Finite Volume Research Articles

Modeling heat and mass transfer in metal hydride hydrogen storage systems: Impact of operating parameters and reactor geometry

This work introduces a transient 2D axis-symmetrical model for hydrogen absorption in a cylindrical LaNi5 reactor employing finite volume method with a fully implicit Euler's time integration scheme, coupling equations for heat, mass, and momentum transport. The validated model is used to investigate the impacts of pressure, cooling fluid temperature, and variations in reactor geometry and size on temperature and reacted fraction profiles. The findings reveal that the charging pressure affects both peak temperature and reaction kinetics, whereas cooling fluid temperature predominantly impacts the absorption kinetics. A comparative analysis of two models, one incorporating Darcy's velocity and one without, demonstrates that while Darcy's law introduces numerical instability in the coupled equations, its impact on the model outcomes is negligible. The effect of changing the non-homogeneous Neumann to Dirichlet boundary condition is also demonstrated to anticipate the utilization of phase change materials (PCM) instead of the cooling fluid.

Physics-informed neural network simulation of two-phase flow in heterogeneous and fractured porous media

Physics-informed neural networks (PINNs) have received great attention as a promising paradigm for forward, inverse, and surrogate modeling of various physical processes with limited or no labeled data. However, PINNs are rarely used to predict two-phase flow in heterogeneous and fractured porous media, which is critical to lots of subsurface applications, due to the significant challenges in their training. In this work, we present an Enriched Physics-Informed Neural Network (E-PINN) to overcome these barriers and realize the simulation of such flow. Specifically, the Embedded Discrete Fracture Model (EDFM) is adopted to explicitly represent fractures, and then the finite volume method (FVM) instead of the Automatic Differentiation (AD) is used to evaluate spatial derivatives and construct the physics-informed loss function, so that the flux continuity between neighboring elements with different properties (e.g. matrix and fracture) can be defined rigorously. Besides, we develop a novel physics-informed neural network (NN) architecture adopting the adjacency-location anchoring, adaptive activation function, skip connection and gated updating to enrich the pressure information and enhance the learning ability of NN. Additionally, the initial and boundary conditions are constrained through a hard approach, which encodes them into network design, to improve the accuracy and efficiency of network training. In order to further reduce the difficulty of training, the Implicit-Pressure Explicit-Saturation (IMPES) scheme is used to calculate pressure and saturation, in which only the pressure needs to be solved by training NN. Finally, the superiority and applicability of E-PINN to complex practical problems is demonstrated through the simulations of immiscible displacement in 2D/3D heterogeneous and fractured reservoirs.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma.

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Assessment of heat transfer capabilities of some known nanofluids under turbulent flow conditions in a five-turn spiral pipe flow

Abstract In this study, the thermo-flow behaviours of the spiral tube were examined using water and some nanofluids such as TiO2, Al2O3, Fe2O3, CuO, ZnO, and CeO2. The computational flow dynamic modelling of the spiral coiled tube was performed with ANSYS 20 software program. The k–ε model with a standard wall function was used to simulate the thermo-flow characteristics. The solution of the governing equations was performed using the discretization method of finite volume. The study was carried out considering the case of fluid-to-fluid heat transfer in turbulent conditions. The influence of different key design parameters such as Reynolds number, different nanofluids, and flow arrangements was of main interest. The volume concentration of the nanofluids is 1%. The experiments were performed at different Reynolds ranges (9,000, 14,000, 20,000, and 25,000). The outlet temperature values, heat transfer coefficient, coefficient of friction, Nusselt number values of water, and nanofluids were found and compared. It was found that the outlet temperature, heat transfer coefficient, and Nusselt number values of water were the lowest, while the coefficient of friction value was the highest compared to the nanofluids. Among the nanofluids, CeO was found to have the highest outlet temperature, heat transfer coefficient, and Nusselt number value, as well as the lowest coefficient of friction value. TiO2 was found to have the lowest outlet temperature (T out), the heat transfer coefficient value, and the highest coefficient of friction value. Al2O3 was found to have the lowest Nusselt number. In addition, Nusselt number values were obtained at different Dean numbers of water (2,200, 3,400, 4,900, 6,100, 7,350, and 8,600) and found to be compatible with previous studies. In addition, the coefficients of friction values of water at different velocities (0.18, 0.24, 0.41, 0.71, 0.95, 1.07, and 1.18) were obtained and found to be compatible with previous studies.

Block Spectral Method Analysis for Turbomachinery Applications

Abstract The block-wise spectral reconstruction of turbomachinery flows has been successfully used in the past to reduce the computational cost of full-annulus turbomachinery simulations. The rationale of the method is based on an explicit representation of the long-wavelengths of the problem using a Fourier expansion of the blocks, which in turn contain the short-wavelength content of the spectrum. This work analyzes the accuracy of this approach and shows that this approximation retains not only the explicit Fourier representation of the long wavelengths and finite volume approximation of the short wavelengths but their interaction as well. This interaction due to the scattering associated with the nonuniformity of the flow is referred to as Tyler–Sofrin modes by turbomachinery practitioners and is highly relevant for many practical applications. The solution’s harmonic content is illustrated by resorting to the linear wave equation with varying propagation speed and the NASA rotor 67 fan.

Numerical and experimental investigation of the hybrid piston compressor using the novel multi-time-scale OpenFOAM®-based model

Strongly coupled thermodynamic and heat exchange models of the hybrid piston compressor with regenerative heat exchange are developed, calibrated, and experimentally validated. The main challenge is the consideration of gas dynamics and heat transfer processes appearing at time scales different by three orders of magnitude. The Finite Volume Method (FVM) within the OpenFOAM® framework is used to discretize the actual three-dimensional compressor domain for heat exchange computation. On the other hand, the lumped zero-dimension approximation is used for gas dynamics. The present study is the first attempt to suggest a multi-time-scale numerical model of the hybrid piston compressor with no constraints on the domain geometry in the heat exchange part. The compressor’s heating during operation was reported to cause a reduction in its energy efficiency. Analysis of the three-dimensional fields of temperature and heat flux demonstrated that the piston and the valve plate are the hottest parts of the domain. Their cooling is not possible with standard approaches to heat exchange enhancement, while regenerative heat exchange within the hybrid compressor helps to circumvent such a constraint. The parametric investigation was carried out by determining the hybrid piston compressor transient processes and its integral characteristics using the proposed numerical model.

Analysis of nonlinear problems using the Dual Mesh Control Domain Method with arbitrary meshes

The Dual Mesh Control Domain Method (DMCDM), proposed and developed by the second author, is a recent advancement in the field of numerical methods. This method represents a blend of the Finite Element Method (FEM) and the Finite Volume Method (FVM), each having its primary domains of popularity. The DMCDM incorporates the concepts of interpolation, duality, and numerical integration from the former and the idea of satisfying the integral (global) form of the differential (or balance) equations from the latter. In this paper, we present a fresh and systematic approach to solving two-dimensional nonlinear problems, including advection–diffusion problems, with arbitrary primal meshes. We develop an approach where element-level equations are derived and assembled in a manner similar to that of the FEM, as opposed to using nodal equations, as has been the convention in all of the previous works involving the DMCDM. Additionally, we extend the previous works to include higher-order interpolation, specifically quadratic interpolation. In short, we provide formulations for four-node bilinear and nine-node biquadratic elements of quadrilateral shape, enabling the application of the DMCDM to arbitrary primal and dual meshes. Finally, we explore the Newton iteration method for linearizing the nonlinear system of equations that arises from the DMCDM discretization. We present numerical results and comparisons against available exact and numerical solutions to verify the accuracy and robustness of the DMCDM.

Thermo-hydraulic Investigation of a Heat Exchanger Tube Equipped with 3D-Printed Swirl Flow Generators

AbstractHeat transfer capabilities of the heat exchangers require enhancements to save energy and decrease their size. For this purpose, the swirl generators have been widely preferred. However, the swirler inserts have not reached their optimum shape. Thus, this study experimentally and numerically investigates the impact of novel 3D-printed swirler inserts with varying twist angles in the range of 0°–450° on the thermo-hydraulic performance of solar absorber tube heat exchangers under laminar flow (Re = 513–2054) condition. Friction factor, Nusselt number, and performance evaluation criterion (PEC) were used to assess heat exchanger performance, and related correlations are provided. Tangential velocity components were also used to explore fluid flow characteristics in local analysis. Numerical investigation was done by using computational fluid dynamics adopting Finite Volume Method in ANSYS Fluent. Results show that 3D-printed swirlers considerably increase heat transfer compared to plain tube. The swirler with a twist angle of 450° led to the maximum enhancements of nearly 217% in average Nusselt number and around 1630% in friction factor at Reynolds number of 2054. Overall, increasing Reynolds number enhanced Nusselt number. The highest PEC of 1.15 was observed at a Reynolds number of 1031 using the swirler with 150° twist angle. Flow near the swirler has higher tangential velocities, hence contributing to local Nusselt number enhancement up to 453.8% compared to plain tube when swirler with twist angle of 450° utilized. It is anticipated that findings of this study can guide further related research and increase the usage of swirlers in heat exchangers.

Efficient WENO Schemes for Nonuniform Grids

A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to implement and computationally efficient. The theoretical analysis to verify the accuracy and the essentially non-oscillatory properties are presented together with some numerical experiments involving algebraic problems in order to validate them. Also, these general schemes are applied for the solution of conservation laws and hyperbolic systems in the context of finite volume methods.

A high order cut-cell method for solving the shallow-shelf equations

In this paper we present a novel method for solving the shallow-shelf equations in the presence of grounding lines. The shallow-self equations are a two-dimensional system of nonlinear elliptic PDEs with variable coefficients that are discontinuous across the grounding line, which we treat as a sharp interface between grounded and floating ice. The grounding line is “reconstructed” from ice thickness and basal topography data to provide necessary geometric information for our cut-cell, finite volume discretization. Our discretization enforces jump conditions across the grounding line and achieves high-order accuracy using stencils constructed with a weighted least-squares method. We demonstrate second and fourth order convergence of the velocity field, driving stress, and reconstructed geometric information.

Numerical study of the optimization of the thermal and flow characteristics of a collector design of microchannels with two inlets and outlets, containing a nanofluid and a water-based fluid

The effect of aluminum microchannel geometry on the flow properties of water and Al2O3–H2O nanofluid was studied numerically using CFD. For this purpose, we studied three cases of three different shapes of microchannels, the first case is rectangular micro channels, and in the second case, we added obstacles to the bottom and top walls of the microchannels. In the last case, we gradually decreased the hydraulic diameter of the channels at a distance of 2L/3 from the outlet of the microchannel. The channels have two inlets and one outlet. There is also a continuous flow heat source at the bottom of the channels. In this study, the Reynolds number varied from 300 to 600 for the two inlets. We also used water and a nanofluid with a low volume concentration of nanoparticles (2%). We considered that the fluid temperature at the inlet of the microchannels changes from 293 K to 300 K. We relied on the finite volume method with the SIMPLE algorithm in the calculation method. According to the results obtained from this study, the effect of changing the value of the Rayleigh number at the two entrances of the channel was observed on the temperature and velocity of the fluid and on the heat exchange inside the channels in the three cases. We also found that difference of the average of the Nusselt number between the nanofluid and the basic one in the three cases at Re =600 is 1.15, 1.74, and 1.57, respectively. In addition, we found that the shape of the studied micro channels has an effect on the friction factor and thermal resistance.

Numerical Calculation and Experimental Study of the Axial Force of Aero Fuel Centrifugal Pumps

Axial force is one of the important factors affecting the life and reliability of centrifugal pumps. Based on the SST turbulence model, the unsteady internal flow field of an aero fuel centrifugal pump under various working conditions was analyzed by using the finite volume method and the axial force of the impeller component was predicted. The position servo force measuring system was used to measure the axial force of the fuel centrifugal pump and the theoretical formula of axial force was modified according to the numerical results and experimental values. The study shows that the pressure distribution of the front and rear pump chambers presented uneven circumferential distribution under the influence of dynamic and static interference through numerical simulation. The simulated head number is basically consistent with the test result and the maximum error of the axial force value obtained by the numerical calculation and the experimental value was 9.7% under different speeds, which verified the accuracy of the numerical simulation. Furthermore, the modified formula can accurately calculate the axial force of the fuel centrifugal pump with an error of less than 9.88%. The results of the study provide a theoretical basis for the calculation and balance of axial force in an aero aero fuel centrifugal pump.

Fully decoupled, linearized and stabilized finite volume method for the time-dependent incompressible MHD equations

In this paper, we consider the stability and convergence of the fully decoupled and linearized numerical scheme for the time-dependent incompressible magnetohydrodynamic equations based on the finite volume method. The lowest equal-order mixed finite element pair (P1-P1-P1) is used to approximate the velocity, pressure and magnetic fields, and the pressure projection stabilization is introduced to bypass the restriction of the discrete inf-sup condition. The semi-implicit treatment is used to linearize the nonlinear terms and the first order projection scheme is adopted to split the velocity and pressure, then a series of fully decoupled and linearized subproblems are formed. From the view of theoretical analysis, some novel stability results of the numerical solutions in both spatial semi-discrete scheme and time–space fully discrete scheme are provided, the optimal error estimates are also presented by using the energy method and choosing different test functions. From the view of computational results, the fully decoupled and linearized numerical scheme not only keeps good accuracy, but also saves a lot of computational cost.

Long-wave instabilities of a power-law fluid flowing over a heated, uneven and porous incline: A two-sided model

The stability conditions of a two-dimensional gravity-driven flow of a thin layer of a power-law fluid flowing over a heated, uneven, inclined porous surface are investigated. A two-sided model is employed to account for the bottom filtration in the porous layer. The governing equations are reduced under the long-wave approximation and the cross-stream dependence is eliminated by means of the Integral Boundary Layer technique. Floquet–Bloch theory is used to investigate at linear level how the porous bottom waviness influences the thermocapillarity stability of the flow in a shear-thinning fluid. Differently from the even case, the linear stability analysis suggests that for flow over sufficiently wavy undulations the thermocapillarity may stabilize the equilibrium flow, depending on the values of dimensionless governing numbers and parameters. This stabilizing phenomenon is enhanced by the shear-thinning rheology of the fluid while it is reduced by the permeability of the layer. Numerical simulations, performed solving the reduced nonlinear model through a second order Finite Volume scheme, confirm the results of the linear stability analysis.

Numerical analysis of optimal control problems governed by fourth‐order linear elliptic equations using the Hessian discretization method

AbstractThis article focuses on the optimal control problems governed by fourth‐order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretization method (HDM). The HDM is an abstract framework that enables the convergence analysis of several numerical methods such as the conforming finite element methods, the Adini and Morley nonconforming finite element methods (ncFEMs), the method based on gradient recovery (GR) operators, and the finite volume methods (FVMs). Basic error estimates and superconvergence results are established for the state, adjoint, and control variables. A companion operator for the GR method with specific property is designed. The article concludes with numerical results that illustrate the theoretical convergence rates for GR method, Adini ncFEM, and FVM.

Deep learning of first-order nonlinear hyperbolic conservation law solvers

In this contribution, we study the numerical approximation of scalar conservation laws by computational optimization of the numerical flux function in a first-order finite volume method. The cell-averaging inherent to finite volume schemes presents a challenge in the design of such numerical flux functions toward achieving high solution accuracy. Dense neural networks, as well as (piecewise) polynomials, serve as function classes for the numerical flux. Using a parametrization of such a function class, we optimize the numerical flux with respect to its solution accuracy on a set of Riemann problems for which we have closed-form solutions. By design, our resulting first-order finite volume schemes are conservative.We show empirically that the proposed schemes can achieve higher accuracy than the Godunov and Enquist-Osher method on a wide range of discretizations.The proposed method can be applied to the inverse problem, i.e., the data-driven synthesis of macroscopic physical laws for real-world flux phenomena.

Analysis of melting behavior of layered different phase change materials for a cylinder insert into a channel

Phase change materials (PCMs) have diverse fields of application due to higher thermal inertia. The present study explores the melting behavior in dual-layered different PCMs in a cylindrical lithium-ion battery module placed in a long channel under the hot air stream. The main cylinder is packed with paraffin wax and covered PCM is chosen as calcium chloridehexahydrate (CaCl2-6H2O). The material between two PCMs is considered highly conductive and impermeable. The involved mathematical equations in two-dimensional forms are numerically simulated the applying the finite volume technique. The primary important parameters of melting behavior are the difference in temperature and inlet air velocity. The analysis is carried out for the effective parameters such as the inlet air temperature (Thot = 100 °C and 120 °C) and air velocity (սair = 2.5 and 5.0 m/s). The results revealed that an increase in air velocity reduces the highest and average temperature of the PCM. The changes in melting time of PCMs decline with time. Higher inlet air temperature also causes fast melting of the PCMs over time. The analysis revealed that the application of PCMs is undue when there is no phase change process. The analysis also revealed that an increment in the inlet air velocity causes a decrease in the average temperature. For the same air inlet temperature (Thot) higher air velocity leads to a slower rate of the melting process Therefore, melting time is less by ∼ 30 % (for the inner layer) and 32 % (for the outer layer) with decreasing air velocity. The findings of this study will help the designer to improve the battery thermal management system by modulating the temperature.

Numerical Analysis of Airflow in Trachea Affected by Thyroid Cancer Using Finite Volume Method

The study aims to analyze the airflow in the trachea due to thyroid cancer. Thyroid cancer is a cancer that attacks the thyroid gland. The thyroid gland is located in the neck below the Adam's apple. In general, thyroid cancer causes stenosis of the trachea due to cancer compression of the tracheal wall. This problem is solved using the finite volume method with SIMPLE (Semi Implicit Method for Pressure Linked Equation) discretization. This method is well suited for the discretization of irregularly shaped fluid flows. The software used is Matlab and Ansys Fluent. Matlab is used to compute numerical solutions and display graphs, while Fluent is used to visualize the air flow. The result of this study is that the greater the percentage of stenosis, the velocity of the airflow is faster and the pressure of the airflow is lower. The most critical condition for respiratory power loss is when the airflow velocity exceeds the normal limit, i.e. when the narrowing is more than 50%, the initial velocity is more than 0,1 m/s.

Numerical analysis of electrothermoconvection of a dielectric nanofluid in a heated cavity

A numerical analysis of electrohydrodynamic (EHD) flow and heat transfer of nanofluid in a heated rectangular cavity is presented. A two-dimensional (2D) rectangular cavity heated from the bottom is considered. An electric potential difference is applied vertically, with the bottom wall acting as a high-voltage electrode, and the top wall is grounded. TiO2-25 # transformer oil nanofluid with nanoparticle volume fraction ranging from 0–5% is considered. The numerical model for EHD flow and heat transfer of nanofluid is implemented in the finite-volume method (FVM) based numerical framework of OpenFOAM. A single-phase approach based on the effective properties is adopted to model the nanofluids. A two-way coupled EHD flow model is employed to consider mutual interactions of flow and electric field variables. The flow and heat transfer behavior of nanofluids in the presence of an electric field is quantified with reference to the key parameters, electric Rayleigh number (T), and the nanoparticle volume fraction ϕ. The addition of nanoparticles increased the viscosity and marginally reduced the natural convective flow and heat transfer. However, EHD flow induced by the electric field aided in overcoming the weak natural convection flow in nanofluids. Results confirm that nanofluids’ net effective heat transfer rates are notably increased in the presence of the electric field. For the parameters under consideration, combining electric fields with nanofluids led to a significant heat transfer enhancement of up to 32.3%. The present study showcases the feasibility of combining passive heat transfer enhancement using nanoparticles and active heat transfer enhancement using EHD flow.

A reduced order model formulation for left atrium flow: an atrial fibrillation case.

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier-Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson's constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up.