Finite Volume Method For Solving Research Articles

Numerical and experimental investigation for helical savonius rotor performance improvement using novel blade shapes

Wind energy is extensively invested as a renewable and clean energy source. Savonius wind rotor, as an energy converter, has the merit of being appropriate for specific applications. The current paper centers on the performance enhancement of a helical Savonius wind rotor through the blade shape modification. The basic objective is to assess and compare, numerically and experimentally, the performance of two rotors with novel blade shapes named delta bladed and two-stage delta bladed shapes in relation to a helical Savonius rotor. Numerical study was conducted using Ansys Fluent software. 3-D unsteady simulations were carried out through the use of the SST k-ω turbulence model based on the finite volume method solver. Aerodynamic flow and performance characteristics were investigated. Static and dynamic experimental tests were undertaken on a wind tunnel. An improvement in Cp by 22.58 % and 29.5 % for the two-stage delta bladed rotor and 19.35 % and 16.4 % for the delta bladed rotor over the helical Savonius rotor was recorded, respectively, numerically and experimentally. In addition, the self-starting ability as well as the aerodynamic flow characteristics of the helical rotor were enhanced with the novel blade shapes.

Numerical study on thermal runaway in a cell and battery pack at critical heating conditions with variation in heating powers

The thermal stability of lithium-ion cell is still a major concern in electric vehicle and energy storage applications affecting the cell to its chemistry level. The thermal abuse is the most common type of thermal runaway which is triggered either by excess heat accumulation or localized heating in the battery pack. Analysis of thermal runaway in the perspective of various critical heating positions with temperature distribution, heat generation still lacks. Thus, the present work is focused on this issue. A three-dimensional homogeneous Multi-Scale, Multi-Dimensional model with a finite volume method solver ANSYS FLUENT has been utilised to assess the effect of heating positions, and variation in spacings on thermal runaway for a 18650 cell and battery pack in a detailed way. It is observed that the direction of flow is the typical deciding factor of the thermal runaway spreading pattern in the cell. The negative solvent is responsible for the generation of maximum heat in the thermal runaway of a 18650 cell. The results show that cell heated at the bottom end (10 mm width) is fast prone to thermal runaway, vertical (5 mm width) being slower in disturbing the separator stability. The NCA cathode material has a safety hierarchy that goes as follows with regard to positions: vertical 10 mm > bottom end > bottom 5 mm > centre 10 mm > bottom 10 mm. The effect of spacing on thermal runaway is varying non-uniformly with the location of the heating position in the 3 × 3 battery pack. The highest temperature attained by the 7000 W/m2 heating power battery pack is discovered to be greater than the 10,000 W/m2 by 10 K. With a power increase from 7000 W/m2 to 10,000 W/m2, there is a reduction in time delay of 17 %.

Large eddy simulation within the smoothed particle hydrodynamics: Applications to multiphase flows

In this paper, the large eddy simulation (LES) model introduced in the smoothed particle hydrodynamics (SPH) by Di Mascio et al. [Phys. Fluids 29, 035102 (2017)] and called δ-LES-SPH, is extended to treat multiphase flows. This is achieved by modifying the multiphase δ-SPH by Hammani et al. [Comput. Methods Appl. Mech. Eng. 368, 113189 (2020)] by switching the viscous and density diffusion constants to dynamic variables evaluated as turbulence closure terms. The equation for energy conservation is also written for the presented model. The validation is performed for two-dimensional problems, by comparison with other established SPH solvers, with a finite volume method solver based on the turbulence closure corresponding to that adopted for the Lagrangian scheme, and with experimental data. The first test case investigated is a modified Taylor–Green vortex in which the introduction of macro-bubbles of a lighter fluid phase inside the domain is considered. In the second test case, a more violent problem involving wave breaking and splashing dynamics is analyzed. In the final test, the dynamic of a sloshing problem is reproduced. An analysis of turbulence resolution is conducted by considering modeled and resolved turbulent kinetic energies, as well as viscous dissipation and turbulent viscosity dissipation.

SPH simulations of thixo-viscoplastic fluid flow past a cylinder

Thixotropic materials are complex fluids that display time-dependent viscosity and/or yield-stress response upon the application of a fixed deformation, while recovering their original structured-state when the deformation is discontinued. Thixotropic effects are presents in many different systems and applications, ranging from food products, such as ketchup, to metals, such as molten aluminum. In this work we present a first attempt to simulate the rheological properties of thixo-viscoplastic flows using a Smoothed Particle Hydrodynamic (SPH) method. The study set up is a 2D flow around a circular cylinder as well as a simple shear flow between parallel plates to validate our numerical results. SPH solutions are compared with simulations performed using the open-source Finite Volume Method solver RheoTool, based on OpenFOAM. The viscoplastic model used in this work is the Papanastasiou model combined with a recently developed microstructural one, in order to include thixotropy. In this thixo-viscoplastic framework, we analyze the flow properties in terms of yield-fronts, streamlines and structure-parameter fields at different Bingham and Thixotropy numbers, through microstructural thixotropic and yield-stress parameters variation. Obtained results show an important novelty: an asymmetry in the thixo-viscoplastic flow around the cylinder. • First attempt to simulate thixo-viscoplastic flows using SPH. • 2D flow around a circular cylinder as well as a simple shear flow are analyzed. • Papanastasiou model is combined with a microstructural one to include thixotropy. • Flow properties are analysed using different Bingham and Thixotropy numbers. • Main finding is an asymmetry in the thixo-viscoplastic flow around a cylinder.

Detonation Stabilization in Supersonic Flow: Effects of Suction Boundaries

In the present work, detonation stabilization in the supersonic flow is numerically investigated in the straight channel with suction boundaries. The two-dimensional reactive Navier–Stokes equations, together with a one-step reaction model, are solved using a second-order-accurate finite volume method solver based on the Structured Adaptive Mesh Refinement framework. The results show that, compared with one jet initiation, detonation initiation can be achieved in a shorter distance using two hot jets subject to the equal total width of the jets. When the suction slots are turned on, the overdriven detonation undergoes a gradual attenuation along with the weakening of the transverse waves, hence leading to dynamic detonation stabilization in the supersonic flow. When the suction slots are closer to the detonation front, the forward propagation of the detonation in the supersonic flow can be more effectively prohibited, implying that the suction slots should be distributed as close as possible to the detonation front in order to realize the maximal suction effect using the minimal suction slots.

A parallel finite volume procedure for phase-field simulation of solidification

We describe an implementation detail of a parallel finite volume solver PPFF2 (2-dimensional parallel phase-field finite volume method solver) for the simulation of solidification in two dimensions using the phase-field model. The governing equations for phase-field and temperature field are discretized with cell-centered finite volume method in a fully implicit way. In each time step, a parallel version strongly implicit procedure is used to solve the discretized equations. The problem of the growth of a solid seed into an undercooled melt is first solved to validate the numerical algorithm. The effects of the dimensionless width (0.0025, 0.0020, 0.0015) and mesh spacing () on the structures of dendrites and interface growth rate are investigated. At last, the competitive growth of the second and ternary arms with different noise term are simulated with the parallel finite volume code developed in this work. In terms of the parallel performance, the maximum speed-up for 3 grid systems are 6.98 and 8.77, its corresponding efficiency 43.6% and 54.8%.

Effect of heat transfer on an angled cavity placed in supersonic flow

Experimental and numerical studies on the effect of heat transfer to an open cavity placed in supersonic crossflow are presented. Cavity floor is subjected to the desired amount of heat flux and the consequent effects in the flow dynamics inside the cavity and its neighborhood are systematically assessed. Cavity flowfield has been visualized using high-speed Schlieren imaging and pressure on the cavity floor has been measured using both steady and unsteady pressure transducers. Two-dimensional unsteady compressible turbulent flow field has been numerically simulated using a Harten-Lax-van Leer-Contact (HLLC) scheme based unstructured finite volume method solver. The numerical method has been validated using both experimental data available in the literature as well as the wall pressure measured in the present study. Significant changes in flow dynamics such as the growth of the recirculation region, shearlayer oscillation, shearlayer impingement on the aft wall of the cavity, and frequency of cavity induced oscillations have been observed. Experimental observations are well complemented by the numerical studies and could reveal the physics of alteration in cavity flow dynamics with the heat addition.

A TCAD device simulator for exotic materials and its application to a negative-capacitance FET

A new device simulator named Impulse TCAD was developed, being built on top of a nonlinear finite volume method solver, which is further based on the Python script language and its associated scientific libraries. The user can fully customize the device properties and/or equations using scripts, which allows ready handling of exotic materials with nonstandard physical models. As a demonstration, a transient analysis of a negative-capacitance field-effect transistor (NC FET) is presented. The ferroelectric material in the NC FET is handled by using the time-dependent Ginzburg–Landau–Devonshire (GLD) equation, while standard device equations are applied for the rest of the device. The simulations show that, starting from the spontaneous polarization state, the ferroelectric regions evolve into the negative-capacitance regime, showing the expected characteristics of a NC FET. They also indicate that the Ginzburg term in the GLD equation, which is related to the correlation radius $$r_{\mathrm{c}}$$ , plays an important role in the appearance of the negative-capacitance effect. When $$r_{\mathrm{c}}$$ is too short compared with the channel length, the ferroelectric region becomes segregated into multiple polarization domains, resulting in loss of the NC FET characteristic.

The influence of numerical parameters in the finite-volume method on the Wigley hull resistance

The equations discretization errors are often overlooked compared to the spatial discretization errors. This article presents the results of the influence of various equations discretization schemes in computational fluid dynamics on the prediction of the ship resistance and wave elevation on the hull. For the analysis, steady flow around a model of the Wigley hull is numerically predicted by employing a finite-volume method solver based on Reynolds-averaged Navier–Stokes equations and the volume-of-fluid method. Six momentum discretization schemes, three multi-fluid discretization schemes and three gradient schemes, are used in the analysis. The results show that the choice of discretization schemes has a significant influence on the results of wave elevation and resistance force in the case of the flow around the Wigley hull. In conclusion, second-order discretization schemes should be used for the resistance evaluation, in order to properly capture the non-linear effects.

CFD Simulation of Cross-Flow Filtration

The aim of the present work is to study the transfer processes in a cross-flow filtration cell, in order to determine the conditions for stable and efficient operation of a side-stream filtration module, integrated with a bioreactor. The current interest in membrane integrated bioreactors is connected with the pursuit of energy and cost efficiency in a wide area of industrial applications, including wastewater treatment, food industry, pharmaceutical industry, and fuel production. A numerical CFD model is employed, based on previous experience with experimental concentration of antioxidants, such as polyphenols and flavonoids from extracts of natural products by nanofiltration. The geometry under investigation is a 3D model of the experimental flat-sheet cell with tangential orientation of the feed inlet. The swirling turbulent flow in the feed channel is favourable for reducing the concentration polarization layer on the membrane surface and preventing fouling. The main factors, affecting the filtration process, are the shear stress distribution and the concentration profiles in the vicinity of the membrane surface. The CFD models of mass transfer in cross-flow nanofiltration are scarce and there are none for the reference experimental filtration cell. The present CFD simulation reveals the concentration distribution in the feed channel. It complements previous data for the flow pattern with new knowledge on the mass transfer there, directed to understanding and control of the concentration polarization phenomenon. The numerical study uses the tools of ANSYS Fluent R13, based on the finite volume method for solving the Reynolds-Averaged Navier-Stokes (RANS) equations. The obtained results are analysed in rapport with available experimental data.

Diffusion and mixing effects in hot jet initiation and propagation of hydrogen detonations

In the present work, the role of diffusion and mixing in hot jet initiation and detonation propagation in a supersonic combustible hydrogen–oxygen mixture is investigated in a two-dimensional channel. A second-order accurate finite volume method solver combined with an adaptive mesh refinement method is deployed for both the reactive Euler and Navier–Stokes equations in combination with a one-step and two-species reaction model. The results show that the small-scale vortices resulting from the Kelvin–Helmholtz instability enhance the reactant consumption in the inviscid result through the mixing. However, the suppression of the growth of the Kelvin–Helmholtz instability and the subsequent formation of small-scale vortices imposed by the diffusion in the viscous case can result in the reduction of the mixing rate, hence slowing the consumption of the reactant. After full initiation in the whole channel, the mixing becomes insufficient to facilitate the reactant consumption. This applies to both the inviscid and viscous cases and is due to the absence of the unburned reactant far away from the detonation front. Nonetheless, the stronger diffusion effect in the Navier–Stokes results can contribute more significantly to the reactant consumption closely behind the detonation front. However, further downstream the mixing is expected to be stronger, which eventually results in a stronger viscous detonation than the corresponding inviscid one. At high grid resolutions it is vital to correctly consider physical viscosity to suppress intrinsic instabilities in the detonation front, which can also result in the generation of less triple points even with a larger overdrive degree. Numerical viscosity was minimized to such an extent that inviscid results remained intrinsically unstable while asymptotically converged results were only obtained when the Navier–Stokes model was applied, indicating that solving the reactive Navier–Stokes equations is expected to give more correct descriptions of detonations.

Numerical simulation of high speed reacting shear layers using AUSM+- up scheme-based unstructured finite volume method solver

Development of an Advection Upstream Splitting Method (AUSM[Formula: see text]-up) scheme-based Unstructured Finite Volume (UFVM) solver for the simulation of two-dimensional axisymmetric/planar high speed compressible turbulent reacting shear layers is presented. The inviscid numerical flux is evaluated using AUSM[Formula: see text]-up upwind scheme. An eight-step hydrogen–oxygen finite rate chemistry model is used to model the development of chemical species in a supersonic reacting flow field. The chemical species terms are alone solved implicitly in this explicit flow solver by rescaling the equation in time. The turbulence modeling has been done using RNG-based [Formula: see text]–[Formula: see text] model. Three-stage Runge–Kutta method has been used for explicit time integration. The nonreacting two-dimensional Cartesian version of the same solver has been successfully validated against experimental and numerical results reported for the wall static pressure data in sonic slot injection to supersonic stream. Detailed validation studies for reacting flow solver has been done using experimental results reported for a coaxial supersonic combustor, in which species profile at various axial locations has been compared. Present numerical solver is useful in simulating combustors of high speed air-breathing propulsion devices.

Locally Conservative Continuous Galerkin FEM for Pressure Equation in Two-Phase Flow Model in Subsurfaces

A typical two-phase model for subsurface flow couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. In this paper, we study a combined method consisting of continuous Galerkin finite element methods (CGFEMs) followed by a post-processing technique for Darcy equation and a nodal centered finite volume method (FVM) with upwind schemes for the saturation transport equation, in which the coupled nonlinear problem is solved in the framework of operator decomposition. The post-processing technique is applied to CGFEM solutions to obtain locally conservative fluxes which ensures accuracy and robustness of the FVM solver for the saturation transport equation. We applied both upwind scheme and upwind scheme with slope limiter for FVM on triangular meshes in order to eliminate the non-physical oscillations. Various numerical examples are presented to demonstrate the performance of the overall methodology.

An Accelerated Iterative Linear Solver with GPUs for CFD Calculations of Unstructured Grids

Computational Fluid Dynamics (CFD) utilizes numerical solutions of Partial Differential Equations (PDE) on discretized volumes. These sets of discretized volumes, grids, can often contain tens of millions, or billions of volumes. The analysis time of these large unstructured grids can take weeks to months to complete even on large computer clusters. For CFD solvers utilizing the Finite Volume Method (FVM) with implicit time stepping or a segregated pressure solver, a large portion of the computation time is spent solving a large linear system with a sparse coefficient matrix. In an effort to improve the performance of these CFD codes, in effect decreasing the time to solution of engineering problems, a conjugate gradient solver for a Finite Volume Method Solver Graphics Processing Units (GPU) was implemented to solve a model Poisson's equation. Utilizing the improved memory throughput of NVIDIA's Tesla K20 GPU a 2.5 times improvement was observed compared to a parallel CPU implementation on all 10 cores of an Intel Xeon E5-2670 v2. The parallel CPU implementation was constructed using the open source CFD toolbox, Open-FOAM.

Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel

The closely coupled approach combined with the finite volume method (FVM) solver and the finite element method (FEM) solver is used to investigate the fluid-structure interaction (FSI) of a three-dimensional cantilevered hydrofoil in the water tunnel. The FVM solver and the coupled approach are verified and validated by comparing the numerical predictions with the experimental measurements, and good agreement is obtained concerning both the lift on the foil and the tip displacement. In the noncavitating flow, the result indicates that the growth of the initial incidence angle and the Reynolds number improves the deformation of the foil, and the lift on the foil is increased by the twist deformation. The normalized twist angle and displacement along the span of the hydrofoil for different incidence angles and Reynolds numbers are almost uniform. For the cavitation flow, it is shown that the small amplitude vibration of the foil has limited influence on the developing process of the partial cavity, and the quasi two-dimensional cavity shedding does not change the deformation mode of the hydrofoil. However, the frequency spectrum of the lift on the foil contains the frequency which is associated with the first bend frequency of the hydrofoil.

Immersed boundary method for unsteady kinetic model equations

SummaryPredicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical investigation of the forward and backward travelling waves through an undulating propulsor: performance and wake pattern

Recently, the mechanisms of natural undulatory locomotion of aquatic animal swimming have become one of the most significant issues for the researchers, swimmers and engineers. This study aims to elucidate and compare the propulsive vortical signature and performance of backward (negative undulation) and forward (positive undulation) travelling waves through a typical fishlike propulsor by a systematic numerical study. The numerical approach uses a pressure-based finite volume method solver to solve Navier–Stokes equations in an arbitrary Lagrangian–Eulerian framework domain containing a two-dimensional NACA 0012 foil moving with prescribed kinematics. Some of the important findings are: (1) time-dependent forces and pitching moments show that both mechanisms suffer from the energy losses; however, the negative undulations show less energy losses, (2) Strouhal number of undulations shows a transition point from drag-dominated regime to thrust-dominated regime for both mechanisms and a transition point from thrust-dominated regime to drag-dominated regime for positive undulation, (3) the consumed power plot shows that at lower and medium St, both mechanisms consume closely same powers, while, at higher St, the negative undulation consumes more power, (4) the efficiency plots show that the efficiency of the positive undulation is close to zero, while, the negative undulation reaches considerably higher performances, (5) low St vortical patterns of the mechanisms show some similarity, while, the patterns at medium and high St reveal appreciable discrepancies, and (6) the most significant difference between the vortical patterns of the mechanisms is appearing more regular and stronger vortices in the wake of the negative undulation.

A Comparative Numerical Study on the Performances and Vortical Patterns of Two Bioinspired Oscillatory Mechanisms: Undulating and Pure Heaving.

The hydrodynamics and energetics of bioinspired oscillating mechanisms have received significant attentions by engineers and biologists to develop the underwater and air vehicles. Undulating and pure heaving (or plunging) motions are two significant mechanisms which are utilized in nature to provide propulsive, maneuvering, and stabilization forces. This study aims to elucidate and compare the propulsive vortical signature and performance of these two important natural mechanisms through a systematic numerical study. Navier-Stokes equations are solved, by a pressure-based finite volume method solver, in an arbitrary Lagrangian-Eulerian (ALE) framework domain containing a 2D NACA0012 foil moving with prescribed kinematics. Some of the important findings are (1) the thrust production of the heaving foil begins at lower St and has a greater growing slope with respect to the St; (2) the undulating mechanism has some limitations to produce high thrust forces; (3) the undulating foil shows a lower power consumption and higher efficiency; (4) changing the Reynolds number (Re) in a constant St affects the performance of the oscillations; and (5) there is a distinguishable appearance of leading edge vortices in the wake of the heaving foil without observable ones in the wake of the undulating foil, especially at higher St.

Comparative numerical analysis of the flow pattern and performance of a foil in flapping and undulating oscillations

Nature presents a variety of propulsion, maneuvering, and stabilization mechanisms which can be inspired to design and construction of manmade vehicles and the devices involved in them, such as stabilizers or control surfaces. This study aims to elucidate and compare the propulsive vortical signature and performance of a foil in two important natural mechanisms: flapping and undulation. Navier–Stokes equations are solved in an ALE framework domain containing a 2D NACA 0012 foil moving with prescribed kinematics. All simulations are carried out using a pressure-based finite volume method solver. The results of time-averaged inline force versus Strouhal number (St) show that in a given Reynolds number (Re), the flapping oscillations begin to produce thrust at a smaller St, and with a greater slope than undulatory oscillations. However, consumed power of the flapping foil versus St varies with considerably higher values and greater slope than undulating foil. In addition, efficiency graphs show similar ascending–descending behaviors versus St, with greater “peak propulsive efficiency” for the undulating foil. Furthermore, one of the most important differences between the vortical structures of flapping and undulatory oscillations is the distinguishable appearance of leading edge vortices in the wake of the flapping foil without observable ones in the wake of undulating foil. Finally, the formation and dissipation patterns of distinct vortices in the wakes of both oscillating foils vary with St.

Numerical analysis of wake structure and performance of two oscillatory mechanisms of a foil: Pure pitching and undulating

There are various propulsion, maneuvering, and stabilization mechanisms in nature, which can provide inspiration for similar mechanisms in man-made vehicles. This study aims to elucidate and compare the propulsive vortical signature and performance of a foil in two important natural mechanisms of pure pitching and undulatory oscillations. Governing equations are solved with a pressure-based finite volume method solver, in an arbitrary Lagrangian–Eulerian framework domain containing a NACA 0012 foil moving with prescribed kinematics. The results show that in a given Reynolds number ( Re), the undulating mechanism produces thrust at a higher Strouhal number ( St) and with smaller growth slope, but mostly higher efficiency, versus St, than pitching mechanism. In addition, vortical structures of these mechanisms have significant differences and also vary considerably with St. One of the distinguishable features of vortical signatures is the presence of the leading-edge vortices for the pitching foil, which are not appearing in the undulating foil’s vortical pattern.