Confined bubbly flows in millimeter-scale channels produce significant heat transfer enhancement when compared to single-phase flows. Experimental studies support the hypothesis that the enhancement is driven by a convective phenomenon in the liquid phase as opposed to sourcing from microlayer evaporation or active nucleation. A numerical investigation of flow structure and heat transfer produced by a single bubble moving through a millimeter-scale channel was performed in order to document the details of this convective mechanism. The simulation includes thermal boundary conditions emulating those of the experiments, and phase change was omitted in order to focus only on the convective mechanism. The channel is horizontal with a uniform-heat-generation upper wall and an adiabatic lower surface. A Lagrangian framework was adopted such that the computational domain surrounds the bubble and moves at the nominal bubble speed. The liquid around the bubble moves as a low-Reynolds-number unsteady laminar flow. The volume-of-fluid method was used to track the liquid/gas interface. This paper reviews the central results of this simulation regarding wake heat transfer. It then compares the findings regarding Nusselt number enhancement to a reduced-order model on a two-dimensional domain in the wake of the bubble. The model solves the advective-diffusion equation assuming a velocity field consistent with fully developed channel flow in the absence of the bubble. The response of the uniform-heat-generation upper wall is included. The model assumes a temperature profile directly behind the bubble which represents a well-mixed region produced by the passage of the bubble. The significant wake heat transfer enhancement and its decay with distance from the bubble documented by the simulation were captured by the reduced-order model. However, the channel surface temperature recovered in a much shorter distance in the simulation compared to the reduced-order model. This difference is attributed to the omission of transverse conduction within the heated surface in the two-dimensional model. Beyond approximately one bubble diameter into the bubble wake, the complex flow structures are replaced by the momentum field of the precursor channel flow. However, the properties and thickness of the heated upper channel wall govern the heat transfer for many bubble diameters behind the bubble.

A numerical investigation of a single highly confined bubble moving through a millimeter-scale channel in the absence of phase change is presented. The simulation includes thermal boundary conditions designed to match those of completed experiments involving bubbly flows with large numbers of bubbles. The channel is horizontal with a uniform-heat-generation upper wall and an adiabatic lower boundary condition. The use of a Lagrangian framework allows for the simulation of a channel of arbitrary length using a limited computational domain. The liquid phase is a low-Reynolds-number laminar flow, and the phase interactions are modeled using the volume-of-fluid (VOF) method with full geometric reconstruction of the liquid/gas interface. Results are presented for three bubble diameters, which include two levels of confinement within the channel and two liquid flow rates. Bubble shape and speed closely match experimental observations for each bubble size and liquid flow rate. Nusselt numbers in the bubble wake for all configurations follow a power law relationship with distance behind the bubble. Important dynamical structures include a pair of vortical structures at the rear of the bubble associated with the primary heat transfer enhancement and a pair of prominent liquid jets oriented in the transverse direction on either side of the bubble.

Confined bubbly flows in millimeter-scale channels produce significant heat transfer enhancement when compared to single-phase flows. This enhancement has been demonstrated in experimental studies, and some of these studies conclude that the enhancement persists even in the absence of active nucleation sites and bubble growth. This observation leads to the hypothesis that the enhancement is driven by a convective phenomenon in the liquid phase around the bubble instead of sourcing from microlayer evaporation or active nucleation. Presented here is a numerical investigation of flow structure and heat transfer due to a single bubble moving through a millimeter-scale channel in the absence of phase change. The simulation includes thermal boundary conditions designed to match those of a recent experiment. The channel is horizontal with a uniform-heat-generation upper boundary condition and an adiabatic lower boundary condition. The Lagrangian framework allows the simulation of a channel of arbitrary length using this smaller computational domain. The fluid phases are modeled using the Volume-of-Fluid method with full geometric reconstruction of the liquid/gas interface. The liquid around the bubble moves as a low-Reynolds-number unsteady laminar flow. In a square region from the trailing edge of the contact line to one nominal bubble diameter behind the bubble, the area-averaged Nusselt number is, at its greatest, 4.7 times the value produced by a single-phase flow. Bubble shape and speed compare well to observations from the recent experiment. The heat transfer enhancement can be attributed to flow structures created by bubble motion. Multiple regions have been observed and are differentiated by their respective vortex characteristics. The primary region exists directly behind the bubble and exhibits the highest enhancement in heat transfer. It contains channel-spanning vortices that move cold fluid along the centerline and edge of the vortices from near the far wall of the channel to the heated wall. The cold fluid delivered by this motion tends to thin the thermal gradient region near the wall and directly behind the bubble and results in the highest local heat transfer coefficients. This vortex drives a bulk exchange of fluid across the channel and elongates the area of heat transfer enhancement to several bubble diameters. The secondary region is a set of vortices that exist to the side and slightly behind the bubble. These vortices rotate at a shallow angle to the primary flow direction and are weaker than those in the other regions.

A numerical investigation of a single highly confined bubble moving through a millimeter-scale channel in the absence of phase change is presented. The simulation includes thermal boundary conditions designed to match those of completed experiments. The channel is horizontal with a uniform-heat-generation upper wall and an adiabatic lower boundary condition. The use of a Lagrangian framework allows for the simulation of a channel of arbitrary length using a limited computational domain. The liquid phase is a low-Reynolds-number unsteady laminar flow, and the phase interactions are modeled using the Volume-of-Fluid method with full geometric reconstruction of the liquid/gas interface. Results are presented for two bubble sizes, two liquid flow rates, and two Prandtl numbers. The paper focuses on heat transfer in the rearward wake of the bubble. Nusselt numbers for the higher Prandtl number case are shown to follow a power law relationship with distance behind the bubble. Important dynamical structures include a pair of vortical structures at the rear of the bubble associated with cold fluid being brought near the wall and fluid jets oriented in the transverse direction to either side of the bubble.