Numerical Simulations of Pulsating Heat Pipes, Part 1: Modeling

The pulsating nature of a closed loop pulsating heat pipe (CLPHP) makes the prediction of its thermal-hydraulic performance extremely challenging. Unfortunately, the design of CLPHPs is still quite an empirical process, requiring testing of many prototypes by cold plate fabricators and thus inhibiting their possibilities for application. This means that a reliable and robust CLPHP simulation code is needed to do the design and prediction of its thermal performance. In this study, an updated code based on a 1-D model that traces out the entire loop is presented, starting from its first version developed in 2015. The present code is based on the principles highlighted in the Three-Zone Model for flow boiling in a micro-channel (i.e. thin liquid film zone, liquid slug zone and dry-out zone), but applied to the oscillating flow of CLPHPs in both evaporating and condensing processes. The heat transfer processes between the wall and the fluid are modelled for both the liquid slugs (convective) and vapor plugs (film evaporation and condensation). The wall receives heat from the electronics to be cooled based on the boundary conditions applied locally and the wall conducts heat axially through a 1-D conduction scheme in addition to the two-phase pulsating mechanism. The present code can be classified as an engineering tool, being pragmatic and thus achieving accurate predictions with reasonably low computational times, as opposed to a research tool. More specifically, the kinetics of the flow are solved exclusively on the liquid slugs as the dynamics of the vapor and liquid film were assumed negligible, except for their changing lengths. The code also includes mechanisms related to bubble creation (new vapor plug formation by nucleation) and collapse (when two liquid slugs coalesce due to the vapor plug in between collapses).

Numerical Modeling of Annular Laminar Film Condensation in Circular and Non-Circular Micro-Channels under Normal and Micro-Gravity

Stefano Nebuloni

A theoretical and numerical model to predict film condensation heat transfer in mini, micro and ultra micro-channels of different internal shapes is presented in this thesis. The model is based on a finite volume formulation of the Navier-Stokes and energy equations and it includes the contributions of the unsteady terms, surface tension, axial shear stresses, gravitational forces and wall thermal conduction. Notably, interphase mass transfer and near-to-wall effects (disjoining pressure) are also included. This model has been validated versus various benchmark cases and versus published experimental results from three different laboratories, predicting micro-channel heat transfer data with an average error of 20 % or better. The conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid and the heat conduction in the channel wall has been studied and analyzed. The work has focused on the effects of three external wall boundary conditions: a uniform wall temperature, a non uniform wall heat flux and single-phase convective cooling. The thermal axial and peripheral conduction occurring in the wall of the channel can affect the behavior of the condensate film, not only because it redistributes the heat, but also because the annular laminar film condensation process is dependent on the local saturation to wall temperature difference. When moving from mini to micro and ultra-micro channels, the results shows that the axial conduction effects can become very important in the prediction of the wall temperature profile and they can not be ignored. Under these conditions, the overall performances of the heat exchanger become dependent not only on the fluid properties and the operative conditions but also on the geometry and wall material. Results obtained for steady state conditions are presented for circular, elliptical and flattened shape cross sections for R-134a and ammonia, for hydraulic diameters between 10 µm and 3 mm. Microscale condensation finds applications in heat pipes and compact heat exchangers for electronic equipment or spacecraft thermal control, in automotive condensers, in residential air conditioning and in refrigeration applications: the influence of the steady or unsteady gravitational field and of the inertia forces on the flow field and consequently on the heat transfer performances is investigated allowing the model to be applied as a design and optimization tool for enhanced heat exchangers.

EPFL2010

Numerical investigation of hydrodynamics and heat transfer of elongated bubbles during flow boiling in a microchannel

Mirco Magnini, John Richard Thome

Flow boiling within microchannels has been explored intensively in the last decade due to their capability to remove high heat fluxes from microelectronic devices. However, the contribution of experiments to the understanding of the local features of the flow is still severely limited by the small scales involved. Instead, multiphase CFD simulations with appropriate modeling of interfacial effects overcome the current limitations in experimental techniques. Presently, numerical simulations of single elongated bubbles in flow boiling conditions within circular microchannels were performed. The numerical framework is the commercial CFD code ANSYS Fluent 12 with a Volume Of Fluid interface capturing method, which was improved here by implementing, as external functions, a Height Function method to better estimate the local capillary effects and an evaporation model to compute the local rates of mass and energy exchange at the interface. A detailed insight on bubble dynamics and local patterns enhancing the wall heat transfer is achievable utilizing this improved solver. The numerical results show that, under operating conditions typical for flow boiling experiments in microchannels, the bubble accelerates downstream following an exponential time-law, in good agreement with theoretical models. Thin-film evaporation is proved to be the dominant heat transfer mechanism in the liquid film region between the wall and the elongated bubble, while transient heat convection is found to strongly enhance the heat transfer performance in the bubble wake in the liquid slug between two bubbles. A transient-heat-conduction-based boiling heat transfer model for the liquid film region, which is an extension of a widely quoted mechanistic model, is proposed here. It provides estimations of the local heat transfer coefficient that are in excellent agreement with simulations and it might be included in next-generation predictive methods.

Elsevier2013

Experimental investigation of heat transfer and flow characteristics in various geometries of 2-pass internal cooling passages of gas turbine airfoils

Denis Chanteloup

An experimental investigation of the flow and heat transfer characteristics in internal coolant passages of gas turbine airfoils has been conducted. The PIV method was employed for the flow measurements. A stereoscopic PIV system was used and automated. The stereoscopic method allowed measuring the three velocity components in measurement planes. The system was capable of measuring 100 planes in each configuration. Each measurement plane was composed of 30*30 measurement points. The transient liquid crystal technique was adopted for the heat transfer measurements. Full surface Nusselt number distributions were obtained on all the five outer walls of the test models. The transient TLC technique was adapted in large-scale models of internal cooling channels. The gas temperature evolution in location and time was taken into account in the data processing. CFD simulations have been performed in the measured passage configurations. For the calculations, the unstructured flow solver FLUENT/UNS was employed. A test rig was designed and constructed for the experiments to meet the requirements of the intended investigation. For the present investigation, the test section was a large-scale model of a two-pass coolant passage with a sharp 180° bend. Four different coolant passage configurations were tested: A passage with 45° ribs (baseline configuration). A passage similar to the baseline configuration with extraction holes simulating film-cooling extraction. A passage with film-cooling extraction and a turning vane in the bend region. A passage with ribs 50% bigger than in the baseline configuration. This passage also had a turn region back wall angled at 30° to the incoming flow. The four configurations were tested at three Reynolds numbers (25,000, 50,000, 70,000 based on the hydraulic diameter). The configurations with extraction were tested at three extractions (30%, 40%, 50% of the inlet massflow). For the first time, the PIV and TLC techniques were employed simultaneously for a detailed investigation of the turbulent flow and heat transfer characteristics within internal coolant passages connected with 180° turns. The following conclusions can be drawn: 3D-streamlines were extracted from the flow measurements in the various cooling channels. The streamlines underlined the strong influence of both the ribs and the bend geometry on the creation of the secondary flow motion in the channels. The secondary flow motion dominates the heat transfer in the entire cooling channel. In the fully developed region, the rib-induced vortex governs the heat transfer distribution on the ribbed walls behind the ribs, and also on the sidewalls. In the bend region, the bend corner flow cells (with low streamwise velocity motion) deviate the bend incoming flow. They act as if the sharp bend geometry was modified. This geometry modification is very dependant on the studied configuration. The resulting heat transfer distribution is thus strongly configuration dependant. The regions of high heat transfer in the channels have been linked with high impinging flow regions. High gradients of mean impinging velocity components near the walls induce high heat transfer on the wall. In these regions, the Nusselt number showed a good correlation with the Reynolds normal stress corresponding to the impinging velocity. The configurations with extractions have the best thermal performances at all the tested Reynolds numbers. The variation of the extraction ratio does not modify substantially the thermal performances. CFD tools has benefited from the tremendous progress of computing power. 3D simulations of internal cooling configurations are now possible. CFD predictions have gained accuracy in such highly 3D flow problems. The predictions compared well with the measurements, with worst discrepancies of 25%.

EPFL2002