Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), 1686–1688

An improved analytical model for the description of the anode contraction zone of a high intensity arc takes radiation effects into account. The conservation equations for the anode contraction zone and the adjacent undisturbed arc column are solved numerically with a relaxation method. Results for atmospheric pressure argon arcs at three different currents demonstrate that radiation losses reduce temperature peaks substantially and, at the same time, provide a smooth matching of arc column and contraction zone solutions. Although the model seems to be adequate for a large portion of the anode contraction zone, the results indicate that refinements of the model are necessary for the region close to the anode, in particular, deviations from LTE have to be taken into account.

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On the origins of spray sectional conservation equations

Combustion and Flame ◽

10.1016/0010-2180(93)90085-h ◽

1993 ◽

Vol 93 (1-2) ◽

pp. 90-96 ◽

Cited By ~ 132

Author(s):

J.B. Greenberg ◽

I. Silverman ◽

Y. Tambour

Keyword(s):

Conservation Equations

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Numerical simulation of gas-solid flow in an interconnected fluidized bed

Thermal Science ◽

10.2298/tsci121220002c ◽

2015 ◽

Vol 19 (1) ◽

pp. 317-328 ◽

Cited By ~ 4

Author(s):

Giuseppe Canneto ◽

Cesare Freda ◽

Giacobbe Braccio

Keyword(s):

Numerical Simulation ◽

Fluidized Bed ◽

Experimental Tests ◽

Solid Particles ◽

Multiphase Model ◽

Cold Model ◽

Conservation Equations ◽

Solid Flow

The gas-particles flow in an interconnected bubbling fluidized cold model is simulated using a commercial CFD package by Ansys. Conservation equations of mass and momentum are solved using the Eulerian granular multiphase model. Bubbles formation and their paths are analyzed to investigate the behaviour of the bed at different gas velocities. Experimental tests, carried out by the cold model, are compared with simulation runs to study the fluidization quality and to estimate the circulation of solid particles in the bed.

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Analytical Formulation-Based Soot Modelling in Ethylene Laminar Jet Diffusion Flames

10.1115/gt2021-58896 ◽

2021 ◽

Author(s):

Amit Makhija ◽

Krishna Sesha Giri

Keyword(s):

Volume Fraction ◽

Diffusion Flames ◽

Soot Formation ◽

Mixture Fraction ◽

Soot Volume Fraction ◽

Smoke Point ◽

Computational Time ◽

Detailed Model ◽

Conservation Equations ◽

Oxidation Rates

Abstract Soot volume fraction predictions through simulations carried out on OpenFOAM® are reported in diffusion flames with ethylene fuel. A single-step global reaction mechanism for gas-phase species with an infinitely fast chemistry assumption is employed. Traditionally soot formation includes inception, nucleation, agglomeration, growth, and oxidation processes, and the individual rates are solved to determine soot levels. However, in the present work, the detailed model is replaced with the soot formation and oxidation rates, defined as analytical functions of mixture fraction and temperature, where the net soot formation rate can be defined as the sum of individual soot formation and oxidation rates. The soot formation/oxidation rates are modelled as surface area-independent processes. The flame is modelled by solving conservation equations for continuity, momentum, total energy, and species mass fractions. Additionally, separate conservation equations are solved to compute the mixture fraction and soot mass fraction consisting of source terms that are identical and account for the mixture fraction consumption/production due to soot. As a consequence, computational time can be reduced drastically. This is a quantitative approach that gives the principal soot formation regions depending on the combination of local mixture fraction and temperature. The implemented model is based on the smoke point height, an empirical method to predict the sooting propensity based on fuel stoichiometry. The model predicts better soot volume fraction in buoyant diffusion flames. It was also observed that the optimal fuel constants to evaluate soot formation rates for different fuels change with fuel stoichiometry. However, soot oxidation strictly occurs in a particular region in the flame; hence, they are independent of fuel. The numerical results are compared with the experimental measurements, showing an excellent agreement for the velocity and temperature. Qualitative agreements are observed for the soot volume fraction predictions. A close agreement was obtained in smoke point prediction for the overventilated flame. An established theory through simulations was also observed, which states that the amount of soot production is proportional to the fuel flow rate. Further validations underscore the predictive capabilities. Model improvements are also reported with better predictions of soot volume fractions through modifications to the model constants based on mixture fraction range.

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