This study proposes a sustainable design framework for plate-fin heat exchangers (PFHEs) based on a chaos-enhanced elk herd optimizer (CEHO), integrating carbon emissions, economic costs, and entropy generation into a unified multi-objective optimization model. The proposed framework simultaneously considers lifecycle CO₂ emissions, total annual cost (TAC), and thermodynamic irreversibility associated with entropy generation, enabling a comprehensive evaluation of system performance under fouling conditions. An asymptotic fouling model is incorporated to describe time-dependent thermal resistance evolution, thereby bridging operational degradation and design optimization. The CEHO algorithm, augmented with ten distinct chaotic maps, addresses the premature convergence issue of standard EHO in high-dimensional design spaces. Comprehensive validation across twelve benchmark functions (unimodal, multimodal, and composite) confirms CEHO's superiority: it achieves the highest Friedman rank, near-zero standard deviations on most functions, and extremely compact 95% confidence intervals, significantly outperforming EHO, PSO, and GA. Applied to an industrial waste heat recovery case, the framework yields a minimum total annual cost (TAC) of $838.96, which is approximately 5.5% lower than the best-reported literature result and up to 88% lower than the initial baseline design. In tri-objective optimization, CEHO achieves a 30 t reduction in CO₂ emissions (equivalent to 60 MWh of electricity savings) relative to standard EHO, while maintaining nearly identical entropy generation. This framework bridges a critical gap between design-stage optimization and fouling-aware maintenance, offering a robust tool for balancing operational sustainability and economic viability in complex thermal systems.

To manage the temperature of liquid-cooled lithium-ion batteries under complex operating conditions, an adaptive Long Short-Term Memory-Model Predictive Control (LSTM-MPC) collaborative control framework is proposed. The LSTM network performs multi-horizon short-term prediction of temperature rise based on historical current, voltage, and temperature profiles, while predictive uncertainty is quantified using Monte Carlo (MC) Dropout. An interval score-based weighting scheme is employed to fuse multi-horizon forecasts and provide reliable look-ahead information for the MPC controller, which optimizes coolant flow under thermal safety and pump power constraints. Under the US06 driving cycle, the maximum temperature overrun is reduced from 1.335 degrees C to 0.352 degrees C, while the over-temperature duration is shortened from 631 s to 202 s. For composite driving cycles at ambient temperatures of 30 degrees C, 35 degrees C, and 40 degrees C, pump energy consumption is reduced by 52%, 58%, and 37%, respectively, compared with constant-flow control, while maintaining comparable peak temperature. The results demonstrate that the proposed LSTM-MPC framework supports anticipatory pre-cooling and improved energy efficiency under thermal safety constraints, indicating promising potential for practical battery thermal management applications.

ObjectiveAir-cooled， parallel-plate channels used in battery packs， electronic chips， and compact heat exchangers are commonly limited by the trade-off between heat transfer and pressure drop. Although dimpled surfaces can intensify near-wall mixing at a relatively low manufacturing cost， their overall thermal-hydraulic performance is highly sensitive to the geometric configuration. To address this issue， this study investigates a novel parallel-plate channel equipped with a dimpled plate featuring reverse-side protrusions. This study aims to clarify the effects of major geometric parameters on the coupled flow and heat transfer characteristics， and to identify an optimal compromise design that enhances heat transfer while suppressing the pressure drop.MethodsA three-dimensional， periodic unit of a plate channel was established and solved using steady-state computational fluid dynamics. Air was treated as an incompressible fluid with constant thermophysical properties. Periodic boundary conditions were adopted for the inlet and outlet of the computational domain. Grid independence was achieved at approximately 5.68 million cells. The numerical method was validated against published pillow plate experimental data. Three geometric parameters were selected as decision variables， namely the depth of the large dimple （R1=2.5-4.0 mm）， the depth of the small dimple （R2=0.5-2.0 mm）， and the dimple inclination angle （α=30°-60°）. A total of 64 design cases were used to construct the sample database. Based on these CFD data， Extreme Gradient Boosting （XGBoost） surrogate models were trained for Nu and Δp. The trained models were then coupled with the Non-dominated Sorting Genetic Algorithm II （NSGAII） to perform multi-objective optimization， and the entropy-weighted technique for order preference by similarity to ideal solution （TOPSIS） was employed to determine the best compromise solution.Results and DiscussionsUnivariate analysis reveals that R1， R2， and α all have significant influences on the thermal-hydraulic performance. Increasing R1 intensifies the flow separation and reattachment and enlarges the recirculation zone. Consequently， the heat transfer performance （h） increases rapidly. However， once R1 exceeds a certain level， the increase in h becomes much smaller than the increase in frictional resistance （f）， resulting in a turning point in the comprehensive performance. Both h and f increase rapidly with an increase in R2； beyond a certain threshold， further increases in R2， cause the trends of h and the performance evaluation criteria （PEC） gradually flatten out. Additionally， h and f show a tendency to increase and then decreasing with the increase of α. The XGBoost surrogate model reproduces the CFD results with high accuracy. The maximum deviations are only 0.44% for Nu and 3.31% for Δp， while the coefficients of determination （R²） reach 0.999 6 and0.998 2， with root mean square errors of 2.94 and 6.42， respectively. Fourteen nondominated solutions were obtained on the Pareto front. The highest ranked compromise solution selected by entropy-weighted TOPSIS corresponds to R1=2.8 mm， R2=0.6 mm， and α=47°. Further CFD simulations over Re=5 000-10 000 confirm that the optimized structure had superior overall heat transfer performance.ConclusionsThe dimpled plate with reverse-side protrusions provides an effective passive strategy for enhancing air-side heat transfer in parallel-plate channels. However， maximizing thermal-hydraulic performance requires a rational combination of large dimple depth， small dimple depth， and inclination angle， rather than merely increasing geometric disturbances. The XGBoost， NSGAII， and TOPSIS frameworks provides a reliable and efficient approach for the multi-objective design of enhanced heat transfer surfaces. For the present channel， the optimized geometry achieves a PEC of approximately 1.55 under equal pumping power over the entire investigated Re range， indicating substantial comprehensive performance improvements， promising application potential in battery thermal management， chip cooling， and other compact forced-air cooling devices.

Traditional stochastic reconstruction method of paper-type gas diffusion layer (GDL) in proton exchange membrane fuel cell (PEMFC) faces the limitation of generation accuracy. Firstly, according to the derivation process of porosity, the coupling effect of carbon fiber porosity and structural element radius on the post-additive-addition structure porosity is proposed, along with an improved inverse derivation method for porosity distribution of GDL. According to the generation process, combined with the principle of morphological processing technology, the influencing factors and mechanism of the porosity of the generated structure are analyzed, and the fitting formula between the porosity and the influencing factors is proposed, with the R2 value of the fitting result larger than 0.98. Based on the above research, an improved two-stage reconstruction framework of GDL is proposed, which achieves high through-plane porosity distribution fidelity. The method shows good applicability for reconstruction across diverse carbon paper substrates with variations in thickness, porosity distribution, and PTFE content, providing an enhanced tool for precise control and optimal design of the structural and component distributions within GDLs.

To enhance hydrogen fuel utilization and power density in proton exchange membrane fuel cells, persistent challenges in water management and efficient reactant transport at the cathode must be addressed. This study introduces and validates a novel gradient double-sided rectangular blockage flow field through a systematic methodology integrating experimental screening, numerical multi-objective optimization, and final experimental validation. Initial experiments evaluated various blockage geometries (triangular, rectangular, trapezoidal, and circular), identifying the rectangular profile as optimal for mass transport enhancement due to its vertical windward face. Multi-objective optimization determined the optimal blockage parameters (0.35 mm width, 0.6535 mm average height and the 0.0404 mm height increment), with experimental validation confirming that this design yields an 11.28 % enhancement compared to the traditional parallel channel. Numerical simulations validated enhanced reactant distribution and water management, with a 19.34 % increase in average oxygen concentration at the MPL/CL interface, a 13.64 % reduction in oxygen non-uniformity, improved water drainage from porous media, and preserved hydration in proton-conducting regions. The proposed cathode flow field provides a reliable approach to enhance reactant transport efficiency and address water management issues, offering a promising solution for next-generation high performance fuel cells.

With the increasing power density in data center, liquid cooling data centers have attracted widespread attention and application. Thermal management has become a critical bottleneck restricting their further development. To address the thermal management challenges across multiple scales in data centers, this study established a multiscale model for the single-phase immersion cooling (SPIC) data centers and obtained the quantitative relationship between the thermal loading in the data center and the temperature increase of the chip. Then, a two-scales Proper Orthogonal Decomposition (POD)-based reduced order model (ROM) was developed for both the immersion tank and server scales, enabling rapid prediction of multiscale flow and temperature fields. Through boundary conditions delivery across the immersion tank and server scales, the rapid prediction of the thermal and flow fields in SPIC systems was achieved. Compared with CFD results, the maximum mean relative deviations of the POD-predicted velocity at the server inlets and outlets were 2.88% and 2.92%, respectively. For the internal three-dimensional temperature field of the server, the maximum mean relative deviation was 3.7%. The POD model achieved a computational speed up of approximately 1500 times over traditional CFD simulations.

This study systematically investigates the effects of five key geometric parameters: fin density, height, thickness, root structure, and secondary fin depth, on the condensation heat transfer performance of externally twodimensional (2D) and three-dimensional (3D) finned tubes. Using R134a as the working fluid at a saturation temperature of 36 degrees C, experiments were conducted on 17 enhanced tubes under heat fluxes ranging from 10 to 80 kW/m2. Results show that 3D fins significantly outperform 2D fins, particularly under higher heat flux conditions, due to improved condensate drainage and liquid film disruption. An optimal fin density of 48 fpi for the 3D finned tubes was identified, balancing increased surface area and drainage efficiency. Square fin root structures are better suited for tubes with low fin density, while deep-secondary-fin tubes exhibit better condensation performance under high heat flux. Increased thickness of 3D fins leads to a decrease in the optimal fin density. This work clarifies the effects of 3D fin parameters, identifies optimal configurations, and provides data to guide the design of high-efficiency condensers.

Proton exchange membrane fuel cell (PEMFC) self-cold start is strongly affected by flow-field design, especially in large-area cells where local transport non-uniformity can be readily amplified into regional freezing and performance degradation. In this work, a three-dimensional transient non-isothermal model was established to explore the self-cold start behavior of 112 cm2 large-area PEMFCs under different cathode flow-field configurations. Particular attention was given to the amplification of flow-field effects by start-up conditions, as well as to the flow-field-dependent spatial freezing characteristics. The results show that under the baseline self-cold start condition, the multi-channel serpentine flow field increased the peak current density by approximately 5.6%, and extended the failure time from 81 to 91 s. More importantly, its superiority was not simply associated with a lower average ice fraction, but with a more favorable freezing pattern. The multi-channel serpentine flow field suppressed early localized icing at the electrochemical reaction interface and delayed the coalescence of isolated ice spots into connected clusters. It also alleviated the direct freezing burden in the cathode catalyst layer, while part of the freezing tendency shifted toward the cathode gas diffusion layer. Lower start-up temperature intensified the consequence of local ice coalescence, whereas the effect of start-up voltage was non-monotonic, with 0.4 V providing the most favorable compromise between heat accumulation and freezing progression. These findings indicate that, for large-area PEMFCs, temperature uniformity and freezing topology are more critical than average thermal response alone, and that multi-channel serpentine cathode flow fields are more suitable for low-temperature start-up.

Low-Pt proton exchange membrane fuel cells (PEMFCs) require cathode catalyst layers (CCLs) capable of mitigating coupled performance-durability trade-offs under variable-humidity operating conditions. Here, a mechanism-guided through-plane ionomer-gradient design is developed for a low-Pt CCL (0.1 mg cm−2) by integrating a three-dimensional multiphase PEMFC model, an agglomerate submodel, and regional sensitivity analysis. The analysis reveals relative humidity (RH)-dependent functional demands along the CCL thickness, motivating an asymmetric dual-segment power-law profile (ADSPLP) to parameterize the ionomer-to-carbon (I/C) ratio distribution using six physically interpretable variables. Single-factor analyses clarify how these variables reshape local transport and reaction distributions, followed by surrogate-assisted multi-RH robust optimization using 50% and 100% RH as boundary scenarios. The results show that dry operation benefits mainly from membrane-side proton-access enhancement that suppresses ohmic loss, whereas fully humidified operation requires stronger oxygen access on the microporous-layer side to alleviate concentration loss. Both single-sided improvements, however, tend to shift the high-reaction region away from the membrane side and increase reaction non-uniformity. The optimized ADSPLP achieves performance close to that of the RH-specific optima by mitigating the dominant bottlenecks at the dry and humid extremes, while preserving balanced proton and oxygen access to deliver the largest gain at intermediate humidity. Relative to the corresponding best uniform I/C designs, it increases peak net power by 3.30%–4.39% across 50%–100% RH while effectively limiting the growth in reaction non-uniformity. This study provides a mechanism-guided gradient-CCL optimization strategy and design guidance for humidity-adaptive low-Pt membrane electrode assemblies.

Reliable cold start of large-area proton exchange membrane fuel cells (PEMFCs) remains a key bottleneck for fuel cell vehicles, because most mechanistic studies have focused on small laboratory cells whose behavior cannot be directly extrapolated to large-scale devices. This study develops a transient three-dimensional non-isothermal multi-physics model of a 79.5 cm 2 PEMFC with an eleven-channel serpentine flow field to elucidate coupled heat, water and ice processes during self-cold start at -30 degrees C. On this basis, three start strategies are examined. The global responses reveal three characteristic stages: reaction-limited, self-heating dominated, and icing/transportlimited. These stages develop in a strongly non-uniform manner: downstream regions heat up faster than inlet zones, and the multi-channel serpentine geometry induces pronounced variations of temperature and current density. Higher ramps increase cathode catalyst layer (CL) heating rates from 0.88 to 1.86 K min - 1 , but also amplify temperature and current-density non-uniformity. Ice forms preferentially in the cathode CL, where limited gas-phase transport and low saturation vapor pressure hinder water removal, and then propagates into the gas diffusion layer (GDL). In-plane distribution and a quantitative uniformity index reveal that aggressive ramps promote early nucleation of ice clusters near channel bends and downstream regions, followed by rapid coalescence into extended ice-rich bands. Through-plane analysis shows that high ramps drive deep ice penetration into the GDL, whereas moderate ramps keep most ice confined near the CL. These results clarify how

Flow field design is key to boosting proton exchange membrane fuel cell (PEMFC) performance. The oftenoverlooked transition zone between the bipolar plate (BPP) flow field's distribution and mainstream zones causes uneven reactant distribution, harming cell performance. This study proposes a hybrid methodology for optimizing the PEMFC transition zone. A 2D topology optimization (TO) framework is established to generate a novel flow structure with low flow resistance and high distribution uniformity, where the objective function balances pressure drop reduction and flow uniformity improvement. The optimized 2D structure is then extruded to form a 3D flow field, and its performance is evaluated using a developed 3D two-phase half-cell multiphysics model. Results show that the TO-derived transition zone structure introduces tailored baffle configurations, reducing the flow velocity standard deviation by 41.6% at 2.0 A & sdot;cm-2 and enhancing cell output performance by 26.7% under the same conditions. Results from the operational condition sensitivity analysis demonstrate that the TO flow field achieves a higher performance improvement rate under high temperature/humidity, low stoichiometric ratio/pressure. The improvement rate is higher under a higher rib width ratio and more flow channel branches-conditions where flow maldistribution or reactant scarcity is more pronounced. This work fills the research lacuna in PEMFC transition zone design, offering valuable insights for future large-area bipolar plate development.

The even distributions of anode, cathode and coolant are of critical significance to the efficiency and lifetime of proton exchange membrane fuel cell (PEMFC) stacks. In this work, a multi-scale approach with upscaling strategy is developed for simulating the flow distribution, along with an efficient algorithm for calibrating the viscous and inertial resistance coefficients in the porous medium model. The proposed framework effectively balances computational accuracy and efficiency in full-scale stack simulations. The flow distribution characteristics of the anode, cathode, and coolant in a commercial-size PEMFC stack with 164 single cells are simulated and compared. Results suggest that the proposed algorithm can calibrate the resistance coefficients within only 11 inner iterations, offering a new approach for rapid and reliable parameter identification. For the studied PEMFC stack, the consideration of the species mass fraction in anode is of crucial importance to the trend of the flow distribution curve. The anode has the most uniform flow distribution, followed by the coolant, while the cathode has the worst flow distribution due to the vortex-dominant flow. The flow distribution uniformity of the U-type configuration generally surpasses that of the Z-type configuration. The U-type configuration may allow for the enhancement of flow distribution uniformity through the design of the eccentricity of end socket, while for the Z-type configuration, the eccentricity always worsens the flow distribution. The anode, cathode and coolant are recommended to be designed as U-type configuration with the eccentricities of 0, 0 and 0.6, respectively, providing reference for the design of the manifold.

In the catalyst layer of proton exchange membrane fuel cells (PEMFCs), the electrochemical active surface area (ECSA) of Platinum (Pt) catalysts experiences degradation during long-term operation, due to Ostwald ripening effects and Pt mass loss to the membrane. In this work, a rapid prediction model of Pt ECSA degradation is developed based on Ostwald ripening theory and a high-fidelity numerical model. The model systematically quantifies the contributions of Ostwald ripening and Pt mass loss to ECSA degradation, yielding a power-law relationship for ECSA loss. Results indicate that, even when Pt oxidation and mass loss is neglected, the pronounced surface energy effects of Pt nanoparticles yield a power-law exponent of p approximate to 0.20-0.25, significantly lower than 0.5 predicted by the classical model. The power-law exponentp is little affected by Pt oxidation, while is significantly increased when Pt mass loss is considered. The deviations of fast prediction results of Pt ECSA degradation are generally below 5%, compared with numerical results and experimental data. These findings provide an efficient tool for PEMFC lifetime assessment and performance degradation prediction.

This study presents a comprehensive analysis of a 2 kW proton exchange membrane fuel cell-based combined heat and power (PEMFC-CHP) system operating under different electrical and thermal following modes across six representative energy demand profiles. The system's operational and structural parameters are thoroughly examined, and a multi-objective optimization is conducted by integrating an artificial neural network (ANN) with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Results indicate that, in winter, the constant power-thermal following mode meets the thermal demand but shortens the PEMFC lifespan due to frequent start-stop cycles. The optimized leveled distributed power mode effectively mitigates shutdowns, achieving a system efficiency (EffCHP) of 0.9784 and a matching degree (phi) of 0.8763, while maintaining stable thermal performance in winter and mid-season. The EffCHP shows an overall improvement of 7% compared with previous studies. In summer, the system operates in electrical-following mode due to reducedthermal demand. According to EWM-TOPSIS analysis, the optimal Pareto solutions achieve phi of 0.9270 and EffCHP of 0.9796 in winter, and phi of 0.9883, EffCHP of 0.9574, with hydrogen consumption of 1.9 kg in summer, confirming superior efficiency and operational coordination.

Molecular diffusion is a ubiquitous phenomenon in nature, where the diffusive flux typically aligns with the concentration gradient of species. However, this conventional relationship between diffusive flux and concentration gradient does not always hold, as seen in reverse diffusion, where the flux and concentration gradient are oriented in opposite directions. An important cause of reverse diffusion is the inverse relationship between species concentration and chemical potential, which can be attributed to the non-ideality of the species involved. This study investigates the conditions for reverse diffusion in binary hydrocarbon systems by calculating the derivatives of chemical potential with respect to molar concentration. The Peng-Robinson Equation of State (PR-EoS) is employed to describe the fluid thermodynamics. Additionally, the derivatives of chemical potential with respect to molar fraction, as well as the eigenvalues and eigenvectors of the Jacobian matrix of chemical potentials with respect to molar concentrations, are calculated. The complete results include binary normal alkane systems ranging from C1 to C 10, and CO2-normal alkane systems at temperatures ranging from 200K to 600K, with molar concentrations between 0 and 20,000 mol /m3. The main conclusions are as follows: (1) Ideal gases and ideal solutions exhibit no reverse diffusion theoretically; (2) Reverse diffusion is strongly temperature-dependent, with a higher likelihood at lower temperatures; (3) Binary mixtures with a near-zero molar concentration of one species are more prone to reverse diffusion than those where both species are present in appreciable molar concentrations; (4) The reverse diffusion phenomenon is most pronounced near phase interfaces.

Enhancing turbulent heat transfer is crucial for a wide range of scientific and engineering problems. A 2D two-layer topology optimization (TO) model is developed for turbulent heat transfer in microchannels, in which turbulent characteristics are carefully incorporated. Effects of the intermediate density and absence of wall function in the TO model are also discussed in detail by comparing a series of 2D modeling and 3D simulations. By adopting the TO model, microchannel structures with enhanced heat transfer performance are obtained compared with straight and airfoil microchannels. Optimized structures with changed pressure constraint, design Reynolds number (Re), TO model (laminar/turbulent), and thermal boundary condition are also generated and analyzed. The results demonstrate that TO structures with larger pressure constraint, lower Re, and non-uniform thermal boundary condition exhibit better performance. Specifically, the balance between thermal resistances is found to dictate the topological layout in the design domain and the optimal design Re depends on the specific problem configuration.

Suboptimal cooling flow field configurations hinder efficient thermal management in proton exchange membrane fuel cells (PEMFCs), limiting performance and durability. To address this, integrated cooling configurations are proposed, along with their wavy integrated (WICs) and hybrid integrated variants. Parallel, tri-serpentine, and serpentine cooling channels are embedded into blocked reactant flow field, with alternating reactant-coolant flow configuration as a benchmark. Employing a three-dimensional multiphase PEMFC model, the thermal and electrochemical performance of these configurations is investigated across coolant temperature differences (ΔT). Theoretical resistance analysis and voltage loss decomposition are used to clarify how these designs improve heat transfer and thus electrical output via gas–water transport effects. Results indicate that, by regulating coolant flow and heat conduction patterns at ΔT = 3 K, WICs improve temperature uniformity relative to basic integrated configurations. Through full rib-width coverage with wavy structures, they also exhibit lower average temperature than hybrid setups and benchmark. This enhanced thermal performance shifts water phase equilibrium, promoting membrane hydration and vapor condensation, thereby elevating proton and oxygen availability, and cutting ohmic and concentration losses by approximately 0.05 V. Across varied ΔT levels, WICs consistently deliver optimal thermal and electrical performance, with greater uniformity advantages but diminished output gains as coolant flow rate rises. Balancing output gain against parasitic consumption, serpentine WIC proves optimal for ΔT of 10 K and 6 K, tri-serpentine for 3 K, and parallel for 1 K, yielding net power increases of 3.61%, 2.92%, 2.60%, and 1.96%, respectively, over the conventional parallel design. This work provides design insights into compact PEMFC cooling-unit development.

With the increasing power of electronic chips, cold plates have become as a promising solution for cooling high thermal load electronic devices. Small channel cold plates are still an effective thermal control device for the manufacturing process convenience. This study numerically investigated the effects of long manifold wave and wave-break cooling plates. Numerical results indicate that long manifolds can ensure a more uniform flow of coolant from the inlet into each channel. The enhancement effects of different arrangements of bionic ribs and circular ribs on secondary flow are also studied. The performance is evaluated using performance evaluation criterion PEC, and the optimal arrangement is applied to the whole-plate simulation of long manifold wave channels cold plate. Experimental results validate the reliability of the numerical simulations, with the maximum relative deviations between the numerical results for temperature and pressure drop and the test data being only 4 % and 9.32 %, respectively. It is found that when the coolant flow velocity is 2.2 m/s, the heat dissipation capacity of the 3 mm ribs wave channel cold plate increases to 209 W/cm2, improving the heat dissipation capacity to 4.5 % compared with the wave channel. When the rib height is increased to 6.5 mm, the heat dissipation capacity increases to 221.5 W/cm2, improving the heat dissipation capacity with 10.75 % compared with the wave channel.

To enhance cathode catalyst layer (CCL) performance of proton exchange membrane fuel cells (PEMFCs), this work proposes a rapid prediction of optimal structures for gradient cathode catalyst layers in diverse operating conditions. First, a one-dimensional agglomerate model is developed to quantifies how the CCL structural and operational parameters synergistically affect peak power density (P-max) and limiting current density (I-lim). Sensitivity analysis identifies relative humidity (RH) and air inlet pressure (p(in)) as dominant factors governing PEMFC performance. A data-driven optimization model is then built to determine the optimal ionomer designs, which exhibit a unified dimensionless polarization curve independent of RH and p(in) (within RH = 0.4-0.9, p(in) = 1-2 atm). Leveraging this physics-based design rule, we propose a physics-based rapid prediction method to determine the optimal structures for both non-gradient and gradient CCL, under varying RH and p(in). Interestingly, the optimal ionomer content obtained by the single-objective optimization is almost identical to the multi-objective optimization results. Results demonstrate that the gradient CCL can improve P-max by >4 % and I-lim by approximate to 40 %. The insights in this work offers quantitative, practical guidance for robust gradient CCL design under variable conditions.