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Numerical and experimental thermal analysis of an industrial kiln used for frit production
Applied Thermal Engineering 48 (2012) 414e425
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Numerical and experimental thermal analysis of an industrial kiln used for frit production T.S. Possamai*, R. Oba, V.P. Nicolau Department of Mechanical Engineering, Federal University of Santa Catarina, Campus Universitário, Trindade, Florianópolis 88.040 900, SC, Brazil
h i g h l i g h t s < Numerical simulation applied to a ceramic frits melting kiln. < Method of finite volumes. < Numerical results compared with experimental data. < Model estimates the global thermal behavior of the kiln.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 March 2011 Accepted 13 May 2012 Available online 24 May 2012
This paper describes a methodology for the study and modeling of the thermal energy in ceramic frit melting kilns with an oxy-fired combustion process through the development of a numerical simulation in CFD software. Ceramic frits are vitreous compounds that provide glazes with specific properties for use in the coating of other ceramics, especially those of the ceramic tile industry. The aim of this study is to generate technical subsidies in order to support economically viable proposals for the ceramic industry. The CFD modeling is performed using the commercial software Ansys CFX 11.0, which is based on the method of finite volumes. The geometric domain of resolution consists of the internal cavity of the kiln. The CFD resolution is coupled to a three-dimensional heat conduction code along the kiln walls to determine the external temperature distribution. The thermal problem is composed of the combustion of natural gas with oxygen, the internal turbulent flow of exhaust gases, the energy loss by convection and radiation to the environment through the walls and the radiation within the kiln cavity with participating media. Data collected in an operating kiln are used to verify the numerical solution, achieving a good agreement in the general analysis of the kiln. The numerical solution provides physically consistent results, making it possible to predict the behavior of the kiln as a whole in similar cases with changes in the parameters of the manufacturing process or in the geometry. Other specific results, such as heat flux inside the kiln, are presented and discussed. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Ceramic frits Numerical simulation Ceramic kiln
1. Introduction Ceramic frits are a product of a ceramic sub-sector that uses melting kilns to melt a compound of oxides at temperatures in the order of 1700 K to create a melted product. The melted product then undergoes an abrupt cooling to 300 K producing the final product e a ceramic frit e which is later used in the preparation of ceramic glazes, providing them with several properties and allowing the safe employment of toxic chemical components such as PbO. The compound is comprised of oxides and varies according to the ceramic frit properties required, however, it is mainly composed of SiO2 (generally 50 to 70 wt.%). Al2O3, CaO, ZnO and * Corresponding author. Tel.: þ55 48 3721 9390; fax: þ55 48 3721 7615. E-mail addresses: [email protected], [email protected] (T.S. Possamai). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.05.025
B2O3 are also usually present although many formulations with other components have been studied [1e4]. The melting kilns differ greatly from the kilns commonly applied for ceramics characterized by a tunnel format and large size reaching up to 200 m [5]. This type of kiln is similar to gas-fired industrial kilns used to melt aluminum in a continuous process. The demand for energy saving requires the application of numerical analysis to this type of equipment. The optimization of kilns involves a large number of variables and complex physical phenomena. An accurate model provides detailed information in an inexpensive manner in addition to allowing the analysis of several cases. Nicolau and Dadam [6] evaluated through a numerical model a complete thermal energy balance including all energy fluxes related to the process of brick production in a tunnel kiln and indicated that the optimization of parameters such as the
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
insulation of the walls and preheating of the combustion air and of the load can result in a fuel saving of up to 10%. Carvalho and Nogueira [7] described the use of modeling tools together with online measurements for the optimization of ceramic and glassmelting furnaces, cement kilns and baking ovens providing a contribution for the pollution abatement strategies in this type of equipment. In the area of fusion kilns, Nieckele et al. [8] presented a numerical analysis of an aluminum melting furnace solved in commercial CFD software (Fluent) with emphasis on the comparison of the type of fuel used, natural gas or liquid. One of their conclusions was that operation with natural gas leads to a more effective configuration, providing longer life for the refractory walls as well as a lower amount of pollutants. Experimental data on kilns operating in the ceramic industry are available mostly for tunnel and roller kilns. Kaya et al. [9] and Nicolau and Dadam [6] have reported data collected on operating tunnel kilns related to the wall and flow temperatures and energy balances indicating temperatures up to 1250 K in the firing zone. The latter study indicated a specific consumption (fired materialbased) of 3.47 MJ/kg. The specific consumption of ceramic kilns varies with the required product but in general it lies within the range of 2.0e4.0 MJ/kg for most ceramic products produced on industrial scale, such as bricks and roof and floor tiles [5]. In the ceramic frits sector there is a lack of literature sources with regard to experimental data and the thermal analysis of the melting kiln used in a continuous process. In this context, the aim of this study is to analyze the energy in a ceramic frits kiln through experimental and numerical approaches. The numerical model was solved in commercial CFD software (Ansys CFX) modeling the phenomena associated with the combustion of natural gas and oxygen, radiation with the combustion gases as participating media and the internal flow. This model is coupled to an independent code in FORTRAN which enables the solid domain to be solved apart, composed of the walls of the kiln and the load, with particular models. The resemblance of this specific kiln to some types of metal melting furnaces enables the extension of this study to other industrial sectors. The importance of a reliable numerical model in the optimization of ceramic kilns is enormous. The validation of the numerical model proposed in this paper based on experimental data collected from real equipment is presented as part of the results of this study. A model based on the eddy dissipation concept (EDC) of Magnussen [10] was used to solve the combustion of natural gas and oxygen. The standard ke3 model was used for turbulence and the radiation was modeled with the first-order Differential Approximation (P1). A method to calculate the absorption and diffusion coefficients for the media composed of the combustion gases proposed by Siegel and Howell [11] based on empirical data was used for a composition of fixed components constant through the fluid domain. This study methodology is divided into four steps: (i) physical problem and geometric model; (ii) acquisition of experimental data; (iii) numerical modeling; (iv) numerical model validation from experimental data.
more than 90% of the fuel in the primary burner. The main components of the kiln are presented in Fig. 1, including an opening in the chimney bottom (1), the raw material inlet (2), the chimney (3), the frit outlet, the secondary burner and the water reservoir (4) and the primary burner (5). The kiln does not possess any internal parts, consisting only of an empty structure with a small slope in the base to assist the flow of the frit mass in the fluid phase to the front exit. The hot gas products of the combustion enter the chimney through an exit in the front portion of the left wall while the frit mass flows through an exit in the front wall, under the primary and secondary burners, directly into a cooling tank filled with water at ambient temperature. The fragmented frits are accumulated at the base of the cooling tank and removed to storage bags. On the chimney bottom there is an extra opening for ambient air to mix with the hot combustion gases from the kiln in order to reduce the flow temperature. The raw mass of frits when pushed to the inside of the kiln piles up at the back forming a “wall” of solid mass with approximately 2 m length inside the kiln, as can be seen in Fig. 2. The internal cavity of the kiln is rectangular with prime dimensions of 1.80 m width, 1.20 m height and 5.65 m length of which 2 m are occupied by the above-mentioned “wall” of solid mass. Because of the high temperatures required in the process, the combustion reaction is promoted by natural gas and pure oxygen instead of atmospheric air. The kiln model solved has the following dimensions: 2.60 m width, 2.00 m height and 6.45 m length. The gentle slope of the bottom is neglected and a straight roof is considered. The walls have a uniform thickness of 0.40 m. Two inlets along the vertical center line of the front wall represent the primary burner. The secondary burner was not modeled in this study as it affects the product when it is on the outside of the kiln. The centers of the two inlets are separated by a distance of 145 mm in the vertical direction. The higher inlet is injected with a mix of fuel and a small percentage of oxygen while the lower one is injected only with oxygen. The diameters are 40 and 80 mm for the inlets of the fuel and oxygen mixture and the oxygen only, respectively. The center of the lower inlet is positioned at a vertical distance of 690 mm
2. Physical problem and geometric model The kiln is suspended at a height of 0.50 m above the ground by metal beams. Two burners for natural gas and pure oxygen are positioned at the front of the kiln. The primary one is placed in the front wall producing a flame inside the kiln that is directed to the raw material volume added to the inside of the structure through the back wall. The secondary burner acts right in front of the kiln exit, on the outside, in order to maintain the fluidity of the flow of product from the exit hole to the cooling tank. The fuel ratio between the primary and secondary burner is high, concentrating
415
Fig. 1. Main components of the frit production kiln.
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Fig. 4. Cavity occupied by the flue gas inside the kiln.
Fig. 2. Lateral sketch of the kiln.
from the internal surface of the base wall. The lateral exit for the flue gas is situated in the front portion of the left wall at the bottom. It is rectangular with dimensions of 100 150 mm (Fig. 3). The “wall” of solid raw material mass is situated in the back portion of the kiln interior and is assumed to be L-shaped with dimensions of 2 m length (starting at the internal surface of the back wall) with 1.2 m height and a strip that runs along the whole of the internal cavity up to the internal surface of the front wall with 150 mm of height. This strip represents the flow of frits in the liquid phase in the bottom of the kiln. Fig. 4 shows the internal cavity of the kiln, with only the space in the internal cavity occupied by the flue gas. No inlets or outlets were considered for the frit mass as it was considered as packages of mass per second.
the kiln. Table 1 presents the measured variables. A flow of ambient air was admitted in the bottom of the chimney (0.40 kg/s, 303 K), in order to reduce the flue gas temperature to 903 K. For the flow measurement Pitot’s Tubes of 350, 1000 and 2000 mm length and 4, 10 and 15 mm diameter, respectively, were used. The only exception was the measurement of the flow of surrounding air that enters the chimney to cool down the flue gas, which was performed with a vane anemometer (Testo, model 521-2). To measure the flow temperature, a type-K thermocouple probe (OMEGA KMQSS-020U12) coupled to a digital thermometer (OMEGA HH-21) was used. The temperature of the external surfaces and the liquid phase flow of frit mass exiting the kiln were measured using an infrared camera (FLIR ThermaCAM SC500).
3. Acquisition of experimental data
4. Mathematical and numerical model
The experimental approach adopted was focused on obtaining the variables required to determine the energy and mass balance in
4.1. Physical phenomena in the internal cavity of the kiln The conservation equations of mass, chemical species, linear momentum and total energy were solved in order to obtain the flow field, temperature and species distributions for the combustion process inside the kiln. The following hypotheses were adopted for the fluid and the flow. For the fluid it is assumed that: (a) it is a continuous medium; (b) its components adhere to the ideal gas law; (c) it is composed exclusively of methane gas (CH4), oxygen (O2), carbon dioxide (CO2) and steam (H2O); (d) it has no soot present; and (e) it obeys the concept of an ideal mixture e in order to estimate the fluid properties. The flow is considered to be: (f) in a steady-regime; (g) compressible with regard to temperature; (h) turbulent; and to have (i) a Lewis number equal to one. In addition, the kiln walls are assumed to be non-catalytic. The FavreeReynolds averaged conservation equations are given by
Table 1 Measured variables.
Fig. 3. Geometric model including kiln walls.
Variable
Mass flow [kg/s]
Flue gas Fuel Oxygen Bottom of the chimney, ambient air Ceramic frit outlet Raw material inlet
0.57 0.020 0.095 0.40 0.24 0.27
5% 1% 1% 5% 2% 2%
Temperature [K] 903 298 298 303 1673 298
5 1 1 2 5 2
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
~ vr v rU j ¼ 0 þ vxj vt ~ v rY i vt
~m v rU vt ~ v rH vt
þ
(1)
~Y ~ v rU j i
þ
vxj
~ vY Gref i vxj
v ¼ vxj
~ mU ~ v rU j vxj
þ
0
vp v ¼ vxj vxm
~ ~ vp v rU j H v ¼ þ vt vxj vxj
! þ Smi ;
meff
l vh cp vxj
!
ZT !!
~ mt vH Prt vxj
! þ Sreac
~ is the velocity, Y ~ is the mass fraction, G where U i ref ¼ Gi þ mt =Sct is the effective diffusion coefficient, Gi is the diffusion coefficient, mt is the turbulent dynamic viscosity and Sct is the turbulent Schmidt number. The subscript “i” stands for the chemical component. The turbulent dynamic viscosity is linked to the turbulent kinetic energy k and the turbulent energy dissipation 3 through the relation mt ¼ Cm rk2 =3 , where Cm ¼ 0.09 is the ke3 turbulence model constant and r is the averaged mixture density defined as
~ 1=r ~i Y i
(5)
i
In the species mass conservation equation (2) Smi is the mass source term which represents the production rate of component “i” defined as the sum of the progress rate for every elementary reaction, n, where that component participates, given by
Smi ¼ Wi
n X n¼1
n00n;i n0n;i Rn
(6)
where Wi is the molar mass, n00n;i is the stoichiometric coefficient on the products side of the equation, n0n;i is the stoichiometric coefficient on the reactants side of the equation and Rn is the elementary reaction rate. The one-step reaction for the oxidation of methane gas was adopted as the combustion reaction. To solve the elementary progress rate for the chemical reaction the EDM model was adopted based on the EDC concept proposed by Magnussen [10]. This model assumes that the elementary reaction rate is given by the lowest value for equations (7) and (8)
ci
3
!
Rn ¼ C1 min 0 nn;i k 0P
ci Wi
(7)
(9)
Tref;i
(3)
(4)
X
cp;i dT þ h0f;i
hi ¼
þ Srad
1=r ¼
conductivity, cp the specific heat at constant pressure and Prt the ~ ¼ ð1=2ÞU ~ U ~ turbulent Prandtl number. H i i þ h is the averaged total P ~ enthalpy where h ¼ i hi Y i is the specific enthalpy. The species enthalpy hi is given by equation (9), with cp,i as the specific heat at constant pressure, h0f;i as the enthalpy of formation at a temperature of reference and T as the temperature.
(2)
~ ~ m vU vU j þ vxj vxm v þ vxj
417
The last two terms on the right side of equation (4) represent the energy source term for chemical reactions from the combustion Sreac and radiation Srad. The energy source due to chemical reactions is given by
Sreac
3 2 ZT X6h0f;i 7 ¼ þ cp;i dT 5Smi 4 Wi i
(10)
Tref;i
and the energy source term due to radiation is solved by the firstorder differential approximation radiative model (P1). The spectral radiative transport equation is simplified by considering the intensity of radiation as the sum of a series of orthogonal harmonics [11]. This allows the radiative transport equation to be solved obtaining the divergence of the radiative flux for an isotropic emitting, absorbing and scattering gray medium as
Srad
v Qrad;j ¼ ¼ Ka G 4Ka sT 4 vxj
(11)
where the second term from the left is the divergence of the total radiative flux defined as the energy source due to radiation. The radiative energy flux is Qrad, the absorption coefficient is Ka, the incident radiation is G and the temperature is T. Assuming gray and diffuse wall surfaces, equation (12) is used to compute the radiative energy flux for the energy equation and for the incident radiation equation boundary condition at the walls. The subscript w stands for “wall”. Further details on the P 1 radiation model can be found in Ref. [11].
3 mw 4 4sTw Qrad;w ¼ Gw 2ð2 3 mw Þ
(12)
In the calculation of the radiative properties of the flue gas a simplified model was used and the medium was considered as a homogeneous and isothermal mixture of gases composed exclusively of 33% and 67% of CO2 and H2O, by volume, respectively, at 2000 K. In addition, the medium inside the kiln was assumed to be gray. The mathematical model proposed by Siegel and Howell [11], based on empirical data, was used. Table 2 presents the estimated radiative properties used in the radiation model applied to the flue gas inside the kiln. No scattering is considered.
1
3 B C Rn ¼ C1 C2 @PP 00 A nn;i Wi k
(8)
Table 2 Properties.
P
where C1 ¼ 4.0 and C2 ¼ 1.0 are the proportionality constants from the EDM model and ci is the molar concentration. In equation (7) the component “i” refers exclusively to the reagents of the elementary chemical reaction, while in equation (8) it refers to the products. In the linear momentum equation (3) the effective dynamic viscosity is defined as meff ¼ m þ mt and the modified pressure as p0 ¼ p þ ð2=3Þrk. In the total energy equation (4) l is the thermal
Properties
Value
Absorption coefficient, Ka 1.0 m1 Mean optical thickness, s 1.12 Ceramic frits Fusion point 1680 K Specific heat at constant pressure, cp 900 J/kg K 3 W/m K Thermal conductivity, l Latent heat, LH 400 kJ/kg At 1200 K, 5.8 W/m K Refractory kiln walls Thermal conductivity, l At 500 K, 7.8 W/m K At 300 K, 20.8 W/m K
Flue gas
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Two additional transport equations are solved, for turbulent kinetic energy k and turbulent dissipation 3 .
" # ~ mt vk vðrkÞ v rU j k v mþ þ Pk r3 ¼ þ sk vxj vt vxj vxj " # ~ 2 mt v3 vðr3 Þ v rU j 3 v 3 3 mþ ¼ þ C3 1 Pk C3 2 r þ s3 vxj vxj k k vt vxj
(13)
(14)
where sk, s3 , C3 1 and C3 2 are the ke3 turbulence model constants and Pk is the turbulence production due to viscous forces, given by
Pk ¼ mt
~ ~ m vU vU j þ vxj vxm
!
~m vU vxj
! (15)
To solve the equations, wall functions [12] were adopted for the variables near the walls. Table 3 shows the boundary conditions applied to the numerical problem on each surface. The surfaces are identified in Fig. 5. The heat flux at the boundary for surfaces front, sides and top is defined as equation (16), where qw is the heat rate at the surface and Tw is the temperature at the surface. The external temperature, i.e., the ambient temperature, Tref, and the equivalent heat transfer coefficient, UAequi, are prescribed. Their values are presented in Table 3. The equivalent heat transfer coefficient can be determined by the equivalent thermal resistance, which is equal to the sum of the wall conduction resistance and external convective and radiative resistance.
qw ¼ UAequi Tw Tref
(16)
4.2. Walls of the kiln, load and external surroundings The temperatures at the refractory walls of the kiln are obtained by solving the conduction heat transfer equation at the wall. Convection and radiation heat transfer to the environment are taken in account. The conduction equation was discretized with the Finite Volume method and implemented in a FORTRAN code, which was coupled with the CFX solver. A constant equivalent heat transfer coefficient equal in value to that prescribed for the CFX numerical model at the walls was used. The temperature field at the internal surface of the walls obtained with the model in CFX was
Table 3 Boundary conditions. Surface
Flow condition
Thermal condition
Fuel inlet
Prescribed mass flow, 0.04 kg/s (0.5 CH4 þ 0.5 O2), 5% prescribed turbulent intensity Prescribed mass flow, 0.06 kg/s of O2, 5% prescribed turbulent intensity Prescribed mass flow, 0.10 kg/s No-slip
Prescribed temperature, 298 K
O2 inlet
Outlet Bottom and back mass Sides, front, top
No-slip
Fig. 5. Identification of surface components.
Prescribed temperature, 298 K
prescribed as the boundary condition at the same surface in the FORTRAN code. This coupling was based on a compromise between computing time and accuracy since a conjugated heat transfer problem required a large number of mesh volumes in the solid domain due to the thick kiln wall. The energy rate required for the frit mass to undergo the fusion process is modeled using equation (17), where ql is the heat rate, Tl,in is the initial temperature of the load, Tl,out is the fusion _ l is the load mass flux, cp,l is the load specific heat at temperature, m constant pressure and LH is the load melting latent heat.
_ l hl;out hl;in ¼ m _ l cp;l Tl;out Tl;in þ LH ql ¼ m
(17)
In this model the maximum temperature that the ceramic frit can achieve is fixed at a temperature defined as the fusion temperature. A fixed fusion point was adopted instead of a fusion zone, considering the ceramic frit as a pure component. The properties of the raw material and of the refractory walls of the kiln adopted for this study were estimated based on an average composition of ceramic frits used in Brazil [13]. Thermal properties for the raw material and refractory walls are presented in Table 2. The kiln was considered enclosed in a large black body cavity at a constant temperature. The corresponding shape factor for the kiln walls is equal to one. The radiation loss from the external wall surfaces is
4 4 qw;rad ¼ 3 mw sAext Tsur Text
(18)
where qw,rad is the radiative heat rate, 3 mw is the emissivity, Aext is the area and Tsur is the temperature considered at the external surface of the walls. The surrounding temperature is Text and s ¼ 5.678 108 W/m2 K4 is the StefaneBoltzmann constant. External convection was considered to be only due to natural convection originating from the heating of the air next to the walls. Equation (19) shows the convection energy losses through the external surface of the walls, where qw,conv is the convection heat rate and htext is the heat transfer coefficient, both at the external surface of the walls. Correlations for the convection heat transfer coefficient were based on the work of Churchill and Chu [14] and Goldstein et al. [15] for isothermal walls.
qw;conv ¼ htext Aext ðTsur Text Þ
(19)
Constant gradient Isothermal wall, 1680 K, emissivity 0.4 Constant heat transfer coefficient, UAequi ¼ 9.16 W/m2 K, external temperature, Text ¼ 303 K, Emissivity 0.4
4.3. Mesh A non-uniform structured hexahedrical mesh composed of 384,422 volume elements was used to solve the numerical problem inside the kiln. The fuel inlet, oxygen inlet and flue gas outlet are more refined. The average volume element size is 29 21 32 mm, varying from one-fifth of this value in the more refined regions to
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419
Table 4 Energy balance e experimental and numerical results. Experimental energy Numerical energy Difference [%] [kW]
[%]
Energy input 1050 100 Flue gas e chimney 346 32.9 Fusion product 428 40.8 Wall losses 314 29.9 Energy output 103.6 Frit production [kg/s] 0.240
[kW]
[%]
1000 251 388 363
100 25.1 38.7 36.2 100
0.237
e 7.8 2.1 6.3 1.25
double this value in the less refined regions. The number of elements in the x, y and z directions are 61, 49 and 114, respectively. A second mesh of 196,000 hexahedrical volume elements was used to solve the solid domain with the FORTRAN code with average size of 20 20 40 mm. A grid test was performed with the total number of volumes increased by a factor of 3. The average total wall heat flux varied less than 4% while the maximum kiln wall temperature changed less than 1%. As a convergence criteria, an RMS residue lower than 2 104 was adopted for every transport equation in addition to a residue lower than 1% in the conservation balance for the variables solved. The problem was solved using an Intel Duo Core, 3.24 GB RAM, 2.80 GHz computer. The time required to obtain the convergence solution for a typical case was approximately 112 h. 5. Results 5.1. Comparison between numerical and experimental results The numerical and experimental results for the global energy balance for the kiln are shown in Table 4. The results related to each energy input and output of the kiln are expressed in terms of energy and the corresponding percentage based on the input energy for each case. The difference between experimental and
Fig. 6. Temperature distribution on the left wall (plane x ¼ 0 m). (a) External surface e experimental results; and (b) external and (c) internal surfaces e numerical results.
numerical results is here defined as the difference between the energy percentage of each energy output. The numerical model overestimates the energy losses through the refractory walls by
Fig. 7. Temperature distribution on the roof (plane y ¼ 2 m). (a) External surface e experimental results; (b) external and (c) internal surfaces e numerical results.
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6.3% compared with the experimental data. The energy leaving the kiln with the flue gas is underestimated by 7.8%. This difference is attributed to the lower mass flow of flue gas prescribed in the numerical model, that is, 0.10 kg/s compared with 0.17 kg/s as the experimental result. The measurement uncertainty, air infiltrations in the kiln and oxygen excess from the burner are considered to be the probable causes for the difference in the mass flow, since the numerical model solves for a stoichiometric combustion in order to simplify the combustion process. The energy consumption attributed to the production of frit mass was overestimated by 2%. This was attributed to the differences in the values for the estimated properties of the ceramic frits and the real ones. Overall, the global energy balance obtained with the numerical model is consistent with the experimental results, indicating a similar behavior. Fig. 6 shows the temperature field for the left wall, and similar results can be observed in Fig. 7 for the roof. Experimental uncertainty in the temperature measurements is included in a 5% deviation. The results are all presented based on the system of coordinates and origin point defined in Fig. 3, located at the bottom of the kiln. The zero on the z-axis corresponds to the external surface of the back wall, where the raw material is inserted into the kiln. It ends at 6.45 m at the external surface of the front wall where the burner is fixed. For the y-axis, zero corresponds to the external surface of the bottom wall and 2 m to the external surface of the roof. For the x-axis zero corresponds to the external surface of the left wall and 2.6 m to the external surface of the right wall. Figs. 6 and 7 analyze planes x ¼ 0 m and y ¼ 2 m respectively. The experimental data is limited to a portion of the wall surface due to space limitations around the operating kiln. The numerical results are presented at two separated surfaces, the external surface with 6.45 m length, Figs. 6(b) and 7(b), and the internal surface with 3.65 m length (Figs. 6(c) and 7(c)). The highest temperatures appear in the central region on the front portion of the kiln walls, near the burner, for both the experimental data and numerical results. It is possible to identify the position of the solid raw material “wall” inside the kiln at the temperature experimental measurements on the external surface of the left wall, Fig. 6(a). It is evidenced by the low temperature
Fig. 8. Temperature profiles for experimental and numerical results for three longitudinal lines along the external surface of the left wall (x ¼ 0 m).
Fig. 9. Temperature profiles showing experimental and numerical results for two longitudinal lines along the external surface of the right wall (x ¼ 2.6 m).
region located between z ¼ 0.6 m and z ¼ 2 m due the low thermal conductivity of the ceramic material (Table 2). The results in Fig. 7 show a similar behavior for the roof. On comparing Fig. 6(b) and (c) the effects of the refractory walls of the kiln can be observed, with a lowering of the internal to external wall temperature. This reduction is around 1000 K. A detailed temperature distribution at the external wall is compared with experimental measurements in Figs. 8e10 for the external surface of the left (plane x ¼ 0 m), right (x ¼ 2.6 m) and roof (y ¼ 2 m) walls, respectively. In these figures the values for the
Fig. 10. Temperature profiles for experimental and numerical results for three longitudinal lines along the external surface of the roof (y ¼ 2 m).
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
Fig. 11. Convective (a) and radiative (b) heat fluxes on the internal surface of the roof (y ¼ 1.6 m).
Fig. 12. Convective (a) and radiative (b) heat fluxes on the internal surface of the left wall (x ¼ 0.4 m).
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temperature along horizontal lines on the z-axis, from the back to the front wall of the kiln, are compared considering experimental and numerical data obtained at different sections of the kiln. For the left wall (Fig. 8) lines y ¼ 0.4 m, y ¼ 1.0 m and y ¼ 1.5 m were analyzed. On the right wall (Fig. 9) lines y ¼ 0.4 m and y ¼ 1.5 m are considered. For the roof (Fig. 10) the analyzed lines were x ¼ 0.4 m, x ¼ 1.2 m and x ¼ 2.0 m. The numerical solution presents the same behavior as the experimental results along the entire length of the curves in Figs. 8 and 9, but reaches higher temperatures near the burner for the external surfaces of the left and right kiln wall. The temperature difference between the numerical and experimental results stays below 100 K. Probable causes for this discrepancy are the fact that the refractory walls suffer abrasion from heat and friction during long periods of use and the numerical model uses the design dimensions for the thickness of the walls. In this kind of kiln the refractory walls are reconstructed every 4e8 months due to this abrasion. In Fig. 10, similar behavior can be observed for the roof, but a greater difference in the temperature values is found in the solid region of the frit. This could be because in the numerical model the “wall of ceramic frits” is considered as a solid block of fixed length occupying the entire space from the bottom to the roof of the kiln, touching the internal surface of the roof and not leaving space for the flue gas between the roof and the pile of mass. However, such a space may be present in the real process. The creation of this space is unpredictable as it can occur at some point during the production and then be closed again by the action of the mass movement through the kiln. Therefore, the numerical model always considers this space as being full of mass. The temperature
difference inside this zone reaches 200 K, while outside this zone it remains below 50 K. 5.2. Radiative and convective heat fluxes on the refractory walls Fig. 11 shows the convective and radiative heat fluxes on the internal roof surface (y ¼ 1.6 m). The minus sign indicates the direction of the heat flux corresponding to heat transfer from the flue gas to the refractory walls. The vertical axis starts at z ¼ 2.4 m, the interface between the raw material “wall” inside the kiln and the flue gas. Due to the high temperatures inside the kiln, the radiative heat flux is around 10e30 times higher than the convective heat flux. The same trend can be observed for the internal surfaces of the left (x ¼ 0.4 m) and right (x ¼ 2.2 m) walls in Figs. 12 and 13, respectively. The horizontal axis starts at y ¼ 0.55 m, the interface between the load material stripe inside the kiln and the flue gas, while the vertical axis starts at z ¼ 2.4 m. On the left wall, where the flue gas exit is located, the convective heat flux reaches values up to twice those for the right wall, indicating a greater influence from the flow itself on this wall. This indicates that the flue gas exit position has strong influence on the flue gas flow. The radiation heat flux is stronger in the central region of the wall, in the upper portion, since the flame is located in that area of the kiln due to the burner position. 5.3. Heat flux for the load Considering the load as the bottom and back interface between the flue gas and solid domain, the heat fluxes can be visualized in
Fig. 13. Convective (a) and radiative (b) heat fluxes on the internal surface of the right wall (x ¼ 2.2 m).
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
423
Fig. 14. Convective (a) and radiative (b) heat fluxes for the load.
Fig. 14(a) and (b), for convective and radiative heat transfer, respectively. Similarly to the other internal surfaces of the kiln, the radiative heat flux dominates, reaching values 10e100 times higher than those of the convective heat flux. On the back surface of the load the participation of convection is greater, reaching 1/10 of the radiative heat flux due to the higher velocities and the impact of the jet of flue gas originating from the combustion flame. The velocity of the flue gas in this region reaches 7 m/s, while on the other kiln surfaces it remains below 2 m/s. The radiative heat flux represents around 90% of the total heat flux for the load. The region of higher heat flux is situated on the bottom surface, where the bath of frit mass is installed. 5.4. Application example One of the first approaches to saving energy in industrial kilns is to improve the insulation of the walls, decreasing the energy losses by convection and radiation to the external ambient. For the type of kiln analyzed in this study, the internal temperatures can reach
above 2500 K for 100% oxy-fired combustion. The walls of the kiln need to be reconstructed after a period of 4e8 months of continuous operation due to the thermal abrasion. Thus, improving the insulation of the walls has an effect in terms of both energy savings and increasing the thermal abrasion of the walls. Numerical results for the temperature on the internal surface of the left wall (x ¼ 0 m) of the kiln for three cases of wall insulation are presented in Fig. 15. Case (b) represents the standard case with the insulation of the kiln analyzed in this paper and its thermal conductivity shown in Table 2. Case (a) corresponds to insulation ten times higher than the standard while case (c) corresponds to a degree of insulation which is one-fifth of the standard. The global energy balance for each case is presented in Table 5. Fig. 15 shows that an improvement in the wall insulation causes an increase in the temperature of the internal surfaces while less insulation reflects in lower temperatures, as expected. However, with less insulation the higher temperature region is slowly shifted to the left, toward the back bottom portion of the kiln, where the
424
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
Fig. 15. Temperature distribution on the internal surface of the left wall e numerical results obtained with three degrees of insulation: a-ten times the standard; b-standard; c-onefifth the standard.
Table 5 Energy balance for kiln with different degrees of wall insulation. Insulation
Case (b)
Case (a)
Case (c)
Flue gas [%] Frit outlet [%] Wall losses [%] Frit production [kg/s]
25.1 38.7 36.2 0.237
25.9 67.9 6.2 0.416
24.0 3.2 72.8 0.0195
raw material is located, forming a zone of more homogeneous temperatures near the load. As this occurs, in the front portion of the kiln, near the burners, more isotherms appear, showing a higher temperature gradient for less insulation. A more homogeneous temperature distribution near the load is favorable to the process, but low temperatures near the frit mass exit (near the burner) can cause the product to solidify before exiting the kiln. The consequence is a reduction in the product quality. With more insulated walls, more energy is directed toward the load, increasing productivity, while the energy carried with the flue gas to the chimney does not show a significant change (Table 5). Additionally, the degradation of the walls due to a high internal temperature tends to increase as the temperatures on the internal surface of the walls were increased by around 50 K. Thus, this effect must also be considered in kiln operation analysis with the objective of achieving an optimal agreement between energy savings and thermal abrasion of the walls. 6. Conclusions The investigation of a numerical model proposed to solve the turbulent flow inside a ceramic frit fusion kiln was described herein. The model was applied to a real case and numerical and experimental results were compared. Numerical results consisting of heat fluxes on the internal surfaces of the kiln walls and load, the internal and external surface temperatures and the global energy balances were presented and analyzed. Three different degrees of wall insulation were compared.
It was observed that the numerical model presented a global energy balance consistent with that obtained for the real kiln through experimental data. Furthermore, the external surface temperatures of the roof and the left and right walls presented the same pattern in the numerical solution as in the experimental data, with slightly higher temperatures being obtained with the numerical model. It should be mentioned here that the actual physical process involves more complex mechanisms than those idealized in the numerical model, such as more chemical species resulting from the combustion process and the dependence of the medium and surface radiation on the wavelength. However, in spite of the simplifications hot spots could be identified in the refractory walls and the estimate of the main energetic behavior was consistent with the data for the real case. These results could provide valuable estimates for the global energy losses and energy optimization. The major contribution to the total heat flux of the load and of the walls is radiation heat transfer, as expected. The highest heat flux occurred around the flame, slightly shifted from the center of the kiln due to the flue gas exit being positioned in the front portion of the left wall causing a deviation in the flow. These higher fluxes are due the higher temperatures concentrated in the flame region. Improving the insulation of the kiln walls presented two conflicting outcomes; it increases the kiln productivity but resulted in higher thermal abrasion of the walls due to higher temperatures. Also, using less insulation than normal contributes to a more homogeneous temperature field near the load, which can improve in the product quality, but leads to a lower estimated productivity. The determination of the best furnace will be dependent on several factors, mainly the design of the geometry to give better energy optimization. However, from the experimental results it is possible to identify energy saving procedures which can be applied, such as through heat exchange with the flue gas in the chimney and determining the optimum insulation conditions for the walls. For better results in kiln optimization, the designer must perform an extensive investigation of several different configurations in order to achieve a conclusive case analysis. Even though
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
absolute quantitative results are difficult to obtain, due to the high complexity of the problem, qualitative comparisons can provide valuable information for the optimization process. Finally, it is important to note that experimental investigation, although expensive and difficult to conduct in the case of industrial equipment, is necessary to assess the validity of the proposed numerical model. Acknowledgements This work was funded by SCGAS e Gas Company of Santa Catarina. The author T. S. Possamai received a grant from the “ ANP Human Resources Program for the Sector of Oil and Natural Gas e PRH09-ANP/MME/MCT” and R. Oba from the CAPES program. References [1] C. Siligardi, P. Miselli, L. Lusvarghi, M. Reginelli, Influence of CaOeZrO2eAl2O3eSiO2 glasseceramic frits on the technological properties of porcelain stoneware bodies, Ceramic International 37 (2011) 1851e1858. [2] I.I. Akomolafe, L.E. Umaru, O.O. Ige, Influence of glass frits on working properties of kaolins, Applied Clay Ceramics 52 (2011) 428e431. [3] E. Bou, A. Moreno, A. Escardino, A. Gozalbo, Microstructural study of opaque glazes obtained from frits of the system: SiO2eAl2O3eB2O3e(P2O5)e CaOeK2OeTiO2, Journal of the European Ceramic Society 27 (2007) 1791e1796. [4] B. Baran, Y. Sarikaya, T. Alemdaroglu, M. Onal, The effect of boron containing frits on the anorthite formation temperature in kaolinewollastonite mixtures, Journal of the European Ceramic Society 23 (2003) 2061e2066. [5] G.B. Remmy Jr., Firing Ceramics e Advanced Series in Ceramics, vol. 2, World Scientific Publishing, 1994. [6] V.P. Nicolau, A.P. Dadam, Numerical and experimental thermal analysis of a tunnel kiln used in ceramic production, Journal of the Brazilian Society of Mechanical Sciences & Engineering XXXI (4) (OctobereDecember 2009) 297e304. [7] M.G. Carvalho, M. Nogueira, Improvement of energy efficiency in glassmelting furnaces, cement kilns and baking ovens, Applied Thermal Engineering 17 (8e10) (1997) 921e933. [8] A.O. Nieckele, M.F. Naccache, M.S.P. Gomes, Combustion performance of an aluminum melting furnace operating with natural gas and liquid fuel, Applied Thermal Engineering 31 (2011) 841e851. [9] S. Kaya, E. Mançuhan, K. Kuçukada, Modeling and optimization of the firing zone of a tunnel kiln to predict the optimal feed locations and mass fluxes of the fuel and secondary air, Applied Energy 86 (2009) 325e332. [10] B.F. Magnussen, On the structure of turbulence and a generalized eddy dissipation concept for chemical reactions in turbulent flow, in: 19th AIAA Sc. Meeting, St. Louis, USA, 1981. [11] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, third ed., Hemisphere Publishing Corporation, 1992. [12] B.E. Launders, D.B. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering 3 (1974) 269e289. [13] F.G. Melchiades, L. Neto, H.J. Alves, A.O. Boschi, Formulação de fritas cerâmicas com auxilio da técnica de planejamento estatístico de experimentos, Cerâmica Industrial 14 (3) (May/Jun, 2009). [14] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a vertical plate, International Journal of Heat and Mass Transfer 18 (1975) 1323. [15] R.J. Goldstein, E.M. Sparrow, D.C. Jones, Natural convection mass transfer adjacent to horizontal plates, International Journal of Heat and Mass Transfer 16 (1973) 1025.
cp: specific heat at constant pressure J/kg K C1: proportionality constant from EDM model, 4.0 C2: proportionality constant from EDM model, 1.0 Cm: ke3 turbulence model constant, 0.09 C3 1: ke3 turbulence model constant, 1.44 C3 2: ke3 turbulence model constant, 1.92 Eb: black body radiation, W/m2 G: incident radiation, W/m2 h: specific enthalpy, J/kg H: total enthalpy, kJ/kg ht: heat transfer coefficient, W/m2 K h0f : enthalpy of formation, J/kg k: turbulence kinetic energy, m2/s2 Ka: absorption coefficient, m1 LH: load melting latent heat, J/kg _ mass flux, kg/s m: p: pressure, Pa Pr: Prandtl number Pk: shear production of turbulence, kg/m s3 q: heat rate, W Q: energy flux, W/m2 R: elementary reaction rate, kmol/m3 s S: energy source, W/m3 _ specific energy source, J/kg S: Sc: Schmidt number Sm: mass source, kg/m3 s t: time, s T: temperature, K U: velocity, m/s UAequi: equivalent heat transfer coefficient, W/m2 K W: molar mass, kg/kmol x: spatial coordinate, m Y: mass fraction Greek symbols
G: diffusion coefficient, m2/s
rate of dissipation of turbulent kinetics energy, m2/s3 emissivity l: thermal conductivity, W/m K m: dynamic viscosity, Pa s n: spectral length, mm n0 : stoichiometric coefficients on the reactants side of the equation n00 : stoichiometric coefficients on the products side of the equation r: specific mass, kg/m3 s: StefaneBoltzmann constant, 5.678 108 W/m2 K4 s3 : ke3 turbulence model constant, 1.3 sk: turbulence model constant for the k equation, 1.0 s: optical thickness 3:
3 m:
Subscript conv: convection eff: effective ext: surroundings i: chemical species in: inlet j: index l: ceramic frit load m: index out: outlet p: products rad: radiation reac: reaction ref: reference sur: surface t: turbulent terms w: wall
Nomenclature A: surface area, m2 c: molar concentration, kmol/m3
Superscripts w: Favre averaged : Reynolds averaged
425
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Numerical and experimental thermal analysis of an industrial kiln used for frit production T.S. Possamai*, R. Oba, V.P. Nicolau Department of Mechanical Engineering, Federal University of Santa Catarina, Campus Universitário, Trindade, Florianópolis 88.040 900, SC, Brazil
h i g h l i g h t s < Numerical simulation applied to a ceramic frits melting kiln. < Method of finite volumes. < Numerical results compared with experimental data. < Model estimates the global thermal behavior of the kiln.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 March 2011 Accepted 13 May 2012 Available online 24 May 2012
This paper describes a methodology for the study and modeling of the thermal energy in ceramic frit melting kilns with an oxy-fired combustion process through the development of a numerical simulation in CFD software. Ceramic frits are vitreous compounds that provide glazes with specific properties for use in the coating of other ceramics, especially those of the ceramic tile industry. The aim of this study is to generate technical subsidies in order to support economically viable proposals for the ceramic industry. The CFD modeling is performed using the commercial software Ansys CFX 11.0, which is based on the method of finite volumes. The geometric domain of resolution consists of the internal cavity of the kiln. The CFD resolution is coupled to a three-dimensional heat conduction code along the kiln walls to determine the external temperature distribution. The thermal problem is composed of the combustion of natural gas with oxygen, the internal turbulent flow of exhaust gases, the energy loss by convection and radiation to the environment through the walls and the radiation within the kiln cavity with participating media. Data collected in an operating kiln are used to verify the numerical solution, achieving a good agreement in the general analysis of the kiln. The numerical solution provides physically consistent results, making it possible to predict the behavior of the kiln as a whole in similar cases with changes in the parameters of the manufacturing process or in the geometry. Other specific results, such as heat flux inside the kiln, are presented and discussed. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Ceramic frits Numerical simulation Ceramic kiln
1. Introduction Ceramic frits are a product of a ceramic sub-sector that uses melting kilns to melt a compound of oxides at temperatures in the order of 1700 K to create a melted product. The melted product then undergoes an abrupt cooling to 300 K producing the final product e a ceramic frit e which is later used in the preparation of ceramic glazes, providing them with several properties and allowing the safe employment of toxic chemical components such as PbO. The compound is comprised of oxides and varies according to the ceramic frit properties required, however, it is mainly composed of SiO2 (generally 50 to 70 wt.%). Al2O3, CaO, ZnO and * Corresponding author. Tel.: þ55 48 3721 9390; fax: þ55 48 3721 7615. E-mail addresses: [email protected], [email protected] (T.S. Possamai). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.05.025
B2O3 are also usually present although many formulations with other components have been studied [1e4]. The melting kilns differ greatly from the kilns commonly applied for ceramics characterized by a tunnel format and large size reaching up to 200 m [5]. This type of kiln is similar to gas-fired industrial kilns used to melt aluminum in a continuous process. The demand for energy saving requires the application of numerical analysis to this type of equipment. The optimization of kilns involves a large number of variables and complex physical phenomena. An accurate model provides detailed information in an inexpensive manner in addition to allowing the analysis of several cases. Nicolau and Dadam [6] evaluated through a numerical model a complete thermal energy balance including all energy fluxes related to the process of brick production in a tunnel kiln and indicated that the optimization of parameters such as the
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
insulation of the walls and preheating of the combustion air and of the load can result in a fuel saving of up to 10%. Carvalho and Nogueira [7] described the use of modeling tools together with online measurements for the optimization of ceramic and glassmelting furnaces, cement kilns and baking ovens providing a contribution for the pollution abatement strategies in this type of equipment. In the area of fusion kilns, Nieckele et al. [8] presented a numerical analysis of an aluminum melting furnace solved in commercial CFD software (Fluent) with emphasis on the comparison of the type of fuel used, natural gas or liquid. One of their conclusions was that operation with natural gas leads to a more effective configuration, providing longer life for the refractory walls as well as a lower amount of pollutants. Experimental data on kilns operating in the ceramic industry are available mostly for tunnel and roller kilns. Kaya et al. [9] and Nicolau and Dadam [6] have reported data collected on operating tunnel kilns related to the wall and flow temperatures and energy balances indicating temperatures up to 1250 K in the firing zone. The latter study indicated a specific consumption (fired materialbased) of 3.47 MJ/kg. The specific consumption of ceramic kilns varies with the required product but in general it lies within the range of 2.0e4.0 MJ/kg for most ceramic products produced on industrial scale, such as bricks and roof and floor tiles [5]. In the ceramic frits sector there is a lack of literature sources with regard to experimental data and the thermal analysis of the melting kiln used in a continuous process. In this context, the aim of this study is to analyze the energy in a ceramic frits kiln through experimental and numerical approaches. The numerical model was solved in commercial CFD software (Ansys CFX) modeling the phenomena associated with the combustion of natural gas and oxygen, radiation with the combustion gases as participating media and the internal flow. This model is coupled to an independent code in FORTRAN which enables the solid domain to be solved apart, composed of the walls of the kiln and the load, with particular models. The resemblance of this specific kiln to some types of metal melting furnaces enables the extension of this study to other industrial sectors. The importance of a reliable numerical model in the optimization of ceramic kilns is enormous. The validation of the numerical model proposed in this paper based on experimental data collected from real equipment is presented as part of the results of this study. A model based on the eddy dissipation concept (EDC) of Magnussen [10] was used to solve the combustion of natural gas and oxygen. The standard ke3 model was used for turbulence and the radiation was modeled with the first-order Differential Approximation (P1). A method to calculate the absorption and diffusion coefficients for the media composed of the combustion gases proposed by Siegel and Howell [11] based on empirical data was used for a composition of fixed components constant through the fluid domain. This study methodology is divided into four steps: (i) physical problem and geometric model; (ii) acquisition of experimental data; (iii) numerical modeling; (iv) numerical model validation from experimental data.
more than 90% of the fuel in the primary burner. The main components of the kiln are presented in Fig. 1, including an opening in the chimney bottom (1), the raw material inlet (2), the chimney (3), the frit outlet, the secondary burner and the water reservoir (4) and the primary burner (5). The kiln does not possess any internal parts, consisting only of an empty structure with a small slope in the base to assist the flow of the frit mass in the fluid phase to the front exit. The hot gas products of the combustion enter the chimney through an exit in the front portion of the left wall while the frit mass flows through an exit in the front wall, under the primary and secondary burners, directly into a cooling tank filled with water at ambient temperature. The fragmented frits are accumulated at the base of the cooling tank and removed to storage bags. On the chimney bottom there is an extra opening for ambient air to mix with the hot combustion gases from the kiln in order to reduce the flow temperature. The raw mass of frits when pushed to the inside of the kiln piles up at the back forming a “wall” of solid mass with approximately 2 m length inside the kiln, as can be seen in Fig. 2. The internal cavity of the kiln is rectangular with prime dimensions of 1.80 m width, 1.20 m height and 5.65 m length of which 2 m are occupied by the above-mentioned “wall” of solid mass. Because of the high temperatures required in the process, the combustion reaction is promoted by natural gas and pure oxygen instead of atmospheric air. The kiln model solved has the following dimensions: 2.60 m width, 2.00 m height and 6.45 m length. The gentle slope of the bottom is neglected and a straight roof is considered. The walls have a uniform thickness of 0.40 m. Two inlets along the vertical center line of the front wall represent the primary burner. The secondary burner was not modeled in this study as it affects the product when it is on the outside of the kiln. The centers of the two inlets are separated by a distance of 145 mm in the vertical direction. The higher inlet is injected with a mix of fuel and a small percentage of oxygen while the lower one is injected only with oxygen. The diameters are 40 and 80 mm for the inlets of the fuel and oxygen mixture and the oxygen only, respectively. The center of the lower inlet is positioned at a vertical distance of 690 mm
2. Physical problem and geometric model The kiln is suspended at a height of 0.50 m above the ground by metal beams. Two burners for natural gas and pure oxygen are positioned at the front of the kiln. The primary one is placed in the front wall producing a flame inside the kiln that is directed to the raw material volume added to the inside of the structure through the back wall. The secondary burner acts right in front of the kiln exit, on the outside, in order to maintain the fluidity of the flow of product from the exit hole to the cooling tank. The fuel ratio between the primary and secondary burner is high, concentrating
415
Fig. 1. Main components of the frit production kiln.
416
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Fig. 4. Cavity occupied by the flue gas inside the kiln.
Fig. 2. Lateral sketch of the kiln.
from the internal surface of the base wall. The lateral exit for the flue gas is situated in the front portion of the left wall at the bottom. It is rectangular with dimensions of 100 150 mm (Fig. 3). The “wall” of solid raw material mass is situated in the back portion of the kiln interior and is assumed to be L-shaped with dimensions of 2 m length (starting at the internal surface of the back wall) with 1.2 m height and a strip that runs along the whole of the internal cavity up to the internal surface of the front wall with 150 mm of height. This strip represents the flow of frits in the liquid phase in the bottom of the kiln. Fig. 4 shows the internal cavity of the kiln, with only the space in the internal cavity occupied by the flue gas. No inlets or outlets were considered for the frit mass as it was considered as packages of mass per second.
the kiln. Table 1 presents the measured variables. A flow of ambient air was admitted in the bottom of the chimney (0.40 kg/s, 303 K), in order to reduce the flue gas temperature to 903 K. For the flow measurement Pitot’s Tubes of 350, 1000 and 2000 mm length and 4, 10 and 15 mm diameter, respectively, were used. The only exception was the measurement of the flow of surrounding air that enters the chimney to cool down the flue gas, which was performed with a vane anemometer (Testo, model 521-2). To measure the flow temperature, a type-K thermocouple probe (OMEGA KMQSS-020U12) coupled to a digital thermometer (OMEGA HH-21) was used. The temperature of the external surfaces and the liquid phase flow of frit mass exiting the kiln were measured using an infrared camera (FLIR ThermaCAM SC500).
3. Acquisition of experimental data
4. Mathematical and numerical model
The experimental approach adopted was focused on obtaining the variables required to determine the energy and mass balance in
4.1. Physical phenomena in the internal cavity of the kiln The conservation equations of mass, chemical species, linear momentum and total energy were solved in order to obtain the flow field, temperature and species distributions for the combustion process inside the kiln. The following hypotheses were adopted for the fluid and the flow. For the fluid it is assumed that: (a) it is a continuous medium; (b) its components adhere to the ideal gas law; (c) it is composed exclusively of methane gas (CH4), oxygen (O2), carbon dioxide (CO2) and steam (H2O); (d) it has no soot present; and (e) it obeys the concept of an ideal mixture e in order to estimate the fluid properties. The flow is considered to be: (f) in a steady-regime; (g) compressible with regard to temperature; (h) turbulent; and to have (i) a Lewis number equal to one. In addition, the kiln walls are assumed to be non-catalytic. The FavreeReynolds averaged conservation equations are given by
Table 1 Measured variables.
Fig. 3. Geometric model including kiln walls.
Variable
Mass flow [kg/s]
Flue gas Fuel Oxygen Bottom of the chimney, ambient air Ceramic frit outlet Raw material inlet
0.57 0.020 0.095 0.40 0.24 0.27
5% 1% 1% 5% 2% 2%
Temperature [K] 903 298 298 303 1673 298
5 1 1 2 5 2
T.S. Possamai et al. / Applied Thermal Engineering 48 (2012) 414e425
~ vr v rU j ¼ 0 þ vxj vt ~ v rY i vt
~m v rU vt ~ v rH vt
þ
(1)
~Y ~ v rU j i
þ
vxj
~ vY Gref i vxj
v ¼ vxj
~ mU ~ v rU j vxj
þ
0
vp v ¼ vxj vxm
~ ~ vp v rU j H v ¼ þ vt vxj vxj
! þ Smi ;
meff
l vh cp vxj
!
ZT !!
~ mt vH Prt vxj
! þ Sreac
~ is the velocity, Y ~ is the mass fraction, G where U i ref ¼ Gi þ mt =Sct is the effective diffusion coefficient, Gi is the diffusion coefficient, mt is the turbulent dynamic viscosity and Sct is the turbulent Schmidt number. The subscript “i” stands for the chemical component. The turbulent dynamic viscosity is linked to the turbulent kinetic energy k and the turbulent energy dissipation 3 through the relation mt ¼ Cm rk2 =3 , where Cm ¼ 0.09 is the ke3 turbulence model constant and r is the averaged mixture density defined as
~ 1=r ~i Y i
(5)
i
In the species mass conservation equation (2) Smi is the mass source term which represents the production rate of component “i” defined as the sum of the progress rate for every elementary reaction, n, where that component participates, given by
Smi ¼ Wi
n X n¼1
n00n;i n0n;i Rn
(6)
where Wi is the molar mass, n00n;i is the stoichiometric coefficient on the products side of the equation, n0n;i is the stoichiometric coefficient on the reactants side of the equation and Rn is the elementary reaction rate. The one-step reaction for the oxidation of methane gas was adopted as the combustion reaction. To solve the elementary progress rate for the chemical reaction the EDM model was adopted based on the EDC concept proposed by Magnussen [10]. This model assumes that the elementary reaction rate is given by the lowest value for equations (7) and (8)
ci
3
!
Rn ¼ C1 min 0 nn;i k 0P
ci Wi
(7)
(9)
Tref;i
(3)
(4)
X
cp;i dT þ h0f;i
hi ¼
þ Srad
1=r ¼
conductivity, cp the specific heat at constant pressure and Prt the ~ ¼ ð1=2ÞU ~ U ~ turbulent Prandtl number. H i i þ h is the averaged total P ~ enthalpy where h ¼ i hi Y i is the specific enthalpy. The species enthalpy hi is given by equation (9), with cp,i as the specific heat at constant pressure, h0f;i as the enthalpy of formation at a temperature of reference and T as the temperature.
(2)
~ ~ m vU vU j þ vxj vxm v þ vxj
417
The last two terms on the right side of equation (4) represent the energy source term for chemical reactions from the combustion Sreac and radiation Srad. The energy source due to chemical reactions is given by
Sreac
3 2 ZT X6h0f;i 7 ¼ þ cp;i dT 5Smi 4 Wi i
(10)
Tref;i
and the energy source term due to radiation is solved by the firstorder differential approximation radiative model (P1). The spectral radiative transport equation is simplified by considering the intensity of radiation as the sum of a series of orthogonal harmonics [11]. This allows the radiative transport equation to be solved obtaining the divergence of the radiative flux for an isotropic emitting, absorbing and scattering gray medium as
Srad
v Qrad;j ¼ ¼ Ka G 4Ka sT 4 vxj
(11)
where the second term from the left is the divergence of the total radiative flux defined as the energy source due to radiation. The radiative energy flux is Qrad, the absorption coefficient is Ka, the incident radiation is G and the temperature is T. Assuming gray and diffuse wall surfaces, equation (12) is used to compute the radiative energy flux for the energy equation and for the incident radiation equation boundary condition at the walls. The subscript w stands for “wall”. Further details on the P 1 radiation model can be found in Ref. [11].
3 mw 4 4sTw Qrad;w ¼ Gw 2ð2 3 mw Þ
(12)
In the calculation of the radiative properties of the flue gas a simplified model was used and the medium was considered as a homogeneous and isothermal mixture of gases composed exclusively of 33% and 67% of CO2 and H2O, by volume, respectively, at 2000 K. In addition, the medium inside the kiln was assumed to be gray. The mathematical model proposed by Siegel and Howell [11], based on empirical data, was used. Table 2 presents the estimated radiative properties used in the radiation model applied to the flue gas inside the kiln. No scattering is considered.
1
3 B C Rn ¼ C1 C2 @PP 00 A nn;i Wi k
(8)
Table 2 Properties.
P
where C1 ¼ 4.0 and C2 ¼ 1.0 are the proportionality constants from the EDM model and ci is the molar concentration. In equation (7) the component “i” refers exclusively to the reagents of the elementary chemical reaction, while in equation (8) it refers to the products. In the linear momentum equation (3) the effective dynamic viscosity is defined as meff ¼ m þ mt and the modified pressure as p0 ¼ p þ ð2=3Þrk. In the total energy equation (4) l is the thermal
Properties
Value
Absorption coefficient, Ka 1.0 m1 Mean optical thickness, s 1.12 Ceramic frits Fusion point 1680 K Specific heat at constant pressure, cp 900 J/kg K 3 W/m K Thermal conductivity, l Latent heat, LH 400 kJ/kg At 1200 K, 5.8 W/m K Refractory kiln walls Thermal conductivity, l At 500 K, 7.8 W/m K At 300 K, 20.8 W/m K
Flue gas
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Two additional transport equations are solved, for turbulent kinetic energy k and turbulent dissipation 3 .
" # ~ mt vk vðrkÞ v rU j k v mþ þ Pk r3 ¼ þ sk vxj vt vxj vxj " # ~ 2 mt v3 vðr3 Þ v rU j 3 v 3 3 mþ ¼ þ C3 1 Pk C3 2 r þ s3 vxj vxj k k vt vxj
(13)
(14)
where sk, s3 , C3 1 and C3 2 are the ke3 turbulence model constants and Pk is the turbulence production due to viscous forces, given by
Pk ¼ mt
~ ~ m vU vU j þ vxj vxm
!
~m vU vxj
! (15)
To solve the equations, wall functions [12] were adopted for the variables near the walls. Table 3 shows the boundary conditions applied to the numerical problem on each surface. The surfaces are identified in Fig. 5. The heat flux at the boundary for surfaces front, sides and top is defined as equation (16), where qw is the heat rate at the surface and Tw is the temperature at the surface. The external temperature, i.e., the ambient temperature, Tref, and the equivalent heat transfer coefficient, UAequi, are prescribed. Their values are presented in Table 3. The equivalent heat transfer coefficient can be determined by the equivalent thermal resistance, which is equal to the sum of the wall conduction resistance and external convective and radiative resistance.
qw ¼ UAequi Tw Tref
(16)
4.2. Walls of the kiln, load and external surroundings The temperatures at the refractory walls of the kiln are obtained by solving the conduction heat transfer equation at the wall. Convection and radiation heat transfer to the environment are taken in account. The conduction equation was discretized with the Finite Volume method and implemented in a FORTRAN code, which was coupled with the CFX solver. A constant equivalent heat transfer coefficient equal in value to that prescribed for the CFX numerical model at the walls was used. The temperature field at the internal surface of the walls obtained with the model in CFX was
Table 3 Boundary conditions. Surface
Flow condition
Thermal condition
Fuel inlet
Prescribed mass flow, 0.04 kg/s (0.5 CH4 þ 0.5 O2), 5% prescribed turbulent intensity Prescribed mass flow, 0.06 kg/s of O2, 5% prescribed turbulent intensity Prescribed mass flow, 0.10 kg/s No-slip
Prescribed temperature, 298 K
O2 inlet
Outlet Bottom and back mass Sides, front, top
No-slip
Fig. 5. Identification of surface components.
Prescribed temperature, 298 K
prescribed as the boundary condition at the same surface in the FORTRAN code. This coupling was based on a compromise between computing time and accuracy since a conjugated heat transfer problem required a large number of mesh volumes in the solid domain due to the thick kiln wall. The energy rate required for the frit mass to undergo the fusion process is modeled using equation (17), where ql is the heat rate, Tl,in is the initial temperature of the load, Tl,out is the fusion _ l is the load mass flux, cp,l is the load specific heat at temperature, m constant pressure and LH is the load melting latent heat.
_ l hl;out hl;in ¼ m _ l cp;l Tl;out Tl;in þ LH ql ¼ m
(17)
In this model the maximum temperature that the ceramic frit can achieve is fixed at a temperature defined as the fusion temperature. A fixed fusion point was adopted instead of a fusion zone, considering the ceramic frit as a pure component. The properties of the raw material and of the refractory walls of the kiln adopted for this study were estimated based on an average composition of ceramic frits used in Brazil [13]. Thermal properties for the raw material and refractory walls are presented in Table 2. The kiln was considered enclosed in a large black body cavity at a constant temperature. The corresponding shape factor for the kiln walls is equal to one. The radiation loss from the external wall surfaces is
4 4 qw;rad ¼ 3 mw sAext Tsur Text
(18)
where qw,rad is the radiative heat rate, 3 mw is the emissivity, Aext is the area and Tsur is the temperature considered at the external surface of the walls. The surrounding temperature is Text and s ¼ 5.678 108 W/m2 K4 is the StefaneBoltzmann constant. External convection was considered to be only due to natural convection originating from the heating of the air next to the walls. Equation (19) shows the convection energy losses through the external surface of the walls, where qw,conv is the convection heat rate and htext is the heat transfer coefficient, both at the external surface of the walls. Correlations for the convection heat transfer coefficient were based on the work of Churchill and Chu [14] and Goldstein et al. [15] for isothermal walls.
qw;conv ¼ htext Aext ðTsur Text Þ
(19)
Constant gradient Isothermal wall, 1680 K, emissivity 0.4 Constant heat transfer coefficient, UAequi ¼ 9.16 W/m2 K, external temperature, Text ¼ 303 K, Emissivity 0.4
4.3. Mesh A non-uniform structured hexahedrical mesh composed of 384,422 volume elements was used to solve the numerical problem inside the kiln. The fuel inlet, oxygen inlet and flue gas outlet are more refined. The average volume element size is 29 21 32 mm, varying from one-fifth of this value in the more refined regions to
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Table 4 Energy balance e experimental and numerical results. Experimental energy Numerical energy Difference [%] [kW]
[%]
Energy input 1050 100 Flue gas e chimney 346 32.9 Fusion product 428 40.8 Wall losses 314 29.9 Energy output 103.6 Frit production [kg/s] 0.240
[kW]
[%]
1000 251 388 363
100 25.1 38.7 36.2 100
0.237
e 7.8 2.1 6.3 1.25
double this value in the less refined regions. The number of elements in the x, y and z directions are 61, 49 and 114, respectively. A second mesh of 196,000 hexahedrical volume elements was used to solve the solid domain with the FORTRAN code with average size of 20 20 40 mm. A grid test was performed with the total number of volumes increased by a factor of 3. The average total wall heat flux varied less than 4% while the maximum kiln wall temperature changed less than 1%. As a convergence criteria, an RMS residue lower than 2 104 was adopted for every transport equation in addition to a residue lower than 1% in the conservation balance for the variables solved. The problem was solved using an Intel Duo Core, 3.24 GB RAM, 2.80 GHz computer. The time required to obtain the convergence solution for a typical case was approximately 112 h. 5. Results 5.1. Comparison between numerical and experimental results The numerical and experimental results for the global energy balance for the kiln are shown in Table 4. The results related to each energy input and output of the kiln are expressed in terms of energy and the corresponding percentage based on the input energy for each case. The difference between experimental and
Fig. 6. Temperature distribution on the left wall (plane x ¼ 0 m). (a) External surface e experimental results; and (b) external and (c) internal surfaces e numerical results.
numerical results is here defined as the difference between the energy percentage of each energy output. The numerical model overestimates the energy losses through the refractory walls by
Fig. 7. Temperature distribution on the roof (plane y ¼ 2 m). (a) External surface e experimental results; (b) external and (c) internal surfaces e numerical results.
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6.3% compared with the experimental data. The energy leaving the kiln with the flue gas is underestimated by 7.8%. This difference is attributed to the lower mass flow of flue gas prescribed in the numerical model, that is, 0.10 kg/s compared with 0.17 kg/s as the experimental result. The measurement uncertainty, air infiltrations in the kiln and oxygen excess from the burner are considered to be the probable causes for the difference in the mass flow, since the numerical model solves for a stoichiometric combustion in order to simplify the combustion process. The energy consumption attributed to the production of frit mass was overestimated by 2%. This was attributed to the differences in the values for the estimated properties of the ceramic frits and the real ones. Overall, the global energy balance obtained with the numerical model is consistent with the experimental results, indicating a similar behavior. Fig. 6 shows the temperature field for the left wall, and similar results can be observed in Fig. 7 for the roof. Experimental uncertainty in the temperature measurements is included in a 5% deviation. The results are all presented based on the system of coordinates and origin point defined in Fig. 3, located at the bottom of the kiln. The zero on the z-axis corresponds to the external surface of the back wall, where the raw material is inserted into the kiln. It ends at 6.45 m at the external surface of the front wall where the burner is fixed. For the y-axis, zero corresponds to the external surface of the bottom wall and 2 m to the external surface of the roof. For the x-axis zero corresponds to the external surface of the left wall and 2.6 m to the external surface of the right wall. Figs. 6 and 7 analyze planes x ¼ 0 m and y ¼ 2 m respectively. The experimental data is limited to a portion of the wall surface due to space limitations around the operating kiln. The numerical results are presented at two separated surfaces, the external surface with 6.45 m length, Figs. 6(b) and 7(b), and the internal surface with 3.65 m length (Figs. 6(c) and 7(c)). The highest temperatures appear in the central region on the front portion of the kiln walls, near the burner, for both the experimental data and numerical results. It is possible to identify the position of the solid raw material “wall” inside the kiln at the temperature experimental measurements on the external surface of the left wall, Fig. 6(a). It is evidenced by the low temperature
Fig. 8. Temperature profiles for experimental and numerical results for three longitudinal lines along the external surface of the left wall (x ¼ 0 m).
Fig. 9. Temperature profiles showing experimental and numerical results for two longitudinal lines along the external surface of the right wall (x ¼ 2.6 m).
region located between z ¼ 0.6 m and z ¼ 2 m due the low thermal conductivity of the ceramic material (Table 2). The results in Fig. 7 show a similar behavior for the roof. On comparing Fig. 6(b) and (c) the effects of the refractory walls of the kiln can be observed, with a lowering of the internal to external wall temperature. This reduction is around 1000 K. A detailed temperature distribution at the external wall is compared with experimental measurements in Figs. 8e10 for the external surface of the left (plane x ¼ 0 m), right (x ¼ 2.6 m) and roof (y ¼ 2 m) walls, respectively. In these figures the values for the
Fig. 10. Temperature profiles for experimental and numerical results for three longitudinal lines along the external surface of the roof (y ¼ 2 m).
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Fig. 11. Convective (a) and radiative (b) heat fluxes on the internal surface of the roof (y ¼ 1.6 m).
Fig. 12. Convective (a) and radiative (b) heat fluxes on the internal surface of the left wall (x ¼ 0.4 m).
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temperature along horizontal lines on the z-axis, from the back to the front wall of the kiln, are compared considering experimental and numerical data obtained at different sections of the kiln. For the left wall (Fig. 8) lines y ¼ 0.4 m, y ¼ 1.0 m and y ¼ 1.5 m were analyzed. On the right wall (Fig. 9) lines y ¼ 0.4 m and y ¼ 1.5 m are considered. For the roof (Fig. 10) the analyzed lines were x ¼ 0.4 m, x ¼ 1.2 m and x ¼ 2.0 m. The numerical solution presents the same behavior as the experimental results along the entire length of the curves in Figs. 8 and 9, but reaches higher temperatures near the burner for the external surfaces of the left and right kiln wall. The temperature difference between the numerical and experimental results stays below 100 K. Probable causes for this discrepancy are the fact that the refractory walls suffer abrasion from heat and friction during long periods of use and the numerical model uses the design dimensions for the thickness of the walls. In this kind of kiln the refractory walls are reconstructed every 4e8 months due to this abrasion. In Fig. 10, similar behavior can be observed for the roof, but a greater difference in the temperature values is found in the solid region of the frit. This could be because in the numerical model the “wall of ceramic frits” is considered as a solid block of fixed length occupying the entire space from the bottom to the roof of the kiln, touching the internal surface of the roof and not leaving space for the flue gas between the roof and the pile of mass. However, such a space may be present in the real process. The creation of this space is unpredictable as it can occur at some point during the production and then be closed again by the action of the mass movement through the kiln. Therefore, the numerical model always considers this space as being full of mass. The temperature
difference inside this zone reaches 200 K, while outside this zone it remains below 50 K. 5.2. Radiative and convective heat fluxes on the refractory walls Fig. 11 shows the convective and radiative heat fluxes on the internal roof surface (y ¼ 1.6 m). The minus sign indicates the direction of the heat flux corresponding to heat transfer from the flue gas to the refractory walls. The vertical axis starts at z ¼ 2.4 m, the interface between the raw material “wall” inside the kiln and the flue gas. Due to the high temperatures inside the kiln, the radiative heat flux is around 10e30 times higher than the convective heat flux. The same trend can be observed for the internal surfaces of the left (x ¼ 0.4 m) and right (x ¼ 2.2 m) walls in Figs. 12 and 13, respectively. The horizontal axis starts at y ¼ 0.55 m, the interface between the load material stripe inside the kiln and the flue gas, while the vertical axis starts at z ¼ 2.4 m. On the left wall, where the flue gas exit is located, the convective heat flux reaches values up to twice those for the right wall, indicating a greater influence from the flow itself on this wall. This indicates that the flue gas exit position has strong influence on the flue gas flow. The radiation heat flux is stronger in the central region of the wall, in the upper portion, since the flame is located in that area of the kiln due to the burner position. 5.3. Heat flux for the load Considering the load as the bottom and back interface between the flue gas and solid domain, the heat fluxes can be visualized in
Fig. 13. Convective (a) and radiative (b) heat fluxes on the internal surface of the right wall (x ¼ 2.2 m).
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Fig. 14. Convective (a) and radiative (b) heat fluxes for the load.
Fig. 14(a) and (b), for convective and radiative heat transfer, respectively. Similarly to the other internal surfaces of the kiln, the radiative heat flux dominates, reaching values 10e100 times higher than those of the convective heat flux. On the back surface of the load the participation of convection is greater, reaching 1/10 of the radiative heat flux due to the higher velocities and the impact of the jet of flue gas originating from the combustion flame. The velocity of the flue gas in this region reaches 7 m/s, while on the other kiln surfaces it remains below 2 m/s. The radiative heat flux represents around 90% of the total heat flux for the load. The region of higher heat flux is situated on the bottom surface, where the bath of frit mass is installed. 5.4. Application example One of the first approaches to saving energy in industrial kilns is to improve the insulation of the walls, decreasing the energy losses by convection and radiation to the external ambient. For the type of kiln analyzed in this study, the internal temperatures can reach
above 2500 K for 100% oxy-fired combustion. The walls of the kiln need to be reconstructed after a period of 4e8 months of continuous operation due to the thermal abrasion. Thus, improving the insulation of the walls has an effect in terms of both energy savings and increasing the thermal abrasion of the walls. Numerical results for the temperature on the internal surface of the left wall (x ¼ 0 m) of the kiln for three cases of wall insulation are presented in Fig. 15. Case (b) represents the standard case with the insulation of the kiln analyzed in this paper and its thermal conductivity shown in Table 2. Case (a) corresponds to insulation ten times higher than the standard while case (c) corresponds to a degree of insulation which is one-fifth of the standard. The global energy balance for each case is presented in Table 5. Fig. 15 shows that an improvement in the wall insulation causes an increase in the temperature of the internal surfaces while less insulation reflects in lower temperatures, as expected. However, with less insulation the higher temperature region is slowly shifted to the left, toward the back bottom portion of the kiln, where the
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Fig. 15. Temperature distribution on the internal surface of the left wall e numerical results obtained with three degrees of insulation: a-ten times the standard; b-standard; c-onefifth the standard.
Table 5 Energy balance for kiln with different degrees of wall insulation. Insulation
Case (b)
Case (a)
Case (c)
Flue gas [%] Frit outlet [%] Wall losses [%] Frit production [kg/s]
25.1 38.7 36.2 0.237
25.9 67.9 6.2 0.416
24.0 3.2 72.8 0.0195
raw material is located, forming a zone of more homogeneous temperatures near the load. As this occurs, in the front portion of the kiln, near the burners, more isotherms appear, showing a higher temperature gradient for less insulation. A more homogeneous temperature distribution near the load is favorable to the process, but low temperatures near the frit mass exit (near the burner) can cause the product to solidify before exiting the kiln. The consequence is a reduction in the product quality. With more insulated walls, more energy is directed toward the load, increasing productivity, while the energy carried with the flue gas to the chimney does not show a significant change (Table 5). Additionally, the degradation of the walls due to a high internal temperature tends to increase as the temperatures on the internal surface of the walls were increased by around 50 K. Thus, this effect must also be considered in kiln operation analysis with the objective of achieving an optimal agreement between energy savings and thermal abrasion of the walls. 6. Conclusions The investigation of a numerical model proposed to solve the turbulent flow inside a ceramic frit fusion kiln was described herein. The model was applied to a real case and numerical and experimental results were compared. Numerical results consisting of heat fluxes on the internal surfaces of the kiln walls and load, the internal and external surface temperatures and the global energy balances were presented and analyzed. Three different degrees of wall insulation were compared.
It was observed that the numerical model presented a global energy balance consistent with that obtained for the real kiln through experimental data. Furthermore, the external surface temperatures of the roof and the left and right walls presented the same pattern in the numerical solution as in the experimental data, with slightly higher temperatures being obtained with the numerical model. It should be mentioned here that the actual physical process involves more complex mechanisms than those idealized in the numerical model, such as more chemical species resulting from the combustion process and the dependence of the medium and surface radiation on the wavelength. However, in spite of the simplifications hot spots could be identified in the refractory walls and the estimate of the main energetic behavior was consistent with the data for the real case. These results could provide valuable estimates for the global energy losses and energy optimization. The major contribution to the total heat flux of the load and of the walls is radiation heat transfer, as expected. The highest heat flux occurred around the flame, slightly shifted from the center of the kiln due to the flue gas exit being positioned in the front portion of the left wall causing a deviation in the flow. These higher fluxes are due the higher temperatures concentrated in the flame region. Improving the insulation of the kiln walls presented two conflicting outcomes; it increases the kiln productivity but resulted in higher thermal abrasion of the walls due to higher temperatures. Also, using less insulation than normal contributes to a more homogeneous temperature field near the load, which can improve in the product quality, but leads to a lower estimated productivity. The determination of the best furnace will be dependent on several factors, mainly the design of the geometry to give better energy optimization. However, from the experimental results it is possible to identify energy saving procedures which can be applied, such as through heat exchange with the flue gas in the chimney and determining the optimum insulation conditions for the walls. For better results in kiln optimization, the designer must perform an extensive investigation of several different configurations in order to achieve a conclusive case analysis. Even though
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absolute quantitative results are difficult to obtain, due to the high complexity of the problem, qualitative comparisons can provide valuable information for the optimization process. Finally, it is important to note that experimental investigation, although expensive and difficult to conduct in the case of industrial equipment, is necessary to assess the validity of the proposed numerical model. Acknowledgements This work was funded by SCGAS e Gas Company of Santa Catarina. The author T. S. Possamai received a grant from the “ ANP Human Resources Program for the Sector of Oil and Natural Gas e PRH09-ANP/MME/MCT” and R. Oba from the CAPES program. References [1] C. Siligardi, P. Miselli, L. Lusvarghi, M. Reginelli, Influence of CaOeZrO2eAl2O3eSiO2 glasseceramic frits on the technological properties of porcelain stoneware bodies, Ceramic International 37 (2011) 1851e1858. [2] I.I. Akomolafe, L.E. Umaru, O.O. Ige, Influence of glass frits on working properties of kaolins, Applied Clay Ceramics 52 (2011) 428e431. [3] E. Bou, A. Moreno, A. Escardino, A. Gozalbo, Microstructural study of opaque glazes obtained from frits of the system: SiO2eAl2O3eB2O3e(P2O5)e CaOeK2OeTiO2, Journal of the European Ceramic Society 27 (2007) 1791e1796. [4] B. Baran, Y. Sarikaya, T. Alemdaroglu, M. Onal, The effect of boron containing frits on the anorthite formation temperature in kaolinewollastonite mixtures, Journal of the European Ceramic Society 23 (2003) 2061e2066. [5] G.B. Remmy Jr., Firing Ceramics e Advanced Series in Ceramics, vol. 2, World Scientific Publishing, 1994. [6] V.P. Nicolau, A.P. Dadam, Numerical and experimental thermal analysis of a tunnel kiln used in ceramic production, Journal of the Brazilian Society of Mechanical Sciences & Engineering XXXI (4) (OctobereDecember 2009) 297e304. [7] M.G. Carvalho, M. Nogueira, Improvement of energy efficiency in glassmelting furnaces, cement kilns and baking ovens, Applied Thermal Engineering 17 (8e10) (1997) 921e933. [8] A.O. Nieckele, M.F. Naccache, M.S.P. Gomes, Combustion performance of an aluminum melting furnace operating with natural gas and liquid fuel, Applied Thermal Engineering 31 (2011) 841e851. [9] S. Kaya, E. Mançuhan, K. Kuçukada, Modeling and optimization of the firing zone of a tunnel kiln to predict the optimal feed locations and mass fluxes of the fuel and secondary air, Applied Energy 86 (2009) 325e332. [10] B.F. Magnussen, On the structure of turbulence and a generalized eddy dissipation concept for chemical reactions in turbulent flow, in: 19th AIAA Sc. Meeting, St. Louis, USA, 1981. [11] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, third ed., Hemisphere Publishing Corporation, 1992. [12] B.E. Launders, D.B. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering 3 (1974) 269e289. [13] F.G. Melchiades, L. Neto, H.J. Alves, A.O. Boschi, Formulação de fritas cerâmicas com auxilio da técnica de planejamento estatístico de experimentos, Cerâmica Industrial 14 (3) (May/Jun, 2009). [14] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a vertical plate, International Journal of Heat and Mass Transfer 18 (1975) 1323. [15] R.J. Goldstein, E.M. Sparrow, D.C. Jones, Natural convection mass transfer adjacent to horizontal plates, International Journal of Heat and Mass Transfer 16 (1973) 1025.
cp: specific heat at constant pressure J/kg K C1: proportionality constant from EDM model, 4.0 C2: proportionality constant from EDM model, 1.0 Cm: ke3 turbulence model constant, 0.09 C3 1: ke3 turbulence model constant, 1.44 C3 2: ke3 turbulence model constant, 1.92 Eb: black body radiation, W/m2 G: incident radiation, W/m2 h: specific enthalpy, J/kg H: total enthalpy, kJ/kg ht: heat transfer coefficient, W/m2 K h0f : enthalpy of formation, J/kg k: turbulence kinetic energy, m2/s2 Ka: absorption coefficient, m1 LH: load melting latent heat, J/kg _ mass flux, kg/s m: p: pressure, Pa Pr: Prandtl number Pk: shear production of turbulence, kg/m s3 q: heat rate, W Q: energy flux, W/m2 R: elementary reaction rate, kmol/m3 s S: energy source, W/m3 _ specific energy source, J/kg S: Sc: Schmidt number Sm: mass source, kg/m3 s t: time, s T: temperature, K U: velocity, m/s UAequi: equivalent heat transfer coefficient, W/m2 K W: molar mass, kg/kmol x: spatial coordinate, m Y: mass fraction Greek symbols
G: diffusion coefficient, m2/s
rate of dissipation of turbulent kinetics energy, m2/s3 emissivity l: thermal conductivity, W/m K m: dynamic viscosity, Pa s n: spectral length, mm n0 : stoichiometric coefficients on the reactants side of the equation n00 : stoichiometric coefficients on the products side of the equation r: specific mass, kg/m3 s: StefaneBoltzmann constant, 5.678 108 W/m2 K4 s3 : ke3 turbulence model constant, 1.3 sk: turbulence model constant for the k equation, 1.0 s: optical thickness 3:
3 m:
Subscript conv: convection eff: effective ext: surroundings i: chemical species in: inlet j: index l: ceramic frit load m: index out: outlet p: products rad: radiation reac: reaction ref: reference sur: surface t: turbulent terms w: wall
Nomenclature A: surface area, m2 c: molar concentration, kmol/m3
Superscripts w: Favre averaged : Reynolds averaged
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