Thermal behavior and dynamics of flow boiling in a pin-fin microchannel

As the need for effective heat dissipation in specialized systems intensifies, the study of flow boiling in microchannels has gained prominence due to its high efficiency and cost benefits. Utilizing a three-dimensional computational model incorporating the Volume of Fluid (VOF) and Saturated Interfacial Volume (SIV) methodologies, this research scrutinizes the behavior of saturated flow boiling in a microchannel featuring a centrally positioned, heated square cylinder. The analysis focuses on variations in bubble morphology, fluidic behavior, and thermal profiles, revealing that the evaporation of a thin liquid film contributes significantly to heat transfer efficacy. A systematic assessment of temperature gradients, heat transfer coefficients, and liquid film metrics uncovers the critical drivers behind effective heat transfer across different surfaces. Additionally, the study elucidates the role of Reynolds number and initial bubble size, indicating that higher Reynolds numbers thicken the liquid film, reducing heat transfer efficiency, while larger initial bubble diameters thin the liquid film, thereby boosting efficiency. Factors such as thermal boundary layer disruption and superheated fluid absorption further contribute to heat transfer optimization. This investigation enriches the current understanding of phase-change heat transfer dynamics and bubble interactions in microchannel environments equipped with a heated square cylinder.


Introduction
Modern engineering trends, particularly in sectors like semiconductors, telecommunications, and microsatellites, increasingly prioritize miniaturization.However, this trend amplifies thermal management challenges due to heightened power densities in confined areas [1] .As solutions, Microchannel and flow boiling methodologies have emerged, distinguished by their low thermal resistance and superior surface-area-to-volume metrics.Their advantages, such as efficient heat transfer, consistent temperature profiles, and energy savings, position them as ideal for surmounting thermal challenges in cutting-edge technologies [2] .
Reduction in scale amplifies certain physical dynamics.Particularly in microchannels, forces like surface tension and shear stress overshadow gravitational effects, significantly impacting flow and thermal patterns [3] .Such complexities have instigated a surge in research to decode these intricate mechanisms [4][5] .Similar to traditional-sized channels, the incorporation of pin-fin structures within microchannels notably elevates heat transfer efficacy [6] .This enhancement stems from an expanded specific surface area, intensified fluid disturbances, and increased vaporization sites [7] .To elucidate heat transfer augmentation and flow dynamics, in-depth research endeavors have been pursued [8][9] .While experimental techniques are recognized for their realism, microscale measurements pose significant challenges.Transient numerical simulations emerge as a viable counter to these constraints.This strategy aids in understanding the core physical principles driving flow boiling in microchannels [10] , setting the stage for potential device enhancement [11][12] .
The above literature highlights the efficacy of pin-fin structured microchannels in flow boiling as a superior cooling method.Yet, the intricate design, coupled with challenges in implementing direct numerical explorations rooted in genuine physical activities, means more research is needed, especially in transport dynamics and heat transfer attributes.Our current work delves into the behavior of a singular vapor bubble passing a heated square cylinder in a microchannel using a tri-dimensional transient numerical simulation.The principal aim is to decode the regulating factors behind dynamics and heat transfer in saturated boiling flows in these microchannels.Employing the saturated-interface volume phase change model [13] , integrated with the volume-of-fluid technique, ensures a meticulous depiction of bi-phase flow behaviors and interfacial phase alterations.Moreover, the study incorporates a parametric assessment examining Reynolds number and bubble size, providing essential knowledge for the creation of high-efficiency cooling systems.

Problem description
Referencing Figure 1, we analyze a lone seed bubble's trajectory through a microchannel, wherein a heated square cylinder is centrally positioned.The channel's square cross-section spans W=100 µm, extending 40 W in length.Nestled at the core (x=20 W, y=0.5 W) is a square cylinder heated uniformly, covering 0.6 W of width.The strategic placement between the channel's inlet/outlet and the cylinder ensures flow consistency and facilitates bubbles reaching hydrodynamic equilibrium before encountering the cylinder.Boundary conditions incorporate a developed laminar velocity at the inlet, saturation temperature alignment, and atmospheric pressure at the outlet.The cylinder surface is consistently exposed to a q=50 kW/m 2 heat flux, with all other internal walls deemed adiabatic.Velocity's no-slip conditions are uniformly applied across the channel's inner surfaces and the cylinder's exterior.
This study delves into two-phase flow analysis, particularly examining the interaction of a single seed bubble with a heated cylinder.Positioned 0.05 W from the wall and 2.5 W from the inlet on the zdirection symmetry plane, the bubble's location mimics its immediate post-nucleation detachment.Ensuring a proper distance from the cylinder allows the bubble to attain hydrodynamic stability upon approaching the heated segment.The study evaluates an initial vapor bubble diameter of d* = d/W = 0.6 at Reynolds numbers ranging from 100 to 300.The chosen fluid for this research is R113, with its attributes detailed in Table 1.

Mathematic model and implementation
This study employs ANSYS Fluent 18.2, augmented with UDFs, for simulation.Assumptions made during these simulations include: (1) Given the minute scale, gravitational effects are disregarded.
(2) Both phases, liquid and vapor, are treated as incompressible and Newtonian.
(3) Channel walls adhere to the no-slip criterion.
(4) At evaporation, the liquid-vapor interface maintains saturation temperature.The interface is traced using the volume of fluid (VOF) approach, with the continuum surface force model addressing the surface tension force Fs as: where κ and C denote the interface curvature and color function, respectively.To counteract spurious currents, the moving reference frame method is utilized.
The evaporation at the interface is governed by the saturated-interface-volume (SIV) phase change model, which is derived purely from physical processes without empirical coefficients.The energy term (Sh, la) is determined as: , ( ) ( ) The aforementioned procedure, devoid of nested iterations, ensures computational efficiency without compromising accuracy.Mass sources for vapor (Sm, v) and liquid (Sm, l) are determined as: ) where the reference temperature Tref is set at 298.15 K as the default value.

Mesh setup and independent study
To bolster the precision of simulating liquid film dynamics during phase change, the mesh on the heated cylinder's surface was refined.This was complemented by the utilization of the boundary layer mesh technique near channel walls for accurate fluid-wall dynamics.A mesh independence test examining four mesh densities ranging from 2, 184, 569 to 4, 845, 268 cells focused on the heat transfer coefficient and the dimensionless bubble diameter under consistent initial conditions.Table 2 illustrates that cell number deviations reduce as mesh density increases.When surpassing 3, 962, 520 cells, deviations remain under 1.5%.Thus, a 3, 962, 520-cell mesh was selected for optimal balance between accuracy and computational efficiency.

Model validation
To validate our model, simulations of an elongated bubble flow boiling in a microchannel, with diameter D=0.5 mm and length L=20 D, were conducted.The channel has an 8 D adiabatic segment for bubble stabilization and a 12 D segment with a uniform heat flux of 9 kW/m 2 .Figure 2 reveals our model's predictions aligning closely with findings from Magnini et al. [10] and Ferrari et al. [11] Figure 2. Dimensionless bubble location (d*) with time (a) and heat transfer coefficient (h) along dimensionless x-axis location at the time instant t=12.5 ms (b) compared with literature data [10,11] .From Figure 3, we observe that the flow within the pin-fin microchannel bifurcates, leading to two heightened spanwise currents that conclude in a symmetric dual vortex downstream of the cylinder.As the bubble moves past the heated cylinder and progresses downstream, it encounters the vortex influence, gravitating it toward the channel's center.This motion impacts the vortex's flow dynamics, with a notable portion of the superheated liquid from the vortex being directed to the bubble surface, facilitating its diameter expansion.Examining the flow dynamics across different Reynolds numbers, a clear association emerges between the bubble-vortex interaction intensity and the Reynolds number.Specifically, a more extensive bubble-vortex interaction and a lower Reynolds number amplify the bubble diameter and reinforce the bubble-vortex interaction.

Heat transfer enhancement and bubble dynamics
Figure 4 illustrates that bubble passage perturbs the thermal boundary layer of the heated cylinder, conspicuously reducing its surface temperature.This reduction is attributable to the diminishing sensible heat in the superheated liquid surrounding the bubble, a consequence of the heat transfer and evaporation interplay at the saturated vapor-liquid interface.This phenomenon progresses, causing a correlative descent in the encompassing liquid's temperature.Detailed analysis reveals that the movement of the bubble and the associated advancing low-temperature region correlates with a diminishing liquid film thickness and surface temperature.This elucidates the substantial relationship between liquid film thickness and bubble-induced heat transfer augmentation.Furthermore, the downstream bubble movement disrupts the vortex structure and intensifies heat absorption at the vapor-liquid interface, augmenting heat transfer efficiency.Delving into the interrelation between liquid film thickness and bubble-mediated heat transfer enhancement, it's discernible that a thinner liquid film correlates with a reduction in the adjacent surface's temperature, signifying elevated heat transfer efficacy.Yet, beyond a thickness of 2.5 µm, this enhancement becomes markedly marginal.The temperature distribution of the liquid film in Figure 4 elucidates this mechanism.One facet of the film is juxtaposed with a high-temperature surface, while its opposite interfaces with a phase transition boundary at saturation temperature.A pronounced temperature gradient in slender films effectively lowers thermal resistance, thus optimizing heat transfer.However, as the film thickens-approaching or surpassing the thermal boundary layer's depth-its internal gradient becomes less pronounced, yielding a subdued heat transfer enhancement and a moderated surface temperature reduction.
Comparatively, the influence of Reynolds numbers on temperature distributions is conspicuous.At lower Reynolds numbers, surface tension propels bubbles to displace surrounding liquid in confined spaces, generating a svelte film on the cylinder's surface, which augments heat transfer.Conversely, with escalating Reynolds numbers, the inertia's dominance on bubble dynamics reduces the liquid-displacing effect, thickening the film.This amplification in film thickness consequently moderates heat transfer enhancement.
Figure 5 showcases the intensification strength of heat transfer and bubble volume increase over time for diverse Reynolds numbers.The bubble volume increase is characterized by the ratio d/d0, where d is the post-growth bubble diameter, and d0 is its initial size.Heat transfer intensification is expressed as htp/hsp, with hsp denoting the single-phase heat transfer coefficient and htp representing the two-phase coefficient when a bubble traverses the gap.The computation for the average heat transfer coefficient is provided: (5) As depicted in Figure 5 (a), optimal heat transfer efficiency is achieved when the bubble's center aligns with the cylinder's midpoint, especially at lower Reynolds numbers.Specifically, at a Reynolds number of 100, the heat transfer efficiency peaks at over 1.5 times that of a mono-phase flow.This heightened efficiency is due to the dominant surface tension at reduced Reynolds numbers, resulting in a more svelte liquid film.In contrast, with increasing Reynolds numbers, fluid inertial forces dominate, yielding a denser liquid layer.
Evaporation at the vapor-liquid boundary causes a consistent bubble diameter expansion, as visualized in Figure 5 (b).The bubble's interface, upon traversing the cylinder, interacts with the thermal boundary, leading to a svelte liquid film formation with the cylinder.This interaction accelerates evaporation, inducing a swift volume surge in the bubble, reflected as an abrupt uptick in the diameter growth rate in the figure.The surge in bubble volume also leads to greater liquid displacement, thinning the liquid film more, which creates positive feedback in enhancing heat transfer.After the bubble passes through, the interaction with the superheated liquid downstream prompts its diameter to expand, depicted in the figure as a sustained diameter growth uptrend.Reynolds number modulates this process.With a lower Reynolds number, rapid diameter augmentation occurs due to thinner liquid films and elevated downstream liquid temperatures.Conversely, elevated Reynolds numbers decelerate growth due to a thicker liquid film and cooler downstream temperatures.

Conclusion
This study employs a three-dimensional computational model to probe saturated flow boiling within a centrally-heated square cylinder microchannel.Relying on the SIV phase change model and the Volume of Fluid (VOF) approach, the model's fidelity is ascertained by juxtaposing its outputs with extant experimental and simulated findings.Mesh optimization and verification further corroborate simulation reliability.Emphasizing inlet Reynolds numbers, the investigation delves into underlying heat transfer processes and bubble dynamics, culminating in key takeaways elucidated as follows: 1.The efficiency of heat transfer on a heated surface is influenced by nearby bubble dynamics.Confinement near the heated cylinder produces a thin liquid film between the surface and the bubbles.This film's thickness exhibits a relationship with the surface's temperature distribution.Specifically, a thinner film correlates with enhanced heat transfer due to pronounced temperature gradients.
2. The enhancement of heat transfer is significantly affected by the disturbance of the thermal boundary layer and the intake of overheated liquids.This disturbance, especially pertinent in thicker liquid films, leads to an indiscriminate intensified heat transfer at the cylinder surface, contrasting the immediate correlation of evaporation and bubble location.Additionally, the intake of overheated liquids induces a delayed restoration of the thermal boundary layer, enhancing heat transfer from a longer time dimension.
3. The Reynolds number profoundly impacts heat transfer efficacy.Elevated Reynolds numbers amplify inertial forces, thickening the liquid film and reducing transfer efficiency.Conversely, lower Reynolds numbers emphasize surface tension, leading to a thinner liquid film, cooler surface temperatures, and heightened transfer efficiency.In cases of pronounced heat transfer augmentation, swift bubble diameter expansion exerts extrusion forces on the liquid, enlarging the film area but decreasing its thickness, thereby promoting a heat transfer enhancement feedback loop.
This study deepens the understanding of seed bubble behavior and phase-change heat transfer in microchannels with a central heated square cylinder, offering insights for microscale phase-change heat exchanger design.In practical scenarios, bubbles often manifest with varied diameters.Subsequent research should explore the influence of these disparities on heat transfer and flow dynamics.

Figure 1 .
Figure 1.Diagram depicting a solitary initial-phase vapor bubble navigating through a microchannel, encountering a centrally-located heated square cylinder.

Figure 3 .
Figure 3. Bubble behavior and flow pattern across diverse Reynolds numbers.

Figure 4 .
Figure 4. Interaction between bubble and temperature profiles at diverse Reynolds numbers.

Figure 5 .
Figure 5. Intensification strength of heat transfer (htp/hsp) and bubble volume increase (d/d0) over time for diverse Reynolds numbers.

Table 1 .
Fluid properties at saturation temperature.