SESSION 14
MODELING OF COMPREHENSIVE SYSTEMS II
COMBINED HEAT TRANSFER OF HIGH TEMPERATURE MULTIPHASE
FLOW IN THE CHANNEL WITH DEPOSITION FILM ON THE WALL AND HOMOGENEOUS
VAPOUR CONDENSATION
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
radiativeconvective 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 radiativeconvective heat
transfer in it.
The first problem of radiativeconvective heat transfer of multiphase flow was solved as twodimensional in the narrow channel approach. The turbulence
characteristics of the flow were predicted by means of semiempirical
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
semiempirical 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 twolayers 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 twopoint algebraic equations for
oneside 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 (C_{v 0}=0.01, C_{d 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.
MODELING OF A SPRAY COMBUSTION WITH NONGRAY
RADIATION
Seung Wook Baek and Chang Eun Choi
Korea Advanced Institute of Science and Technology
Aerospace Engineering Department,
3731 Gusungdong, Yusungku, 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 centerhole and assisting air from the concentric annulus with swirling. EulerianLagrangian 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
CO_{2} and H_{2}O 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.
UNSTEADY COMBUSTION OF DUST/AIR MIXTURES IN AN
ENCLOSED VOLUME
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 twotemperature, onevelocity
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 highfrequency 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.
USE OF THE 2D COLLAPSED DIMENSION METHOD IN
ABSORBINGEMITTING MEDIA WITH ISOTROPIC SCATTERING
David A. BLANK  Subbash Chandra Mishra^{*}
 Visiting Faculty  Research Scholar
 Mechanical Engineering Dept.  Mechanical Engineering Dept.
 IIT Kharagpur  720 302  IIT 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 (3D) nature of radiation, even if
fluid flow and heat transfer phenomena are two dimensional, radiation has to be treated as 3D 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 3D radiative information of the problem
into its 2D 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 2D Radiation Calculations
in Absorbing Emitting Media”, Int. J. of Numerical Methods in Engineering,
Vol. 37, No. 18, pp. 30233036, 1994.
^{*}All correspondences should be made to:
Subbash Chandra Mishra EMail: scmNiitk.ernet.in
c/o Dr. Manohar Prasad
Dept. of Mechanical Engineering
IIT Kanpur  208 016
(UP) INDIA
