simulation of radiative heat transfer in combustion … · flame day 2012, jan. 26th, 2012...
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Flame Day 2012,
Jan. 26th , 2012 Lappeenranta, Finland.
Simulation of Radiative Heat Transfer in
Combustion Systems
M. Hadi Bordbar, [email protected]
Laboratory of Modelling of Energy Systems
Lappeenranta University of Technology
Radiative Heat Transfer; Challenges
26.01.2012
42
4
0
( ) :
( , )( ) ( , )
( , ) ( . )4
s
s
Radiative Transfer Equation RTE
dI r s Ta I r s an
ds
I r s s s d
1- Integro-differential governing equation
2- Wavelength dependency ; Gray/Non gray modeling
3- Scale dependent phenomenon
4- Accuracy vs. computational time
Wavelength dependency Non gray Behavior
2
The spectral radiation feature is missing in the
current engineering approaches.
There is uncertainty in selecting the suitable
radiation model in different application
Review of LUT Activities
Research on
Radiative Heat
Transfer in LUT
Energy
Developing RTE solver;
Models for numerical
simulation of radiative heat
transfer in participating
media
Spectral Radiative
Properties of Molecular
Gases of combustion
products.
Developing multi-scale radiative exchange
method (MREM).
Mesh size analysis for MREM theory.
Developing the conventional version of the
Zonal code.
A correlation based Zone method.
Radiative heat transfer calculation in industrial
combustion systems using the CFD approaches
such as DOM, P1,…
Development of a code for exponential wide
band model (EWBM) using 6 different molecular
gases.
Development of a correlation based approach for
gray and non gray modeling.
Development of an artificial neural network
model (ANNM) to model the total emissivity of
CO2-H2O mixture.
Development of new weighted summation of gray
gas model
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25.2.2010
Radiative Heat Transfer; Modeling Tools
Type Ray Tracing Approaches
Radiative Heat Flux Approaches
CFD based Approaches Zonal Type Approaches
Examples •Monte Carlo •Discrete Transfer Radiation Method •REM2 Method
•Discrete Ordinate Method •Finite Volume Method
•Hottel Zone Method •MREM Method
Base of Theory
Tracing the emitted radiative energy bundles until they absorbed or exit from system.
Solving RTE in a discretized computational domain using CFD fine mesh structure and diffuse radiation heat transfer between neighboring cells
Using Coarser Mesh Structure for Solving RTE. Writing the radiative balance for each coarse volume and surface cell using the pre-calculated exchange factors. Using the exchange factor to obtain the amount of radiative heat exchange between each pair of coarse cells in the system.
Points & Difficulties
•High level of accuracy •High computational cost •Different algorithm than CFD methods- difficult to be used in hybrid system with CFD solvers.
•Several assumptions to evaluate the term of integral in RTE. •Radiative interaction only between neighboring cells •Low computational cost •Using the same mesh structure as one used for flow calculation •Accuracy and computational time depends on the used discretization and optical thickness of system. •Evaluation of right path length used for calculation of absorption coefficient is approximated.
•Better physical basis •Radiative interaction between all the radiative cells in the system. •High accuracy & Computational cost. •Capability of working with CFD solver in a hybrid system. •The computational cost increases as the size of system increases.
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Algorithm of Zonal Type Approaches
(MREM, Zonal Codes)
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Mesh generation: an optically
thick cell structure is used.
Calculation of exchange factors
Writing radiative balance for
coarse surface and volume cells.
Solving the algebraic system of
equations to obtain the radiative
source terms in coarse volume cells
and radiative heat flux in the walls.
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Zonal Type Methods(MREM, Zonal Codes);
Points & Difficulties.
Points:
Better physical bases: considering radiative transfer between all points of the space.
Possibility of doing non gray modeling in an easier way.
More realistic way for approximating path length in gray and non gray modeling.
Difficulties:
Different mesh structure
Correct calculation of exchange factors
Supporting complex geometries
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Correlation Based Zonal Tools
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Mesh Generation and the Supported Geometries
The square-cubic Cartesian mesh structure is created by the code.
Rectangular geometry is easily supported, the more complex geometries need modification in
the mesh generation subroutine.
EF calculation
The profound correlations have been implemented by the code resulting to a big
improvement in cpu time without losing accuracy.
Outputs
The radiative source term in the volume cells and radiative heat flux in the surface cells. The
flexible format is available for the outputs, interpolation files, data files, etc.
Useful Features
Different approach for calculation of gas emissivity can be used easily.
A ready code structure for non gray modeling with WSGGM has been built .
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Validation: Analysis of Benchmarks
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Three different benchmarks have been analyzed. The results of one is presented here.
Inhomogeneous temperature, Homogenous gas composition H2O = 20%, CO2=10% Wall Temperature = 300K, All walls are black. DOM results have been produced by using S8 spatial discretization 26.01.2012
Effect of Path Length Approximation
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1 2 12
2
exp(- )
i j
ij
i j j i
ijV V
k k k rg g dV dV
r
Averaging Varying PL K1 and k2 are calculated based on average distance of the cell center to all other cells in the system and transmissivity between two cells is calculated by using real distance between two cells. Varying PL only transmissivity between two cells is calculated by using real distance between two cells. 26.01.2012
Sample Results (MREM):
A Simplified Geometry of CFB Boilers
10 Radiative heat flux in the walls when a gas hot stream enters the bottom of geometry and goes out from exits 26.01.2012
Sample Results (MREM):
A Simplified Geometry of Recovery Boilers
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Temperature distribution when a gas hot stream enters the bottom of geometry and goes out from exits
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