Finite Volume Research Articles

Assessment of Multigrid Schemes with Fixed Patterns for a Two-Dimensional Heat Transfer Problem

Heat transfer problems and their solutions are of critical importance in almost all areas of engineering and technology, while many real-world problems are inherently three-dimensional. Simplifying them to 2D models offers practical advantages with reasonable models. With being the fundamental class of problem of heat transfer, the 2D thermal diffusion problem was selected for the study. Multigrid methods were referred to as standing out in terms of cost reduction while keeping solution accuracy. The effectiveness of multigrid methods employing fixed pattern schemes was subject to investigation. To set up numerical experimentation, an authentic code generation effort was given that implements a basic finite volume method, intergrid operations and iterative solvers. A reference case with an analytical Laplace solution was selected and properly validated by the results. A variety of multigrid schemes with fixed patterns were explored around parameters, iterations per sweep and maximum coarsening level. Results were compiled on the focal points of cost and performance. A comparison of the direct iterative methods with multigrid schemes proved the effectiveness of multigrid schemes. With the assessment of the cost and performance outcomes, it is concluded that any multigrid scheme should visit the maximum coarsest level possible while keeping a minimum number of iterations on each grid resolution.

Direct hydroacoustics analyses of pipe orifice using lattice Boltzmann method

Acoustic waves in water pipes pose a structural threat but also offer a valuable tool for non-invasive inspection. Complex pipe geometries such as bends and surface liners create complex fluid boundaries, triggering interactions between fluid flow and acoustics. The lattice Boltzmann method (LBM) excels at capturing these interactions near complex boundaries, in contrast to the finite volume method, which can result in errors. However, the application of LBM in water pipes has been limited by stability problems. This study proposes a two-step (DM-TS) collision operator based on a direct method (LBM-HA) for stable LBM simulations in water pipes. LBM-HA enables direct hydroacoustic predictions for both acoustic and dynamic flow fields in a pipe orifice. A novel acoustic-dynamic complex boundary condition was formulated from the linearized Euler's equation to account for the physical effects of the bounded domain of the LBM-HA analysis. To distinguish between dynamic and acoustic components, wavenumber and frequency decomposition techniques were applied to the pressure data obtained within the pipe. In addition, mode decomposition of the acoustic pressure was conducted to identify the dominant acoustic modes. By comparing the LBM-HA results with experimental data, we highlighted the method's potential for direct hydroacoustic analysis considering the acoustic characteristics of the water pipe.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Effect of foulant on temperature and steam quality profiles in once-through steam generator tubes

Once-through steam generators (OTSGs) are commonly used in the oil sands industry for steam generation forin-situthermal recovery of extra heavy oil. These are expensive operations with challenges associated with the deposition of foulants, arising from solids and hydrocarbons in the boiler feed water, on the inner tube wall that leads to a decreasedheat transfer rate. The foulant deposition also causes elevated tube-wall temperatures, which may lead to tube failure. This study examines the impact of foulant on the tube-wall temperature profile and vapor-to-liquid ratio in an OTSG. A three-dimensional finite volume model of multiphase flow and heat transfer in a single pass of a field-scale OTSG unit is described. Detailed flow behavior and heat transfer characteristics of water and steam from the CFD model were compared to field data. Thereafter, fouling was added to the model to explore overheating and erosion zones in the OTSG tubes. Velocity, temperature distribution, and steam generation in the OTSG tubes in the convection section and radiant section were investigated for areas prone overheating. It was found that the CFD model simulation results closely matched the bulk fluid temperature of the field unit. In the presence of fouling, the outer skin temperature from the model was well within the range of the thermocouple data from the field unit, enabling the application of the model to identify the foulant thickness based on the outer skin temperature. Lastly, the model demonstrated that the bends are the most likely sites for erosion within the pass.

Heat transfer analysis of CuO-ZnO/water hybrid nanofluid in a Shell and tube heat exchanger with various tube shapes

Heat exchangers are widely used in various applications, including heating and cooling systems. Adding nanoparticles to the base working fluid can enhance the fluid's thermophysical properties, thereby increasing the thermal performance of heat exchangers. Further heat transfer enhancement can be done by using a hybrid nanofluid, which contains two or more different nanoparticles. The findings of the paper can be utilized to enhance the thermal efficiency of a shell and tube heat exchanger with different tube shapes and by using CuO-ZnO/ water hybrid nanofluid as a working fluid. Numerical simulations were conducted to model thermal heat exchangers with different configurations. Copper tubes of circular, hexagonal, and elliptical geometry were considered for the experiment. The model is solved using Ansys software with a finite volume approach. The solver employs an upwind-based multidimensional linear approach and upwind discretization schemes. The water inlet velocity in the Shell ranges from 0.5m/sec to 3.2 m/sec at a Reynold number of 10,000 to 15,000 whereas the velocity of cold fluid in the tube varies from 1.4 to 2 m/sec. All experiments were conducted with a 0.01–0.1 %vol % CuO-ZnO (80:20)/ water hybrid nanofluid. The hybrid nanofluid on the tube side is used to cool hot fluid (water) on the shell side. Hybrid nanofluid inlet temperature was maintained at 30°C to cool hot water at 60°C. Hexagonal tube geometry increases the contact surface area, resulting in a 22.11 % increase in heat transfer rate compared to round tubes and an 18.42 % increase compared to round tubes. Experimental and numerical results for the convective heat transfer coefficient, Nusselt number, and pressure drop were also reported.

Direct numerical simulation of coalescence and separation of binary droplet collision with lamella stabilization

Binary droplet collision is a fundamental aspect of various natural phenomena and industrial applications. In this work, direct numerical simulation of coalescence and separation of binary droplet collision is performed over a wide range of Weber numbers and impact factors. The incompressible Navier–Stokes equations are solved by the finite volume approach, coupled with the volume of fluid method. To address the inaccurate prediction of thin lamella in simulation, a lamella stabilization method is introduced to resolve the lamella by adjusting the grid resolution. Compared with experimental data, it is validated that the lamella can be accurately and fully captured with this lamella stabilization method. Moreover, the analysis of shape and energy during the collision is conducted, and the variation of lamella is described in detail, particularly the evolution of the thickness of lamella. The results suggest that for obtaining the full variation of lamella, the maximum refinement size of the grid can reach D/4096. It is also found that without lamella stabilization, excessive dissipation can lead to the failure of predicting coalescence and separation, especially for the cases in the transition between coalescence and separation. Furthermore, even if the same collision outcome can be obtained without lamella stabilization, the number and size of droplets have obvious differences.

Effect of wall contact angle on the conjugate heat transfer for flow boiling processes in rectangular microchannels

Microchannel boiling heat transfer offers a promising solution to address extreme high heat flux in miniaturized and high-density integrated electronic devices. In this work, we performed numerical studies to elucidate the complex flow boiling process in a square microchannel using the open-source platform OpenFOAM. The governing equations of the two-phase flow was solved based on the finite volume framework, and the surface tension together with phase change models were incorporated to study the wettability and conjugate heat transfer in the microchannel. First, the stability of the liquid film shows that smaller contact angles lead to thicker and stable liquid films near the solid wall, while larger contact angles result in thinner and fragile films. Second, the heat transfer, represented by the dimensionless parameter Nu, shows that smaller contact angles result in higher and more uniform distribution of Nu. The velocity gradient causes the Nu to be higher for the sidewalls than for the bottom wall. The contact angle also affects the peak value of Nu. Small contact angles result in large solid wall temperature gradients and more efficient heat transfer. Finally, the simulation results show that smaller thermal conductivity of the solid results in larger temperature gradient in the flow direction, implying that the conjugate heat transfer is less efficient. Overall, the present numerical findings provide useful guidance for efficient thermal management in electronic devices.

A high-fidelity finite volume scheme for ideal magnetohydrodynamics equations using boundary variation diminishing algorithm

A high-fidelity finite volume scheme based on the BVD (boundary variation diminishing) principle is proposed in this study to solve ideal magnetohydrodynamics (MHD) equations. A hybrid spatial reconstruction profile, based on a quadratic polynomial and a steepness-adjustable hyperbolic tangent function, is adopted to reproduce accurate solutions of complex magnetohydrodynamics flows. The BVD principle is used to find an optimal combination of these two types of functions by comparing variations between reconstructed interface values. Non-physical oscillations around discontinuities are removed by switching the quadratic polynomial to the step-shaped function. Additionally, an eight-wave method is applied in this study to control divergence errors of the magnetic field. The widely used numerical tests in one- and two-dimensional cases were checked in this study. The proposed scheme can achieve the accuracy of a third-order linear scheme in convergence tests for both advection and MHD equations and capture strong MHD shock waves without spurious oscillations. In comparison with a third-order WENO (weighted essentially non-oscillatory) scheme, the proposed one gains more accurate solutions for not only strong discontinuities but also smooth structures across scales. To our knowledge, this is the first attempt to build a high-fidelity model for ideal MHD equations by the BVD algorithm. Numerical results demonstrate that the BVD algorithm has promising potential to build practical models for various MHD flows.

Design and analyses of an AB5 - metal hydride based canister for hydrogen compressor application

The reversible hydrogen storage nature of metal hydride (MH) is widely accepted for the development of MH based energy devices like energy storage, hydrogen compressors, etc. For efficient working of such devices, the appropriate thermal management of canister is very important i.e. extraction and supply of heat during hydrogenation and dehydrogenation, respectively. The accumulation of heat reduces the hydrogen storage capacity as well as detoriarates the reaction rates because of increase in MH temperature. Therefore, to optimise the MH heat transfer, in the present work, a helical coil is introduced within the MH Canister (MHC) to circulate the heat transfer fluid in addition to an external cooling jacket. The purpose of using helical coil is to get more surface contact with MH because of the poor thermal conductivity of MH. The performance analyses have been carried out through a 3-D Finite Volume Approach employed with La0.9Ce0.1Ni5. The analyses include the influence of coefficient of heat transfer, pressure, and temperature on the designed canister as well as the compressor performance. Initially, the numerical model is validated with experimental results available in the literature and observed in good match. Later, the performance of MHC is predicted for different operating conditions which results in the estimated storage capacity of hydrogen is about 1.48wt% at 25bar and 298K. In addition, it is observed that at an elevated supply pressure, the reaction rates increased as well as the rise in MHC temperature increased due to exothermic heat. Later, the MHC is tested for the application as hydrogen compressor which results in the compression ratio of 10.8 with a discharge pressure of 270bar at 140°C providing ~20% efficiency.

Overlapping domain decomposition methods for finite volume discretizations

Two-level additive overlapping domain decomposition methods are applied to solve the linear system arising from the cell-centered finite volume discretization methods (FVMs) for the elliptic problems. The conjugate gradient (CG) methods are used to accelerate the convergence. To analyze the preconditioned CG algorithm, a discrete L2 norm, an H1 norm, and an H1 semi-norm are introduced to connect the matrices resulting from the FVMs and related bilinear forms. It has been proved that, with a small overlap, the condition number of the preconditioned systems does not depend on the number of the subdomains. The result is similar to that for the conforming finite element. Numerical experiments confirm the theory.

A Study on the Effectiveness of Climate Adaptation Materials for Urban Heat Islands using Digital Twin and Computational Fluid Dynamics

This study analyzed the impact of climate adaptation materials on the mitigation of urban heat islands (UHI) using digital twin visualization and computational fluid dynamics (CFD) technology. The effects of UHI due to increased impervious surfaces have become more pronounced, and climate-adaptation materials are gaining attention as potential solutions. In this study, the impact of climate adaptation materials on UHI mitigation was analyzed using the CFD program STAR-CCM+ based on the finite volume method (FVM). The selected research site was Byeoryang-dong, Gwacheon City, and four simulation scenarios were created based on the emissivity values of the asphalt and concrete materials. The results showed that application of climate adaptation materials decreased the surface and aboveground (1.5 m) temperatures by 6.3 and 0.8 °C, respectively. This study suggests that climate adaptation materials can significantly mitigate UHI.

Multi-Objective Numerical Analysis of Horizontal Rectilinear Earth–Air Heat Exchangers with Elliptical Cross Section Using Constructal Design and TOPSIS

This study presents a numerical evaluation of a Horizontal Rectilinear Earth–air Heat Exchanger (EAHE), considering the climatic and soil conditions of Viamão, Brazil, a subtropical region. The Constructal Design method, combined with the Exhaustive Search, was utilized to define the system constraints, degree of freedom, and performance indicators. The degree of freedom was characterized by the aspect ratio between the vertical and horizontal lengths of the elliptical cross-section duct (H/L). The performance indicators for the EAHE configurations were assessed based on thermal potential (TP) and pressure drop (PD). The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was applied for multi-objective evaluation, and a methodology for EAHE is proposed. The problem was solved using FLUENT software (version 2024 R2), which employs the Finite Volume Method to solve the conservation equations for mass, momentum, and energy. The (H/L)T,o = 6.0 configuration showed a 16.4% increase in thermal performance for heating and 15.9% for cooling compared to the conventional circular duct. Conversely, the (H/L)F,o = 1.0 configuration reduced pressure loss by 65.33%. The integration of Constructal Design with TOPSIS facilitated the identification of optimized geometries that achieve a balance between performance indicators and those that specifically prioritize thermal or fluid dynamic aspects, being this approach an original scientific contribution of the present work.

An Elastohydrodynamic model of the slot-die coating process

Abstract The slot-die coating process plays an important role in the industry, as it is employed in many different fields. The characteristics of the final application are determined by the flow between the die and the roller. This research paper aims to develop a mathematical model of such flow that takes into account the roller deformations caused by high pressure values reached by the coating fluid. This Elastohydrodynamic model is made up of a coupling between the mathematical model of the flow and the mathematical model of the roller deformations. Model resolution is undertaken numerically by deforming the flow domain according to the roller deformations using computational fluid dynamics (CFD) and computational solid mechanics (CSM) techniques. For its part, the finite volume method (FVM) is used to perform the flow model analysis while the finite element method (FEM) is employed to deal with roller deformations. The results obtained from this model give information on the flow pressure distribution, coating gaps, meniscus position, extent of roller deformations in the coating flow and the influence of different operating conditions. The information obtained from this study is valuable for industrial applications, as it gives insights into the coating process that can help manufacturers to define a suitable combination of operating parameters in order to obtain coating applications that meet quality and performance requirements.

Numerical Simulation of the Hysteresis Phenomenon and Asymmetrical Configuration of Turbulent Gas Flow in an Over-Expanded Nozzle Flows

The turbulent flow within Over-Expanded Nozzles is characterized by shock waves inducing unsteady separation of the boundary layer, which can exhibit both free and restricted detachment. This study investigates various physical phenomena encountered during the expansion regime, including supersonic jet formation, jet separation, adverse pressure gradients, shockwave interactions, turbulent boundary layers, compressible mixture layers, and large-scale turbulence. These complex phenomena significantly influence nozzle performance. Utilizing numerical simulations based on the resolution of Navier-Stokes equations via finite volume methods and employing the CFD-FASTRAN code, this research analyzes detachment characteristics, transition phenomena, and the predictive accuracy of different turbulence models. A test case from the ATAC project CNES-ONERA (Aerodynamics of Hoses and Back-bodies), is examined to elucidate the hysteresis phenomenon and asymmetrical configurations resulting from boundary layer detachment.

Cosmological Radiation Simulation Analysis: Taking Arepo-RT as an Example

With the fast-growing progress in computational physics, astrophysical simulations are made possible and continually upgraded with novel physical models. Contemporarily, many modern simulations feature the capability of cosmological radiation. In order to collate the recent improvements in this field, the numerical solver Arepo-RT is discussed as an important example. This study reorganizes and interprets the main physical models and numerical techniques used in Arepo-RT and similar solvers, with some details simplified to suit common readers. This paper describes simply and briefly the finite volume method, the radiative transfer model, the radiation source model, the Godunov-type schemes and the time integration, all of which are frequently used in modern radiation simulations. Apart from the realizations of the solvers, the results and limitations are also outlined in this paper, including the justification of reduced speed of light approximation, the results compared with JWST, and the issue of missing photons. These results shed light on guiding further improvements for Arepo-RT.

Impacts of geometric factors on the hydrothermal characteristics in a shell and cone-shaped coil heat exchanger

Cone coils have a larger surface area and produce more turbulence, which enhances the heat exchange rate, making them a more efficient option for improved heat transfer than simple coils in shell-and-coil heat exchangers. In addition to reducing fouling and the requirement for maintenance, the cone shape may also provide the benefit of a self-cleaning action. Ensuring a more even flow distribution maximizes the heat exchanger's surface area use and reduces poor-flow zones. Applications needing compact solutions without compromising performance significantly benefit from this design's versatility, allowing customization to meet unique operational demands. This work evaluates numerically the impact of employing a cone-shaped coil tube in a shell-and-coil tube heat exchanger, considering various configurations and coil pitches. A commercial CFD code is used to perform the numerical simulations based on the finite volume approach. The present study has two sections. In the first part, three different coil configurations were considered. The best case was considered according to the numerical results obtained from the first section. Then, in the second part, the impact of the cone coil pitch on the hydrothermal characteristics was analyzed. The obtained numerical outcomes revealed that the best performance evaluation criteria factor belongs to the cone-shaped coil with divergent configuration by about 64.1 % and 57.45 % more than the cone-shaped coil with convergent configuration at De = 1,000 and De = 2,500, respectively. Moreover, the cone-shaped coil with a divergent configuration displayed higher JF values by approximately 61.54 % and 58.06 % than a cone-shaped coil with a convergent configuration at De = 1,000 and De = 2,500, respectively. Among different evaluated cone coil pitches, the maximum performance evaluation criteria factor belongs to the case with pitch values of 40 mm. Moreover, the JF value increases by approximately 4.76 % and 5.56 %, respectively, at De = 1,000, when the pitch value grows by around 60 % and 100 %. Furthermore, when the pitch value climbs by 60 % and 100 %, at De = 2,500, the JF value rises by roughly 12.16 % and 19.59 %, respectively.

A finite discrete element approach for modeling of desiccation fracturing around underground openings in Opalinus clay

Understanding and predicting potential failure mechanisms during the excavation and open drift stages of geological repository construction are among the crucial aspects of performance evaluation and safety assessment of nuclear waste storage facilities. The development of the Excavation Damage Zone (EDZ) and the generation of shrinkage-induced cracks during operational phases are prominent examples of failure mechanisms that can compromise the integrity of the repository systems. This study presents an integrated framework for investigating shrinkage-induced cracking of Opalinus Clay in niches and tunnels. To achieve this, the hybrid Finite Discrete Element Method (FDEM) is employed. The methodology incorporates a two-way staggered hydro-mechanical coupling scheme, where solid phase analysis relies on 2D FDEM and fluid flow is modeled using the nonlinear Richards’ equation and solved via Finite Volume discretization. To account for the effects of EDZ, characterized by a pronounced increase in hydraulic conductivity, a numerical simulation of tunnel excavation is first carried out. The resulting failure pattern around underground openings is then abstracted through the definition of an altered hydraulic conductivity field. Comparison of the numerical results with field observations demonstrates the framework’s ability to capture a wide range of failure mechanisms inherent in various stages of underground repository construction in Opalinus Clay.

Computational analysis of pulsatile blood flow and heat transport dynamics in middle cerebral artery aneurysms in different body physiologies

This paper presents a comprehensive hemodynamic evaluation of two endovascular techniques for treating cerebral aneurysms. Using the finite volume method, we simulated pulsatile blood flow and heat transport dynamics in two saccular aneurysms of varying sizes and shapes. We assessed hemodynamic factors under two coiling conditions with different porosities and deformation stages to identify the most effective treatment for each case. Our computational analysis reveals that stent and coiling applications are more efficient for aneurysms with low-sac volume. Notably, stent placement proves to be more effective than coiling in treating saccular aneurysms. Our findings indicate that stent-induced deformation sufficiently diverts the main blood flow, thereby reducing the risk of aneurysm rupture near the ostium region.

Numerical Simulations of Flow and Heat Exchange in Zigzag-Shaped Microchannels

Cooling of electronic components is of great importance currently. One of the most important methods of integrated circuit cooling is the use of microchannel heat sinks. The aim of this work is to analyze the cooling capacity of zigzag shaped microchannels. The heat exchange for four different microchannels was tested depending on the flow rate of the cooling liquid (water) and the temperature of the cooled element. The system of differential equations that describe fluid flow and heat transport is presented in the paper. The equations were solved using the finite volume method. The work showed that both the increase in the number of zigzag sections and the increase in the flow velocity cause an increase in the flow resistance. In contrast, an increase in the temperature of the cooled element causes a decrease in fluid viscosity, which results in a decrease in flow resistance. From the point of heat exchange, both the increase in the number of segments, the flow rate, and the temperature of the cooled element increase the cooling capacity of the microchannel. Research shows that zigzag shaped microchannels are excellent cooling elements, especially for geometrically small heat sources such as electronic components.

Role of two isothermal cylinders towards three-dimensional flow and melting of phase-change materials

Recently, investigators focused on examining the melting of phase change materials (PCM) in regular two-dimensional or three-dimensional flow domains. At the same time, this topic still needs more study to get a better understanding of it. Also, such problems should be reported using the local thermal non-equilibrium (LTNE) model because the latent heat substances and the included porous elements have different temperatures. Therefore, this study examines the three-dimensional flow and melting process of phase change materials (PCM) within cubic enclosures filled with copper foam, using a local thermal non-equilibrium model (LTNE). The system includes two isothermal cylinders with different temperature conditions, varying distances, and radii, placed within the flow domain. The enthalpy-porosity approach is applied to model the PCM behavior, while the Brinkman-extended non-Darcy model accounts for high-velocity flow situations. A magnetic field is introduced to control the flow, with the Lorentz force acting opposite to gravity. The governing equations are solved using a home-developed code based on the finite volume method with the SIMPLE algorithm. Key parameters investigated include cylinder radii, Fourier number, Hartmann number, horizontal and vertical distances between cylinders, and Darcy number. The results are presented through streamlines, temperature distributions for fluid and solid phases, and profiles of the Nusselt number and average liquid fraction.