Total Droplet Surface Area Research Articles

On the interaction of Taylor length-scale size droplets and homogeneous shear turbulence

The main objective of the present work is to explain the physical mechanisms occurring in droplet-laden homogeneous shear turbulence (HST) with a focus on the modulation of turbulence kinetic energy (TKE) caused by the droplets. To achieve such an objective, first, we performed direct numerical simulations (DNS) of HST laden with droplets of initial diameter approximately equal to twice the Taylor length scale of turbulence, droplet-to-fluid density and viscosity ratios equal to ten and a 5 % droplet volume fraction. We investigated the effects of shear number and Weber number on the modulation of TKE for $Sh \approx 2$ and $4$ , and $0.02 \le {{We_{rms}}} \le 0.5$ . Then, we derived the TKE equations for the two-fluid, carrier-fluid and droplet-fluid flow in HST and the relationship between the power of surface tension and the rate of change of total droplet surface area, providing the pathways of TKE for two-fluid incompressible HST. Our DNS results show that, for ${{We_{rms}}} = 0.02$ , the rate of change of TKE is increased with respect to the single-phase cases, for ${{We_{rms}}} = 0.1$ , the rate of change of TKE oscillates near the value for the single-phase cases and, for ${{We_{rms}}} = 0.5$ , the rate of change of TKE is decreased with respect to the single-phase cases. Such modulation is explained from the analysis of production, dissipation and power of surface tension in the carrier-fluid and droplet-fluid flows. Finally, we explain the effects of droplets on the production and dissipation rate of TKE through the droplet ‘catching-up’ mechanism, and on the power of the surface tension through the droplet ‘shearing’ mechanism.

Simulation Study of the Swirl Spray Atomization of a Bipropellant Thruster under Low Temperature Conditions

The spray atomization of an injector significantly influences the performance and working life span of a bipropellant thruster of a spacecraft. Deep space exploration requires the thruster to be able to operate reliably at a low temperature range from −40 °C to 0 °C, so the effect of low temperature conditions on the atomization characteristics of injector spray is motivated to be comprehensively investigated. To study the swirl atomization characteristics of MMH (methylhydrazine), which is more difficult to atomize than NTO (nitrogen tetroxide), numerical simulations were conducted, employing the methods of VOF (volume of fluid) and LES (large eddy simulation) under low temperature conditions. The physical model with a nozzle size of 0.5 mm and boundary conditions with a velocity inlet of 3.89 m/s both follow the actual operation of thrusters. The development of spray atomization at low temperatures was observed through parametric comparisons, such as spray velocity, liquid total surface area, droplet particle size distribution, spray cone angle and breakup distance. When the temperature decreased from 20 °C to −40 °C at the same condition of flowrate inlet, those atomization characteristics of MMH propellant vary following these rules: the spray ejection velocity of MMH is significantly reduced by 7.7%, and gas-liquid disturbance sequentially decreases; the liquid film development is more stable, with a negative influence on atomization quality, causing difficulties for primary and secondary breakup, so the total surface area of droplets also decreases by 6.4%; the spatial distribution characteristics, spray cone angle and breakup distance vary less than 5%. Therefore, the low temperature condition can directly lower the combustion efficiency of thrusters with obvious performance degradation, but there are no significant changes in the propellant mixing and liquid film cooling. It is concluded that the bipropellant thruster can reliably work at low temperatures around −40 °C for deep space probe operation.

The impact of ethanol addition on the droplet combustion mechanism of saturated and unsaturated fatty acid/fatty acid methyl ester molecules

The combustion of biodiesel requires complex analysis because it is composed of multicomponent constituents. The use of additives in biodiesel is an option widely used to improve the combustion performance of the fuel blend. The droplet combustion characteristics of single compounds of biodiesel and vegetable oil constituents with ethanol additives were investigated under normal gravity at room temperature and atmospheric pressure. This study reveals the different combustion mechanisms and their interactions with ethanol between laurate and oleate as the base fuel. Ethanol breaks the base fuel into smaller molecular aggregates, reducing the fuel blend density with many larger gaps between the clusters. Thermal expansion and child droplet ejection are key mechanisms that effectively increase the total droplet surface area, causing an increase in the diffusion contact between the fuel vapor and the air. Three mechanisms of child droplet ejection occur during the heating phase until the microexplosive combustion phase. The period of child droplet ejection during the microexplosive combustion phase is determined by the boiling point difference and the solubility level between the base fuel and ethanol. The addition of ethanol increases the burning rate of the fuel mixture with a higher peak temperature in the laurate-ethanol blend compared to the base fuel. Ethanol plays an important role in delaying the start of evaporative cooling with a significant temperature increase rate. This behavior is an effective mechanism to initiate droplet combustion with a short ignition delay time.

Numerical analysis of heat transfer between a wall and diesel spray: Effect on ignition characteristics

The heat transfer between the wall and spray has an important effect on the in-cylinder ignition characteristics of the diesel engine, especially during cold start conditions. To better understand the effect of heat transfer between the wall and spray at different wall temperatures on the ignition characteristics, a numerical analysis was conducted with a large-eddy simulation (LES) based on optical experiments. The results show that the spray/wall interaction led to a smaller Sauter mean diameter (SMD) and more small and large droplets compared to the free spray. Furthermore, the total surface area of droplets increases, and heat transfer between droplets and the surrounding hot gas is promoted, which is conducive to the ignition process. On the other hand, when the wall temperature is low, the spray is cooled by the wall during impingement, thus inhibiting ignition. As a result of this competing effect, the air entrainment rate increases with the increase of wall temperature due to the cooling effect weakening and gradually changing to a heating effect. However, when the wall surface temperature increases to a high temperature, the heating effect is suppressed and the local heat transfer coefficient decreases due to the Leidenfrost effect. It is worth emphasizing that the Leidenfrost effect only occurs near the stagnation point in this study, and the heat transfer between the wall and the vapor-phase spray still impacts the ignition process, resulting in a shorter ignition delay time (IDT) as the wall temperature increases. Interestingly, the low-temperature reactions of both the free spray and spray/wall interaction cases started at the same moment, and the transition period from the low-temperature ignition delay time (τ1) to IDT shows a significant difference, indicating that the interaction between the wall and spray primarily affects the heat accumulation of the low-temperature reaction (LTR).

External group combustion of droplet clouds under two-stage autoignition conditions

The present study aims to extend the understanding of the external group combustion for droplet clouds under two-stage autoignition conditions. First, an exemplar case has been chosen to analyze the two-stage ignition behavior and flame structure. It was found that the fuel vapor transport of the droplet cloud is mainly supported by the thin vaporization layer near the edge of the cloud, which is the dominant factor of the ignition process. The case shows that a typical two-stage ignition includes the following detailed processes: first stage ignition, quasi-steady non-premixed cool flame, second stage ignition, and premixed hot flame. Three possible ignition modes for droplet clouds were identified through parametric studies, i.e. no ignition, single-stage ignition, and two-stage ignition. The transition between these modes is mainly controlled by the competition between chemical reaction and the vaporization of a thin layer of fuel droplets. Phase diagrams of different ignition modes at different ambient temperatures and sub parameters of the group number were presented. The previous group number G = 2πndRc2 demonstrated unsatisfactory prediction in the ignition modes of the droplet clouds. Basing on the vaporization layer feature of the droplet clouds, a new dimensionless group ignition number with much better predictability is first proposed in this work, i.e. Gig = 4πn2/3d2. The physical meaning of Gig is the dimensionless total surface area of droplets within a local layer.

Effects of prefilmer edge thickness on spray characteristics in prefilming airblast atomization

The effects of prefilmer edge thickness on the spray characteristics of a prefilming airblast atomizer were experimentally investigated. The Sauter mean diameter (SMD), variation of the mean diameter with time, and droplet number density were experimentally measured for various prefilmer edge thicknesses and air velocities at various measurement points. The liquid flow rate was kept constant. The effect of prefilmer edge thickness on SMD was large in the primary atomization region, but small in the secondary atomization region. In the primary atomization region, with increasing edge thickness, the droplet size distribution became broader, the SMD dispersion increased, and the droplet number density dispersion decreased. In the secondary atomization region, the SMD dispersion in time was small for all prefilmer edge thicknesses. The effect of prefilmer edge thickness on droplet number density dispersion was small. For a large prefilmer edge thickness, the SMD and the total droplet surface area varied randomly with time, whereas the arithmetic mean surface area was almost constant over the whole sampling period.

SURFACE PHENOMENA PECULIARITIES IN THE BOF STEELMAKING BATH

BOF steelmaking technology is largely determined with processes taking place in the LD-converter reaction zone, which consists of “primary” and “secondary” sub-zones. The “primary” zone is a crater formed as result of supersonic gas stream impact on metal melt sur- face, fulfilled with metal droplets of 0.1 – 2 mm in diameter. Surrounding in the “secondary” zone consists of the large amount of gas bubbles of 0.2 – 4 mm in diameter. The total surface area of droplets and bubbles is by four orders of magnitude larger as compared with the stable metal surface of magnitude larger as compared with the stable metal surface place. This suggests important role of interface phenomena at steel refining processes. The reaction zone structure and its temperature distribution were studied with “hot” modeling method, where molten cast iron was blown with oxygen in transparent quartz crucible. Each blow was accomplished with photo- and cinema filming through crucible wall. Besides temperature distribution obtained material also allowed study of metal bath hydrodinamics directly in blowing zone. The most unexpected result here was the motion trajectory of bubbles in the “secondary” zone. They moved normally to the crater surface, i.e. almost in a horizontal direction instead of vertical float as it was noticed at “cold” modeling with water. This very important phenomenon is caused by surface tension in homogeneity, due to which the bubbles are moved at higher temperatures direction. Surface tension forces in front of and behind gas bubble in liquid with temperature gradient are different. Because contact forces behind bubble are larger as compared that in front, it is pushed out in direction of surface tension decrease. Surface tension inhomogeneity is generated with temperature (up to 1200 °C) and oxygen concentration gradients in the “secondary” reaction zone. Iron-carbon surface tension changes with temperature rise inconsistently. Surface tension increases with temperature rise up to 1550 °C. At reaching 1550 – 1600 °C there is a bend, which after surface tension begin to decrease. This bend point is as higher as lower carbon concentration in alloy gas bubbles and heterogeneous phase’s motion in surface decrease direction starts from 1550 °C isotherm. So it is outward border of “secondary” reaction zone, which separates it from main metal bath. Inside it resulting surface tension forces push gas bubbles and slag particles into accelerating motion with mass of metal melt in horizontal direction to the crater. This phenomenon determines whole steelmaking bath hydrodynamics with oxygen redistribution between molten metal components and hence the steel refining process in general.

On the interaction of Taylor length scale size droplets and isotropic turbulence

Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$. In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ($0.1\leqslant \mathit{We}_{rms}\leqslant 5$), the droplet- to carrier-fluid density ratio ($1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$) or the droplet- to carrier-fluid viscosity ratio ($1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing $\mathit{We}_{rms}$, $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}$ increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than $\pm 5\,\%$ of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

Heat transfer upon motion in the channel of a dispersed water-steam flow

A modified version of the Hein-Koehler model for heat transfer in the dispersed flow is proposed; the model is based on the introduction of a correction when calculating the nonequilibrium factor of a droplet-laden steam flow. The correction considers the decrease in the total droplet surface area upon evaporation of the droplets in the superheated steam. Comparison of the calculated and the experimental maximum wall temperatures yielded a relative error of 5% at most. The predicted results can be applied to establish closure correlations for two-fluid models of a two-phase flow used in computer programs.

Effect of Droplets on Corrosion Resistanceof Tantalum Oxide Films Fabricated by PLD

Tantalum oxide films were prepared using pulsed laser deposition without any exchange of the Ta target. As the number of laser shots increased, the density of metal-rich droplets on the film increased and the droplet diameter became larger, leading to an increase in the total surface area of droplets. The corrosion resistance of the films was characterized by potentiostatic testing in a 3.5 mass% NaCl solution at 400 mV. It was found that the corrosion resistance improved as the O/Ta composition ratio approached its stoichiometric value. Corrosion was observed to originate at local surface pits produced by Cl -1 ions. These pits were formed at the boundaries between the film and droplets whose diameters were larger than the film thickness.

Auto-ignition of a polydisperse fuel spray

In the present paper, the effect of fuel spray polydispersity on the auto-ignition process in a fuel cloud is considered. In many engineering applications it is common practice to relate to the actual polydisperse spray as being equivalent to a monodisperse spray with all droplets therein having some average diameter. In combustion systems, the Sauter mean diameter (SMD) is frequently used for this purpose; it is based on the ratio between the total droplet volume and the total droplet surface area of all the droplets in the polydisperse spray. The main purpose of the current work is to examine qualitatively the dynamics of ignition of a truly polydisperse spray in a combustible gas medium and compare it with the dynamics of an equivalent monodisperse spray based on the SMD. Since the system of governing equations represents a multi-scale problem the method of integral manifolds is applied in order to extract the dynamical behavior. Preliminary computed results suggest that the use of the usual SMD-based monodisperse spray leads to quite a significant over-estimate of the ignition time. An alternative modified definition of the SMD, in which the overall liquid fuel volume is also conserved in the averaging process, reduces the discrepancy between the ignition time for the polydisperse spray and that of the equivalent monodisperse spray. However, it seems that some other sort of average droplet size needs to be determined to minimize the aforementioned discrepancy. These results highlight the care that must be exercised before dispensing with the behavior of the actual polydisperse spray in favor of that of an equivalent monodisperse spray, even at the expense of complexity.

Numerical Investigation of Gas Scavenging by Weak Precipitation

A one-dimensional cloud model with size-resolved microphysics and size-resolved aqueous-phase chemistry, driven by prescribed dynamics, has been used to study gas scavenging by weak precipitation developed from low-level, warm stratiform clouds. The dependence of the gas removal rate on the physical and chemical properties of precipitation has been explored under controlled initial conditions. It is found that the removal of four gaseous species (SO2, NH3, H2O2 and HNO3) strongly depends on the total droplet surface area, regardless the mean size of droplets. The removal rates also correlate positively with the precipitation rate, especially for precipitation having a mean radius larger than 20 μm. The dependence of the scavenging coefficients on the total droplet surface area is stronger than on the precipitation rate.

The influence of nitric acid on the cloud processing of aerosol particles

Abstract. In this paper we present simulations of the effect of nitric acid (HNO3) on cloud processing of aerosol particles. Sulfuric acid (H2SO4) production and incloud coagulation are both affected by condensed nitric acid as nitric acid increases the number of cloud droplets, which will lead to smaller mean size and higher total surface area of droplets. As a result of increased cloud droplet number concentration (CDNC), the incloud coagulation rate is enhanced by a factor of 1–1.3, so that the number of interstitial particles reduces faster. In addition, sulfuric acid production occurs in smaller particles and so the cloud processed aerosol size distribution is dependent on the HNO3 concentration. This affects both radiative properties of aerosol particles and the formation of cloud droplets during a sequence of cloud formation-evaporation events. It is shown that although the condensation of HNO3 increases the number of cloud droplets during the single updraft, it is possible that presence of HNO3 can actually decrease the cloud droplet number concentration after several cloud cycles when also H2SO4 production is taken into account.

Numerical studies of aerosol scavenging by low-level, warm stratiform clouds and precipitation

Abstract Numerical studies have been performed to investigate aerosol scavenging by low-level, warm stratiform clouds and precipitation using a one-dimensional model with detailed cloud microphysics and size resolved aerosol particles and hydrometeors. Activation processes remove most aerosol mass within the cloud layer despite the very low supersaturation, since a large fraction of the aerosol mass is associated with large aerosols which can be quickly activated into cloud droplets. Impaction scavenging inside the cloud layer removes little aerosol mass; however, this process removes aerosols as high as 50% in number during a period of a few hours. Total in-cloud scavenging removes more than 70% of aerosols in number and more than 99% in mass. Below cloud scavenging is linked to aerosol concentration and size distribution, precipitation intensity and droplet spectra. During a 4-h period, weak precipitation having less than 0.1 mm h−1 intensity can remove 50–80% of the below-cloud aerosol in both number and mass. Scavenging coefficients for large particles vary significantly with precipitation rates and/or droplet mean radii while for small particles such variation is not apparent. As a result, bulk aerosol mass-scavenging coefficients depend strongly on precipitation intensity while bulk number scavenging coefficients have less dependence. A dependence of scavenging coefficients for all size particles on total droplet surface area is found to be possible and such dependence is stronger for smaller particles. With the same precipitation amount, precipitation with more small droplets can remove aerosols more effectively due to larger total droplet surface area. Size-resolved scavenging coefficients have to be used in order to correctly track both aerosol number and mass distributions. It is suggested that parameterizations for bulk or size-resolved scavenging coefficients should be a function of other precipitation properties as well as precipitation intensity.

Experimental Study on the Spray Characteristics in the Spray Drying Absorber

A pilot-scale spray drying absorber (SDA) system was set up to evaluate the effect of spray characteristics on flue gas desulfurization efficiency. Varying spray injection conditions and inlet gas conditions, SO2 concentrations were measured using a combustion gas analyzer. As a reagent, a slaked lime (Ca(OH)2) slurry was treated with flue gas containing SO2. The influence of each parameter is determined by the compromise between the droplet absorption capability and SO2 gas supply to the region of the droplet cloud. When the SO2 molecules are sufficiently supplied to the wet droplet surface, the variation of the total droplet surface area plays a dominant role in the desulfurization process. The conditions of low inlet gas temperature and low slurry feed rate are included in this case. However, when the droplets of sprayed slurries are too small or evaporation proceeds too fast, the SO2 molecules cannot be sufficiently transferred to the droplet surface. The excess calcium sorbents in the droplets dry out before they react with the hot gas. Consequently, the desulfurization efficiency as well as the utilization efficiency of Ca decreases for the smaller droplets. This trend appears to be dominant in conditions of high gas temperature and large slurry feed rate with the small Sauter mean diameter (SMD) of spray droplets. From the experimental results, we proposed two empirical models for the desulfurization efficiency and operating conditions.

An Experimental Approach to Evaluate the Desulfurization Yield in Spray Drying Sorber

A pilot-scale Spray Drying Sorber (SDS) system was set up to evaluate the effect of spray characteristics on the desulfurization yield. The size distribution and the Sauter Mean Diameters of slurry droplets were measured in advance using the optical size measurement system, Malvern 2600. The desulfurization yield of the drying chamber by size was measured for the conditions of inlet gas and spray injection. As a reagent, 10% limestone slurry of was treated with flue gas containing , and the combustion gas analyzer and gas detectors were attached to measure the concentration. With a flow rate of 144 Nm3/h and a temperature range of , the experiments were performed for the Stoichiometric Ratio (SR) of 1.0 to 3.0 and droplet mean diameter of 6.5 to . In case of smaller spray droplets, the desulfurization efficiency improved due to the increase of total droplet surface area, while the reduction in evaporation time reduced the contact time between the droplets and gas. In some typical region of droplet diameter, this negative effect, reduction of contact time, became dominant and the desulfurization yield decreases the desulfurization yield in spite of the expansion in absorption area. These results revealed that there exists the optimal size of spray droplets for a given state, which is determined by the compromise between the total surface area of slurry droplets and the evaporation time of droplets. The measurements also indicated that the inlet temperature of flue gas changes the optimal injection condition by varying the driving force for evaporation. The results confirm that the effect of the evaporation time of slurry droplets should be considered in analyzing the desulfurization yield as well as the total surface area, for it is a significant aspect of the correlation with the capabilities of absorption in wet droplets. In conclusion, the optimal condition of spray can be determined based on these results, which might be applied to design or scale-up of SDS system.