NUMERICAL SIMULATION OF A TEMPERING FURNACE
Jerónimo Monteiro Barreira Duarte
Under supervision of Prof. Viriato Sérgio de Almeida Semião
Mechanical Departmenent, IST, Lisbon, Portugal
May, 2013
Abstract
The aim of this work is to simulate numerically a tempering furnace, designed to temper discs of
agricultural equipment, through the use of a commercial CFD code (FLUENT 6.3.26), that predicts the
fluid flow, combustion, heat transfer and temperature distribution in its interior. Natural gas similar to
that supplied in the gas networks was chosen as fuel for the furnace.
Two computational meshes were generated by the GAMBIT 2.4.6 software, a grid generator code
compatible with FLUENT, to mimic numerically the complex furnace geometry. The coarsest mesh
has got 790800 cells, and the finest one has got 1960200 cells.
In the simulations the RNG
turbulence model, the non-premixed combustion model, and the
discrete ordinates model for radiation were used. Numerical simulations were performed for steadystate and transient regime, with three different power inputs: 80, 100 and 130 kW.
Although the results obtained quantify in detail the relevant variables and properties inside the furnace
in steady state, and in transient regime with the disc packs to be tempered remaining static inside the
furnace, they do not yield the actual furnace dynamic behavior with the disc packs advancing
periodically inside it. Even though, those results are most useful for the design of this kind of furnace
as they provide an accurate information on the furnace behavior trends.
Key-words:
Computational fluid dynamics; combustion; radiation; heat treatment; tempering furnace.
1. INTRODUCTION
The construction of industrial furnaces and controlled temperature chambers have had remarkable
evolution in their project and temperature control, during the last years, specially because of the
implementation of physical and numerical models that allow to simulate their performance with the
required precision, for certain operating regimes.
The furnace that is studied in this work is conceived for tempering steel discs, which are the main
element of an agricultural equipment because it is used to till the ground. Therefore, they are
submitted to intense mechanical strains, requiring a good commitment between hardness and
resilience. No scientific articles have been found concerning tempering furnaces.
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Concentric nozzles are commonly used to inject reactants in the combustion chamber and promote
the mixture of both air and fuel; the swirl motion of the major flow (air flow) is used to assure flame
stabilization and to improve the mixing process between fuel and oxidizer [1].
The values provided for the turbulent kinetic energy and for its rate of dissipation are more precise
when using the RNG
model, since this model allows capturing in a more precise way the shear
flow characteristics developed. Compared to RNG
, the standard
model does not perform
so well near the region where the streamlines present high curvature, while the RNG
allows
capturing the mean stress of this flow [2].
2. MATHEMATICAL FORMULATION
2.1.
Flow and energy equations
RNG has been chosen for the turbulence model. The unsteady continuity, momentum, energy,
turbulent kinetic energy and eddy dissipation rate equations can be written, respectively, as
(1)
(2)
(3)
(4)
(5)
where
1.42,
1.68,
and
are the inverse effective Prandtl numbers and
represents the source term containing heat generated by divergence of radiative heat flux.
is given
by
(6)
where
given by
,
4.38 and
0.012.
is a scalar measure of the deformation tensor, and is
where
(7
The enthalpy is defined as
(8)
The turbulent viscosity and the Reynolds stress and are assumed to be
2
(9)
2.2.
Turbulent combustion model
The PDF model is based on the assumptions of fast chemistry and unit Lewis number [3, 4]. On these
assumptions, the instantaneous thermo-chemical state of the fluid is related to a single conserved
scalar quantity known as the mixture fraction, , which is defined by
(10)
where
is the elemental mass fraction for element, . The subscript
oxidizer stream inlet and subscript
for the mean and variance of
denotes the value at the
denotes the value at fuel stream inlet. The conserved equation
can be written as
(11)
(12)
where the value for the constants
,
, and
are 0.85, 2.86, and 2.0, respectively. Then, the
instantaneous values of species mass fraction, density, and temperature in an adiabatic system can
be computed as
(13)
where
is assumed
2.3.
-function which is characterized by
and
.
Radiative heat transfer
The radiant intensity at any position
along a path
through an absorbing, emitting, and non-
scattering medium is given by
(14)
where
is intensity,
is black-body intensity, and
is an absorption coefficient. Black-body intensity
depends only on the local temperature. The effect of radiation in energy equation is expressed in the
form of divergence of radiative heat flux is given by
(15)
2.4.
Boundary conditions
Different boundary conditions were used, since three different power inputs were analyzed. Air and
natural gas are injected at 293 K, and the remaining boundary conditions can be seen in table 1. Both
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mass fluxes were chosen so that an overall combustion with 30% of excess air could be achieved. All
external wall boundary conditions are displayed in table 2.
Discs and the fire piping are made of regular carbon steel, and all the furnace insulation is made of
refractory fiber ceramic. Both material properties are described in table 3. Natural gas is a mixture of
various gaseous compounds, and its properties depend strongly on its country of origin. The precise
composition of natural gas that was considered is shown in table 4.
Table 1: Boundary conditions for air and fuel inlets
80
Air
100
80
Natural gas
100
130
130
Axial velocity (m/s)
Angular velocity (rad/s)
3.42
30.0
4.28
30.0
5.57
30.0
1.85
0
2.31
0
3.00
0
Swirl number
1.16
0.93
0.71
0
0
0
2.043e-2
2.557e-2
3.328e-2
7.625e-4
9.521e-4
1.236e-3
81.9
81.9
81.9
38.1
38.1
38.1
Heat rate (kW)
Mass flux (kg/s)
Hydraulic diameter (mm)
Table 2 - Wall boundary conditions
External heat transfer coefficient
(
)
Free stream temperature (K)
293
Internal emissivity
0.75
External emissivity
0.5
External radiation temperature (K)
293
Wall thickness (mm)
100
Thermal conductivity (
10
)
Material
0.170
Ceramic fiber
No slip condition
(u, v, w = 0 m/s)
Table 3 - Material proprieties
Material
Steel
Ceramic fiber
Density (
)
7850
290
Thermal conductivity
(
)
51.17
0.170
Specific heat
(
)
577.9
1130
Emissivity
0.5
0.75
Table 4 - Composition of fuel mixture
Element
Molar fraction
0,9030
0,0680
0,0126
3. FURNACE CONFIGURATION
4
0,0027
0,0059
0,0078
Figure 1 shows a horizontal cross section of the furnace. Figure 2 shows a side view of the furnace,
which allows one to realize the concave form of the discs and how they are piled together. It can also
be seen the square shape of the fire pipe, and concentric circular nozzles of both fuel (on the center)
and air (on the annulus).
The main purpose of the furnace is to work on relatively low temperatures (around 300 ºC), since it is
for tempering the discs.
Figure 1 - Top view of the furnace
Figure 2 - Side view of the furnace
Two computational grids were generated to simulate the furnace. Due to the symmetry of the
geometry, only half of the furnace was simulated. Both meshes have similar cell arrangement,
although the finer mesh has got a larger concentration of cells on the discs and through the length of
the fire pipe. Figure 3 shows how the cells are disposed in the fire pipe and figure 4 shows a detailed
view of the air and fuel inlets. Figure 5 and 6 show the cell arrangement of the discs, its surroundings
and of the fire pipe along its length. Figure 7 and 8 show the arrangement of the cells on a vertical
plane passing through a pile’s center, for the coarse and fine mesh respectively. The main difference
that may be observed is on top of the fire pipe, since the difference in the discs cannot be perceived.
There are a total of 790800 and 1960200 cells on the coarse and fine mesh, respectively.
Figure 3 – Cross-cut view of cell arrangement on
the fire pipe
Figure 4 - Detailed view of cell arrangement on
the nozzle
The discrete ordinates (DO) model for radiation was used for the prediction of radiation [5, 6]. The DO
model is a flux type method. A geometrical space is discretized into a finite number of control volumes
and each octant is also discretized into a finite number of control angles (
is equal to 4 and
). In this study,
is equal to 8 with 32 discretized angular components of the radiation intensity.
The inflow and outflow of radiant energy across the control volume faces are balanced with
attenuation and augmentation of radiant energy within each control volume and each control angle.
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Figure 5 – Top view of cell arrangement on the
coarse mesh
Figure 6 - Top view of cell arrangement on the
fine mesh
Figure 7 - Side view of the cell arrangement on
the coarse mesh
Figure 8 - Side view of the cell arrangement on
the fine mesh
4. RESULTS AND DISCUSSION
Simulations were performed on a Quad-Core 3,60 GHz pc, with 8.00 GB of RAM memory. The coarse
mesh was simulated on both steady-state and transient regime. The finer mesh was only used for
steady state simulations. Each simulation, in either the coarse or fine mesh, would require between 4
to 7 days to complete calculations, although on the transient regime it required a few more days.
4.1.
Coarse mesh
4.1.1. Steady-state regime
Figure 9 shows a temperature distribution for the discs for 80 kW of thermal power input, in a top sided
view that shows the discs surfaces facing the firing pipe. Figure 10 shows vertical planes crossing the
centre of each pile. It can be clearly seen that there is a thermal gradient along the Y and Z axis. This
gradient along the Z direction may be better perceived by analyzing figure 11, which shows the
temperature distribution of pile 6 on that direction.
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Figure 12 shows the flow pattern on the plane Z = 850 mm, that is near the top of the furnace. It
exhibits a well developed flow, with a swirl motion around pile 6 that is caused by an inversion of the
flow direction near the end wall.
Figure 9 - Temperature distribution for 80 kW, on the coarse mesh
Figure 10 - Temperature distribution on plans that cross-cut each pile for 100 kW, on the coarse mesh
Figure 11 - Temperature distribution of pile 6 along Z for 100 kW, on the coarse mesh
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Figure 12 - Flow patern vectors along Z = 850 for 130 kW, for the coarse mesh
4.1.2. Transient regime
Figures 13 and 14 show the time evolution of the temperature in all piles, and it can be clearly seen
that they all perform in the same way. This may indicate a good thermal performance of the furnace,
that allows for an equal heating rate to all piles inside the furnace. The time required to reach the
minimum temperature of 600 K is very large, which shows the non-linear behavior of the heat transfer
process, either with time or thermal power variation. Figure 15 shows a temperature distribution for Y
= 700 mm, showing the thermal gradient along Z and the high temperature values on the top of the
furnace.
Figure 13 - Temporal evolution of temperature for the 130 kW transient simulation with the coarse mesh
Figure 14 – Temporal evolution of temperature for the 100 kW transient simulation with the coarse mesh
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Figure 15 - Temperature distribution on Y = 700 mm for the 130 kW transient simulation, on the coarse
mesh
4.2.
Fine mesh
Figure 16 shows the same temperature profile as figure 11, and it can be observed that they are in
agreement qualitatively, although a considerable numerical difference may be noticed for the thermal
gradient at each fixed position.
Figure 17 shows the temperature distribution for the Z = 250 mm vertical plane. It can be seen that at
the lower zone of the furnace the hottest zone is near the exhaustion, rather than the end wall.
Figure 16 - Temperature distribution of pile 6 along Z for 100 kW, on the fine mesh
Figure 17 - Temperature distribution on Z = 250 mm for 100 kW, on the fine mesh
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5. CONCLUSIONS
A numerical study of a tempering furnace prototype was performed using the CFD commercial code
FLUENT. Two computational meshes were implemented on GAMBIT: the coarsest mesh containing
790800 cells; and the finest mesh containing 1960200 cells.
To simulate the furnace differential equations of continuity and momentum were used, total enthalpy
was used for energy,
RNG model was chosen for turbulence, non-premixed combustion model
for combustion and discrete ordinates for radiation. Steady-state and transient regime calculations
were performed with 80, 100 and 130 kW of thermal power input.
The steady-state regime solutions provided some important qualitative information on the furnace
behavior, such as evaluating warm and cold zones, understanding the fluid flow dynamics, analyzing
the temperature distribution of the several piles of discs and studying the combustion inside the fire
duct.
From the transient calculations it was possible to analyze the time temperature evolution and its
homogeneity within the discs. Both cases show identical profiles up to 500 seconds, although with
very different heating periods required. On the 130 kW simulation only 500 seconds were required for
the minimum temperature to reach 600 K, while for the 100 kW case 4000 seconds were required to
reach the same target. The temperature distribution was similar in both cases, and qualitatively
predicted by the steady-state calculations.
The finest mesh was only used for the steady-state regime. In this case the second order upwind
scheme was used. A large number of qualitative similarities have been observed. The major
differences were the fluid flow at the top of the fire duct and temperature range within the furnace. In a
general way, the furnace behavior has shown to have the same tendencies with both meshes.
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