The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.

Bubbles, Drops, and Particles

Reverse osmosis desalination: Water sources, technology, and today's challenges

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.

On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion

An introduction to heat transfer

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

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Heat and Mass Transfer

The calculation of local flow properties in two-dimensional furnaces

Numerical predictions are presented for seven different two-dimensional turbulent “elliptic” flows. The solution procedure, which is embodied in the TEACH computer program, is described and numerical tests reported. The calculated properties of the seven flows are compared with experimental results and demonstrate that the procedure, with a two-equation turbulence model, provides adequate precision for many engineering applications. The two-equation model is shown, however, to be deficient in detail.

The Calculation of Two-Dimensional Turbulent Recirculating Flows

Measurements of the three components of mean velocity, the corresponding normal stresses, mean temperature, and wall heat flux are reported in a model furnace; they were obtained with a coaxial burner with a 20° quarl angle and swirl numbers of 0.3 and 0.5. Particular attention is devoted to the influence of the profiles in the plane of the burner exit; it is shown, for example, that combustion results in large increases in the values of maximum positive and negative velocity in the near-burner region and that the two swirl numbers result in significantly different profiles of all the measured flow properties. The variations in local furnace properties, including the wall heat flux, are quantified for the two swirl numbers and shown to agree, in general terms, with previous calculations; the location of maximum heat flux, for example, is significantly closer to the burner exit for the larger swirl number. Calculations, obtained from the numerical solution of conservation equations in differential form, are presented and compared with the measurements. Particular attention is devoted to the uncertainties associated with density fluctuation correlation and with the specification of a probability density distribution of scalar fluctuations. An attempt is made to quantify the precision with which calculations of furnace flow properties can presently be calculated.

Measurement and Calculation of Furnace-Flow Properties

The Calculation of Furnace-Flow Properties and Their Experimental Verification

The recent energy crisis and environmental burden are becoming
increasingly urgent and drawing enormous attention to solar-energy utilization.
Direct solar thermal power generation technologies, such as, thermoelectric,
thermionic, magneto hydrodynamic, and alkali-metal thermoelectric methods, are
among the most attractive ways to provide electric energy from solar heat. Direct
solar thermal power generation has been an attractive electricity generation
technology using a concentrator to gather solar radiation on a heat collector
and then directly converting heat to electricity through a thermal electric
conversion element. Compared with the traditional indirect solar thermal power
technology utilizing a steam-turbine generator, the direct conversion
technology can realize the thermal to electricity conversion without the
conventional intermediate mechanical conversion process. The power system is,
thus, easy to extend, stable to operate, reliable, and silent, making the
method especially suitable for some small-scale distributed energy supply
areas. Also, at some occasions that have high requirements on system stability,
long service life, and noiselessness demand, such as military and deep-space
exploration areas, direct solar thermal power generation has very attractive
merit in practice. At present, the realistic conversion efficiency of direct
solar thermal power technology is still not very high, mainly due to material
restriction and inconvenient design. However, from the energy conversion
aspect, there is no conventional intermediate mechanical conversion process in
direct thermal power conversion, which therefore guarantees the enormous
potential of thermal power efficiency when compared with traditional indirect
solar thermal power technology [1].

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Essam E. Khalil

Papers

The calculation of local flow properties in two-dimensional furnaces

The Calculation of Two-Dimensional Turbulent Recirculating Flows

Measurement and Calculation of Furnace-Flow Properties

The Calculation of Furnace-Flow Properties and Their Experimental Verification

Energy Analyses of Thermoelectric Renewable Energy Sources