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.     

Numerical simulation of fuel sprays at high ambient pressure: the influence of real gas effects and gas solubility on droplet vaporisation

This paper deals with the numerical simulation of the vaporisation of an unsteady fuel spray at high ambient temperature and pressure solving the appropriate conservation equations. The extended droplet vaporisation model accounts for the effects of non-ideal droplet evaporation and gas solubility including the diffusion of heat and species within fuel droplets. To account for high-temperature and high-pressure conditions, the fuel properties and the phase boundary conditions are calculated by an equation of state and the liquid/vapour equilibrium is estimated from fugacities. Calculations for an unsteady diesel-like spray were performed for a gas temperature of 800 K and a pressure of 5 MPa and compared to experimental results for droplet velocities and diameter distribution. The spray model is based on an Eulerian/Lagrangian approach. The comparison shows that the differences between the various spray models are pronounced for single droplets. For droplet sprays the droplet diameter distribution is more influenced by secondary break-up and droplet coagulation.     

A review of spray ignition phenomena: Present status and future research

Theoretical and experimental studies dealing with the spray ignition phenomena are reviewed. Two major topics covered are external-source ignition of liquid fuel sprays and spontaneous spray ignition. Experimental and theoretical investigations of external-source ignition of sprays employing different configurations are discussed first. Three major topics included here are: (i) ignition of quiescent and flowing fuel sprays; (ii) ignition of monodisperse and polydisperse sprays; and (iii) ignition of single-component and multicomponent fuel sprays. Then, experimental studies of autoignition of sprays employing constant-volume enclosures, injection in a uniform air flow, and shock tube techniques, are discussed. Theoretical investigations dealing with spray autoignition phenomena range from phenomenological models to one-dimensional numerical models using global one-step as well as detailed multistep chemistry, and to multidimensional simulations with reduced mechanisms. These models are also discussed in the review. Finally, some advanced topics which are common to both external-source ignition and spontaneous ignition are identified and discussed. An attempt is made to provide a common link between the three dominant ignition modes in sprays, namely individual droplet ignition, droplet cluster ignition, and spray ignition. In a similar manner, common features of external-source ignition and spontaneous ignition of sprays are identified. A general spray ignition model along with important numerical and physical issues are presented. The effect of pressure on spray ignition processes is also discussed. Potential topics for further research are suggested.     

Evolution of liquid and gas phases in multi‐plume spray injection

In this study, the unsteady development of multi‐plume sprays has been investigated by large eddy simulations with Eulerian–Lagrangian multiphase approach for both global spray characteristics and local flow features. Multi‐plume sprays are injected at the injection pressures of 10 MPa and 15 MPa, and the temperature of T_s = 297.65 K into the ambient air at the atmospheric pressure and temperature of T_a = 293.15 K. Experimentally obtained global multi‐plume spray characteristics in terms of spray shape and penetration are used to validate the present numerical simulations. The present numerical predictions for Sauter mean diameter and its temporal variation agree well with the empirical correlations. The predicted droplet size distribution evolves temporally and spatially, and exhibits bimodal distribution, until eventually the mode for small droplet sizes dominates. The spray plumes are found to have limited interaction due to the relatively large orientation angles between the plumes. Because of the momentum transfer from the liquid to gas phase, spray‐induced air jets appear in the multi‐plume sprays. Using vorticity, pressure, and λ₂ − criterion fields, it is shown that the spray‐induced air jets form similar vortical structures as single phase jets. Similarities between the spray‐induced air jets and single phase jets in terms of the shear layer vortical structures such as hairpin‐like vortices improves our understanding of the entrainment and mixing processes in multi‐plume sprays. Copyright © 2016 John Wiley & Sons, Ltd.     

Flame structure in fuel rich mono-dispersed sprays

The flame structure and the mechanism of the flame propagation in fuel sprays is studied through a one-dimensional, laminar, monodispersed spray of n-octane fuel. A hybrid Eulerian-Lagrangian method is used in this analyses. The results show that for sprays with small initial droplet radii (e.g., γ_κ = 29.6 μm), the flame structure resembles that of a premixed gaseous combustion. However, as the droplet size is increased, the flame becomes more heterogeneous. When droplet interaction is added to the model the heterogeneity of the flame is enhanced and large fluctuations both in the flame temperature and fuel vapor concentrations are observed.     

Mechanisms of film boiling heat transfer of normally impacting spray

The heat transfer mechanisms of horizontally impacting sprays were studied experimentally. An impulse-jet liquid spray system and a solid particle spray system were used. The liquid spray system is capable of producing uniform droplets with the independent variables of droplet size, velocity, liquid flow rate, and air velocity. The horizontally impacting sprays give a lower heat transfer at film boiling than the corresponding vertically impacting spray. The film boiling heat transfer is mainly controlled by the liquid mass flux. At low liquid mass flux and low droplet Weber number, the heat transfer increases with the droplet Weber number. At high droplet Weber number or high liquid mass flux, the heat transfer is not significantly affected by the droplet Weber number.     

Analytical and computational methodology for modeling spray quenching of solid alloy cylinders

Heat-treating of solid alloy cylinders is an important practical problem for which no optimal production methods have been developed, especially in terms of the most crucial quenching stage. This study explores the use of spray quenching as an alternative to the commonly used bath quenching, which is known to yield relatively slow quench rates and provide few options for spatial optimization of cooling rate. A carefully configured spray cooling system is examined, which provides maximum coverage of the surface of a solid alloy cylinder with full-cone pressure sprays. A new analytical model is derived to determine the shape and size of the spray impact zone, as well as the distribution of volumetric flux across the curved surface of the cylinder. This distribution is combined with heat transfer correlations for all spray boiling regimes to generate a local boiling curve for every location across the impact surface. Using these boiling curves as boundary conditions, a transient analysis is conducted for aluminum alloy and steel cylinders. Increasing the nozzle pressure drop or decreasing the orifice-to-surface distance are shown to hasten the exit from the poor film boiling regime to the more efficient transition boiling regime, resulting in a quicker quench. Relatively high thermal diffusivity causes faster transmission of the spray cooling effect through the cylinder and milder temperature gradients in aluminum compared to steel. This also causes the outer surface to cool earlier but deeper points much slower for steel. Large temperature gradients are encountered on the surface during the quench because of different boiling regimes occurring at different locations exposed to the spray. This study highlights several practical advantages of spray quenching compared with bath quenching, including the ability to achieve a wide range of fast quench rates, uniformity and predictability of quench rate, and the ability to predict and guard against imperfections caused by thermal stresses.     

Vapor/liquid phase interaction in flare flashing sprays used in dermatologic cooling

Little knowledge exists concerning the atomization mechanisms and dispersion of flashing sprays in dermatologic cooling. This study examines flashing of a high superheat fluid flowing through micro tube nozzles resembling current medical devices. A one-dimensional, semi-empirical model of refrigerant flow through capillary tubes is used to quantify internal flow characteristics. These results provide nozzle exit conditions that are then correlated to external spray characteristics determined experimentally. One-dimensional expressions for external vapor/liquid interaction are developed to determine evolution of droplet size distribution and explain measured droplet accelerations near the nozzle exit. Droplet drag coefficients are subsequently calculated and compared to existing literature.     

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.     

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The lowest surface temperature possible for the existance of spray evaporative cooling is determined experimentally to be a linear function of the impinging spray mass flux. A conduction-controlled analytical model of droplet evaporation gives fairly good agreement with experimental measurements at atmospheric pressure. At reduced pressures droplet evaporation rates are decreased significantly such that an optimum operating pressure exists for each desired surface heat flux. The initiation of the ‘Leidenfrost state’ provides the upper surface temperature bound for spray evaporative cooling.     

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.     

Spherical-shaped ice particle production by spraying water in a vacuum chamber

A theoretical and experimental study was performed to examine the water spray evaporation method for ice particle production. The conditions for the formation of ice particles were investigated theoretically by the diffusion-controlled evaporation model. The prediction by the model was proved to agree relatively well with experiments. The production of cold storage heat will increase almost proportionally to the number of spray nozzles because no substantial difference was found in the mean droplet size of the overlapped sprays from twin nozzles. Finally, based on the results, the vacuum chamber was designed, and spherical ice particles of size below 300 μm were experimentally obtained by spraying water droplets of ambient temperature in the vacuum chamber where pressure is maintained below the freezing point of water. From the experiment for producing ice particles, it was found that the spray flow rate influences the performance of the system more than the position of spray nozzle.     

Cooling characteristics of an impinging spray jet which forms an ellipsoidal liquid film

The cooling characteristics of an impinging spray jet which forms an ellipsoidal liquid film were experimentally investigated in order to estimate the cooling performance of a rotating roll in a hot mill system. The following four conclusions were reached in the study. (1) In the case of a single spray jet, the local heat transfer coefficient at the center position depends on the forced convective heat transfer by the impinging jet. However, the average heat transfer coefficient is proportional to the flow rate density of the cooling water, and it does not depend on the distance between the nozzle and heated surface. (2) In the case of a double spray jet, liquid film interference occurs. The local heat transfer coefficient at the center position is greater, and the cooling performance increases with the increasing flow rate density of the cooling water. (3) The cooling performance of a multispray jet is proportional to the flow rate density of the cooling water. It does not depend on the nozzle construction, distance, or specifications. Also, there is no relation to the liquid film interference. (4) When the optimum specifications of the spray nozzle are used, thermal analysis of a rotating roll shows that the temperature at a depth of 1.3 mm from the surface is below 130 °C. © 2000 Scripta Technica, Heat Trans Asian Res, 29(4): 280–299, 2000     

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.     

Percolation theory for flame propagation in non- or less-volatile fuel spray: A conceptual analysis to group combustion excitation mechanism

A percolation theory for flame propagation in non- or less-volatile fuel spray is developed based on a cubic lattice model representing a local spray state. The interdroplet flame propagation characteristics found from microgravity experiments on flame spread along a linear droplet array are applicable to describing interdroplet flame propagation between neighboring droplets in any distribution of droplets because the effect of heat conduction from the flame front is shielded by the nearest unburned droplet, which acts as a heat sink. Thus, once the method by which the unburned droplet nearest to the flame front is ignited is identified and formulated into a simple algorithm rule, we can examine by computer simulation the statistical flame propagation behavior in a non- or less-volatile fuel spray in the framework of the percolation theory. In non- or less-volatile fuel, an unburned droplet swallowed by an envelope diffusion flame of other droplets is heated and becomes a new supplier of fuel vapor to the flame front, allowing the flame front to advance. For randomly distributed droplets, the flame front selects the path that minimizes its propagation time. These two phenomena occur when the grid spacing of the cubic lattice model is equal to the maximum flame radius of an isolated droplet immersed in the same air conditions as the local spray state. Furthermore, physical considerations reveal that the lattice size that leads to statistically meaningful information can be rather small, i.e., 20×20×20 vertices. Therefore, the proposed percolation theory is tractable and useful in finding the probability that a flame front propagates across a spray element and for exploring the mechanism of the excitation of group combustion for non- or less-volatile fuel sprays.     

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.     

Large eddy simulation of dilute reacting sprays: Droplet evaporation and scalar mixing

Large eddy simulation (LES) of turbulent reacting sprays is performed to investigate the interactions of droplet evaporation and subfilter scalar mixing processes. A stochastic method is proposed to generate the subfilter fluctuations in gas-phase reactive scalars in the framework of a mixture-fraction-based combustion model. The subfilter fluctuations of the gas-phase temperature and composition, seen by droplets, are used to refine the estimates of the interphase heat/mass transfer rates. Gas-phase combustion is described by the flamelet progress variable approach. The effects of droplet evaporation on subfilter scalar mixing are considered by solving the transport equation for the subfilter mixture fraction variance. The mixture fraction that is valid instantaneously in both the gas and the liquid phases is adopted and its implication on the modeling of the evaporation source term in the subfilter variance equation is discussed. The modeling approach has been applied to the Sydney dilute reacting sprays. To account for uncertainty in the modeling of scalar dissipation rates in spray flames, a parametric study is performed for the constant in the scalar dissipation model for the subfilter variance equation. The effects of subfilter fluctuations on droplet evaporation are found to depend on the inflow condition of the pre-evaporated gas-phase mixture and the liquid injection rate in the present dilute reacting sprays.     

A General Matrix Approach to Model Steady-State Performance of Cross-Flow Heat Exchangers

A steady-state performance model of multirow multipass cross-flow tubular heat exchangers is developed. The proposed matrix approach uses the concepts of local effectiveness, energy balance, and number of transfer units (NTU) applied to every pass/row in the cross-flow heat exchanger to predict thermal performance. The method can predict the total effectiveness of assemblies of heat exchangers. Several circuiting configurations, such as overall counter-cross-flow, overall parallel cross-flow, and fluids in parallel in one of the streams, were considered. Predictions of the steady heat transfer performance of selected multirow multipass cross-flow heat exchangers are obtained by applying the general matrix approach. The heat exchanger geometries selected for the comparative study represent common cross-flow heat exchanger configurations used in industry. For these heat exchangers the overall heat exchanger effectiveness values were computed for various capacity rate ratios and NTU values. The validity of the matrix approach was then verified by comparing the resulting predictions with those obtained using the P-NTU approach and the Domingos method for the selected complex cross-flow heat exchanger configurations.     

直喷汽油机中空锥形燃油喷雾的雾化和蒸发模型

高压旋流中空燃油喷雾日益广泛地应用于缸内直喷(GDI)汽油机中，为此发展了一种适合于模拟这种燃油喷雾雾化过程的薄膜喷雾模型．燃油薄膜的破碎过程采用表面波破碎理论来模拟．对Spalding蒸发模型和油滴阻力模型进行了改进，用来计算油滴的蒸发和阻力变形过程，同时引入初始喷雾液团的计算模块．在多维内燃机计算程序KIVA3的基础上建立了改进的数值计算模型，并对不同喷射条件下的定容压力容器中空旋流燃油喷雾过程进行了数值计算，对计算和实验所得的喷雾特性包括油束外形结构，油束喷雾贯穿度和油滴粒径进行了详细的比较，同时对单液滴的蒸发过程也进行了数值计算，油束模型的计算结果与实验结果吻合良好。     

Radiation driven evaporation for polydisperse water sprays

This study concerns the prediction of radiation heat transfer in evaporating water sprays for a 1D planar media. The spray evolution is described by a Lagrangian sectional approach with the initial diameter size classes defined by normal and log–normal distributions. The spray and the gas-phase radiative properties are recast in terms of cumulative distribution functions (CDF) for use with a correlated-k approach to solve the radiative transfer equation (RTE). The spectral properties required for constructing the CDFs for the droplets and gas are determined using Mie theory and the HITEMP databases, respectively. Cases are conducted to explore the sensitivity of radiative energy attenuation to time evolving droplet size distributions as a function of initial distribution, distance to the energy source, volume fraction and temperature. Results from this study show that the PDFs generate a positive skewness due to the size dependent absorption properties of the droplet. These findings suggest that the droplet size distribution can be adequately described by prescribed, non-symmetrical PDFs that are parameterized by lower order moments.