressure. Additionally, they found an increased H/D value pushed the stagnation location outward, as did an increased S/D ratio.

The four studies shown here, which represent a large proportion of converging jet literature, have provided useful findings regarding the effects of Reynolds number, the respond of stagnation pressure to inclination, and associated heat transfer. However, the result of merged jets in an unconfined configuration versus jet deflection at sufficiently low height ranges begs the question of whether an optimum convergence point exists. More specifically, additional research is needed into the effects of convergence height with respect to the target plate on the heat transfer of liquid jets. In this study, we present a method for experimentally and computationally evaluating the effect of heat transfer rates of inclined, converging water jets with respect to geometric characteristics and maximum stagnation pressures. Moreover, this study investigates the effect of jet height, jet Reynolds number, and the spacing between dual jets on effective hot spot management and provides an empirical correlation model.

Figure 2 defines the geometric parameters used to analyze various factors in the performance of converging jets. Included in this image are the jet-to-surface spacing, H, nozzle diameter, D, radial convergence length from the jet centerline, r, the nozzle-to-nozzle pitch, P, and finally the corresponding angle of inclination, θ. Based on these values, one can calculate the theoretical convergence point of dual jets. For this study, the height will be varied with respect to a given pitch. This will provide results where the jets would converge before, at, or after the heated base plate. A modular jet impingement cooler was developed for the purpose of quickly performing parametric testing across various nozzle Reynolds numbers, jet-to-target spacings, and types of jet impingement setups. Figures 3(a)–3(c) give an overview of the experimental setup. Highlighted in the image are the 200 W, 12 mm × 12 mm resistive heater used to emulate a hot spot, the plate on which the fluid jet impinges, the overall jet housing, and the fluidic fittings. For fine-tuned junction temperature estimation, the heater has an imbedded thermocouple for fast and accurate thermal response. The pressure applied to the heater to maintain proper contact with the plate via a thermal interface layer is provided by a clamping system assembled at 0.5 N·m of torque. This clamp directly integrates with the ten bolt locations that seal the base plate to the main housing. Figure 3(b) shows a cut-view from the side of the apparatus. Noted is the modular jet section that is interchangeable to quickly test multiple jet configurations. Furthermore, spacers were added between the housing and baseplate to achieve variable height settings. The housing was manufactured via multijet fusion three-dimensional printing and is made of a high temperature-stable Nylon material. Not shown here are the details concerning the flow loop apparatus used for experimental testing. More information is available in a previous study [15].

In this study, three different jet arrangements are tested and analyzed for their effects on heat transfer due to fluid behavior. Figure 4 provides an overview of these configurations. Figure 4(a) shows a parallel jet with 2 mm nozzles placed at a 3 mm pitch (P = 3) with the coolant exiting at 90 deg with respect to the exit surface. Next, Figs. 4(b) and 4(c) depict the two converging jet arrangements of focus in this study. Each with two, 2 mm nozzles at an angle of 70 deg, the two variations are modified by the pitch. The 3 mm pitch option gives a theoretical convergence point of 8 mm; the 6 mm pitch would converge the jets at 16 mm. For parametric analysis, the height between the jet exit and target surface is studied at 2, 8, and 14 mm. These values were chosen to evaluate whether an optimum convergence height with respect to the target plate exists.

During testing of the three configurations, flowrate, pressure, and heater temperature were the primary data collected. The aluminum-nitride heater with a maximum power rating of 200 W was tested at 50, 100, and 200 W. The flowrate of the fluid was varied to achieve equivalent Reynolds numbers across multiple configurations as a function of the total hydraulic area. Fluid temperature was maintained at 20 °C using an external chiller rated for 1000 W. Finally, the jet-to-target spacing was tested at 2, 8, and 14 mm. These values were chosen to evaluate heat transfer as a function of convergence height in relation to the jet-to-surface distance. The experimental data will highlight these effects by using raw heat temperature and thermal resistance. Then, computational fluid dynamics are used to gain further insight into the fluid behavior caused by geometric parameters.

Figure 5 presents heater temperature versus jet-to-surface spacing (H) for the three jet configurations at 50, 100, and 200 W. This data represents heat transfer at a Reynolds number of 11,000. In total and not shown in this figure, four Reynolds numbers were tested: 6800, 11,200, 17,300, and 22,500. Figure 5 is presented to investigate the uniformity and consistency of cooling rates across multiple heater levels. Where the general trends of cooling remain constant, this would indicate constant thermal performance. As indicated in these figures, the data does support multiple observations. First, there is a consistent proportional increase in heater temperature in relation to the jet-to-surface spacing in all configurations except for the parallel jet where a decrease is seen at the 8 mm spacing. With rising power, the variation in temperature response as a function of height also increased. At 100 W, the 3 mm pitch jet temperature rose by 2.8% compared to H = 2. The 6 mm pitch jet rose increased by 10% and the parallel jet by 3.3%. Additionally, in all three heater power levels, the converging jet arrangement with a pitch of 3 mm provided the best cooling performance.

When directly comparing the parallel and converging jets, both having a pitch of 3 mm, we start to see the effects of convergence. For standard parallel jets, an optimum point is seen with a height of 8 mm, which is consistent with single-jet behavior [9]. This does not hold true when convergence is introduced. At a height of 8 mm, the 3 mm pitch-inclined jets would theoretically merge or deflect depending on the strength of the generated fountain region. Based on reviewed literature showing the existence of a potential core in merged jets [12], one would expect behavior imitating parallel or single jets with respect to an optimum point. However, the optimum point seems to exist at very confined geometries. In practical applications, the ability to reduce the total volume of the thermal management system may give great power density returns. Assuming all other dimensions remain constant, using converging jets as opposed to parallel jets can provide a volume reduction of 75%. Based on these values, and in conjunction with the presented data, one can draw the conclusion that the convergence point in relation to the overall jet-to-surface spacing plays a significant role in heat transfer efficiency. This will be further analyzed in Sec. 4 utilizing computational fluid dynamics simulations.

Across all three jet configurations, the % increase in temperature with respect to H is present across the tested Reynolds number range, except for the parallel jet. In Fig. 6(a), it can be observed that the H = 2 mm distance provides the lowest thermal resistance at the smallest Reynolds numbers but performs worst as the flowrate increases. This trend is not seen in the converging jets configurations. In fact, the 3 mm pitch displays an average standard deviation across all height values of 0.0029, compared to 0.0191 for the 6 mm pitch jets and 0.0078 for the parallel jets. As a function of Reynolds numbers, all three configurations display similar responses. With single jet impingement, a power law relationship between thermal resistance and mass flowrate to have an exponent of –0.6 to –0.8 [9]. In this study, the parallel jet shows the best curve fit with an exponent of –0.26 for the 8 mm and 14 mm heights, and –0.187 for the highly confined 2 mm height. The 3 mm pitch jet fits best with an exponent between –0.378 and –0.442, and the 6 mm pitch jet with a smaller range of –0.241 to –0.285. From these values, we can quantity the magnitude of response of thermal resistance to Reynolds number and conclude flowrate to have the largest impact on the 3 mm pitch converging jet by. While the cooling performance might be best in this configuration, it quickly drops off with a decrease in Reynolds number.

The experimental results provided insight into the thermal and performance of the various jet configurations. However, the results do not characterize the specific mechanisms creating such performance differences. For this reason, ansysfluent computational fluid dynamics simulations were performed to supplement and explain the previously reported behaviors. In these simulations, a two-dimensional (2D) approach is taken to study the velocity contours and location of maximum stagnation pressure for each jet type. The velocity contours will identify if true jet convergence is occurring. The stagnation pressures will identify locations of maximum heat transfer, as is customary with jet impingement cooling. Figure 7 shows the domain for the 2D simulations, including the line of symmetry to save on computational costs. Shown in this figure is the dual jet with a pitch of 6 mm. The model was discretized using a hex-dominant approach with a cell size of 0.1 mm. To sufficiently capture the fluid-wall boundary, 10 inflation layers with a growth rate of 1.2 were placed to achieve a y+ value approximately equal to 1 for the selected turbulence model. Table 2 provides the boundary conditions and solver details implemented for this simulation. The inlet velocity condition matches that of the experiments shown in Fig. 5, with a Reynolds number of 11,200. During the solution process, all equation residuals were converged to 1 × 10^–6, and the maximum facet velocity was plotted to monitor a physical value and ensure no oscillations or divergence occurred.

In general, the location of the maximum stagnation pressure will be determined by a few factors including jet convergence height, jet-to-base plate height, flowrate, and nozzle diameter. For these simulations, flowrate and nozzle diameter remain constant. The three 2D configurations are tested at a height spacing of 2, 8, and 14 mm. Theoretically, the inclined jets would converge in the absence of a base plate. What's not immediately clear is whether recirculation flows will push them apart in confined operation, thereby moving the stagnation points radially outward. Figure 8 presents the resulting contour plots for all simulations.

From these images, we begin to observe how converging jets do not necessarily converge due to recirculation regions. The only jet configuration that exhibited a merging is seen in the dual jets with a pitch of 3 mm at a height of 14 mm. From this, one can reasonably deduce that with an increased height value, the 6 mm pitch dual jet would also converge. However, without this condition, the fluid flow exhibits a stagnation point that is pushed away from the centerline due to the fountain effects by the impinging fluid. The fountains seen here recirculate back toward the centerline and are then entrained back into the main jet flow. And as the height increases, the fountain is able to push further back toward the jet exit surface, additionally influencing the location of the stagnation point.

For analysis using quantifiable values, fluid pressure profiles 0.5 mm above the impingement plate and in the radial direction are extracted from the contours. Figure 9 presents this data. Along with pressure profile lines, the location of maximum stagnation pressure for each configuration is identified by a circular marker. The charts are then aligned to easily observe how the stagnation point moves with respect to height and setup. Immediately, one can see the effects of height on the stagnation point location in Fig. 9(a) with the parallel jets. First occurring at 3.2 mm radially at H = 2 mm, the parallel jet stagnation point shifts outward approximately 3.5 mm at H = 8, and another 2.8 mm at H = 14. Furthermore, the stagnation pressure magnitude decreases from 1121 Pa to 300 Pa and finally to 250 Pa at the three high levels. The large decrease in pressure from H = 2 to H = 8 can be attributed to the highly confined geometry creating a high velocity wall jet, indicated by the large pressure drop after the stagnation point. In Figs. 9(b) and 9(c), similar behavior is observed, except for the stagnation point occurring at the zero-radial point for the 3 mm pitch jet at H = 14 mm. At this point, although the jets have seemingly merged, the stagnation pressure remains similar to the other jet configurations. As seen in the experimental data, the merged jet condition did not result in drastic thermal performance. This is supported by the CFD results in that the stagnation pressure was unchanged, although occurring in a merged state.

In terms of practical applications for a dual converging jet, the amount of deflection can play a significant role in electronics heat transfer. Assuming impingement onto an external base plate, too much jet deflection will relocate the highest heat transfer areas away from the electronics hot spot. While this may not be critical should the conduction layer provide sufficient thermal spreading, printed circuit board-based devices will need fine-tuned stagnation points for more efficient heat transfer. To further illustrate this, Fig. 10 directly compares the experimental results with the corresponding CFD stagnation point location. In this figure, the effects of height are not explicitly shown but are realized through the stagnation location. This study utilizes a 12 mm × 12 mm heater to emulate an electronics hot spot. Therefore, it is reasonable to predict good jet thermal performance when it is focused on the critical area. In Fig. 10, this effect is seen as higher thermal resistance is noted when the stagnation point occurs beyond 6 mm.

Figures 11 and 12 present plots of the Nusselt number versus the Reynolds number to directly compare experimental and the correlation model for the 3 mm and 6 mm pitch converging jets, respectively. From this comparison, an average percent error of 5.14% was achieved for the 3 mm pitch jet, and an average percent error of 5.67% was achieved for the 6 mm jet. Due to the large influence of height on the 6 mm jet, the model is biased toward increasing the Nusselt number with decreasing height. This trend matches well with the large pitch but is nonexistent with the smaller-pitched converging jets that remain relatively consistent as a function of height.

This study introduced and evaluated a modular jet impingement setup to analyze the effects of convergence height on heat transfer. Experimental evaluation was performed to understand the thermal resistance of parallel and jets converging at 8 and 16 mm with jet-to-surface (H) spacings ranging from 2 to 14 mm. Large variations in thermal performance were found with the jet converging at a larger distance than the smaller. Compared to parallel jets, the converging jets shifted the optimum cooling point to a lower H value, providing the potential to save on total volume. Next, computational fluid dynamics simulations were used to analyze the effects of convergence on the location of maximum stagnation pressure. In most cases, the stagnation point moved radially outward with increased H, except for the single jet merge that was observed at H = 14 for the 3 mm pitch converging jet. Other than keeping the point of maximum heat transfer under the emulated hot spot, the magnitude of thermal resistance remained similar to other test conditions. Finally, an empirical Nusselt number model was proposed which considers the ratio of convergence height to the total H. With an average error of less than 6%, the model was able to capture the relationship between Reynolds number, the H/D radio, and the new Hc/H ratio.

With respect to electronic applications, this type of converging jet may most be suited for irregularly shaped objects requiring the fine-tuned location of maximum hot spots, but in a very low volume configuration. Further research directions for this work include the testing of additional inclination angles and generating optimization guidelines for convergence conditions versus hot spot size.

• National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal systems (POETS) with Cooperative Agreements (EEC-1449548; Funder ID: 10.13039/100000001).

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

$D$ =

nozzle diameter

$H$ =

jet-to-surface height

$Hc$ =

jet convergence distance from nozzle

$Nu$ =

Nusselt number

$P$ =

nozzle distance from centerline

$Pr$ =

Prandtl number

$Re$ =

Reynolds number

$S$ =

jet-to-jet spacing

$θ$ =

jet inclination angle