POSTER SESSION II
METHOD OF RADIATIVE COEFFICIENTS AND ITS APPLICATION
IN THERMAL CALCULATIONS OF PRACTICAL INDUSTRIAL CASES
Department of Process Engineering
Technical University of Brno, Czech Republic
Considering heat exchange equipment in general, heat transfer
is usually a combined process consisting of conduction, convection
and radiation. In Calculation procedures there is a need to determine
a certain strategy taking into consideration a prevalent component
of heat transfer, the influence of other components, the degree
of simplification of a mathematical model being created, available
data from experiment, the ratio of operation etc.
The application of the method of radiative coefficients has proved
itself to be an efficient and useful tool for the evaluation of
the radiative component of combined heat transfer in various industrial
The dependence between the temperature of surfaces and the heat
fluxes in an enclosure with isothermal gas is defined by a set
of non-linear algebraic equations. By their modification, a direct
expression of the radiative heat flux at the surface has been
obtained through radiative coefficients and source and sink temperatures.
Radiative coefficients can be determined analytically for some
fundamental systems - infinite parallel plates, part of plate
and enclosing area, infinitely long cylinders and concentric spheres.
These systems are represented by an enclosure consisting of two
surfaces with given emissivities and temperatures filled with
gas of a known constant temperature. Radiative coefficients are
functions of configuration factors, emissivities of surfaces and
emissivity of gas for determined mean beam length dependent on
the system in question. The application of this method is very
effective especially in the case of simple isothermal enclosures
consisting of two surfaces with given emissivities and temperatures,
filled with gas of a known temperature.
Using the method of radiative coefficients, quite new and original
methods for the evaluation of the radiative component in the case
of combined heat transfer have been developed. The creation of
these methods was initiated by attempts to solve industrial cases.
The mathematical model for the evaluation of the radiative component
in the case of bare tube banks/bundles considers individual tubes
surrounded by gaseous layers. The actual surrounding volume of
these layers was substituted by an equivalent cylindrical surrounding
volume for the simplification of geometry to be able to apply
the fundamental system with infinitely long cylinders. The main
result of the calculation is the evaluation of heat flux density
at the tube outer surface which is represented by the inner cylinder
of the substituting system. Consequently the radiative heat transfer
coefficient is evaluated.
As an application the thermal calculation of the heat exchanger
primary reformer - type TANDEM can be mentioned. The radiation
shares on the total heat flux with 18 to 30% dependent on the
number of baffles in this special shell -and- tube heat exchanger.
The mathematical model based on the method of radiative coefficients
can be incorporated into any program used to predict the thermal
performance of a tubular heat exchanger and/or of a convective
section with bare tubes in a furnace. A computer program based
on the above method has been incorporated into HTRI software.
A method for comparatively simple calculation of combined heat
transfer in the case of finned tubes (convection + radiation +
conduction in fins) is compatible with the above method for calculation
of heat transfer in the case of bare tubes. The application of
the method of radiative coefficients is a common point of the
two methods. The resulting value of heat flux density is given
by the product of this value in the case of bare tubes, correction
factor for fin thickness and above all the heat flux multiplicator
which expresses the fins influence from the radiation point of
view. This factor is given by the ratio of the radiative heat
flux on the tube surface in the case with the presence of fins
and that on the bare tube surface. The values of both heat fluxes
can be obtained by solving equations of the heat balance for surface
zones (using a simple application of the zone method) considering
conduction in fins. In the case of calculating a convective section
in the furnace, considering cooling the flue gas from about 400oC
to 250oC the share of the radiative heat transfer is
A model for the calculation of the radiative heat flux from a
radiation chamber to the shield tubes of a furnace and the evaluation
of the radiative heat transfer coefficient as a boundary condition
in calculating temperature distribution using the method of finite
elements can be considered as another applications of the method
of radiative coefficients.
Relatively simple procedures based on this method have been developed
with the purpose of being convenient for practising engineers.
These procedures are based on some simplifications enabling the
evaluation of the radiative component in combined heat transfer.
Computer programs enable us to explore the sensitivity of selected
parameters as a result of e.g. the variation in geometrical parameters
and operation conditions.
METHODS FOR MODELLING PROCESS FURNACES
Department of Process Engineering
Technical University of Brno, Czech Republic
Furnaces are inherent equipment in many processes in both the
chemical and petrochemical industry. In a number of this processes,
particularly in those for bulk chemical production, a process
furnace forms the core of the chemical/petrochemical plant. It
is quite usual that cost of the furnace system ranges between
10 and 30 % of the total investment and, as for the operating
cost, fuel burned in the furnace can represent up to 90 % of the
energy bill. It is therefore evident that furnace design methods
play an important role. An experimentally verified mathematical
model which enables us to simulate the behavior of various arrangements
of furnace system belongs to a list of designer's powerful tools.
The application of the model in assisting effective operation
is of even greater importance.
The basic requirements and aspects concerning the methods for
modelling have to be specified in connection with the choice of
methods (the purpose, use and the field of application of a mathematical
model, the complexity of furnace geometry, the input data available
for simulation, etc.). Two different approaches are presented:
(i) the first one deals with a detailed and complex mathematical
model for a specific purpose;
(ii) a simple mathematical model convenient for rapid calculation
of tubular fired heaters is the subject of the second one.
The mathematical model of a radiation chamber in steam reforming
based on the zone method (i) is a result of long term research.
It enables us to simulate thermal chemical processes both in the
combustion space and inside the reaction tubes. This model was
verified by measurements in a process plant.
A complete mathematical model capable of simulating the conditions
in a reaction furnace is formed by connecting the combustion space
model with that of reactions inside the tubes during its development
the model has passed through several stages due to its continuous
confrontation with the plant data and measured values obtained
in the specially designed testing program on an industrial size
steam reformer furnace. The permanent comparison of calculated
and measured values has made it possible to introduce a few simplifying
assumptions and some improvements in the practical application
of the zone method. A two dimensional section of radiation chamber
cross-section can be considered for modelling. This section is
limited by two tube rows which are considered as so called "specled
walls". An approximative way for the fast evaluation of direct
exchange areas has been developed based on analytical relations
and approved comparing the resulting values with those obtained
using the Gaussian method for numerical integration. the real
gas (flue gas) is substituted by three gray and one diathermic
component. A universal set of absorption coefficients independent
on temperature and gas composition was used which is advantageous
for repeated calculations (e.g. different regime of furnace operation
) because direct exchange areas can be calculated only once. As
the calculations in the early developmental stage of a model considering
plug flow of flue gas led to an unrealistic maximum of the tube
outer surface temperature ( compared with the measured one) a
suitable level of back mixing, based on flue gas flow visualization,
has been introduced into the model.
By means of the model the influence of selected parameters on
main characteristic quantities in steam reforming was investigated,
a method for steam reforming design was developed (and applied
in practise) and a knowledge base for fuzzy expert system was
created. The widest possible application of the verified mathematical
model is obviously in the sphere of furnace operation in technological
processes. The model enables technologists and operators to simulate
expected operation conditions.
The simple mathematical model of furnaces (ii) based on Hottel's
One-Gas-Zone Method is extended a verified. The mathematical model
is constructed in such a way as to enable the calculation to be
applied to any tubular fired heater. This implies that the furnace
with an arbitrary geometry and consisting of both radiation chamber
and convective sections can be calculated. The computer program
based on this model basis involves two major alternatives for
calculation. The first one deals with complete calculation of
process fluid heating inside tubes by considering the pressure
drop. In the second one the model of heat transfer inside the
tubes is replaced by given values of the heat transfer coefficient
and input/output temperature of the medium.
Special attention is given to a model for the calculation of heat
flux from a radiation chamber to the shield tubes. Heat flux at
the shield tubes is evaluated using the application of the method
of radiative coefficients for an enclosure where the analytical
solution is known. Assuming the radiative heat transfer from the
radiation chamber flue gas to the shield tubes is approximated
by that of an equivalent gaseous volume belonging to the shield
tubes and surrounded by two surfaces- the absorbing one (shield
tubes transferred to the "specled wall" ) and the radiatively
adiabatic one, substitution by a simple fundamental system is
feasible and the radiative heat flux density at the tube surface
can be evaluated.
The radiative component of heat transfer is also considered in
the calculation of convective sections.
Compared with the model based on the zone method a simple mathematical
model for relatively rapid calculations for process furnaces provides
designers and operators with a useful tool in those cases where
distribution of temperatures, heat fluxes and other quantities
are not required. An algorithm for a furnace with arbitrary geometry
consisting of radiation chamber and convective sections has been
created. Special emphasis was laid on simplicity and universality.
This model proved itself to be very useful in a new method for
effective furnaces integration into processes based on Pinch Technology.
MONITOR SYSTEM FOR RADIATION TRANSFER
Sergey T. Surzhikov
Institute for Problems in Mechanics
Russian Academy of Sciences, Moscow, Russia
Monitor System for Radiation Transfer (MSRT) is an interactive
computer system intended for creating radiative models.
Thee concept radiative model includes the following three parts:
This interactive system consists of the following three parts:
Base of Models, Data Base, Software.
- optical model (spectral, group and total absorption and emission
- model for radiation heat transfer.
At the present time MSRT contains information about following
components: H, He, C, N, o, Na, Mg, AL, Si, Ar, K, Ca, N-, O-,
O2, N2, NO, C2, CO, CN, H2, C3, H20, CO2, CO+, N2+, SiO, NO2,
He (+1), He (+2), C (+1)-C (+5), N (+1)-N (+5), O (+1)-O (+5),
Na (+1)-Na (+5), Mg (+1)- Mg (+5), Al (+1)-Al (+5), Si (+1)-Si
(+5), Ar (+1)-Ar (+5), K (+1)-K (+5), Ca (+1)-Ca (+5). Temperature
range: 1000-20000-150000 K, pressure range: 0.001-100 atm.
- Base of Models.
This part of the MSRT consists of the program modules which are
realize the mathematical models of radiative processes in gases,
plasma, dispersive media:
- The calculation methods for modeling of elementary radiative
processes: probabilities and cross-section at the bound-bound,
bound-free and free-free transitions; oscillator strengths, Franck-Condon
factors; modeling of scattering processes by theory Mie;
- The calculation methods for modeling of complex radiative
processes in gases and plasma: the group and spectral models of
low temperature plasma optical properties: absorption coefficients,
half-spherical emission capability, Plank and Rosseland coefficients.
- The calculation methods for problem of radiative transfer
in selective-emitting, selective-absorbing and selective-scattering
- Data Base
This part of the MSRT contains the following data:
- probability, cross-section, rate constant;
- spectroscopic properties of the particles (atoms, molecules,
This part of the MSRT consists of computer implementation of the
models, service procedures, program modules for data manipulation.
The different radiative models are presented: spectral absorption
coefficients of low-temperature plasma with atomic lines structure,
"smeared rotational line"absorption coefficients for
diatomic molecules, absorption coefficients of diatomic molecules
with rotational line structure.
For example, the figures show spectral absorption coefficients
of air plasma without and with atomic lines structure.
THE INTERACTION OF RADIATION WITH CONVECTION
IN SUBSONIC LAVAL NOZZLES OF LASER'S PLASMA ACCELERATORS
Sergey T. Surzhikov
Institute for Problems in Mechanics
Russian Academy of Sciences, Moscow, Russia
The laser-heated plasma accelerator (LHPA) operation is based
on the phenomenon of stationary existence of a low-temperature
plasma (continuous optical discharge, COD) in a focused laser
beam (as a rule, CO2-continuous wave laser)1-3.
The major parameters of LHPA are1-5: temperature region
- 300-20000 K, pressure - 1 atm, inlet velocity - 1-100 m/s, nozzle
length- 20-30 cm, height of the plane laval nozzle critical section
- 1-2 cm.
The LHPA operation mode is determined by the following set of
Physical and mathematical models of radiative-gas dynamic process
in an subsonic Laval nozzle of laser-heated plasma accelerator
operating in the mode of radiative combustion of a continuous
optical discharge are described.
- the laser radiation power, the laser radiation wave number,
the quality and geometry of the beam, and time characteristics
of laser radiation;
- type of gas and working pressure;
- the velocity and the spatial distribution of gas flow in the
vicinity of COD;
- the structural peculiarities of the gas dynamic flow, first
of all, the channel shape and the manner of gas flow supply and
The evolution of temperature and gas dynamical characteristics
distributions in the laser radiation field in a Laval nozzle is
described by a system that comprises the two-dimensional equations
of conservation of energy, the continuity and Navier-Stokes equations,
the equations of selective thermal radiation transfer (in the
form of a multigroup P1-approximation of the spherical harmonics
method), and laser radiation transfer (in the geometrical optics
The implicit-explicit numerical method is developed for solving
the self-consistent equations system in a curvilinear calculated
grid. Because the pressure variation was small, only the temperature
dependence of the thermodynamic, optical, and transport properties
of the gas was taken into account. The main iteration process
was organized using the equations of conservation of energy and
the equations of transfer of selective thermal and laser radiations.
At this stage, we were in fact solving the truly nonstationary
problem of radiative-conductive heat exchange. On reaching the
convergence of the iteration process at each time step, the iteration
solution of the system of gas dynamical equations was started,
after which all of the indicated iteration processes were repeated
until a full convergence of the unknown functions at a time step
The results of numerical modelling of subsonic air flow in various
Laval nozzles are discussed. The parameters of LHPA operating
under conditions of radiative combustion of COD are found by calculations,
and conditions are established under which stationary eddy flow
structures may be expected to occur because of a large gas mass
flowing around the COD combustion region. The calculation results
make it possible to point out one of the probable mechanisms of
COD stability loss in a gas flow, namely, the mechanism associated
with the occurrence of intense vortex motion behind a discharge.
This suggests sum means of improving the efficiency of operation
of power devices of the indicated class.
- Jones, L.W., Keefer, D.R., NASA's Laser-Propalsion Project,
Astronautics & Aeronautics, V.20, No.9, pp.66-73, 1982.
- Glumb, R.J., Krier, H., Concepts and Status of Laser-Supported
Rocket Propulsion, Journal of Spacecraft and Rockets, Vol.21,
No.1, pp.70-79, 1984.
- Merkle, C.L., Prediction of the Flowfield in Laser Propulsion
Devices, AIAA Journal, Vol.22, No.8, pp.1101-1107, 1984.
- Myrabo, L.N., Airbreathing Laser Propulsion for Transatmospheric
Vehicles, Proceeding 1987 SDIO Workshop on Laser Propulsion, University
of California, pp.173-208, 1990.
- Surzhikov, S.T., Radiative-Convective Heat Transfer in an
Optical Plasmotron Chamber, High Temperature, V.28, No.6, pp.1205-1213,
THE EFFECT OF ASH PARTICLES' COMPLEX REFRACTIVE
INDEX ON RADIATIVE HEAT TRANSFER WITHIN A BOILER FURNACE
Dusan N. Trivic*, and Milan Mitrovic**
*The Institute of Nuclear Sciences "Vinca"
Department of Thermal Engineering and Energy Research
P.O. Box 522, 11001 Belgrade, Yugoslavia
**Faculty of Technology and Metallurgy, Belgrade University
A three-dimensional mathematical model for predicting turbulent
flow with combustion and radiative heat transfer within a furnace
was developed. The model consists of two linked sections: (1)
the transport equations which are nonlinear partial differential
equations solved by a finite difference scheme, and (2) the radiative
heat transfer which was analyzed by the zone method. The Monte
Carlo method was used to evaluate total radiative interchange
in the system between the zones. An existing rigorous theory of
interaction between infrared waves and solid particles developed
for several simple particle geometries was used. The resulting
set of equations, called the Mie equations, enable the calculation
of absorption and scattering coefficients, for given particle
shape, particle size, complex refractive index, mass concentration,
density of particle materials, and wavelength of the incident
radiation. With this model the series of calculations with varying
gas radiative properties models, loads, types of fuel, excess
air, burner tilt angles, and several particle parameters can be
performed. The effect of these variables on the gas temperature
and heat flux distribution within the furnace can be studied.
The mathematical model was previously validated against experimental
data collected on two large furnaces by comparison of the measured
and predicted gas temperature and heat flux distribution. The
purpose of this paper is to study only the influence of the ash
particles' complex refractive index on the radiative heat transfer
within the furnace of a pulverized-coal-fired boiler. The method
of approach is mathematical modelling and simulation. Three various
complex refractive indices (for three particle materials: soot,
alumina and simulated ash) were considered. The effects of these
complex refractive indices on: 1. Heat absorbed by water wall
and secondary superheater from combustion chamber gases (radiation,
convection and total); 2. Combustion chamber exit temperature
and 3. Heat flux distribution on furnace walls were presented.
Among the others, the following conclusions are drawn. Soot and
alumina were compared for 25 m mean particle diameter, and it
was found that complex refractive index of the soot gives a higher
heat transfer to the sink surfaces and a lower gas temperature
at the furnace exit than the alumina complex refractive index.
The comparison of complex refractive index for simulated ash and
for soot, for 5 m
mean particle diameter, shows that the soot
complex refractive index gives a higher heat flux to the water
walls and lower gas temperature at furnace exit than the complex
refractive index for simulated ash. The real value of the complex
refractive index for ash material in pulverized-coal-fired boiler
would be somewhere between the values given for soot and alumina.
The mathematical model given here is believed to be widely applicable
for the analyses of furnace combustion chambers.
THERMAL RADIATION IN A PASSIVE CONTAINMENT COOLING SYSTEM BY
NATURAL AIR CONVECTION
Xu Cheng*, Franz-Josef Erbacher**,
*Technische Universität Karlsruhe
Institut für Strömungslehre und Strömungsmaschinen
Postfach 6980, D-76128 Karlsruhe, Germany
Institut für Angewandte Thermo-und Fluiddynamik
Postfach 3640, D-76021 Karlsruhe, Germany
The Karlsruhe Research Center and the University Karlsruhe have
proposed a new containment concept for future pressurized water
reactors. This containment should ensure that it remains intact
even in severe core meltdown accidents and the decay heat can
be removed in a passive way by natural air convection and by thermal
To determine the coolability limit of such a passive containment
cooling system, experimental investigations are performed in the
PASCO (acronym for passive containment cooling) test facility
of the Karlsruhe Research Center. By these experiments different
effects, e.g. the effect of the heated wall temperature and the
wall emissivity, on heat transfer are studied. Moreover, a data
base is provided for validating advanced multi-dimensional computer
In addition to the experimental work, numerical calculations are
performed by using the three-dimensional computer code FLUTAN
to simulate flow conditions and heat transfer behavior in the
PASCO test channel, an one-sided heated rectangular flow channel.
Even though the FLUTAN code was successfully applied to many complex
thermalhydraulic problems, it did not contain radiative heat transfer.
To extend the application of the FLUTAN code to the PASCO problem,
a radiation model is developed with the following main features:
This radiation model is implemented in the FLUTAN code and numerical
calculations are performed. The numerical results agree well with
the experimental data concerning the distribution of the air temperature
and the surface wall temperature. For high wall emissivity thermal
radiation enhances the entire heat transfer of natural air convection
significantly, even at low temperature of the heated wall. Further
research works are underway to develop heat transfer correlations
of natural air convection coupled with thermal radiation in non-uniformly
heated, rectangular vertical channels.
- Radiatively non-participating fluids, grey and diffuse wall
- Net radiation method for enclosures.
- Analytical methods for view factor calculation.
- Macro-element method for improving numerical efficiency.
THERMAL SIMULATION OF A GLASS PANEL SUBJECTED
TO A FIRE RADIATIVE AND CONDUCTIVE MODELIZATION OF THE SEMI-TRANSPARENT
Joseph Virgone+*, Patrick Depecker+*,
+Université LYON 1, 69622 VILLEURBANNE Cedex,
* Centre de Thermique de l''I.N.S.A. de LYON, U.R.A.
Bat.307, I.N.S.A., 20 Av. A. Einstein, 69621 VILLEURBANNE Cedex,
This paper presents a study of the modelization of the thermal
behavior of glass used for windows in buildings subjected to the
typical solicitation of an accidental fire. The manufacturers
of this glass are concerned about predicting its behavior in the
kind of difficult conditions which generally lead to its mechanical
destruction, given that glass breaks when subjected to large,
rapid temperature variations. Safety standards require that sheet
glass resist for a certain length of time, to enable the evacuation
of people inside a burning building.
With the model we have constructed it is possible to follow, over
a period of time the thermal state of a glass sheet subjected
to a solicitation which is representative of a fire situation.
Radiation data are processed with the P1 method, transfer being
taken as unidirectional, given the thickness of the glass. Conduction
is represented by the heat equation, radiative and conductive
transfers being coupled. A detailed representation is given of
the boundaries of the mediums, radiative as well as conductive.
The aim of this study is to bring out not only the influence of
the thickness of the glass, but also its thermo-optic characterization,
using a spectrum of nongray medium, in relation to the traditional
opaque medium hypothesis. There is also to be an analysis of the
influence of the optic properties of the surfaces, which are different
for the two sides of the physical boundaries: those on the outside,
facing the external conditions, and those on the inside of the
glass. The results are given in the form of diagrams showing sensitivity
to these hypotheses.
IDENTIFICATION OF SIZE AND STRUCTURE OF SOOT
AGGLOMERATES AT THE EXHAUST OF DIESEL ENGINES
1Department of Mechanical Engineering,
University of Kentucky, Lexington, KY 40506-0046, U.S.A.
2Istituto Motori, CNR,
80125 Napoli, ITALY
Feasibility of multi-wavelength laser diagnostic to characterize
the soot agglomerates structure at diesel engine exhaust is invstigated.
Normalized scattered intensities and dissymmetry ratios are obtained
numerically for different soot agglomerates. Primary soot diameters
considered are between 20 and 50 nm, and the number of primary
spheres varies from 25 to 125. The results are obtained for incident
radiation wavelength spectrum of 200 to 500 nm. From the preliminary
analyses it is found that if the primary sphere diameter is estimated
a priori from TEM pictures (or other means), measurement of spectral
variation of dissymetry ratios can be used in characterizing the
morphology of the agglomerates accurately. It is concluded that
a more general study, which includes multiple fractal dimensions
for mono-or poly - dispersed agglomerates can easily be performed
by extending the approach presented here.
PRELIMINARY STUDY ON AIR-FUEL MIXING AND COMBUSTION
OF A DIVIDED-CHAMBER DIESEL ENGINE SYSTEM
F.E. Corcione, A. Fusco, G. Mazziotti, B.M.
Istituto Motori, CNR - Napoli, Italy
In recent years, numerous experimental studies were carried out
in optically accessible closed vessel, model combustion chamber
and rapid compression machines in order to understand the Diesel
combustion process. The advantage of using these devices is to
study the influence of a single parameter on the engine internal
process and to have large optical access for non-intrusive optical
measurement techniques. However, it is difficult to operate simultaneously
at high ambient temperature and pressure and with air swirl typical
of real engines. Therefore, optically accessible engines are used
to overcome these intrinsic limitations, even though severe constructive
modifications are need. In particular, measurement techniques
such as laser Doppler velocimetry (LDV), light extinction, Mie
scattering, 2-D particle image velocimetry (PIV), laser induced
incandescence (LII) and laser induced fluorescence (LIF) techniques
require special design since the orthogonal optical accesses could
influence negatively the engine behavior.
In the present paper, an alternative way to investigate the combustion
process with optical techniques which allows a realistic design
is proposed. It consists of a divided-chamber with longitudinal
and lateral optical accesses, connected to a flat piston engine
that supplies air swirl and typical of both direct injection and
prechamber diesel engines. This device allows to apply the optical
techniques mentioned above and the direct cinematography and flame
spectroscopy. Moreover, the internal processes can be reproduced
using the new KIWA-3 developed by A. Amsden at Los Alamos National
Laboratory, a computer program with block-structured mesh for
The present preliminary study aims at analyzing experimentally
and numerically the in-cylinder processes focusing the attention
on two main aspects of Diesel combustion: I) air- fuel mixture
preparation and ii) spatial distribution of soot temperature and
concentration. High-speed direct cinematography at 8,000 frame/s
was used to visualize the spray distortion and to follow the entire
Diesel combustion process. The appearance of flame luminosity
was used to indicate the spatial region of the Diesel jet where
the combustion starts and the temporal evolution of the combustion.
The ignition start downstream the spray in the region where the
fuel is well atomized and the flame expands rapidly filling up
the chamber volume. This trend is confirmed by the computations
implemented with a new droplet breakup model and turbulent mixing-controlled
The computations confirm also the flame emissivity measurements
carried out by multicolor pyrometry at the same crank angle. Spectral
emissivity measurements, in the range 300 to 700 nm, were used
to investigate more quantitatively the combustion phenomenon.
In fact the chemical species such as OH and CH radicals as well
as the soot temperature and concentration were estimated in the
different locations of chamber volume.
SURFACE RADIATION EFFECTS ON NATURAL CONVECTION
COOLING OF A DISCRETE HEAT SOURCE IN AN OPEN-TOP CAVITY
A.A. Dehghan*i, M. Behnia**
*School of Mechanical Engineering
Yazd University, Yazd, Iran
**School of Mechanical and Manufacturing Engineering
The University of New South Wales
Sydney 2052, Australia
The heat transfer performance of an electronic heat generating
device mounted on one of the vertical conductive walls of a two-dimensional
open-top cavity is modelled numerically. Natural convection in
the fluid, radiation heat exchange between the surfaces of the
cavity, and condition in the vertical walls are considered. The
results are obtained for air in a cavity of 100 mm height, 20
mm width and with 2 mm thick vertical walls. The imposed heat
flux on the heating element is varied leading to a variation of
the heat flux based Rayleigh number from 1.148x104
to 8.03x104. Walls with different values of thermal
emissivity are considered in order to explore the effects of surface
radiation. Initial results were obtained neglecting radiation.
However, comparison of the numerical results with the experimental
data highlighted the importance of this mode of heat transfer.
This led to the inclusion of a radiative heat transfer model in
the computations. Noticeable changes in the thermal and flow fields
in the cavity are observed when the radiation is included. A reversed
flow in the cavity with the formation of a recirculation zone
in the proximity of the cold vertical wall is observed for the
conjugate radiation-convection case. This is attributed to a rise
in the temperature of the cold wall due to the radiation heat
exchange with the heating device. This behavior can not be predicted
if only natural convection is considered. Hence, it was concluded
that fully conjugate analysis, i.e. natural convection, radiation
and conduction, must be considered in the numerical modelling
of heat transfer from cavities with discrete heat sources for
accurate prediction of heat transfer data and flow and thermal
EFFECT OF AN EVOLVING AEROSOL CLOUD ON AN
UPWARD RADIATIVE HEAT TRANSFER
M. Zabiego*, G. Cognet, C. de Pascale
Centre d'Etudes de Cadarache Cadarache
*Present address: Department of Nuclear Engineering
and Engineering Physics, University of Wisconsin, Madison, WI
The present paper deals with radiative heat transfer through a
dense aerosol cloud.
We explain here the theoretical basis of a numerical model. In
this model we solve the radiative heat transfer equation which
coefficients are calculated with respect to the aerosol optical
properties (extinction and scattering coefficients). These optical
properties are determined using the Mie or Rayleigh theory, depending
on the aerosol size.
This model can be used in different cases, here we applied it
to the later phase of an hypothetical severe Pressurized Water
Reactor (PWR) accident, in a Molten Core Concrete Interaction
(MCCI) framework. We then show that the numerous aerosols generated
during the concrete ablation by the corium melt have a significant
effect on the radiative transfer in the reactor containment.
Indeed, we present an example of calculation using given aerosol
size and concentration distributions which allow us to determine
extinction and scattering coefficient profiles. Our instance does
not exactly model any experiment, however the physical conditions
are very close to the test L4 from the Advanced Containment Experiment
We also provide a calculation with constant values (with respect
to the position) for the extinction and scattering coefficients.
This last study will then allow us to simplify the radiative transfer
equation in our model and therefore shows the effect of such a
RADIATIVE AND CONVECTIVE HEAT TRANSFER IN
Z.F. Dong, M.A. Ebadian
Department of Mechanical Engineering
Florida International University
Miami, FL 33199 U.S.A.
The radiative and convective heat transfer in circular sectors
is numerically investigated in this paper. The flow is assumed
to be a steady and fully developed incompressible flow and the
entrance effects are considered. The momentum method is applied
to simulate the radiation of the fluid, which is nonscattering
absorptive gas. The thermal boundary condition is a constant temperature
on the wall. The control volume method is used to discrete the
governing equations for flow, heat transfer, and radiation. The
results show that the participation of radiation leads to the
enhancement of heat transfer, but changes the behavior of the
variation of the local Nusselt number along the axial direction.
For pure forced convection, the local Nusselt number decreases
monotonically from a large value at the entrance to an asymptotic
value. However, for combined radiative and convective heat transfer,
the local Nusselt number decreases until it reaches a minimum
value at certain downstream locations and then increases again.
NUMERICAL SIMULATION FOR RADIANT GAS FLOWS
IN COMPLEX STRUCTURES
BenWen Li, HaiGeng Chen
Thermal Engineering Department, Northeastern University,
Shenyang, Liaoning (110006), P.R. China
A new hybrid method is described for numerically solving radiative-convective
heat transfer in complex structures. The simulated thermal installations
can be combustion chambers or furnaces in which the obstructing
walls are set.
In this paper, Hottel zone method has been greatly improved. The
development include three parts. First, based on the analysis
of uniform sampling theorem and thermal radiation, the Uniform
Deterministic Discrete Method (UDDM) is presented for radiative
heat transfer in complex structures with participating media.
By uniform sampling versus random sampling in radiation, this
new technique is superior to Monte Carlo in accuracy, convergence,
speed and computer cost. In present paper it is applied to evaluate
the direct exchange areas of zone method even using fine grid.
Second, for energy matrix equations, the Principal Variable Correction
Method is described together with its physical principle analysis.
By using this new approach instead of Newton-Raphson or Broyden
iteration, the convergent solution can be achieved more fast and
easily. Finally, considering the combination of convective heat
exchange, a two-level grid is used, one for zone method, the other
for the Navier-Stokes finite- difference equation of gas fluid
KEYWORDS: thermal radiation, fluid flow, numerical method, Monte
MODELING OF A SOLAR RECEIVER DEDICATED TO
LPG CRACKING FOR ETHYLENE PRODUCTION
M. Epstein and A. Segal
Solar Research Facilities Unit, Weizmann Institute of Science, Rehovot, ISRAEL
A large solar central receiver plant for the cracking of liquid
petroleum gas (LPG) to produce 20.000 tone/yr ethylene has been
designed. The solar power required for this receiver is more than
30 MW at design point. This receiver has an hexagonal cross section
with 8 m each side and 8 m height. Two hundred forty cracking
tubes, 7.3 cm in diameter each, are distributed in parallel to
the receiver walls. The solar energy is introduced through the
top of this receiver.
The model of this receiver calculates the mode in which the concentrated
radiation entering the receiver aperture is redistributed through
radiative heat transfer between the various refracting and absorbing
surfaces, and then calculates the heat fluxes on the reactor walls.
These fluxes heat up the reacting gases and supply the enthalpy
for the endothermic cracking reactions.
In a series of similar cases for radiation heat transfer calculations
we used the zonal method where the internal surface of the receiver
and external surface of the reactor tubes are divided into surface
elements considered isothermal and equi-energetic. The dimensionality
of the problem depends the number of zones considered. the computational
time associated with formulating net radiative exchange in such
a type of enclosure varies roughly with the cube of the number
of zones into which the surface is divided. Therefore to treat,
by zonal method, a receiver with hundreds reactor tubes, where
each tube is considered a separately is an impossible task even
if we were using the most powerful computer. And for reactor modelling,
this accuracy can be superfluous.
In this case can be used successfully the classical concept of
equivalent gray plane introduced by Hottel and Sarofim. According
to this concept a row of tubes mounted parallel to a refractory
wall which received the radiative heat from exterior can be replaced
in calculations by an equivalent grey plane having that emissivity
which is a full measure of the effects of tube spacing and of
Following this concept we considered the receiver with six walls
having the equivalent emissivity as in Hottel and Serafim's model.
Each of these equivalent walls are divided into a number of zones.
In order to decrease the number of zones to a reasonable dimensionality
of the problem, we assumed that a few neighboring tubes belong
to the same zone. The height of this equivalent wall is divided
into a few parallel regions, therefore each zone characterizes
equal portion of the length of a group of few tubes.
The flux calculated on each zone following our previous model
(see for example: A. Segal and M. Levy: Solar Chemical Heat Pipe
in Closed Loop Operation: Mathematical Model and Experiments,
Solar Energy, Vol 51, No.5, pp. 367-376) gives the possibility
for evaluation of the flux on each segment from the length of
each reactor tube. The fluxes on the reactor tube are used as
an input to the endothermic reactions of LPG cracking for ethylene
production. The interface between the radiative part of this model
(into receiver enclosure) and its chemical part (inside the tube
reactor) is done through the wall temperatures on each reactor
segment. The chemical part generates a temperature profile on
the reactor walls which is used as improved boundary conditions
for the radiative part and a new heat flux calculation is generated.
The calculation converges to a unique steady state solution and
generates the final receiver wall temperatures, net heat flux
profile, reactor wall temperature profile and various other parameters.
This model has been helpful in designing this receiver for better
understanding of its properties. The computer program based on
this model was run for a variety of flow conditions, feed composition,
the catalyst activity, and pressure. Using this model made it
possible to establish optimal conditions for operating the receiver
and to establishment of the optimal configuration of the solar
field of heliostats required for this application.