CFD Solver Research Articles

A Green's Function Wind Turbine Induction Model That Incorporates Complex Inflow Conditions

ABSTRACTIn this work, we develop a new analytical turbine induction model that can incorporate complex inflow conditions including cases where the wind velocity and temperature profiles can vary as functions of height. This induction model is derived from the linearized Navier–Stokes and leads to a second‐order ODE that can be solved using a Green's function formulation. The corresponding Green's function for several configurations are found including the infinite domain, semi‐infinite domain with ground plane, and a power law velocity inflow profile. The results of this approach are then compared with simulations of the turbine induction field using the AMR‐Wind CFD solver with a uniformly loaded actuator disk model. These comparisons show that the Green's function approach captures the centerline blockage, three‐dimensional blockage flow field, and streamwise velocity slow down, with very good agreement for lower thrust conditions and at larger distances away from rotor disk. The effects of shear on the turbine blockage were also compared using a power law inflow profile, and we show that this approach matches the CFD predictions for the cases considered.

Development and testing of hybrid (PNM–CFD) mathematical model and numerical algorithm for description of fluid flows in three-dimensional digital core models

Numerical simulation of fluid flow in porous and fractured rocks is an important task for many industrial applications. The most common approaches to constructing such models are direct (CFD or lattice Boltzmann) and porous network (PNM) modeling. Each approach has its own advantages and disadvantages. This paper presents a hybrid mathematical PNM–CFD model for describing fluid flows in three-dimensional digital core models, which has the high speed performance of PNM approaches and high accuracy of CFD models. Numerical technique has been developed for describing fluid flows in three-dimensional digital core models using a hybrid PNM–CFD model. The numerical technique links a one-dimensional pore network solver and a three-dimensional CFD solver into a combined model in original way by constructing a single pressure field for the entire computation domain. To validate the model, several tests were performed, including flow in straight channels and numerical simulation of fluid flow in a microfluidic chip. The test results have shown the adequacy of the hybrid model performance. The hybrid model for determining pressure drop in a branched network with three-dimensional chambers has an error of no more than 5 % when compared to experimental data. Similarly, the error in calculating velocity does not exceed 7 % when compared to the full three-dimensional calculation. The hybrid model has shown an almost twofold increase in calculation speed compared to the full three-dimensional model.

Hull shape optimization of autonomous underwater vehicles using a full turbulent continuous adjoint solver

The present study aims at simultaneously optimizing the nose and tail of two distinct Autonomous Underwater Vehicles (AUVs) using a full turbulent continuous adjoint solver. The entire procedure is carried out utilizing two open-source software: Salome (CAD and mesh generator) and OpenFOAM v2206 (CFD solver and optimizer). Reynolds-Averaged Navier–Stokes (RANS) equations closed by the k-ω SST model are employed to simulate the turbulent flow around AUV hulls. Besides, adjointOptimisationFoam solver is used to perform the shape optimization. Two different unconstrained and constrained optimizations of AUV hulls are conducted at an angle of attack (α) equal to 0°. In the unconstrained optimization, the drag force is chosen as an objective function to be minimized while a partial volume is considered as a geometric constraint in the constrained optimization. The predicted drag force is validated against experimental results from the literature, indicating a mere 0.58% discrepancy. In the unconstrained optimizations, the first and second AUV hulls reveal a 4.17% and 3.66% reduction in the drag force, respectively. In the constrained optimizations of the first and second AUV hulls, drag force is reduced by 3.25% and 2.63%, respectively.

Large Eddy Simulation of Ammonia-Hydrogen Non-Premixed Flames Stabilized on a Bluff Body Burner

Abstract The demand for carbon-free fuels such as NH3 and H2 has been growing due to stricter environmental policies on carbon emissions. Since ammonia is easier to store and transport, it is considered an alternative fuel for marine, aviation, and gas turbine industries. However, the narrow flammability, low reactivity, and potential emissions of NOx are important challenges that need to be overcome if ammonia is to be used as a practical fuel for industrial use. Recent works have provided experimental data on the characteristics of NH3 flames under premixed and non-premixed combustion, focusing on flame speed, turbulence-chemistry interaction, and especially the dissociation/cracking of NH3 into H2 and N2. These measurements have encouraged the use of CFD for the simulation and scaling of practical ammonia systems, evaluating the performance of different numerical models for NH3 combustion. In this study, LES is utilized to predict a series of NH3/H2/N2 non-premixed flames stabilized on a bluff body burner. The accuracy of the FGM combustion model combined with LES has been examined, using a commercial CFD solver. The different cracking levels of NH3 into H2 and N2 lead to simulation cases ranging from an H2/N2 flame (i.e., “fully cracked”), to a flame with 50% NH3 (i.e., “half cracked”). The different flame shapes, temperature distributions, and NOx emissions have been simulated, generally matching well experimental data. The developed numerical settings and workflows may be applied to simulating more complex combustors which use NH3 as a fuel.

Numerical Study of Low Engine Order Excitations due to Manufacturing Variability Part 1: Characterization of the Geometric Scatter and its Effect on Forced Response

Abstract The geometric scatter in the surfaces of blades and vanes due to manufacturing variability has an impact on the dynamics but also on the aerodynamics. The loss of the spatial periodicity of the flow due to the geometric variations generates an aerodynamic forcing with a wave number different from the airfoil count on the adjacent rows. In this paper, deviations from the nominal geometry are obtained from a set of scanned parts. The average manufactured geometry is computed through the point-by-point deviations between the scanned parts and the nominal geometry. Then, Principal Component Analysis is applied to the deviations from the average geometry to find a way to describe them in a simple manner. The cold geometries are reconstructed using the mean geometry and the PCA geometric modes; afterwards, a cold-to-hot process is applied to obtain the hot geometry, and finally the resulting aerodynamics are obtained using an in-house CFD solver. The described method is applied to a representative row constituted by packets of vanes. Firstly, the average packet geometry is used to analyze the aerodynamic forcing associated to the geometric variation of the airfoils inside the vane packet. After that, a conceptual study is carried out under some simplified assumptions in order to relate the geometric variability to random low engine order disturbances, using the geometric modes obtained from the PCA analysis. In both cases, the induced vibrations on the adjacent rotor row are comparable to the excitation due to the nominal blade-passing.

Application of graph neural networks to predict explosion-induced transient flow

We illustrate an application of graph neural networks (GNNs) to predict the pressure, temperature and velocity fields induced by a sudden explosion. The aim of the work is to enable accurate simulation of explosion events in large and geometrically complex domains. Such simulations are currently out of the reach of existing CFD solvers, which represents an opportunity to apply machine learning. The training dataset is obtained from the results of URANS analyses in OpenFOAM. We simulate the transient flow following impulsive events in air in atmospheric conditions. The time history of the fields of pressure, temperature and velocity obtained from a set of such simulations is then recorded to serve as a training database. In the training simulations we model a cubic volume of air enclosed within rigid walls, which also encompass rigid obstacles of random shape, position and orientation. A subset of the cubic volume is initialized to have a higher pressure than the rest of the domain. The ensuing shock initiates the propagation of pressure waves and their reflection and diffraction at the obstacles and walls. A recently proposed GNN framework is extended and adapted to this problem. During the training, the model learns the evolution of thermodynamic quantities in time and space, as well as the effect of the boundary conditions. After training, the model can quickly compute such evolution for unseen geometries and arbitrary initial and boundary conditions, exhibiting good generalization capabilities for domains up to 125 times larger than those used in the training simulations.

Numerical simulation of interior ballistics two-phase flow in modular charge based on the particle element method

The full combustibility and strong discontinuity characteristics of module charge result in significant differences from conventional mode, making it challenging for traditional two-fluid methods to effectively reveal its particle dispersion mechanism. In this study, the particle element method for module charge were developed and applied for modeling the interior ballistics to overcome above drawback. Firstly, based on the characteristics of module charge and particle aggregation, criteria for dividing particle elements and methods for motion calculation are proposed. Next, particle element solver and CFD solver are constructed and mutually coupled for solution. Finally, validation is conducted under the condition of three modules charging. The computational results show that the particle element method can effectively predict the pressure and velocity inside the chamber, consistent with experimental results, the pressure error is 5.55 % and the velocity error is 0.79 %. The particle element method reproduces the combustion process with variable particle mass, accurately presenting the distribution of the flow field and temperature. Moreover, it fundamentally explains that pressure fluctuations occur due to the presence of free space and changes in the flow field caused by the movement of the propellant bed. The particle element method can provide scientific research methods and technical support for the development of module charge technology.

Physical mechanism for prolonged test duration in shock tubes

The main challenge in the operation of shock tubes is the very short test time. Hence, this work was carried out to optimize the ratio of driver section to driven section length and to investigate its effect on the test time in a shock tube. Three different cases were tested in this paper for driver to driven tube length ratio of 2, 1, and 0.5. The study was conducted numerically using ANSYS Fluent CFD solver and k-epsilon realizable turbulent model. The shock wave strength and speed were monitored at two different locations downstream the driven tube for diaphragm pressure ratio of 10. The numerical model was verified with experimental measurements in a shock tube apparatus at the College of Engineering, Universiti Tenaga Nasional, Malaysia (UNITEN). From the numerical and experimental data, the primary shock strength was very comparable, while using low pressure ratio of 10. Subsequently, higher pressure ratio of 20 and 30 were implemented and the results were compared to select the longest test time. A driver section to driven section ratio of 2 resulted in a longer test time of approximately of 20 ms. In addition, insignificant reduction in the test duration of about 5 % was observed after increasing the driver tube pressure to 30 kPa. In contrast, higher peak pressure was recorded for pressure ratio of 30 for all three cases.

Comparison of applied loads on horizontal axis wind turbine blades using an open-source software Qblade and CFD solver ANSYS-FLUENT

Comparison of applied loads on horizontal axis wind turbine blades using an open-source software Qblade and CFD solver ANSYS-FLUENT

Multiscale CFD analysis of urban air pollution dome and ventilation enhancement via an urban chimney

Air pollution episodes are critical environmental challenges in urban areas, primarily linked to the lack of ventilation during calm and stable atmospheric conditions, rather than a significant increase in emissions. The prevailing circulation pattern under these conditions is the Urban Heat Island Circulation (UHIC), which governs the characteristics of the urban pollution dome and the distribution of pollutants. This study aims to assess the UHIC's influence on spatial and temporal variations in pollutant concentrations and to investigate the efficiency of an Urban Chimney (UC) in improving air quality. Due to the interaction of micro- and meso-scale flows, a multi-scale analysis is required. For this purpose, a pressure-based CFD solver is adapted for analyzing airflow and pollutant dispersion in a multi-scale environment. A coordinate transformation method is used to account for meso-scale effects, and the resulting source terms are applied to the solver. The species transport equation is transformed to the new coordinate system, and the effects of species diffusion on enthalpy transport are included in the governing equations. The results demonstrate that UHIC reduces the average pollutant concentration and causes pollution peaks near ground level and at the city center. The interaction of micro-scale flow within the chimney with meso-scale UHIC impacts the flow field and pollutant concentration across the entire domain, decreasing the urban plume's vertical velocity by 40 percent and the mixing height at the city center by 20 percent. It also increases the vertical velocity within the UC by 23 percent. The UC can serve as a controlling tool for urban ventilation, and its capacity to remove pollutants increases sixfold when interacting with UHIC, reducing pollutant concentration citywide.

A generalized framework of two-way coupled numerical model for fluid-structure-seabed interaction (FSSI): Explicit algorithm

In a complex marine dynamics environment, the consideration of fluid-structure-seabed interaction (FSSI) plays a vital role in reliably analyzing the dynamic response of marine structures, and in assessing their structural dynamic stability. Currently, the predominant numerical analysis used worldwide for the problems of wave-seabed interaction and seawater-structure-seabed interaction is primarily the one-way coupling method. While only a few two-way coupled models are being developed. Consequently, two issues are brought up: (1) For the cases involving small deformation and displacement, the degree of discrepancy can't be quantitatively identified between the results obtained respectively from one-way coupling models and two-way coupled models which are more rigorous in mathematics and physics. (2) For the cases involving large deformation and displacement, one-way coupling models should be non-applicable. To address this problem, this study first proposes an explicit two-way coupling theory for the fluid-structure-seabed interaction. Then, a two-way coupled numerical model is developed by integrating the soil-structure dynamics software FssiCAS, and an OpenFOAM-based CFD solver OlaFlow by utilizing the data exchange library preCICE. This two-way coupled model has been embedded into the software FssiCAS. The reliability of the developed two-way coupled model is systematically validated through a rigorous verification process. Subsequently, a comparative study is conducted between the newly developed two-way coupled model and the existing one-way coupling model, to investigate the ocean wave-seabed interaction, as well as the interaction process between ocean wave, a breakwater, and seabed foundation. A comprehensive analysis is performed by comparing the differences in the wave profiles in fluid domain, dynamic displacement of structure and seabed foundation, seepage, pore pressure accumulation, and liquefaction in seabed foundation solved by the two-way and one-way coupled models. Finally, the suitability of the one-way and two-way coupled models in different applicable scenarios was discussed.

Numerical Simulations of a Ship’s Maneuverability in Shallow Water

It is necessary to maintain maneuverability for ship navigation in shallow water, such as channels, ports and other confined waters. In this study, a turning circle maneuver with 35° rudder deflection and a 20/5 zigzag maneuver for KVLCC2 in shallow waters are tested numerically to directly predict the maneuverability of the ship in shallow water. A viscous in-house CFD solver is applied with the dynamic overset grid approach. The impacts of the water depth on the ship’s maneuverability in terms of turning and zigzag competence are evaluated, and the underlying mechanism is analyzed. The numerical method is validated by comparing it with experimental data on the turning indices, which shows good agreement. It is demonstrated that the turning capability become worse with a smaller depth–draft ratio, thus resulting in a lower yaw rate and a greater steady turning diameter. However, the drift angle and lateral speed are reduced with a smaller depth–draft ratio for zigzag maneuvers, but the overshoot angle and turn lag vary with the water depth non-monotonically.

Cause-and-effect chain analysis of combustion cyclic variability in a spark-ignition engine using large-eddy simulation, Part I: From tumble compression to flame initiation

Understanding, modeling, and reducing the cycle-to-cycle variability (CCV) of combustion in internal combustion engines (ICE) is a critical challenge to design engines of high efficiency and low emissions. A high level of CCV may contribute to partial burn, misfire, and knock in extreme engine cycles, which affects engine performance and eventually damages the engine. The origins of CCV have been studied both experimentally and numerically, and the variability of in-cylinder aerodynamics is recognized as one of the most important sources of CCV. However, a detailed and quantitative explanation of how in-cylinder flow CCV is generated is not yet clear. The objective of the present study is to develop a methodology to localize inside the chamber of a spark-ignition engine (SIE) the origins of flow variabilities and to identify some driving mechanisms leading to combustion variabilities. Multi-cycle wall-modeled large-eddy simulations (LES) for the TU Darmstadt optical engine under fired conditions are performed using the CFD solver Converge 3.0. The evolution of organized large-scale structures and the small-scale turbulence of the in-cylinder flow are analyzed using a developed methodology that includes the empirical mode decomposition (EMD) method adapted for 2D and 3D flow fields, and a vortex identification tool Γ3p. The contributions of different parts of the flow to CCV are quantified. In Part I of this work, the LES framework is validated against experimental data, and CCV of large-scale structures is characterized at spark timing. In Part II, the overall flow development during compression and intake strokes are quantitatively analyzed, and links are built between different engine phases to establish the cause-and-effect chain. Other CCV factors, such as spray injection and exhaust gas recirculation, are not included in the current study. However, the developed methodology for in-cylinder flow analysis could be used in studies on other engine configurations to improve the development of engine designs.Novelty and significance statementIn this work, the cycle-to-cycle variability (CCV) of combustion in a spark ignition engine is investigated to give a deeper understanding of CCV generation. The present study focuses on CCV caused by the stochastic nature of internal turbulent flow structures. LES approach is chosen due to its ability to capture CCV. The LES methodology was validated in a motored case in Ding et al. (2023). In the present study, it is validated in a reactive case against experimental in-cylinder pressures and velocity fields.A first novelty is the application of EMD methods combined with topology-based techniques to reactive LES results to characterize flow structures of different scales in the three-dimensional domain and to quantify separately their impacts on combustion.A second novelty and important finding is that a link is established between the combustion speed and the tumble formation and destabilization near BDC.Throughout our analyses in Part I and II, starting from the spark-ignition timing and going back to the early intake phase, a cause-and-effect chain is finally established between the development of in-cylinder flow and the combustion variability.

Numerical prediction of aerodynamic loads acting on a blade section-model oscillating in stall

For blades operating close to stall angle of attack, one of the potential instabilities is known as stall flutter. It is a dynamic instability in torsion for which the mechanism of energy transfer relies on a dynamic stall process where the flow separates partially or completely during each cycle of oscillation. It leads to dynamic loops in lift, drag and moment that affect the aerodynamic performance of the blade, create unsteady stresses in the blades and can lead to fatigue damage. In the present study, dynamic loops of a NACA 634421 airfoil in forced pitch oscillations have been simulated with the FastS CFD solver based on a URANS modelling approach and compared to benchmark experiments as well as results obtained with the ONERA semi-empirical dynamic stall model using a unique set of dynamic parameters that best fit the experimental dynamic loops. The dynamic tests have been conducted for a mean angle of attack of 13.5°, an amplitude of oscillation of 8° and three reduced frequencies k 1 = 0.0183, k 2 = 0.0785 and k 3 = 0.183. This study has shown that the CFD FastS solver can satisfactorily reproduce the unsteady lift and moment coefficients experienced by a section model oscillating in stall.

Multi-fidelity, steady-state aeroelastic modelling of a 22-megawatt wind turbine

In this work we present multi-fidelity steady-state aeroelastic framework that leverages the state-of-the-art simulation tool HAWC2 for the structural model, and a variety of aerodynamic models, comprising of the low fidelity blade element momentum (BEM) method, the medium fidelity blade element vortex cylinder (BEVC) method and the coupled near wake and vortex cylinder method, and finally the high-fidelity CFD solver EllipSys3D. The aeroelastic framework is part of AESOpt, an aerostructural framework for design of wind turbine blades. The different aerodynamic models are applied to compute the aeroelastic steady state of the newly designed IEA 22 MW Reference Wind Turbine. The results show a very good agreement between the medium- and high-fidelity aerodynamic models with a maximum of 2.7% difference between the high-fidelity aeroelastic response and that of the lower fidelities.

Parametric investigation of the effects of variables controlling thermal characteristics during continuous and high-speed cold stamping processes with active cooling structures

Knowledge of the thermal phenomena that occur during stamping is important for improving the design and performance of stamping die thermal structures. A new mathematical full-scale model for energy and carbon flows is established based on operational data from a cold stamping production line in China. Moreover, numerical simulations of the thermal-fluid–solid coupling field for a cooling medium in an asymmetrically heated rectangular channel with high heat flux and strong wall superheating are carried out with a suitable CFD solver. The results are discussed in detail and compared with theoretical calculations, and the deviation of the surface heat transfer coefficient is ± 11.9 %. Emphasis is placed on parametric effects of variables controlling thermal characteristics on cold stamping with an active cooling structure. The effects of heat flux, and ambient temperature on temperature rise, pressure drops, and heat transfer coefficients are limited less than 7 °C, 167 Pa and 45.11 % under specific operating conditions, respectively. While the heat transfer coefficient and pressure drops are increased hundreds of times with inlet velocity. The fluid cooling performance, threshold value, and approaches for heat transfer enhancement are obtained. Finally, the CO2 emissions rates is assessed as approximately 1.8 g per piece associated with stamping operations, as well as major contributors, CO2 reduction potential, and economic impacts. Negative energy consumption can be achieved with active cooling. These results can help to improve production quality in the future application and provide theoretical support for determining the causes of metal sheet tensile cracking accidents.

Coupling a nonlinear finite element mooring model with an overset CFD solver for dynamic analysis of floating structures in waves

An accurate prediction of motion responses of a moored floating structure requires high-fidelity coupled analysis between the structure and its mooring system in waves, which involves both mooring line dynamics and fluid dynamics. In this paper, we develop a nonlinear finite element dynamic mooring analysis module that allows large axial stretching of mooring lines under the open source CFD framework OpenFOAM, and couple it with an Overset CFD solver to establish a fully coupled finite element mooring-CFD analysis model for floating structures. The coupled model is advantageous over existing models in that it is able to deal with large axial mooring stretching and complex mesh motions induced by significant structure responses under severe operating conditions. The developed dynamic mooring analysis method is firstly validated against publicly available data. In order to validate the coupled model, a series of experimental tests were carried out for a semi-submersible platform moored by eight catenary lines under different operating conditions, including free decay, regular and irregular wave tests. The dynamic responses of the floating structure and mooring tension are analyzed and compared with experimental data. Results show that numerically predicted structure responses and mooring tension are generally in good agreement with experimental measurements. Meanwhile, the strongly nonlinear large-amplitude resonant motions generated by the interaction of irregular waves with the moored floating structure are also investigated. Comparisons reveal that the coupled model can accurately predict the resonant spectral peaks of the structure responses, indicating that the it is capable of simulating large-amplitude motions of moored floating structures. The coupled model developed in this paper can be further applied to study the survivability of moored floating structures under harsh sea conditions.

On the Features of Numerical Simulation of Hydrogen Self-Ignition under High-Pressure Release

The paper is devoted to the comparative analysis of different CFD techniques used to solve the problem of high-pressure hydrogen release into the air. Three variations of a contemporary low-dissipation numerical technique (CABARET) are compared with each other and a conventional first-order numerical scheme. It is shown that low dissipation of the numerical scheme defines better resolution of the contact surface between released hydrogen and ambient air. As a result, the spatial structures of the jet and the reaction wave that arise during self-ignition are better resolved, which is useful for predicting the local effects of high-pressure hydrogen release. At the same time, the dissipation has little effect on the induction delay, so critical conditions of self-ignition can be reliably reproduced even via conventional numerical schemes. The test problem setups formulated in the paper can be used as benchmarks for compressible CFD solvers.

Numerical analysis of the effect of wave amplitude on thermohydraulic performance in a heat exchanger with sinusoidal wavy channels

With the increasing application of heat exchangers, the research has become increasingly comprehensive. Previous studies mainly focused on comparing the amplitudes to investigate the performance of heat exchangers, while the study of variable amplitude channel structures was limited. This study investigated the thermal-hydraulic performance of seven different sinusoidal channels with inclination angles of 20° and 30°, and their combinations. Using the CFD solver, simulations were conducted to assess the heat transfer capabilities of sinusoidal channels under various Reynolds numbers and different amplitude conditions, compared to straight channels and single amplitude sinusoidal channels. The results indicated that within one period, both the pressure drop and temperature difference exhibited a ripple trend of gradually decreasing amplitude. When evaluating the comprehensive performance of the channels, three trends emerged across the seven models, with the performance of the cold fluid and the hot fluid within the same group showing opposite trends. This suggested that more variations could enhance the overall performance of the hot fluid while reducing the performance of the cold fluid. For structures with the same amplitude, in terms of amplitude variation frequency, models with six periods per group exhibited higher overall heat transfer performance than those with three periods per group, with an average increase of 36.37%. For the arrangement of amplitudes (taking the hot fluid inlet as an example), configurations with a smaller amplitude at the inlet outperformed those with a larger amplitude, indicating that in combined amplitude models, a structure with a larger group and a smaller amplitude at the inlet (taking the hot fluid as an example) should be designed.

Transient and Dynamic Simulation of the Fluid Flow through Five-Way Electric Coolant Control Valve of a 100 kW Fuel Cell Vehicle by CFD with Moving Grid Technique

In order to maintain the performance of a fuel cell vehicle, it is essential to maintain a constant temperature of the stack. Therefore, it is very important to distribute the optimal coolant flow rate to each major component under very diverse and rapidly changing dynamic operating conditions. The part responsible for this is a five-way electric coolant valve. Therefore, this study aims to investigate transient dynamic flow characteristics of the fluid flow through a five-way electric coolant valve (PCCV: Penta-Control Coolant Valve). To achieve this goal, this paper attempts a three-dimensional dynamic simulation of the fluid flow through the valve using a commercial CFD solver with moving mesh technique to consider flow inertia and dynamic flow in the opening and closing stages of the ball valve rotating motion. The dynamic flow characteristics and the thermal mixing inside the PCCV ball valve during the opening and closing stages are analyzed. It was found that the discrepancies between dynamic and steady-state simulations are remarkable when fluxes with different levels of enthalpy and momentum flow into the PCCV, leading to strong flow interference and flow inertia, while the discrepancies are relatively small at low rotation speed and weak flow interference. Subsequently, the effect of the dynamic flow characteristics of the valve on the dynamic thermal mixing characteristics at two different ball valve rotation speeds and rotation directions are investigated. It was found that the dynamic flow and thermal mixing characteristics inside the PCCV are greatly affected by the rotation speed, rotation direction, and degree of flow interference between fluxes. It also helps design better coolant control strategies and improves the FCEV thermal management system.