Flame Day 2012,

Jan. 26th , 2012 Lappeenranta, Finland.

Simulation of Radiative Heat Transfer in

Combustion Systems

M. Hadi Bordbar, bordbar@lut.fi

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

3 26.01.2012

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.

4 26.01.2012

Algorithm of Zonal Type Approaches

(MREM, Zonal Codes)

5

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.

26.01.2012

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

6

26.01.2012

Correlation Based Zonal Tools

7

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 .

26.01.2012

Validation: Analysis of Benchmarks

8

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

9

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

11

Temperature distribution when a gas hot stream enters the bottom of geometry and goes out from exits

26.01.2012

Non Gray Modeling; Banded Approach

26.01.2012

Validation; Non Gray Modeling

by Banded Approach

26.01.2012

Thanks for your attention!