Daniel N. Pope

Effects of gravity and ambient pressure on liquid fuel droplet evaporation

An axisymmetric numerical model has been developed to conduct a study of single droplet evaporation over a wide range of ambient pressures both under normal and microgravity conditions. Results for droplet lifetime as a function of ambient pressure and initial droplet diameter are presented. The enhancement in the droplet evaporation rate due to natural convection is predicted. This enhancement becomes more dominant with increasing ambient pressure due to the increase in the Grashof number. The higher the ambient pressure, the closer the Grashof number remains to its initial value throughout most of the droplet lifetime because of the droplet swelling and the heat-up of the droplet interior. Results should be particularly of interest to researchers conducting experiments on droplet evaporation at elevated pressures within a normal gravity environment. The model developed is in good agreement with experimental data at low pressures. Explanations have been provided for its deviation at high pressures.

A new multicomponent diffusion formulation for the finite-volume method: Application to convective droplet combustion

A new multicomponent formulation, appropriate for use with the finite-volume method, has been developed to describe mass diffusion velocities accurately. The new formulation is applied in a quasi-steady numerical model for n-heptane fuel droplet combustion in a forced-convection environment. Results obtained using the complete formulation are compared to the results obtained under various assumptions. Using a single binary diffusion coefficient produces results for extinction velocity, maximum temperature, flame dimensions, evaporation constant, and drag coefficient that are significantly different from the results obtained using the complete formulation. Neglecting thermal diffusion (Soret effect) causes only minor changes (less than 2%).

Combustion of moving droplets and suspended droplets: Transient numerical results

A numerical investigation of unsteady liquid fuel droplet combustion with droplet heating and internal circulation under forced convection is presented. The droplet is burning within an airstream at atmospheric pressure and under zero-gravity conditions. Combustion is modeled using finite rate kinetics and a one-step overall reaction. The numerical model includes a new multicomponent formulation, which is appropriate for use with the finite volume method, to describe mass diffusion in the gas phase accurately. Numerical results were obtained for both suspended droplets (constant relative velocity) and for moving droplets. It is shown that the flame configurations

Effect of Non-Luminous Flame Radiation During Methanol Droplet Combustion

The effect of non-luminous thermal radiation on the combustion of a suspended methanol droplet in a low temperature (300 K) and low pressure (1 atm) environment is discussed in detail. Numerical results are obtained using a predictive, transient, two-phase, axisymmetric numerical model that includes surface tension effects. Radiation is modeled using the optically thin approximation with the product species CO2 and H2O as the radiating species. Results for combustion in a nearly quiescent atmosphere (initial Reynolds number 0.01) and initial droplet diameters in the range of 0.43 mm to 3 mm are presented. In agreement with the reported literature, it is shown that the effect of flame radiation is negligible when the initial droplet diameter is less than approximately 1 mm and becomes increasingly important for larger droplets. As a result, the average evaporation constant decreases with the initial droplet diameter. Radiation and surface tension combined as well as surface tension alone have a significant effect on the predicted extinction diameters of methanol droplets. However, when surface tension is neglected, radiation alone has a negligible effect on the prediction of the extinction diameter. The extinction diameter presents a non-linear variation with the initial droplet diameter for initially large droplets. The agreement with experimental results available in the literature is very good.

Effects of forced convection and surface tension during methanol droplet combustion

A numerical investigation of surface tension and forced convection effects on moving and suspended methanol droplets burning in a zero-gravity, low-pressure air environment is presented. Simulations were conducted using a predictive, transient, axisymmetric model for an initial droplet diameter of 0.5 mm, an ambient temperature of 1200 K, and initial Reynolds numbers (Re 0 ) in the range of 1-100. Results indicate that, for moving droplets, due to the presence of an envelope flame at some stage during the droplet lifetime, surface tension is important over the range of Ke 0 considered; the extinction diameter decreases with increasing Re 0 . For suspended droplets, when transition or envelope flame is present (Ke 0 less than approximately 15), surface tension is important; when an envelope flame is present (Re 0 less than approximately 10), the extinction diameter increases with Re 0 . Both for suspended and moving droplets, the droplet lifetime is weakly sensitive to surface tension. The variation of droplet lifetimes with Re 0 is much stronger for suspended droplets than for moving droplets. Depending on the Reynolds number, results on methanol droplet lifetimes and extinction diameters measured through suspended droplet experiments may not be applicable to moving droplets.

Numerical Modeling of Steady Burning Characteristics of Spherical Ethanol Particles in a Spray Environment

A numerical study of steady burning of spherical ethanol particles in a spray environment is presented. A spray environment is modeled as a high temperature oxidizer stream where the major products of combustion such as carbon dioxide and water vapor will be present along with reduced amounts of oxygen and nitrogen. The numerical model, which employs variable thermophysical properties, a global single-step reaction mechanism, and an optically thin radiation model, has been first validated against published experimental results for quasi-steady combustion of spherical ethanol particles. The validated model has been employed to predict the burning behavior of the ethanol particle in high temperature modified oxidizer environment. Results show that based on the amount of oxygen present in the oxidizer the burning rate constant is affected. The ambient temperature affects the burning rate constant only after a sufficient decrease in the oxygen content occurs. In pure air stream, ambient temperature variation does not affect the evaporation constant. Results in terms of burning rates, maximum temperature around the particle, and the evaporation rate constants are presented for all the cases. The variation of normalized Damkohler number is also presented to show the cases where combustion or pure evaporation would occur.

Modeling of an Integrated Wind Energy Building

This study presents the design and modeling of an integrated wind energy building. It is proposed that a building be constructed with an integral wind turbine that takes advantage of the funneling of wind from the building structure and the low pressure area above or leeward of the building. Computational Fluid Dynamics (CFD) was used to evaluate different building geometries and wind potentials. Preliminary investigations using two dimensional numerical modeling in both the horizontal and vertical planes are presented. Three dimensional analyses are also presented of promising geometries from the two dimensional preliminary results. While additional modeling efforts will be necessary to optimize this system, results indicate a significant improvement in performance over free standing turbines, allowing for utilization of wind power in geographic regions that have traditionally not been feasible.Copyright

Combined Non-Luminous Flame Radiation and Surface Tension Effects During Methanol Droplet Combustion

The effect of non-luminous thermal radiation on suspended (constant relative velocity) methanol droplet combustion in a low temperature (300 K) and low pressure (1 atm) environment is discussed in detail. Numerical results are obtained using a predictive, transient, two-phase, axisymmetric numerical model that includes surface tension effects. Radiation is modeled using the optically thin approximation with the product species CO2 and H2 O as the radiating species. Results for combustion in a quiescent atmosphere (initial Reynolds number 0.01) and initial droplet diameters in the range of 0.43 mm to 3 mm are presented. The results show that the effect of flame radiation is negligible when the initial droplet diameter is less than approximately 1 mm and becomes increasingly important for droplets with initial diameters greater than approximately 1 mm, as reported in previous literature. The average evaporation constant decreases with the initial droplet diameter. Both radiation and surface tension have a significant effect on the predicted extinction diameters of initially larger droplets. The extinction diameter presents a non-linear variation with the initial droplet diameter for initially larger droplets and agreement with experiments is good.© 2007 ASME

The role of surface tension effects during methanol droplet combustion

A numerical investigation of methanol droplet combustion in a zero-gravity and low-pressure convective environment is presented. Simulations have been carried out using a predictive, transient and axisymmetric model, which includes droplet heating, liquid-phase circulation and water absorption. First, a suspended droplet (constant relative velocity) burning in an ambient of air at 300K is considered. A nearly quiescent environment (initial Reynolds number Re0 =0.01) is used to impose a weak gas-phase convective flow, introducing a deviation from spherical symmetry. The resulting weak liquid-phase circulation is greatly enhanced due to surface tension effects, which create a complex, time-varying, multicellular flow pattern within the liquid droplet. The complex flow pattern, which, in the presence of surface tension, results in nearly perfect mixing, causes increased water absorption within the droplet, leading to larger extinction diameters. Surface tension effects are shown to be dominant in causing water absorption, even at initial Reynolds numbers as high as 5. Results for combustion in a nearly quiescent environment (Re0 =0.01) with varying initial droplet diameters, (d0 = 0.16 to 1.72 mm), show that predictions of droplet extinction diameters, although they are still below the experimental data, do improve substantially when surface tension effects are included. Next, results for suspended droplets and for moving droplets burning in an ambient of air at 1200K, for a range of initial Reynolds numbers that are of interest in spray combustion (Re0 =1-100) are presented. It is shown that, for moving droplets, due to the presence of an envelope flame at some stage during the droplet lifetime, surface tension is important over the entire range of Re0 considered; the extinction diameter decreases with increasing Re0 . Extinction is not observed for a moving droplet when surface tension effects are neglected. For suspended droplets, when transition or envelope flame is present, which corresponds to Re0 less than approximately 15, surface tension is important; when an envelope flame is present (Re0 less than approximately 10), the extinction diameter increases with Re0 . The variation of droplet lifetime with Re0 is much stronger for suspended droplets than for moving droplets. Depending on the Reynolds number, results on methanol droplet lifetimes and extinction diameters measured through suspended droplet experiments may not be applicable to moving droplets.Copyright

A new multicomponent diffusion formulation for the finite-volume method

A new multicomponent formulation, which is appropriate for use with the finite-volume method, has been developed to accurately describe the diffusion velocity. The new formulation is presented and applied to the numerical simulation of n-heptane fuel droplet combustion in a zero-gravity, forced convection environment at 1 atm. Combustion is modeled using finite-rate chemical kinetics and a one-step overall reaction. Results obtained using the complete formulation are compared to the results obtained while assuming (1) thermal diffusion (Soret effect) is negligible and (2) thermal diffusion is negligible and all binary diffusion coefficients are the same. The effect these assumptions have on the results at a fixed Reynolds number (Re∞=10) is investigated for a low (300 K) and a high (1200 K) ambient temperature. The use of a single binary diffusion coefficient produces results that are significantly different from the results obtained using the complete formulation. These differences include a much lower maximum temperature (700 K lower), a “longer” flame and lower (8–20%) values for the evaporation constant and drag coefficient. Thermal diffusion caused only minor changes (~1%) in the numerical predictions for the maximum temperature, evaporation constant and drag coefficient.Copyright