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... Abu Dhabi, United Arab Emirates b Mechanical Engineering Program, University of Michigan-Flint, Flint, MI 48502, USA. ARTICLE INFO. Keywords: Flue-wall.
Applied Energy xxx (2018) xxx-xxx

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Applied Energy

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journal homepage: www.elsevier.com

The effects of flue-wall design modifications on combustion and flow characteristics of an aluminum anode baking furnace-CFD modeling Abdul Raouf Tajika⁠ , Tariq Shamima⁠ ,⁠ b⁠ , Mouna Zaidania⁠ , Rashid K. Abu Al-Ruba⁠ ,⁠ ⁎⁠ a b

Department of Mechanical Engineering, Masdar Institute, Khalifa University of Science and Technology, Masdar City, PO Box 127788, Abu Dhabi, United Arab Emirates Mechanical Engineering Program, University of Michigan-Flint, Flint, MI 48502, USA

ABSTRACT

Keywords: Flue-wall Anode baking furnace Packing coke Flow blockage Baffles Presumed PDF

A modern aluminum smelter has a capacity of 1–2 million tons of aluminum per annum which requires more than 0.5–1.0 million tons of heat treated (baked) carbon anodes per year. The anode baking process is very energy intensive, approximately requires 2 GJ of energy per ton of carbon anodes which will be approximately 1–2 million GJ of energy per year. Since the plant testing is very expensive, anode baking furnace modeling is imperative to investigate the effects of different operational and geometrical parameters on the furnace energy consumption. In the numerical modeling of turbulent reactive flows, the accuracy of the model highly depends on the description of turbulence-chemistry interaction, and the robustness of the radiative transfer equation solver. Hence, the present study tested different turbulence-chemistry interaction frameworks and radiative transfer equation solvers for confined turbulent diffusion flames and results are compared with the experimental data. It was observed that the k - ε realizable turbulence model combined with the presumed probability density function method as turbulence-chemistry interaction, and discrete ordinates method as radiative transfer equation solver illustrate excellent agreement with the experimental data. Anode baking homogeneity is an important consideration in the design of the anode baking furnace, which requires appropriate flow distribution in the flue-wall cavity. Hence, the developed numerical framework was employed to investigate the effects of flue-wall design modifications on combustion and heat transfer characteristics of anode baking furnace energy consumption. It was observed that the modified design results in a higher thermal efficiency (lower energy consumption), and more homogenous temperature and flow fields which result in the baking of anodes more uniformly which consequently result in the evolution of more homogenous material properties. Consequently, the energy consumption in the aluminum reduction cell will also be significantly reduced. The present study also investigated the effect of flue-wall flow blockage due to packing coke infiltration on baking energy consumption for the aged anode baking furnaces and introduced three modified flue-wall designs.

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ARTICLE INFO

Nomenclature a keff φ Dh Gb



absorption coefficient effective thermal conductivity external body force field variable (velocity and temperature) flue-wall hydraulic diameter generation of turbulence kinetic energy due to buoyancy

Corresponding author. Email address: [email protected] (R.K. Abu Al-Rub)

https://doi.org/10.1016/j.apenergy.2018.08.078 Received 31 December 2017; Received in revised form 8 August 2018; Accepted 15 August 2018 Available online xxx 0306-2619/ © 2018.

Gk

generation of turbulence kinetic energy due to the mean velocity gradients G incident radiation mair mass flux of the mainstream air Ypr, Yfu, and Yox mass fractions of products, fuel, and oxidizer f mixture fraction Sh source term due to radiation, and heat transfer to wall boundaries P static pressure L suitable length scale for the computational domain Ibλ the blackbody intensity given by the Planck function

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Table 1 Summary of literature review on anode baking furnace design modeling.

Year

Objectives

Ping et al.

2002

Influence of the baffles on flowing field

Severo et al. Keller et al.

2005

Developing a 3D CFD model for Flue-wall design modification

2006

Application of CFD simulation for crossover design off-gas cleaning system optimization training purposes

Ordronneau et al.

2011

Application of CFD simulation for anode baking furnace modeling

Grégoire et al.

2013

Comparison of two modeling approaches to predict variability

Kocaefe et al.

2013

Different modeling approaches on anode baking furnace

Baiteche et al.

2015

Effects flue-wall deformation, and employing different radiation models

Ghaui et al.

2016

Implementation of baffle-less flue-wall technology

2017

Effects of flue-wall deformation

• Non-reactive flow

Not included

2018

Optimization and development of the furnace structures, process parameters and firing control system

Not specified

Not specified

Chaodong et al.

Detailed kinetics

Radiation model

• Non-reactive flow • EDM

Not included

• Not included • P1

• Not specified

Not included Not included

• Not specified • Not

Nongray medium Not included

Not specified Not specified

men-

Not included

• Hot air jet approximation • Mixture frac-

Not specified

• DO method

Not specified

Not included

• Not specified • P1

Not specified

• Not tioned

tion model • Not mentioned

• Empirical kinetic expression • Not tioned

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Zaidani et al.

Combustion model

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Authors' name

men-

Not included Not included

specified

• Monte Carlo • Not specified

• Not specified Not specified

Not specified

Not specified Not specified Not included Not specified

Fig. 1. Longitudinal view of a flue-wall in a firing section.

YM

the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate Zi, Zox and Zfu the elemental mass fraction of ith element, oxidizer and fuel mCH4 the fuel mass flux of both the burners the gravitational body force C the linear anisotropic phase function coefficient Di,m the mass diffusion coefficient of ith species the mass diffusion flux of the jth species hj the mixture enthalpy Iri the radiative intensity Ri,j the reaction rate n the refractive index E the total energy AT the transversal area between two adjacent baffles I the unit tensor Dt turbulent diffusivity K turbulent kinetic energy

k Sct kt f′ Lw

turbulent kinetic energy turbulent Schmidt number turbulent thermal conductivity the variance of mixture fraction velocity vector the wetted perimeter of the transversal area

Greek symbols ρ density μ laminar absolute viscosity μt turbulent absolute viscosity λ the wavelength Ε kinetic energy dissipation rate σε turbulent Prandtl number for kinetic energy dissipation rate σk turbulent Prandtl number for turbulent kinetic energy ω angular velocity Fγa area averaged flow uniformity index

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Fig. 2. Different combustion, turbulence, and radiation models to be tested in the present study.

Parameters Values

Tγa Tγm Fγm κ σs κB ϕglob

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Table 2 Computational grid and boundary conditions. Mesh size

Mesh orthogonal quality

Mesh orthoskew

66,568

1.0

0

B.C. for the mainstream flow inlet

B.C. for the fuel inlets

Velocity Inlet (depends on the ϕglob value)

Velocity Inlet (depends on the ϕglob value)

area averaged temperature uniformity index mass averaged temperature uniformity index mass averaged flow uniformity index the absorption coefficient of the medium the scattering coefficient of the medium the Boltzmann constant global equivalence ratio the stress tensor C1ε and C2 constants

B.C. for the mainstream flow outlet Pressure Outlet (−20 Pa)

1. Introduction

A modern smelter has a capacity of 1–2 million tons of aluminum per annum which requires 0.5–1.0 million tons of carbon anodes per year. The anode baking process is very energy intensive, approximately requires 2 GJ of energy per ton of carbon anodes which will be 1–2 million GJ of energy per year. There are four stages in the production of carbon anode namely mixing of raw materials (i.e., coke, binder pitch, and recycled anode butts), paste compaction, baking for approximately the duration of two weeks and subsequently, anode rodding. During the overall anode manufacturing process, baking contributes to approximately 44% of the total processing cost and hence, is the most expensive component of the process. In the anode baking process, generally energy provided by the methane/natural gas combustion is employed for the heat treatment. Heating by flame jets are widely used in many applications and they are preferred over the induction heating techniques because of their high convective heat transfer, faster heating response time, saving the energy by switching on the burners only when heat is demanded and starting up and cooling down periods are much shorter which also result in an energy saving. The main drawback of the heating/baking by flame jets is non-uniform heat flux distribution which results in variability of anodes properties such as electrical resistivity, air and CO2⁠ reactivity, thermal shock resistance and density. This non-homogeneity in the properties of anodes leads to various difficulties in aluminum production cell resulting in overconsumption of carbon and energy. The reason for this inconsistent property is that during baking, every anode in the furnace experiences different temperature history. It is observed that in some furnaces, anodes positioned in the same pit display temperature gradient of more than 100 °C based on their locations.

Abbreviations ABF Anode Baking Furnace CFD Computational Fluid Dynamics DO Discrete Ordinates EBU Eddy Break-Up EDM Eddy Dissipation Model FSD Flow Standard Deviation FUI Flow Uniformity Index GIT Grid Independence Test PDF Probability Density Function RTE Radiation Transfer Equation SIMPLE Semi-Implicit Method for Pressure-Linked Equations SHM Spherical Harmonics Method TSD Temperature Standard Deviation TUI Temperature Uniformity Index TI Turbulence Intensity TCI Turbulence-Chemistry Interaction WSGGM The Weighted-Sum-Of-Gray-Gases Model

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Fig. 3. Model's validation for (a) Axial temperature (°C) assuming gray medium, (b) Axial temperature (°C) employing WSGGM, (a) Radial temperature (°C) assuming gray medium and (b) Radial Temperature (°C) employing WSGGM.

Approximately 17% of the total cost of the aluminum production is due to the consumption of anodes and can reach up to 25% for anodes with poor quality. For instance, for a plant, with a capacity of 2 million tons of aluminum per annum, and anode price of US$400 per ton, an increase in carbon consumption from 410 to 440 kg per ton of aluminum, i.e. 30 kg above the assumed optimum, results in US$36 additional cost per ton of aluminum, or in total US$72 million additional cost per year. In the worst case scenario, an increase in carbon consumption from 410 to 470 kg per ton of aluminum leads to US$144 additional cost per ton of aluminum, or in total to an additional cost of US$288 million per year [1]. The anode baking is performed in a furnace called anode baking furnace (ABF) where the preheated oxidizer is mixed with the fuel jets in a sealed flue-wall cavity and form confined turbulent non-premixed combustion. It is imperative to understand the nature of the combustion process in the anode baking furnace to minimize the overconsumption of energy. In the literature, various numerical and experimental investigations are performed on the effect of various parameters on combustion, emissions and heat transfer characteristics of premixed and non-premixed flame jets for the other applications [2–7]. In case of anode baking furnace, the operational and geometrical parameters of the anode baking furnace have a significant influence on furnace energy consumption characteristics and the anode quality. Investigating the effect of these parameters on furnace performance by plant test is a very challenging and expensive task. Computational tools can be a more cost-effective means to investigate the effect of these parameters. Anode baking furnace modeling can be broadly di

vided into two categories; namely, anode baking furnace process modeling and anode baking furnace design/computational fluid dynamic (CFD) modeling. Anode baking furnace process models represent all the phenomena taking place in the furnace by using simple energy balance [8–10]. However, these simple process models may not be able to assist in the investigation of the effects of coupled transient heat transfer and turbulent fluid flow, and combustion and emission characteristics simulations. CFD modeling provides a better alternative for incorporating the coupled effects of turbulent combustion, detailed reaction kinetics, and radiative heat transfer and yields more accurate and predictive simulation results. Several studies on anode baking furnace CFD modeling are carried out. Assuming a non-reactive flow, Ping et al. [11] have investigated the effect of baffles and tie bricks arrangements on flow characteristics of anode baking process. They concluded that baffles and tie-bricks positioning has a significant impact on flow homogeneity. Severo et al. [12] studied the effect of flue-wall design modification on anode temperature distribution. They have considered two different flue-wall designs. They have shown that the optimized design results in an improved performance. Keller at al. [13] demonstrated that anode baking furnace CFD modeling can be employed as a tool for designing the crossover channel and off-gas cleaning system optimization. Ordronneau et al. [14] presented the simulation tools developed in Rio Tinto Alcan. They demonstrated the necessity of employing different simulation tools in meeting the challenge of increasing anode baking furnace productivity. Grégoire et al. [15] conducted a comparative study on

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Fig. 4. Model's Validation for (a) Axial Temperature (°C), (b) Radial Temperature (°C), (c) Axial Mixture Fraction, and (d) Radial Mixture Fraction.

two different modeling approaches for anode baking furnace combustion modeling. They concluded that approximating non-premixed flames in anode baking furnace with hot air jets results in a significant deviation from actual temperature distribution. However, the hot air jet approximation can be employed to reduce computational time. Baiteche et al. [16] studied the effect of flue-wall deformation on anode temperature distribution. Comparing the temperature profiles on a line in the pit transverse direction for straight and deformed flue-walls, it was observed that after flue-wall deformation, the temperature profile is no more symmetric which indicates a non-uniform baking process. Kocaefe et al. [17] demonstrated that using different computational tools with a different level of complexities are imperative to enhance the physical understanding of anode baking furnace performance. Ghaui et al. [18] demonstrated the use of baffle-less flue-wall design in anode baking furnace. They have shown that baffle-less flue-wall results in a better baking homogeneity and at the same time a higher thermal efficiency. Considering a non-reactive flow, Zaidani et al. [19–21] studied the effect of flue-wall deformation on anode temperature distribution. They concluded that based on the type of flue-wall deformation (concave, convex, combination of both), anode temperature can be significantly impacted, and furnace aging might result in under-baking or overbaking of carbon anodes. Chaodong et al. [22] carried out a study on developing a large scale, high efficiency and energy saving baking furnace. Using a finite element method (FEM) based model, they proposed two optimized designs for the flue-wall and exhaust ramp. Table 1 provides a summary of the literature review on an

ode baking furnace CFD/design modeling. The table also provides information about combustion and radiation models employed in the previous studies. In the numerical modeling of turbulent combustion, the accuracy of the results highly depends on the description of turbulence-chemistry interaction. As shown in Table 1, most of the previous studies on anode baking furnace CFD simulations employed standard k - ε combined with eddy dissipation model (EDM) with one step reaction mechanism as turbulence-chemistry interaction framework. Since the eddy dissipation model assumes complete combustion and that turbulent mixing is sufficient to describe the combustion process, it results in over predicting the temperature and species concentrations. Furthermore, thermal radiation plays an important role in turbulent combustion systems. Because of the difficulties associated with radiation calculations, it has been common practice in turbulent flame simulations to invoke the optically-thick approximation, and/or to assume the medium to be gray. The gray model offers a huge simplification to real problems. However, for a more precise answer a non-gray radiation model should be employed. Thus, in the first part of the present study, it is aimed to develop an accurate numerical platform to simulate confined non-premixed turbulent combustion in anode baking furnace flue-wall. In doing so, different turbulence-chemistry interaction frameworks, and radiative transfer equation solvers are tested for confined turbulent diffusion flames and results are compared with the reported experimental data in the literature. As shown in Fig. 2, with a view to developing a highly accurate CFD model for the confined non-premixed turbulent

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Fig. 5. Contours of static temperature (°C) for different turbulence-chemistry interaction and radiation models.

Fig. 6. Thermocouples arrangement inside the flue-wall cavity (at EGA).

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the top of the first and the last baffles. These openings are considered to be accountable for the loss of momentum of the flame jets in the vertical direction, and consequently non-uniform distribution of the flow and extra energy consumption. The effects of non-uniform flow and heat transfer distributions caused due to these openings on anode baking furnace energy consumption are investigated. To illustrate how the modified designs proposed in the present study result in a more energy efficient anode baking furnace, the effect of varying air-fuel ratio (equivalence ratio) is also studied. As time progresses, anode baking furnace ages and cracks may occur on the flue-walls. The packing coke can be infiltrated through the cracks and causes the flow blockage. By closing those openings, which are meant for the flow by-pass at the time of packing coke infiltration, the flue-wall explosion may occur. As the next step, considering the possibility of flue-wall blockage for the aged furnaces, three more flue-wall designs are introduced which can be implemented in the aged furnaces. Implementing changes in the flue-wall design are costly and sometimes are not practical. These factors should be taken into consideration for proposing modified designs that can be implemented for the existing anode baking furnaces.

Fig. 7. Validation with the experimental results (at EGA).

combustion in the aluminum anode baking furnace, a comprehensive sensitivity study is conducted on the effect of different combinations of combustion, turbulence, and radiation models on flow and temperature distributions. Anode baking homogeneity is an important consideration in the design of the anode baking furnace, which requires appropriate flow distribution in the flue-wall cavity. Hence, the developed model in the first part of the present work is employed to investigate furnace energy characteristics in the flue-wall of anode baking furnaces for different flue-wall designs. The current design of the flue-wall has openings at

2. Model specifications and numerical procedure

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Fig. 1 shows the computational domain of the flue-wall which is selected for the present study. Followings are the main governing equations that are solved in the present study.

Fig. 8. Contour plots of (a) velocity (m/s) (b) static temperature (°C) for different flue-wall designs.

Table 3 Comparison of current and modified flue-wall designs.

Current design Modified design

Tavg (°C)

CO (%)

TI (%)

ΔP (Pa)

a

TSD (°C)

FSD (m/ s)

Tγa

Fγa

Tγm

Fγm

1256

0.52

16.9

10

0.024

146

1.5

0.979

0.603

0.977

0.811

1457

2.7

24

14

0.077

208

2.6

0.956

0.616

0.956

0.843

Fig. 9. Contours of static temperature (°C) for (a) ϕglob = 1.0, (b) ϕglob = 0.5, (c) ϕglob = 0.25, and ϕglob = 0.125 in case of modified design.

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Fig. 10. Effects of varying ϕglob for the modified design.

Conservation of momentum in an inertial (non-accelerating) reference frame is described by:

is given by:

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The stress tensor

(2)

Fig. 11. Flow blockage in flue-wall due to packing coke infiltration.

2.2. Turbulence modeling

2.1. Conservation equations

The realizable k - ε model was considered for the closure of the conservation equations. Followings are the equations for turbulent kinetic energy (k) and its dissipation rate (ε):

The equation for conservation of mass, or continuity equation, can be written as follows: (1)

Fig. 12. Modified flue-wall designs for aged anode baking furnaces.

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Fig. 13. Flow and temperature fields for current and modified flue-wall designs during flow blockage due to packing infiltration.

[24,25]. As per this proposed model, the large-eddy mixing time-scale, defined as k/ε decides the rate of chemical reaction [25]. The turbulent eddies dissipation rates for the fuel, oxidizer and product eddies respectively are incorporated as follows:

Table 4 Flow descriptions of the current and modified (Case-II) design at the time of flow blockage. Design

Tavg (°C)

Fγa

TSD (°C)

FSD (m/ s)

ΔP

Current Modified

1213 1306

0.477 0.546

133.6 209°

2.3 3.12

112 156

2.3.2. Presumed probability density function method To estimate the fluctuating characteristics of scalar properties in a turbulent mixing process, probability density function (PDF) method can be successfully employed. The probability density function can be determined based on two approaches. The first one is the transported probability density function method, which is to solve the evolution of the probability density function. The transported probability density function method is computationally very expensive. Hence, the other approach is to assume that the probability density function has a certain form in terms of two conserved scalar quantities known as the mixture fraction, f, and its variance, f′, to predict temperature field and species concentrations. A large number of intermediate species and radicals involved in the combustion process can be modeled based on a pre-calculated library as a function of mixture fraction and strain rate. The basis of the non-premixed modeling approach is that under the assumption of chemical equilibrium, all thermochemical scalars (species fractions, density, and temperature) are uniquely related to the mixture fraction. The mixture fraction can be written in terms of the atomic mass fraction as [26]:

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(3)

(4)

2.3. Combustion modeling

In the present study, the eddy dissipation model and presumed probability density function methods are tested for the prediction of the reaction rate. Below are the governing equations for both the models. 2.3.1. Eddy dissipation model (EDM) The energy equation for eddy dissipation model can be expressed as follows (5)

where the mixture enthalpy is computed as is the mass fraction of jth species, and

(7)

(8)

The turbulent fluctuations should be accounted for by means of a joint probability density function, . The computation of , however, is not practical for most engineering applications. The problem can be simplified significantly by assuming that the enthalpy fluctuations are independent of the enthalpy level (i.e., heat losses do not significantly impact the turbulent enthalpy fluctuations). With this assumption, and mean scalars are calculated as:

,

.

Species transport equation can be written as:

(6)

where is the mass diffusion flux of species i, which arises due to gradients of concentration and temperature:

(9)

Determination of in the non-adiabatic system thus requires the solution of the modeled transport equation for mean enthalpy:

The rate of production or consumption Ri of the ith species is determined by considering the contribution of each reaction, Ri = Mi∑j = 1Ri,i. The reaction rate Ri,j depends on the reaction scheme adopted. Turbulent mixing is an important parameter in the reaction rate definition. Magnussen and Hjertager [23] proposed a method to incorporate this effect based on Spalding’s eddy-breakup (EBU) model

(10)

For turbulent reacting flow, however, we are concerned with the prediction of the averaged values of fluctuating scalars. How these averaged values are related to the instantaneous values depends on the turbulence-chemistry interaction model which is presumed probability density function method in our case. The Favre mean (density-aver

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aged) mixture fraction and its variance equations are [27]:

The P-1 approximation is usually only accurate when the radiation intensity field is nearly isotropic under which conditions the divergence of the radiative heat flux reduces to a diffusion equation with a spatially varying source term as a function of temperature only, such that:

(11)

(16)

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(12)

The expression for - ∇·q can be directly substituted into the energy equation to account for heat sources (or sinks) due to radiation. For the P-1 model, the radiative transfer equation is a diffusion equation. The model includes the effect of scattering as well. For combustion applications, where the optical thickness is large, the P-1 model works reasonably well. In addition, the P-1 model can easily be applied to complicated geometries with curvilinear coordinates.

However, the presumed PDF method cannot be used universally. Due to the unique dependence of ϕi (species mass fractions, density, or temperature) on f requires that the model meets the following conditions: • The fuel and oxidizer inlets must be discrete. • The Lewis number must be unity. (This implies that the diffusion coefficients for all species and enthalpy are equal, a good approximation in turbulent flow). • Only one type of fuel and one type oxidizer can be involved. The fuel may be made up of a burnt mixture of reacting species. The oxidizer may consist of a mixture of species. The multiple fuel and oxidizer inlets must, however, have the same composition. • The flow must be turbulent.

2.4.2. Discrete ordinates (DO) method The P-1 model assumes that all surfaces are diffuse. This means that the reflection of incident radiation at the surface is isotropic with respect to the solid angle. There may be a loss of accuracy, depending on the complexity of the geometry, if the optical thickness is small. The P-1 model tends to over-predict radiative fluxes from localized heat sources or sinks. The P-1 approximation is usually only accurate when the radiation intensity field is nearly isotropic which is true for optically thick media. But for gaseous combustion, the optically thick assumption is not suitable for pure molecular gasses which are transparent or optically thin 4×nϕ×nθ over large spectral regions. Therefore, the results of the P-1 approximation, though satisfactory, are not very accurate when compared to that of the more comprehensive discrete ordinates method. The discrete ordinates method can be used as an alternative to P-1 radiation model when more accurate temperature predictions are desired. The discrete ordinates method solves the radiative transfer equation for a finite number of discrete solid angles, each associated with a vector direction in a participating media. The fineness of the angular discretization can be controlled. The discrete ordinates model does not perform ray tracing. Instead, the discrete ordinates model transforms Eq. (13) into a transport equation for radiation intensity in the spatial coordinates . The discrete ordinates model solves for as many transport equations as there are directions . The solution method is identical to that used for the fluid flow and energy equations. The discrete ordinates model considers the radiative transfer equation in the direction as a field equation. Thus, Eq. (13) is written as [28]:

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2.4. Radiation modeling

Until recently it was not possible to make high-accuracy predictions of radiative heat transfer rates in high-temperature combustion applications. The reasons for this deficiency were: (i) lack of high accuracy and efficient radiative transfer equation (RTE) solvers and (ii) lack of versatile, robust and computationally efficient models to predict radiation from non-gray combustion systems. In an absorbing, emitting, and scattering medium, the radiative transfer is mathematically modeled by the radiative transfer equation which describes the rate of change of the spectral radiation intensity, Iλ, of a radiation beam traveling in the medium at the point r that propagates along a direction s and can be written as [28]: (13)

The radiative transfer equation describes the radiation intensity Iri (W/m2⁠ ) in a particular direction at a particular wavelength. Common methods for the solution of the radiative transfer equation in turbulent combustion simulations are: (i) SHM, and (ii) the discrete ordinates method, which are deterministic in nature. Both the methods approximate the directional variation of the radiative intensity. However, the underlying approaches to represent the directional dependence of radiative intensity for SHM and discrete ordinates are quite different. The discrete ordinates model employs a discrete representation of the directional variation with integrals over total solid angle 4π while the SHM captures the directional distribution of intensity by expressing it into a series of spherical harmonics.

The radiative transfer equation for the spectral intensity be written as:

(17) can

(18)

2.4.2.1. The weighted-sum-of-gray-gases model (WSGGM) The weighted-sum-of-gray-gases model (WSGGM) is a reasonable compromise between the oversimplified gray gas model and a complete model which takes into account particular absorption bands. The basic assumption of the weighted-sum-of-gray-gases model is that the total emissivity over the distance s can be presented as:

2.4.1. P1 approximation The P-1 radiation model is the simplest case. The following equation is obtained for the radiation flux [28]: (14)

where G is the incident radiation, and C is the linear-anisotropic phase function coefficient. The transport equation for G is: (15)

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For aε,i and κi, the values depend on gas composition, and aε,i also depends on temperature [29,30].

(solid) average temperatures and not based on the local gas temperature. In doing so, identifying the accurate numerical framework will be highly erroneous since the flow and temperature fields are highly non-uniform. Therefore, due to lack of experimental data on flame temperature and species concentrations in the case of anode baking furnace, after carrying out extensive literature review, the numerical model used in the present study is initially validated with the experimental work carried out on confined turbulent diffusion flames (in case of anode baking furnace, the preheated oxidizer is mixed with the fuel jets in a sealed flue-wall cavity and form confined turbulent non-premixed combustion) by Brookes and Moss [33] on a different geometry. The results are validated with the temperature and species measurements collected at the combustor axial and radial direction. As shown in Fig. 3, the case studies are divided into two groups, (i) assuming the gray medium, and (ii) incorporating the weighted-sum-of-gray-gases model (WSGGM) for absorption coefficient calculation. For all case studies in Fig. 3, the turbulence model is chosen to be realizable k - ε which provides accurate results as reported by Saqr et al. [34] which is also verified in the present study and shown in Fig. 4. The result obtained by the eddy dissipation model and presumed probability density function is compared with the experimental measurements while employing P-1 and discrete ordinates radiation models. As shown in Fig. 3, the eddy dissipation model results in overestimating both the radial and axial temperatures for both groups. Since the eddy dissipation model assumes complete combustion and that turbulent mixing is sufficient to describe the combustion process, it results in over predicting the temperature and species concentrations. Eddy dissipation model sometimes also predicts unphysical behavior, such as the flame creeping across walls. This is because the ratio of the turbulence quantities k/ε becomes large close to wall boundaries, but the turbulence in these regions is low. Hence, it can be observed that due to complete combustion and gray medium assumptions, the highest maximum flue gas temperature is obtained in the case of eddy dissipation model with the P-1 as the radiation model. Moreover, the P-1 model also tends to over-predict due to the optically thick assumption. Incorporating the weighted-sum-of-gray-gases (WSGGM) model into the P-1 model results in a more accurate prediction. It can be perceived from Fig. 3 that the presumed probability density function model for both P-1 and discrete ordinates models while employing the weighted-sum-of-gray-gases model shows very good agreement with the experimental data. As mentioned in the combustion modeling section, in case of presumed PDF method instead of solving evolution of the probability density function, it is assumed that the PDF has a certain form. This simplification makes the combustion modeling computationally much more efficient. However, it causes in slightly higher flame length which consequently results in modestly over predicting the temperature at the end of axial distance. As a result, as shown in Fig. 3, the numerical results over predict the experimental data at a larger axial distance of about 450 mm. In Fig. 4, we investigate the deviation in results while employing turbulence models other than realizable k - ε. The discrete ordinates radiation model combined with the weighted-sum-of-gray-gases model is used for all the cases depicted in Fig. 4. It can be observed from Fig. 4 that realizable k - ε results in a better agreement for the axial and radial temperatures, and mixture mean fraction as reported in the literature. Reynolds stress model (RSM) is the best match after realizable k - ε. However, RSM is computationally more expensive since the model solves five additional transport equations instead of two in case of the k - ε models. Results by RNG k - ε show the least agreement with the experimental data. Fig. 5 shows a comparison of results obtained employing eddy dissipation model and Presumed probability density function, for anode baking furnace flue-wall CFD simulation employing different radiation models for (a) a gray medium assumption, and (b) incorporating the weighted-sum-of-

2.5. Standard deviation and uniformity index

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To provide quantitative understanding, the results are evaluated by calculating the area and mass averaged flow and temperature uniformity indices (Tγa, Fγa, Tγm and Fγm), standard deviations of temperature and flow (TSD and FSD), turbulence intensity (TI), the absorption coefficient (a), and CO concentration for each case study. TI is used to specify the intensity of the turbulence. Increase in TI indicates a higher turbulence rate and a better air-fuel mixing which results in an improved combustion. The standard deviation of a specified field variable on a surface is computed using the mathematical expression below: (20) where X is the cell value of the selected variables at each facet, X0 is the mean of X:

and n is the total number of facets. The unifor-

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mity index represents how a specified field variable varies over a surface, where a value of 1 indicates the highest uniformity. The uniformity index can be weighted by area or mass. The area-weighted uniformity index (γa) of a specified field variable φ is calculated using the following equation [28,31]: (21)

where i is the faceted index of a surface with n facets, and erage value of the field variable over the surface:

is the av-

(22)

The equation for the mass-weighted uniformity index (γm) is different than Eq. (21) in that it incorporates flux terms: (23)

where

is the average flux of the field variable through the surface:

(24)

The steady-state numerical simulations are performed using a CFD software (Fluent 17.2) which is based on the finite volume discretization. The second-order upwind scheme is adopted for spatial discretization. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is selected for pressure interpolation and coupling of pressure and velocity. Grid independence tests (GIT) are carried out, and the difference in area-weighted average gas temperature and CO2⁠ average concentration, after increasing the cell size from 45,000 to 250,000 is found to be less than 1%. Hence, a cell size of 66,568 is selected for the present study. The orthogonal quality and ortho-skew are one and zero, respectively, which correspond to a high mesh quality [32]. Table 2 provides information about computational grid and boundary conditions (B.C.) used in the present study. 3. Results and discussions

Till the date no measurements on species concentrations and flame temperature in the case of anode baking are reported. The computational models have been validated based on comparing the anode

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downward in the flue-wall height direction. As can be observed, closing the openings results in a more uniform flow field and a higher flue gas temperature. Table 3 provides a summary of the two flue-wall designs. Closing the openings results in an increase of more than 200 °C in the flue gas temperature which indicates a much higher thermal efficiency. The area averaged temperature uniformity index, Tγa, is higher in the case of the current design which seems to be advantageous. However, this more uniform temperature field is due to the much lower average temperature and not a more uniform flow field. It can be observed that in the case of modified design, the area averaged flow uniformity index, Fγa, is higher and it can be confirmed by the contour maps shown in Fig. 8. The pressure drop, ΔP, for the modified design is slightly higher, which is expected. Absorption coefficient, temperature and flow standard deviations, and CO concentration are higher in case of the modified design which is due to a much higher flue gas temperature. As mentioned earlier, the anode baking process is very energy intensive, approximately requires 2 GJ of energy per ton of baked carbon anodes. To illustrate how the modified designs proposed in the present study result in a more energy efficient anode baking furnace, the global equivalent ratio, ϕglob is defined as the ratio of the fuel-to-air ratio to the stoichiometric fuel-to-air ratio. Obtaining the required flue-gas temperature (target flue-gas temperature) with a lower equivalence ratio is an indication of higher thermal efficiency or in the other words lower energy consumption. Mathematically it can be expressed as:

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gray-gases model. In problems with localized sources of heat, the P-1 model over-predicts the radiative fluxes (see Fig. 5). The optical thickness aL is a good indicator of which model is more appropriate. Here, L is a suitable length scale for the domain. If aL≫1, the best alternative is the P-1 model. For optically thin problems (aL < 1), the discrete ordinates model is more accurate [28]. For the combustion in anode baking furnace, the appropriate length scale is the hydraulic diameter of the flue-wall, Dh = 4AT/Lw where, AT is the transversal area between two adjacent baffles and Lw is the wetted perimeter of the transversal area [35]. The hydraulic diameter for the case in hand is 0.548 m. Hence, the aL is less than one. It can be concluded that the discrete ordinates method combined with the weighted-sum-of-gray-gases model provides a more reliable result. The observation made from Fig. 5 is in harmony with the conclusion obtained from Fig. 3. As shown in Fig. 6, the geometrical characteristics of the anode baking furnace do not allow to mount burners and thermocouples into the same peep-hole simultaneously during the firing sections. Hence, the thermocouples are positioned in the other two peep-holes inside the flue-wall cavity at different flue-wall heights. As depicted in Fig. 5, flue-gas temperature distribution varies between flow downstream and upstream. Hence, three thermocouples are placed in the flue-wall downstream (DS1, DS2 and DS3) and the other three are positioned in the flow upstream (US1, US2 and US3), a total of six thermocouples in one flue-wall cavity. The measurements are carried out in two different flue-walls, during the flue-gas soaking period (34 h), in 10 min’ intervals (approximately 200 measurements for each thermocouple) . As shown in Fig. 7, the experimental measurements are compared with the numerical results presented in Fig. 5 (cases I to VI). Due to a confidential agreement with Emirates Global Aluminium (EGA), only the normalized flue-gas temperature at different flue-wall locations are presented. As previously concluded, the realizable turbulence model combined with the presumed probability density function (PDF) method as turbulence-chemistry interaction, and discrete ordinates method as radiative transfer equation solver combined with WSGGM illustrate the closest match with the experimental data. In the case of eddy dissipation combustion model, the temperature is overestimated because of complete combustion assumption. It is noteworthy that the main advantages of the developed CFD framework are: [1] The model is computationally very efficient; [2] a large number of intermediate species and radicals involved in the combustion process are modeled; and [3] radiative heat transfer is estimated more accurately employing discrete ordinates (DO) method combined with the non-gray model.

(25)

Fig. 9 depicts the temperature contour plots for varying ϕglob (the global equivalent ratio). For different values of ϕglob, the mair (air flow rate) value is retained as a constant and mCH4 (fuel flow rate) values are changed accordingly. It can be observed that for the higher equivalence ratio values the temperature gradient is very high which results in the non-uniform baking of the carbon anodes. Moreover, since the temperature reaches above 1600 °C, the probability of NOx formation and CO2⁠ dissociation will also be higher. Fig. 10 shows the effect varying ϕglob (the global equivalent ratio) on flue-gas average temperature (Ta⁠ vg), CO concentration, turbulence intensity (TI), flow/velocity standard deviation (FSD), temperature standard deviation (TSD), and flow uniformity index (FUI). Be noted that in Fig. 10, considering a particular color, the legends and the title of the y-axes are the same. It can be observed that by closing the openings, the same average temperature can be obtained by reducing the global equivalence ratio from 1.0 to 0.125. Lower ϕglob value stands for a lower fuel consumption (higher fuel efficiency) which consequently translates into a less CO emission as well. The velocity and temperature standard deviation reduce as equivalence ratio value decrease which indicates higher flow and temperature fields. As shown in Fig. 10, it should be noted that lowering the equivalence ratio beyond 0.25 results in a drastic decrease in flue-gas temperature and increase in CO emission which is an indication of incomplete combustion. Hence, based on the fire-cycle time and the flue-gas soaking temperature the desired equivalence ratio and fuel flow rates should be estimated.

3.1. Anode baking furnace energy consumption

As shown in Fig. 1, preheated air is mixed with the fuel, and combustion occurs in the firing sections of an anode baking furnace. Despite significant improvements in the anode baking furnace flue-wall design in the last decade, guiding high-temperature flue gasses in such a way that all anodes, experience the optimum homogenous baking level remains a challenging task, mainly due to a large section size (5 m by 5 m). The current design of the flue-wall has openings at the top of the first and the last baffles. As mentioned earlier, these openings are considered to be accountable for the loss of momentum of the flame jets in the vertical direction, and consequently non-uniform distribution of the flow and extra fuel consumption. Fig. 8 shows the effects of closing the openings located at the top of the first and the last baffles. It can be observed that in the current design of the flue-wall due to the burners downstream openings, non-uniform distribution of flow and temperature fields are caused. In the anode baking furnace due to the exhaust fan location, the underpressure increases in the fire direction towards preheating sections. Due to this negative pressure, the flame jets are pulled in the fire direction instead of spreading

3.2. Effect of the flow blockage As time progresses, anode baking furnace ages and cracks may occur on the flue-walls. As shown in Fig. 11, the packing coke can be infiltrated through the cracks and causes the flow blockage. This flow obstruction ultimately triggers the flue-wall explosion. As the next step, considering the possibility of flue-wall blockage for the aged furnaces, three more flue-wall designs are introduced which can be implemented in the aged furnaces.

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Acknowledgement

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This research was supported by Emirates Global Aluminum (EGA) and the Government of Abu Dhabi to help fulfill the vision of the late President Sheikh Zayed Bin Sultan Al Nahyan for sustainable development and empowerment of the UAE and humankind. References

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Hindasageri, A numerical investigation on heat transfer and emissions characteristics of impinging radial jet reattachment combustion (RJRC) flame, Appl Therm Eng 89 (2015) 534–544. [7] J. Oh, D. Noh, E. Lee, The effect of CO addition on the flame behavior of a non-premixed oxy-methane jet in a lab-scale furnace, Appl Energy 112 (2013) 350–357. [8] N. Oumarou, D. Kocaefe, Y. Kocaefe, B. Morais, Transient process model of open anode baking furnace, Appl Therm Eng 107 (2016) 1253–1260. [9] Tajik AR, Shamim T, Al-Rub RKA, Zaidani M, editors. Performance analysis of a horizontal anode baking furnace for aluminum production. ICTEA: international conference on thermal engineering; 2017. [10] N. Oumarou, D. Kocaefe, Y. Kocaefe, An advanced dynamic process model for industrial horizontal anode baking furnace, Appl Math Model 53 (2018) 384–399. [11] P. Zhou, C. Mei, J.-m. Zhou, N.-j. Zhou, Q.-h. Xu, Simulation of the influence of the baffle on flowing field in the anode baking ring furnace, J Central South Univ Technol 9 (3) (2002) 208–211. [12] D.S. Severo, V. Gusberti, E.C. Pinto, Advanced 3D modelling for anode baking furnaces, Light Metals 2005 (2005) 697–702. [13] Mannweiler U. Computational modeling in anode baking. [14] Ordronneau F, Gendre M, Pomerleau L, Backhouse N, Berkovich A, Huang X. Meeting the challenge of increasing anode baking furnace productivity. Light metals 2011. Springer; 2011. p. 865–70. [15] F. Grégoire, L. Gosselin, H. Alamdari, Sensitivity of carbon anode baking model outputs to kinetic parameters describing pitch pyrolysis, Ind Eng Chem Res 52 (12) (2013) 4465–4474. [16] M. Baiteche, D. Kocaefe, Y. Kocaefe, D. Marceau, B. Morais, J. Lafrance, Description and applications of a 3D mathematical model for horizontal anode baking furnaces, Light Metals (2015.1115-20.). [17] Kocaefe Y, Oumarou N, Baiteche M, Kocaefe D, Morais B, Gagnon M. Use of mathematical modelling to study the behavior of a horizontal anode baking furnace. Light metals 2013. Springer; 2016. p. 1139–44. [18] El Ghaoui Y, Besson S, Drouet Y, Morales F, Tomsett A, Gendre M, et al. Anode baking furnace fluewall design evolution: a return of experience of latest baffleless technology implementation. Light metals 2016. Springer; 2016. p. 941–5. [19] M. Zaidani, R.A. Al-Rub, A.R. Tajik, T. Shamim, 3D multiphysics model of the effect of flue-wall deformation on the anode baking homogeneity in horizontal flue carbon furnace, Energy Proc 142 (2017) 3982–3989. [20] Zaidani M, Al-Rub RA, Tajik AR, Shamim T, editors. Investigation of the flue-wall aging effects on the anode baking furnace performance. ICTEA: international conference on thermal engineering; 2017. [21] Zaidani M, Al-Rub RA, Tajik AR, Shamim T, editors. Computational modeling of the effect of flue-wall deformation on the carbon anode quality for aluminum production. ASME 2017 heat transfer summer conference; 2017. American Society of Mechanical Engineers. [22] Chaodong L, Yinhe C, Shanhong Z, Haifei X, Yi S, editors. Research and application for large scale, high efficiency and energy saving baking furnace technology. TMS annual meeting & exhibition; 2018. Springer. [23] Magnussen BF, Hjertager BH, editors. On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Symposium (international) on combustion. Elsevier; 1977. [24] Spalding D, editor. Mixing and chemical reaction in steady confined turbulent flames. Symposium (international) on combustion. Elsevier; 1971. [25] A. Frassoldati, S. Frigerio, E. Colombo, F. Inzoli, T. Faravelli, Determination of NOx emissions from strong swirling confined flames with an integrated CFD-based procedure, Chem Eng Sci 60 (11) (2005) 2851–2869. [26] Y. Sivathanu, G.M. Faeth, Generalized state relationships for scalar properties in nonpremixed hydrocarbon/air flames, Combust Flame 82 (2) (1990) 211–230. [27] W. Jones, J. Whitelaw, Calculation methods for reacting turbulent flows: a review, Combust Flame 48 (1982) 1–26. [28] Fluent A. 12.0 theory guide. Ansys Inc.; 2009. p. 5. [29] T. Smith, Z. Shen, J. Friedman, Evaluation of coefficients for the weighted sum of gray gases model, J Heat Transfer 104 (4) (1982) 602–608. [30] A. Coppalle, P. Vervisch, The total emissivities of high-temperature flames, Combust Flame 49 (1–3) (1983) 101–108.

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Fig. 12 illustrates the contours of static temperature (°C) and velocity magnitude (m/s) for the proposed modified designs. In these modified designs, two openings are considered so that the flow can bypass in the case of flow blockage. The openings at the top of the baffles in the case of the current design are shifted to different flue height positions. It can be observed that for all the three proposed designs, the flue gas average temperature is higher than the current design which indicates a higher thermal efficiency. The ΔP (pressure drop across the flue-wall) for all the three cases experiences only a modest increment which can be afforded by an increase in exhaust fans capacity. The Fγa (area averaged flow uniformity index) is also higher in all the three cases which implies a more uniform flow field. The coke infiltration and flow blockage usually occur in the flow downstream. In this section, we aim to investigate the flow and temperature distributions in case of packing coke blockage for the current and modified designs (see Fig. 13). Table 4 shows that in the case of modified design, the average flue gas temperature is higher by 100 °C which signifies a higher thermal efficiency. The pressure drop does not differ significantly in both the designs. One thing to be noted that temperature and flow standard deviations are lower in case of the current design which gives the wrong impression of a more homogenous temperature field. However, the area averaged flow uniformity index is 0.477 which denotes a high level of flow non-homogeneity. This observation can be verified from the qualitative representation of the flow field through the contour plot of velocity magnitude. The area-averaged flow uniformity index for the modified design is 0.546. Thus, uniformity index appears to be a more dependable criterion to settle on a certain design. 4. Conclusions

The current study develops a computational CFD model for an aluminum anode baking furnace. The model considers the effect of turbulence-chemistry interactions by employing k - ε realizable turbulence model with presumed probability density function (PDF) method. The discrete ordinates (DO) method is used as the radiative transfer equation solver. The weighted-sum-of-gray-gases model is used to calculate the absorption coefficient. After conducting comprehensive sensitivity studies on different combustion, turbulence, and radiation models, the developed numerical platform was employed to investigate the effects of flue-wall design modifications on the anode baking furnace energy consumption characteristics. It was observed that in the case of modified flue-wall design, the same average flue gas temperature can be obtained by reducing the global equivalence ratio (ϕglob) from 1.0 to 0.125 which indicates a high level of energy saving which consequently translates into less CO emission. Furthermore, more homogeneous flow and temperature fields are observed which result in the baking of anodes more uniformly which consequently result in the evolution of homogenous anode material properties. As a result, the energy consumption in the aluminum reduction cell will also be significantly reduced. Considering the possibility of flow blockage due to packing coke infiltration for the aged anode baking furnaces, three modified flue-wall designs are also introduced. It was observed that for all the three proposed designs, the average flue gas temperature is higher than the current design which indicates a higher thermal efficiency. The Fγa (area averaged flow uniformity index) was also higher in all the three cases which implies a more uniform flow field. It should be pointed out that the radical changes in the flue-wall design, such as baffle-less flue-wall designs are difficult and costly to be implemented. Taking these constraints into consideration, all the proposed designs in the present study are straightforward to be implemented for the existing anode baking furnaces.

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Applied Energy xxx (2018) xxx-xxx [34] K. Saqr, M. Wahid, Comparison of four eddy-viscosity turbulence models in the eddy dissipation modeling of turbulent diffusion flames, Int J Appl Math Mech 7 (19) (2011) 1–18. [35] Severo DS, Gusberti V. User-friendly software for simulation of anode baking furnaces. In: Proceeding of 10th Australisian; 2011.

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[31] A.R. Tajik, T. Shamim, R.K.A. Al-Rub, M. Zaidani, Two dimensional CFD simulations of a flue-wall in the anode baking furnace for aluminum production, Energy Proc 105 (2017) 5134–5139. [32] A.R. Tajik, R.K.A. Al-Rub, M. Zaidani, T. Shamim, Numerical investigation of turbulent diffusion flame in the aluminum anode baking furnace employing presumed PDF, Energy Proc 142 (2017) 4157–4162. [33] S. Brookes, J. Moss, Measurements of soot production and thermal radiation from confined turbulent jet diffusion flames of methane, Combust Flame 116 (1) (1999) 49–61.

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