On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion
01 Jan 1977-Vol. 16, Iss: 1, pp 719-729
TL;DR: In this paper, a model for the rate of combustion which takes into account the intermittent appearance of reacting species in turbulent flames is presented, which is applicable to premixed as well as diffusion flames.
Abstract: Principles of mathematical models as tools in engineering and science are discussed in relation to turbulent combustion modeling. A model is presented for the rate of combustion which takes into account the intermittent appearance of reacting species in turbulent flames. This model relates the rate of combustion to the rate of dissipation of eddies and expresses the rate of reaction by the mean concentration of a reacting specie, the turbulent kinetic energy and the rate of dissipation of this energy. The essential features of this model are that it does not call for predictions of fluctuations of reacting species and that it is applicable to premixed as well as diffusion flames. The combustion model is tested on both premixed and diffusion flames with good results. Special attention is given to soot formation and combustion in turbulent flames. Predictions are made for two C 2 H 2 turbulent diffusion flames by incorporating both the above combustion model and the model for the rate of soot formation developed by Tesner et al., as well as previous observations by Magnussen concerning the behavior of soot in turbulent flames. The predicted results are in close agreement with the experimental data. All predictions in the present paper have been made by modeling turbulence by the k -∈ model. Buoyancy is taken into consideration in the momentum equations. Effects of terms containing density fluctuations have not been included.
Citations
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TL;DR: In this article, the RNG κ-e turbulence model derived by Yakhot and Orszag (1986) based on the Renormalization Group theory has been modified and applied to variable-density engine flows in the present study.
Abstract: The RNG κ-e turbulence model derived by Yakhot and Orszag (1986) based on the Renormalization Group theory has been modified and applied to variable-density engine flows in the present study. The original RNG-based turbulence transport approximations were developed formally for an incompressible flow. In order to account for flow compressibility the RNG e-equation is modified and closed through an isotropic rapid distortion analysis. Computations were made of engine compressing/expanding flows and the results were compared with available experimental observations in a production diesel engine geometry. The modified RNG κ-e model was also applied to diesel spray combustion computations. It is shown that the use of the RNG model is warranted for spray combustion modeling since the ratio of the turbulent to mean-strain time scales is appreciable due to spray-generated mean flow gradients, and the model introduces a term to account for these effects. Large scale flow structures are predicted which ar...
1,200 citations
TL;DR: In this paper, an existing discrete droplet model of liquid sprays has been extended to include a stochastic representation of turbulent dispersion effects, and applications to simple test cases, including the dispersion of single particles, produce reasonable agreement.
Abstract: An existing ''discrete droplet'' model of liquid sprays has been extended to include a stochastic representation of turbulent dispersion effects. Applications to simple test cases, including the dispersion of single particles, produce reasonable agreement. However, two further applications involving volatile and combusting sprays show that the turbulent dispersion effects are small in comparison to those due to uncertainties about the initial conditions of the spray.
1,152 citations
Book•
01 Jan 2005TL;DR: This paper presents a meta-modelling framework for convection-Cartesian grids that automates and automates the very labor-intensive and therefore time-heavy and expensive process of convection itself.
Abstract: Introduction to Computational Fluid Dynamics is a textbook for advanced undergraduate and first year graduate students in mechanical, aerospace and chemical engineering. The book emphasizes understanding CFD through physical principles and examples. The author follows a consistent philosophy of control volume formulation of the fundamental laws of fluid motion and energy transfer, and introduces a novel notion of 'smoothing pressure correction' for solution of flow equations on collocated grids within the framework of the well-known SIMPLE algorithm. The subject matter is developed by considering pure conduction/diffusion, convective transport in 2-dimensional boundary layers and in fully elliptic flow situations and phase-change problems in succession. The book includes chapters on discretization of equations for transport of mass, momentum and energy on Cartesian, structured curvilinear and unstructured meshes, solution of discretised equations, numerical grid generation and convergence enhancement. Practising engineers will find this particularly useful for reference and for continuing education.
885 citations
Cites background or methods from "On mathematical modeling of turbule..."
...For further variations on Spalding’s model, see [44, 24]....
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...If turbulent reacting flow is considered then the effective Rfu is given by a variant [44] of the eddy-breakup model due to Spalding [74],...
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TL;DR: Oxy-coal combustion has generated significant interest since it was proposed as a carbon capture technology for newly built and retrofitted coal-fired power plants, and numerical models for sub-processes are also used to examine the differences between combustion in an oxidizing stream diluted by nitrogen and carbon dioxide as mentioned in this paper.
866 citations
Cites methods from "On mathematical modeling of turbule..."
...The eddy dissipation model (EDM) [234] was used in some numerical studies of oxy-coal combustion [95,201] in which the chemical reaction is governed by the large-eddy mixing time scale based on the eddy break-up (EBU)model proposed by Spaling [235]....
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01 Jul 1997
TL;DR: KIVA-3V as discussed by the authors is an extended version of KIVA3 that can model any number of vertical or canted valves in the cylinder head of an internal combustion (IC) engine.
Abstract: This report describes an extended version of KIVA-3, known as KIVA-3V, that can model any number of vertical or canted valves in the cylinder head of an internal combustion (IC) engine. The valves are treated as solid objects that move through the mesh using the familiar snapper technique used for piston motion in KIVA-3. Because the valve motion is modeled exactly, and the valve shapes are as exact as the grid resolution will allow, the accuracy of the valve model is commensurate with that of the rest of the program. Other new features in KIVA-3V include a particle-based liquid wall film model, a new sorting subroutine that is linear in the number of nodes and preserves the original storage sequence, a mixing-controlled turbulent combustion model, and an optional RNG {kappa}-{epsilon} turbulence model. All features and capabilities of the original KIVA-3 have been retained. The grid generator, K3PREP, has been expanded to support the generation of grids with valves, along with the shaping of valve ports and runners. Graphics output options have also been expanded. The report discusses the new features, and includes four examples of grids with vertical and canted valves that are representative of IC engines in use today.
852 citations
Additional excerpts
...32 and the valves (blocks 1, 10, 13, 17, 21, 26, 29, 33, 37), the level of the valve body (2, 11, 27), the level of valve travel below the valve pockets (3, 12, 15, 19, 28, 31, 35), and the level of the valve pockets (4, 7, 16, 20, 32, 36)....
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References
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TL;DR: In this article, a unified statistical analysis of premixed turbulent flame supported by a single-step global reaction is presented, where a set of time-averaged balance equations derived from the exact equations of reacting turbulent flow under a thin shear layer, fast chemistry approximation are employed.
417 citations
TL;DR: In this article, a physical model for the prediction of the turbulent diffusion flame is presented, where the turbulence is represented by differential equations for its kinetic energy and dissipation, equilibrium chemical reaction without intermediates is assumed, standard relations for the thermodynamic properties are applied, a differential equation for the concentration fluctuations is solved, and a "clipped" normal probability distribution function is proposed for the mixture fraction fluctuations.
343 citations
TL;DR: In this paper, the formation of soot particles is regarded as a result of a branched-chain process and of the destruction of active particles on the surface of the soot particle being formed.
240 citations
TL;DR: In this paper, values of local flow properties, obtained by solving appropriate conservation equations in finite-difference form and with boundary conditions corresponding to four furnace arrangements, are presented and compared with measurements.
234 citations
TL;DR: The validity of light-scatter measurements as a basis for determining soot particle size and concentration from point to point within a flame has been examined in relation to measurements on a special propane burner as discussed by the authors.
116 citations