Iosif G. Zaltsman, Michail V. Brykin
Department of Gas Dynamics and Heat- and Mass Transfer
Inst. of High Temperatures, Russia Academy of Sciences, Moscow

It'’s examined a problem of turbulent flow and heat- and mass transfer of high temperature gas, containing micron size polydispersed particles (droplets) and vapour of condensing media (which models the products of coal dust combustion at temperatures over 2500 K). The conditions are considered when due to radiative-convective cooling along the channel at some distance from its entrance a homogeneous condensation and appearance of sub micron droplets in the flow take place.

The existence of slag film on the wall due to droplets deposition from the flow and heterogeneous vapour condensation on the film surface is taken into account. The wall of the plane channel is considered to be metal and water cooled, which leads to formation of frozen slag layer and slowly moving liquid slag film on it.

The solution is obtained by means of splitting of the whole problem as follows: at first we predict the mean flow parameters, Stanton number and friction in the channel with chosen wall temperature; then the characteristics of homogeneous condensation are predicted and then we employ the obtained data for prediction of the deposition film thickness and radiative-convective heat transfer in it.

The first problem of radiative-convective heat transfer of multi-phase flow was solved as two-dimensional in the narrow channel approach. The turbulence characteristics of the flow were predicted by means of semi-empirical dependence. The characteristics of homogeneous condensation were predicted on the basis of kinetics equation solution with known flow velocity and bulk temperature variation along the channel. Then the first problem could be resolved with known sub micron droplets concentration and size distribution, and the following influence of flow parameters on droplets characteristics is small due to the predicted fact, that distribution function rapidly establishes after abrupt homogeneous condensation process and slowly changes along the channel (without taking the coagulation process into consideration).

In radiative fluxes predictions the particles optical properties were defined by means of Mie theory for spectral complex refraction indexes (for large droplets - on the basis of data for slag, for small droplets - on the basis of data for optial silicon glass). In view of the predicted factor of primary influence of large droplets deposition on film formation its absorption coefficient was defined on the basis of data for slag. The input of both droplets fractions was taken into account.

Mass transfer rate of the flow with film surface was predicted on the basis of semi-empirical approach. The main mechanism of large droplets deposition was considered to be the turbulent migration, of small droplets- the thermophoresis.

The problem of combined heat transfer in two-layers liquid/frozen film was solved by means of iterative algorithm for definition of film thickness, corresponding to heat- and mass transfer rates in the channel. The discrete form of energy equation and system of two-point algebraic equations for one-side radiative fluxes were solved with the aid of vector sweep method.

The results of predictions of heat transfer and film characteristics are presented for the case when radiative heat transfer rate is substantially higher, then the convective one. In the considered case of low inlet vapour and slag droplets mass concentrations (Cv 0=0.01, Cd 0=0.02) the contribution of small silicon condensed droplets in heat - and mass transfer is small, but micron size slag droplets make a substantial input in radiative fluxes, as well as in mass transfer rate of the flow, and hence strongly influence the film characteristics and heat transfer in the channel.

The legitimacy of the problem solution splitting method is discussed.


Seung Wook Baek and Chang Eun Choi
Korea Advanced Institute of Science and Technology
Aerospace Engineering Department,
373-1 Gusung-dong, Yusung-ku, Taejon, Korea

The vaporization and combustion of liquid spray in a cylindrical combustor was numerically studied. Mixture of liquid droplets and air was assumed to be ejected from the center-hole and assisting air from the concentric annulus with swirling. Eulerian-Lagrangian scheme was adopted for the two phase calculation. The interactions between two phases were considered with the PSIC model. The effect of radiation has been evaluated by adopting the discrete ordinates method (DOM) to solve the radiative transfer equation (RTE). The weighted sum of gray gas model (WSGGM) was applied to estimate the nongray radiation by CO2 and H2O gases.Absorption coefficients obtained from WSGGM is used with DOM by summing solution of the RTE for each gray gas. Gas flow patterns, droplet trajectories and contours of temperature and mass fraction of the gas species were predicted with swirl number, droplet diameter, and equivalence ratio taken as parameters. Calculations showed that the vaporization and the consequent combustion efficiency were enhanced with the increase of the swirl number and with the decrease of the droplet size. Due to the effect of radiation, the gasification of the droplets occurred faster at far upstream position in the chamber, which caused a thicker flame. The exhaust gas temperature was also found to decrease.


Petr M. Krishenik, Konstantin G. Shkadinskii
Institute of Structural Macrokinetics Russian Academy of Sciences,
Chernogolovka, Moscow Region, 142432 Russia.

Combustion of dust/air mixture is studied which account of convective, radiative and conductive heat transfer. A two-temperature, one-velocity mathematical model is proposed for the analysis of the unsteady processes of the combustion of the dust/air mixture in an enclosed volume. Temperatures of the particles and gas are assumed to be different. The radiative heat transfer is described by the diffusion approximation. The number of Mach is taken to be M<<1. The pressure of gas was uniform on space (homobaric flow) and only depended on time. We follow this since the high-frequency perturbations are absent and the velocity of gas small compared to the velocity of sound.

In addition, it was assumed that the forces of friction between the gas and the particles are great. Only in this case, the velocity of the gas is equal to the velocity of the particles. The system of differential equations was derived in Lagrangian form. The solutions of differential equations are characterized by two different characteristic time and spatial dimensions. This results in the formation of the time and spatial boundary layers of a complicated structure that changes with variation parameters. Numerical solutions involved an adaptive implicit, finite difference scheme.

Depending on the characteristics of the condensed matter (sizes and ignition temperature of the particles, a kinetic law of heterogeneous reaction), dynamic regimes of unsteady process of combustion for the suspension were investigated. Our theoretical studies are focused on the dynamic regime of combustion. The unsteady combustion regime is determined by combination of the following factors: radiative, convective and conductive heat transfer. If the chemical reaction is accompanied by the gasification of condensed phase and the radius of particles exceed the critical value, then the maximum temperature of particles, front velocity and velocity of convective flow increase. At the stage of formation of combustion processes, the convective heat heat transfer results in a decrease of combustion wave. Transition from slow conductive combustion to the fast radiative one has an explosive character.

If the particles absorption the gaseous oxidizer, then the rate of heterogeneous reaction, the velocity of combustion wave and maximum temperature of particles decrease. If the particle size is lower than the critical one, the convective flux leads to an increase in duration of time initiation and in limiting case this time tends to infinity.


David A. BLANKSubbash Chandra Mishra*
Visiting Faculty Research Scholar
Mechanical Engineering Dept.Mechanical Engineering Dept.
IIT Kharagpur - 720 302IIT Kanpur - 208 016
(W.B) India(U.P.) India

Thermal radiation is very important aspect of industrial processes involving high temperatures. Due to three dimensional (3-D) nature of radiation, even if fluid flow and heat transfer phenomena are two dimensional, radiation has to be treated as 3-D phenomenon. Hence for conjugate convection - conduction - radiation problems, numerous computational complexities arise resulting in increased computer time and problem formulational difficulties. The available practical methods such as Monte Carlo, Zone, Discrete Ordinate, Discrete Transfer, Discrete Intensity and Heat Ray methods have limited applications for the solution of such radiative problems. Of these only Monte Carlo method has been shown to give accurate solutions below an optical thickness of 0.1. However, Monte Carlo is expensive and hard to use in full combustion simulations. For the scattering case, the use of such methods become even more restrictive. Moreever, it is important to note that in internal clean burning combustion engines the typical optical thickness one encounters are of the order of 0.1 - 0.001. Yet because of extremely high temperatures encountered, radiation transport remains very significant in such problems.

For the first time a Cartesian based method is proposed for combustion problems involving one ordinate symmetry and absorbing - emitting media with isotropic scattering. This method collapses the 3-D radiative information of the problem into its 2-D solution plane and is applicable for all ranges of optical thicknesses while maintaining almost analytic accuracy. To accomplish this task, this method makes use of effective intensity rays (EIR) each of which contains the information of a plane of real intensity rays perpendicular to the solution plane. As demonstrated in the reference A, this novel procedure thus eliminates the use of solid angles from the formulation and reduces both the complexity and computational expense involved in the solution of such problems.

Reference (A) : David A. Blank, “The Cartesian Collapsed - Dimension Method for use in Numerical 2-D Radiation Calculations in Absorbing- Emitting Media”, Int. J. of Numerical Methods in Engineering, Vol. 37, No. 18, pp. 3023-3036, 1994.
*All correspondences should be made to:
Subbash Chandra Mishra E-Mail:
c/o Dr. Manohar Prasad
Dept. of Mechanical Engineering
IIT Kanpur - 208 016

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