Momentum Equations Research Articles

A comprehensive modeling, analysis, and optimization of two phase, non–isobaric, and non–isothermal PEM fuel cell

This study models a non-isobaric, non-isothermal two-phase flow in a Polymer Electrolyte Membrane Fuel Cell (PEM-FC), focusing on conservation equations for mass, energy, and momentum across its components. Verification involves comparing PEM-FC performance and temperature distribution with experimental and literature data, showing consistent agreements. Results indicate that increasing cathode channel pressure enhances membrane moisture and reduces power loss. Higher oxygen partial pressure improves PEM-FC performance, whereas increased anode channel pressure heightens ohmic losses and lowers output voltage. Temperature distribution reveals highest temperatures near the cathode catalyst layer due to electrochemical reactions. Adjusting pressures in cathode and anode channels affects these temperatures accordingly. PEM-FC power density is optimized using various algorithms, with simulated annealing proving most effective. Optimal values for gas diffusion layer thickness, electrode porosity, and inlet humidity are determined. Under constant current density, power density increases by 6 % compared to baseline conditions, demonstrating effective parameter optimization for enhancing PEM-FC performance.

Performance of surface roughness of MHD slip velocity on curved circular and flat plates lubricated with non-Newtonian fluid

The current communication aims to discuss the influence of MHD slip velocity on curved circular and rough flat plate under the non-Newtonian fluid is considered. MHD momentum equation is reduced to ordinary differential equation and solved analytically. Christenson Stochastic theory is used to derive the radial and azimuthal surface roughness expression. From the Stochastic theory we derived non dimensional Reynolds equation also mathematical derivations for squeeze film pressure, load and squeezing time are derived analytically. Applied numerical method to illustrate pressure, load support & response time graphically. In contrast to the smooth case, the load-carrying capacity and response time for azimuthal (radial) roughness patterns are affected by the roughness parameter. Also the impact of MHD couple stress with slip velocity provides the rise of squeeze film attributes than the case of non-magnetic, Newtonian and smaller values of slip velocity.

A modal momentum method for the identification of structural weak links

In order to meet the demands of weak-link identification of mechanical structures in high-precision equipment, this paper introduces the concepts and equations of modal momentum and modal momentum difference ratio (MMDR), as well as an identification method of weak links based on modal momentum. In this method, the modal data of the mechanical structure is acquired first through experimental modal analysis or finite element analysis. The modal momentum of each measured point is calculated based on the modal data and transformed to the global coordinate system. Then, the MMDRs between the measured point with the largest magnitude of modal momentum and its adjacent measured points are calculated. Weak links are judged if the MMDR exceeds a predefined threshold. Twelve different multi-degrees-of-freedom systems incorporating weak links were designed and then identified using the proposed method. The accuracy of identification is up to 100% for these systems. The method was applied to a double pendulum angle milling head of a five-axis numerically controlled machine tool, and the result reveals that the side plate lacks bending stiffness.

Numerical investigation of different transverse Rib shapes on thermal convection in a channel filled with nanofluid

With the growing interest in energy optimization, corrugated surfaces are arguably an excellent choice, finding applications in areas as diverse as heat exchangers, automobiles, building energy efficiency, and chemical reactors. However, due to the poor thermal properties of conventional fluids, heat transfer is limited. The introduction of nanoparticles into fluids is a promising solution to improve their thermal performance. This paper does a detailed numerical analysis of how different factors affect the forced convection heat transfer in a two-dimensional ribed channel. The shape of the ribs is one of the factors that are looked at, along with some new parameters like e/H, which is the ratio of rib height to channel height, and L2/P, which is the test section to the pitch between the ribs. The aim is to determine the optimum geometry that maximizes the Nusselt number while minimizing the pressure drop. The study also examines the effects of nanoparticle type and concentration on heat transfer and fluid flow characteristics. To this end, the continuity, momentum, and energy equations were solved with the finite volume method using the SIMPLE scheme with the k-ε turbulence model at different Reynolds numbers ranging from 4000 – 14,000. The results indicate that triangular ribs with ratios e/H = 0.15 and L2/P = 4 increase the Nusselt number by 63.3 % while reducing the pressure drop by 22 % compared with the other cases. The improvement in heat transfer in the water-SiO2 case was the greatest compared with the other nanofluids tested. Particle size fraction and Reynolds number increased the Nusselt number in ribbed channels by 20.7 % compared with water.

Numerical modeling of transient water table in shallow unconfined aquifers: A hyperbolic theory and well-balanced finite volume scheme

We present a new methodology capable of modeling transient motion of shallow phreatic surface of groundwater in unconfined aquifers. This methodology is founded on a new and comprehensive theory for water table motion and a corresponding efficient numerical scheme. In the theoretical aspect, we derived a new set of governing equations constituted by a depth-averaged continuity equation and momentum equations based on unsteady Darcy’s law. The derived governing equations are of the hyperbolic type and possess stiff terms in the momentum equations due to the inertia motion in a characteristic time scale that is relatively shorter than the time scale of seepage motion. To effectively solve the derived hyperbolic system with stiff terms, in the numerical aspect, we utilize f-wave propagation algorithm, an explicit finite volume method, that can ensure numerical convergence and well-balancing solutions when momentum is rapidly relaxing to an equilibrium of steady state. Verification is successfully performed by comparing the results with analytic solutions to the classic problem of multidimensional spreading of a groundwater mound. This study demonstrates that the proposed methodology can accurately and satisfactorily simulate the spatiotemporal distribution of shallow water table and its wetting front in unconfined aquifers.

Thermohaline convection in MHD Casson fluid over an exponentially stretching sheet

Abstract This study investigates the thermohaline convection in MHD Casson fluid over an exponentially stretching sheet. This study has practical significance in industrial processes, materials processing, energy systems, and environmental applications. The governing equations describing the conservation for an electrically conducting fluid flow, thermal and concentration transports are considered based on the principles of mass, momentum, energy and concentration equations. Our first step involves transforming the governing nonlinear partial differential equations into a coupled nonlinear ordinary differential equations with the help of suitable similarity transformations. Second step, infinite domain [0, ∞) of the problem to a finite domain [0, 1] through a coordinate transformations. This specific choice is motivated by the wavelet's significance in the finite domain of [0, 1]. Third step, we effectively solve the resulting coupled nonlinear ordinary differential equations using the numerical Hermite wavelet method (HWM). This approach proves to be a valuable technique for obtaining significant results and insights in our study. Finally, the effect of known physical parameters on velocity, temperature and concentration are analysed through tables and graphs.

An immersed multi-material arbitrary Lagrangian–Eulerian finite element method for fluid–structure-interaction problems

Fluid–structure-interaction (FSI) phenomena are widely concerned in engineering practice and challenge current numerical methods. In this article, the finite element method is strongly coupled with the multi-material arbitrary Lagrangian–Eulerian (MMALE) method to develop a monolithic FSI method named the immersed multi-material arbitrary Lagrangian–Eulerian finite element method (IALEFEM). By immersing the finite elements in the MMALE computational grid, the fluid–solid interface is directly tracked by the element boundary with accurate normal directions. The fluid–structure-interaction is implicitly implemented by assembling the nodal variables and updating the Lagrangian momentum equation on the MMALE grid. Combining the advantages of both MMALE and FEM with the immersed boundary method, the IALEFEM is effective for solving complicated FSI problems with multi-material fluid flow. A slip fluid–structure-interaction method is also proposed to enhance the computational accuracy in simulating FSI problems with significantly different velocity fields. The accuracy and effectiveness of the IALEFEM are verified and validated by several benchmark numerical examples including the shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave, dam break problem with large structural deformation, water entry of a wedge, fragmentation of a cylinder shell induced by blast, response of elastic plate subjected to spherical near-field explosion and structural damage of open-frame building under blast loading.

A fuel cell performance simulation method based on pore-scale gas diffusion layer models obtained from X-ray computed tomography under different assembly pressures

The assembly pressure significantly influences the performance of proton exchange membrane fuel cells. In earlier studies, performance simulations based on volume-averaged formulae tended to smooth out the inherent non-uniformity of the gas diffusion layer (GDL) and this needs to be improved. In this study, an innovative simulation method is proposed for high-temperature proton exchange membrane fuel cells (HT-PEMFCs), which can directly couple pore-scale GDLs with fuel cells when examining fuel cell performance. We used X-ray CT to reconstruct a carbon fiber paper sample (TGP-H-060) under different pressures. These reconstructions were then directly coupled with volume-averaged components to form multiscale models of HT-PEMFCs. Governing equations of mass, momentum, species and charge were directly solved in the microstructure and fluid channels to obtain the polarization curve of the HT-PEMFC. The proposed model combines studies of fuel cell performance with evaluation of the properties of pore-scale GDLs. The results show that using the proposed method, not only can the influence of assembly pressure on the overall performance (i.e. polarization curves) of fuel cells be obtained, but also the influence of assembly pressure on the gas distribution in pore-scale channels of GDLs can be clearly revealed, which can guide the optimization of GDL structure.

Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction

This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is <i>θ</i>. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.

Viscoelasticity of maxell fluid in a permeable porous channel

This study examines the flow dynamics and heat transfer characteristics of Maxwell fluid in a channel influenced by magnetohydrodynamics (MHD), Joule heating, thermal radiation, and boundary layer suction/blowing effects. The governing partial differential equations (PDEs) for momentum, energy, and concentration are transformed into ordinary differential equations (ODEs) using similarity transformations. The boundary value problem (BVP) is solved numerically using the bvp4c solver in MATLAB, yielding accurate solutions for velocity, temperature, and concentration profiles under various parameters. Key findings reveal that the porous parameter decreases the velocity profile but increases the temperature profile for both suction and blowing effects. Additionally, the MHD, Deborah, and Eckert numbers significantly influence the velocity and temperature profiles differently under these conditions. This study highlights the crucial role of integrating MHD, thermal, and boundary control effects to optimize performance and efficiency in engineering systems involving Maxwell fluids, with applications in polymer processing, biomedical engineering, electronics cooling, oil recovery, and chemical processing.

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Thermohydrodynamic analysis of magnetorheological conical bearings with conjugated heat transfer

This study presents a comprehensive investigation into a 3D simulation of magnetorheological (MR) conical bearings, focusing on considering viscous dissipation using the conjugated heat transfer approach. The behavior of MR fluids is expressed through the utilization of the Bingham-Papanastasiou constitutive equation. Notably, this study considers variations in viscosity and yield stress as functions of both magnetic field intensity and temperature. The study utilizes a multidisciplinary approach, encompassing fluid dynamics, magnetism, and heat transfer, to model and analyze the behavior of MR fluids within conical bearing geometries. The governing equations containing Cauchy momentum, energy, and Maxwell equations are solved using the finite element method. This research delves into the impacts of viscous dissipation on the functional and characteristic attributes of conical bearings. The energy equations in solid and fluid domains and extended considerations to the plug region within viscous dissipation are specifically addressed. Extensive validation is performed through a comparative analysis involving experimental, numerical, and analytical studies to ensure the validity of results. The results reveal the substantial impact of temperature on both the characteristics and functionality of magnetorheological conical bearings.

Finite orbit width effects on turbulent transport of ion parallel momentum

Abstract A kinetic model for ion turbulent parallel momentum transport is developed with finite orbit width effects for Tokamak plasmas. It is shown that the curvature and gradient drifts of ions can introduce pressure perturbations into the transport equation of ion parallel momentum, which leads to a new source term. And the source term can be understood as a Coriolis force and can play a key role in the toroidal symmetry breaking during the spontaneous spin-up process.

Analysis of Nearshore Near-Inertial Oscillations Using Numerical Simulation with Data Assimilation in the Pearl River Estuary of the South China Sea

The High-Frequency (HF) radar network has become an effective method for detecting coastal currents. In this study, we confirmed the effectiveness of the HF radar measurements by comparing with the Acoustic Doppler Current Profiler (ADCP) and explore the possibility of assimilating radar data into a regional coastal ocean model. A regional high-resolution model with resolution of 10 m was first built in the Pearl River Estuary (PRE). However, analysis of the Hovmöller diagrams from the model simulations in this study indicated a significant deficiency in representing Near-Inertial Oscillations (NIOs) in the PRE, particularly in the east–west direction, despite including wind fields in the input data, during the week from 3 to 8 August 2022. To overcome the model deficiency, we conducted a set of assimilation experiments and performed sensitivity analyses. The results of sensitivity experiments indicate that the model exhibits a sufficient capacity to replicate NIOs after assimilation, lasting approximately 5–6 days. To further analyze the reasons for the decay in the magnitude of the NIOs, data from the three ADCP stations were compared with model results by applying the momentum equation. The assimilated vertical diffusion term outperforms the unassimilated model in representing NIOs. These findings highlight the importance of the vertical diffusion term for simulating NIOs and the data assimilation in improving the model’s representation of physical processes.

Analysis of the influence of the daily regulation of power stations on navigable flow conditions at river confluences using the LSTM model

The daily operations of large hydropower stations on rivers induce frequent variations in downstream water levels and flow velocities, resulting in unsteady and complex hydraulic characteristics at the confluence of the main stream and its tributaries, which adversely affect navigation safety. The continuity and momentum equations, along with the RNG k-ϵ turbulence model and the VOF model, were employed to simulate the river flow process at the confluence under unsteady flow conditions. The simulated results for water levels and velocity vector fields are in good agreement with experimental data. Variations in hydraulic characteristics, including water level, flow velocity, and longitudinal gradient at the confluence of the main stream and its tributaries, were analysed. The results indicated that the water level at the confluence decreases when the tributary merges with the main stream. As the confluence ratio increases, fluctuations in the water level at the confluence decrease. However, an increase in the staggered period results in greater fluctuations in the water level within this region. Moreover, a crescent-shaped high-speed flow region is formed at the confluence of the tributary and the main stream. As the unsteady flow discharge of the main stream increases, the relative area of this region correspondingly enlarges, reaching its maximum at peak discharge, and subsequently gradually diminishes as the discharge decreases. Based on these simulation data, a Long Short-Term Memory (LSTM) model was developed to effectively predict water levels and flow velocities, providing a more convenient and accurate method for obtaining real-time information on confluence areas than traditional mathematical and statistical approaches. This study provides novel insights into predicting flow characteristics in confluence areas, thereby offering a basis for formulating navigation safety plans.

Critical revision of check dams hydraulic design criteria

This paper addresses the problem of sizing the spillway of a closed check dam. Check dams are structures designed to control the solid transport and morphology of mountain streams. Paradoxically, however, their spillways are typically sized in clear-water conditions. The paper first analyses the behaviour of a check dam under clear water and then under live-bed conditions which is by far the most frequent operating condition. The theoretical approach is based on the conservation equations of solid mass, total mass, momentum and energy of the flow. The results of the theory are then compared with the results of some experiments in a laboratory channel equipped with a closed circuit for solid and liquid flow rates. The comparison between experiments and theory shows the validity of the approach. As expected, in some conditions that are far from rare, the design made in the clear-water condition is not safe.

Computational study of magnetohydrodynamic squeeze flow between infinite parallel disks

This paper explores the magnetohydrodynamic (MHD) squeeze flow of an electrically conducting fluid between two infinite parallel disks with a perpendicular magnetic field. The study focuses on the case where the upper disk moves towards a stationary lower disk. By employing similarity variables, we reduce the MHD momentum and continuity equations into a fourth-order linear boundary value problem, solved using a modified operational matrix method. The numerical approach is validated through L2-truncation error analysis, boundary condition comparisons, and by comparing results with other methods like HAM, HPM, and bvp4c that produce analytical and numerical solutions. Graphical analyses reveal the effects of the squeeze number, Hartman number, and the boundary parameter on velocity and flow profile. Results indicate that the Hartman number significantly affects the velocity due to the Lorentz force, while the squeeze number and boundary parameter influence the velocity and flow profile differently in suction and injection cases. The numerical solution demonstrates high accuracy and convergence compared to previous methods in terms of absolute error.

Exact Analysis of MHD Casson Fluid Flow Past an Exponentially Accelerated Vertical Plate in a Porous Medium with Radiation Absorption, Heat Generation, and Diffusion-Thermo Effects with Thermal and Solutal Ramped Conditions

The current investigation aims at to examine the effect of radiation absorption, heat generation and Dufour number on MHD Casson fluid flow past an exponentially accelerated vertical plate in a porous medium with chemical reaction. The governing equations for momentum, energy and concentration are solved by implementing the Laplace transformation method. Skin friction, rate of heat transfer and rate of mass transfer expressions are also extracted and depicted in tabular form. Investigation simulates that Casson parameter diminished the fluid velocity, whereas energy flux due to a mass concentration gradient improves the temperature field of the flow problem. In addition to this, temperature field is observed to be developed under the influence of radiation absorption and heat generation. Furthermore, the effects of different non-dimensional parameters on velocity field, temperature fluid and species concentration are exhibited graphically.

Adaptive momentum equation method for overcoming singularities of dispersed phases

The singularity issue arising from the phase fraction approaching zero in multiphase flow can significantly intensify the solution difficulty and lead to nonphysical results. By employing the conservative form of momentum equations in high-phase-fraction and discontinuity regions and the phase-intensive form of momentum equations in low-phase-fraction regions, computational reliability can be assured while avoiding the singularity issue. Regarding the proposed adaptive momentum equation method, the form of momentum equations for each cell is determined by a conversion bound and a phase fraction discontinuity detector. A comparative analysis is conducted on this method and other singularity-free methods. For discontinuities of dispersed phases, an error estimation method of the conversion bound is presented through theoretical analysis. Computational results demonstrate that the discontinuity detector accurately captures discontinuities in high-phase-fraction regions while disregarding pseudo-discontinuities in low-phase-fraction regions. Compared to the conservative form corrected by the terminal velocity method, the method yields higher-quality flow fields and potentially exhibits an efficiency improvement of over 10 times. Compared to the phase-intensive form, the method benefits from the physical quantity conservation, providing higher computational reliability. When encountering discontinuities, the expected error from the error estimation method aligns well with the actual error, indicating its effectiveness. When the conversion bound is below 1/10 000 of the inlet phase fraction, the errors of the adaptive method are essentially negligible.

Squeeze force of a Maxwell fluid between circular smooth surfaces with simple harmonic motion

The force and mechanical power required to maintain the simple harmonic motion (SHM) of the upper circular surface squeezing a viscoelastic fluid film is analyzed. The amplitude of the displacement of the upper surface is very small compared to the gap width as a function of time. The smoothness of the upper and lower surfaces is characterized by the slip model with two constant parameters, a slip length and a critical surface shear stress. The nonlinear convection terms in the momentum equation are neglected since the viscous forces dominate the inertial forces. The acceleration and deceleration terms are retained since the upper plate oscillates harmonically and the velocity in the fluid is strictly periodic. An exact solution of the governing equations is found as a function of the Deborah number, the Womersley number, the slip length, and the critical surface shear stress. A circular region without slip condition, bounded by a time-dependent radius, appears when the shear stress of the fluid does not exceed a critical surface shear stress. In addition, an annular region with slip up to the radius of the disk appears when the critical surface shear stress is exceeded. Our results show that viscoelastic and hydrophobic effects together with the Womersley number and a critical surface stress cause changes in the amplitude and phase lag of the waveform of the time-dependent radius and the force acting on the wall surface to maintain the SHM of the upper disk.