Understanding pulsed jet impingement cooling by instantaneous heat flux matching at solid-liquid interfaces

In recent decades, jet impingement cooling has gained significant attention due to its ability to remove large thermal loads from local heating zones. This study demonstrates the performance of pulsed jet impingement cooling on a Ti-coated glass window. Infrared (IR) thermography data are analyzed to generate heat transfer coefficient (HTC) maps for a range of heat fluxes ($q{}^{\prime \prime }\approx 20$–60 W/${\mathrm{cm}}^2$) and jet pulsation frequencies ($f_p\approx$ 7–25 Hz). Heat transfer coefficients are observed to scale as $h\propto \sqrt{2f_p}$ with local maximum values at the center of the jet stagnation zone. For reference, $h^{\max }\approx 15\mathrm{kW}/{\mathrm{m}}^2\mathrm{K}$ is found for $q{}^{\prime \prime }\approx$ 60 $\mathrm{W}/{\mathrm{cm}}^2$ and $f_p\approx 25$ Hz. Moreover, a jet pulsation frequency of $f_p\approx 15$ Hz matches well with both the bubble release rate and dry-out occurrence rate within 50 and 80 ms, respectively, at $q{}^{\prime \prime }=60 \mathrm{W}/{\mathrm{cm}}^2$. At heat fluxes $>40$ $\mathrm{W}/{\mathrm{cm}}^2$, boiling regimes were captured in terms of cyclic events of bubble growth, bubble collapse, dry-out, partial rewetting, and full rewetting. Finally, a theoretical model is proposed based on both the HTC expected for a steady jet and HTC augmentation due instantaneous heat flux matching for a pulsed jet at the jet-wall interface. The correlation between experiments and theory are reasonable, yet there are still unresolved complexities associated with thermofluid instabilities, decoupling the transient latent heat and sensible heat transfer mechanisms, and first-principles modeling of the spatiotemporal surface temperature and flow-field oscillations induced by a pulsed jet.

Figure 1

Schematic diagram of the apparatus and flow-loop for pulsed jet impingement studies.

Figure 2

Fabrication steps for the 1 cm $\times$ 1 cm Ti thin-film heater or thermometer. (a) Ultrasonically cleaned substrate with presputtered, heat-treated $\mathrm{Ti}/\mathrm{Ti}{\mathrm{O}}_2$ adhesion coating ($\approx 10$ nm). (b) Polyamide mask application. (c) Primary Ti thin-film deposition ($\approx 100$ nm). (d) Polyamide mask removal. (e) The Al mask application for subsequent Au deposition (“band-aid” Ti heater or thermometer). (f) Electrically conductive Ag paste application on Au busbars. (g) Application of Cu foil or busbar wraps. (h) Final heater configuration for loading into spray or jet chamber.

Figure 3

(a) Comparison between the temperatures measured using IR ($T_{\mathrm{IR}}$) and thermocouple ($T_{\mathrm{TC}}$) thermometry. Data are provided for three different heat flux configurations and two different measurement configurations. The curvature in the data is due to transient heating effects (i.e., steady-state conditions are only applicable at $T_{\mathrm{IR}}\approx$ 90, 120, and $153{}^{\circ }\mathrm{C}$. (b) Schematic depiction of the “front-side” measurement configuration (not to scale). The open-symbol data in (a) were acquired for this “front-side” configuration. (c) Schematic depiction of the “back-side” measurement configuration (not to scale). This “back-side” schematic depicts an impinging jet; however, no jets were used during the data acquisition for the temperature data provided in (a). As illustrated in (b) and (c), the working distance (WD) was the same for both measurement configurations. Also, the emissive black paint coating on the Ti heater or thermometer was removed after these temperature cycling experiments.

Figure 4

Infrared (IR) temperature map for pulsed jet cooling. The image dimensions are centered to the jet stagnation point $\left[\right(X,Y)=(0,0)$ mm]. The circle and square overlays correspond to the jet impingement zone (JIZ) and radial-flow zone (RFZ) for subsequent analysis (areas: $A_{\mathrm{JIZ}}\approx 4.2{\mathrm{mm}}^2, A_{\mathrm{RFZ}}\approx 9.7{\mathrm{mm}}^2$). Experimental details: $t\approx$ 0.936 s (relative to the start of IR data acquisition), $q{}^{\prime \prime }=60\pm 2\mathrm{W}/{\mathrm{cm}}^2, f_p=14.95\pm 0.97$ Hz, $G\approx$ 795 $\mathrm{kg}/{\mathrm{m}}^2\mathrm{s}, \mathrm{Re}\approx$ 970, $\mathrm{St}\approx 0.003, D\approx 410\mu \mathrm{m}, H/D\approx$ 200, and $z>0$ into the page or image.

Figure 5

Overview of key spatiotemporal temperature and HTC data for pulsed jet cooling using IR thermography. (a) Temporal Ti thin-film (wall-interface) temperature (left axis) and HTC (right axis). The data correspond to area-averaged values within the JIZ. (b) Spatial temperature (left axis) and HTC (right axis) profiles across the jet stagnation point $\left[\right(X,Y)=(0,0)$ mm]. (c) The IR temperature map and corresponding HTC distribution at $t\approx$ 0.936 s. (d) Zoom view of the RFZ and corresponding JIZ within it. Experimental details: $t\approx$ 0.936 s (relative to the start of IR data acquisition), $q{}^{\prime \prime }=60\pm 2\mathrm{W}/{\mathrm{cm}}^2, f_p=14.95\pm 0.97$ Hz, $T_{\mathrm{jet}}\approx 22.5{}^{\circ }\mathrm{C}, D_{\mathrm{jet}}\approx 410\mu \mathrm{m}, G\approx$ 795 $\mathrm{kg}/{\mathrm{m}}^2\mathrm{s}$, Re $\approx$ 970, $\mathrm{St}\approx$ 0.003, $H/D\approx$ 200, and $z>0$ into the page or images.

Figure 6

HTC data as a function of jet pulsation frequency and applied heat flux. The HTC values are based on area-averaged wall-interface temperatures within the JIZ. The relative error in $f_p$ is based on temporal analysis of the acquired $T_{\mathrm{JIZ}}$ data, where $T_{\mathrm{JIZ}}$ is the average spatiotemporal wall temperature recorded within the jet impingement zone during an IR acquisition period of $\approx 5$ s (see Supplemental video 1). The relative error in $h_{\mathrm{JIZ}}$ is provided based error propagation using the standard deviation in the applied heat flux ($\delta q{}^{\prime \prime }$) combined with either (i) $\delta T_{\mathrm{IR}}$ (“larger error-bar data”) estimated from the temperature cycling studies (Sec. 2c) or (ii) $\delta T_{\mathrm{JIZ}}$ (“smaller error-bar data”) due to temporal drift in $T_{\mathrm{JIZ}}$ measured throughout an entire $\approx 5$-s IR data acquisition. Experimental details: $T_{\mathrm{jet}}\approx 22.5{}^{\circ }\mathrm{C}, D_{\mathrm{jet}}\approx 410\mu \mathrm{m}, G\approx$ 795 $\mathrm{kg}/{\mathrm{m}}^2\mathrm{s}$, Re $\approx$ 970, $\mathrm{St}\approx$ 0.003, $H/D\approx 200, q{}^{\prime \prime }=20\pm 0.6, 34\pm 1$, and $60\pm 1.8\mathrm{W}/{\mathrm{cm}}^2, f_p=7.99\pm 0.77, 14.95\pm 0.97$, and $25.21\pm 2.81$ Hz.

Figure 7

High-speed visible imagery data for the jet impingement and falling thin-film boiling cycles ($f_p\approx$ 15 Hz, $q{}^{\prime \prime }\approx 60\mathrm{W}/{\mathrm{cm}}^2, G\approx 795 \mathrm{kg}/{\mathrm{m}}^2\mathrm{s}$, Re $\approx$ 970). (a) Image of bubbles starting to appear at a radial location from center of the impinging jet. (b) Visual representation of dry-out zones as the bubbles tend to grow and collapse. (c) Image showing that the surrounding water coolant tends to wet the dry-out zones with the appearance of partially rewetted zones. (d) Imagery of the fully wetted zones as the next jet or droplet pulse of liquid starts to impact the heated wall.

Figure 8

Impact of the jet pulsation frequency on the maximum heat transfer coefficient measured (symbols) and predicted (dashed lines) in this work. The HTC values correspond to the maximum values measured at the jet stagnation point. The error bars for the HTC data are derived based on the same methodology addressed in Fig. 6. The predicted HTC is based on ${\mathrm{h}}_{\max }$: Eq. (10). The vertical dashed line is predicted frequency for Kapitza instability criterion $[f_{\mathrm{Ka}}$ via Eqs. (3, 4, 5)].