Conventional Computational Fluid Dynamics Methods Research Articles

Strategies for multi-case physics-informed neural networks for tube flows: a study using 2D flow scenarios

Fluid dynamics computations for tube-like geometries are crucial in biomedical evaluations of vascular and airways fluid dynamics. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional computational fluid dynamics (CFD) methods. However, vanilla PINNs often demand longer training times than conventional CFD methods for each specific flow scenario, limiting their widespread use. To address this, multi-case PINN approach has been proposed, where varied geometry cases are parameterized and pre-trained on the PINN. This allows for quick generation of flow results in unseen geometries. In this study, we compare three network architectures to optimize the multi-case PINN through experiments on a series of idealized 2D stenotic tube flows. The evaluated architectures include the ‘Mixed Network’, treating case parameters as additional dimensions in the vanilla PINN architecture; the “Hypernetwork”, incorporating case parameters into a side network that computes weights in the main PINN network; and the “Modes” network, where case parameters input into a side network contribute to the final output via an inner product, similar to DeepONet. Results confirm the viability of the multi-case parametric PINN approach, with the Modes network exhibiting superior performance in terms of accuracy, convergence efficiency, and computational speed. To further enhance the multi-case PINN, we explored two strategies. First, incorporating coordinate parameters relevant to tube geometry, such as distance to wall and centerline distance, as inputs to PINN, significantly enhanced accuracy and reduced computational burden. Second, the addition of extra loss terms, enforcing zero derivatives of existing physics constraints in the PINN (similar to gPINN), improved the performance of the Mixed Network and Hypernetwork, but not that of the Modes network. In conclusion, our work identified strategies crucial for future scaling up to 3D, wider geometry ranges, and additional flow conditions, ultimately aiming towards clinical utility.

Evaluation of the overset method applied to an active lift turbine

In the current context of energy transition, the development and improvement of energy recovery systems is essential. These system are numerous and some of them use turbines to convert flow kinetic energy into electricity. For a long time, vertical-axis turbines were considered less efficient than horizontal-axis ones. However, they are still better suited to urban areas. Thus, they are now being studied again and new turbine concepts are emerging that can works differently from today’s turbines. The entire dynamics of these new-generation turbines can be completely different from those of conventional turbines. The active lift turbine, for example, changes the trajectory of the blades (by varying the turbine radius) to convert the normal forces applying on them into torque. This particularity hinders the use of conventional rotation methods for turbines (Arbitrary Mesh Interface (AMI), Rotating Frame of Reference (RFR), …) in Computational Fluid Dynamics (CFD) and an innovative method such as overset could be an alternative. The purpose of this work is to evaluate the overset method for these new-generation turbines modelling. It enables the motion of a structure in its environment to be controlled at will. Various modelling parameters are being tested. The impact of the mesh size (mesh convergence), the turbulence modelling approach (RANS/LES) and the interpolation method between the background mesh and the overset mesh (Cell Volume Weight/Inverse distances) are evaluated and compared. The overset method is first validated on a conventional turbine (Darrieus turbine). The results obtained for the conventional turbine are close to those expected, with a relative error (numerical/experimental) between 3% and 8% depending of the Tip Speed Ratio (TSR) with an averaged error around 7%. Then overset method is extended to an active lift turbine to assess the potential of this new technology. The overset method proves its worth for this type of problem, which cannot be solved by conventional CFD methods of setting structures into motion. It provides control over blade motion without loss of information. Overall, this study demonstrates the interest and applicability of the overset method to the Active Lift Turbine or other kind of turbines that have a specific motion.

Photogrammetry-based computational fluid dynamics

Computational fluid dynamics (CFD) is the cornerstone of the design and analysis process in many engineering applications. Not only has it been applied in the design phase, but it has also been employed for analyzing the fluid flow phenomena during the operation phase for many in-use structures, such as vehicles, buildings, and landscapes. However, creating a 3D mesh-based model of in-use structures that can be used by conventional boundary-fitted CFD methods is labor-intensive, time-consuming, and sometimes impossible. Due to the challenges introduced by geometry complexity and lack of design information, it is often difficult to perform an accurate and efficient CFD analysis of these objects. This paper aims to overcome such challenges by proposing a novel photogrammetry-based CFD framework for simulating in-use structures whose design models and analysis meshes are hard to obtain. The proposed framework integrates machine learning-based 3D point cloud reconstruction of structures from 2D images obtained from portable devices (e.g., cell phones and drones) and an immersogeometric approach that can carry out flow analysis directly on reconstructed point clouds. We first present the technical details of point cloud reconstruction techniques and the immersogeometric analysis method. We then simulate the flow past a standard 12 oz soda can reconstructed using photogrammetry and compare the results with reference solutions to assess the accuracy of the approach. Finally, the proposed photogrammetry-based CFD is applied to simulations of a bell tower and the Kavita and Lalit Bahl Smart Bridge on the University of Illinois Urbana-Champaign (UIUC) campus to demonstrate the robustness of the framework and its applicability to real-world in-use civil structures.

Modeling of 3D Blood Flows with Physics-Informed Neural Networks: Comparison of Network Architectures

Machine learning-based modeling of physical systems has attracted significant interest in recent years. Based solely on the underlying physical equations and initial and boundary conditions, these new approaches allow to approximate, for example, the complex flow of blood in the case of fluid dynamics. Physics-informed neural networks offer certain advantages compared to conventional computational fluid dynamics methods as they avoid the need for discretized meshes and allow to readily solve inverse problems and integrate additional data into the algorithms. Today, the majority of published reports on learning-based flow modeling relies on fully-connected neural networks. However, many different network architectures are introduced into deep learning each year, each with specific benefits for certain applications. In this paper, we present the first comprehensive comparison of various state-of-the-art networks and evaluate their performance in terms of computational cost and accuracy relative to numerical references. We found that while fully-connected networks offer an attractive balance between training time and accuracy, more elaborate architectures (e.g., Deep Galerkin Method) generated superior results. Moreover, we observed high accuracy in simple cylindrical geometries, but slightly poorer estimates in complex aneurysms. This paper provides quantitative guidance for practitioners interested in complex flow modeling using physics-based deep learning.

Direct modeling for computational fluid dynamics and the construction of high-order compact scheme for compressible flow simulations

Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, numerical scale-consistent transport process, and similar domain of dependence and influence in the physical and the numerical wave propagations. Therefore, a physically soundable numerical scheme should be a compact one which involves the closest neighboring cells within the domain of dependence for the solution update under a CFL number (∼1). In order to keep the compactness of the scheme and be high-order, subcell flow distributions or the equivalent degrees of freedom beyond the cell averaged flow variables are needed, such as the gradients of the flow variables inside each control volume. Under the above consideration, the direct use of Riemann solver as the evolution model doesn't provide such a mechanism. High-order dynamic evolution process should be used to update the time accurate cell-averaged flow variables and their gradients. The direct modeling of flow evolution under generalized initial condition will be developed. In order to provide reliable cell averaged flow variables and their gradients for the compact data reconstruction, the evolution process is constructed to provide possible discontinuous time-dependent flow variables across a cell interface. At the same time, the time accurate flux function at a cell interface can become a discontinuous function of time in its evolution process. Same as the spatial limiter in the conventional computational fluid dynamics methods, such as the total variation diminishing and weighted essentially non-oscillatory methods, the temporal limiter for the time accurate flux function is designed as well. The direct modeling method in this paper will update flow variables differently on both sides of a cell interface and nonlinearly limit the high-order time derivatives of the flux function in case of shock wave passing through a cell interface within a time step. The direct modeling method unifies the concepts of nonlinear limiters in spatial data reconstruction and temporal flux transport. The equivalent treatment of space and time makes the compact gas-kinetic scheme be super robust and accurate for the compressible flow simulation. At the same time, the 4th to 8th-order compact schemes can use a large CFL number (∼0.8) in flow computation, even for the hypersonic flow simulation.

Simplified hydrodynamic-wave particle method for the multiscale rarefied flow

Coupling the Computational Fluid Dynamics (CFD) with the stochastic particle method to address multi-scale rarefied flows remains of great interest to many researchers. Rather than involving the field decomposition and the information exchange, the simplified hydrodynamic-wave particle method (SHWPM) has been proposed in this paper to automatically switch from the stochastic particle solver to the conventional CFD method in the multi-scale simulation. The weights to couple the respective numerical fluxes are derived based on the integral solution of the Boltzmann equation. By introducing the simplified hydrodynamic-wave flux that can be computed by the linear combination of inviscid and viscous fluxes from the conventional CFD solver, the collision effects of particles are calculated in a macroscopic approach and the number of sampling particles could be significantly reduced in the near-continuum regime. Error analysis demonstrates that the simplified treatment can preserve the second-order accuracy and asymptotic preserving property of the present method in both the continuum and free molecular limits. Several numerical cases over a wide range of Knudsen and Mach numbers exhibit the capability of SHWPM for modeling the multiscale flow accurately and efficiently. The example of hypersonic flow passing a cylinder shows that the SHWPM could achieve tens of times speedup ratio compared to the discrete velocity method (DVM) in the continuum regime.

Fast 3D computations of compressible flow discharge in buildings and complex networks

This paper presents under-resolved simulations of compressible flows in complex structures like buildings. The mean pressure field is the primary focus as it is of high importance in many cases, such as the overpressure generated by the detonation of an explosive charge. In such high-risk situations, the mean pressure in the different building rooms has to be determined as quickly as possible, in order to help first responders evaluating the risk level of entering the building right after an explosion for instance. Conventional computational fluid dynamics methods are obviously able to deliver those requested pressure fields. However, they also require a long and tedious meshing process due to the presence of small openings in the computational domain (doors, windows or stairwells). In turn, these small openings need spatial and temporal resolution having significant consequences on computation time. But when dealing with pressing situations, a long pre-processing is not acceptable. The present paper proposes a two-step solution method. First, a very rough mesh is constructed which does not consider small openings. The mesh is constructed in an easy and particular way such that simplifications can be made when computing the fluid flux through these openings. Second, a specific Riemann solver dealing with geometric discontinuities is developed to estimate the fluid flow. The Riemann solver takes advantage of the simplifications provided by the meshing method, and accounts for both unchoked and choked flows through openings. The overall method then consists of both a specific meshing process that requires very little pre-processing, which considerably reduces the time needed to produce a complete simulation, and a Riemann solver. The proposed method is named MUZO in reference to its “MUlti-ZOne” flow solver. The MUZO solver is validated against resolved computations and provides accurate simulated mean pressure fields within a realistic building in a few seconds.

Quantifying the Permeability Enhancement from Blast-Induced Microfractures in Porphyry Rocks Using a Cumulant Lattice Boltzmann Method

The permeability of rocks is important in a range of geoscientific applications, including hbox {CO}_{2} sequestration, geothermal energy extraction, and in situ mineral recovery. This work presents an investigation of the change in permeability in porphyry rock samples due to blast-induced fracturing. Two samples were analysed before and after exposure to stress waves induced by the detonation of an explosive charge. Micro-computed tomography was used to image the interior of the samples at a pixel resolution of 10.3,mu m. The images were segmented into void, matrix, and grain to help quantify the differences in the rock samples. Following this, they were binarised as void or solid and the cumulant lattice Boltzmann method (LBM) was applied to simulate the flow of fluid through the connected void space. A correction required with the use of inlet and outlet reservoirs in computational permeability assessment was also proposed. Interrogation of the steady-state flow field allowed the pre- and post-loading permeability to be extracted. Conclusions were then drawn as to the effectiveness of blasting for enhancing fluid accessibility via the generation of microfractures in the rock matrix within the vicinity of a detonated charge. This paper makes contributions in three fundamental areas relating to the numerical assessment of permeability and the enhancement of fluid accessibility in low-porosity rocks. Firstly, a correction factor was proposed to account for the reservoirs commonly imposed on digitised rock samples when investigating sample permeability through numerical methods. Secondly, it validates the benefits of the LBM in handling complex geometries that would be intractable with conventional computational fluid dynamics methods that require body-fitted meshing. This is done with a novel implementation of the cumulant LBM in the open-source TCLB code. Finally, the improvement in fluid accessibility in low-permeability rock samples was shown through the assessment of multiple regions within two blasted samples. It was found that the blast-induced loading can generate extended microfractures that results in multiple orders of magnitude of permeability enhancement if the target rock possesses existing weaknesses and/or mineralisation.

Dual-Solver Hybrid Computational Approach to Integrated Propulsion Aerodynamics

The demand for high-efficiency air vehicles and the development of distributed electric propulsion systems for aircraft are exposing the need for accurate aerodynamic prediction of multiple integrated propulsion systems. Conventional high-fidelity computational methods are too expensive, and low-cost low-fidelity methods make too many aerodynamic assumptions to be applied to these analyses. Dual-solver hybrid computational fluid dynamics (CFD) methods bridge the gap between these two categories of solvers, but many lack capabilities that are needed for complex vehicles. Recent improvements to the hybrid solver OVERFLOW-CHARM provide efficient and accurate analysis of integrated propulsion systems with hybrid CFD methods, as demonstrated on the wing–propeller system of the AIAA Workshop for Integrated Propeller Prediction. Predictions of propeller thrust are within 1% of conventional CFD data, and wing pressure coefficient distributions agree well with both experimental data and conventional CFD methods. The dual-solver results were obtained at half the computational cost of the full CFD simulation.

Adaptive mesh refinement method for the reduction of computational costs while simulating slug flow

Microchannel flow boiling has been the focus of many experimental and numerical investigations due to the high heat transfer coefficients that it can induce. However, experimental research has been limited due to the small scales involved, leading researchers to employ computational fluid dynamics (CFD) simulations to resolve the dearth of research on microchannel flow boiling. Conventional CFD methods use a fine uniform mesh to capture the small scales and gradients, such as the liquid-vapour interface. This method has a large computational cost, and as a result, most research reported in the literature has been limited to two-dimensional axisymmetric domains. An interface-tracking adaptive mesh refinement model was created in this study to overcome the limitation of high computational costs without losing accuracy. This model dynamically refined the mesh only in the regions of interest and allowed a coarser mesh in the rest of the domain. This novel approach was able to recreate previously published results with a maximum error of 6.7%, while using less than 1.6% of the mesh elements. Several simulations were conducted in ANSYS Fluent 19.1 to determine the optimal settings for this new method to maintain accuracy and reduce cell count. These settings were determined as three levels of refinement (δL = 3), four refined cells on either side of the interface (δM = 4), and was implemented every five time steps (δT = 5). Finally, a case study was conducted to illustrate the possibility of simulating two-phase flow in microchannels in three dimensions with this method.

Prediction of 3D Cardiovascular hemodynamics before and after coronary artery bypass surgery via deep learning

The clinical treatment planning of coronary heart disease requires hemodynamic parameters to provide proper guidance. Computational fluid dynamics (CFD) is gradually used in the simulation of cardiovascular hemodynamics. However, for the patient-specific model, the complex operation and high computational cost of CFD hinder its clinical application. To deal with these problems, we develop cardiovascular hemodynamic point datasets and a dual sampling channel deep learning network, which can analyze and reproduce the relationship between the cardiovascular geometry and internal hemodynamics. The statistical analysis shows that the hemodynamic prediction results of deep learning are in agreement with the conventional CFD method, but the calculation time is reduced 600-fold. In terms of over 2 million nodes, prediction accuracy of around 90%, computational efficiency to predict cardiovascular hemodynamics within 1 second, and universality for evaluating complex arterial system, our deep learning method can meet the needs of most situations.

A velocity decomposition method combining potential and viscous flow for the estimation of submarine's hydrodynamic coefficients

Estimating hydrodynamic coefficients is important in the design of submarines. To enhance the efficiency of the computational fluid dynamics (CFD) method for evaluating the hydrodynamic performance of submarines, we have developed a velocity decomposition solver for the simulation of a moving body based on the open-source CFD platform OpenFOAM. The total velocity is decomposed into potential flow velocity and non-potential flow velocity. The potential flow velocity is further decomposed into unit components, which can be computed by the proposed method with less interpolation cost. Further, the original potential flow velocity can be recovered by linear summation of these unit velocity components. This avoids solving Laplace equation at each time step. The non-potential flow velocity is solved by using a complementary Navier–Stokes equation in a smaller domain as compared to that used in the conventional CFD method. In addition, a buffer source term is introduced for the transition of non-potential flow velocity to potential flow velocity. Oblique towing test and planar motion mechanism test are numerically simulated using the proposed method, which reveal good consistency between the experimental data and simulation results. This validates the efficiency and reliability of the proposed method in estimating the hydrodynamic coefficients of submarines.

Hypothesis-driven compartment model for stirred bioreactors utilizing computational fluid dynamics and multiple pH sensors

The ability to understand and predict mixing behaviour in stirred bioreactors through the use of mathematical models is an effective strategy to improve or ensure the performance of a process. Historically, compartment models have been developed to facilitate the prediction of hydrodynamics and in the last decade, computational fluid dynamics (CFD) has become the standard tool to assess this in detail. Despite the continuous increase in computational capacity, performing CFD simulations of bioreactors remains a challenge in industry, where the need for simplified models is apparent due to the complex phenomena occurring at the industrial scale. The combination of CFD and compartment models has been investigated in this work using a pilot scale stirred bioreactor equipped with three Rushton disc turbines and multiple pH sensors as a case study. A hypothesis-driven compartmentalization strategy, comprised of five steps, has been developed and applied to the pilot scale stirred bioreactor. The compartmentalization resulted in 56 compartments with unidirectional flow between adjacent compartments. The performance of the methodology was evaluated against a data-driven compartment approach and the full CFD simulation, in terms of its ability to recreate transient tracer profiles following top and bottom feeding of the tracer. The data-driven compartment model proved to be the most accurate of the three investigated methods, whereas the hypothesis-driven compartment method had a 10–12% higher error on prediction. Nevertheless, the developed methodology should be considered a viable alternative to conventional CFD methods, especially when models of complex phenomena – for example multi-dimensional population balance models – are to be incorporated in the final model as well.

Multiple-relaxation-time lattice Boltzmann method of hydrodynamic lubrication in lemon-bore bearing

The lattice Boltzmann method has superiority over conventional computational fluid dynamics methods, particularly for the flow simulations in complex geometries. In the present work, the performance of hydrodynamic lemon-bore (elliptical) journal bearings was investigated with the implementation of the lattice Boltzmann method. The steady-state laminar flow of a homogeneous oil was considered in the computations. A linear interpolation method was exploited to obtain the surface curvatures. The comparison of the results obtained from the proposed methodology with available literature data showed a satisfactory agreement. The effect of geometrical parameters on the hydrodynamic lubrication in an elliptical journal bearing was analyzed. It was found that the ellipticity ratio has profound effects on the bearing load capacity, oil flow rate and bearing power loss.

Consistent lattice Boltzmann equations for phase transitions.

Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

Innovative Grid-Based Vorticity–Velocity Solver for Analysis of Vorticity-Dominated Flows

Unsteady vorticity-dominated flows are prevalent in a wide variety of engineering applications and are particularly challenging to predict efficiently. Perhaps in no other application is this more apparent than rotorcraft, where prediction is complicated by a wide variety of interactional aerodynamics between strong vortical wakes shed from rotating components and various bodies and wings immersed in the flow. While conventional computational fluid dynamics methods are equipped with the modeling capabilities to support these flow behaviors, they are subject to significant numerical diffusion whose practical import is that high computational costs involving large grids, complex adaptation methods, and high interpolation orders are required to produce sufficiently accurate simulations and prevent the artificial diffusion of vortical structures. Hybrid computational fluid dynamics methods that couple a body-fitted solver to a vorticity–velocity method hold considerable promise in alleviating these costs while effectively preserving vorticity. However, several fundamental and long-standing issues identified with vorticity–velocity methods have precluded their wider adoption. Here, the four most prominent concerns are addressed: 1) maintaining a solenoidal vorticity field; 2) supporting a low-dissipation/dispersion scheme on a general multiresolution grid; 3) providing a consistent and efficient implementation of the viscous terms; and 4) properly including the unsteady pressure contributions.

Layout synthesis of fluid channels using generative graph grammars

AbstractThis paper presents a new technique for shape and topology optimization of fluid channels using generative design synthesis methods. The proposed method uses the generative abilities of graph grammars with simulation and analysis power of conventional computational fluid dynamics methods. The graph grammar interpreter GraphSynth is used to carry out graph transformations, which define different topologies for a given multiple-inlet multiple-outlet problem. After evaluating and optimizing the generated graphs, they are first transformed into meaningful three-dimensional shapes. These solutions are then analyzed by a computational fluid dynamics solver for final evaluation of the possible solutions. The effectiveness of the proposed method is checked by solving a variety of available test problems and comparing them with those found in the literature. Furthermore, by solving very complex large-scale problems, the robustness and effectiveness of the method is tested. To extend the work, future research directions are presented.

A New Single-blade Based Hybrid CFD Method for Hovering and Forward-flight Rotor Computation

A hybrid Euler/full potential/Lagrangian wake method, based on single-blade simulation, for predicting unsteady aerodynamic flow around helicopter rotors in hover and forward flight has been developed. In this method, an Euler solver is used to model the near wake evolution and transonic flow phenomena in the vicinity of the blade, and a full potential equation (FPE) is used to model the isentropic potential flow region far away from the rotor, while the wake effects of other blades and the far wake are incorporated into the flow solution as an induced inflow distribution using a Lagrangian based wake analysis. To further reduce the execution time, the computational fluid dynamics (CFD) solution and rotor wake analysis (including induced velocity update) are conducted parallelly, and a load balancing strategy is employed to account for the information exchange between two solvers. By the developed method, several hover and forward-flight cases on Caradonna-Tung and Helishape 7A rotors are performed. Good agreements of the loadings on blade surface with available measured data demonstrate the validation of the method. Also, the CPU time required for different computation runs is compared in the paper, and the results show that the present hybrid method is superior to conventional CFD method in time cost, and will be more efficient with the number of blades increasing.

A fourth‐order Cartesian local mesh refinement method for the computational fluid dynamics of physiological flow in multi‐generation branched vessels

AbstractSince abnormal fluid states in our body cause critical diseases, patient‐specific computational fluid dynamics (CFD) probably become a standard diagnosis tool in the near future. The vessels in our body are multiple‐branched tubes, which makes it difficult to obtain accurate solutions from conventional CFD methods. In this report, we propose a fourth‐order local mesh refinement (LMR) method based on an interpolated differential operator scheme for simulating flow in multi‐generation branched vessels. The proposed LMR method has the accuracy of fourth‐order for three‐dimensional advection and diffusion equations, respectively. We describe how to apply the LMR method to patient‐specific pulmonary airflow simulations. In our method, the computational mesh size is determined locally by geometrical parameters: the diameter of airways and the distance from the airway wall. To demonstrate our method, an LMR model and a fine mesh model were compared for flow in the central airway, and there was no significant difference between results. We also show the applicability of the method to a maximum eleventh‐generation airway model, where the number of computational nodes was reduced by 85% compared with the case using uniform fine meshes. Copyright © 2010 John Wiley & Sons, Ltd.

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations.