Volume Based Finite Element Method Research Articles

Cu and Al2O3-based hybrid nanofluid flow through a porous cavity

Abstract In this study, the (Cu and Al2O3/water) hybrid nanofluid flow is carried out in a porous cavity. The thermophysical structures of solid materials are used from the available literature to improve the thermal performance of the base fluid. The mathematical model as a porous cavity is mainly used in the distillation process and is vital for the storage of thermal energy. The magnetic field is also employed perpendicular to the flow field and the impact of the magnetic parameter examined versus fluid motion. Similarity variables are used to transform governing equations as simplified partial differential equations. The model is solved using the control volume-based finite element method. Boussinesq–Darcy force is employed for the motion of the fluid flow, and the Koo–Kleinstreuer–Li model is used to assess the characteristics of the hybrid nanofluids. The roles of the Hartmann number, Rayleigh number, porosity factor in the porous medium, and drag fin improve traditional fluids’ thermal distribution presentation. Recent results predict that the two different kinds of nanoparticles speed up the heat transfer through the porous cavity. The percentage analysis shows that the hybrid nanofluids (Cu and Al2O3/water) are prominent in improving traditional fluids’ thermal distribution. Finally, the grid sensitivity test is also carried out for hybrid nanoparticles to demonstrate that the results are asymptotically coherent.

Simulation for magnetic force impact on nanomaterial transportation through a porous closed curved container as a multi physics problem

It is a practical application to use porous zones for cooling systems of magnetic sensors. The importance of MHD (Magnetohydrodynamic) on the irreversibility of liquid within a chamber consisting of porous zone has been incorporated in current article. CVFEM (Control Volume based Finite Element Method) has been employed to model the simplified model obtained after employing the vorticity formula. Outputs indicated that the intensity of nanomaterial circulation increases as Ra increases, while it decreases with the inclusion of a magnetic field, which converts the heat transmission mode to conduction, and due to the appearance of a stretching eddy, the heat plume is removed. A reduction in permeability reflects an increase in the exergy drop, which means greater thermal irreversibility. A nonessential impact on the Bejan number (Be) distribution was reported with altering Darcy number (Da) if the buoyancy force was negligible. Regardless of the changing maximum magnitude of Be, augmenting Da results in lower Be. Due to the dependence of Nusselt number (Nu) on the inner surface temperature, Hartmann number (Ha) has a reverse relation with Nu, which means a lower cooling rate with the inclusion of Ha.

Research on building cryo-compressed test condition on large CcH2 vessel for heavy-duty fuel cell trucks

To test the performance of cryo-compressed hydrogen vessels for heavy-duty fuel cell trucks, a novel inconstant filling method was proposed by applying liquid nitrogen and compressed helium to create the target cryo-compressed environment. The computational fluid dynamics method was used to simulate the loading process of generating suitable conditions in a large cryo-compressed vessel. The element-based finite volume method and the k – ω based shear stress transport model were applied to simulate the thermal flow of filled gas. Temperature distribution and loading performance were carefully analyzed under different filling cases. In a bid to compare the loading performance, five key factors (gas consumption, temperature rise of aluminum layer and carbon fiber, average filling rate, and time consumption) were put in a radar map for discussing the optimized strategy of each application. The simulation results revealed that the cryo-compressed test condition can be well established by using liquid nitrogen precooling and gas helium pressurization. Nevertheless, the mass flow should be maintained at a low rate before the construction of high-pressure. These findings help design and operate the cryo-compressed test by enhancing its safety and improving efficiency.

Rugosity and blocking indices of artificial reefs and their correlations with wake volume

Like aquatic habitats in nature, artificial reefs (ARs) have been investigated to determine whether their complexity affects species diversity. Moreover, studies have been carried out to investigate wake regions of ARs, which provide a shelter, feeding ground, rest area, and temporary stopover for marine species; however, few have examined the correlation between the complexity of the AR and characteristics of the wake region. In this study, we first modelled three ideal scenarios and six real ARs, all designed with different degrees of rugosity and/or water-blocking effects. Second, we obtained the wake volumes of the target structures using the element-based finite volume method and investigated their correlations with the rugosity index (RI), blocking index (BI), and rugosity-blocking index (RBI). Our results showed that for securing a large wake region, it is necessary to implement not only a large upper surface with a certain degree of rugosity (e.g. 2.0 for a tunnel- or arch-type AR) but also a large front surface area with sufficient water-blocking effects (e.g. 0.5 for a cube- or box-type AR). Overall, the RI, BI, and RBI were useful for distinguishing the characteristics of the upper and front surfaces, and accordingly to estimate wake volumes.

Thermal and flow calculations of platen superheater in large scale CFB boiler

Circulating Fluidized Bed (CFB) boilers are desirable technology to utilize solid fuels, operate within a wide load range, and promote the high flexibility in burning a wide range of coal and other solid fuels, keeping high efficiency and low gaseous pollution. The paper presents thermal and flow modeling results of steam superheater operated in the large-scale coal-fired CFB boiler, both in steady and transient states. The mathematical model of the superheater wall was developed using Control Volume-based Finite Element Method. The heat transfer coefficient as the sum of radiative and convective heat transfer coefficients was considered in the presented approach to modeling thermal processes in a circulating fluidized bed. The overall heat transfer coefficient was computed for the analyzed type of the boiler at full load and steady-state conditions using available measuring data and results obtained using Computational Fluid Dynamics (CFD) modeling. Depending on the modeling approach adopted in the CFD model, the heat transfer coefficient at full boiler load varies between 159.96 and 189.63 W/(m2·K). In the analyzed period of boiler start-up, results of steam outlet temperature (455 °C–485 °C), heat transfer coefficients on the flue-gas side (100 W/(m2∙K) and 120 W/(m2∙K)), and heat transfer coefficients on the steam-side (925–2008 W/(m2∙K)) vary with time. The methods presented in the paper can be applied to modeling transient flow and thermal processes in superheaters with complicated flow arrangements. The advantage of the proposed method is a short computing time compared to detailed and complex 3D models. The developed model of the superheater with the transfer coefficient determination methods can be used to perform calculations in the full range of boiler load, both during steady and transient boiler operation.

Thermomechanical investigation of the continuous casting of ingots using the element-based Finite-Volume Method

A computational thermomechanical simulator using the Element-based Finite-Volume Method (EbFVM) has been elaborated to investigate the solidification of continuous casting ingots. The thermal behavior was evaluated using the two-dimensional transient heat conduction equation with phase change in conjunction with numerical-experimental film coefficients. In addition, the thermal-mechanical approach includes three inelastic representations, which are based at the Ramberg-Osgood plastic and Odqvist's viscoplastic models. The simulator is validated using several benchmarks tests, along with the analytical solution of the Stefan's problem. In the context of continuous casting, in order to enhance the cooling stage in the spray zone, as well as the crack formation, a new set of sprays were proposed for the investigated case. The thermomechanical study provided by EbFVM is able to provide good results for the temperature profile and thermomechanical state that could be used to address problems caused by the cooling process of continuous casting of ingots.

Study of Non-Newtonian blood flow - heat transfer characteristics in the human coronary system with an external magnetic field.

This paper proposes a novel mathematical model of non-Newtonian blood flow and heat transfer in the human coronary system with an external magnetic field. As the blood viscosity is assumed to depend not only on shear rate but also on temperature and magnet strength, the modified Carreau-Yasuda viscosity model is formulated. The computational domain includes the base of the aorta, the right coronary artery, and the left coronary artery, with the left circumflex and left anterior descending arteries. The element-based finite volume method is derived for the solution of the proposed model. Numerical simulations are carried out to investigate the magnetic field effect on the blood flow-heat transfer characteristic in the human coronary system. It is found that the magnetic field has a significant impact on fluid viscosity, leading to enhanced fluid velocity.

Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves

Faraday instability is a classic problem that occurs due to the relative displacement of the interface that separates two immiscible fluids placed in a closed container under oscillating acceleration parallel to gravity. The interface deformation and the induced flow patterns of this two-phase flow are very complex and numerical simulations could allow a deeper understanding of the dynamics of these systems. Some tests have been performed to establish a reference solution, but further validation is needed in order to ensure the validity of these solutions. In this work, we compare some numerical solutions for the linear and nonlinear regimes using the phase field scheme with predictions obtained using different numerical schemes such as Front Tracking, Volume of Fluid, and Element-based Finite Volume Method. The results show that, in both linear and nonlinear regimes, some important differences in the prediction of the interface dynamics between the methods are observed, and the need to provide a reference numerical solution for future benchmarks is highlighted.

Effect of transverse and parallel magnetic fields on thermal and thermo-hydraulic performances of ferro-nanofluid flow in trapezoidal microchannel heat sink

Purpose This paper aims to study the thermal and thermo-hydraulic performances of ferro-nanofluid flow in a three-dimensional trapezoidal microchannel heat sink (TMCHS) under uniform heat flux and magnetic fields. Design/methodology/approach To investigate the effect of direction of Lorentz force the magnetic field has been applied: transversely in the x direction (Case I);transversely in the y direction (Case II); and parallel in the z direction (Case III). The three-dimensional governing equations with the associated boundary conditions for ferro-nanofluid flow and heat transfer have been solved by using an element-based finite volume method. The coupled algorithm has been used to solve the velocity and pressure fields. The convergence is reached when the accuracy of solutions attains 10–6 for the continuity and momentum equations and 10–9 for the energy equation. Findings According to thermal indicators the Case III has the best performance, but according to performance evaluation criterion (PEC) the Case II is the best. The simulation results show by increasing the Hartmann number from 0 to 12, there is an increase for PEC between 845.01% and 2997.39%, for thermal resistance between 155.91% and 262.35% and ratio of the maximum electronic chip temperature difference to heat flux between 155.16% and 289.59%. Also, the best thermo-hydraulic performance occurs at Hartmann number of 12, pressure drop of 10 kPa and volume fraction of 2%. Research limitations/implications The embedded electronic chip on the base plate generates heat flux of 60 kW/m2. Simulations have been performed for ferro-nanofluid with volume fractions of 1%, 2% and 3%, pressure drops of 10, 20 and 30 kPa and Hartmann numbers of 0, 3, 6, 9 and 12. Practical implications The authors obtained interesting results, which can be used as a design tool for magnetohydrodynamics micro pumps, microelectronic devices, micro heat exchanger and micro scale cooling systems. Originality/value Review of the literature indicated that there has been no study on the effects of magnetic field on thermal and thermo-hydraulic performances of ferro-nanofluid flow in a TMCHS, so far. In this three dimensional study, flow of ferro-nanofluid through a trapezoidal heat sink with five trapezoidal microchannels has been considered. In all of previous studies, in which the effect of magnetic field has been investigated, the magnetic field has been applied only in one direction. So as another innovation of the present research, the effect of applying magnetic field direction (transverse and parallel) on thermo-hydraulic behavior of TMCHS is investigated.

Study of Compact Heat Exchangers Operating in Self-Sustained Oscillatory Flows

Abstract Computer codes were developed to study the performance of compact heat exchangers (CHEs) operating in self-sustained oscillatory flow (SSOF) regimes. The methods were based on a control volume-based finite element (CVFEM) method for geometric discretization and the explicit first stage, single diagonal coefficient, diagonally implicit, Runge–Kutta (ESDIRK) method for temporal discretization. The developed codes were validated for both steady and unsteady cases. A study of nine geometrically related domains of flat tubes in staggered configurations was performed. Grid independence was established subject to double cyclic conditions—periodically fully developed flow and heat transfer in the stream-wise direction and cyclic or repeating flow and heat transfer in the cross-stream direction. The maximum Reynolds number was established at approximately 2000 for the cases studied to avoid the turbulent flow regime. Parameters of interest like Nusselt number, friction factor, and pumping power were calculated for steady and SSOF regimes. An approach was proposed to determine critical Reynolds number (Recrit) for the SSOFs such that for Reynolds number below Recrit the flow remains steady, and above Recrit, the flow exhibits the characteristics of SSOFs before finally transitioning to fully turbulent conditions. The results indicated a sensitivity of performance parameters to transverse spacing but not to longitudinal spacing.

인공어초 후류역을 증가시키는 두 가지 관점

Wake region of an artificial reefs (AR) is a significant space to recruit marine species around the AR because the region gathers nutrients and prey (e.g., phytoplankton). Previous studies have focused on relatively small, simple ARs for the estimation of wake regions. Thanks to progressive artificial reef industry, nowadays relatively large, complex ARs are being installed on the seabed; hence, it is necessary to investigate how to secure wake region of those ARs. In this study, the concept of wake volume was used to estimate the wake regions of five relatively complex artificial reefs (ARs). The element-based finite volume method was used to estimate wake volume, and its fluctuation due to the size of the ARs and the inflow velocity was calculated. From the analysis results, it was found that the thickness and area of the structural members of the ARs are important to secure wake region. However, wake region was not created if the AR is composed of only a thin steel frame. This indicates that the function of the structural members of the ARs that blocks the flow is important for the creation of the wake region. In the case of AR in which a wake region occurs, the AR size (height) has a significant positive correlation with the magnitude of the wake region, and if the inflow flow velocity is 1.0 m·sSUP-1/SUP or more, a sufficient eddy currents occur and accordingly no variation in wake volume is observed. Thus, to increase wake region, it is shown that not only the size of AR, but also the thickness and area of the structural members play an important role.

Development of an embedded discrete fracture model for 2D and 3D unstructured grids using an element-based finite volume method

Recently, the unstructured gridding technique has been extensively used in reservoir simulation because of the high flexibility it provides to represent geologically realistic reservoirs. The embedded discrete fracture model (EDFM) has also attracted attention in recent years for the simulation of complex fractures in various types of computational grids. In this work, we develop a methodology to apply the EDFM in 2D and 3D unstructured grids using an element-based finite volume method (EbFVM). In this method, triangular and quadrilateral elements are used in 2D grids, and tetrahedron, prism, hexahedron, and pyramid elements are used in 3D grids. New approaches to addressing matrix-fracture connectivity and reducing the number of fracture unknowns in this type of grid are presented. The methodology is implemented in an EDFM preprocessing code.A series of case studies are presented to demonstrate the methodology in 2D and 3D simulations using an in-house compositional reservoir simulator. Different types of elements are used in the simulations to represent the reservoir geometries. Both primary and secondary recovery processes are simulated. The results show that when the number of control volumes is similar, the proposed method can obtain similar results on different grids with various types of elements, which confirms the effectiveness of the approach. Case studies with complex reservoir geometries are also presented to demonstrate the applicability of the model.This work demonstrates the extensiveness of the EDFM to unstructured matrix grids. It also shows the compatibility of the EDFM with various numerical approximation schemes. The use of unstructured gridding with mixed types of elements facilitates the representation of complex reservoir geometries, and through the combination with the EDFM, complicated gridding around fractures is avoided. Therefore, the approach in this work has high flexibility for simulating densely fractured media with complex geometries.

Loading procedure for testing the cryogenic performance of cryo-compressed vessel for fuel cell vehicles

To overcome the disadvantages of high cost and hazards in the cryo-compressed vessel test with liquid hydrogen, a combined process with liquid nitrogen and compressed helium was carried out. A computational fluid dynamics (CFD) model was introduced to simulate the loading procedures required to generate suitable conditions in a cryo-compressed vessel with a Carbon Fiber wrapped Aluminum liner. Element-based finite volume method (FVM) and a k – ω based shear stress transport (SST) model have been used to simulate the thermal flow of helium. The simulation model was validated by a similar experiment result and the data from the U.S. National Institute of Standards and Technology reference database. To investigate the thermal characteristics of the vessel, temperature distribution, loading performance, and helium consumption were analyzed at various filling mass flow rates. The simulation results confirmed that cryo-compressed test conditions could be achieved by liquid nitrogen precooling followed by pressurization with compressed helium. The cryogenic conditions were highly depended on the inlet mass flow rate and the corresponding loading time. Lower inlet mass flow rates (longer loading times) leaded to a high temperature increase of 84.04 K in Carbon Fiber during the loading, which was minimized to only 1.65 K when using the highest mass flow rate. Considering both final condition and loading efficiency, high filling speed is optimal for single tests, while lower filling speeds were more appropriate for cyclic fatigue testing of vessels because of lower helium consumption and equipment costs. Not only thermal fluid was simulated to investigate the loading parameters to generate cryo-compressed conditions, but also the thermal transfer result of composite materials. Our findings are expected to assist in the design and operation of this challenging experiment in a safe and efficient way.

CVFEM modeling of fluid flow induced by convective heat transfer from a hot pipe buried in soil

In this investigation, fluid flow numerical evaluation induced by convective heat transfer due to a buried hot pipe in the soil is performed. The numerical method implemented is the control volume-based finite element method (CVFEM). The physical domain consists of a circular pipe enclosed in a square cylinder. The temperature of the enclosure upper wall was kept uniform cold while remaining walls were insulated. The research was conducted by fixed non-dimensional parameters, that is, porosity (e), location of pipe (K), Prandtl number (Pr), permeability (K (X, Y)), Darcy number (Da), and the Rayleigh number (Ra). The simulation of porous medium was performed by the application of Brinkman-extended Darcy model. Results are illustrated through isotherm and streamlines. The results depicted that the effect of Darcy on the average Nusselt number (Nuave), at larger Ra, is more noticeable. Additionally, Da reduction causes suppression in the fluid flow and, in addition, less heat transfer among the hot pipe and enclosure. The non-homogeneity reduces the Nu over the hot pipe. Moreover, the value of pipe location, as well as its radius, significantly affects the pipe heat transferring.

Second law analysis of magneto-natural convection in a nanofluid filled wavy-hexagonal porous enclosure

Purpose Natural convection heat transfer analysis can be completed using entropy generation analysis. This study aims to accomplish both the natural convection heat transfer and entropy generation analyses for a hexagonal cavity loaded with Cu-H2O nanoliquid subjected to an oriented magnetic field. Design/methodology/approach Control volume-based finite element method is applied to solve the non-dimensional forms of governing equations and then, the entropy generation number is computed. Findings The results portray that both the average Nusselt and entropy generation numbers boost with increasing aspect ratio for each value of the undulation number, while both of them decrease with increasing the undulation number for each amplitude parameter. There is a maximum value for the entropy generation number at a specified value of Hartmann number. Also, there is a minimum value for the entropy generation number at a specified value of angle of the magnetic field. When the volume fraction of nanoparticles grows, the average Nusselt number increases and the entropy generation number declines. The entropy generation number attains to a maximum value at Ha = 14 for each value of aspect ratio. The average Nusselt number ascends 2.9 per cent and entropy generation number decreases 1.3 per cent for Ha = 0 when ϕ increases from 0 to 4 per cent. Originality/value A hexagonal enclosure (complex geometry), which has many industrial applications, is chosen in this study. Not only the characteristics of heat transfer are investigated but also entropy generation analysis is performed in this study. The ecological coefficient of performance for enclosures is calculated, too.

Numerical simulation of hydrothermal features of Cu–H2O nanofluid natural convection within a porous annulus considering diverse configurations of heater

The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend.

Analysis of hybrid nanofluid behavior within a porous cavity including Lorentz forces and radiation impacts

We investigate the hybrid nanofluid convection transportation within a permeable medium in appearance of an externally applied magnetic force by modeling it through control volume-based finite element method. To employ the permeability effect terms, one term was added in momentum and radiation was involved to show the diverse states of nanoparticles. The impact of Darcy and Rayleigh as well as magnetic and radiation parameters on the nanofluid performance is investigated and presented. We observe that the conduction mode enhances with higher values of Ha. Nusselt number Nu augments with the consideration of radiation source term. The addition of Lorentz force makes the conduction mode more sensible. The agreement with the published results makes us more confident about the validity of our numerical computations.

Simulation Examination for Nanoparticle Flow in a Permeable Enclosure via CVFEM Involving MHD Effect

In the present investigation, innovative complex porous enclosure is chosen to simulate the MHD (magnetohydrodynamic) natural convection. One side of porous cavity packed with radiative nanofluid (CuO–water) has curve-shaped triangular wave pattern. To gain insight into outputs, CVFEM (control volume-based finite element method) has been used. Nanofluid behavior is inspected by employing two-temperature model for solid matrix and nanoliquid and KKL model for effective properties of nanofluid with an extensive range of key parameters acting as Hartmann number, radiation parameter, buoyancy impact, phase interacting heat transfer factor. Not only imposing magnetic field but also wavy surface and dispersion of nanomaterial have been considered in the current paper. New numerical approach has been utilized to demonstrate the behavior of nanomaterial through the porous tank. Interrelation of average Nusselt number with involved parameters is also proposed. Outcomes reveal that radiation term has straightforward association with Nusselt number. Greater vortex generates with the rise in shape factor.

The influence of hybrid nanoparticle (Fe3O4 + MWCNT) transportation on natural convection inside porous domain

In this study, hybrid nanofluid free convection has been simulated within a permeable domain involving Lorentz effect. To solve and simulate the problem, Control Volume-based Finite Element Method (CVFEM) method is applied. In addition, the non-Darcy model has been used to apply permeable condition in equations. The influence of hybrid nanoparticles (Fe3O4[Formula: see text][Formula: see text][Formula: see text]MWCNT) inside water as base fluid has been studied. Meanwhile, source term of radiation impact has been described for different nanoparticle shapes. The impacts of substantial variables such as Darcy number, radiation factor, magnetic strength and Rayleigh number on nanofluid behavior were fully revealed. It can be concluded that enhancing permeability factor can improve the Nusselt number but reverse behavior can be reported for Lorentz forces.

Entropy generation and economic analyses in a nanofluid filled L-shaped enclosure subjected to an oriented magnetic field

Natural convected heat transportation attributes can be elaborated better using entropy generation analysis. In current framework, we scrutinized magnetized Al2O3-H2O nanomaterial natural convection based on entropy generation and L-shaped cavity. Non-dimensional forms of governing expressions are computed through Control Volume-based Finite Element Method (CVFEM). Entropy generation number is calculated. Features of active parameters e.g. Rayleigh number, nanoparticles volume-fraction, nanoparticle shape, Hartmann number, magnetic field angle and aspect ratio versus average heat transportation rate (Nusselt number) and the entropy generation number are investigated. For the first time, an economic analysis is introduced for evaluating the performance of the enclosure with consideration cost of nanofluid. Also, in order to assess the performance of the enclosure, six criteria are introduced which two of them are based on the cost of nanofluids. The results were compared with references and a good compromise was seen. According to the results, both the entropy generation number and average heat transportation rate rise when Rayleigh number upsurges. The average heat transportation rate rises with ascending the nanoparticle volume-fraction whereas the entropy generation number declines when nanoparticles concentration ascends. The entropy generation number decreases 15.14% and 8.15% for Ha=25 and Ha=75, respectively, when ϕ increases from 0 to 0.1.