Control Volume Finite Element Method Research Articles

Investigation of entropy generation in a square inclined cavity using control volume finite element method with aided quadratic Lagrange interpolation functions

One of the most concerned subjective in Mechanical science is natural convection study in a cavity. Furthermore, the investigation of entropy generation can be useful for better designing of the thermal systems. In the present study, natural convection flow and entropy generation are numerically investigated in the presence of a magnetic field in a square inclined cavity which known as the effect of magneto-hydrodynamic (MHD). Firstly, governing equations, including mass, momentum, and energy balance equations are applied to the problem. Then, governing equations are rewritten in dimensionless form using non-dimensional parameters, vorticity, and stream function. Furthermore, the entropy generation equation is written as a non-dimensional equation. Then, the contribution of the heat transfer entropy generation into the total entropy generation rate is determined using the Bejan number. A new measure for evaluation of the thermal performance of the cavity is presented that is the so-called ecological coefficient of performance (ECOP) based on the second law of thermodynamics. Flow and heat transfer characteristics are investigated for different values of the Rayleigh number, inclination angle, and Hartmann number. The new correlations of entropy generation as a function of Rayleigh number are obtained using the two-dimensional version of quadratic Lagrange interpolation functions (QLIFs). The obtained values for the average Nusselt number and the entropy generation number are compared with those of the literature and excellent agreement is observed. The results show that the entropy generation number rises with increasing of Hartmann number and whereas it has a maximum value for a specified inclination angle. Also, ECOP increases with increasing of Hartmann number for low values of Rayleigh number. The results discover that the optimum values of the inclination angle are 20°, 35° and 48°for Hartmann number 0, 25 and 75 at Ra = 105, respectively. Also, with increasing Ha from 25 to 75, the contribution of the Ngen due to magnetic field decreases from 23% to 9% for β = 0° and it decreases from 24% to 6% for β = 45°.

Numerical investigation of heat and mass transfer within different configurations of LaNi5–H2 reactor using the unstructured Lattice Boltzmann Method

In this study, the Control-Volume Lattice Boltzmann Method (CVLBM) based on the unstructured grids is proposed as a numerical solver for transient heat and mass transfer in a Metal Hydrogen Reactor (MHR) during the absorption process. To check the validity of the numerical approach, computational results were compared with those of the literature and a good agreement was obtained. The obtained results were also compared with those of the unstructured Control Volume Finite Element Method (CVFEM). We found that the new approach correctly predicts hydrogen absorption phenomena and has less CPU time compared with the CVFEM (about 8 times faster). In addition, various tank geometries were numerically studied and a new geometric configuration is proposed. The dynamic performances of these layouts were compared based on the numerical simulation. We found that the geometrical modification improves the hydriding performance. For the new configuration, we found that the storage time can be reduced by 87% compared to the basic configuration.

Heat transfer in a permeable cavity filled with a ferrofluid under electric force and radiation effects

The behavior of ferrofluid inside a porous space due to electric field has been investigated through an innovative approach. The coupled equations were solved with Control volume finite element method. Properties of Fe3O4- Ethylene glycol nanofluid are functions of electric field and nanoparticles’ shape. Radiative term has been involved in energy equation. Impacts of nanoparticles’ shape with various relevant parameters on nanofluid thermal behavior have been depicted.

Numerical investigation of MHD nanomaterial convective migration and heat transfer within a sinusoidal porous cavity

In this investigation, the simulation of nanoparticle convective motion in permeable space has been presented numerically in the presence of the Lorentz effect. The working fluid is a H2O-based nanofluid. The non-Darcy model was utilized to employ porous terms in momentum equations. A radiation effect has been reported for various shapes of nanoparticles. The impact of shape factor, radiation parameter, magnetic force, shape of the nanoparticles and Rayleigh number on nanofluid conduct was demonstrated. The CVFEM (control-volume finite-element method) approach was utilized. The radiative flow is considered and the impact of physical parameters on nanofluid performance was demonstrated. The results prove that higher values of shape factor lead to stronger convection. By adding Lorentz forces, conduction becomes more practical.

Simplification of 3D transient heat conduction by reducing it to an axisymmetric heat conduction problem and a new inverse method of the problem solution

Most IHCP-solving methods available in literature are formulated for simple-shaped bodies and cannot be applied to complex geometries. In this work, the 3-D problem is simplified to an axisymmetric analysis. If the nozzle diameter is not much smaller than the diameter of the cylindrical component, a corrected axisymmetric model is proposed. Next, a method is presented for solving the axisymmetric IHCP in a complex domain. It is based on the control volume finite element method. Based on temperature transients measured on the outer surface, the temperature distribution is reconstructed by marching from the known to the unknown boundary. The developed method is applied for temperature identification in a cylindrical component with a nozzle. The presented algorithm is tested using measured temperatures generated from a direct solution. The transient temperature distribution obtained from the method presented in the paper is compared with the values obtained from the direct solution. The proposed method is also used to estimate the unknown boundary condition. The information about the heat transfer coefficient value makes it possible to describe the heat transfer phenomena occurring inside the component.The presented method makes it possible to optimize the power unit start-up and shutdown, contributes to a reduction in heat losses arising during the operations and enables extension of the power unit life. The method can be used in monitoring systems of both conventional and nuclear power plants.

Macroscopic modeling for convection of Hybrid nanofluid with magnetic effects

Hybrid nanofluid free convection within a permeable media was presented with CVFEM (control volume finite element method) including magnetic effect. Momentum equations have been updated with adding non-Darcy model terms. Hybrid nanoparticles (Fe3O4+MWCNT) with a base fluid of water have been considered. Impacts of Darcy number, magnetic, radiation, and Rayleigh number on migration of nanomaterial were depicted. A numerical and graphical comparison is also presented to make sure that the present analysis is correct. From the graphical results it is found that radiation parameter and magnetic boosts the Nusselt number whereas the magnetic effect shows converse relation.

Transmissivity Identification by Combination of CVFEM and Genetic Algorithm: Application to the Coastal Aquifer

The solution of inverse problems in groundwater flow has been massively invested by several researchers around the world. This type of problem has been formulated by a constrained optimization problem and this constraint is none other than the direct problem (DP) itself. Thus, solving algorithms are developed that simultaneously solve the direct problem (Darcy’s equation) and the associated optimization problem. Several papers have been published in the literature using optimization methods based on computation of the objective function gradients. This type of method suffers from the inability to provide a global optimum. Similarly, they also have the disadvantage of not being applicable to objective functions of discontinuous derivatives. This paper is proposed to avoid these disadvantages. Indeed, for the optimization phase, we use random search-based methods that do not use derivative computations, but based on a search step followed only by evaluation of the objective function as many times as necessary to the convergence towards the global optimum. Among the different algorithms of this type of methods, we adopted the genetic algorithm (GA). On the other hand, the numerical solution of the direct problem is accomplished by the CVFEM discretization method (Control Volume Finite Element Method) which ensures the mass conservation in a natural way by its mathematical formulation. The resulting computation code HySubF-CVFEM (Hydrodynamic of Subsurface Flow by Control Volume Finite Element Method) solves the Darcy equation in a heterogeneous porous medium. Thus, this paper describes the description of the integrated optimization algorithm called HySubF-CVFEM/GA that has been successfully implemented and validated successfully compared to a schematic flow case offering analytical solutions. The results of this comparison are qualified of excellent accuracy. To identify the transmissivity field of the realistic study area, the code HySubF-CVFEM/GA was applied to the coastal “Chaouia” groundwater located in Western of Morocco. This aquifer of high heterogeneity is essential for water resources for the Casablanca region. Results analysis of this study has shown that the developed code is capable of providing high accuracy transmissivity fields, thus representing the heterogeneity observed in situ. However, in comparison with gradient method optimization the HySubF-CVFEM/GA code converges too slowly to the optimal solution (large CPU-time consuming). Despite this disadvantage, and given the high accuracy of the obtained results, the HySubF-CVFEM/GA code can be recommended to solve in an efficient and effective manner the identification parameters problems in hydrogeology.

Simulation of Fe3O4-H2O nanoliquid in a triangular enclosure subjected to Cattaneo–Christov theory of heat conduction

PurposeThe purpose of this research is to describe the importance of the Cattaneo–Christov theory of heat conduction in a triangular enclosure with a semi-circular heater. Analysis subjected to Fe3O4-H2O nanofluid is reported. Viscosity dependent on magnetic field is taken into consideration to simulate ferrofluid viscosity. Besides, heat generation and shape factor of nanoparticles are also considered.Design/methodology/approachThe well-known control volume finite element method is used for simulations.FindingsThe outcomes reveal that the magnetic field can be introduced to the system as a controlling element.Originality/valueNo such analysis exists in the literature.

Investigation of natural convection of magnetic nanofluid in an enclosure with a porous medium considering Brownian motion

In this work, magnetic nanofluid natural convection in the porous enclosure considering Brownian motion is studied numerically using Control Volume Finite Element Method (CVFEM). The effective viscosity and thermal conductivity of nanofluid are specified by Corcione correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered porous enclosure is heated from the inner circular side and it cooled from the outer circular side while two other walls are insulated. The impacts of various controlling parameters such as the Rayleigh number, Hartmann number, Darcy number and angle of magnetic field parameter are examined on the streamlines and isotherms. In addition, the average and local Nusselt numbers are obtained and presented via figures. The results state that the intensity of the convective flow has a direct relationship with the Rayleigh number and Darcy number while it has a reverse relationship with the Hartmann number and inclination angle of the magnetic field.

Numerical investigation of viscous flow instabilities in multiphase heterogeneous porous media

A critical aspect of multiphase flow in porous media is the displacement efficiency, which measures the amount of fluid that can be pushed by another fluid driven by pressure gradient. Migration of contaminants and reservoir waterflooding are typical applications where understanding the dynamics of immiscible fluid displacement helps mitigating water resources contamination and improving hydrocarbons production, respectively. Due to large viscosity ratios, flow instabilities at fluids’ interface may arise leading to the formation of fingers, i.e., uneven fronts with elongation at the outside edge of fluids interface with strong impact on the displacement efficiency. Initial studies of viscous instabilities indicated that the development of fingers mostly depends on mobility and capillary forces, however heterogeneity of the porous domain may also affect the onset of instabilities. Therefore, the main aim of this work is to numerically investigate formation and growth of viscous fingers in heterogeneous porous media. The model used here is based on a novel control volume finite element method (CVFEM) formulation with families of FE-pairs, PnDG-Pm and PnDG-PmDG, specially tailored for Darcean flows. Dynamic mesh adaptivity enables capturing fingers development whilst saving computational overheads. Numerical experiments were performed to investigate the impact of viscosity ratio and heterogeneity on Saffmann–Taylor instabilities. Numerical simulations demonstrated that the heterogeneity of the domain triggers the early-onset formation of fingers under prescribed viscosity ratio conditions. Also, effective numerical capture of growth (in particular tip-splitting) and coalescence of dendritic finger branching induced by large viscosity ratio largely depends on mesh resolution at the fluids interface.

Control volume finite element method for entropy generation minimization in mixed convection of nanofluids

A numerical study is performed to analyze the heat transfer and entropy production for both natural and mixed convection in a rectangular enclosure filled with water-based nanofluids. This article presents a new approach for minimizing the entropy production rate in different flow configurations with nanofluids. The governing equations are discretized with a control-volume-based finite element method (CVFEM). The thermophysical properties of the nanofluids are evaluated based on experimental data. The analysis considers the effects on entropy production due to variations of the volume fraction () of the nanofluid, aspect ratio of the enclosure, and moving wall velocity The article compares the entropy production rates and heat transfer rates for three different nanofluids. The results for a natural convection case indicate a reduction in the rate of entropy production as the nanoparticle volume fraction increases. Results for the mixed convection case establish the optimal nanoparticle volume fraction that minimizes the total entropy production. Through this numerical model, the distribution of nanoparticles and cavity aspect ratio can be effectively controlled to minimize the entropy production rates.

Viscous Dissipation Impact on Free Convection Flow of Cu-water Nanofluid in a Circular Enclosure with Porosity Considering Internal Heat Source

In this work, free convection of Cu-water nanofluid in an enclosure by considering internally heat generated in the porous circular cavity and the impacts of viscous dissipation are numerically evaluated by control volume finite element method (CVFEM). The outer and inner sides of the circular porous enclosure are maintained at a fixed temperature while insulating the other two walls. The impacts of diverse effective parameters including the Rayleigh number, viscous dissipation, and nanofluid concentration on features of heat transfer and fluid flow are examined. Moreover, a new correlation for the average Nusselt number is developed according to the study’s active parameters. It can be deduced by the results that the maximum value of the temperature is proportional to the viscous dissipation parameter.

Natural convection analysis in a square enclosure with a wavy circular heater under magnetic field and nanoparticles

The aim of the current study is to investigate the natural convection heat transfer in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. The governing equations that are expressed in dimensionless form are solved by means of control volume finite element method employing a validated FORTRAN code. The dimensionless controlling parameters of the present investigation are shape factor of nanoparticles (m), Hartmann number (Ha), Rayleigh number (Ra), and nanoparticle volume fraction (ϕ). In this study, the amplitude A and number of undulations N are fixed at a constant value of 0.2 and 8, respectively. The obtained results portray that in the presence of waves on the inner wall of the annulus, the heat transfer rate is an ascending function of Rayleigh number, nanoparticle volume fraction and less obvious function of their shape factor, while it is a descending function of the Hartmann number.

A High Order Control Volume Finite Element Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

This paper describes a new two-dimensional (2-D) control volume finite element method (CV-FEM) for transient heat conduction in multilayer functionally graded materials (FGMs). To deal with the mixed-grid problem, 9-node quadrilateral grids and 6-node triangular grids are used. The unknown temperature and material properties are stored at the node. By using quadratic triangular grids and quadratic quadrilateral grids, the present method offers greater geometric flexibility and the potential for higher accuracy than the linear CV-FEM. The properties of the FGMs are described by exponential, quadratic and trigonometric grading functions. Some numerical tests are studied to demonstrate the performance of the developed method. First, the present CV-FEM with mixed high-order girds provides a higher accuracy than the linear CV-FEM based on the same grid size. Second, the material properties defined location is proved to have a significant effect on the accuracy of the numerical results. Third, the present method provides better numerical solutions than the conventional FEM for the FGMs in conjunction with course high-order grids. Finally, the present method is also capable of analysis of transient heat conduction in multilayer FGM.

Numerical simulation for thermal radiation and porous medium characteristics in flow of CuO-H2O nanofluid

Researchers have a wide-ranging tradition in endeavoring to rise the thermophysical aspects of convection heat transferors for illustration, transformer oil and water. Technological advancements in recent years permit the dispersal of elements having ranges between 10 and 100 nm in such liquids. Recent researches regarding nanoliquids have been elaborated to exhibit anomalously higher convection heat transportation. Keeping such implications in mind, we formulated CuO-H2O nanoliquid flow with wavy circular cylinder as heater subjected to magnetohydrodynamics. The well-known Darcy model featuring porous medium along with KKL (Koo–Kleinstreuer–Li) model is considered simultaneously for analysis. Heat transportation is reported considering radiation effect. The impact of shape factor of nanoparticles is also considered. Simulations are presented employing the novel control volume finite element method. The influences of notable parameters like Darcy number, Rayleigh and Hartmann numbers, radiation parameter, amplitude of undulations, nanofluid volume fraction and shape factor of nanoparticles have been investigated on flow and heat transfer features. Moreover, a novel correlation regarding average Nusselt number has been developed subject to analysis’s active parameters. Our outcomes report that lower values of amplitude of undulations provide the uppermost estimations of average Nusselt number.

A hybrid numerical-semi-analytical method for computer simulations of groundwater flow and heat transfer in geothermal borehole fields

The formulation of a hybrid numerical-semi-analytical method for cost-effective simulations of heat transfer in fields of vertical geothermal boreholes, in the presence of groundwater flow, is presented. An amalgamation of a co-located control-volume finite element method and a finite volume method is used to solve 1) a volume-averaged continuity and the Darcy-Brinkman-Frochheimer equations to obtain the distribution of the groundwater flow; and 2) an unsteady three-dimensional volume-averaged advection-conduction equation to calculate the related ground temperature distribution, assuming local thermodynamic equilibrium between the groundwater and the soil particles. The bulk temperature distribution of the working fluid (flowing inside the legs of a U-tube pipe inserted inside each borehole and kept in place by grout) and the related heat extraction (or addition) rate are obtained using a semi-analytical method to solve a quasi-steady quasi-one-dimensional model. The conditions of no-slip, impermeability, equality of temperature, and continuity of heat flux are used at the interface between each borehole and the groundwater-saturated soil in the borehole field. The proposed method is applied to test and demonstration problems to demonstrate its capabilities.

Thermal management of MHD nanofluid within the porous medium enclosed in a wavy shaped cavity with square obstacle in the presence of radiation heat source

In this manuscript, we present nanofluid thermal management inside a porous media including magnetic force and radiation heat sources. The systems of PDEs were changed into the non-dimensional form by means of the suitable transform. To gain the outputs, control volume finite element method (CVFEM) was utilized. Radiative source term was involved in final PDEs. Isotherms and streamlines are plotted to demonstrate the variation of Hartmann number, radiation factor, buoyancy and nanoparticles' shape on nanofluid behavior. Outputs demonstrate that convective mode becomes stronger with augment of shape factor. By involving source terms of magnetic field, conduction becomes more effective. Average Nusselt number grows as enhancing the shape effect parameters “m”, Radiation effect and Raleigh number. As increasing Radiation and Raleigh parameters average temperature deceases gradually. The comparative study is also presented, which shows the reliability and efficiency of the CVFEM. Graphical study also shows strengthen of suggested technique.

A simulator for production prediction of multistage fractured horizontal well in shale gas reservoir considering complex fracture geometry

Shale gas is becoming an increasingly supplementary energy source because of its clean-burning and abundance. Economic gas production in shale requires the techniques of horizontal drilling and multistage hydraulic fracturing to create complex fracture network (CFN). How to accurately describe the characteristics of geometry and flow mechanisms of the CFN and select the most efficient approach for modeling are challenging. In this paper, a production forecasting model for multistage fractured horizontal well (MFHW) with CFN in shale is proposed based on the multiple interacting continua (MINC) theory (organic/inorganic matrix, natural fractures system) and lower-dimensional discrete fracture network (DFN) model (hydraulic fractures system). The model is designed to describe the unconventional flow mechanisms in shale system, such as fractal porous media and non-Darcy multiscale flow in ultra-tight matrix, ad-desorption on organic materials’ surface, rock un-consolidation within natural fractures, high-velocity turbulent flow near well range, and multiphase behaviors. We also propose a novel hybrid control volume finite element (CVFE) and finite-difference (FD) simulation method to obtain the numerical results of the model based on the unstructured 3D tri-prisms. The accuracy of the simulator is successfully validated and sensitivity analysis of some key factors (e.g.: fractal model permeability, Langmuir volume, heterogeneities of reservoir and fractures, well platform) are conducted to evaluate the impacts on production performance. Combing with the micro-seismic monitoring (MSM) data and engineering analyses, the DFN model is applied in Longmaxi shale formation to obtain the history matching with the field data and predict the production.

Numerical and experimental study on the thermal performance of the concrete accumulator for solar heating systems

The article presents the concept of the solar facility operating in the domestic hot water and space heating system, equipped with thermal energy storage based on a water tank and an auxiliary storage module made of concrete elements. A mathematical model of transient heat transfer in the concrete structure using the Control Volume Finite Element Method (CVFEM) has been proposed. The method allows modelling the transient heat conduction based on a rare mesh of nodes in a relatively short time, with accuracy comparable to traditional Finite Element Method (FEM) results including CFD modelling. A laboratory stand has been made for the verification of the model, and a set of comparative measurements has been carried out.

Large eddy simulation of turbulent flow over and through a rough permeable bed

This work elucidates the impacts of model construction choices on turbulence characteristics and solution fidelity in the simulation of coupled freestream and porous turbulent flows. A freestream-porewater interface is modeled numerically as a matrix of regularly spaced spheres submerged in a surrounding flow. Simulations are conducted to solve the continuity and momentum equations via Large Eddy Simulation (LES) using the Control Volume Finite Element Method (CVFEM) on an unstructured, surface-conforming mesh, and simulated flow fields are compared with experimental results. Key parameters are identified, allowing for model creation recommendations. A mesh refinement study is performed, and characteristic required mesh sizes in both the bed and the freestream are identified that achieve a good trade-off between accuracy and efficiency. Additionally, it is shown that similar to wall-bounded flows, the computational domain for a coupled freestream and porous flow must be sufficiently large to capture the relevant largest-sized eddies and to avoid the spanwise locking of flow structures; such structures may affect the flow field in the pores as well as in the freestream. Dimensions of 7.5H × 3.5H × H, where H is the freestream height, are found to give satisfactory comparison with experimental results for the cases studied. Finally, it is found that the wall-adapting local eddy-viscosity (WALE) turbulence closure scheme is better able to model the fluid velocity in the problem domain compared with the Smagorinsky model. Failure to select the proper turbulence closure model or domain size leads to a misrepresentation of the turbulent structures. Because of the strong coupling between the porewater flow and the freestream, these modeling errors propagate in both flow regions.