Stefan Flow Research Articles

Flame Spread Over Ultra-thin Solids: Effect of Area Density and Concurrent-Opposed Spread Reversal Phenomenon

There are no existing experimental studies of flame spread rate trends for ultra-thin solid samples. Previous theory has predicted that for concurrent flame in kinetic regime, the flame spread rate decreases as the sample thickness decreases and there is a critical thickness below which burning is not possible. To test this hypothesis, a series of microgravity experiments of concurrent-flow flame spread over samples of ultra-low area densities are conducted using NASA Glenn Research Center’s Zero Gravity Research Facility (the 5.18 s drop tower). The tested samples are cellulose-based materials of various area densities, ranging from 0.2 mg/cm2 to 13 mg/cm2, as low as one order of magnitude less than those ever tested before. Each sample is 30 cm long by 5 cm wide and is burned in a low-speed concurrent air flow (5 to 30 cm/s). The results show that the concurrent flame spread rate is proportional to the flow velocity relative to the flame and is inversely proportional to the sample area density. A theoretical formulation, provided in this work, suggests that the flame length has a linear relationship with the relative flow speed and has no direct dependency on the sample area density. The experimental data supports this conclusion. From the images recorded in the experiments, a unique flame base tubular structure directed upstream away from the burnout zone is observed for thin samples. This structure is suspected to be due to flame stretching and localized blowoff caused by the oxidative pyrolysis Stefan flows at the sample burnout. This can be an indication that the chemical time becomes comparable to the flow time of the Stefan flow and the tested samples are approaching the kinetically-limited thickness. For the thinnest tested sample (0.2 mg/cm2), flames with concurrent and opposed dual natures are observed when the air flow rate is low (< 20 cm/s). At the lowest tested flow rate (5 cm/s), the flame spread rate exceeds the air flow rate and the flame transits to an opposed flame in the concurrent flow. The dual nature and flame transition are presented and discussed. This study provides detailed examination through high-resolution images of the transition between the concurrent to opposed flame spread modes.

Study of wall ablation on low-voltage arc interruption: The effect of Stefan flow

Low-voltage circuit breakers provide essential protection for industrial and residential power installations, by taking advantage of the voltage drop at the electrode–plasma interface to force current zero. This is accomplished by using the magnetic force and unbalanced pressure on the arc as the contacts open to push the arc toward a stack of steel plates that break the arc into subarcs and thereby multiply the number of voltage drops. As the fault current can be high, substantial energy can be dissipated, which results in interactions among the arc and solid counterparts in terms of wall ablation and metal evaporation. In this study, ablation experiments are conducted to demonstrate its great influence on the arc voltage and on the pressure field. Significant progress has been accomplished in the computation of arc dynamics through the coupling of fluid motion with electromagnetics, although an important mechanism in arc breaking simulation, the effect of Stefan flow caused by species generation, has not been considered. We report out a numerical approach for taking into account the effect of Stefan flow, particularly for the breakers with high gasifying wall materials. This approach accounts for the diffusion induced convection due to added-in species from the evaporation surfaces, which will largely influence the flow field and the properties of the plasma mixture. Apart from the voltage drop, this mechanism plays an important role in simulating arc interruption. The ability of conducting Stefan flow computation further enhances the understanding of arc behaviors and improves the design of practically oriented low-voltage circuit breakers.

Comparative Analysis of a Single Fuel Droplet Evaporation

In this research, the results of comparative analysis of a single fuel droplet evaporation models are presented. Three well-known evaporation models including Spalding, Borman-Johnson and Abramzon-Sirignano models are analyzed using Computational Fluid Dynamic (CFD). The original Spalding model is extended to consider the effects of the Stefan flow, unsteady vaporization, and variable properties. The evaporation models are validated using already existing experimental data. Numerical results show that the Spalding model overestimates the temperature of the droplet surface in comparison with the other two models, although some modifications were made in the aforementioned model. Our final evaluation concludes that Abramzon-Sirignano model predictions are in good agreement with the experimental data. Therefore, in this paper, this model is used for the parametric study of the effects of droplet size, ambient temperature and pressure on the droplet lifetime and temperature. Results indicate that by increasing the droplet size, the lifetime of the droplets will increase and the steady-state droplet temperature is higher at higher ambient pressures and temperature.

Study on the combustion characteristics of a two-dimensional particle group for coal char and petroleum coke particles

The combustion characteristics of particle group are different from the combustion of a single particle, owing to the physicochemical effect and interaction among particles. The current work investigated the effect of the increasing particle concentration on the group combustion with the consideration of temperature and solid fuel type, including bituminous coal char and petroleum coke. A visual imaging technology was used to record and analyze the combustion process and group evolution of burning particles in the two-dimensional scale. Results showed that a delayed combustion phenomenon was found for both coal char and petroleum coke with the increasing particle concentration in a group. The burnout time increased in multiples from the combustion of a single particle, dispersed particles to a particle group. The total carbon conversion and combustion rate of the particle group significantly decreased with the increasing particle concentration in the group, especially for the bituminous char of a high reactivity. With increasing the combustion temperature, the burnout time was additionally prolonged from 20% to 80% between the internal and external particles in the particle group. The theoretical analysis with the consideration of Stefan flow, gas diffusion, and gas-solid reaction was used to propose the delayed combustion mechanism, and the results matched well with the experimental data. The increasing particle concentration in the group, which consumed the oxygen, generated the advance effect of Stefan flow, and hindered the oxygen diffusion, was the key factor to delay the group combustion. For the group combustion of petroleum coke with low reactivity, although the surface reaction was the controlling step, the reactant gas diffusion inside the group could not be ignored. For the group combustion of coal char particle with high reactivity, the diffusion of the reactant gas in the group was the dominant controlling step for the delayed combustion behavior.

The effect of Stefan flow on the drag coefficient of spherical particles in a gas flow

Particle laden flows with reactive particles are common in industrial applications. Chemical reactions inside the particle can generate a Stefan flow that affects heat, mass and momentum transfer between the particle and the bulk flow. This study aims at investigating the effect of Stefan flow on the drag coefficient of a spherical particle immersed in a uniform flow under isothermal conditions. Fully resolved simulations were carried out for particle Reynolds numbers ranging from 0.2 to 14 and Stefan flow Reynolds numbers from (−1) to 3, using the immersed boundary method for treating fluid-solid interactions. Results showed that the drag coefficient decreased with an increase of the outward Stefan flow. The main reason was the change in viscous force by the expansion of the boundary layer surrounding the particle. A simple model was developed based on this physical interpretation. With only one fitting parameter, the performance of the model to describe the simulation data were comparable to previous empirical models.

Influence of crucible shape on mass transport in AlN crystal growth by physical vapor transport process

We develop a fully 2D incompressible flow model for the AlN physical vapor transport (PVT) growth process by the Finite Element Method. In this model, the effects of multiphase vapor diffusion, buoyancy, and the Stefan flow are taken into account. We also investigate the influences of the crucible shape on the mass transport in a 2-in. AlN growth chamber with numerical experiments. The simulation results show that the uniformity of the initial growth rate on the deposition surface is strongly dependent on the crucible shape, and it could be improved by increasing the crucible sidewall expansion angle. The optimal expansion angle is found to be between 15° and 18° in order to obtain a slight convex growth interface under our specified growth conditions. The improvement of the initial growth interface uniformity is mainly due to the local Al gas pressure gradient near the deposition surface. The simulation results also reveal that a transport limitation of Al atoms at the deposition surface could be the most likely rate-limiting step for AlN PVT growth.

Cold condensing scrubbing method for fine particle reduction from saturated flue gas

The wet scrubbing method can be used for reducing particles and recover waste heat from flue gas. But its particle reduction performance is relatively poor, and an outward Stefan flow caused by droplet evaporation may be the main adverse cause. This work aims to improve the performance through developing a cold condensing scrubbing method, wherein an inward Stefan flow is created through water vapor condensing on cold droplets to prompt the particle capture from saturated flue gas. This method has barely been studied, except a few theoretical predictions. These predictions lack experimental verification, which has been performed in this work. The particle reduction efficiencies obtained in our experiments are much higher than previous predicted results, thereby increasing the possibility of application. Besides the work to confirm the inward Stefan flow is the dominant mechanism for a condensing droplet capturing fine particles, the contributions of a preceding scrubber and a subsequent demister are also explored to refine the mechanism knowledge system. Variable analysis on scrubbing temperature, liquid-to-gas ratio, and droplet size are addressed to create a valuable characteristic curve figure and to provide guidelines for engineering applications. Furthermore, the technical feasibility and the economic performance of the proposed method are discussed.

Research on real-time simulation modelling of a diesel engine based on fuel inter-zone transfer and an array calculation method

This paper proposed a real-time simulation model of a diesel engine based on the fuel transfer in the combustion zone and an array calculation method. The proposed model conducts real-time optimized modelling of the diesel engine multi-zone model from two aspects: a modelling method and a model algorithm. From the modelling method perspective, the model proposed a combustion process model that transfers fuel mass and momentum between the combustion zones. Based on the diesel combustion characteristics, this modelling method divides the cylinder into three thermodynamic zones: an unburned area, a premixed combustion zone, and a diffusion combustion zone. This division addresses the assumption that fuel mass and momentum transfer are not performed between combustion zones in the traditional multi-zone model. While reducing the computation regions and improving the simulation calculation speed, the combustion process of the premixed combustion zone and the diffusion combustion zone were described using the method of Stefan flow and entrainment combustion. The physical depth and the predictivity of the model was enhanced, which rendered the description of the combustion process more consistent with the diesel combustion characteristics. The thermodynamic calculation process of the three regions was maintained throughout the entire cyclic operation in the entire diesel engine operating cycle. From the model calculation perspective, the model proposed a direct single-step calculation method for temperature and pressure to satisfy the demand of real-time model calculation. To optimize the multi-cylinder multi-zone plan in a real-time environment, the model utilizes an array method for calculation. The results of the model verification of a diesel engine in high and low loading conditions and using fixed combustion model parameters indicate that the difference between the calculation results and the experimental data is less than 5% and the results are consistent, which proves that the model has predictivity. The analysis of the model calculation results indicates that the model can accurately reflect the performance change pattern and regional change characteristics for different working conditions and provide a suitable foundation platform for controlling system combustion performance optimization. In addition, the array algorithm and multi-zone through-operation calculation method were validated in a real-time hardware system test environment. The methods can effectively reduce the multi cylinder multi-zone model simulation time to 30%. The application range of the real-time system model was expanded; thus, this method is very suitable for real-time system calculation.

Autoignition and combustion behavior of emulsion droplet under elevated temperature and pressure conditions

In this study, experiments were conducted to investigate the combustion characteristics of an water-in-oil W/O emulsion droplet under elevated temperature and pressure conditions. The base fuel used was n-decane, and total volume ratios of 10, 20, and 30% of distilled water were mixed for producing the emulsion fuel. Span 80 with a volume ratio of 2% was added as a surfactant, and the emulsion fuel was homogeneously mixed via ultrasonication. The combustion process of an emulsion droplet was divided into five stages: droplet heating, classical combustion, puffing, secondary classical combustion, and surfactant combustion. The ignition delay decreased with elevated ambient temperatures, whereas an increase in the ambient pressure and water volume ratio resulted in longer ignition delays. The droplets did not ignite in 500 °C or 600 °C conditions at 1 bar because of the significant Stefan flow of fuel vapor. After droplet ignition, the droplet combustion process, including classical combustion, puffing, and surfactant combustion, followed. The average burning rate increased with ambient pressure, but it was insensitive to ambient temperatures and water volume ratios. After flame extinction, a secondary flame reappeared because of the combustion of surfactant and residues.

Effect of Stoichiometric Ratio on Char-Nitrogen Conversion under High-Temperature Entrained Flow Combustion Conditions

The char-O2 reaction under high-temperature entrained flow conditions was investigated experimentally and numerically to study the effect of the stoichiometric ratio (SR) on char-nitrogen conversion. A numerical model was established based on the unsteady convection-diffusion and reaction equations, in which Stefan flow was considered. The change of specific surface area during char combustion was considered by locally using the Random Pore Model (RPM). The intrinsic reactivity parameters of char-O2 and char-NO reactions were measured using a thermal gravimetric analyzer (TGA) and drop tube furnace (DTF), respectively. The numerical results indicated that the predictions of carbon conversion and NO release agreed well with experimental data. Based on numerical results, for a given carbon conversion, with the decrease of SR, the kinetics-diffusion controlled char-O2 reaction is pushed toward the kinetics-controlled regime, leading to more significant local carbon conversion and thus more developed pore structure inside char particles, including higher porosity and larger specific surface area. Therefore, the oxidation of char-nitrogen occurs more deeply inside char particles and NO release prefers to diffuse toward the particle center, rather than outward. The larger specific surface area deep inside the char particle also gives rise to the total char-NO reaction rate at a lower SR. As a result, the total fractional conversion of char-N to NO decreases as SR decreases under high-temperature entrained flow combustion conditions.

Fully resolved simulations of single char particle combustion using a ghost‐cell immersed boundary method

A novel ghost‐cell immersed boundary method for fully resolved simulation of char particle combustion has been developed. The boundary conditions at the solid particle surface, such as velocity, temperature, density, and chemical species concentration, are well enforced through the present method. Two semiglobal heterogeneous reactions and one homogeneous reaction are used to describe the chemical reactions in the domain, and the Stefan flow caused by the heterogeneous reactions is considered. A satisfactory agreement can be found between the present simulation results and experimental data in the literature. The method is then used to investigate the combustion property of a char particle and the interaction between CO2 gasification and O2 oxidation. Furthermore, combustion effect on the exchange of mass, momentum and energy between gas‐ and solid‐ phase is explored. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2851–2863, 2018

Boundary conditions for a one-sided numerical model of evaporative instabilities in sessile drops of ethanol on heated substrates.

The work is focused on obtaining boundary conditions for a one-sided numerical model of thermoconvective instabilities in evaporating pinned sessile droplets of ethanol on heated substrates. In the one-sided model, appropriate boundary conditions for heat and mass transfer equations are required at the droplet surface. Such boundary conditions are obtained in the present work based on a derived semiempirical theoretical formula for the total droplet's evaporation rate, and on a two-parametric nonisothermal approximation of the local evaporation flux. The main purpose of these boundary conditions is to be applied in future three-dimensional (3D) one-sided numerical models in order to save a lot of computational time and resources by solving equations only in the droplet domain. Two parameters, needed for the nonisothermal approximation of the local evaporation flux, are obtained by fitting computational results of a 2D two-sided numerical model. Such model is validated here against parabolic flight experiments and the theoretical value of the total evaporation rate. This study combines theoretical, experimental, and computational approaches in convective evaporation of sessile droplets. The influence of the gravity level on evaporation rate and contributions of different mechanisms of vapor transport (diffusion, Stefan flow, natural convection) are shown. The qualitative difference (in terms of developing thermoconvective instabilities) between steady-state and unsteady numerical approaches is demonstrated.

Non-isothermal evaporation in a sessile droplet of water-salt solution

Experimental data on nonisothermal evaporation of sessile droplets of water-salt solutions (LiBr + H2O; CaCl2+H2O) were obtained. Evaporation of droplets of volatile liquids occurs with almost constant evaporation rate, and the problem is solved in a stationary approximation. High-temperature evaporation of water-salt solutions leads to significant difficulties at modeling the heat and mass transfer. In this case, the evaporation rate substantially decreases with time. With the growth of salt concentration in the solution from 11% to 60%, the partial pressure of water vapor at the interface falls by an order of magnitude. In this work, we have performed simulation, considering diffusion in solutions, a non-isothermal character, and the Stefan flow, and proposed a simple method for calculating the mass flow. The resulting technique can qualitatively and quantitatively predict the solution behavior with a significant change in the external boundary conditions in time.

A fixed-grid model to track the interface and porosity of a chemically reacting moving char particle

The main objectives of this work are to present a new CFD-based model for tracking the chemically reacting particle interface and particle porosity, and to numerically explore the influence of particle velocity on the dynamics of the particle porosity. As an illustrative example we consider the gasification of a single spherical particle moving in a hot CO2 gas. The interface tracking model has been validated against a moving-grid method using a commercial CFD software. Excellent agreement has been achieved. Several cases for a moving porous particle have been studied numerically. Simulation results showed that the Stefan flow inside the gasifying particle plays a significant role in the mass transfer governed by the Thiele modulus. Besides this, we show that the Stefan flow significantly modifies the hydrodynamic boundary layer around the particle at low values of the Reynolds number corresponding to unity order of magnitude. Finally, we show that in all regimes (from kinetically controlled to diffusion controlled), particle porosity is at a minimum in the center of the particle, and increases towards its outer surface at all stages of particle conversion. Additionally, we found out that the diffusion-controlled regime is characterized by the particle porosity gradient reaching higher values in comparison to the pore diffusion regime.

Study of conversion of ammonia from urea water solution droplets using CFD

This paper deals with the numerical analysis of the spray behaviour of urea water solution (UWS) droplets used in Selective catalytic reduction (SCR) process. The study uses the ANSYS-Fluent-14 as a basic framework for numerical simulations. The evaporation modelling is based on multi-component droplet evaporation approach along with the consideration of Stefan flow. The urea decomposition treated as direct thermolysis approach, where the modelling is based on the single kinetic rate approach by the proper fitting of pre-exponent. This developed model was used for spray simulation of UWS droplet evaporation to determine the urea to ammonia conversion efficiency. The obtained spray simulation results were compared with the available experimental data. The comparison shows the pre-exponent developed in the study is suitable for direct thermolysis approach to get promising results in determining the ammonia conversion efficiency.

Influence of the Stefan Flow on Heat Transfer in the System “Gas–Solid Particle” in Thermochemical Conversion of a Solid Fuel

Recommendations are presented on calculating interphase heat transfer in gas-disperse systems of plants for thermochemical conversion of ground solid fuel. An analysis is made of the influence of the gas release of fuel particles on the heat transfer during their heating. It is shown that in the processes of thermal treatment of oil shales, the presence of gas release reduces substantially the intensity of interphase heat transfer compared to the heat transfer in the absence of thermochemical decomposition of the solid phase.

Particle shape and Stefan flow effects on the burning rate of torrefied biomass

Experiments and subsequent analysis were conducted to gain insight into combustion phenomena of raw and torrefied biomass chars, and to describe the char combustion phase with respect to their frequently discussed non-spherical particle shape. Torrefied beech wood and miscanthus were burned in a laminar flow reactor at high heating rates (104–105K/s). A stereoscopic imaging pyrometry system was used to measure particle temperatures, sizes and shapes of sub-mm particles in-flight. Additionally, partially reacted samples were collected and analyzed by means of scanning electron and digital microscopy. A good agreement was found between collected and in situ measured particle sizes and aspect ratios. The initially high aspect ratio of the aspherical biomass particles was observed to decrease during the burnout progress. Reaction rates were derived by conducting an energy balance around a burning particle, accounting for the effects of both the particle shape and Stefan flow. The char burnout rate was found to decrease with torrefaction intensity of beech wood; beech wood showed a slightly higher reaction rate than torrefied miscanthus being treated with the same thermal parameters. The effect of Stefan flow was found to be of minor relevance during combustion in air; neglecting it, in the case of small particles and/or particles with high aspect ratios, particularly those burning in elevated oxygen atmospheres, leads to underprediction of particle temperatures and hence, burnout times.

The boundary condition for vertical velocity and its interdependence with surface gas exchange

Abstract. The law of conservation of linear momentum is applied to surface gas exchanges, employing scale analysis to diagnose the vertical velocity (w) in the boundary layer. Net upward momentum in the surface layer is forced by evaporation (E) and defines non-zero vertical motion, with a magnitude defined by the ratio of E to the air density, as w = E/ρ. This is true even right down at the surface where the boundary condition is w|0 = E/ρ|0 (where w|0 and ρ|0 represent the vertical velocity and density of air at the surface). This Stefan flow velocity implies upward transport of a non-diffusive nature that is a general feature of the troposphere but is of particular importance at the surface, where it assists molecular diffusion with upward gas migration (of H2O, for example) but opposes that of downward-diffusing species like CO2 during daytime. The definition of flux–gradient relationships (eddy diffusivities) requires rectification to exclude non-diffusive transport, which does not depend on scalar gradients. At the microscopic scale, the role of non-diffusive transport in the process of evaporation from inside a narrow tube – with vapour transport into an overlying, horizontal airstream – was described long ago in classical mechanics and is routinely accounted for by chemical engineers, but has been neglected by scientists studying stomatal conductance. Correctly accounting for non-diffusive transport through stomata, which can appreciably reduce net CO2 transport and marginally boost that of water vapour, should improve characterisations of ecosystem and plant functioning.

Numerical study of a reacting single coal char particle with different pore structures moving in a hot O2/CO2 atmosphere

Based on pseudo-steady-state approach, the effect of particle size and porosity on conversion characteristics of single coal char particle moving in high temperature O2/CO2 atmosphere was studied to analyze the particle conversion mechanism. The particle size and porosity were variable in the range of 0.1–1.0mm and 0–0.4 respectively. The particle structure model is developed referring to experimental coal char particle pore structure. The Navier-Stokes equations were coupled with energy and species conservation equations to solve the problem. Stefan flow, Maxwell-Stefan equation and Soret effect were considered for mass transport. Water-gas-shift reaction, CO oxidation reaction and four heterogeneous reactions were taken into account. The reacting particles moving in different oxygen concentration were modeled for validation against experimental results of literatures. The results show that with the decrease of particle size, the reactive zone expands relative to the particle but shrinks relative to the space and attaches to the particle surface because of the low Reynolds number and the small pore size. The particle with high porosity is more sensitive to the change of the ambient oxygen concentration due to the large contact surface with gas flow. Additionally, the detaching of the flame sheet and the endothermic Boudouard reaction are two significant factors affecting the surface temperature. The insufficient supply of oxidant causes the decrease of the specific carbon consumption rate along with the enhancing of the particle size and porosity.

Evaporation and crystallization of a droplet of desulfurization wastewater from a coal-fired power plant

Relationship between evaporation and crystallization characteristics of a droplet of desulfurization wastewater from a coal-fired power plant and some operating conditions was studied experimentally using a thermogravimetric analyzer (TGA) with differential scanning calorimetry (DSC) function and a scanning electron microscope (SEM). The results shows that, between 15°C/min and 45°C/min, a higher temperature increasing rate leads to higher evaporation and crystallization rates. The increment in the evaporation rate, caused by the same increment of temperature increasing rate, is larger, when the temperature increasing rate is lower. In addition, the final temperatures, ranging from 90°C to 150°C, have little impact on the evaporation and crystallization rates of the 0.5μL droplet. Ultimately, for the droplets, ranging from 0.2μL to 2.5μL, evaporation rate increases with increasing volumes of the droplets, but the crystallization rate decreases. From the SEM results, it can be observed that the quantity of cracks on the surface of the crystals also declines with the increase in volumes. Furthermore, the Stefan flow becomes a significant and unneglectable factor in order to decrease the evaporation rate at the end of the evaporation period.