Dropwise cooling: Experimental tests by infrared thermography and numerical simulations

In this paper, infrared thermography is used to measure the transient contact temperature between impinging droplets and hot solid surfaces. Droplets are released onto the heated solid surface of a barium fluoride (BaF₂) disk, which has a high transmittance (about 90%) in the 8–12 μm range (typical of longwave infrared cameras). The interface temperature is measured from below, through the solid material, by infrared thermography. Since the solid is IR-transparent, a black coating layer is used to allow radiative heating of the surface and provide a method to measure the liquid–solid interface temperature. A numerical code is then presented, which simulates the evaporation of water droplets on hot solid surfaces. At the present stage of development, single-phase evaporation is addressed. The three-dimensional energy diffusion equation, discretized using the finite volume method, is employed to model the transient within both the droplets and the solid substrate. The numerical results are validated by comparison with the experimental data.     

Numerical model of evaporative cooling processes in a new type of cooling tower

A numerical model for studying the evaporative cooling processes that take place in a new type of cooling tower has been developed. In contrast to conventional cooling towers, this new device called Hydrosolar Roof presents lower droplet fall and uses renewable energy instead of fans to generate the air mass flow within the tower. The numerical model developed to analyse its performance is based on computational flow dynamics for the two-phase flow of humid air and water droplets. The Eulerian approach is used for the gas flow phase and the Lagrangian approach for the water droplet flow phase, with two-way coupling between both phases. Experimental results from a full-scale prototype in real conditions have been used for validation. The main results of this study show the strong influence of the average water drop size on efficiency of the system and reveal the effect of other variables like wet bulb temperature, water mass flow to air mass flow ratio and temperature gap between water inlet temperature and wet bulb temperature. Nondimensional numerical correlation of efficiency as a function of these significant parameters has been calculated.     

Numerical investigation of the cooling effectiveness of a droplet impinging on a heated surface

Computational fluid dynamics numerical simulations for 2.0 mm water droplets impinging normal onto a flat heated surface under atmospheric conditions are presented and validated against experimental data. The coupled problem of liquid and air flow, heat transfer with the solid wall together with the liquid vaporization process from the droplet’s free surface is predicted using a VOF-based methodology accounting for phase-change. The cooling of the solid wall surface, initially at 120 °C, is predicted by solving simultaneously with the fluid flow and evaporation processes, the heat conduction equation within the solid wall. The range of impact velocities examined was between 1.3 and 3.0 m/s while focus is given to the process during the transitional period of the initial stages of impact prior to liquid deposition. The droplet’s evaporation rate is predicted using a model based on Fick’s law and considers variable physical properties which are a function of the local temperature and composition. Additionally, a kinetic theory model was used to evaluate the importance of thermal non-equilibrium conditions at the liquid–gas interface and which have been found to be negligible for the test cases investigated. The numerical results are compared against experimental data, showing satisfactory agreement. Model predictions for the droplet shape, temperature, flow distribution and vaporised liquid distribution reveal the detailed flow mechanisms that cannot be easily obtained from the experimental observations.     

Heat and mass transfer predictions of the early contact of a liquid metal on an intensely cooled moving substrate

This article describes a CFD model to predict the heat and mass transfer in the region of the initial contact of a liquid metal supplied to a cooled moving substrate. The situation resembles closely the early conditions for solid phase surface formation in many continuous casting operations. For near-net-shape applications where surface finish is important, the article describes a modeling approach for incorporating the key elements of water side cooling, intervening moving substrate, active contact layer, and liquid metal with binary-alloy solidification behavior. These elements provide the necessary macroscale results for incorporating models of the microstructure development of the cast along the surface. For the present article the results are compared to experimental data derived from the continuous casting of Al-4.5 wt%Cu.     

Experimental determination of the interfacial heat transfer during cooling and solidification of molten metal droplets impacting on a metallic substrate: effect of roughness and superheat

The interfacial heat transfer between a solidifying molten metal and a metallic substrate is critical in many processes such as strip casting and spray deposition. As the molten metal cools down and solidifies, the interface undergoes a change from the initial liquid/solid contact to a solid/solid contact, leading to very dynamic variations in the rate of interfacial heat transfer. This article presents the results of an experimental study of the contact heat transfer when molten nickel or copper droplets are dropped on an inclined metallic substrate. The interfacial heat transfer coefficient, h, between the melt and the substrate is evaluated by matching model calculations with the top splat surface temperature history measured by a fast-response pyrometer. The results suggest that a high value of the interfacial heat transfer coefficient h (10⁴ to 3×10⁵ W/m² K) is achieved when the molten splat is in contact with the substrate, followed by a smaller value (<10⁴ W/m² K) during the later stages of solidification and the solid cooling phase. A parametric study was performed to investigate the effect on h of the metal/substrate materials combination, the melt superheat, and the substrate surface roughness, and some of the results are also presented.     

Development and validation of a coupled heat and mass transfer model for green roofs

This paper describes a dynamic model of transient heat and mass transfer across a green roof component. The thermal behavior of the green roof layers is modeled and coupled to the water balance in the substrate that is determined accounting for evapotranspiration. The water balance variations over time directly impact the physical properties of the substrate and the evapotranspiration intensity. This thermal and hydric model incorporates wind speed effects within the foliage through a new calculation of the resistance to heat and mass transfer within the leaf canopy. The developed model is validated with experimental data from a one-tenth-scale green roof located at the University of La Rochelle. A comparison between the numerical and the experimental results demonstrates the accuracy of the model for predicting the substrate temperature and water content variations. The heat and mass transfer mechanisms through green roofs are analyzed and explained using the modeled energy balances, and parametric studies of green roof behavior are presented. A surface temperature difference of up to 25 °C was found among green roofs with a dry growing medium or a saturated growing medium. Furthermore, the thermal inertia effects, which are usually simplified or neglected, are taken into account and shown to affect the temperature and flux results. This study highlights the importance of a coupled evapotranspiration process model for the accurate assessment of the passive cooling effect of green roofs.     

Prediction of micro-explosion delay of emulsified fuel droplets

Burning a water-in-oil emulsion enables reduction in solid and gaseous pollutants in comparison with neat oil. In the emulsion, Heavy Fuel-Oil and water lie in distinct phases, having a high difference in boiling point (up to 200 K). In an emulsion droplet injected and subsequently heated inside a flame, the internal water droplets are enclosed inside the emulsion and do not systematically vaporise at boiling point. They are known to reach a metastable state, breaking up at a temperature below the spinodal limit of water. From this moment, the surrounding Fuel-Oil is fragmented into numerous faster and smaller droplets by the suddenly expanding steam. This physical phenomenon is called “micro-explosion”. This work demonstrates a numerical modelisation of unsteady heat and mass transfer at the surface and inside of the emulsion droplet, and provides a prediction of its micro-explosion delay, using homogeneous nucleation hypothesis. This assumption of homogeneous nucleation for internal water droplets matches the use of a “drop tower” experimental facility. Finally, comparisons between predicted ranges for micro-explosion delays and experimental delays from literature are discussed, along with combustion parameters (ambient temperature, relative velocity) and combustible emulsion parameters. As a result, the experimental and numerical micro-explosion delays decrease with liquid or ambient temperature and relative velocity, and increase with water content and radius of emulsion droplet. Their low average deviation reveals the accuracy of the assumption of homogeneous nucleation in the considered situations.     

CONJUGATE NUMERICAL MODEL FOR COOLING A FLUID FLOWING THROUGH A SPIRAL COIL IMMERSED IN A CHILLED WATER CONTAINER

A conjugate numerical model has been proposed to investigate the problem of cooling a fluid flowing through a spiral coil immersed in a chilled water container, which is common in many beverage dispensers. A simple axisymmetric numerical procedure is described to determine the temperature of the fluid in the spiral coil and that of the coil surface. A one-dimensional heat balance equation for the fluid within the coil is utilized to update the fluid and wall surface temperatures, which are needed to calculate the temperature field in the water container with solid ice walls. The SIMPLE algorithm has been adopted along with the standard k-epsilon turbulence model equations. A reasonably good agreement between the numerical predictions and experimental results has been achieved.     

NUMERICAL SIMULATION OF HEAT TRANSFER IN MIST FLOW

A numerical simulation of heat transfer over a row of tubes, in the presence of mist flow, is described. Computations include the solution of the flow field around the tubes, the prediction of the motion of water droplets, and the evaluation of the cooling effect of the water film on the tube surface. The entire analysis is carried out using FENSAP-ICE (Finite Element Navier-Stokes Analysis Package for In-flight icing), a simulation system developed by Newmerical Technologies for icing applications. The numerical model is described, including the Navier-Stokes solution, the water thin film computation, the droplet impingement prediction, and the conjugate heat transfer procedure. The predictions are verified against experimental data for different droplet mass flow rates, showing satisfactory agreement and allowing a useful insight in the physical characteristics of the problem.     

柴油机冷却水套中无水冷却液的数值模拟分析

运用FLUENT软件对某型号柴油机冷却水套三种无水冷却液在不同温度下的冷却效果进行数值模拟分析.模拟结果表明:由于冷却液表面换热系数的变化受冷却液粘度及导热率的影响,而这两个因素随温度的变化而变化;温度较低时,冷却液的导热率的影响占主导地位,表面换热系数随温度的增大而减小;温度较高时,冷却液粘度的影响占主导地位,表面换热系数随温度的升高而增大.     

Mist film cooling simulation at gas turbine operating conditions

Air film cooling has been successfully used to cool gas turbine hot sections for the last half century. A promising technology is proposed to enhance air film cooling with water mist injection. Numerical simulations have shown that injecting a small amount of water droplets into the cooling air improves film-cooling performance significantly. However, previous studies were conducted at conditions of low Reynolds number, temperature, and pressure to allow comparisons with experimental data. As a continuous effort to develop a realistic mist film cooling scheme, this paper focuses on simulating mist film cooling under typical gas turbine operating conditions of high temperature and pressure. The mainstream flow is at 15 atm with a temperature of 1561 K. Both 2D and 3D cases are considered with different hole geometries on a flat surface, including a 2D slot, a simple round hole, a compound-angle hole, and fan-shaped holes. The results show that 10–20% mist (based on the coolant mass flow rate) achieves 5–10% cooling enhancement and provides an additional 30–68 K adiabatic wall temperature reduction. Uniform droplets of 5–20 μm are used. The droplet trajectories indicate the droplets tend to move away from the wall, which results in a lower cooling enhancement than under low pressure and temperature conditions. The commercial software Fluent is adopted in this study, and the standard k–ε model with enhanced wall treatment is adopted as the turbulence model.     

Numerical simulation of duct flow with fog droplets

Evaporative cooling is a widely used air cooling technique. In this method, evaporation of a liquid in the surrounding air cools the air in contact with it. In the current investigation, numerical simulations are carded out to visualize the evaporation and dynamics of tiny water droplets of different diameters in a long air duct. The effect of initial droplet size on the temperature and relative humidity distribution of the air stream in the duct is investigated. Three different initial conditions of air are considered to verify the influence of ambient conditions. Droplet spray patterns are also analyzed to identify the suitable locations for the spray nozzles within the duct. The resuits obtained are displayed in a series of plots to provide a clear understanding of the evaporative cooling process as well as the droplet dynamics within the ducts.     

On the Successive Impingement of Droplets Onto a Substrate

Numerical simulations of successive impingement of water droplets onto a substrate have been performed. The objective is to understand the hydrodynamics of the impingement process, particularly the interaction between successive droplets. The Navier-Stokes equations are solved using a finite-volume formulation. A two-step projection method is used along with a fixed, nonuniform, staggered rectangular grid. The free surface of the liquid is tracked by the volume-of-fluid method with a second-order-accurate piecewise-linear scheme. A continuum surface force model is used to calculate the surface tension force. The numerical results are in general agreement with experimental data.     

Analysis of three-dimensional heat transfer in micro-channel heat sinks

In this study, the three-dimensional fluid flow and heat transfer in a rectangular micro-channel heat sink are analyzed numerically using water as the cooling fluid. The heat sink consists of a 1-cm² silicon wafer. The micro-channels have a width of 57 μm and a depth of 180 μm, and are separated by a 43 μm wall. A numerical code based on the finite difference method and the SIMPLE algorithm is developed to solve the governing equations. The code is carefully validated by comparing the predictions with analytical solutions and available experimental data. For the micro-channel heat sink investigated, it is found that the temperature rise along the flow direction in the solid and fluid regions can be approximated as linear. The highest temperature is encountered at the heated base surface of the heat sink immediately above the channel outlet. The heat flux and Nusselt number have much higher values near the channel inlet and vary around the channel periphery, approaching zero in the corners. Flow Reynolds number affects the length of the flow developing region. For a relatively high Reynolds number of 1400, fully developed flow may not be achieved inside the heat sink. Increasing the thermal conductivity of the solid substrate reduces the temperature at the heated base surface of the heat sink, especially near the channel outlet. Although the classical fin analysis method provides a simplified means to modeling heat transfer in micro-channel heat sinks, some key assumptions introduced in the fin method deviate significantly from the real situation, which may compromise the accuracy of this method.     

Approximate model for break-up of solidifying melt particles due to thermal stresses in surface crust layer

Fast cooling and solidification of high-temperature droplets of opaque melt is considered. The problem parameters correspond to interaction of core melt with ambient water in hypothetical severe accident in some industrial nuclear reactors. A recently suggested approximation for transient temperature profile in the particle during solidification is employed. This approach is combined with an analytical solution for quasi-steady stress–strain state of growing solid crust layer. A computational analysis showed that the resulting tensile stress on the particle surface is maximal at a certain position of solidification front. The latter is considered to be a reason of mechanical breakage of corium particles at time preceding this stress maximum. The results obtained are in qualitative agreement with recently reported observations of some fragments of thick-wall hollow spherical particles in laboratory experiments.     

3-D modeling of the dynamics and heat transfer characteristics of subcooled droplet impact on a surface with film boiling

The impact of a subcooled water and n-heptane droplet on a superheated flat surface is examined in this study based on a three-dimensional model and numerical simulation. The fluid dynamic behavior of the droplet is accounted for by a fixed-grid, finite-volume solution of the incompressible governing equations coupled with the 3-D level-set method. The heat transfer inside each phase and at the solid–vapor/liquid–vapor interface is considered in this model. The vapor flow dynamics and the heat flux across the vapor layer are solved with consideration of the kinetic discontinuity at the liquid–vapor and solid–vapor boundaries in the slip flow regime. The simulated droplet dynamics and the cooling effects of the solid surface are compared with the experimental findings reported in the literatures. The comparisons show a good agreement. Compared to the water droplet, it is found that the impact of the n-heptane droplet yields much less surface temperature drop, and the surface temperature drop mainly occurs during the droplet-spreading stage. The effects of the droplet’s initial temperature are also analyzed using the present model. It shows that the droplet subcooling degree is related closely to the thickness of the vapor layer and the heat flux at the solid surface.     

Evaporative cooling of water in a mechanical draft cooling tower

A new mathematical model of a mechanical draft cooling tower performance has been developed. The model represents a boundary-value problem for a system of ordinary differential equations, describing a change in the droplets velocity, its radii and temperature, and also a change in the temperature and density of the water vapor in a mist air in a cooling tower. The model describes available experimental data with an accuracy of about 3%. For the first time, our mathematical model takes into account the radii distribution function of water droplets.Simulation based on our model allows one to calculate contributions of various physical parameters on the processes of heat and mass transfer between water droplets and damp air, to take into account the cooling tower design parameters and the influence of atmospheric conditions on the thermal efficiency of the tower. The explanation of the influence of atmospheric pressure on the cooling tower performance has been obtained for the first time.It was shown that the average cube of the droplet radius practically determines thermal efficiency. The relative accuracy of well-defined monodisperse approximation is about several percent of heat efficiency of the cooling tower. A mathematical model of a control system of the mechanical draft cooling tower is suggested and numerically investigated. This control system permits one to optimize the performance of the mechanical draft cooling tower under changing atmospheric conditions.     

Experimental Studies of Nanofluid Droplets in Spray Cooling

Spray cooling is used in cooling of electronic devices to remove large heat fluxes. Heat transfer to droplets impinging on a heated surface and boiling off has been studied. Most work is on a well-controlled system of a single drop falling onto a horizontal heated plate from a fixed height. These have revealed the droplet impingement mechanics to be a function largely of Weber number and excess temperature, and a range of regimes is observed similar to those in pool boiling, with a clearly identifiable critical heat flux. Nanofluids exhibit enhanced boiling heat transfer in pool boiling. The effect of nanoparticles on droplet boil-off was studied in this work. Nanofluid drops were let fall onto a surface at temperature greater than the saturation temperature, and behavior and heat flux were recorded and contrasted to that of a pure fluid. The working fluids used were pure water, ethanol, and dimethyl sulfoxide (DMSO) and ethanol– or DMSO–nanoparticle solutions (the nanoparticles were aluminum, with concentrations of up to 0.1% by weight in DMSO and 3.2% by weight in ethanol). High-speed photographic images of droplet evolution in time were obtained and indicate that there are differences in the behavior of nanofluid droplets as they boil off the surface, compared to pure fluids. Increasing nanoparticle concentration decreases the receding droplet breakup on rebound after impingement and appears to reduce the maximum spreading of a droplet as well. Maximum recoil height is reduced with increasing nanoparticle concentration. Experimental measurements of the heat fluxes associated with the pure and nanofluid droplets did not show significant enhancement, though there was noticeable improvement in the DMSO nanofluids.     

Numerical modelling of heat and mass transfer in finned dehumidifier

In several heat exchange devices, phase transition occurs in a small region adjacent to the wall, and the secondary phase is present only in a thin layer running along the wall, allowing for decoupling between the fluid dynamic computation of the core flow and the numerical analysis of the secondary phase. This happens in finned dehumidifier, but also in spray cooling or defogging problems. In a finned dehumidifier, or in air conditioning evaporators, the secondary phase is provided by moist air condensation, and may consist of discrete droplets, continuous film or a collection of rivulets. Several levels of approximation may be adopted, depending on the specific problem: perfect drain assumption requires only the addition of a heat source in the energy equation, otherwise the water layer behaviour has to be taken into account. Furthermore, a heat and mass transfer analogy may or may not be appropriate; in the latter case, the solution of the diffusion equation of humidity is required.Here, different levels of approximation are compared with literature experimental data for condensation over a vertical fin. Results show that thermal resistance and gravity effects, in the considered geometry, are negligible, and the condensate takes the form of a collection of still droplets, rather than a flowing film. This has an effect on the actual heat transfer and water layer build-up, and the variation of temperature along the fin induces some discrepancy with respect to the straightforward application of the heat and mass transfer analogy.     

Characterization of the heat transfer accompanying electrowetting or gravity-induced droplet motion

Electrowetting (EW) involves the actuation of liquid droplets using electric fields and has been demonstrated as a powerful tool for initiating and controlling droplet-based microfluidic operations such as droplet transport, generation, splitting, merging and mixing. The heat transfer resulting from EW-induced droplet actuation has, however, remained largely unexplored owing to several challenges underlying even simple thermal analyses and experiments. In the present work, the heat dissipation capacity of actuated droplets is quantified through detailed modeling and experimental efforts. The modeling involves three-dimensional transient numerical simulations of a droplet moving under the action of gravity or EW on a single heated plate and between two parallel plates. Temperature profiles and heat transfer coefficients associated with the droplet motion are determined. The influence of droplet velocity and geometry on the heat transfer coefficients is parametrically analyzed. Convection patterns in the fluid are found to strongly influence thermal transport and the heat dissipation capacity of droplet-based systems. The numerical model is validated against experimental measurements of the heat dissipation capacity of a droplet sliding on an inclined hot surface. Infrared thermography is employed to measure the transient temperature distribution on the surface during droplet motion. The results provide the first in-depth analysis of the heat dissipation capacity of electrowetting-based cooling systems and form the basis for the design of novel microelectronics cooling and other heat transfer applications.