Finite Volume Research Articles

Numerical Analysis of the Heat and Mass Transfer in a Ventilated Cavity for Turbulent Convective Flow With Extreme Hot and Humid Climate Conditions

ABSTRACTTo analyze the temperature and relative humidity (RH) in a room located in the Lacandona jungle in Chiapas, Mexico, a numerical heat and mass transfer study was performed. The study was carried out in a ventilated cavity, by introducing air flow into user‐occupied spaces. The study analyzed the combination of temperature and humidity percentage to create thermal comfort conditions. The finite volume method was used to solve the governing equations, while pressure–velocity coupling was done with the SIMPLEC algorithm. Turbulent airflow was considered, and modeled using the k–ε turbulence model, with Reynolds numbers (Re) in the range from 100 to 5000. Seven sets of weather conditions were considered for a warm April day with solar radiation values that ranged from 0 to 981 W/m², outdoor temperatures between 19.9°C and 35.3°C, as well as RH from 42% up to 100%. The study analyzed temperature, RH, distribution efficiencies, and heat fluxes. It was found that the average temperature closest to thermal comfort was 25.8°C. This corresponds to an Re = 5000, being the best hygrothermal conditions with an average RH of 50%. However, this level of RH is unattainable by many air conditioning systems.

Influence of vortex generator dimensions on film cooling efficiency

Enhancements in gas turbine blade cooling techniques, such as film cooling, have significantly advanced the aerothermal effi-ciency of turbines, especially in transportation sectors like aeronautics and automotive industries. This study aims to enhance turbine blade cooling by incorporating an obstruction at the jet exit. The vortex generator angle has been modified to 25°, 45°, 60°, 90° and 110°. These five designs were assessed in comparison to the conventional cylindrical hole configurations. Two injection ratios (M = 0.25, and M = 0.5) were studied within the ANSYS CFX 16 software, utilizing the finite volume method to solve the average Reynolds equations and the energy equation. The findings show qualitative alignment with experimental data for the base scenario, indicating that the vortex generator angle notably amplifies film cooling effectiveness. Typically, the vortex generator configured at 90° exhibits a stronger mixing capability compared to the other cases and cylindrical design.

Impact of MHD mixed convection on heat and mass transfer in a typical DCLL breeder blanket

Abstract A typical dual-coolant lead lithium (DCLL) liquid blanket employs eutectic liquid lithium lead alloy (PbLi) as coolant and tritium breeder for Tokamak nuclear fusion reactor, and is responsible for transporting heat and tritium. The blanket is subjected to both strong magnetic field and strong radially non-uniform neutron volume heating. The flow of liquid metal is influenced by the combined effects of magnetohydrodynamics (MHD), buoyancy, and inertial effects, resulting in a complex MHD mixed convection phenomenon. This study employs direct numerical simulation (DNS) based on finite volume method to analyze the flow, heat transfer, and mass transfer within blanket unit. The results demonstrate that mixed convection has a significant impact on the MHD pressure drop and flow characteristics. The complex MHD mixed convection gives rise to a considerable number of vortices, particularly in regions of the turn and the downward poloidal duct. The formation of low-speed zones and jets within the blanket has the potential to significantly impact heat and mass transfer, leading to the accumulation of heat and tritium. On the other hand, the markedly elevated tritium production rate is a significant contributing factor to the obviously elevated tritium concentration in the vicinity of the first wall.

Development of heat exchanger modelling capability for a finite volume aeroelasticity solver

Abstract Heat exchangers are frequently used in aero engines and are known to significantly affect the surrounding steady and unsteady flow. In certain applications, they may thereby also influence the aeroelastic stability of upstream or downstream components but there is limited research on this in the public domain. This paper aims to demonstrate the influence of heat exchangers on unsteady flows relevant to aeroelastic problems. This is achieved by developing heat exchanger modelling capability for an in-house finite volume aeroelasticity solver, for which heat exchanger is represented as a porous medium, as this is the established approach in existing aerodynamic studies using commercial CFD software. The governing equations for a Darcy-Forchheimer porous media model suitable for unsteady and compressible flows are presented, which are derived by the application of volume averaging theory to the Navier-Stokes equations. The implementation of this model within the time integration method used for the solver is then described and verified by comparison of results for steady flows against an established commercial CFD solver, where close agreement between both in-house and commercial solvers has been observed. Lastly a preliminary demonstration of the capability to model unsteady heat exchanger flows is presented by application to an aeroacoustic problem, where the interaction of the pressure waves and the heat exchanger is investigated.

An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions.

We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form . A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.

Fluid Dynamic and Thermal Performance of a V-Shape Slotted Cylinder

The flow characteristics and thermal performance of circular cylinders with V-shape slots are investigated numerically. The simulation is a two-dimensional incompressible flow that employs the semi-implicit finite volume multi-material algorithm MPM-ICE, which is a module of the Uintah framework. The normalized slot width s2/D ranges from 0.1 to 0.2, and the corresponding increases in total surface area are from ~99% to ~70%, respectively. Compared to the solid cylinder, the slotted cylinder has the largest total drag reduction of ~67% at s2/D of 0.2. Meanwhile, although the heat transfer is proportional with the surface area, the thermal performance of the V-shape slot first improves with the slot width, and then declines. The heat transfer improvement has an optimum value of ~192% at s2/D of 0.15. The overall slot performance, defined by the ratio of the heat transfer to the drag force, is best at 0.175.

Release of a finite volume of viscous fluid over rigid curvilinear surfaces

Viscous gravity currents play a fundamental role in many natural and industrial applications, where practical scenarios often involve the current propagating over rigid curvilinear surfaces. In this study, we employ lubrication theory to develop low-dimensional models for such two-dimensional and axisymmetric propagation, resulting from the release of a finite volume of viscous fluid. A key dimensionless parameter is identified, representing the volume ratio between the released fluid and the curvilinear surface, which governs the current evolution. By simplifying the curvilinear surface with linear–exponential and sinusoidal shapes, we observe distinct flow behaviours. Over linear–exponential surfaces, the current may become trapped, bypass the peak or flow downward, while over sinusoidal surfaces, the propagation is hindered compared with the behaviour over horizontal straight surfaces. The low-dimensional models are validated using the volume of fluid method in computational fluid dynamics, showing consistent predictions of the current evolution over rigid curvilinear surfaces.

Numerical study of the influence of the geometrical aspect ratio and nanoparticles diameter on forced convection in a micro-channel heat sink of a nanofluid water/CuO based on a Brownian diffusion model

In order to cool electronic equipment with a high efficiency we can use the flow of a nanofluid in a rectangular micro-channel heat sink. The paper reports the results of the study of a hydrodynamically fully developed laminar forced convective heat transfer flow in two different geometries G1and G2. The study is numerical and was achieved using as nanofluid with and a single-phase approach. Calculations were first made with constant thermo-physical properties at and then made using temperature and nanoparticles diameter dependent thermo-physical properties based on a Brownian diffusion model. A three-dimensional conjugate heat transfer model was used and numerical simulations were based on a finite volume method. The simulations were made for a range of Reynolds numbers , for nanoparticle diameter in the range of and for a heat flux through the bottom surface of the heat sinks .The results of thermal and hydrodynamic fields show that nanofluids can provoke an increase in the local and average Nusselt numbers, a decrease of bottom surface local temperature and a slight decrease of the shear stress on the wall, particularly in the case of geometry G2. At the end of the study, the best geometry, volume fraction of nanofluid and nanoparticle diameter to be recommended for cooling were found based on minimum total thermal resistance of the micro-channel heat sink.

Effect of bridgmanite-ferropericlase grain size evolution on Earth’s average mantle viscosity: implications for mantle convection in early and present-day Earth

Recent experimental investigations of grain size evolution in bridgmanite-ferropericlase assemblages have suggested very slow growth for these bimodal phases. Despite numerous speculations on grain size-dependent viscosity, a comprehensive test with realistic grain size evolution parameters compatible with the lower mantle has been lacking. In this study, we develop self-consistent 2-D spherical half-annulus geodynamic models of Earth’s evolution using the finite volume code StagYY to assess the role of grain size on lower mantle viscosity. We explore several models with and without grain size evolution to compare their effects on mantle viscosity. In models with grain size evolution, we consider three scenarios: (1) uniform grain growth throughout the entire mantle with a composite rheology, (2) different grain growth in the upper and lower mantle with a composite rheology, and (3) different grain growth in the upper and lower mantle with purely diffusion creep rheology. In the case of different grain size evolution, the upper mantle’s grain size evolution law is controlled by forsterite-enstatite grain growth, while the lower mantle’s grain size evolution law is controlled by bridgmanite-ferropericlase grain growth. Our results suggest that mantle viscosity is primarily controlled by temperature, whereas grain size has a minor effect compared to the effect of temperature. We attribute two primary reasons for this: First, the bridgmanite-ferropericlase growth is very slow in the lower mantle and the grain size variation is too small to significantly alter the mantle viscosity. Secondly, if grains grow too fast, thus the mantle deforms in the dislocation creep regime, making viscosity grain size-independent. To establish the robustness of this finding we vary several other model parameters, such as surface yield strength, phase transition grain size reset, different transitional stresses for creep mechanisms, pressure dependence on grain growth, and different grain damage parameters. For all our models, we consistently find that grain size has a very limited effect on controlling lower mantle viscosity in the present-day Earth. However, large grain size may have affected the lower mantle viscosity in the early Earth as larger grains of single phase bridgmanite could increase the viscosity of the early mantle delaying the onset of global convection.

Numerical simulation method of grease flow in a grease groove with experimental validation

The flow process and characteristics of lubricating grease have a significant impact on the lubrication performance of bearings. Based on the rheological parameters of lubricating grease and the Cross rheology model, this paper proposed a lubricating grease flow simulation method in the grease groove based on user defined functions (UDFs) combined with the Finite Volume Method (FVM) and verifies the rationality of the simulation method through visualization experiments. The flow characteristics of lubricating grease in the grease groove were studied under three different grease delivery angles. Additionally, it was observed that the lubricating grease ceased to flow in the groove during the delivery process, and the simulation method was used to analyze and explain this phenomenon.

Characterization of Guest DNA Transport and Adsorption within Host Porous Protein Crystals.

Nucleic acid transport through protein-based pores is a well-characterized phenomenon due in part to advancements in nanopore sequencing. A less studied area is nucleic acid transport through extended protein-based channels, where the additional surface area and increased contact time allow for the study of prolonged binding interactions. Porous protein crystals composed of "CJ", a putative polyisoprenoid-binding protein from Campylobacter jejuni, represent a favorable, highly ordered material for studying DNA transport and binding/unbinding along protein-based channels. These crystals adopt a hexagonal prism habit and contain a densely packed hexagonal array of 13 nm diameter axial nanopores that run from the top to the bottom of the crystal. After cross-linking, the crystals are easily manipulated for experimentation. An adsorption isotherm between host crystals and guest double-stranded 8 base pair DNA (8mer) revealed a high equilibrium adsorption constant of 206 ± 30 L/g. Fluorescence confocal microscopy tracked the loading of guest DNA into host crystals predominately along the major axial crystal nanopores. Four different computational models based on the finite volume (FV) method were assessed to model the transport process for guest 8mer and 15mer dsDNA loading into empty host crystals in terms of fundamental parameters, such as the intrapore diffusion constant. Fitting the models to the data revealed that the most basic FV model sufficed to describe the observed loading behavior, characterized by a single effective diffusion coefficient. Leveraging Fick's first law, we more directly fit a numerical range for the observed intrapore diffusion coefficient as a function of time, position within the crystal, and relative guest concentration. This new transport analysis strategy was applied to both out-of-equilibrium loading and fluorescence recovery after photobleaching (FRAP) experiments. The intrapore diffusion constants are comparable between 8mer and 15mer dsDNA and were found to be 2 orders of magnitude faster for DNA loading into empty crystals than that observed in FRAP experiments, which averaged (10 ± 4) × 10-11 cm2/s.

Numerical examination of wave forces on partially submerged horizontal circular cylinders near free surface

Determining wave forces on partially submerged horizontal circular cylinders near free surface is a significant issue. This study explores hydrodynamic coefficients and wave forces on horizontal circular cylinders near free surface under large-amplitude wave actions using a viscous fluid numerical wave tank model based on the finite volume method, with a particular aim to accurately predicting the slamming force. By analyzing the characteristics of the wave forces and slamming forces on the circular cylinder, the influences of wave amplitude, wave frequency and vertical position of the cylinder on the wave forces are investigated, and the relationships between the slamming forces and fluid velocity are discussed. Additionally, a modified Morison's equation for predicting the wave forces is derived considering the slamming force and the condition of the circular cylinder completely exposed to the air phase under the action of large-amplitude wave. The results of this study reveal that the wave forces on the circular cylinder are significantly influenced by wave amplitude, frequency and vertical position of the cylinder, and the influences of the cylinder position on the predicted minimum slamming velocity are remarkable. The present study demonstrates that modified Morison's equation is plausible and accurate in predicting the wave and slamming forces for submerged or floating structures.

Topology optimization for 3D fluid diode design considering wall-connected structures

This paper proposes a density-based topology optimization method for the three-dimensional design of fluid diodes considering wall-connected structures based on the fictitious physical modeling approach. The optimum design problem of fluid diodes is formulated as maximizing the energy dissipation in the reverse flow subject to the upper bound constraint of the energy dissipation in the forward flow. A fictitious physical model and a geometric constraint are constructed to detect and restrict the “floating” solid domains, which are not connected to the outer boundaries. The sensitivities of cost functions are derived and computed based on the continuous adjoint method. The finite volume method is employed to discretize the governing and adjoint equations to mitigate the huge computational costs of three-dimensional fluid analysis. Numerical investigations are presented to validate the fictitious physical model and the geometric constraint for excluding “floating” islands. Finally, topology optimization for fluid diodes with and without the geometric constraint is performed, and the result demonstrates that the proposed method is capable of generating fluid diodes with wall connectivity, while maintaining a good functional performance.

Vertically heated natural convection loop model

Abstract We present a comprehensive analytical model for laminar flow in a vertically heated rectangular convection loop, with applications to oil cooling in transformer systems. Starting from an integral equation, we apply a quasi-one-dimensional approach to derive equations for both loop velocities and temperature distributions. In this model, we account for temperature-dependent dynamic viscosity and introduce cooling at the loop top and in the fin. The analytical predictions are rigorously validated against finite volume method (FVM) simulations across different geometries and heat flux conditions, demonstrating strong agreement within a 2% discrepancy range for most parameters. This model provides a viable analytical alternative to computationally intensive simulations, offering insights into natural convection dynamics within closed-loop configurations.

Heat Transfer in Annular Channels with the Inner Rotating Cylinder and the Radial Array of Cylinders

Numerical investigations of heat transfer for forced, mixed, and natural convection conditions within an annular channel are carried out. The main objective was to investigate, for the first time, the effect of the radial cylinder array on heat transfer in the annular channel with the rotating cylinder. The governing equations for velocity and temperature with the Boussinesq approximation were solved using the finite-volume method. The heat transfer quantities were obtained for different Rayleigh numbers (104–106), the radius ratios (1.4–2.6), the radial cylinder spacing, and for different rotating velocities in the form of the Richardson number (10−2–104). The Prandtl number was 0.7. It has been shown that radial cylinders do not influence significantly the intensity and the local distribution of heat transfer on the inner rotating cylinder. The Nusselt number was 1.4–2.0 times higher on the radial cylinder array for all convection modes relative to the outer flat surface. For all annuli gaps with radial cylinders, the maximal values of the Nusselt number were observed with an increase of the radial spacing of cylinders.

IGG(χ): A new and simple implicit gradient scheme on unstructured meshes

A new and simple implicit Green-Gauss gradient (IGG) scheme for unstructured meshes is proposed exploiting the ideas from the linearity-preserving U-MUSCL scheme to define values at cell faces. We construct an implicit one-parameter family of gradient schemes referred to as IGG(χ) where χ is a free-parameter. The computed gradients are at least first-order accurate on generic polygonal meshes and second-order accurate on uniform Cartesian meshes except when χ=1/3 for which fourth-order accuracy can be realised. A theoretical analysis is carried out to understand the effect of the control parameter χ on accuracy and resolution of the gradients and numerical experiments on various mesh topologies confirm the theoretical findings. Finite volume simulations of the Poisson and Euler equations on Cartesian and unstructured meshes further highlight that the IGG(χ) is a versatile gradient scheme that gives second-order accurate solutions with the iterative convergence of the solver dependent on the choice of the χ parameter. The framework described in this study can also be employed to devise an implicit least-squares gradient scheme that applies equally well to unstructured finite volume and meshfree solvers.

Adaptive Local Mesh Refinement in 2-D Finite Volume Method for Steady State and Transient Simulations of Semiconductor Devices

Adaptive Local Mesh Refinement in 2-D Finite Volume Method for Steady State and Transient Simulations of Semiconductor Devices

OpenBF: an open-source finite volume 1D blood flow solver

Computational simulations are widely adopted in cardiovascular biomechanics because of their capability of producing physiological data otherwise impossible to measure with non-invasive modalities.Objective.This study presents openBF, a computational library for simulating the blood dynamics in the cardiovascular system.Approach.openBF adopts a one-dimensional viscoelastic representation of the arterial system, and is coupled with zero-dimensional windkessel models at the outlets. Equations are solved by means of the finite-volume method and the code is written in Julia. We assess its predictions by performing a multiscale validation study on several domains available from the literature.Main results.At all scales, which range from individual arteries to a population of virtual subjects, openBF's solution show excellent agreement with the solutions from existing software. For reported simulations, openBF requires low computational times.Significance.openBF is easy to install, use, and deploy on multiple platforms and architectures, and gives accurate prediction of blood dynamics in short time-frames. It is actively maintained and available open-source on GitHub, which favours contributions from the biomechanical community.

TwoPhaseInterTrackFoam: an OpenFOAM module for Arbitrary Lagrangian/Eulerian Interface Tracking with Surfactants and Subgrid-Scale Modeling

We provide an implementation of the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian (ALE) Interface-Tracking method for simulating incompressible, immiscible two-phase flows as an OpenFOAM module. In addition to interface-tracking capabilities that include tracking of two fluid phases, an implementation of a Subgrid-Scale (SGS) modeling framework for increased accuracy when simulating sharp boundary layers is enclosed. The SGS modeling framework simplifies embedding subgrid-scale profiles into the unstructured Finite Volume discretization. Our design of the SGS model library significantly simplifies adding new SGS models and applying SGS modeling to Partial Differential Equations (PDEs) in OpenFOAM. Program summaryProgram Title: twoPhaseInterTrackFoamCPC Library link to program files:https://doi.org/10.17632/6b49wb7fvd.1Developer's repository link:https://gitlab.com/interface-tracking/twophaseintertrackfoamreleaseLicensing provisions: GPLv3Programming language: C++Nature of problem: Two-phase flow problems involving surface-active agents (surfactants), variable surface tension force and very sharp boundary layers.Solution method: An OpenFOAM implementation of the Arbitrary Lagrangian / Eulerian Interface Tracking method.

An opportunity for streamlined computational fluid dynamics integration via a semi-analytical method for weighted finite volume fragmentation equations

An opportunity for streamlined computational fluid dynamics integration via a semi-analytical method for weighted finite volume fragmentation equations