Performance and Transport Characteristics of Planar SOFCs with Connected-Rib Interconnectors

1. Introduction

Solid oxide fuel cells (SOFCs) are regarded as a promising high-temperature electrochemical energy conversion technology for distributed power generation, combined heat and power (CHP), and hybrid energy systems [1,2,3]. The attractiveness of SOFCs for these applications arises from high electrical efficiency, broad fuel flexibility, and favorable integration with thermal processes [4,5,6,7]. A typical planar SOFC mainly consists of an anode, a cathode, an electrolyte, and an interconnector. Fuel is supplied to the anode, while the oxidant stream is delivered to the cathode, and the electrolyte separates the two electrodes and permits oxygen-ion transport. In practical applications, multiple single cells are usually connected in series to form a stack in order to achieve higher power output. Cell performance is governed not only by electrode and electrolyte materials, but also by transport and current-collecting components [8]. Among these components, the interconnector plays a particularly important role, since it provides gas separation and current collection while also affecting reactant distribution, pressure balance, and flow-field uniformity [9,10,11]. Accordingly, optimization of interconnector structures and flow-field configurations has become an important research direction for improving the performance of planar SOFCs.

Early studies on interconnector optimization mainly focused on conventional geometric parameters. Lin et al. [12] clarified the influence of interconnect rib size on concentration polarization in planar SOFCs, thereby establishing one of the earliest quantitative links between rib geometry and transport losses. Liu et al. [13] further examined the effect of interconnect rib contact resistance and optimized rib dimensions from the viewpoint of electrical loss and stack performance. Kong et al. [14] subsequently analyzed the influence of interconnect ribs on planar SOFC performance and proposed formulae for optimal rib sizes, while Kong et al. [15] extended this line of work to cathode-supported cells and demonstrated that rib geometry optimization can effectively reduce polarization losses. In a related study, Moreno-Blanco et al. [16] showed that channel width, rib width, and, in particular, the channel–electrode interfacial area strongly affect reactant transport and concentration overpotential. These studies collectively established that, even under conventional straight-channel configurations, the geometric characteristics of interconnectors can exert a substantial influence on transport behavior and cell performance.

With the development of three-dimensional numerical modeling, research interest gradually expanded from simple rib-size optimization to more diverse flow-field geometries. Khazaee and Rava [17] numerically investigated SOFCs with different flow-channel geometries and demonstrated that non-rectangular flow channels can significantly alter local transport behavior. Canavar and Timurkutluk [18] demonstrated that nickel-based woven meshes can serve simultaneously as anode current collectors and anode flow fields in commercial-size SOFC short stacks with an active area of 81 cm². The highest performance was achieved with three meshes of 0.6 mm wire diameter and 2 mm opening width. Further, Canavar and Kaplan [19] evaluated three nickel-based meshes in eight short-stack configurations and showed, through performance and impedance measurements, that Ni-mesh based flow-field and interconnector design has a strong influence on gas distribution and cell output. Bhattacharya et al. [20] and Saied et al. [21] examined various bipolar-plate and serpentine flow-field designs, demonstrating that serpentine-type configurations can increase fuel residence time and enhance mass transfer, although the associated pressure drop should also be considered. These studies indicated that flow-field design is not merely a geometric issue, but a transport-regulation strategy involving the balance between residence time, reactant accessibility, and hydraulic resistance.

Subsequent studies moved beyond conventional straight-channel or serpentine layouts and proposed more distinctive interconnector concepts. Yan et al. [22] developed a spiral-like interconnector and showed that enhanced lateral transport can significantly improve mass transfer in planar SOFCs. Fu et al. [23] proposed a beam-and-slot interconnector for an anode-supported SOFC stack and demonstrated that the modified structure enhanced gas disturbance and alleviated concentration polarization. Kong et al. [24] introduced an X-type interconnector and found that the design was beneficial to under-rib gas transport and current collection, thereby improving SOFC performance. Dong et al. [25] analyzed a planar anode-supported SOFC stack and emphasized the importance of structural design for local flow distribution and electrochemical behavior. At a larger scale, Kim et al. [26] proposed a novel interconnect design for thermal management of a commercial-scale planar SOFC stack, highlighting that interconnector geometry also affects temperature distribution and stack stability. More recently, Gong et al. [27,28] designed novel flow fields aimed at reactant redistribution and temperature homogenization, demonstrating that the function of interconnector and channel design has gradually expanded from performance enhancement alone to broader control of coupled transport and thermal fields. Guo et al. [29] developed new interconnector designs through three-dimensional modeling and showed that improved oxygen distribution beneath the ribs can lead to enhanced electrical performance. These studies collectively indicate that structural optimization of interconnectors and flow fields plays a critical role in regulating transport behavior and electrochemical performance in planar SOFCs.

Despite these advances, several issues remain insufficiently clarified. Most existing studies have focused on performance comparisons among specific interconnector geometries, whereas the more general effect of rib continuity on under-rib transport, local species redistribution, and polarization reduction has not been systematically established. In particular, the transport characteristics associated with conventional continuous straight ribs and connected-rib structures remain inadequately understood under comparable geometric and operating conditions. Moreover, structural modifications that enhance transverse transport and reactant redistribution are often accompanied by an increase in flow resistance, yet the relationship between electrochemical improvement and hydraulic penalty has not always been evaluated in a balanced manner. With increasing emphasis on transport uniformity and engineering applicability in planar SOFC design, interconnector optimization should be assessed not only in terms of output performance, but also in terms of distribution quality and flow-field effectiveness. Therefore, a systematic investigation of the effects of rib configuration on species transport, polarization behavior and pressure-drop characteristics remains necessary.

Accordingly, this study investigates four interconnector configurations for an anode-supported planar SOFC, including a conventional straight-rib interconnector (SI) and three connected-rib interconnectors, namely a circular-rib interconnector (CI), a rectangular-rib interconnector (RI), and a triangular-rib interconnector (TI). A three-dimensional multi-physics model coupling electric field, flow field, species transport and temperature field is established. The model is validated against experimental polarization data for the conventional cell. On this basis, the effects of rib configuration on polarization behavior, overpotential components, species distribution, velocity uniformity, fuel utilization, and pressure-drop characteristics are systematically analyzed. In addition, the influences of electrode porosity and operating temperature are examined in order to evaluate the robustness of the structural effects. The aim of this study is to clarify the transport mechanism associated with different rib interconnectors and to provide theoretical guidance for the structural optimization of planar SOFC interconnectors.

2. Experimental

The configuration of the experimental system is shown in Figure 1(a). The SOFC test system consisted of a gas supply and control module, an SOFC module and a data acquisition module. Gas flow rates were controlled by DFC10-500SCCM-B01 and DFC50-1000SCCM-B01 mass flow controllers (Flows Instrument, China). Deionized water was delivered into a preheating furnace by an infusion pump (MP0102D, Sanotac, China) for vapor generation. The polarization curves of the SOFC were measured using an IT8812 electronic load (ITECH, China).

An anode-supported planar SOFC (Huatsing Power, China) with an active area of 5×5 cm² and equipped with the conventional straight-rib interconnector was tested for model validation. The geometries of the four interconnector configurations considered in this study are shown in Figure 1(b). The conventional straight-rib interconnector was experimentally tested, whereas the other three connected-rib interconnectors were investigated numerically under the same geometric and operating conditions. Mica sheets and ceramic adhesive were used to seal the contact region between the SOFC and the interconnectors. Silver mesh current collectors and silver wires were pressed against the electrode surfaces on both sides.

The furnace temperature was raised from 25 °C to 600 °C at a heating rate of 5 °C/min and then increased to 750 °C at 2 °C/min. Before testing, nitrogen (250 SCCM) was introduced into both the anode and cathode sides for 15 min to remove air from the chambers. Hydrogen (200 SCCM) was then fed into the anode chamber as the reducing gas, and the cell was maintained at 750 °C for 4 h to reduce NiO to Ni. After the reduction process was completed, a gas mixture of nitrogen (395 SCCM) and oxygen (105 SCCM) was introduced into the cathode side.

3. Model Description

3.1. Geometric Models

The cell considered in this study was an anode-supported planar SOFC. The porous anode consisted of NiO and yttria-stabilized zirconia (YSZ) with a weight ratio of 4:6 and included a 500 μm anode support layer (ASL) and a 10 μm anode functional layer (AFL). The dense electrolyte layer (EL) was composed of YSZ with a thickness of 15 μm and served as the oxygen-ion conducting phase. A 3 μm gadolinium-doped ceria (GDC) barrier layer (BL) was introduced between the electrolyte and cathode to suppress Sr diffusion. The porous cathode was composed of La_0.6Sr_0.4Co_0.2Fe_0.8O₃ (LSCF) and included a 10 μm cathode functional layer (CFL). Figure 2 shows the cross-sectional SEM image of the tested anode-supported planar SOFC.

Full-size cell geometries were adopted in the simulations in order to capture the influence of boundary effects on gas transport. Four interconnector configurations were considered, including a conventional straight-rib interconnector and three connected-rib interconnectors with circular, rectangular, and triangular rib characteristics. All interconnectors were assumed to be made of the same material, and the interconnector-electrode contact area was kept identical for all configurations so that the effect of rib geometry could be evaluated under comparable conditions. The detailed geometrical parameters of the interconnectors are presented in Figure 1(c-f) and Table 1.

3.2. Governing Equations

A three-dimensional multi-physics model was established to describe the coupled electrochemical and transport phenomena in the planar SOFC. The model simultaneously considers electrochemical reactions, mass and momentum transport, species transport, charge transport, and heat transfer. Electrochemical reactions are assumed to occur at the triple-phase boundaries (TPBs) in the functional electrode layers. Meanwhile, local thermodynamic equilibrium is assumed for heat transfer in the porous electrodes. The governing equations used in the present model are described as follows.

3.2.1. Electrochemical Reactions

The actual operating voltage of the SOFC is expressed as the reversible Nernst potential minus the polarization losses, including activation, ohmic and concentration overpotentials [16].

$$V_{cell}=E_{Nernst}-{\eta }_{act}-{\eta }_{ohm}-{\eta }_{conc}$$

(1)

Where $V_{cell}$ is the actual cell operating voltage [V]; $E_{Nernst}$ is the reversible potential derived from the Nernst equation [V]; ${\eta }_{act}$is the activation overpotential of electrodes [V]; ${\eta }_{ohm}$ is the ohmic overpotential [V]; ${\eta }_{conc}$ is the concentration overpotential [V].

Electrode reaction kinetics are described by the extended Butler–Volmer equations, in which the dependence of the exchange current density on local species concentrations at the TPBs is taken into account.

$$i^{an}=i_{0,ref}^{an}\left[\mathit{exp}\left({\displaystyle \frac{{\alpha }^{an}nF{\eta }_{act}}{RT}}\right)-\mathit{exp}\left({\displaystyle \frac{\left(1-{\alpha }^{an}\right)nF{\eta }_{act}}{RT}}\right)\right]$$

(2)

$$i^{ca}=i_{0,ref}^{ca}\left[\mathit{exp}\left({\displaystyle \frac{{\alpha }^{ca}nF{\eta }_{act}}{RT}}\right)-\mathit{exp}\left({\displaystyle \frac{\left(1-{\alpha }^{ca}\right)nF{\eta }_{act}}{RT}}\right)\right]$$

(3)

Where ${\alpha }^{an}$=0.5 and ${\alpha }^{ca}$=0.5 are the charge transfer coefficient; $n$ is the number of electrons; $F$ is the Faraday’s constant [C/mol]; R is the universal gas constant [J/mol/K]; T is the temperature [K]; $i_{0,ref}^{an}$ and $i_{0,ref}^{ca}$ represent the exchange current density of the anode and cathode [A/m²].

The activation overpotential, ohmic overpotential, and concentration overpotential are formulated to characterize the major electrochemical losses in the cell.

$${\eta }_{act}={\eta }_{act}^{an}+{\eta }_{act}^{ca}$$

(4)

$${\eta }_{act}^{an}={\displaystyle \frac{RT}{{\alpha }^{an}nF}}{\mathit{sinh}}^{-1}\left({\displaystyle \frac{i^{an}}{i_{0,ref}^{an}}}\right)$$

(5)

$${\eta }_{act}^{ca}={\displaystyle \frac{RT}{{\alpha }^{ca}nF}}{\mathit{sinh}}^{-1}\left({\displaystyle \frac{i^{ca}}{i_{0,ref}^{ca}}}\right)$$

(6)

$${\eta }_{ohm}={\eta }_{ohm}^{IC,an}+{\eta }_{ohm}^{ASL}+{\eta }_{ohm}^{AFL}+{\eta }_{ohm}^{EL}+{\eta }_{ohm}^{BL}+{\eta }_{ohm}^{CFL}+{\eta }_{ohm}^{IC,ca}$$

(7)

$${\eta }_{conc}={\eta }_{conc}^{an}+{\eta }_{conc}^{ca}$$

(8)

$${\eta }_{conc}^{an}=-{\displaystyle \frac{RT}{nF}}ln\left({\displaystyle \frac{p_{H_2}^{TPB}}{p_{H_2}^0}}{\displaystyle \frac{p_{H_{2}O}^0}{p_{H_{2}O}^{TPB}}}\right)$$

(9)

$${\eta }_{conc}^{ca}=-{\displaystyle \frac{RT}{nF}}exp\left({\displaystyle \frac{p_{O_2}^{TPB}}{p_{O_2}^0}}\right)$$

(10)

3.2.2. Mass and Momentum Transport

The flow of gases in the flow channels and porous electrodes is modeled by the following mass conservation equation [14]:

$$\nabla ·\left(\rho \mathit{u}\right)=Q_m$$

(11)

The momentum transport in both flow channels and porous electrodes was described by a unified equation. For the flow channels, the porosity was set to 1 and the permeability was assumed to be infinite, so that the equation reduced to the Navier-Stokes equation. For the porous electrodes, the equation reduced to the Brinkman equation with the prescribed porosity and permeability.

$${\displaystyle \frac{\left(\rho \mathit{u}·\nabla \right)\mathit{u}}{\epsilon }}=-\nabla p+\nabla \left[{\displaystyle \frac{\mu }{\epsilon }}\left(\nabla \mathit{u}+(\nabla \mathit{u}{)}^T\right)-{\displaystyle \frac{2}{3}}{\displaystyle \frac{\mu }{\epsilon }}\nabla \mathit{u}\right]-{\displaystyle \frac{\mu \mathit{u}}{B_p}}$$

(12)

Where $\rho$ is the density of the mixture gases [kg/m³]; $B_p$represents the permeability of each porous electrode layers [m²]; $\mu$ is the dynamic viscosity of the mixture gases [Pa∙s].

3.2.3. Species Transport

The species conservation equations within the flow channels and porous electrodes layers can be described as:

$$\nabla ·\left(\rho x_i\mathit{u}\right)-\nabla ·\left({\rho D}_i^{eff}{\nabla x}_i\right)=S_i$$

(13)

Where $D_i^{eff}$is the effective diffusion coefficient of species i [m²/s]; $S_i$ is the mass flux term of species i due to electrochemical reactions [kg/m³/s].

In the porous electrodes, molecular diffusion and Knudsen diffusion occur simultaneously. Therefore, the effective diffusivity of species i was calculated by combining these two mechanisms through the Bosanquet relation [30]:

$$D_i^{eff}={\displaystyle \frac{\epsilon }{\tau }}\left[{\left({\displaystyle \frac{1}{D_{i,j}}}+{\displaystyle \frac{1}{D_{i,K}}}\right)}^{-1}\right]$$

(14)

$$D_{i,j}={\displaystyle \frac{3.198\times {10}^{-8}{T}^{1.75}}{p{\left(v_i^{\frac{1}{3}}+v_j^{\frac{1}{3}}\right)}^2}}{\left({\displaystyle \frac{1}{M_i}}+{\displaystyle \frac{1}{M_j}}\right)}^{0.5}$$

(15)

$$D_{i,K}={\displaystyle \frac{1}{3}}{d}_{pore}\sqrt{{\displaystyle \frac{8RT}{\pi M_i}}}$$

(16)

Where $D_{i,j}$ is the binary diffusion coefficient between species i and j [m²/s]; $D_{i,K}$ is the Knudsen diffusion coefficient of species i [m²/s]; $v_i$ and $v_j$ are the diffusion volume of species i and j [m³/mol]; $d_{pore}$ is the pore diameter of electrodes [m].

3.2.4. Charge Transport

The charge transport equations of ion and electron can be written as:

$$\nabla ·i_{io}=\nabla ·\left(-{\sigma }_{io,eff}\nabla {\Phi }_{io}\right)=\{\begin{array}{c}i·S_{eff}^{an} \left(\mathrm{AFL}\right) \\ -i·S_{eff}^{ca} \left(\mathrm{CFL}\right) \\ 0 \left(\mathrm{Other} \mathrm{layers}\right)\end{array}$$

(17)

$$\nabla ·i_{el}=\nabla ·\left(-{\sigma }_{el,eff}\nabla {\Phi }_{el}\right)=\{\begin{array}{c}-i·S_{eff}^{an} \left(\mathrm{AFL}\right) \\ i·S_{eff}^{ca} \left(\mathrm{CFL}\right) \\ 0 \left(\mathrm{Other} \mathrm{layers}\right)\end{array}$$

(18)

Where $i_{el}$ and $i_{io}$ are the current density of electronic and ionic [A/m²]; ${\Phi }_{el}$ and ${\Phi }_{io}$ are the potential of electronic and ionic [V], respectively.

3.2.5. Heat Transport

The temperature difference between the solid and gas phases in the porous electrodes was assumed to be negligible, according to the local thermodynamic equilibrium assumption reported by Andersson et al. [31]. Since electrochemical reactions occur mainly in the anode functional layer (AFL) and cathode functional layer (CFL), electrochemical heat generation was considered only in these functional layers. Accordingly, heat transport in the present model was described by the following energy conservation equation [32]:

$$\nabla \rho C_p\mathit{u}·\nabla T=\nabla ·\left(k_{eff}\nabla ·T\right)+Q_h$$

(19)

$$Q_h=\{\begin{array}{c}0 (\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{s}) \\ {\sigma }_e{\left(\nabla {\Phi }_{el}\right)}^2 \left(\mathrm{Interconnectors}\right)\\ {\sigma }_{io}{\left(\nabla {\Phi }_{io}\right)}^2 \left(\mathrm{EL},\mathrm{BL}\right) \\ {\sigma }_{el}{\left(\nabla {\Phi }_{el}\right)}^2+{\sigma }_{io}{\left(\nabla {\Phi }_{io}\right)}^2 \left(\mathrm{ASL}\right) \\ {\sigma }_{el}{\left(\nabla {\Phi }_{el}\right)}^2+{\sigma }_{io}{\left(\nabla {\Phi }_{io}\right)}^2+S_{eff}i\left({\displaystyle \frac{∆S_{e}T}{nF}}+{\eta }_{act}\right) \left(\mathrm{AFL},\mathrm{CFL}\right) \end{array}$$

(20)

Where $Q_h$ is the heat source term [W/m³]; $∆S_e$ is the entropy change of the electrochemical reactions [J/mol/K]; $C_p$ and $k_{eff}$ are specific heat capacity [J/kg/K] and effective thermal conductivity [W/m/K] of the gases and solid phases, respectively.

3.3. Boundary Conditions

Mass-flow inlet boundary conditions were prescribed at the anode and cathode channel inlets with flow rates of 200 SCCM and 500 SCCM, respectively. No-slip conditions were imposed on the channel walls, and a zero-gauge pressure condition was specified at the outlet boundaries. The anode inlet gas composition was set to 97 mol% H₂ and 3 mol% H₂O, whereas the cathode inlet gas composition was set to 79 mol% N₂ and 21 mol% O₂. For charge transport, a constant operating voltage was applied to the top surface of the cathode-side interconnector, while the bottom surface of the anode-side interconnector was set to ground potential. For heat transfer, constant temperature boundary conditions were imposed on the selected external boundaries of the computational domain.

3.4. Model Validation

The commercial finite element software COMSOL Multiphysics was employed to solve the coupled multi-physics model. The convergence criterion was set such that the residuals of all governing equations were lower than 1×10^-4. To balance numerical accuracy and computational cost, three mesh levels were compared for each interconnector configuration. The mesh containing 543,250, 640,164, 523,447, and 1,487,398 elements for the SI-SOFC, CI-SOFC, RI-SOFC, and TI-SOFC, respectively, was adopted in the subsequent simulations. The model was validated against experimental polarization data obtained for the SI-SOFC. Figure 3 compares the simulated and experimental polarization curves under 200 SCCM wet hydrogen and 500 SCCM air at 700, 750, and 800 °C. The numerical results agree well with the experimental data, with deviations below 3.6%, 4.3%, and 4.4% at 700, 750, and 800 °C, respectively. This agreement demonstrates that the present model is capable of describing the electrochemical and transport behavior of the SOFC with reasonable accuracy.

4. Results and Discussion

4.1. Electrical Performance

Figure 4 compares the polarization and power-density curves of SOFCs with different interconnector configurations at 800 °C. All cases exhibit the typical electrochemical behavior of SOFCs, and concentration polarization becomes increasingly pronounced at high current densities, particularly above 0.9 A/cm². Among the four configurations, TI-SOFC shows the best overall performance, followed by RI-SOFC and CI-SOFC, whereas SI-SOFC gives the lowest power output. The maximum power density reaches 0.46 W/cm² for TI-SOFC. Compared with SI-SOFC, the peak power densities of CI-SOFC, RI-SOFC, and TI-SOFC increase by 4.9%, 9.7%, and 11.7%, respectively. In addition, the inflection points of the power-density curves shift from 0.93 A/cm² for SI-SOFC to 0.87, 0.89, and 0.84 A/cm² for CI-SOFC, RI-SOFC, and TI-SOFC, respectively, indicating that the interconnector configuration significantly affects the high-current-density behavior of the cell. These results suggest that SOFC performance depends not only on channel connectivity but also on rib geometry. Since all interconnectors were designed with the same interconnector-electrode contact area (1300 mm²), the observed differences can be mainly attributed to the longer contact perimeter(1352 mm for SI-SOFC, 1405.9 mm for CI-SOFC, 1586.4 mm for RI-SOFC and 2708.2 mm for TI-SOFC) and enhanced lateral gas transport in the connected-rib designs, which promote reactant redistribution between adjacent channels and improve mass transfer at the ASL/interconnector interface.

Figure 5 compares the activation, concentration, ohmic, and total overpotentials of SOFCs with different interconnector configurations at 800 °C. In all cases, activation overpotential and concentration overpotential dominate the total polarization loss, whereas the ohmic overpotential remains nearly unchanged. The anode-side activation and concentration overpotentials vary only slightly with interconnector geometry, while the cathode-side losses are significantly reduced in the connected-rib designs. At 0.5 A/cm², the cathode activation overpotential decreases from 0.198 V in SI-SOFC to 0.180, 0.166, and 0.152 V in CI-SOFC, RI-SOFC, and TI-SOFC, respectively. Similarly, the cathode concentration overpotential decreases from 0.045 V to 0.037, 0.030, and 0.023 V. Since the material properties and thicknesses of the cell components are identical in all cases, the effect of interconnector geometry on ohmic loss is limited. Consequently, the reduction in total overpotential from SI-SOFC to CI-SOFC, RI-SOFC, and TI-SOFC is mainly attributed to the improved reactant redistribution and enhanced mass transfer enabled by the connected-rib structures.

4.2. Concentration Distribution

Figure 6(a-d) shows the hydrogen mole fraction at the interconnector/ASL interface under 0.7 V and 800 °C. In all cases, the hydrogen mole fraction decreases along the flow direction due to continuous electrochemical consumption. Compared with SI-SOFC, the connected-rib interconnectors lead to lower downstream hydrogen mole fractions, indicating enhanced fuel utilization. Among the four configurations, TI-SOFC exhibits the lowest outlet value, approximately 0.64, although the hydrogen mole fraction remains above 0.55 even at the end of the channel. The line profiles in Figure 6(e-f) further show that SI-SOFC exhibits a clear difference between the regions beneath the ribs and channels, with hydrogen mole fractions of about 0.79 and 0.83, respectively, indicating limited lateral diffusion under the conventional straight-rib structure. By contrast, this difference becomes smaller in the connected-rib designs, confirming that channel connectivity promotes transverse hydrogen redistribution and improves mass transfer in the porous anode. Among the three novel configurations, RI-SOFC shows a relatively moderate side-to-center concentration gradient, suggesting a stronger ability to redistribute hydrogen across the channel width.

Figure 7(a-d) shows the oxygen mole fraction at the interconnector/CFL interface under 0.7 V and 800 °C. In SI-SOFC, the oxygen mole fraction beneath the ribs decreases rapidly along the flow direction, forming extended oxygen-deficient zones that limit the electrochemical performance of the cathode. This behavior is mainly associated with the limited oxygen diffusion in the porous cathode, where the transport of oxygen is inherently slower than that of hydrogen. In contrast, the connected-rib interconnectors break up the continuous oxygen-deficient regions and promote oxygen transport toward the rib-covered areas, leading to a more distributed oxygen field. The line profiles in Figure 7(e-f) further illustrate this effect. Along the flow direction, the oxygen mole fraction decreases sharply from about 0.21 beneath the channels to approximately 0.025 beneath the ribs in TI-SOFC, whereas it approaches zero in CI-SOFC and RI-SOFC. In SI-SOFC, the oxygen-deficient zones persist almost continuously to the channel end, indicating weak transverse oxygen redistribution. Along the channel width direction, the oxygen mole fraction beneath the ribs remains about 0.02 in TI-SOFC, while the value beneath the channels is about 0.14. This channel value is 0.01, 0.02, and 0.03 lower than those in RI-SOFC, CI-SOFC, and SI-SOFC, respectively, indicating that more oxygen is consumed in TI-SOFC due to the enhanced electrochemical reaction. The connected-rib interconnectors alleviate oxygen depletion beneath the ribs, and TI-SOFC shows the most effective cathode side mass-transfer enhancement among the four configurations.

4.3. Velocity Distribution

Figure 8 shows the velocity distribution beneath the ribs in the ASL at the cross-section of Y=25 mm under 0.7 V. Compared with SI-SOFC, all connected-rib interconnectors produce significantly higher gas velocities beneath the ribs, indicating enhanced convective transport in the porous anode. Among the four configurations, TI-SOFC exhibits the highest local velocity, reaching about 0.05 m/s, which is more than one order of magnitude higher than that in SI-SOFC(0.004 m/s). In CI-SOFC and TI-SOFC, the high-velocity regions are mainly distributed near the channel-rib junctions above the ASL, where the local geometry drives part of the gas from the flow channel into the porous anode. By contrast, RI-SOFC shows a more uniform velocity distribution along the channel length.

Figure 9 shows the velocity distribution beneath the fuel channels in the ASL under 0.7 V. In SI-SOFC, the velocity in the porous anode remains relatively low and varies only slightly along the channel length, indicating weak gas penetration from the fuel channel into the ASL. In contrast, the connected-rib interconnectors generate distinct high-velocity regions near the upper part of the ASL, especially close to the channel-rib junctions, demonstrating enhanced convective transport from the fuel channel into the porous electrode. Among the three modified configurations, CI-SOFC and TI-SOFC exhibit more pronounced local velocity peaks, whereas RI-SOFC shows a comparatively smoother and more uniform velocity distribution along the flow direction. The results indicate that the connected-rib designs strengthen under-channel mass transfer in the porous anode, while the rectangular-rib configuration provides the best velocity uniformity and the triangular-rib configuration gives the strongest local flow enhancement.

Figure 10 compares the velocity distributions in the porous anode along line 5 (under the ribs) and line 6 (under the fuel channels) for the four SOFC configurations under 0.7 V. SI-SOFC shows the largest difference between the two lines, with the velocity on line 5 remaining below 0.002 m/s, whereas that on line 6 decreases gradually from about 0.03 m/s near the inlet to about 0.017-0.018 m/s at the channel end. CI-SOFC and TI-SOFC exhibit pronounced periodic velocity peaks on both lines, and the peak values on line 5 reach nearly 0.048-0.05 m/s in the inlet region before decaying to around 0.02 m/s in the downstream region. RI-SOFC maintains a relatively stable velocity on line 6, fluctuating only within about 0.018-0.022 m/s, together with smaller fluctuations on line 5, resulting in the most uniform velocity distribution among the four configurations. The CI-SOFC and TI-SOFC provide stronger local flow enhancement, whereas RI-SOFC is more effective in maintaining uniform mass transfer throughout the porous anode. To quantify this difference, the velocity uniformity index γ is defined in Equation (21).

$$\gamma =1-{\displaystyle \frac{\left|{\overline{u}}_{uc}-{\overline{u}}_{ur}\right|}{{\overline{u}}_{uc}}}$$

(21)

Where ${\overline{u}}_{uc}$ is the mean velocity at the cross section (Y = 25 mm) of ASL under the channels; ${\overline{u}}_{ur}$ is the mean velocity at the cross section (Y = 23 mm) of ASL under the ribs.

Figure 11(a) compares the mean velocities beneath the ribs and beneath the fuel channels in the ASL at different current densities. In all configurations, the mean velocity increases gradually with current density. SI-SOFC shows the largest difference between the two regions. The mean velocity under the ribs remains lower than 0.002 m/s over the whole current-density range, whereas the corresponding value beneath the fuel channels increases to about 0.023 m/s at 0.9 A/cm². In contrast, the connected-rib interconnectors significantly increase the mean velocity beneath the ribs. At 0.9 A/cm² current density, the under-rib mean velocity reaches about 0.015 m/s in CI-SOFC and RI-SOFC, and further increases to about 0.023 m/s in TI-SOFC. Beneath the fuel channels, the mean velocities in CI-SOFC and TI-SOFC rise to about 0.027 m/s, which is slightly higher than those in SI-SOFC and RI-SOFC. The connected-rib interconnectors enhance both the mean velocity beneath the ribs and the velocity uniformity in the porous anode, with TI-SOFC showing the strongest under-rib flow enhancement among the four configurations.

Figure 11(b) further compares the velocity uniformity index $\gamma$. The value of $\gamma$ follows the order of TI-SOFC, RI-SOFC, CI-SOFC, and SI-SOFC over the whole current-density range. SI-SOFC exhibits the lowest $\gamma$, remaining in the range of about 8% to 12%, which corresponds to the largest velocity difference between the rib-covered and channel-covered regions. By contrast, TI-SOFC maintains the highest $\gamma$, decreasing from about 98% at 0.1 A/cm² to about 85% at 0.9 A/cm². RI-SOFC and CI-SOFC remain in the ranges of about 60% to 68% and 54% to 60%, respectively. Therefore, the connected-rib interconnectors not only enhance mass transfer in the porous anode but also improve the velocity uniformity, with TI-SOFC showing the best overall performance among the four configurations.

4.4. Pressure Drop

Figure 12 compares the pressure drops in the air and fuel channels of the four SOFC configurations at different current densities. In all cases, the connected-rib interconnectors introduce a significantly larger hydraulic penalty than the conventional straight-rib design, and the pressure drop follows the order of TI-SOFC, CI-SOFC, RI-SOFC, and SI-SOFC. This trend is mainly associated with the narrower flow passages and stronger local flow constriction in the connected-rib configurations. As the current density increases from 0.1 to 0.9 A/cm², the pressure drop in the fuel channel increases for all cases, reaching about 73.3 Pa in TI-SOFC, which is the highest among the four configurations. By contrast, the pressure drop in the air channel decreases slightly with increasing current density, owing to the gradual consumption of oxygen along the cathode side. Although CI-SOFC and RI-SOFC have similar connected-channel characteristics, RI-SOFC shows a lower pressure drop because its rectangular flow passages produce weaker local contraction and expansion losses. At 0.9 A/cm², the total pressure drops of SI-SOFC, CI-SOFC, RI-SOFC, and TI-SOFC are about 16.9, 64.9, 56.9, and 154.9 Pa, respectively. Such a hydraulic penalty is relatively small compared with the pressure levels reported for pressurized SOFC and SOFC-GT hybrid systems, which commonly operate under elevated pressure [33,34,35,36]. Therefore, the improvement in mass transfer achieved by the connected-rib interconnectors is accompanied by an increase in hydraulic resistance.

4.5. Porosity Effect

Figure 13 show the effects of anode porosity and cathode porosity on the power density at 0.7 V. In all cases, the power density exhibits an initial increase with porosity, followed by a relatively stable region within the range of 0.3-0.6 and a slight decrease at higher porosity. This trend indicates a balance between improved gas diffusion and the reduction of effective electrochemical reaction sites at excessive porosity. For both anode and cathode porosity variations, the relative performance ranking remains unchanged. TI-SOFC exhibits the highest power density throughout, followed by RI-SOFC, CI-SOFC, and SI-SOFC. This result confirms that the advantage of the connected-rib interconnectors is preserved over a relatively wide porosity range.

4.6. Temperature Effect

Figure 14 shows the effect of operating temperature on the power density of SOFCs with different interconnector configurations. In all cases, the power density increases monotonically with temperature over the range of 600-800 °C. The performance ranking remains unchanged throughout, with TI-SOFC showing the highest power density, followed by RI-SOFC, CI-SOFC, and SI-SOFC. At 800 °C, the power densities of SI-SOFC, CI-SOFC, RI-SOFC, and TI-SOFC reach about 0.33, 0.35, 0.38, and 0.41 W/cm², respectively. Compared with SI-SOFC, the power density is higher by about 7% in CI-SOFC, 16% in RI-SOFC, and 24.5% in TI-SOFC. These results indicate that the performance advantage of the connected-rib interconnectors is maintained over the whole temperature range, and the triangular-rib configuration remains the most effective for improving cell output.

5. Conclusions

Connected-rib interconnectors improve the electrochemical performance of anode-supported planar SOFCs under the condition of identical interconnector–electrode contact area. At 800 °C, the peak power densities of CI-SOFC, RI-SOFC, and TI-SOFC increase by 4.9%, 9.7%, and 11.7%, respectively, compared with SI-SOFC. The performance enhancement mainly originates from the reduction of cathode-side activation and concentration overpotentials, whereas the ohmic overpotential remains nearly unchanged. The connected-rib structures also promote reactant redistribution and strengthen under-rib transport in the porous electrodes.

The three connected-rib designs do not provide the same balance between transport enhancement and hydraulic cost. TI-SOFC delivers the strongest under-rib transport enhancement and the highest power density, but it also causes the largest pressure drop. RI-SOFC provides a more uniform velocity distribution in the porous anode and a lower pressure-drop penalty than CI-SOFC and TI-SOFC, giving a better compromise between mass-transfer enhancement and hydraulic resistance.