COMSOL 6.4 - Radiative Heat Transfer in a Utility Boiler

Radiative Heat Transfer in a Utility Boiler

In recent years, many studies have been conducted in the field of performance optimization of large power plant boilers. The main aims have been to extend the lifetime, increase the thermal efficiency, and reduce the pollutant emissions of the boilers. A good furnace design is the most important part in the energy conversion process in the boilers. A furnace is where the fuel is burnt and the chemical energy is converted into heat to be transferred into the water walls of steam boilers. The temperatures in fuel furnaces are high enough that the radiation becomes the most important mechanism in heat transfer. Due to complexity of the radiation mechanism and its dependence on the enclosure’s geometry, there is no analytical solution except for very simple problems. This fact along with expensive experimental modeling leads researchers to develop numerical models for analyzing these enclosures. Three of the most attractive methods, as far as accuracy and computational requirement are concerned, are the discrete transfer, the discrete ordinates and the finite-volume methods.

Solving this application requires approximately 5 GB of memory.

Model Definition

Of practical relevance is the radiative heat transfer in furnaces containing obstacles, such as protrusions and obstructions. In some applications, the thickness of the obstacles is very small as it occurs in utility boilers, where panels are often hanged in the radiation chamber.

In order to reduce the mesh (and then the computational cost), these obstructions are modeled as baffles (zero thickness). This study handles zero thickness obstacles containing an emitting-absorbing medium.

A three-dimensional enclosure resembling the combustion chamber of a utility boiler is modeled. The study takes advantage of symmetries to model only one half of the combustion chamber, thereby reducing model size and computational costs. The enclosure contains three baffles, as shown in Figure 1, which simulates the panels of superheaters suspended at the top of the combustion chamber.

Figure 1: Half of the utility boiler with obstructions.

In this example, the S4 discrete ordinates method was employed for predicting the heat flux on the side walls of enclosures and incident radiation distribution within the furnace. It results in a set of 24 discrete directions to represent radiative intensity transport.

The main assumption is using an existing uniform temperature and properties within the volume and surface zones, as proposed in Ref. 1. The temperature and emissivity of the boundaries, including the surface of the baffles, are taken as 800 K and 0.65, respectively, except at x = 10 m and for 22 ≤ z ≤ 30 m, where the temperature was set equal to 1200 K and a blackbody surface is assumed. An emitting-absorbing medium is assumed, with the following distribution of temperature and absorption coefficient:

Table 1: Distribution of temperature and aBsorption coefficient.
Coordinate (m)	Absorption coefficient (1/m)	Temperature (K)
z ≤ 5	0.20	1600
5 < z ≤ 10	0.25	2000
10 < z ≤ 20	0.20	1600
20 < z ≤ 30	0.18	1200

Thermal Analysis

The discrete-ordinates method (DOM) relies on the discrete representation of the directional dependence of the radiation intensity. The radiative transfer equation (RTE) is solved for a set of discrete directions, si, which span the total solid angle range of 4π around a point in space.

The RTE for this type of configuration can be written as:

where

•

I(r, s) is the radiative intensity at a given position r, following s direction

•

T is the temperature

•

κ, β, σs are absorption, extinction, and scattering coefficients, respectively

•

Ib(T) is the blackbody radiative intensity

•

ϕ(r, s′, s) is the scattering function. ϕ(r, s′, s) = 1 + a1μ0 and μ0 = s′ ⋅ s is the cosine of the scattering angle.

The boundary intensities in the furnace walls are given physically by the effective emitted intensity plus reflected incident intensities into a respective direction.

where

•

εw is the surface emissivity, which is in the range [0, 1]

•

ρd = 1 − εw is the diffusive reflectivity

•

n is the outward normal vector

•

qout is the heat flux striking the wall:

The above equations can be discretized in Cartesian coordinates for monochromatic or gray radiation as

The Sn approximation of the RTE in the m direction can be expressed as

For a discrete direction, si, the values of si, 1, si, 2, and si, 3 define the direction cosines of si obeying the condition si, 12 + si, 22 + si, 32 = 1. The j index in the above equation denotes the direction of incoming radiation contributing to the direction si.

For a diffuse reflecting surface on a wall boundary, the boundary condition equation is transformed as

Results and Discussion

Figure 2 and Figure 3 show the predicted incident radiation surface plots. The maximum incident radiation occurs at the level where the temperature and absorbing coefficient of the medium are the highest (that is, at the boiler’s burner level).

Figure 2: Incident radiation.

Figure 3: Incident radiation on the front of the boiler (W/m2).

The predicted outgoing heat flux is shown in Figure 4 and is in good agreement with published data (Ref. 1).

Figure 4: Outgoing heat flux on walls of the boiler (W/m2).

Reference

1. P.J. Coelho, J.M. Goncalves, and M.G. Carvalho, “Modelling of Radiative Heat Transfer in Enclosures with Obstacles,” Int’l J. Heat and Mass Transfer, vol. 41, no. 4–5, pp. 745–756, 1998.

Heat_Transfer_Module/Thermal_Radiation/boiler

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
Thot	1200[K]	1200 K	Temperature, hot surface zone
Tlow	800[K]	800 K	Temperature, cool surfaces
em	0.65	0.65	Emissivity, cool surfaces
scattC	0[1/m]	0 1/m	Scattering coefficient

Piecewise 1 (pw1)

In the toolbar, click

and choose > .

In the window for , type T in the text field.

Locate the section. In the text field, type z.

Find the subsection. In the table, enter the following settings:


Start	End	Function
0	5	1600
5	10	2000
10	20	1600
20	30	1200

Locate the section. In the text field, type m.

In the text field, type K.

Piecewise 2 (pw2)

In the toolbar, click

and choose > .

In the window for , type absC in the text field.

Locate the section. In the text field, type z.

Find the subsection. In the table, enter the following settings:


Start	End	Function
0	5	0.20
5	10	0.25
10	20	0.20
20	30	0.18

Locate the section. In the text field, type m.

In the text field, type 1/m.

Geometry 1

Work Plane 1 (wp1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

Work Plane 1 (wp1) > Polygon 1 (pol1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the text field, type 0 0 0 10 10 10 10 8 8 10 10 10 10 6 6 4 4 0.

In the text field, type 4 30 30 30 30 22 22 20 20 18 18 4 4 0 0 0 0 4.

In the toolbar, click

Work Plane 1 (wp1) > Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 4.

In the text field, type 10.

Locate the section. In the text field, type 20.

In the toolbar, click

Extrude 1 (ext1)

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Distances (m)
2
4
6

In the toolbar, click

Click the

button in the toolbar.

Click the

button in the toolbar.

The geometry should correspond to that in Figure 1.

Materials

Add a material to specify the absorption and scattering coefficients inside the boiler.

Chamber

In the toolbar, click

In the window for , type Chamber in the text field.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Absorption coefficient	kappaR	absC(z)	1/m	Basic
Scattering coefficient	sigmaS	scattC	1/m	Basic

Analogously, specify the emissivity of the boiler walls using a material.

Walls

In the toolbar, click

In the window for , type Walls in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Surface emissivity	epsilon_rad	em	1	Basic

Radiation in Participating Media (rpm)

By default, the is , which corresponds to 24 discrete angular directions.

Participating Medium 1

In the window, under > click .

In the window for , locate the section.

In the T text field, type T(z).

Initial Values 1

In the window, click .

In the window for , locate the section.

In the Tinit text field, type T(z).

Opaque Surface 1

In the window, click .

In the window for , locate the section.

In the T text field, type Tlow.

Opaque Surface 2

In the toolbar, click

and choose .

Select Boundaries 43, 45, and 47 only.

For more convenience in selecting these boundaries, you can click the button and paste the above numbers.

In the window for , locate the section.

In the T text field, type Thot.

Locate the section. From the list, choose .

Opaque Surface 3

In the toolbar, click

and choose .

Select Boundaries 12 and 19 only.

In the window for , locate the section.

In the T text field, type Tlow.

Opaque Surface 4

In the toolbar, click

and choose .

Select Boundary 5 only.

In the window for , locate the section.

In the T text field, type Tlow.

Locate the section. Select the checkbox.

Find the subsection. From the εu list, choose .

Symmetry 1

In the toolbar, click

and choose .

Select Boundary 2 only.

Mesh 1

Mapped 1

In the toolbar, click

and choose .

Select Boundary 5 only.

In the window for , click

Free Quad 1

In the toolbar, click

and choose .

Select Boundary 2 only.

In the window for , click

Swept 1

In the toolbar, click

Size

In the window, click .

In the window for , locate the section.

From the list, choose .

In the window, right-click and choose .

Study 1

In the toolbar, click

Results

Incident Radiation (rpm)

The default plot group shows the multislice plot. Follow the instructions below to replace the multislice plot for by a contour plot.

Multislice 1

In the window, expand the node.

Right-click and choose .

Click to confirm.

Incident Radiation (rpm)

In the window, under click .

Contour 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the text field, type range(0,1e5,21e5).

Locate the section. From the list, choose .

Click to expand the section. From the list, choose .

From the list, choose .

In the toolbar, click

Click the

button in the toolbar to get the results shown in Figure 2.

Click the

button in the toolbar to reproduce the results in Figure 3.

In Figure 4, the outgoing radiative heat flux is plotted for the full 3D geometry. Even if only one half of the utility boiler is modeled the solution can be mirrored to obtain a full 3D view of the results. To do so, follow the steps below:

Mirror 3D 1

In the window, expand the > node.