Analytical Model for Describing Experimental Results on Parameters Influencing Heat Transfer in Film Boiling with Spray Quenching

An analytically solvable mathematical model is developed to estimate heat transfer quantities in the film boiling region of metal quenching with water sprays. The model is based on the hydrodynamic of a single droplet which is separated from the metal by a vapor film. The temperature profile within the droplet is calculated as semi-infinite body because of the short contact time. It is validated with own experimental results and those from the literature. The influence of size and velocity of the droplet, spray flux, surface temperature, temperature of the cooling water and the salinity level are discussed. The droplet size and velocity play a less significant influence on the heat transfer. The heat transfer coefficient is found to increase linearly with the spray flux. The heat flux is proportional to the difference of boiling and water temperature. With the model it is shown, that even for the high impingement densities the droplet covered area is very small.     

Single-phase and two-phase cooling characteristics of upward-facing and downward-facing sprays

Experiments were performed to ascertain the cooling characteristics of PF-5052 sprays impacting a square heated test surface in an upward orientation. Three full-cone spray nozzles were used to span a broad range of volumetric flux. Also examined were the effects of Sauter mean diameter and subcooling. The present data were compared to prior data for downward-oriented FC-72, FC-87 and water sprays to assess the effects of spray orientation on cooling performance. The combined database facilitated the development of generalized correlations for single-phase heat transfer, nucleate boiling, and critical heat flux (CHF). The nucleate boiling data for different fluids and both upward and downward orientation were fitted using a single correlation based on density ratio, Weber number and Jacob number. A CHF correlation previously developed for downward-oriented sprays was equally successful at predicting the present upward-oriented PF-5052 spray data. Overall, orientation showed no measurable influence on any of the spray cooling regimes examined.     

Characterisation of the spray cooling heat transfer involved in a high pressure die casting process

A systematic experimental study was conducted to examine the heat transfer characteristics from the hot die surface to the water spray involved in high pressure die casting processes. Temperature and heat flux measurements were made locally in the spray field using a heater made from die material H-13 steel and with a surface diameter of 10 mm. The spray cooling curve was determined in the nucleate boiling, critical heat flux, as well as the transition boiling regimes. The hydrodynamic parameters of the spray such as droplet diameters, droplet velocities, and volumetric spray flux were also measured at the position in the spray field identical to that of the test piece. Droplet size and velocity distribution were measured using a PDA system. A new empirical correlation was developed to relate the spray cooling heat flux to the spray hydrodynamic parameters such as liquid volumetric flux, droplet size, and droplet velocity in all heat transfer regimes. The agreement between experimental data and predicted results is satisfactorily good.     

Evaporative heat transfer characteristics of a water spray on micro-structured silicon surfaces

Experiments were performed to evaluate the evaporative heat transfer characteristics of spray cooling of water on plain and micro-structured silicon surfaces at very low spray mass fluxes. The textured surface is made of an array of square micro-studs. It was found that the Bond number of the microstructures is the primary factor responsible for the heat transfer enhancement of evaporative spray cooling on micro-structured silicon surface in the present study. A qualitative study of evaporation of a single water droplet on plain and textured silicon surface shows that the capillary force within the microstructures is effective in spreading the deposited liquid film, thus increasing the evaporation rates. Four distinct heat transfer regimes, which are the flooded, thin film, partial dryout, and dryout regimes, were identified for evaporative spray cooling on micro-structured silicon surfaces. The microstructures provided better cooling performance in the thin film and partial dryout regime and higher liquid film breakup heat flux, because more water was retained on the heat transfer surface due to the capillary force. Heat transfer coefficient and temperature stability deteriorated greatly once the liquid film breakup occurred. The liquid film breakup heat flux increases with the Bond number. Effects of surface material, system orientation and spray mass flux were also addressed in this study.     

Spray cooling characteristics of water and R-134a. Part I: nucleate boiling

An experimental study was made in the first of two papers to determine the effect of liquid sprays used to cool a hot surface. Both pure water and R-134a were served as a working medium sprayed from a single circular nozzle onto a Cu (oxygen free) metal of an electrically heated surface which was heated to an initial temperature with a range of wall superheat for steady-state nucleate boiling experiments using thermocouples for heat transfer measurements. Cooling characteristics (boiling curves) were obtained over a range of spray mass flux, Weber number, wall superheat and degree of subcooling. Boiling visualization was also conducted with varied heat flux levels at a specified We for R-134a and water.     

Molecular Dynamics–Continuum Hybrid Simulation for the Impingement of Droplet on a Liquid Film

A molecular dynamics–continuum hybrid method is used to study the droplet impingement process on a liquid film. The hybrid code is validated by simulating the sudden-start Couette flow and unsteady heat transfer problem. The impingement process is strongly affected by Weber number. At low Weber number, the evolution of the crown after droplet impingement is stable, while at high Weber number the secondary droplets emerge and the splash phenomenon occurs. The effect of liquid film thickness on the evolution of crown diameter is also investigated.     

Spray impingement cooling with single- and multiple-nozzle arrays. Part II: Visualization and empirical models

The performance of single- and multiple-nozzle sprays for high heat flux electronics cooling using nitrogen-saturated FC-72 was studied in a multi-chip module (MCM) test setup, similar to MCM’s used in current high-end computer systems. An additional facility was constructed for visualization of the sprays and heat transfer behavior using clear heating elements coated with an indium tin oxide (ITO) film. Using both the heat transfer and visualization data, it was determined that the heat transfer could be broken down into two or three components: a dominant single-phase component in and around the droplet impact region, a two-phase liquid film boiling component in the corners away from this region, and, for the multiple-nozzle sprays, a single-phase drainage flow component. Empirical models were generated based on this conceptual model, and the correlations predict the data to within about 6%. In addition, a phenomenological critical heat flux (CHF) model was generated based on previous work with thin liquid-film boiling that suggests CHF in thin films occurs due to a homogeneous nucleation mechanism. This model predicts the current data to within about 12% for both single- and four-nozzle arrays.     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

Monodisperse Spray Cooling of Small Surface Areas at High Heat Flux

Spray cooling is an effective method to remove high heat fluxes from electronic components. To understand the physical mechanisms, this work studies heat transfer rates from single and dual nozzle distilled water sprays on a small heated surface (1.3 mm × 2 mm). Thermal ink jet atomizers generate small droplets, 33 μm diameter, at known frequencies, leading to controlled spray conditions with a monodisperse stream of droplets interacting with the hot surface. Of particular interest in this work is the dissipated heat flux and its relation to the liquid film thickness, the surface superheat, and the cooling mass flow rate. Experimental results show the heat flux scales to the cooling mass flow rate. In comparison to published spreading–splashing correlations, these experiments indicate that the drops impinge on the liquid film and spread without generating splashing, leading to high-efficiency stable heat transfer. Surface temperatures range from 120 to 140°C. In addition, the liquid film thickness is investigated in relation to the heater superheat and a stable thin film is seen at superheats beyond 20°C. The efficiency of the spray system is inversely related to the film thickness and may be due to ejection of liquid from the surface due to bursting of vapor bubbles.     

Analysis of non-adiabatic excess enthalpy spray flames

A steady, one dimensional, low speed flame propagating in a dilute, monodisperse, sufficiently off stoichiometric and weakly heterogeneous spray with external heat recirculation is analyzed using activation energy asymptotics. A completely prevaporized mode and a partially prevaporized mode of flame propagation are identified. Heat recirculation is achieved by transferring heat through a tube wall within a given distance L. The external heat transfer results in either globally external heat loss or excess enthalpy burning (which is globally adiabatic) to the spray system with increasing wall temperature. The influences of external heat recirculation and liquid fuel spray on the combustion characteristics of the spray flames are examined with five parameters, namely the heat transfer length for excess enthalpy burning, the heat transfer coefficient, the amount of external heat transfer, the liquid fuel loading and the droplet size. It is found that the extent of flammability is enlarged with increasing heat transfer length and heat transfer coefficient or decreasing external heat loss. The range of flammability is also enlarged with increasing liquid loading or decreasing droplet size for lean sprays, while the opposite holds for rich sprays.     

Experimental study on the interaction of fine water spray with liquid pool fires

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A coupled level set and volume-of-fluid simulation for heat transfer of the double droplet impact on a spherical liquid film

A coupled level set and volume-of-fluid method is applied to investigate the double droplet impact on a spherical liquid film. The method focuses on the analysis of surface curvature, droplet diameter, impact velocity, double droplets vertical spacing, the thickness of the liquid film of two liquid droplets after the impact on a spherical liquid film, and the influence of flow and heat transfer characteristics. The results indicate that the average wall heat flux density of the double liquid droplet impact on a spherical liquid film is greater than that of a flat liquid film. Average wall heat transfer coefficient increases with the increase in the liquid film’s spherical curvature. When the liquid film thickness is smaller, the average wall heat flux density of the liquid film is significantly reduced by the secondary droplets generated from the liquid film. When the liquid film thickness is larger, the influence of liquid film thickness on the average wall heat flux density gradually decreases. The average wall heat flux density increases with the increase in impact velocity and the droplet diameter; it also decreases with the increase in double droplets vertical spacing.     

Vaporization and collision modeling of liquid fuel sprays in a co-axial fuel and air pre-mixer

Droplet collision occurs frequently in regions where the droplet number density is high. Even for Lean Premixed and Pre-vaporized (LPP) liquid sprays, the collision effects can be very high on the droplet size distributions, which will in turn affect the droplet vaporization process. Hence, in conjunction with vaporization modeling, collision modeling for such spray systems is also essential. The standard O’Rourke’s collision model, usually implemented in CFD codes, tends to generate unphysical numerical artifact when simulations are performed on Cartesian grid and the results are not grid independent. Thus, a new collision modeling approach based on no-time-counter method (NTC) proposed by Schmidt and Rutland is implemented to replace O’Rourke’s collision algorithm to solve a spray injection problem in a cylindrical coflow premixer. The so called “four-leaf clover” numerical artifacts are eliminated by the new collision algorithm and results from a diesel spray show very good grid independence. Next, the dispersion and vaporization processes for liquid fuel sprays are simulated in a coflow premixer. Two liquid fuels under investigation are jet-A and Rapeseed Methyl Esters (RME). Results show very good grid independence in terms of SMD distribution, droplet number distribution and fuel vapor mass flow rate. A baseline test is first established with a spray cone angle of 90° and injection velocity of 3 m/s and jet-A achieves much better vaporization performance than RME due to its higher vapor pressure. To improve the vaporization performance for both fuels, a series of simulations have been done at several different combinations of spray cone angle and injection velocity. At relatively low spray cone angle and injection velocity, the collision effect on the average droplet size and the vaporization performance are very high due to relatively high coalescence rate induced by droplet collisions. Thus, at higher spray cone angle and injection velocity, the results expectedly show improvement in fuel vaporization performance since smaller droplet has a higher vaporization rate. The vaporization performance and the level of homogeneity of fuel–air mixture can be significantly improved when the dispersion level is high, which can be achieved by increasing the spray cone angle and injection velocity.     

Theoretical and experimental study of the effects of spray inclination on two-phase spray cooling and critical heat flux

Experiments were conducted with PF-5052 liquid sprays impacting a 1.0 × 1.0 cm² heated test surface at different inclination angles, flow rates, and subcoolings. Inclination angle had no noticeable effect on the single-phase or two-phase regions of the boiling curve. Maximum CHF was always achieved with the spray impinging normal to the test surface; increasing angle of inclination away from the normal decreased CHF appreciably. Video analysis showed inclined sprays produced lateral liquid film flow towards the farthest downstream region of the test surface. The film liquid provided partial resistance to dryout despite the weak volumetric spray flux in the downstream region. A new theoretical model of the spray’s impact area and volumetric flux proves this decrease is the result of a sharp reduction in the fraction of the test surface area that is directly impacted by the spray. Combining the model and video results with a previous point-based CHF correlation for normal sprays is shown to accurately predict the effects of orientation angle on CHF for different nozzles and operating conditions.     

A discrete multicomponent fuel evaporation model with liquid turbulence effects

A new approach to simultaneously account for finite thermal conductivity, finite mass diffusivity and turbulence effects within atomizing multicomponent liquid fuel sprays has been developed in this study. The main contribution of this paper is to incorporate the liquid turbulence effect in modeling the boundary layer heat and mass resistance during multi-component droplet evaporation. The finite conductivity model is based on an existing two-layer film theory, where the turbulence characteristics of the droplet are used to estimate the effective thermal conductivity. The present paper extends the two-layer film theory formulation to include multi-component mass diffusivities within the droplet liquid phase. In this model four regions are considered: the interior region of the droplet, droplet-side interface, gas-side interface, and the surrounding gas phase. Approximate solutions to the quasi-steady energy and mass transfer equations were used to derive an explicit expression for the heat and mass flux from the surrounding gas to the droplet–gas interface, and within the multi-component droplet. Extension of the model to high pressures using the Peng–Robinson equation of state is also considered. The validation study was carried out for a bi-component decane/hexadecane fuel, followed by application studies of complex gasoline–ethanol blended fuels evaporating in hot gas environments.     

Heat and mass transfer of combusting monodisperse droplets in a linear stream

Heat and mass transfer phenomena in fuel sprays is a key issue in the field of the design of the combustion chambers where the fuel is injected on a liquid form. The development and validation of new physical models related to heat transfer and evaporation in sprays requires reliable experimental data. This paper reports on an experimental study of the energy budget, i.e. internal flux, evaporation flux and convective heat flux for monodisperse combusting droplets in linear stream. The evaporation flux is characterized by the measurement of the droplet size reduction by the phase Doppler technique, and the droplet mean temperature, required for the internal and convective heat flux evaluation, is determined by two-color, laser-induced fluorescence. The Nusselt and Sherwood numbers are evaluated from the heat and mass fluxes estimation, as a function of the inter-droplet distance. The results are compared to physical models available in the literature, for moving, evaporating and isolated droplets. A correction factor of the isolated droplet model, taking into account drop-drop interaction on the Sherwood and Nusselt numbers, is proposed.     

The influence of downstream external heat loss on extinction of dilute spray flames

The extinction characteristics of a dilute spray burning in a steady, one-dimensional, low-speed, sufficiently off-stoichiometric, two-phase flow and experiencing downstream external heat loss are analyzed using activation energy asymptotics. The heat transfer mechanism is composed of external heat loss produced by bulk heat conduction from the spray to a downstream tube wall and internal heat loss or heat gain associated with the gasification process for rich or lean sprays. Results show that for both lean and rich sprays, if the liquid droplet is large enough, the S-shaped extinction curve is produced; and it gradually approaches the C-shaped extinction curve with increasing initial droplet size. These interesting characteristics differ from the previous findings based on upstream heat transfer.     

Boiling heat transfer and dryout phenomenon of CO2 in a horizontal smooth tube

Evaporation heat transfer characteristics of carbon dioxide (CO₂) in a horizontal tube are experimentally investigated. The test tube has an inner diameter of 6.0 mm, a wall thickness of 1.0 mm, and a length of 1.4 m. Experiments are conducted at saturation temperatures of 5 and 10 °C, mass fluxes from 170 to 320 kg/m² s and heat fluxes from 10 to 20 kW/m². Partial dryout of CO₂ occurs at a lower quality as compared to the conventional refrigerants due to a higher bubble growth within the liquid film and a higher liquid droplet entrainment, resulting a rapid decrease of heat transfer coefficients. The effects of mass flux, heat flux, and evaporating temperature are explained by introducing unique properties of CO₂, flow patterns, and dryout phenomenon. In addition, the heat transfer coefficient of CO₂ is on average 47% higher than that of R134a at the same operating conditions. The Gungor and Winterton correlation shows poor prediction of the boiling heat transfer coefficient of CO₂ at low mass flux, while it yields good estimation at high mass flux.     

A mixture fraction framework for the theory and modeling of droplets and sprays

A mixture fraction is carefully defined for evaporation and combustion of droplets and sprays. The definition is valid at points in either the liquid or gas phases and care is taken to distinguish between definitions based on conserved scalars appropriate for heat transfer and those for mass transfer. Results are presented for Spalding B numbers and values of the mixture fraction at the droplet surface for the fast chemistry case and for the case where the droplet cannot sustain an envelope flame. The classical theory for an isolated droplet with spherical symmetry yields simple formulae when expressed in mixture fraction terms. New results are then readily obtained for several quantities of interest in spray modeling. The formulation provides a seamless unification of droplet evaporation processes with gas-phase mixing and reaction. Mixing in a turbulent spray jet is identified as a model problem that clarifies the role of large scale structures in the overall mixing process. Important constraints on the parameter space for sprays are shown to be greatly clarified when expressed in the mixture fraction framework. It is shown how the classical approach for segregated flow with Eulerian/Lagrangian modeling of dispersion and transfer processes in turbulent sprays can be upgraded to include fluctuations in the temperature and composition surrounding the droplets on top of those coming from the turbulent velocity fluctuations. Such preliminary calculations that assume a simple chemically reacting system can readily be upgraded using flamelet functions derived from counterflow experiments or computations: these can then form the starting point for full chemistry calculations using such approaches as conditional moment closure.     

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.