Variable Area Jet Impingement for Enhanced Junction Temperature Control of High-Power Electronics

Jet impingement is an effective method for mitigating intense power loads created by high density power electronics. Elevated local heat transfer coefficients at the source aid in reducing junction temperatures, which have the downstream effect of improving device function and reliability. With industry targets approaching 25 kW/kg specific power, packaging reliability becomes more sensitive to thermal cycling parameters driven by system-wide demands and thermal management efficiency [1]. While steady-state jet impingement is a well-studied low thermal resistance method, opportunities for further development concerning transient operation exist. Pulsating jet flows have been shown via synthetic jet actuators to improve heat transfer but have little implementation in a nonzero mass flux condition [2]. Further, a transient jet capable of a variable hydraulic diameter can respond to power schedules to reduce junction temperature changes and fluid pressure losses. In this study, we aim to develop a variable diameter jet impingement apparatus to analyze the feasibility of pulsating jet flows for increased heat transfer and the impact of matching heat transfer rates with power schedules for junction temperature and pressure control.

A great breadth of literature examining both steady and transient jet impingement over the span of many decades has elucidated the heat transfer benefits and the physical mechanisms responsible. On a time-average basis, a steady jet behaves such that turbulence dynamics can be disregarded and replaced with bulk-fluid motion in the free jet and wall jet regions. This assumption allows for the direct comparison between studies without knowing the intricate fluid dynamic details. Nondimensional analysis relating the jet diameter, jet-to-surface spacing, Reynolds number, and Prandtl number is employed often, where the correlation coefficients on each term are modified for specific jet configurations. While this method is quite effective for designing an impingement cooler based on spatially averaged junction temperatures, more detailed physics descriptions of these jets have uncovered the underlying mechanisms responsible for localized high heat fluxes. Fluid turbulence levels present at the exit of the jet nozzle are highly dependent on the opening type, initial velocity profiles, flow speeds and upstream turbulence levels. Across these wide range of conditions, the introduction of advanced fluid imaging techniques, supercomputing of fluid dynamics simulations, and machine learning techniques have demonstrated primary heat transfer fluctuations can be attributed to vortical structures. On the same size scale as of the jet nozzle, these primary vortices found in the free-jet region are initiated by shear flow conditions in a submerged configuration [3]. Smaller jet-to-surface spacings prevent these structures from pairing but will merge into fully turbulent motion at heights that allow for fluid entrainment into the potential core. Should these vortices reach the target plate, these toroidal-shaped structures aid in boundary layer disruption [4]. One drawback from the many correlations developed to describe the Nusselt number response is the inability to capture secondary peaks seen in more detailed heat transfer experiments. Some attempts have been made to capture this response but are largely unsuccessful given the variety of setup conditions [5]. Therefore, there is motivation to purposely force the impinging jet to contain disruptive structures for predictable heat transfer enhancement.

A popular method of active jet impingement is the use of a synthetic jet [6]. Piezo-electric diaphragms act to force fluid out the orifice of a cavity in the form of vortices in an expansion stroke. The vortices move downstream just as those naturally formed by shear flows and disrupt boundary layers on the target force. Once the piezo-electric material has actuated, it returns to its original position and pulls back the fluid resulting in a net zero mass flux configuration in the compression stroke. These devices are well studied and have been shown to improve experimental heat transfer efficiency by up to 30% compared to a single jet [7]. Similar to a standard impinging jet, key parameters can be used to parametrize the synthetic performance. Reynolds number, nozzle diameter-to-height ratio (H/D), and the Strouhal number as a function of driving frequency are the most common metrics. Ghaffari et al. found a performance increase of slot jets compared to semiconfined circular nozzles for small jet-to-surface spacings and developed a corresponding Nusselt number correlation that includes a dimensionless stroke length [8]. Silva-Llanca et al. found a highly coupled response between larger jet spacings and low frequency operation where flow transition to turbulence was dominant [9]. To correlate new synthetic jet data to steady jets, He et al. Developed a dynamic Reynolds number to show the 40% increase in heat transfer is related to the fluid velocity [10]. These three references depict the common types of experimental and simulated evaluation metrics for a nonsteady jet, including nondimensional analysis and overall heat transfer performance. Further information is available in the comprehensive review by Krishan et al. [6].

Given the benefits of the synthetic jet, there is motivation to find a solution to create pulsating flows at the component level of a jet impingement device in a nonzero mass flux configuration. For heat transfer research, upstream ball valves are frequently used for mass flowrate control [11]. Acoustical loudspeakers, solenoid valves, and mechanical piston are additional methods for imposing pulsating flows [12]. One common trait between these methods is the inherent on-off forcing condition. This presents the challenge for more advanced heat transfer analysis with respect to forcing waveforms. Some efforts have been made to analyze the effects of various waveforms, amplitudes, and frequencies. Using a mass flowrate control valve, Middelberg et al. analyzed the time-dependence nature of nonsteady jets with respect to sinusoidal, triangular, and rectangular forcing waveforms [13]. Before performing the heat transfer study, they discussed the inherent heat transfer challenge with the different waveforms. In standard correlations, the Nusselt number is proportional to the Reynolds number to the power of an exponent less than 1. Therefore, alterations in heat transfer due to waveform modifications will be greater at lower Reynolds numbers. These results in a reduction of heat transfer enhancement for all waveforms assuming nonlinear effects are not present. In the end, they observed both enhancements and deterioration of heat transfer for all waveforms, with the primary difference being the vortex generation rate and the RMS value of the Reynold's number.

The reliability of high-power electronic devices is highly coupled to the internal thermal cycling generated by transient drive schedules [14]. Coefficient of thermal expansions mismatches between the power die, interconnect, copper, and ceramic layers in a standard direct bonded copper (DBC) are accentuated by quick thermal excitations. In terms of thermal management, systems are often designed to continuously cool for worse-case power loads. Pumps, fans, compressors and even jet engines bleed air systems often waste energy to satisfy this requirement. The alternative of electronic failure is critical enough to justify the extra cost. From a physics of failure perspective, number of cycles to failure is shown to be a function of mean junction temperature and maximum change of temperature in Arrhenius form [15]. In a DBC stack the delamination or cracking of larger surfaces will typically occur before more localized die interconnect failure. Nonetheless, the thermal gradients in the package are generated at the die level, so cooling must still be focused on these locations to reduce mean temperatures. The change in junction temperature during thermal cycling is a more complex problem to solve.

Phase change materials (PCMs) and two-phase cooling utilize latent heat to dampen temperature fluctuations and can be quite effective [16]. However, PCMs are integrated in lower power systems to avoid fully melting the material. With two-phase liquid to gas heat transfer, an entire field of study is devoted to the development of analytical and computational models to predict phase transition and the many other associated intricacies. Although well studied and useful for many applications, localized phase transition at the device level must be precisely predicted to manage transient operation. Without the aid of phase change, liquid cooling pumps or valve systems are then relied on for responsive mass flow rates, placing stress on the mechanical components. This is where a jet impingement cooler with a variable nozzle size could aid in both junction temperature management and pressure drop control. Based on the extent of studies showing the value of pulsating flows, this paper presents another method that incorporates the benefits transient jet formation at the local component level without the need for valves, speakers, or diaphragm actuators.

This study aims to implement a variable diameter iris mechanism to achieve pulsating jet flows, mitigate junction temperature swings during power cycling, and reduce wasted pumping power. Conditions shown by the synthetic jet actuator suggest that enhanced heat transfer can occur at specific combinations of pulse amplitude, frequencies, and waveforms. A parametric study through these variables will explore the feasibility of a lower frequency modulation up to 20 Hz with sinusoidal and square waveforms. Then, these same waveforms are applied to the heated test section to evaluate the ability to reduce temperature swings and simultaneously save pumping costs.

Figure 1 gives an overview of the iris-based pulsating jet setup. A commercially available linear voice coil actuator with an integrated hall effect position sensor is used for high-speed actuation of the pulsating liquid jet. Table 1 provides details regarding model information, sizing, force, stroke, and resolution. The jet test section is comprised of a fluid seal assembly, jet housing, base plate, and a 200 W resistive heater. The base plate is made of stock aluminum and is representative of the thickness and size found in commercial Silicon Carbide power modules. The resistive heater is 12 mm × 12 mm × 2.5 mm aluminum nitride variant with an imbedded K-type thermocouple for junction temperature measurement.

Figure 2 gives further details of the jet test section. The method of varying the jet area is to use an optical iris mechanism capable of an area range of 2–12 mm² (Edmund Optics 7 mm max aperture motorizable iris). The actuator interfaces with the iris using a rod with a slot-cam to translate linear motion to rotational iris motion. A common theme with unsteady jet impingement research is the tendency to use air as the fluid medium to avoid the need for fluid seals. In this study, a dynamic seal assembly on the primary actuation rod solves this issue. Although it does add additional friction force for the actuator to overcome, custom PID tuning for each testing configuration was performed to achieve accurate waveforms with respect to ideal sine and square waves.

For thermal-fluid measurements, a recirculating flow loop was constructed, consisting of a pump, fluid sensors, and a heat exchanger for temperature control. Table 2 provides component details and the range of measurement error. In summary, a variable frequency drive is used to control the shaft speed of a three-phase centrifugal pump with water being provided by a reservoir with a 5-micron filter. A combination of stainless-steel fittings and chemical-resistant silicone tubing was integrated for long-term durability. A turbine flowmeter measures the flowrate, along with two k-type thermocouple and pressure transducers, one on the upstream and downstream side of the test section. After passing through the test section, the water is brought back to the set temperature by a counterflow heat exchanger using an external 1 kW chiller. Heater control in the test section is achieved using software provided by the power supply and is imbedded in a LabVIEW script for fine-tune waveform control during transient tests. The fluid sensors and heater temperature data are collected through a DATAQ DI-2008 voltage DAQ. For accessibility, the loop was built onto a mobile platform to accommodate testing in other lab spaces. Finally, also present in the loop is a downstream control valve for the purpose of raising the fluid pressure of the entire test section. For this testing, it remained open. The entirety of the setup can be seen in Figs. 3 and 4. Before calculating the pressure drop across the test section, baseline pressure measurements were recorded and subtracted from the final values.

Many types of nozzle options exist for jet impingement configurations including slot, pipe, and orifice nozzles. While the iris is of an orifice type, the upstream geometry is that of a pipe nozzle. Therefore, steady-state testing must be performed to compare against existing correlations and determine optimum nozzle area versus flowrate conditions for transient effects. At a heater power of 100 W, Fig. 6 presents thermal resistance data plotted against the nozzle Reynold's number (1–6 lpm) as a function of increasing flow rates. There is a significant drop-off of thermal resistance as the flowrate increases, but the advantages quickly become negligible. In their review of jet impingement physics, Zuckerman et al. describe the relationship between thermal resistance and the mass flowrate [17].

Typically seen is a power law function with an exponent range of −0.6 to −0.8 on the mass flowrate term [17]. From the data in this study, we find the iris geometry produces an exponent of −0.3. This can primarily be attributed to the thermal resistance of the aluminum base plate present between the coolant and heater. With a plate thickness of 3 mm, and using an effective area equal to the heater, the conduction resistance is equal to 0.12 K/W. Therefore, a thinner base plate would give an experimental result closer to that normally seen with an orifice-type nozzle.

As is common with jet impingement studies, the jet-to-surface spacing over nozzle diameter ratio (H/D) is an important nondimensional factor for heat transfer correlations. A value between 2 and 8 is an optimum point across most studies [16]. With this study, a constant height of 12 mm is used as a middle ground between the smallest diameter of 1.25 mm (H/D = 9.6) and 3 mm (H/D = 4). Figure 7 plots the thermal resistance data versus the nozzle area as a function of flowrate. Through this data, an optimum nozzle area exists between 4 and 6 mm². This result aligns with previous studies where an orifice nozzle exhibits better behavior at more confined configurations due to the velocity profile at the jet exit [5]. For a fully developed pipe nozzle, a parabolic profile is present with a potential core gradually forming downstream. Orifice nozzles, with a flatter velocity profile, will produce a turbulent jet more quickly. In addition to the effect of nozzle geometry, a smaller variation in performance as a function of nozzle area is seen as the flowrate increases.

After characterization of the iris in a steady-state condition, pulsating operation was studied. Frequencies up to 20 Hz were achieved by the voice coil actuator where the full range of requested nozzle amplitude was achieved. A frequency greater than 20 Hz would require a motor force of up to 60 N due to friction in the rod seal creating PID tuning challenges. Furthermore, above this threshold it was found that the square wave forcing function resulting in an iris motion which closely resembled a sine wave. This is due to the reduced maximum velocity of the rod resulting from the seal friction. With this testing, the primary goals were to evaluate if the iris can withstand the pressures and forces associated with mechanical and hydraulic effects and if pulsing at <20 Hz has any effect on heat transfer. Made of steel, the iris exhibited slight rusting issues but was never critical enough to cause material failure. Other than this, successful pulsating was achieved for all waveforms and frequencies.

The testing parameters include a flowrate range between 1 and 4 lpm, a jet height range of 7–20 mm, and pulsating frequencies between 0 and 20 Hz. For data organization, the smallest jet height, 7 mm, is labeled as H0 and the largest height, 20 mm, is H3. The waveforms for the jet actuation were directed in the motor control software that accompanied the voice coil actuator developer's kit. For both the sine and square waves, an interpolation period of 0.001 s was used as the default setting. Modification of this value, especially for the square wave, would generate triangle waves, but this feature was ignored in the present study. To analyze the data, raw temperatures are first evaluated, then an enhancement factor is applied. Next, the dependency of the calculated Nusselt number is graphed, which leads into the development of a Nusselt number model for the presented data. An error analysis is performed and plotted for the new correlation.

Figure 8 plots the raw temperature values across all testing conditions as a function of pulsating frequency, waveform, jet height, and flowrate. Significant information can be discerned about the state of the pulsating jet based on the comparison of temperature between steady (0 Hz) and unsteady conditions.

For almost all setups, an initial rise in temperature is seen, followed by a point where the thermal performance begins to be recovered. In the Mid-delberg et al. study of waveforms, a similar effect was observed [13]. They estimated a performance decrease of 9% with the sine wave and 26% with a rectangular waveform resulting from the exponential effects on the Reynold's number [13]. From this, one can note the point of performance recovery is likely due to nonlinear effects being introduced into the boundary layer on the target surface. Interestingly, the 1 lpm case gives an average performance recovery frequency of 10.25 Hz, whereas this value is 4.75 Hz at a flowrate of 4 lpm. Effectively, increasing the flowrate of a pulsating iris jet at <20 Hz will give a lower performance recovery frequency.

Figure 9 presents the processed enhancement factor data. In total, only 23.75% of all conditions resulted in a heat transfer enhancement. The detailed breakdown of % enhancement for H0, H1, H2, and H3 is 6.25%, 26.25%, 47.5%, and 15%, respectively. A minimum performance of 0.959 is noted at 4 lpm, H3, 2 Hz with a sine wave. A maximum performance is of 1.016 is seen at 2 lpm, H2, 18 Hz with a square wave. From this data, it is clear there is a relationship between all four testing parameters, with the highest dependency being on the height of the jet and pulsating frequency. Figure 10 is presented to shed light onto the best overall performing conditions using an enhancement factor averaged across all height ranges per given flow rates. These plots show a combination of 2 lpm, and a jet height of 17 mm to be the ideal setup in the given test range. Going further, we can conclude that an H/D at that height setting of 5.66 is an optimal value for allowing for nonlinear flow effects to develop. A smaller height does not allow for maximum disruption to occur, while larger spacings will dissipate turbulent energy due to viscous effects.

Beyond providing a useful value for average heat transfer, the model gives the chance to evaluate the contribution of each term. A visual representation of these effects is found in Figs. 11 and 12. The dependency of heat transfer on each variable (Re, H/D, St) is clearest in the first two plots, with the data spread appearing nonuniform as a function of jet pulsations. As with most single-phase thermal management systems, there is a drop-off in performance benefit with an increasing flowrate, which is noted in these figures. Further, there is an apparent optimal H/D ratio for the iris-type nozzle, with an approximate peak at 4.06 according to the given testing conditions. From the pulsating data presented earlier, an optimal point existed at the H/D value of 5.66. Therefore, a key conclusion from this analysis is an ideal H/D ratio between 4 and 6 for an iris-type nozzle in the given testing range. This value could possibly shift either higher or lower at greater frequencies due to the relationship between viscous losses and vortex strength.

Next, the two Nusselt models are used to predict the heat transfer from the experimental conditions and compared against the real data. Percent error relative to the experimental values is used. This analysis is presented in Fig. 13, with Table 4 providing a summary of the % error values.

To further discern how well the models fit experimental data, values from the same volumetric flowrate are grouped together using transparent, colored overlays. For each waveform type, the error spread increases proportionally with flowrate. The model displays accurate behavior at low flow rates where the effect of jet height isn't as prominent. Then with higher flow rates, the error spread increases in magnitude and approaches 10% difference. Future studies with the intention of using this model should consider these effects. Additionally, the effect of base plate spreading on the overall Nusselt number should be accounted for.

The final experimental data in this study relates to the ability of the variable area iris to mitigate junction temperature swings and reduce hydraulic pumping power consumption. Sinusoidal and square waves of both the iris and heater power are tested. Phase shifting in increments of π/4 radians is applied between the two with a range between 0 (waveform match) and 7π/4. In this case, a zero-phase shift would theoretically give the best performance with a shift of π radians being the worst. However, what's not automatically clear is the effect of waveform type and if the thermal response is symmetric about the idealized case. Figure 14 gives a graphical depiction of the test conditions with a phase shifted heater power waveform. The testing frequency is 0.25 Hz with a heater power range of 75–200 W. The coolant flowrate is 2 lpm with an iris area range of 2–12 mm².

Figure 10 presents the thermal response of the transient junction temperature mitigation test. Four configurations were tested, including sine and square waves for both the iris and heater, then a combination of the two types. “Square” and “Sine” represent matched waveforms. “SqH_SiI” is a heater square wave and the iris in sinusoidal, and opposite for the final condition. As discussed earlier, the square wave will result in lower performance in the absence of nonlinear effects due to Reynold's number dependency. This is also seen in this data. Figure 15(a) shows the normalized temperature rise with respect to the zero-phase shifted condition. Figure 15(b) plots the raw heater temperature rise during the transient heater profile. Automatically we see a temperature increase as the waveforms become more phase shifted with a peak at π or within π/4 radians. The square wave is affected most by the phase shifting, with a maximum temperature increase of 2.4 °C. The sine wave increase is slightly less at 2 °C. For further analysis, we can see a closer dependency of the thermal response on the heater waveform than the iris in mixed conditions. Upon changing the iris waveform, the profile matches within 2% of the original. Finally, the waveforms exhibit a nonuniform symmetry about the idealized case with exact matching. In the square waves, the 3π/2 and 7π/4 have little effect on thermal performance, indicating the cooling response to transient conditions can lag slightly and maintain ideal performance. With the sine wave, the opposite is true. A control scheme would need to have a predictive component to avoid temperature increases due to phase lag.

In terms of the benefits of a variable diameter jet impingement apparatus on junction temperature and pressure drop, Table 5 shows this data. The point of reference is for the smallest diameter nozzle of 1.25 mm to represent a worst-case-scenario cooling requirement. By opening the iris during low power modes and only closing during high power, pumping power was reduced by 25% in both waveforms. While good for pumping power reduction, this will also inherently increase the minimum temperature. However, this effect was little as the time-averaged temperature only rose by 2.1%. And finally is the effect on junction temperature swing. By matching the heater and iris waveforms, up to 8.9% reduction in temperature variation was achieved.

This study examined the construction, characterization, and experimental validation of a variable area nozzle jet impingement cooler. A voice coil motor was used to actuate an optical iris mechanism in a submerged water environment. High speed imaging was performed to calibrate the motor movement to the area of the iris, allowing for precise flow control with respect to oscillation frequency and waveform type. Experimental testing was then performed, with the key results as follows:

• The iris mechanism can be successfully implemented in a liquid coolant environment and can withstand sustained pulsations at common pressures found in thermal management systems.

• Steady-state jet testing indicates the iris mechanism can be defined as an orifice nozzle, which is given by the increase in performance at a lower H/D ratio.

• Pulsating jet testing showed the iris mechanism, in both square and sinusoidal waveforms, began to produce nonlinear fluid effects at a frequency between 4 and 10 Hz.

• An optimal H/D value of 4–5.6 is noted for the given test range

• During transient power cycling, the variable area jet cooler can both reduce pumping power and junction temperature variation compared to a worse-case-scenario jet configuration.

The results in this study indicate further analysis is needed for full characterization of the variable area iris mechanism. First, the base plate thickness should be optimized for junction temperature management and could also aid in improving pulsating performance. Second, higher frequency forcing functions can be applied to the iris mechanism for further heat transfer benefits. Lastly, the variable area jet should be implemented in a control scheme and applied to real-world drive schedules to compare against other active cooling methods.

• National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal Systems (Award No. EEC-1449548; Funder ID: 10.13039/100000001).

The authors attest that all data for this study are included in the paper.