Numerical investigations to determine the optimal operating conditions for 1 kW-class flat-tubular solid oxide fuel cell stack

Accepted Manuscript Numerical investigations to determine the optimal operating conditions for 1 kW-class flat-tubular solid oxide fuel cell stack Kashif Rashid, Sang Keun Dong, Muhammad Taqi Mehran PII:

S0360-5442(17)31603-1

DOI:

10.1016/j.energy.2017.09.082

Reference:

EGY 11576

To appear in:

Energy

Received Date: 20 April 2017 Revised Date:

20 July 2017

Accepted Date: 18 September 2017

Please cite this article as: Rashid K, Dong SK, Mehran MT, Numerical investigations to determine the optimal operating conditions for 1 kW-class flat-tubular solid oxide fuel cell stack, Energy (2017), doi: 10.1016/j.energy.2017.09.082. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Numerical investigations to determine the optimal operating conditions for 1kW-class flat-tubular solid

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oxide fuel cell stack

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Kashif Rashid1, 2, Sang Keun Dong2, 1*, Muhammad Taqi Mehran3

Department of Energy System Engineering, Korea University of Science and

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Technology (UST)

217, Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea 2

Thermal Energy System Laboratory, Korea Institute of Energy Research (KIER), 152, Gajeong-ro, Yuseong-gu, Daejeon, 34129, Republic of Korea

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Department of Advanced Energy and Technology, Korea University of Science and Technology (UST),

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217, Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea

*Corresponding author contact number and email:

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Tel: 82-42-860-3342, Fax: 82-42-860-3133

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E-mail: [email protected]

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Abstract In this study, a detailed three-dimensional numerical model is developed which

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simultaneously assimilates the transport processes, the electrochemical and chemical reactions to

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optimize the performance of 1 kW-class flat-tubular solid oxide fuel cell stack while operating

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on H2 and pre-reformed methane fuels. The unique feature of this CFD (computational fluid

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dynamic) model is that it encompasses the electrochemical oxidation of H2 and CO as well as

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internal steam reforming reactions including radiation heat transfer analysis in the full stack. A

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CFD model validated with the experiments performed in-house is utilized to explore the optimal

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operating conditions by investigating the effect of pre-reforming rate, air/fuel inlet temperatures,

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oxidant utilizations and radiative heat transfer effect on the temperature distributions. The

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numerical results elucidated that temperature and the current density distributions can be

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regulated by adjusting the methane conversion in the pre-reformer. It is also observed that

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neglecting the CO electro-oxidation in the modeling can underestimate the stack performance;

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whereas increasing the inlet temperature increases the stack performance. The oxidant utilization

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analysis established that higher oxidant utilization adversely affects the stack performance due to

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higher cathodic activation polarization losses. Radiation heat transfer analysis demonstrates that

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it curtails peak temperature and minimizes temperature gradients of the stack components.

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Keywords: - Hydrogen and carbon monoxide parallel electrochemical reactions, internal steam

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reforming, methane conversion, thermal management, radiative heat transfer

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Highlights

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3D numerical model developed for real-scale 80 FT-SOFC stack with external manifold

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Electrochemical (H2 and CO), internal reforming reactions executed simultaneously

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Inclusion of radiative heat transfer effectively reduces the temperature gradients

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Pre-reforming rate significantly affects the temperature and current density

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Increase of oxidant utilization rate adversely affects stack performance

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1. Introduction The global warming due to the greenhouse gas emissions is becoming an alarming issue,

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and many efforts are being made to explore an environmentally friendly systems to replace the

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conventional and less efficient combustion-based power generation technologies [1–4]. Solid

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oxide fuel cell (SOFC) has shown great promise to serve an alternative electricity generation

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technology. SOFC offers many attractive features such as high energy conversion efficiency

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along with the low emission of greenhouse gasses, and fewer mechanical parts than the

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conventional systems [5,6]. The ability of SOFC to reform hydrocarbon internally, disseminate

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them as a prime candidate which will lead the transformation from conventional power

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generation to SOFC-based electricity generation, as they can be operated on different types of

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hydrocarbon fuels such as methane, syngas, biogas, coal, gasoline, etc. [7–9].

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As SOFC’s are manufactured from ceramic materials, therefore, the high temperature is

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required to attain the better ionic conductivity and this high operating temperature of SOFC

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offers additional potential for co-generation applications [10,11]. The natural gas (NG) is being

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extensively studied and utilized as a most attractive fuel for medium sized SOFC-based

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stationary applications. The methane is a major constituent of NG, which should be reformed

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either internally or externally because electrochemical oxidation of methane in SOFC is not

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favorable [12]. The strong endothermic internal steam reforming reaction (MSR) utilizes the

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waste heat of irreversible polarizations and joule heat [13,14]. The internal reforming in SOFC’s

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suppresses the need to cool the stack through a vast amount of excess air supplied across the

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cells. This attractive feature significantly reduces the cost of operation and hence improves the

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system efficiency [15]. However, Yoshida et al. [16], Stimming et al. [17] and Klein et al. [18]

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stated that intense endothermic reforming reaction creates a problem in SOFC stable operation

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because of thermal management which is severely affected by the temperature gradients. It is,

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therefore, essential to have an appropriate understanding and perhaps the control over the

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reforming reaction in the SOFC’s to operate the stack at optimum efficiency with internal steam

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reforming [19–21].

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When H2 and CO present in the fuel stream, the total current produced is the summation

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of both the reactant species at the anode/electrolyte interface due to the electrochemical reactions

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(ECR). CO electro-oxidation directly influences the performance of stack, whereas,

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overpotentials losses affect the output voltage directly [22]. In SOFC modeling studies, it is 3

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pervasive practice to neglect the ECR of CO or in some cases, polarizations losses are not fully

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implemented [23–28]. Li et al. [29], Haberman et al. [30] and Hofman et al. [31] have made

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assumptions in their work that when H2 and CO both are present in the fuel stream, CO only

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participate in the water gas shift reaction (WGSR) instead of ECR because of very fast kinetics

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of WGSR. These simplified assumptions for electrochemical modeling are debatable from the

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accuracy point of view. However, some authors have considered ECR of CO as well in their

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research work. The summary of some of the research work related to ECR of H2 and CO is

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presented in Table 1.

72 Table 1: - Selected studies related to ECR of H2 and CO Authors

Iwai et al. [34]

Andersson et al. [36]

Ni et al. [37] B. Lin et al. [38]

-Concentration polarization neglected -Pressure drops neglected - Heat transfer by convection only

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-MSR and WGSR modeling incorporated along with ECR of H2 and CO -Both ECRs are treated parallel reactions -Activation, ohmic and concentration losses included -Pre-reforming rate was used to control local temperature and current density - ECR’s of both H2 and CO were considered - MSR and WGSR modeling also included -Different reforming models included for comparisons -An alternative method proposed for OCV calculation -Finite element approach -ECR’s of both H2 and CO were considered -Both ECRs are treated parallel reactions -MSR and WGSR modeling also included -Activation, ohmic and concentration losses included

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Ni et al. [35]

-Two methodologies adopted to handle the CO presence in the fuel stream -WGSR was considered in the first strategy -Whereas, in the second approach both ECR and WGSR modeling of CO were implemented -ECR’s of both H2 and CO were considered -Developed model further applied to predict carbon formation

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Suwanwarangkul et al. [33]

Limitation

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Petruzzi et al. [32]

Approach

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-ECR’s of both H2 and CO were considered -Only WGSR included -Model developed to predict the non-uniform flow velocity distribution among the cell channels -Model developed to predict the cell to cell performance variations

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4

-Isothermal modeling for button SOFC -Ohmic loss for electrolyte only -WGSR occurred at anode/electrolyte interface -Single planar SOFC -No radiation heat transfer (RHT) -Adiabatic condition on side walls -Isothermal conditions in flow channel

-Selected portion of single SOFC selected for study -Fixed exchanged current densities used for anode and cathode -No thermal BC specified on the outer walls -Selected portion of single SOFC selected for study -Local thermal equilibrium (LTE) applied -No radiation heat transfer -Symmetry BC at the top and bottom side walls -No RHT -LTE in electrodes -Pressure gradient neglected in porous flow -Isothermal BC at the outer walls of stack

Model assumption 3D, transient

2D, steady state

quasi-3D, steady state

2D, steady state

2D, steady state

3D, steady state

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During the literature review, it was established that all the developed models have incorporated

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temperature dependent transport properties, chemical kinetics and material properties of cell and

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stack. In order to predict the fuel cell performance correctly, it is, therefore, indispensable to

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develop a model that can accommodate various modes of heat transfer in solid as well as in flow

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channel components. Owing to the high operating temperature of SOFC, radiative heat transfer

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(RHT) becomes an important mode of heat transfer that cannot be neglected (especially for stack

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level study) because temperature gradients are crucial in determining the thermal stresses and to

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envisage the cell failure. However, in most of the existing models, RHT is either neglected

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because of isothermal assumption [39–43] or simplified form of the heat transfer model is used

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to estimate radiative heat transfer [44–47]. There are numbers of model exist in the literature that

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includes RHT, however, they do not assimilate the effects of CO2 and water vapors in the anode

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electrode despite their high concentration. It is considered that these participating gases absorb,

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emit and scatter radiation of certain wavelength [48].

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All of the studies discussed above are limited either to a button cell or a single

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planar/tubular SOFC cell. The stack level study, for other design of SOFCs such as FT-SOFC,

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which models/implements ECR’s of both H2 and CO in detailed along with chemical reactions

90

MSR/WGSR, is either missing or very limited. And secondly, RHT modeling is either neglected

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completely or selected features are incorporated to avoid complexity and to reduce

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computational time. Bessette et al. numerically exhibited that single cell have different attributes

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than those of the stack, and it is an inaccurate methodology to predict the output characteristics

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of SOFC stack based on the unit cell results [49]. In the present work, a detailed three-

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dimensional (3D) numerical analysis is performed on a 1kW-class anode-supported FT-SOFC 80

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cells stack fueled by humidified hydrogen and pre-reformed methane. The current CFD model

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exclusively accounts for intricate transport phenomena (mass, momentum, and heat transfer),

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electrochemical reactions (including both H2 and CO) with overpotential losses such as

99

activation, ohmic, and concentration, as well as MSR/WGSR on the real-scale stack. The

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experiments are performed with both the fuels to validate the modeling. The validated model is

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employed to examine the effect of pre-reforming rate, neglecting the electro-oxidation of CO,

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different inlet temperatures, and oxidant utilization on the stack performance to optimize the

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stack operating conditions. RHT is also included in the modeling to improve the temperature

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distributions inside the cell components and also near the side walls. There are two major

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objectives of this study; first to improve the modeling presented in our previous work [50] and

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secondly, to develop an improved SOFC system design for medium-scaled residential power unit

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by exploring optimum operating conditions for safe and long-term operation.

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2. Experimental setup

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Fig. S1 (a, b) shows the experimental setup of 1 kW-class FT-SOFC stack installed in a

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residential power generating unit (RPG) with the essential balance of plant (BOP). The BOP

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system comprises of heat exchangers (HX’s) positioned on both sides of the stack; a steam

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reformer mounted over the stack and startup burner embedded between the stack and the steam

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reformer.

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Figure S1 (a): Experimental setup and compact hotbox design

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The stack consists of 80 anode-supported flat tubular SOFC (FT-SOFC) cells, vertically mounted

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on the manifold. The stack was first operated with 3% humidified hydrogen then pre-reformed

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methane was supplied as a second fuel to validate the numerical modeling. In the first case, the

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system was heated up to 760°C through startup burner by supplying 1.2 lpm methane. When the

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system and equipment’s temperature stabilizes to 760°C; 18 lpm hydrogen gas after passing

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through the humidifier was supplied at the manifold inlet, whereas 150 lpm pre-heated air was

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supplied through the exit holes of both the heat exchangers (75 lpm through each HX) positioned

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across the stack. After attaining steady temperature, startup burner was switched off; an external

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load was applied to draw electrical current ranging from 0 to 18.48 A.

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Figure S1 (b): 80 FT-SOFC Stack with platform

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The stack output voltages were recorded for each of the corresponding current drawn once the

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system got stabilized. In the second case, 4.55 lpm methane was supplied to the external steam

131

reformer and 10 ccm of water was supplied to the steam generating tube when the reformer inlet

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temperature reaches about 650°C. Similarly, an external load is applied to draw electrical current

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ranging from 0 to 18.7 A when the temperature of the stack is steadied at 760°C. The stack

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output voltages were recorded for each of the corresponding current drawn once the system got

135

stabilized. To maintain stable reforming operation and air/fuel pre-heating; spent fuel and the

136

excess air were burned in the combustion chamber to provide necessary heat energy when startup

137

burner was cut off.

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3. Model development

A computational domain of anode-supported flat tubular SOFC (FT-SOFC) stack is

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presented in Fig. 1 along with the necessary dimensions whereas geometric parameters for single

141

FT-SOFC are presented in Table 2.

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Figure 1: Fluid domain with necessary dimensions

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The stack consists of 80 cells divided into four assemblies each containing 20 cells positioned

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vertically in an air enclosure. The fuel is supplied to these cells with the help of manifold

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attached at the bottom. The manifold is modeled in such a way to distribute the incoming fuel

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gas uniformly to the anode channels. The pre-heated air is supplied across the stack through the

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exit holes of heat exchangers.

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Table 2: Geometric dimensions of single FT-SOFC (mm) Cell length 200 Anode channel 200 x 1.2 x 1.2 dimensions (L x W x H) Number of channels 21 Rib width 1.15 Cathode electrode 45 x 168 dimensions Anode thickness 0.725 Cathode thickness 0.020 Electrolyte thickness 0.010

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3.1.

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151 Reactions considered for modeling

In the present analysis, pre-reformed methane mixture (H2, H2O, CH4, CO, CO2) is

154

considered as fuel and when a fuel is comprised of methane and carbon mono oxide, methane

155

steam reforming (MSR) and water gas shift reactions (WGSR) are taking place in the anode.

156

CH + H O → CO + 3H CO + H O → CO + H

(WGSR)

(1) (2)

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(MSR)

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The volumetric reaction rates of MSR and WGSR are adopted from the work of Lehnert

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et al. [51] and the rate expressions are summarized in Table 3. Hydrogen and carbon monoxide

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reacts with oxygen ions (O2-) at the anode-electrolyte interface (TPB) to produce steam, carbon

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dioxide respectively and releases electrons.

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H + O → H O + 2e

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CO + O → CO + 2e



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O + 2e → O

(Reaction at anode-electrolyte interface)

(3)

(Reaction at anode-electrolyte interface)

(4)

(Reaction at cathode-electrolyte interface)

(5)

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2.3 x 10-8

#

(mol m-3 Pa-4 s-1) $%&

1.4 x 10-20

# (mol m-3 Pa-2 s-1) '(%

1.5 x 10-7

#

(mol m-3 Pa-2 s-1) '(%

1.4 x 10-7

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3.2.

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# (mol m-3 Pa-2 s-1) $%&

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Table 3: Model equations for the calculation of internal steam reforming  

Reforming reaction rate  =     -     -3 -1 (mol m sec ) 

Shift reaction rate  = !"    - !"   -3 -1 (mol m sec )

Electrochemical models

The electrochemical modeling is employed to determine the local current density

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distribution at the operating voltage. The equilibrium/open circuit potentials for the

173

electrochemical reactions of H2 and CO are locally calculated by the following Nernst equations

174

[35,36] and their expressions are provided in Table 4.

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The activation polarization is an additional potential required to overcome the energy

176

barrier (activation energy) to precede the electrochemical reactions at the interfaces at the

177

expected rate. The Butler-Volmer equation is used to determine the relationship of electrodes

178

activation overpotentials and current densities because of ECRs.

179

) = )* +,

1

2 − 456 ,−

7 -8./0 1

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-./0

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29

(6)

The exchange current density (Io) at the electrode/electrolyte interface depends upon

181

many factors like material properties, ECR kinetics, operating conditions as well as

182

reactant/product concentrations. A general Arrhenius type expression is employed for its

183

calculation.

184

)* =  456 :−

;<

1

=

(7)

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In the present work, the exchange current densities expressions presented by

186

Suwanwarangkul et al. [33] and Negata et al. [52] are considered and detail explanation can also

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be approached in ref. [53]. The summary of the selected expressions for exchange current density

188

is described in Table 4. Table 4: Nernst potentials and exchange current density calculations H.J

K

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   C >,@A.B = + EF G   2D   >* = 1.253 − 2.4516. 10  ∗ C >*

Nernst potential (H2)

H.J

   C >,@A.B = + EF G K 2D  * > = 1.46713 − 4.527. 10  ∗ C 2DWTXB,T.,  −DWTXB,T.,  C ) = ST., U456 V Y − 456 V YZ 3D C C C 2DWTXB,T., −DWTXB,T., ) = ST., U456 V Y − 456 V YZ 2.5 × 3D C C −2DWXTB, 2DWXTB, C ) = SXTB, U456 V Y − 456 V YZ 4D C C H.aa   −12000 ` ST., = Ȃ 456 V Y] . C ^A_,   H.aa  −12000 ` ST., = Ȃ 456 V Y] C ^A_,  −13000 H.JH SXTB, = Ȃ 456 V Y  C * >

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Nernst potential (CO)

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Interface conduct ivies

c /;b 

c /;de

Y, ^A_, = 456 :

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^A_,  = 456 V

Equilibrium constant

1

1

=

Ȃ = 2.15 × 10  , Ȃ = 2.0 × 10  , Ȃ = 1.95 × 10

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Adjustable parameter (validation) 189

The ohmic polarization is the resistance encounter by the movements of ions and

191

electrons through the electrolyte, and electrodes respectively. The effective electronic

192

conductivities of the anode and cathode electrodes and the ionic conductivity of the electrolyte is

193

adopted from the work of Andersson et al. [36] and they are displayed in Table 5. The overall

194

ohmic loss can be evaluated by combining the conductivities of electrodes and electrolyte.

195

W*

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g

= )U

B
i
+

Bl
il
+

Bj

ij,jkk

Z

(8)

196 197

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Electrolyte YSZ

6864

5950

607

400

10 35

198

2.7 -

-

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2.5

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Cathode electrode LSM

0.5 2.9

nXTB,Aoo 4.2 × 10p −1200 qXTB = 456 U ZV Y C C rXTB

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Table 5: Physical properties of cell components* Anode electrode Component Ni-YSZ material Density (Kg m-3) 6380 Specific heat 440 (J Kg-1 k-1) Thermal 3.6 conductivity (W m-1k-1) Porosity (ε), % 40 Average particle 2.5 diameter, dp (µm) Mean pore radius, 0.5 rm (µm) Tortuosity (ξ) 3.5 Effective nT.,Aoo electronic/ionic 9.5 × 10p −1150 qT. = 456 U ZV Y conductivities C C rT. -1 (S.m )

nA,Aoo

-

= 3.34 × 10 456 U

−10300 qA ZV Y C rA

When the current is being drawn from the system, reactants are consumed in the vicinity

200

of the electrode-electrolyte interface. The concentration difference of reacting species between

201

the bulk and at the TPB becomes significant because of the mass transport process. These mass

202

transport phenomena take place in two steps (i) external diffusion i.e. gasses diffuse from

203

channels to the electrode surface (ii) in/out transport of reactants/products within the porous

204

electrodes. The expressions used for the calculated of diffusion coefficients are summarized in

205

Table 6 [54]. On the other hand, concentration polarization depends on many factors such as;

206

type of the electrochemically active species, the thickness of diffusion path as well as

207

porosity/tortuosity of the electrodes. The expressions for concentration polarization are presented

208

as [55,56]:

209

X*.X WT., = 

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X*.X WT., =

X*.X WXTB, = 

1 /

1 /

1

ln V

u ∗ b e u ° b

u ∗ b u ° b e

ln V V

u ∗ de u ° de u ∗ de u ° de

u ° e

/ u ∗ e

Y

Y

(9)

Y

(10) (11)

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Table 6: Diffusion coefficient calculations

Multicomponent diffusion coefficient

wxy

1 − ƒx wx g‚ = ƒ ƒ ƒ y +  + € + ⋯⋯ wxy wx wx€ C w…,x = 4850 †‡*A ˆ |x

Effective gas diffusion coefficients (m2 s-1) H2/H2O/CH4/CO/CO2/ O2/N2

4.73e-5/1.20e-5/ 1.97e-5/1.74e-5 /1.41e-5/1.27e-5/1.30e-5

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Knudsen diffusion coefficient

3.3.

Electrical circuit model

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} 

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Binary diffusion coefficient

1 1 0.001858 C + + 9 |x |y =  ~xy € ⁄

The electrochemical reactions are schematically demonstrated as an equivalent circuit in

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the Fig. 2. In the present work, two different fuels (H2 and pre-reformed methane) have been

217

considered for the stack analysis; therefore, two separate approaches are adopted to handle the

218

ECR of H2 fuel and reformed gas mixture (considering ECR of both H2 and CO). In the Fig. 2

219

(a), only the ECR of H2 is considered, and in this method, all the resistances are following series

220

circuit model and ohm’s law is used to calculate circuit voltage. In the second circuit, Fig. 2 (b),

221

the model comprises of two electromotive forces (EMF) generated by electrochemical oxidations

222

of H2 and CO and their relevant activation and concentration resistances. Whereas ohmic loss

223

(due to ionic and electronic resistance), activation and concentration resistances of oxidant at the

224

cathode are connected in series in the model. The average current density at the TBP is

225

maintained invariable whereas local current density varies over the reaction surface and is

226

calculated based on heat/mass transfer together with both electrochemical reactions. The two

227

ECR’s given in the equations (3) and (4) are represented in the circuit diagram as two parallel

228

reactions. Mass and charge transports phenomenon will regulate these reactions to acquire

229

distinct cell output voltage.

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X*.X X*.X ‰_XA‹‹ = > ,@A.B − WTXB, − WTXB, − WT., − WXTB, − W*  

X*.X X*.X ‰_XA‹‹ = >,@AB − WTXB, − WTXB, − WT., − WXTB, − W* 

) = ) = ) + )

13

g

g

(12) (13) (14)

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(b)

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Figure 2: Schematic diagram of equivalent electrical circuits (a) ECR of H2 only (b) ECR of

236

both H2 and CO

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The exchange current densities of H2 and CO at anode and O2 at the cathode are calculated from

238

the interface conductives mentioned in Table 4 by adopting the method provided by [22,32,57].

239

The Kirchhoff’s junction and loop rules are applied to solve the equivalent circuit model, and the

240

total local current density obtained at the anode current collector is the summation of ECR’s of

241

H2 and CO. Whereas, the contribution of H2 and CO oxidations towards the total current is

242

determined locally by iteration method in such a way that similar potential difference across the

243

parallel circuit part is obtained [34].

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3.4.

Radiative heat transfer modeling To execute the heat transport analysis of the system, it is imperative to identify locations

246

where heat is being produced and consumed. The majority of the heat energy is generated at

247

electrolyte interfaces with the electrodes through reversible and irreversible processes. Most of

248

the produced heat is recovered from the system through anode fuel channels and air by

249

convection but it did not cover all the energy balance. To design a real system, it is, therefore,

250

important that radiative heat transfer (RHT) process should be included in the modeling. The

251

RHT mechanism not only involves radiation transfer in electrodes, electrolyte and participating

252

gases but it also involves surface-to-surface radiation energy transfer in the channels [58]. In the

253

present work, DO (discrete ordinates) method is selected to approximate the RHT as it covers the

254

entire range of optical thicknesses and allows to solve problems for both surface-to-surface and

255

radiation in participating media. This method also allows non-gray properties and specular

256

surfaces. Scattering is modeled using a scattering coefficient and a scattering phase function is

257

defined isotropic. As in the present study, gases are also considered as participating media in

258

RHT and their properties are assumed composition dependent by adopting weighted sum of gray

259

gas model (WSGGM). The porous electrodes are treated as opaque [59] and electrolyte

260

considered as optically thin, non-diffusing gray medium (isotropic) [44]. For angular

261

discretizations in DO model, default settings are opted to avoid computational delay.

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3.5.

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CFD models and solution procedure

The governing equations for the continuity, momentum, energy and species conservations

264

are summarized in Table 7 along with their related source terms. In the continuity equation, Sρ is

265

the source term which characterizes the mass consumption and generation because of ECR’s at

266

the electrode-electrolyte interfaces and MSR in anode electrode. In the momentum equation, u is

267

the velocity component in x, y, z directions; density (ρ) of the gaseous mixture is computed by

268

ideal gas law and viscosity (µ) by Sutherland’s Law using the kinetic theory of gasses [60]. Sm is

269

the momentum source term which contains viscous loss term (described by Darcy’s Law) and

270

inertial loss term (defined by Power Law) [61]. Where α is the permeability (m2) and C is the

271

inertial resistance factor. In the energy equation, Cp is the specific heat of the gas mixture and keff

272

is effective thermal conductivity, whereas Sh is the source term (Wm-3) comprise of the

273

electrochemical heat generation source term and methane steam reforming heat sink source term.

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Table 7: Governing equations for mass, momentum, and heat transport calculations ,T.7;8 =  +   +  +  +  Œ. 7Ž8 =  Continuity ,XTB = 

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Œ. •‡ ŽC = Œ. Aoo Œ C +  Aoo = qo + 71 − q8

“ 1 Ž + • |Ž|Ž Z 2 ”  =  —d˜ +  ™š˜ In anode (Heat sink):  ™š˜ =  › +  › g = − U

› = −7206205.5 + 19.5175 C8 › = 45063 − 10.28 C

In electrolyte (Heat source): ) WB*BT‹ )  —d˜ = 7−C∆; 8. + A 2DA 1 1 ∆; = V  −  −  Y + V −  −  Y 2 2 WB*BT‹ = ž4Ÿ  6¡4F¢£E − ž4 ¤¡E£¥4 [35]

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Energy

Œ. ‘7Ž8Ž ’ = Œ. 7 + “. ŒŽ 8 + g

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Momentum

In anode: ‡,b = 3 +  , ‡,  = −  − 

Œ. 7Ž¦ 8 = Œ. w,g Œ. ¦  + ‡

275

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Species

‡, = −  , ‡, =  −  ‡, =  At anode-electrolyte interface: ) ) ‡,b = −  | , ‡,  =  |  2DA 2DA §de §de ‡, = − | , ‡, = | /Bj

/Bj

At cathode-electrolyte interface: ) ul
ECR heat source includes ECR’s entropy change ( S) due to both H2 and CO and irreversible

277

polarization losses [36,62–64]. Internal reforming reaction consists of two reactions, MSR (eq.1)

278

which is endothermic in nature whereas WGSR (eq.2) is a weak exothermic. In the specie

279

equation, Yi is the mass fraction and Di,m is the effective mass diffusivity of component i in a

280

gaseous mixture of fuel and oxidant streams (Table 6). Ssp is species source term, which

281

determines the rate of consumption and generation of each gas component in the

282

multicomponent gas mixture due to the electrochemical and chemical reactions.

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The mesh was constructed to attain a finer mesh at the reaction sites and in the regions of

284

possible high gradients. A finer mesh was made at the anode-electrolyte interfaces, and at the

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285

location where the sharp deviations in flow distribution were expected; whereas relatively

286

coarser mesh was made away from interfaces to accomplish required goal. The non-conformal

287

mesh strategy was adopted [61] and Ansys® ICEM CFD was utilized to construct hexahedral

mesh for all the stack components. The accuracy of the numerical calculations was carried out by

289

grid independence to ascertain the optimum number of nodes. Fig. 3 (a, b, c) show grid quality of

290

manifold, 80 cells, and air enclosure at the selected region.

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Figure 3: Mesh quality of stack components (a) Manifold (b) 80 FT-SOFC (c) Air Enclosure

293

First, the single cell was tested for several numbers of nodes to obtain an optimized mesh and

294

then optimized mesh was applied to the full-scale 80 FT-SOFC stack. The optimal mesh

295

resolution of a single cell on the active surface is presented in Fig. 3 (b). The final mesh size of

296

the stack is about 52 million elements.

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297

To solve the intricate transport, ECR’s and chemical processes simultaneously, some

298

simplifications are required to be made to get the numerical solution accurately and efficiently.

299

The following assumptions are made during the CFD calculations: 1)

Steady state analysis.

301

2)

Laminar and incompressible flow.

302

3)

CH4 only involved in MSR; all other possible reactions are neglected.

303

4)

Dry reforming is neglected because of high water contents in the pre-reformed gas

304

mixture.

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5)

MSR/WGSR is only taking place in the anode.

306

6)

The mass flow inlet boundary condition is applied at the inlet of the manifold and for

308

incoming preheated air stream. 7)

309 310 311

313 314

Side walls of HX with air inlet holes are assumed isothermal as it is expected that temperature at the walls will be close to the air inlet temperature.

9)

External emissivity (0.8) and external radiation temperature (1050 K) are fixed on other walls and their boundary type is opaque [65].

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The pressure outlet boundary condition is applied at anode and cathode outlets, and gauge (reference) pressure of 0 Pa is set.

8)

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The main operating parameters opted from the experiment are presented in Table 8 whereas

316

physical properties of the cell components are provided in Table 5. Different pre-reformed

317

methane fuels (based on CH4 conversion) are supplied at the manifold inlet to determine the

318

influence of internal reforming on the stack performance. Steam to carbon ratio (S/C) of 2.5 is

319

fixed in the pre-reformer, Whereas various input fuel compositions are summarized in Table 9.

320

During the simulation, the effect of oxidant utilization on stack performance and thermal

321

management are also tested. The necessary airflow rates based on different oxidant utilizations

322

against the reference fuel are provided in Table 10.

324

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Being the complex nature of the SOFC structure, commercial CFD software

Ansys® Fluent is selected as a solver because of it is broadly established accuracy [66]. The user-

325

defined function (UDF) in-house code written in C language is implemented in the solver to

326

compute ECR and MSR models and to generate an electrical field. The finite volume approach is

327

employed to discretize the governing equations. A brief description of the solution procedure is

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Mole fraction H2 CO 0.65 0.15 0.655 0.11 0.509 0.076 0.523 0.0723 0.263 0.0294

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Table 9: Pre-reformed methane composition CH4 Conversion (%) Fuel Type CH4 H2O 99 [24] F1 0.01 0.15 90.1 [STX] F2 0.023 0.13 79.2 [STX] F3 0.038 0.301 75.4* [STX] F4 0.051 0.269 30 [24] F5 0.171 0.493

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1033.15 101325 2473 3.463e-5 2.1850e-4 2.962e-3

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Table 8: Operating parameters for 80 cells stack * Operating temperature (K) Operating pressure (Pa) Operating average current density (Am-2) Fuel inlet (kg s-1) 3% humidified H2 Fuel inlet (kg s-1) pre-reformed methane Air inlet (kg s-1) *Calculated parameters from STX operated stack

330

CO2 0.04 0.082 0.076 0.085 0.0436

332 333 334

presented in the Fig. S2. At the beginning, the solution is initialized with UDF macro, and then

after each iteration USER DEFINED ADJUST macro provided by Ansys® Fluent is used to

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Table 10: Air flow rates at different oxidant utilization (for 80 cells stack) Oxidant Utilization Air Flow rate (%) (LPM) (Kg s-1) 20 122.6 2.631E-03 30 81.704 1.754E-03 40 61.28 1.315E-03 50 49.02 1.052E-03

compute the ECR and MSR models to determine the current densities distribution and the rate of

MSR/WGSR. The source terms generated from the solution of ECR/MSR models are

336

implemented in the solver (CFD models) to update the mass, flow field, species and temperature

337

distributions in the cells at the relevant zones. This updated information is subsequently utilized

338

to compute the electrochemical and chemical models again. The solution procedure is repeated

339

until the desired degree of accuracy is achieved. The pressure-based solver is selected to execute

340

CFD calculations with second-order upwind interpolation scheme is employed to solve the

341

model equations whereas the convergence criteria on the residual scale are set to 10-3 for

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342

continuity, momentum, and species whereas 10-6 for energy equation. However, for DO-model, a

343

first-order upwind scheme with 0.6 under-relaxation factor (URF) is used to avoid divergence.

345 346 347 348

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Figure S2: Solution procedure

349 350 351 352

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353

4. Results and discussion Before exploring the optimized operating conditions of SOFC stack, presented modeling

355

has been validated with the experiments performed at STX (Daegu, South Korea) facility. The

356

numerical calculations are carried out for different average current densities (I_ave) i.e. 0-2500

357

Am-2 and the stack voltage is iteratively adjusted during the simulation in such a way that

358

proposed I_ave be obtained [34]. The stack is simulated with both 3% humidified H2 and 75.4%

359

pre-reformed methane mixture at 1033.15 K, and the performance curves are compared with the

360

experimental data. During simulations, for all average current densities, utilization of fuel and

361

oxidant are kept invariable, i.e., ~60% and ~20% respectively and the same material properties

362

of SOFCs are employed those were used in experimental stack cells (Table 5). Meanwhile,

363

adjustable parameters of interface conductivities are adjusted to fit the I-V-P curves with

364

experimental data and their final values are displayed in Table 4. Fig. 4 shows a comparison of

365

simulated results with the experimental data for both the fuels.

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Figure 4: Model validation with H2 and pre-reformed methane fuels 21

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The numerical results exhibited good agreement with the experimental results except at the lower

369

current densities, where simulated stack voltages are slightly higher because of some

370

assumptions like no contact resistance, the current collector with infinite electrical conductance,

371

etc. However, the maximum difference between the simulated and experimental data is less than

372

5 % [67].

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In this section, a brief comparison of the stack performance, running with 3% humidified

374

H2 and pre-reformed methane (reference case, F4) is made. From Fig. 4, it is clearly evident that

375

the stack running with H2 fuel exhibited much higher performance, i.e., 1216 W as compared to

376

1123 W. One of the reasons for higher performance is that thermodynamically higher mole

377

fraction (partial pressure) of H2 steers to higher stack output power.

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Figure 5: Comparison of H2 and pre-reformed methane performance (a) temperature

380

distributions (b) current density distributions (c) polarization losses (d) nernst potentials

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Second reason is that higher EMF and current density are obtained through H2 fuel. All the pre-

382

reformed fuel cases stated in Table 9 have less than 66% mole fraction of H2 in their gaseous

383

mixture in comparison to 97% for H2 fuel. In the subsequent part, reduction in the stack

384

performance with reformed gas is more elaborated by temperature Fig. 5 (a) and current density

385

distributions by Fig. 5 (b) along the fuel stream. Fig. 5 (a) and Fig. 6 (b) show that temperature

386

first increases near the inlet (Y<0.04 m) due to ECR reactions then decreases steadily towards

387

the end due to the depletion of H2.

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389 390 391 392

(d)

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Figure 6: H2 fuel distributions (a) H2 mole fraction (b) temperature distributions (K) (c) H2 activation resistance (Ωm2) (d) O2 activation resistance (Ωm2) (e) total polarization resistance (Ωm2) (f) current density distributions (Am2) 23

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However, in the case of reference fuel, temperature first decreases due to MSR then increase

394

because of ECRs. The current density distribution for H2 fuel in Fig. 5 (b) and Fig. 6 (f) shows a

395

steep decline, whereas, for reference fuel, current density first rises due to the addition of ECR

396

species (H2 and CO) until Y=0.1m then it decreases due to the consumption of H2 and CO and

397

fast depletion of internal reforming reaction. In the Fig. 5 (c) and Fig. 6 (c, d, e), a comparison of

398

polarization losses due to activation, ohmic, and accumulative, have been presented to explore

399

the reason why H2 fuel exhibited higher stack performance. Only the ohmic polarization has

400

shown similar results, rests of losses for reference case fuel are much greater at all the regions on

401

the active surfaces. Similarly, nernst potential distribution of H2 fuel along the flow stream (Fig.

402

5 (d)) is significantly higher than the individual reference fuel because of the much higher H2

403

partial pressure in the fuel mixture. From the comparison of EMF’s and system polarization

404

losses, it can be deduced that H2 is a preferable fuel to get higher stack performance, however, its

405

ease of availability and storage are still challenging issues. In the subsequent sections, different

406

methodologies have been presented to obtain the optimal stack performance from the same stack.

407

4.1.

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Effect of pre-reforming on the stack performance

In this section, the numerical results of 5 different cases of fuel (based on pre-reformed

409

methane conversion) are evaluated to determine their effect on the performance of the stack. Fig.

410

7 (a, b) demonstrate the variations of localized temperature and current density distributions

411

along the flow stream for all the 5 cases (Table 9). In the case of fuel F1 and F2, the strong

412

endothermic MSR has limited effect on their temperature distributions, as most of the CH4 is

413

already consumed in the pre-reformer. Whereas in the case of fuel F3 and F4, MSR has a visible

414

effect of on the temperature distribution that can be seen in the Fig. 7 (a). However, in the case of

415

F5, a strong effect on temperature distribution is evident because CH4 is present at the inlet of the

416

manifold with highest mole fraction among all the fuels examined. The current density

417

distributions for the fuel (F1 to F4) exhibited similar trends over the whole active surfaces. Near

418

the inlet of Y-axis, F1 and F2 have shown higher current densities in comparison to F3 and F4

419

due to the higher molar concentration of H2, CO, and higher EMFs. However, at the middle of Y-

420

axis, fuel with higher CH4 content at the inlet exhibited higher current densities due to the

421

production of H2 and CO (MSR and WGSR). F5 is the only fuel which has shown largest

422

variations of temperature and current density distributions due to their lower content of H2 and

423

CO and relatively higher CH4 mole fraction at the inlet.

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(a)

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(b)

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(d)

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Figure 7: Effect of pre-reforming (along Y-axis) on (a) temperature distributions (b) current

427

density distributions (c) mole fraction distributions of CH4 (d) total polarization losses (V) (e)

428

nernst potential distributions (V) (f) stack performance curves for different fuel cases 25

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However, as CH4 is reformed internally, an appreciable amount of H2 and CO is available in the

430

middle of Y-axis causing temperature and current density to reach maximum or even goes

431

beyond other fuels. It is clearly evident from Fig. 7 (a, b) that local temperature and current

432

density distributions are strongly affected by the pre-reformed methane conversion rate. The

433

reason for the difference in distributions of different fuels can also be envisioned by probing Fig.

434

7 (c), which demonstrates CH4 mole fraction distributions along the main flow stream. The sharp

435

decline in the mole fraction means fast MSR reaction rate and it is also ascertained from Fig. 7

436

(c) that higher the pre-reforming conversion rate, more gradual is the internal reforming rate.

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The distribution of total polarization over the whole active surfaces and generation of

438

electromotive force (EMF) are also compared to analyze the stack performance. The

439

distributions of polarization losses and EMF are shown in Fig. 7 (d, e) further supports the

440

conclusion made in the Fig. 7 (a, b) that robust internal reforming reaction rate (in the case of F5)

441

causes highest total overpotential. However, relatively higher EMF of F5 is observed at

442

Y>0.04m, compared to F3 and F4 because of low temperature and gradual increase of H2 and

443

CO mole fractions. The comparison of the stack performance for all 5 fuel cases is also made to

444

determine which fuel can deliver the highest performance under same operating conditions. It is

445

cleared in Fig. 7 (f) that fuel F1 and F2 have attained similar performance, so as fuel F3 and F4.

446

However, F5 exhibited the least performance for present operating conditions. From the above

447

discussion, it is evident that uniform temperature and current density distributions in the stack

448

can be achieved by controlling the pre-reforming rate. Fuel F1 and F2 are the fuels which

449

exhibited the highest stack performance and most uniform temperature and current density

450

distributions. However, larger air flow rates or bigger HX’s are required to dissipate the excess

451

heat that is harmful to overall system efficiency. The results of F3 and F4 fuels are more trade-

452

off between system efficiency and stack long-term stable operation.

453

4.2

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Effect of CO as electrochemical fuel on the stack performance

In the previous SOFC modeling, it was common practice to neglect the electrochemical

455

oxidation of CO. So, it is crucial to determine whether its negligence has any effect on the stack

456

performance. In this section, the stack performance is analyzed by comparing the results with

457

and without electro-oxidation of CO. When ECR of CO is not considered, total current density

458

obtained is only related to the H2 fuel, whereas CO is assumed to utilize in WGSR. And when

459

both H2 and CO are considered as ECR species, total current density is a summation of both 26

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individual current densities of H2 and CO. Fig. 8 (a) provides a comparison of performance

461

curves for both the modeling. It is evident that there is a drop in the stack performance when

462

ECR of CO is not considered. In the Fig. 8 (b) this decline in stack performance is further

463

clarified by total stack polarization over the whole active surface. The model without the ECR of

464

CO has shown higher polarizations at all the regions along the fuel streamwise direction.

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Figure 8: Effect of with and without CO ECR on (a) stack performance curves (b) total

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polarization losses (c) temperature distributions (d) MSR and WGSR rates

469

It is also demonstrated in Fig. S3 (b) that relatively lower current density distributions are

470

obtained in comparison to the Fig. S3 (a). It is also noticed that whether ECR of CO is included

471

in the modeling or not, specie distribution of H2 (Fig. 9 (a, b)) and rate of MSR reaction (Fig. 8

472

(d)) is not changed significantly. However, numerical results of the model which neglect the CO

473

ECR has extensively affected the temperature distribution (Fig. 9 (g, h), rate of WGSR (Fig.

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474

8(d)), and CO molar concentration along the anode channels (Fig. 9 (c, d)). The increase in

475

temperature distribution is due to a couple of reasons; first reason is that higher polarizations

476

contribute to higher irreversible ECR heat, whereas, the second reason is that positive rate of

477

WGSR is found (without CO ECR) which is exothermic in nature and reduces the heat sink term

478

of internal reforming.

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Figure S3: Current density (Am-2) distributions on active surfaces (I_ave = 2473 Am-2)

(a)

(b)

(c)

(d)

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(f)

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Figure 9: Effect of CO ECR with and without on the contours distributions

484

This positive rate of WGSR reaction is quite distinct in the (Fig. 8 (d) and 9 (e, f)) because CO is

486

only participating in WGSR reaction. That is why WGSR rate and CO mole fraction along the

487

flow stream are higher as compared to the model which is considering CO ECR (WGSR is

488

mostly negative along the Y-axis for model considering CO ECR).

489

4.3.

Effect of inlet temperature on the stack performance

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The current density and temperature distributions for two different temperatures (1033.15

491

K and 1073.15 K) have been presented in the Fig. 10 (a, b) to establish the effect of inlet

492

temperature (fuel and air) on the stack performance. It is evident that with the increase of inlet

493

temperature, current densities generated by both the electrochemical species (H2 and CO)

494

increases which signify that higher inlet temperature is beneficial for acquiring higher output

495

power. It is also noticeable in Fig. 10 (a, b) that current densities and temperature for both the

496

fuels vary along the flow stream which is quite clear in (Fig. S4 (e) and S4 (f)).

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(b)

(c)

(d)

(e)

(f)

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498 499

Figure 10: Inlet temperature effect on (a) current density distributions (b) temperature variations

500

along the flow stream (c) MSR and WGSR rates (d) stack performance curves (e) ohmic

501

polarization (f) activation (H2 and CO) and accumulative overpotentials distributions

30

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(e) (f)

503 504

Figure S4: Inlet temperature (1073.15 K) effect on (a) H2 mole fraction (b) CO mole fraction (c)

505

MSR reaction rate (Kgm-3S-1) (d) WGSR reaction rate (Kgm-3S-1) (e) temperature distributions

506

(K) (f) current density distributions (Am-2)

507

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A slide decline in the current densities is observed near the inlet due to the lower temperature

509

caused by MSR. The current density associated with the H2 for both the temperatures is

510

increasing along the flow direction until Y= 0.14m then begins to decline again due to a decrease

511

in temperature and decrease in H2 mole fraction (Fig. S4 (a)). However, the current density

512

related with CO fuel exhibited linear behavior along the flow stream with slight decline towards

513

the end of the active surfaces. The difference in current densities is mainly due to the molar

514

concentration distribution in the anode electrodes. Mole fractions of both H2 and CO are

515

relatively higher at the inlet for 1073.15 K due to the higher MSR rate, as a steam reforming

516

efficiency is accelerated by higher temperature. In the case of WGSR, higher temperature has an

517

adverse effect due to Le Chatelier principle and the strong backward reaction is observed due to

518

the build-up of CO2 (CO ECR). It is important to note that CH4 and CO mole fractions in the

519

reference fuel stream are only 5 and 7 %, respectively. Their contribution to the supplement of

520

H2 in the flow stream is quite low which is quite evident from the Fig. 10 (c). No distinct

521

deviations of MSR and WGSR for both the temperatures are observed. As a result, species

522

distributions shown in Fig. S4 (a, b) and reactions rates in Fig. S4 (c, d) are similar to those of

523

observed for 1033.15 K case. However, noticeable improvement in the stack performance is

524

recorded due to the increase of inlet temperatures which is reflected in the Fig. 10 (d).

525

Polarization curves are plotted along the Y-axis (Fig. 10 (e, f)), to unveil why there is an

526

enhancement in the stack performance despite the minimum effect of internal reforming. The

527

ohmic polarization (Fig. 10 (e)) shows steep decline along the downstream for both the

528

temperatures due to the rise of temperature by ECR heat (Fig. S4 (e)). Its values are lower for

529

higher inlet temperature fuel at the whole active surfaces. A similar effect of temperature on the

530

other polarizations like activation and system total losses is observed in the Fig. 10 (f). It evident

531

that stack performance can be enhanced by decreasing the overpotential losses by increasing the

532

operating temperature without increasing methane concentration in the inlet fuel.

533

4.4.

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Effect of oxidant utilization on the stack performance

It was reviewed in the introduction section that internal reforming is a useful tool to

535

utilize the waste heat of ECR by smothering the need of excess air which ultimately increases the

536

system efficiency. However, it is numerically demonstrated that control of pre-reforming rate is a

537

crucial strategy to avoid large thermal gradients on the stack cells which poses challenges to

538

stable and long-term operation. In this section, different oxidant utilizations are examined to 32

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explore optimum air flow rate which delivers the best stack performance. The oxidant

540

utilizations are varied from 20-50 % while fuel utilization fixed at ~60%. The stack performance

541

curves have been presented in the Fig. 11 (a). It is cleared that with the decrease of oxidant

542

utilization, stack performance increases steadily, indicating excess air supply is favorable for

543

obtaining higher stack output power. Oxidant utilization also affects the temperature and current

544

density distributions which can be seen in Fig. 11 (b, c). Fig. 11 (b) shows that oxidant utilization

545

has an opposing effect on the temperature distribution along the flow stream; higher

546

temperatures are observed for higher utilization rates. 20% oxidant utilization has the lowest

547

temperature rise because excess air is available to carry the waste heat of the stack.

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Figure 11: Effect of different oxidant utilizations on (a) Stack performance curves (b)

551

temperature distributions (c) current density distributions (d) O2 activation and total

552

overpotentials

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In the case of current density (CD) distributions (Fig. 11 (c)), higher oxidant utilization has

554

shown higher current density distributions because temperature distributions are higher for

555

higher air utilizations. The reason for a decline in the stack performance with the increase of

556

oxidant utilization is further clarified with the help of polarization losses especially cathode

557

activation and total polarization losses. Fig 11 (d) provides a comparison of activation and total

558

polarization losses among the different oxidant utilization used during simulation. Air stream

559

with 50% oxidant utilization exhibited highest polarizations (both activation and total) among the

560

other examined; that is the reason why it delivered the least performance (Fig. 11 (a)). It is

561

cleared from above discussion that lower oxidant utilization is more favorable for achieving

562

higher stack performance. However, excess air supply will consume parasitic energy which

563

results in lower system efficiency.

564

4.5.

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Effect of thermal radiation modeling

The effect of radiation heat transfer inside the stack cells and on the outer walls of air

566

enclosure are presented in Fig 12 and Fig. 13. To elaborate the temperature distributions, YZ, ZX

567

and XY planes are drawn about the stack (80 cells and air enclosure only). Fig. 12 (a) illustrate

568

the temperature distribution along the X-axis (149 mm, YZ plane) with and without the inclusion

569

of radiative heat transfer. Noticeably, the heat transfer improvement due to RHT results in

570

overall reduction of the temperature distribution within the stack, as well as the less steep

571

temperature gradients along the cell is examined. The maximum difference in temperatures

572

between the two cases varies from 8-10 K throughout the YZ plane. However, the temperature

573

distribution near the side walls is relatively flat for the RHT case. Fig. 12 (b) demonstrate the

574

RHT modeling effect along the Y-axis (200mm, along the fuel stream) and it cleared that

575

temperature difference between two cases is lowest at the entrance of anode channels. However,

576

the gap becomes wider towards the end of the anode electrode because of the absorption of heat

577

energy by the fuel cell components due to radiation heat transfer. The temperature rise of ~18 K

578

from the entrance to peak region is observed for the case without RHT whereas this rise in

579

temperature is about 12 K for the case with thermal radiation effects which further endorses that

580

radiative heat transfer helps in decreasing the temperature gradients on the cell components. In

581

the case of XY plane (332mm, along the Z-axis), the different temperature distribution is

582

observed for both the cases. The reason for this behavior for the case without RHT is that fuel is

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583

first supplied to the manifold, positioned at the bottom, from there gases are distributed to the

584

anode channels.

(b)

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(a)

(c)

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Figure 12: Temperature distributions on (a) YZ plane (b) ZX plane (c) XY plane (d) RHT effect

(a)

on the internal steam reforming

(b)

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(d)

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Figure 13: Temperature distributions on (a) air enclosure without RHT (b) air enclosure with

590

RHT

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The first 40 cells near the manifold entrance receive higher fuel than the last 40 cells of the stack

592

as uniformity index of this manifold design is 0.826 [50]. Therefore it can be seen (Fig. 12 (c))

593

that temperature distribution is lower for last 40 cells (without RHT). However, the case that is

594

considering thermal radiation effects revealed similar temperature profile for the first and last 40

595

cells which ascertained that radiation heat transfer is an effective mode of heat transfer in

596

minimizing the thermal gradients among the stack cells. Radiation heat transfer has also imparted

597

the positive effect on the methane steam reforming which can be seen in the Fig. 12 (d). The

598

higher reforming rate is observed near the entrance of anode channels for the case with RHT,

599

however, radiation heat effect diminishes around Y=0.125m. In the case of WGSR, the reverse

600

reaction rate is increased further for RHT case due to the higher mole fraction mole of CO2 than

601

without RHT case. A localized high-temperature region on the air enclosure wall (facing the

602

active surfaces of cells) is spotted in Fig. 13 (a) whereas the decline in temperature on the side

603

and top walls from assemblies 1,2 to assemblies 3,4 can be clearly seen. However, the case with

604

RHT revealed uniform temperature profile (Fig. 13 (b)) on the side and top walls and there is no

605

localized high-temperature region on other walls.

606

5. Conclusions

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In this study, a comprehensive three-dimensional (3D) numerical model was developed to

608

explore the optimum operating conditions for anode-supported flat tubular (FT-SOFC) 80 cells

609

stack, running on H2 and pre-reformed methane fuels. The CFD model coupled the complex

610

transport processes (mass, momentum, and heat transfers) with electrochemical reactions (with

611

and without electrochemical oxidation of CO). Internal steam reforming and water gas shift

612

reactions were also integrated with the modeling. The effect of radiative heat transfer on the

613

temperature distribution of stack components was also presented. The CFD model was validated

614

with experiments conducted with both the fuels separately. The findings of the above analysis

615

are summarized as follows:

616

1)

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Stack running with H2 fuel exhibited the highest performance among all the fuel considered

617

for analysis due to higher nernst potential and lower polarizations, i.e., 1216 W and 1123 W

618

respectively.

619 620

2)

5 cases of fuel with different pre-reformed methane conversion were investigated to establish the effect of pre-reforming rate on the stack performance. It was found that fuel

36

ACCEPTED MANUSCRIPT

with highest pre-reforming conversion exhibited the highest stack performance. From the in-

622

depth analysis, it is revealed that lowers the pre-reforming rate, higher is the non-uniformity

623

of temperature and current density distributions along the flow stream. It was also concluded

624

that although higher pre-reformed fuel delivered higher power, relatively uniform

625

temperature, and current density distributions, however, it necessitates the use of a large

626

excess of air to remove the irreversible heat which may reduce overall system efficiency.

627

3)

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Modeling comparison considering with and without CO electro-oxidation revealed that model without CO oxidation underestimates the stack performance due to higher

629

polarizations. It was identified that stack showed higher temperature distributions without

630

CO electro-oxidation. The positive rate of WGSR was the main reason for this temperature

631

increment which is also a weakly exothermic reaction. 4)

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The stack performance was also tested by increasing the inlet temperature from 1033.15 K to 1073.15 K. It was found that operating the stack at 1073.15 K, demonstrated higher

634

output power. Higher current density distributions have been achieved with the higher

635

temperature. For inlet temperature analysis, reference fuel was considered for both the

636

temperatures. However, due to lower CH4 and CO mole fractions at the manifold inlet, the

637

diminutive effect of temperature on the internal reforming was observed.

638

5)

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The performance analysis on the stack was also implemented by varying oxidant utilizations to estimate appropriate air supply by maintaining a balance between effective heat recovery

640

and efficient system operation. It was revealed that higher oxidant utilization exhibited

641

lower stack performance due to the higher polarizations. It was also found that higher

642

oxidant utilization yields higher temperature distributions due to a lower excess air supply.

643

Similarly, higher oxidant utilization has shown higher current density distributions. 6)

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From the radiative heat transfer analysis, it was revealed that inclusion of this mode of heat

645

transfer in the modeling is critical to accurately predict the temperature field of the stack.

646

Neglecting the RHT will result in incorrect temperature distribution and hence different

647

reaction rates and component properties will be overestimated. From the temperature

648

profiles on XY, YZ and ZX planes it was learned that RHT works to lessen the peak

649

temperature in the stack components and it also helps to decrease the temperature gradients.

650

The maximum temperature rise was 12 K for RHT case compared to 18 K for the case

37

ACCEPTED MANUSCRIPT

651

without RHT and noticeable improvement of temperature distribution on XY plane was

652

observed for the RHT case.

653

7)

From the parametric analysis, it was established that present 1kW-class FT-SOFC stack design performed best when operated at 75-80% pre-reforming rate, air utilization kept

655

around 20-30%, fuel utilization around 60% and finally, the operating temperature

656

maintained at 760-780°C. The reason for limiting fuel utilization to 60% is that afterburner

657

is installed along with steam generator/reformer in the complete hotbox design. The excess

658

fuel and cathode air are burned to supply the necessary heat to sustain the endothermicity of

659

BOP components.

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Acknowledgements

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661

The author gratefully appreciates the financial support of the Ministry of Trade, Industry

662

and Energy, MOTIE (Grant No. R0002207), and Korea Institute for Advancement of

663

Technology (KIAT) and DaeGyeong Institute for Regional Program Evaluation (DGIRPE)

664

through the Leading Industry Development for Economic Region.

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Nomenclature:-

Mass diffusivity of specie A through B, m2 s-1

DKA

Knudsen diffusion coefficient of A, m2 s-1

DA,eff

Effective diffusion coefficient of species A in gas mixture, m2 s-1

E°

Standard state potential, V

F

Faraday constant, 96485.3 C mol-1

I

Current density, Am-2

L

Length of diffusion path, m

M

Molecular weight, g/gmole

P

Pressure, Pa

P°

Pressure at standard state, Pa

Ract

Activation resistance, Ω m2

Rconc

Diffusion/concentration resistance, Ω m2

Rohm

Ohmic resistance, Ω m2

Rsr

Rate of internal steam reforming reaction, mol m-3 s-1

Rsh

Rate of water gas shift reaction, mol m-3 s-1

Sρ

Source term in continuity equation, Kg m-3 s-1

Sm

Source term in momentum equation, Kg m-2 s-2

Sh

Source term in energy equation, W m-3

Ssp

Source term in species equation, Kg m-3 s-1

T

Temperature, K

t

Thickness of cell components, m

X Y

SC M AN U

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EP

AC C

Vcell

RI PT

DAB

Cell voltage, V Mole fraction

Mass fraction

Greek letters

η

¨©ª

Overpotential, V Electronic conductivities of anode, Ω-1 m-1

39

ACCEPTED MANUSCRIPT ¨«©

Electronic conductivities of anode, Ω-1 m-1

µ

Fluid viscosity, Kg m-1 s-1

δ

Interface conductivity, Ω-1 m-2

¨¬

Subscripts

Anode

bulk

Bulk flow/flow through the anode channel

conc

Concentration

cat

Cathode

ECR

Electrochemical reaction

ohm

Ohmic

TPB

Triple phase boundary

*

Partial pressure at TPB

°

Partial pressure in bulk flow

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an

EP

667

Activation

AC C

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act

SC

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Ionic conductivities of electrolyte, Ω-1 m-1

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Reference:-

669 670

[1]

Chatrattanawet N, Saebea D, Authayanun S, Arpornwichanop A, Patcharavorachot Y. Performance and environmental study of a biogas-fuelled solid oxide fuel cell with

672

different reforming approaches. Energy 2017:1–10. doi:10.1016/j.energy.2017.06.125. [2]

Gong W, Yan X, Liu X, Cai Z. Parameter extraction of different fuel cell models with

674

transferred

675

doi:10.1016/j.energy.2015.03.117.

676

[3]

adaptive

differential

evolution.

Energy

2015;86:139–51.

Luo Y, Shi Y, Li W, Cai N. Comprehensive modeling of tubular solid oxide electrolysis

SC

673

RI PT

671

cell for co-electrolysis of steam and carbon dioxide. Energy 2014;70:420–34.

678

doi:10.1016/j.energy.2014.04.019.

679

[4]

M AN U

677

Mushtaq U, Mehran MT, Kim SK, Lim TH, Naqvi SAA, Lee JW, et al. Evaluation of

680

steady-state characteristics for solid oxide carbon fuel cell short-stacks. Appl Energy

681

2017;187:886–98. doi:10.1016/j.apenergy.2016.11.015. [5]

683 684

Barelli L, Bidini G, Cinti G, Gallorini F, Pöniz M. SOFC stack coupled with dry reforming. Appl Energy 2017;192:498–507. doi:10.1016/j.apenergy.2016.08.167.

[6]

Yan D, Liang L, Yang J, Zhang T, Pu J, Chi B, et al. Performance degradation and

TE D

682

685

analysis of 10-cell anode-supported SOFC stack with external manifold structure. Energy

686

2017;125:663–70. doi:10.1016/j.energy.2016.12.107.

687

[7]

Andersson M, Yuan J, Sundén B. SOFC Cell Design Optimization Using the Finite Element

689

doi:10.1002/fuce.201300160. [8]

Based

CFD

Approach.

694 695

2016;113:1051–61. doi:10.1016/j.energy.2016.07.087.

691

different

692 693

696

Fuel

Cells

2014;14:177–88.

Khazaee I, Rava A. Numerical simulation of the performance of solid oxide fuel cell with

AC C

690

Method

EP

688

flow

channel

geometries.

Energy

2017;119:235–44.

doi:10.1016/j.energy.2016.12.074.

[9]

Mehran MT, Lim T-H, Lee S-B, Lee J-W, Park S-J, Song R-H. Long-term performance

degradation study of solid oxide carbon fuel cells integrated with a steam gasifier. Energy

[10]

Xenos DP, Hofmann P, Panopoulos KD, Kakaras E. Detailed transient thermal simulation

697

of a planar SOFC (solid oxide fuel cell) using gPROMSTM. Energy 2015;81:84–102.

698

doi:10.1016/j.energy.2014.11.049.

41

ACCEPTED MANUSCRIPT

699

[11]

Chitsaz A, Hosseinpour J, Assadi M. Effect of recycling on the thermodynamic and

700

thermoeconomic performances of SOFC based on trigeneration systems; A comparative

701

study. Energy 2017;124:613–24. doi:10.1016/j.energy.2017.02.019. [12]

703 704

Peters R, Riensche E, Cremer P. Pre-reforming of natural gas in solid oxide fuel-cell systems. J Power Sources 2000;86:432–41. doi:10.1016/S0378-7753(99)00440-1.

[13]

RI PT

702

Priyakorn F, Laosiripojana N, Assabumrungrat S. Modeling of Solid Oxide Fuel Cell with

705

Internal Reforming Operation Fueled by Natural Gas. J Sustain Energy Environ

706

2011;2:187–94. [14]

Liso V, Olesen AC, Nielsen MP, Kær SK. Performance comparison between partial

SC

707 708

oxidation and methane steam reforming processes for solid oxide fuel cell (SOFC) micro

709

combined

710

doi:10.1016/j.energy.2011.04.022. [15]

and

power

(CHP)

system.

Energy

2011;36:4216–26.

M AN U

711

heat

Mogensen D, Grunwaldt J-D, Hendriksen P V., Nielsen JU, Dam-Johansen K. Methane

712

Steam Reforming over an Ni-YSZ Solid Oxide Fuel Cell Anode in Stack Configuration. J

713

Chem 2014;2014:1–8. doi:10.1155/2014/710391. [16]

715 716

management in solid oxide fuel cell systems. Eng Conf Int 2005;CHE2005-01. [17]

717 718

Ishizuka M, Rudy TM, Wadekar V V, Conferences E, Yoshida H, Iwai H. Thermal

TE D

714

Meusinger J, Riensche E, Stimming U. Reforming of natural gas in solid oxide fuel cell systems. J Power Sources 1998;71:315–20. doi:10.1016/S0378-7753(97)02763-8.

[18]

Klein J-M, Bultel Y, Georges S, Pons M. Modeling of a SOFC fuelled by methane: From direct internal reforming to gradual internal reforming. Chem Eng Sci 2007;62:1636–49.

720

doi:10.1016/j.ces.2006.11.034. [19]

Timmermann H, Sawady W, Reimert R, Ivers-Tiffée E. Kinetics of (reversible) internal

725

AC C

721

EP

719

726

their

727

doi:10.1016/j.jpowsour.2010.06.091.

722

reforming of methane in solid oxide fuel cells under stationary and APU conditions. J

723 724

728 729

Power Sources 2010;195:214–22. doi:10.1016/j.jpowsour.2009.07.019.

[20]

Mogensen D, Grunwaldt J-D, Hendriksen PV, Dam-Johansen K, Nielsen JU. Internal

steam reforming in solid oxide fuel cells: Status and opportunities of kinetic studies and

[21]

impact

on

modelling.

J

Power

Sources

2011;196:25–38.

Baldinelli A, Barelli L, Bidini G. Performance characterization and modelling of syngasfed SOFCs (solid oxide fuel cells) varying fuel composition. Energy 2015;90:2070–84.

42

ACCEPTED MANUSCRIPT

730 731

doi:10.1016/j.energy.2015.07.126. [22]

Hajimolana SA, Hussain MA, Soroush M, Wan Daud WMA, Chakrabarti MH. Modeling

732

of a Tubular-SOFC: The Effect of the Thermal Radiation of Fuel Components and CO

733

Participating

734

doi:10.1002/fuce.201200056. [23]

the

Electrochemical

direct

737

doi:10.1016/j.jpowsour.2007.07.008.

740

internal

reforming

conditions.

J

Power

Sources

2007;172:296–307.

M.M. Hussain, X. Li ID. Mathematical analysis of planar solid oxide fuel cells. J Power Sources 2006;161:1012–22. doi:10.1016/j.ijhydene.2008.02.043.

[25]

741 742

2012;12:761–72.

Ni M. 2D thermal-fluid modeling and parametric analysis of a planar solid oxide fuel cell.

M AN U

739

Cells

SC

[24]

Fuel

Janardhanan VM, Heuveline V, Deutschmann O. Performance analysis of a SOFC under

736

738

Process.

RI PT

735

in

Energy Convers Manag 2010;51:714–21. doi:10.1016/j.enconman.2009.10.028. [26]

Ho TX, Kosinski P, Hoffmann AC, Vik A. Numerical analysis of a planar anode-

743

supported SOFC with composite electrodes. Int J Hydrogen Energy 2009;34:3488–99.

744

doi:10.1016/j.ijhydene.2009.02.016.

745

[27]

Aguiar P, Adjiman CS, Brandon NP. Anode-supported intermediate temperature direct internal reforming solid oxide fuel cell. I: Model-based steady-state performance. J Power

747

Sources 2004;138:120–36. doi:10.1016/j.jpowsour.2004.06.040.

748

[28]

TE D

746

Amedi HR, Bazooyar B, Pishvaie MR. Control of anode supported SOFCs (solid oxide fuel cells): Part I. mathematical modeling and state estimation within one cell. Energy

750

2015;90:605–21. doi:10.1016/j.energy.2015.07.095. [29]

Li PW, Chyu MK. Simulation of the chemical/electrochemical reactions and heat/mass

752

transfer for a tubular SOFC in a stack. J Power Sources 2003;124:487–98.

753

AC C

751

EP

749

754

doi:10.1016/j.jpowsour.2003.06.001.

[30]

755

in the porous support structure of an integrated-planar solid oxide fuel cell. Int J Heat

756 757

Haberman BA, Young JB. Three-dimensional simulation of chemically reacting gas flows

Mass Transf 2004;47:3617–29. doi:10.1016/j.ijheatmasstransfer.2004.04.010.

[31]

Hofmann P, Panopoulos KD, Fryda LE, Kakaras E. Comparison between two methane

758

reforming models applied to a quasi-two-dimensional planar solid oxide fuel cell model.

759

Energy 2009;34:2151–7. doi:10.1016/j.energy.2008.09.015.

760

[32]

Petruzzi L, Cocchi S, Fineschi F. A global thermo-electrochemical model for SOFC

43

ACCEPTED MANUSCRIPT

761

systems design and engineering. J Power Sources 2003;118:96–107. doi:10.1016/S0378-

762

7753(03)00067-3.

763

[33]

Suwanwarangkul R, Croiset E, Entchev E, Charojrochkul S, Pritzker MD, Fowler MW, et al. Experimental and modeling study of solid oxide fuel cell operating with syngas fuel. J

765

Power Sources 2006;161:308–22. doi:10.1016/j.jpowsour.2006.03.080.

766

[34]

RI PT

764

Iwai H, Yamamoto Y, Saito M, Yoshida H. Numerical simulation of intermediate-

767

temperature direct-internal-reforming planar solid oxide fuel cell. Energy 2011;36:2225–

768

34. doi:10.1016/j.energy.2010.03.058.

770 771

Ni M. Modeling of SOFC running on partially pre-reformed gas mixture. Int J Hydrogen

SC

[35]

Energy 2012;37:1731–45. doi:10.1016/j.ijhydene.2011.10.042. [36]

Andersson M, Yuan J, Sundén B. SOFC modeling considering hydrogen and carbon

772

monoxide

773

doi:10.1016/j.jpowsour.2012.12.122.

774

[37]

as

electrochemical

M AN U

769

reactants.

J

Power

Sources

2013;232:42–54.

Lin B, Shi Y, Ni M, Cai N. Numerical investigation on impacts on fuel velocity

775

distribution nonuniformity among solid oxide fuel cell unit channels. Int J Hydrogen

776

Energy 2015;40:3035–47. doi:10.1016/j.ijhydene.2014.12.088. [38]

Lin B, Shi Y, Cai N. Numerical simulation of cell-to-cell performance variation within a

TE D

777 778

syngas-fuelled planar solid oxide fuel cell stack. Appl Therm Eng 2017;114:653–62.

779

doi:http://dx.doi.org/10.1016/j.applthermaleng.2016.12.014.

780

[39]

Izzo JR, Peracchio AA, Chiu WKS. Modeling of gas transport through a tubular solid oxide fuel cell and the porous anode layer. J Power Sources 2008;176:200–6.

782

doi:10.1016/j.jpowsour.2007.10.075. [40]

784

switching

785 786

mode

conditions.

J

Power

Sources

2010;195:6652–8.

doi:10.1016/j.jpowsour.2010.04.018.

[41]

787 788

Jin X, Xue X. Mathematical modeling analysis of regenerative solid oxide fuel cells in

AC C

783

EP

781

Zhu H, Kee RJ. A general mathematical model for analyzing the performance of fuel-cell

membrane-electrode assemblies 2003;117:61–74. doi:10.1016/S0378-7753(03)00358-6.

[42]

Shi Y, Cai N, Li C, Bao C, Croiset E, Qian J, et al. Modeling of an anode-supported Ni-

789

YSZ|Ni-ScSZ|ScSZ|LSM-ScSZ multiple layers SOFC cell. Part I. Experiments, model

790

development

791

doi:10.1016/j.jpowsour.2007.04.037.

and

validation.

J

Power

44

Sources

2007;172:235–45.

ACCEPTED MANUSCRIPT

792

[43]

Lee S, Park M, Kim H, Yoon KJ, Son JW, Lee JH, et al. Thermal conditions and heat

793

transfer characteristics of high-temperature solid oxide fuel cells investigated by three-

794

dimensional

795

doi:10.1016/j.energy.2016.11.084.

798

Murthy S, Fedorov AG. Radiation heat transfer analysis of the monolith type solid oxide fuel cell. J Power Sources 2003;124:453–8. doi:10.1016/S0378-7753(03)00732-8.

[45]

VanderSteen JDJ, Pharoah JG. Modeling Radiation Heat Transfer With Participating

799

Media

800

doi:10.1115/1.2134738.

801

[46]

802 803

2017;120:293–305.

in

Solid

Oxide

Fuel

Cells.

J

Fuel

Cell

Sci

Technol

2006;3:62.

SC

797

Energy

RI PT

[44]

simulations.

Mejri I, Mahmoudi A, Abbassi MA, Omri A. Radiation Heat Transfer Effect in Solid Oxide Fuel Cell : Application of the Lattice Boltzmann Method 2014;8:642–6.

[47]

M AN U

796

numerical

Wang Y, Zeng H, Shi Y, Cao T, Cai N, Ye X, et al. Power and heat co-generation by

804

micro-tubular flame fuel cell on a porous media burner. Energy 2016;109:117–23.

805

doi:10.1016/j.energy.2016.04.095.

806

[48]

M.F.Modest. Radiative Heat Transfer. 2nd ed. New York, USA: Academic press; 2003.

807

[49]

N O R M A N F. Bessette II and William J. Wepfer. PREDICTION OF ON-DESIGN AND OFF-DESIGN PERFORMANCE FOR A SOLID OXIDE FUEL CELL POWER

809

MODULE. Energy Convers Manag 1996;37:281–93.

810

[50]

TE D

808

Rashid K, Keun S, Ali R, Hwan S. Optimization of manifold design for 1 kW-class fl attubular solid oxide fuel cell stack operating on reformed natural gas. J Power Sources

812

2016;327:638–52. doi:10.1016/j.jpowsour.2016.07.077. [51]

814 815

anodes. J Power Sources 2000;87:57–63. [52]

816

Nagata S, Momma A, Kato T, Kasuga Y. Numerical analysis of output characteristics of

tubular

817 818

Lehnert W, Meusinger J, Thom F. Modelling of gas transport phenomenan in SOFC

AC C

813

EP

811

SOFC

with

internal

reformer.

J

Power

Sources

2001;101:60–71.

doi:10.1016/S0378-7753(01)00547-X.

[53]

Arpino F, Carotenuto A, Massarotti N, Nithiarasu P. A robust model and numerical

819

approach for solving solid oxide fuel cell (SOFC) problems. Int J Numer Methods Heat

820

Fluid Flow 2008;18:811–34. doi:10.1108/09615530810898971.

821 822

[54]

Welty JR, Wicks CE, Wilson RE, Rorrer GL. Fundamentals of Momentum, Heat, and Mass Transfer. 5th editio. John Wiley Sons, Inc.; 2007.

45

ACCEPTED MANUSCRIPT

823

[55]

Suwanwarangkul R, Croiset E, Fowler MW, Douglas PL, Entchev E, Douglas M a.

824

Performance comparison of Fick’s, dusty-gas and Stefan-Maxwell models to predict the

825

concentration overpotential of a SOFC anode. J Power Sources 2003;122:9–18.

826

doi:10.1016/S0378-7753(02)00724-3. [56]

Costamagna P, Selimovic A, Del Borghi M, Agnew G. Electrochemical model of the

RI PT

827 828

integrated planar solid oxide fuel cell (IP-SOFC). Chem Eng J 2004;102:61–9.

829

doi:10.1016/j.cej.2004.02.005. [57]

832

fuel cell stack 1994;49:333–48. [58]

833 834

SC

831

Achenbach E. Three-dimensional and time-dependent simulation of a planar solid oxide

Damm DL, Fedorov AG. Radiation heat transfer in SOFC materials and components. J Power Sources 2005;143:158–65. doi:10.1016/j.jpowsour.2004.11.063.

[59]

M AN U

830

David L. Damm AGF. Spectral Radiative Heat Transfer Analysis of the Planar SOFC.

835

ASME 2004 Int. Mech. Eng. Congr. Expo., Anaheim, California, USA: ASME; 2004, p.

836

399–405. doi:doi:10.1115/IMECE2004-60142. [60]

Hayre RPO, Prinz FB. Fuel Cell Fundamentals. John Wiley Sons 2006.

838

[61]

Guide AFT. Ansys Fluent Tutorial Guide. Ansys INC n.d.;15.0.

839

[62]

Fischer K, Seume JR. Location and Magnitude of Heat Sources in Solid Oxide Fuel Cells.

840 841

TE D

837

J Fuel Cell Sci Technol 2009;6:11002. doi:10.1115/1.2971042. [63]

Navasa M, Andersson M, Yuan J, Sund?n B. Transport phenomena in solid oxide fuel cell electrodes focusing on heat transfer related to chemical reactions. J Phys Conf Ser

843

2012;395. doi:10.1088/1742-6596/395/1/012086. [64]

Andersson M, Yuan J, Sundn B. SOFC modeling considering electrochemical reactions at

845

the active three phase boundaries. Int J Heat Mass Transf 2012;55:773–88.

846

AC C

844

EP

842

847

doi:10.1016/j.ijheatmasstransfer.2011.10.032.

[65]

848

fuel cell stack considering radiation. Energy Convers Manag 2007;48:1491–8.

849 850

doi:10.1016/j.enconman.2006.11.019.

[66]

851 852 853

Tanaka T, Inui Y, Urata A, Kanno T. Three dimensional analysis of planar solid oxide

Autissier N, Larrain D, Van Herle J, Favrat D. CFD simulation tool for solid oxide fuel cells. J Power Sources 2004;131:313–9. doi:10.1016/j.jpowsour.2003.11.089.

[67]

Tushar C, Sanjay. Thermodynamic assessment of SOFC-ICGT hybrid cycle: Energy analysis

and

entropy

generation

minimization.

46

Energy

2017;134:1013–28.

ACCEPTED MANUSCRIPT

854

doi:10.1016/j.ijhydene.2017.04.277.

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