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Journal ArticleDOI

A numerical approach for the study of glass furnace regenerators

01 Oct 2005-Applied Thermal Engineering (Pergamon)-Vol. 25, Iss: 14, pp 2299-2320

AbstractRegenerative heat exchangers used in glass industry are complex systems owing to the transient nature of their operating cycle, as well as to the complexity of the heat exchange phenomena involved: aiding mixed convection during the cold period and combined presence of radiation and forced convection during the hot period. The present study describes an open method to simulate the behaviour of such regenerators. Preliminary results allowed us to validate our model in comparison with experimental and/or analytical data obtained on simple geometries. In a second step, a complete validation is proposed on a large scale experimental set-up which reproduces the exact behaviour of an industrial glass furnace regenerator. An original method based on the Boussinesq approximation with a “fictitious thermal expansion coefficient” was successfully introduced for this complete validation.

Summary (3 min read)

1. Introduction

  • Regenerators are widely used in many industrial sectors such as cryogenic, metallurgical, chemical process and glass industry.
  • Regenerator operation relies on the successive alternation of hot and cold periods.
  • Heat exchange is indeed dominated by free turbulent convection mechanisms next to the entrance of the channel whereas, next to the exit, mechanisms of laminar forced convection prevail.
  • The closed methods only calculate the cyclic equilibrium and only the periodic conditions are taken into account in the problem.
  • That is the reason why the present work proposes an open method, using the Computational Fluid Dynamics (CFD) code Fluent, able to estimate the mean heat transfer coefficients with a satisfactory accuracy.

2.1. General equations

  • Its direction is characterized by the unity vector~s and the coordinates are defined by the vector~r (Fig. 2).
  • The authors consider an absorbing, emitting and grey medium in which scattering phenomena are negligible.
  • Under these assumptions, the radiant transport equation (RTE) can then be written ~s grad !ðLÞ ¼ jI eq jI ð5Þ where Ieq ¼.
  • I eqð~rÞ is the equilibrium radiant luminance, given by the Planck s function and j the absorption coefficient.

2.2. Similitude criteria for the cold period

  • The dimensionless form of the momentum equation (2) gives rise to two similitude criteria (see Padet [23,24]).
  • Dh of the channel and the velocity scale is the mass-flow velocity Um. Moreover, as the hydraulic diameter is constant, the mass conservation equation (1) involves qU = q0U0.
  • Two models can be considered to satisfy the similitude criterion on the Richardson number: First model.
  • For a buoyancy-driven flow, this model (called model 1) is known to give poorer results than those given with the use of the Boussinesq approximation.

2.3. Similitude criteria for the hot period

  • During the hot period, the effect of free convection is negligible so that the buoyancy term gq in the momentum equation (2) no longer exists and as a consequence the similitude criterion for the Richardson number.
  • The Peclet number and the Reynolds number are still two similitude criteria and are respected in the same way as in the cold period.
  • But, the dimensionless energy equation give rise to a new similitude criterion defined as (the refraction index is equal to unity, n = 1) The Planck number; jk n2rT 3 ð13Þ where r is the Stefan–Boltzmann constant.
  • As the dependence of the thermal conductivity with temperature is considered in their models, this similarity criterion will be respected when the absorption coefficient j is correctly taken into account.
  • The model WSGG is of great interest thanks to its reduced CPU time and some authors, as Denison and Webb [26], have recently made improvements on it.

2.4. Calculation procedure

  • The calculations need an initial temperature condition in the channel: the value (Tc,in + Th,in)/2 is then imposed.
  • The transient calculation starts with a hot period followed by a cold period.
  • This operation goes on until the cyclic equilibrium is reached.
  • For each period, only one step time is made as the evolution of temperature is linear with time and height in the channel [9].
  • The typical CPU time was approximately 4 weeks on one processor of a modern multiprocessor SUN powerstation.

3. Test results

  • As preliminary work, this section proposes to simplify the problem under consideration by comparing the results of their method to reliable experimental or analytical data from the literature describing each physical phenomenon (free convection, mixed convection, radiation) on a simple geometry (tube, vertical flat plate).
  • Thus, the simulation can be made with a two-dimensional grid, contrary to the complete simulation described in Section 5 which is three-dimensional.
  • For the cold period, a turbulence model using wall functions and a computation grid are chosen by studying both free convection along a vertical plate and aiding mixed convection in a smooth tube.
  • For the hot period, a model of radiation is chosen to describe the RTE.

3.1. Turbulent free convection

  • The well-known k–emodel combined with wall functions has been developed for forced convection flows.
  • Grid independence tests have been carried out, but only the results obtained with the most efficient grids are reported in this paper.
  • The two-dimensional calculation field is sufficiently wide (0.8 m) to neglect the interaction between the lateral boundary and the growing boundary layer along the vertical plate.
  • This statement leads to the conclusion that the heat transfer coefficient is constant.
  • As for forced convection, the ‘‘enhanced’’ wall functions are then much better than the ‘‘standard’’ wall functions for the determination of both heat exchange and flow pattern.

3.2. Mixed convection

  • Many papers reporting experimental studies deal with aiding mixed convection.
  • The authors use the lowReynolds number k–e model proposed by Launder and Sharma [34] which is a slight modification of the Jones and Launder model.
  • The results of Cotton and Jackson show that the low-Reynolds number k–e model is able to predict the aiding mixed convection regime with a good accuracy.
  • They use a fine mesh in their study and the calculation points which are close to the wall are located in the viscous sub-layer (yþw 0:5).
  • The mesh used is identical to the one validated for the study with free convection, as the authors use a 2D-axisymmetric approach.

3.3. Radiation

  • To simulate the thermal radiation exchange, the discrete ordinates (DO) method has been chosen.
  • This method has first been developed for other applications than radiant heat transfer [36,37] and has been extended for thermal radiation.
  • For their test, the dimensions of the geometry are given in Fig.
  • The use of the DO method gives satisfactory results whatever the value of the parameter N*.

4. Experimental set-up and instrumentation

  • The work presented below has been done in their laboratory by Lagarenne [9] and co-workers.
  • In addition, the internal envelop of the test section is insulated to minimize thermal losses.
  • On the contrary, the suction pyrometer enables us to minimize the impact of the radiation of the environment and to measure the real gas temperature.
  • To calculate the mean spatial temperature over the section of the regenerator, the authors found that it was helpful to maximize the measurement duration or the number, say N, of periods.
  • To realize local measurements, thermocouples were installed into the wings of the cruciforms at several heights in one of these insulated channels.

5. Results and discussion

  • The global results reported in [9] are given in Table 7.
  • The gas temperatures measured by SP1 and SP2 for the hot period (Tout,h) and the cold period (Tout,c), respectively, were recorded at each half period.

6. Conclusion

  • The authors have proposed an open method based on a CFD code which has been shown successful.
  • The k–e RNG turbulence model combined with the ‘‘enhanced’’ wall functions is chosen to describe the turbulent aiding mixed convection phenomena from the region where heat transfer is dominated by free convection to the region where heat transfer is controlled by forced convection.
  • So, convective heat exchange is correctly computed for the cold period and for the hot period.
  • Moreover, as the cold period is the limiting factor of the heat exchanges, the assumption of a grey medium for waste gas is proved to be adequate for a glass furnace regenerator.
  • Based on the Boussinesq approximation, it introduces a fictitious thermal expansion coefficient which includes the evolution of density with temperature.

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A numerical approach for the study of glass furnace
regenerators
Y. Reboussin, Jean-François Fourmigue, Philippe Marty, Olivier Citti
To cite this version:
Y. Reboussin, Jean-François Fourmigue, Philippe Marty, Olivier Citti. A numerical approach for the
study of glass furnace regenerators. Applied Thermal Engineering, Elsevier, 2005, 25, pp.2299-2320.
�10.1016/j.applthermaleng.2004.12.012�. �hal-00265717�

A numerical approach for the study of
glass furnace regenerators
Y. Reboussin
a
, J.F. Fourmigue
´
b,
*
, Ph. Marty
c
, O. Citti
d
a
Saint-Gobain C.R.E.E., 550 Avenue Alphonse Jauffret, B.P. 224, 84306 Cavaillon, France
b
C.E.A/GRETh, 17 rue des Martyrs, 38054 Grenoble cedex 9, France
c
LEGI—GRETh, 17 rue des Martyrs, 38054 Grenoble cedex 9, France
d
Saint-Gobain Ceramics and Plastics R&D center, Goddard Road, Northboro, MA 01532, USA
Regenerative heat exchangers used in
glass industry are complex systems owing to the transient nature of
their operating cycle, as well as to the complexity of the heat exch ange phenomena involved: aiding mixed
convection during the cold period and combined presence of radiat ion and forced convection during the
hot period. The present study describes an open method to simulate the behaviour of such regenerators.
Preliminary results allowed us to validate our model in comparison with experimental and/or analytical
data obtained on simple geometries. In a second step, a complete validation is proposed on a large scale
experimental set-up which reproduces the exact behaviour of an industrial glass furnace regenerator. An
original method based on the Boussinesq approximation with a ‘‘fictitious thermal expansion coefficient’’
was successfully introduced for this complete validation.
Keywords: Regenerator; Radiation; Mixed convection; Transient heat transfer
*
Corresponding author. Tel.: +33 4 38 78 49 06; fax: +33 4 38 78 54 35.
E-mail address: fourmiguejf@chartreuse.cea.fr (J.F. Fourmigue
´
).
1

Nomenclature
c
p
specific heat capacity (J/kg/K)
g gravity (m/s
2
)
Gr, Gr
*
Grashof number
h heat transfer coefficient (W/m
2
/K)
L characteristic length (m)
L
th
thermal loss (%)
M mass of the regenerator (kg)
_
m mass flow rate (kg/s)
N
*
angular discretization
p porosity
P
*
pressure (Pa)
Pe Peclet number
Pr Prandtl number
Q flow rate (Nm
3
/h), (O C, 1 atm)
Re Reynolds number
Ri Richardson number
S surface (m
2
)
SP suction pyrometer
T temperature (K)
t time (s)
U, u velocity (m/s)
u
*
friction velocity (m/s)
y
+
dimensionless normal distance
Greek symbols
b thermal expansion coefficient (1/K)
q density (kg/m
3
)
e emissivity
U surface heat flux (W/m
2
)
U
R
radiant surface heat flux (W/m
2
)
g
th
thermal efficiency
k conductivity (W/m/K)
K reduced length
l dynamic viscosity (Pa s)
P reduced period
Subscripts
1/2 half period
b bulk conditions
c cold period
2

1. Introduction
Regenerators are widely used in many industrial sectors such as cryogenic, metallurgical, chem-
ical process and glass industry. They are indeed attractive due to their wide range of temperature
and compactness over which they can be used. A glass industry regenerator for example operates
at temperatures up to 1650 C whereas a cryogenic regenerator can operate close to a few Kelvin.
Although their design depends on the application requirements and can range from rotary regen-
erators to fixed bed regenerators, regenerator operation relies on the successive alternation of hot
and cold periods. During hot periods energy is transferred from the hot fluid to the solid packing,
whereas during cold periods the energy previously stored is restored to the cold fluid. A hot period
followed by a cold period forms a cycle of operation which duration, for a glass furnace regener-
ator, is about 40 min. If several cycles of operation are necessary to reach a thermal equilibrium,
industrial regenerators usually operate for years under stabilized cyclic conditions and can be con-
sidered as fully periodic exchangers.
In the case of a glass regenerator, the solid packing is fixed and basically composed of elemen-
tary channels having a square cross-section of about 0.15 m. Hot fluids mainly come from the
combustion of the air–fuel mix (exhaust gases) that occurs in the furnace laboratory, whereas
the cold fluid is air introduced at the ambient temperature in the regenerator.
During the air period, air is supplied to the regenerator using large fans designed to control the
intake flow rate into the regenerator: the flow pattern created by the fan is a forced convection
flow. During the exhaust-gas period, the flow rate is controlled through pressure adjustments
at the stack.
During the hot period (Fig. 1(a)) the thermal exchange between the fluid and the solid packing
is characterized by laminar forced convection combined with radiation [1–3]. This thermal radi-
ation is due to the presence of waste gas which gives rise to a semi-transparent medium. This ther-
mal radiation represents between 80% and 90% of the global heat exchange.
On the contrary, during the cold period (Fig. 1(b)), an important temperature gradient occurs
between the wall and the core of the air flow which is the origin of free convection flow. This free
convection effect produces a flow in the same direction as the forced flow. In that case, the flow is
qualified as an aiding mixed convection flow [4–8].
The contribution of free convection to the aiding mixed convection flow decreases from the
inlet to the outlet of the channel by a factor of one hundred owing to the increase in temperature.
In the same way, the contribution of forced convection decreases by a factor three. These strong
variations involve that heat transfer mechanisms significantly evolve from bottom to top. Heat
f film conditions
h
hot period
in, out inlet, outlet conditions
0
reference value
sol reference to the solid packing
TF turbulent forced
w wall conditions
3

exchange is indeed dominated by free turbulent convection mechanisms next to the entrance of the
channel whereas, next to the exit, mechanisms of laminar forced convection prevail. Between the
entrance and the exit, the flow pattern is then transitional [9].
Eventually it must be noted that since there is no thermal exchange by radiation between the air
and the walls of the channel during this period, the mean heat transfer coefficient during the cold
period is therefore significantly lower than the one obtained during the hot period. Thus, once the
cyclic equilibrium is reached, the air period is considered as the limiting phase for global heat
transfer enhancement.
Historically, the study of regenerators has been accompanied by the development of closed
methods since the theoretical approach of Hausen [10]. Starting from a theoretical approach,
Hausen has introduced two dimensionless numbers, for a fixed bed regenerator: the reduced
length K ¼
hS
_
mc
p
and the reduced period P ¼
hS
Mc
p
ðt
1=2
L
U
Þ from which it is possible to express the
thermal efficiency g
th
= f(K
c
, P
c
, K
h
, P
h
). Let us notice that several authors [11–13] have gradually
proved the equivalence between this approach and the g
th
-NTU approach which is widely used for
rotary regenerators. The mathematical equations involved by the problem of the regenerator are
quite difficult to solve with closed methods. Many authors have proposed to improve the field of
validity, function of the reduced length and the reduced period, as well as the accuracy and the
rapidity of the procedures proposed [14–22]. The link between the thermal efficiency, the reduced
lengths and the reduced periods is nowadays well known.
Unfortunately, from a practical point of view, the use of such methods not only requires a good
knowledge of the operating conditions (intake temperature/flow rates) but also a good knowledge
of the heat exchange coefficients during both periods. Because of the complexity of the heat
exchange phenomena as well as of the geometry, these approaches are very difficult to implement
and very limited application of such models can be achieved.
(b)
free convection
(a)
solid packing
Forced flow
Velocity profile
Fig. 1. Sketch of the flow in the channel of a glass furnace regenerator during each hot (a) and cold (b) period.
4

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  • ...Radiation heat transfer between air and particles should be negligible unless there are combustion gases present (Reboussin et al., 2005)....

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  • ...2 Comparison with analytical solutions The temperature profiles are plotted in dimensionless form with the step-change analytical solutions of Riaz et al. (1976) and Adebiyi and Chenevert (1996) in Figure 60 and Figure 61 for 13 mm and 26 mm crushed rock, respectively....

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  • ..., 2011), or regenerators in the glass industry, which may be used at temperatures as high as 1650 °C (Reboussin et al., 2005)....

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  • ...Tests at higher temperatures would require more shielding for radiation, for example the double-shield gas-suction system used by Reboussin et al. (2005). The positioning of the layers is shown in Figure 27....

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  • ...Examples are cowper stores in the iron industry (Glück et al., 1991; Zunft et al., 2011), or regenerators in the glass industry, which may be used at temperatures as high as 1650 °C (Reboussin et al., 2005)....

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References
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Abstract: The paper presents a new model of turbulence in which the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate. The major component of this work has been the provision of a suitable form of the model for regions where the turbulence Reynolds number is low. The model has been applied to the prediction of wall boundary-layer flows in which streamwise accelerations are so severe that the boundary layer reverts partially towards laminar. In all cases, the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.

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  • ...The model of Jones and Launder [29] is indeed the best to predict heat transfer for a free turbulent convection flow but it also overestimates the temperature difference between the wall and the air....

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  • ...The authors use the lowReynolds number k–e model proposed by Launder and Sharma [34] which is a slight modification of the Jones and Launder model....

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TL;DR: A new finite-volume method is proposed to predict radiant heat transfer in enclosures with participating media and test results indicate that good accuracy is obtained on coarse computational grids, and that solution errors diminish rapidly as the grid is refined.
Abstract: A new finite-volume method is proposed to predict radiant heat transfer in enclosures with participating media. The method can conceptually be applied with the same nonorthogonal computational grids used to compute fluid flow and convective heat transfer. A fairly general version of the method is derived, and details are illustrated by applying it to several simple benchmark problems. Test results indicate that good accuracy is obtained on coarse computational grids, and that solution errors diminish rapidly as the grid is refined.

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