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.     

Comparative Investigation on Droplet Evaporation Models for Modeling Spray in Cross-Flow

The coupling model of flow and heat and mass transfer for gas-spray droplet two-phase flow has been developed to simulate the evaporating spray in cross-flow. The correlations used for describing the droplet evaporation and motion in convective flow have been compared. The comparisons of calculated results show that the different correlations for determining Nusselt number and Sherwood number impose a significant influence on the lifetime of droplet. The modification of Nusselt number and Sherwood number with regard to the heat and mass boundary around the droplet is of great importance, while different mixing laws for mixture properties and different drag coefficient equations only demonstrate a slight effect on the evaporation characteristics of droplet. The characteristics of spray droplets and cross-flow in terms of both evaporation and motion are obtained. The secondary flow phenomenon is observed in the simulation results and contributes to achieving a more even distribution of temperature and an improved mixing effect of the vapor and cross-flow.     

Interacting effects of uniform flow, plane shear, and near-wall proximity on the heat and mass transfer of respiratory aerosols

Individual and interacting effects of uniform flow, plane shear, and near-wall proximity on spherical droplet heat and mass transfer have been assessed for low Reynolds number conditions beyond the creeping flow regime. Validated resolved volume simulations were used to compute heat and mass transfer surface gradients of two-dimensional axisymmetric droplets and three-dimensional spherical droplets near planar wall boundaries for conditions consistent with inhalable aerosols (5 ? d ? 300 μm) in the upper respiratory tract. Results indicate that planar shear significantly impacts droplet heat and mass transfer for shear-based Reynolds numbers greater than 1, which occur for near-wall respiratory aerosols with diameters in excess of 50 μm. Wall proximity is shown to significantly enhance heat and mass transfer due to conduction and diffusion at separation distances less than five particle diameters and for small Reynolds numbers. For the Reynolds number conditions of interest, significant non-linear effects arise due to the concurrent interaction of uniform flow and shear such that linear superposition of Sherwood or Nusselt number terms is not allowable. Based on the validated numeric simulations, multivariable Sherwood and Nusselt number correlations are provided to account for individual flow characteristics and concurrent non-linear interactions of uniform flow, planar shear, and near-wall proximity. These heat and mass transfer correlations can be applied to effectively compute condensation and evaporation rates of potentially toxic or therapeutic aerosols in the upper respiratory tract, where non-uniform flow and wall proximity are expected to significantly affect droplet transport, deposition, and vapor formation.     

Monodisperse droplet heating and evaporation: Experimental study and modelling

Results of experimental studies and the modelling of heating and evaporation of monodisperse ethanol and acetone droplets in two regimes are presented. Firstly, pure heating and evaporation of droplets in a flow of air of prescribed temperature are considered. Secondly, droplet heating and evaporation in a flame produced by previously injected combusting droplets are studied. The phase Doppler anemometry technique is used for droplet velocity and size measurements. Two-colour laser induced fluorescence thermometry is used to estimate droplet temperatures. The experiments have been performed for various distances between droplets and various initial droplet radii and velocities. The experimental data have been compared with the results of modelling, based on given gas temperatures, measured by coherent anti-stokes Raman spectroscopy, and Nusselt and Sherwood numbers calculated using measured values of droplet relative velocities. When estimating the latter numbers the finite distance between droplets was taken into account. The model is based on the assumption that droplets are spherically symmetrical, but takes into account the radial distribution of temperature inside droplets. It is pointed out that for relatively small droplets (initial radii about 65 μm) the experimentally measured droplet temperatures are close to the predicted average droplet temperatures, while for larger droplets (initial radii about 120 μm) the experimentally measured droplet temperatures are close to the temperatures predicted at the centre of the droplets.     

Energetic budget on an evaporating monodisperse droplet stream using combined optical methods: Evaluation of the convective heat transfer

Aerothermal properties in a fuel spray is a central problem in the field of the design of the combustion chambers of automotive engines, turbojets or rocket engines. Heat and mass transfer models are necessary in the predictive calculation schemes used by the motorists. Reliable experimental data must be obtained for both the validation and development of new physical models linked to heat transfer and evaporation in sprays, where aerodynamic interactions have a key role. This paper proposes an experimental study of the energetic budget of a monodisperse ethanol droplet stream, injected in the thermal boundary layer of a vertical heated plate. The droplet size reduction is measured using a light scattering technique (interferential method) in order to characterize the evaporation, as the droplet mean temperature is monitored using the two colors laser-induced fluorescence technique. The convection heat transfer coefficient and the Nusselt number are inferred from the overall energetic budget, as a function of the inter-droplet distance, characterizing the interaction regime. The results are compared to physical models combined with numerical simulations available in the literature, for moving, evaporating isolated droplets and for three droplets arrangement in linear stream.     

Marangoni convection flow and heat transfer characteristics of water–CNT nanofluid droplets

ABSTRACT

The heat transfer characteristics of liquid droplets are influenced by the hydrophobicity of the surfaces. Fluid properties and surface energy play important roles in heat transfer assessment. In the present study, the influence of the contact angle on the flow field developed inside a nanofluid droplet consisting of a mixture of water and carbon nanotubes (CNT) is investigated. Flow field and heat transfer characteristics are simulated numerically in line with the experimental conditions. It is found that the flow velocity predicted numerically is in good agreement with the experimental data. Nusselt and Bond numbers increase at large contact angles and Marangoni force dominates over buoyancy force.     

Natural convection heat and mass transfer of non-Newtonian power law fluids with yield stress in porous media from a vertical plate with variable wall heat and mass fluxes

This work studies the heat and mass transfer by natural convection from a vertical plate with variable wall heat and mass fluxes in a porous medium saturated with a non-Newtonian power law fluid with yield stress for the general case of power law variations in wall heat and mass fluxes. The governing equations are transformed into a dimensionless form by the similarity transformation and then solved by a cubic spline collocation method. Results are presented for velocity, temperature, and concentration profiles, as well as the Nusselt and Sherwood numbers for various parameters of the power law fluid with yield stress in porous media. The existence of threshold pressure gradient in the power law fluids tends to decrease the fluid velocity and the local Nusselt and Sherwood numbers. An increase in the power law exponent increases the local Nusselt and Sherwood numbers.     

Heat transfer and flow field in a pipe with sinusoidal wavy surface—I. Numerical investigation

The majority of publications in the field of convective transport enhancement in conduits with wavy walls have provided the distribution of the mean Sherwood or Nusselt number per wavelength. The mechanisms, however, driving the increase in heat and mass transfer have not been clearly understood so far. This paper presents the results of a detailed numerical investigation of local heat and mass transfer enhancement in a pipe with sinusoidally varying diameter, covering a wide range of Reynolds numbers from laminar to turbulent flow. The discussion is focused on the predicted flow field and the turbulence structure, allowing a better understanding of the calculated Sherwood and Nusselt numbers. Part II of this paper deals with the experimental validation of the numerically achieved results.     

Soret and Dufour effects on heat and mass transfer by natural convection from a vertical truncated cone in a fluid-saturated porous medium with variable wall temperature and concentration

This work studies the Soret and Dufour effects on the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a fluid-saturated porous medium. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary layer equations are solved by the cubic spline collocation method. Results for local Nusselt number and the local Sherwood number are presented as functions of Soret parameters, Dufour parameters, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to decrease the local Nusselt number, while it tends to increase the local Sherwood number. An increase in the Soret number leads to an increase in the Nusselt number and a decrease in the Sherwood number from a vertical truncated cone in a fluid-saturated porous medium. The local Nusselt number and the local Sherwood number of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents.     

Numerical simulation of laminar flow development with heat and mass transfer in PEM fuel cell flow channels having oxygen and hydrogen suction at one channel wall

Numerical simulation has been carried out of the fluid flow, heat and mass transfer for the developing laminar flow in polymer electrolyte membrane (PEM) fuel cell cathode and anode flow channels, respectively. Each flow channel is considered to be composed of two parallel walls, one porous (simulating electrode surface) and one non‐porous, or impermeable, wall (simulating bipolar plate surface). Various flow situations have been analyzed, and the local and the averaged friction coefficient, Nusselt number for heat transfer and Sherwood number for mass transfer are determined for various flow conditions corresponding to different stoichiometries, operating current densities and operating pressures of the cell. The effect of suction or injection (blowing) wall boundary condition has also been investigated, corresponding to the oxygen consumption in the cathode and hydrogen consumption in the anode. Correlations for the averaged friction coefficient, Nusselt and Sherwood numbers are developed, which can be useful for PEM fuel cell modeling and design calculations. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental and numerical investigation of droplet evaporation under diesel engine conditions

Evaporation of mono-disperse fuel droplets under high temperature and high pressure conditions is investigated. The time-dependent growth of the boundary layer of the droplets and the influence of neighboring droplets are examined analytically. A transient Nusselt number is calculated from numerical data and compared to the quasi-steady correlations available in literature. The analogy between heat and mass transfer is tested considering transient and quasi-steady calculations for the gas phase up to the critical point for a single droplet. The droplet evaporation in a droplet chain is examined numerically. Experimental investigations are performed to examine the influence of neighboring droplets on the drag coefficients. The results are compared with drag coefficient models for single droplets in a temperature range from T = 293–550 K and gas pressure p = 0.1–2 MPa. The experimental data provide basis for model validation in computational fluid dynamics.     

Condensation on a spray of water drops: A cell model study-I. Flow description

A unit cylinder cell model with a body-fitted coordinate system is employed to analyze the hydrodynamics and heat transfer associated with steam condensation on a spray of equal sized water droplets. The droplets are assumed to be moving in the intermediate Reynolds number regime, Re_g = O(100). The distance between neighboring droplet centers is allowed to be arbitrary in the plane of motion, but the droplets are assumed to be uniformly spaced in the plane perpendicular to the direction of motion. Furthermore, once a particular configuration of the droplets is set, the subsequent spacings between the droplet centers in that configuration are taken to remain constant during the entire condensation process. The formulation entails a simultaneous numerical solution of the quasi-steady elliptic partial differential equations that describe the flow field in both the dispersed and continuous phases in each cell. In part 1 of this study, the results for the velocity, surface pressure and drag are presented. In part II of this study, the results for the condensation induced velocities, surface shear stress, the Nusselt number and the Sherwood number are provided. In both parts of the study, the interactions between neighboring drops have been examined.     

Laminar droplet flow in combined hydrodynamically and thermally developing region of circular tubes

Forced convective heat transfer to laminar droplet flow in the combined hydrodynamically and thermally developing region of a circular tube is studied numerically for constant heat flux conditions. The saturated liquid droplets in the vapor flow are considered as equivalent heat sinks distributed in the superheated vapor stream. Numerical calculations are performed for the variations of droplet size, mean vapor velocity, and the local Nusselt number in the streamwise direction until the single-phase fully developed condition is reached. The important roles of the liquid droplets and the developing vapor velocity on the forced convective heat transfer to droplet flow in the combined entrance region of a circular tube are clearly demonstrated.     

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.     

Investigation of heat and mass transfer between the two phases of an evaporating droplet stream using laser-induced fluorescence techniques: Comparison with modeling

Heat and mass exchanges between the two phases of a spray is a key point for the understanding of physical phenomena occurring during spray evaporation in a combustion chamber. Development and validation of physical models and computational tools dealing with spray evaporation requires experimental databases on both liquid and gas phases. This paper reports an experimental study of evaporating acetone droplets streaming linearly at moderate ambient temperatures up to 75 °C. Two-color laser-induced fluorescence is used to characterize the temporal evolution of droplet mean temperature. Simultaneously, fuel vapor distribution in the gas phase surrounding the droplet stream is investigated using acetone planar laser-induced fluorescence.Temperature measurements are compared to simplified heat and mass transfer model taking into account variable physical properties, droplet-to-droplet interactions and internal fluid circulation within the droplets. The droplet surface temperature, calculated with the model, is used to initiate the numerical simulation of fuel vapor diffusion and transport in the gas phase, assuming thermodynamic equilibrium at the droplet surface. Influence of droplet diameter and droplet spacing on the fuel vapor concentration field is investigated and numerical results are compared with experiments.     

Heat and mass transfer in a randomly packed hollow fiber membrane module: A fractal model approach

Hollow fiber membrane modules are widely used in various industries. The disordered nature of hollow fiber distributions in the module exhibits the existence of a fractal structure formed by the voids between the fibers. The area fractal dimension of the voids on the module cross section is obtained. Then the shell side flow distribution and convective heat and mass transfer are investigated based on the fractal theory developed. An experimental work where an air flow in the shell side is humidified by a water flow in the tube side is performed to validate the model. It is found that the model predicts the flow distribution and the heat and mass transfer deteriorations well with local data for a triangular array. With the model, friction factor and Sherwood number deteriorations which take into account of the degree of irregularity, in terms of fractal dimension, are analyzed. The results show that the higher the packing density is, the less the fractal dimension is, and the less the non-uniformity of the flow distribution is. The Sherwood and Nusselt numbers of a randomly distributed fiber module are only 1–5% of a uniformly spaced tube array. Correlations are proposed for the estimation of friction factor and Sherwood numbers considering the degree of irregularity. The predictions are also compared to the available mass transfer correlations in the literature.     

Soret and Dufour effects on free convection boundary layers over an inclined wavy surface in a porous medium

This work studies the heat and mass transfer characteristics of natural convection near a vertical wavy cone in a fluid saturated porous medium with Soret and Dufour effects. The surface of the wavy cone is kept at constant temperature and concentration. The governing equations are transformed into a set of coupled differential equations, and the obtained boundary layer equations are solved by the cubic spline collocation method. The heat and mass transfer characteristics are presented as functions of Soret parameter, Dufour parameter, half angle of the cone, Lewis number, buoyancy ratio, and dimensionless amplitude. Results show that an increase in the Dufour parameter tends to decrease the local Nusselt number, and an increase in the Soret parameter tends to decrease the local Sherwood number. Moreover, a greater half angle of the cone leads to a greater fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinates.     

Integral treatment of coupled heat and mass transfer by natural convection from a cylinder in porous media

This paper deals with the study of the buoyancy induced heat and mass transfer from a slender body of revolution embedded in a saturated porous medium. The study has reported the important case of a cylinder with linear temperature and concentration distributions. The governing parameters for the problem under study are buoyancy ratio (N) and Lewis number (Le). The numerical values of local Nusselt and local Sherwood numbers have also been computed for a wide range of N and Le. The results pertaining to the variations of local Nusselt number, local Sherwood number, N and Le with one another have been studied graphically, and it has been concluded that the local Nusselt number decreases while the local Sherwood number increases along with N > 0 for increasing Lewis number. The local Nusselt number decreases while the local Sherwood number increases along with Le for positive values of N. Also the boundary layer thickness ratio decreases along with Le for N > = 0. In this study, an integral method of Von-Karman type has been used in order to obtain mathematical expressions for local Nusselt and local Sherwood numbers.     

Soret and Dufour effects on free convection boundary layer over a vertical cylinder in a saturated porous medium

This paper deals with an analysis of the Soret and Dufour effects on the boundary layer flow due to free convection heat and mass transfer over a vertical cylinder in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A suitable coordination transformation is used to derive the similar governing boundary-layer equations, and the cubic spline collocation method is then employed to solve the similar governing boundary-layer equations. The variation of the Nusselt number and the Sherwood number with the Dufour parameter and the Soret parameter for various Lewis numbers and buoyancy ratios have been presented in this work. Results show that an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number. The local Nusselt number tends to decrease as the Dufour parameter is increased. Moreover, an increase in the Lewis number enhances the effect of the Dufour parameter on the local Nusselt number.     

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.