Second-order Discretization Scheme Research Articles

Computational fluid dynamics study of Savonius rotors using OpenFOAM

In this work, two-dimensional models of Savonius rotors are simulated using OpenFOAM® in order to predict the aerodynamic performance of small-scale vertical-axis wind turbines. The results are reported analyzing the aerodynamic performance and forces acting on the rotors. Power coefficient, [Formula: see text], is compared with experimental data for each operation point, and for three different geometries. Simulations with first- and second-order discretization schemes are carried out and compared, both quantitative and qualitative. Since usual grid dimensions result not to be suitable for simulations of Savonius rotors, an analysis of different domains is performed and compared. Finally, a set up for computational fluid dynamics simulation of two-dimensional Savonius rotors is proposed. The fluid–rotor interaction is analyzed and the vortex shedding is correlated with [Formula: see text] values and wake description.

Effect of sinus size and position on hemodynamics during pulsatile flow in a carotid artery bifurcation

Background and objectivesHemodynamics plays a crucial role in the progression of atherosclerosis and the treatment of arterial diseases. Stroke is one of the arterial diseases and a leading cause of death worldwide. Hemodynamics in the carotid artery plays a vital role in the stroke. The common carotid artery bifurcates into the internal carotid artery and the external carotid artery. Carotid sinus, a slightly dilated area, exists in the internal carotid artery just after the bifurcation and acts as a pressure receptor and regulator. The location and size of the sinus can vary in different people; the change in sinus size and location may affect the hemodynamics. It is necessary to study the shift in hemodynamics due to changes in sinus size and position on atherosclerosis. The change in flow behavior may suggest the probable sites of backflow and low wall shear stress, and therefore the sites prone to atherosclerosis. MethodsThe model of the carotid artery has been constructed using patient data. Transient computational fluid dynamics simulations have been performed using a finite volume method for the numerical solution in a three-dimensional computational domain using ANSYS Fluent 19.2. Pulsatile flow is specified at the inlet boundary. The coupled scheme is used for the pressure-velocity coupling. The second-order discretization scheme is used for pressure interpolation and second-order upwind scheme is used for the discretisation of momentum equation. The temporal term is discretized using the first-order implicit scheme. ResultsThe effect of sinus size and location on the overall flow behavior, wall shear stress, and secondary flow are presented. Results show that the outer wall of bifurcation has low wall shear stress and bigger recirculation as compared with that on the inner wall of bifurcation. Numerical results obtained for varying sinus size and position are shown in graphs and contours, including wall shear stress, secondary flow, and velocity streamlines. ConclusionNumerical results reveal that sinus away from bifurcation, and larger diameter sinus has more recirculation and low wall shear stress. Therefore, the person having sinus away from bifurcation and larger sinus diameter are more susceptible to plaque formation.

A Discontinuous Galerkin Method for Stochastic Conservation Laws

In this paper we present a discontinuous Galerkin (DG) method to approximate stochastic conservation laws, which is an efficient high-order scheme. We study the stability for the semidiscrete DG methods for fully nonlinear stochastic equations. Error estimates are obtained for smooth solutions of semilinear stochastic equations with variable coefficients. We also establish a derivative-free second-order time discretization scheme for matrix-valued stochastic ordinary differential equations. Numerical experiments are performed to confirm the analytical results.

Numerical Solutions of Unsteady Advection-Diffusion Equations by Using EG Iteration with Wave Variable Transformation

The primary goal of this paper is to investigate the effectiveness of the 4-point Explicit Group (4-point EG) iterative method for solving one-dimensional unsteady advection-diffusion problems via similarity transform. By using this transformation approach, the proposed problem can be reduced into the corresponding two-point boundary volume problem. By imposing the second-order central finite difference discretization scheme, then the corresponding approximation equation can be derived to construct a system of linear equations. Having a large linear system, the 4-point EG iterative method has been used to solve the generated system of linear equations. The formulation of the 4-point EG method is also derived. Some numerical experiments are conducted that to verify the 4-point EG method is more effective than the Gauss-Seidel (GS) method.

Experimental and steady-RANS CFD modelling of cross-ventilation in moderately-dense urban areas

Computational fluid dynamics (CFD) models based on the steady Reynolds-averaged Navier Stokes (SRANS) equations are vastly used for calculation of airflow field inside and around cross-ventilated buildings. However, most of the developed CFD guidelines neglect CFD challenges related to cross-ventilation modeling in terms of flow unsteadiness, high level of gradients of airflow parameters, and complex interactions between the indoor and outdoor flows.Hence, a systematic parametric study was performed in this study for a generic cross-ventilated building model with a planar area ratio of 0.25 against different wind angles while effects of different CFD parameters, including advection and diffusion terms’ discretization methods, mesh generation techniques, and turbulence models on prediction accuracy and convergence behavior of CFD solver were comprehensively studied.Results show that a particularly generated unstructured tetrahedral mesh configuration with significantly lower cell numbers can provide comparable results with structured hexahedral mesh configurations. Furthermore, the second-order discretization scheme for the advection terms encounters convergence issues against the normal wind angle, but generally presents more accurate results against oblique wind angles. Moreover, two-equation turbulence models show a very low accuracy in the case of the normal wind angle, but acceptable results can be found for oblique wind angles.

Computational investigation of laminar premixed hydrogen flame past a quenching mesh

PurposeThe purpose of this study is the computational analysis of atmospheric, laminar, stoichiometric and premixed hydrogen-air flames in the presence of a quenching mesh. The assessment of the predictive capability of different reaction mechanisms, the clarification of the relative importance of the thermal and chemical effects for mesh quenching and the investigation of the influence of the mesh geometry on the quenching effectiveness are the focal points of the investigation.Design/methodology/approachThe problem is posed as unsteady, two-dimensional. Differential governing equations are numerically solved by the finite volume method for the reacting hydrogen/air mixture, assuming an ideal gas behaviour. Thermal radiation and buoyancy are neglected. A coupled solver is used to treat the velocity-pressure coupling, along with a stiff-chemistry solver for the chemical kinetics. Second-order discretization schemes are used in space and time. A uniform grid resolution is used, where the grid independence in terms of the flame speed prediction is ensured in preliminary calculations for one-dimensional flames.FindingsIt is found that a detailed reaction mechanism is necessary for an accurate prediction. Meshes with round openings are found to be more effective that those with slit openings (SOs), by a factor of two in the maximum safe gap size. A perforated plate is observed to have a higher quenching potential compared to a wire mesh, for SOs. It is also found that the heat loss to the wall is the dominating quenching mechanism for the present problem, whereas adsorption of radicals plays a subordinate role.Originality/valueIn contrast to the previous studies in the field, a detailed reaction mechanism is applied instead of a single-step one, while still using the latter for comparison. The role of wall-radicals interaction for the quenching effectiveness of the mesh is addressed for the first time. Parametric studies are performed on the mesh geometry, which was not done before. Hydrogen is considered as fuel in contrast to the great majority of the previous work.

Vector Penalty-Projection Methods for Open Boundary Conditions with Optimal Second-Order Accuracy

Recently, a new family of splitting methods, the so-called vector penalty-projection methods (VPP) were introduced by Angot et al. [2, 3] to compute the solution of unsteady incompressible fluid flows and to overcome most of the drawbacks of the usual incremental projection methods. Two different parameters are related to the VPP methods: the augmentation parameter r ≥ 0 and the penalty parameter 0 < e ≤ 1. In this paper, we deal with the time-dependent incompressible Navier-Stokes equations with outflow boundary conditions using the VPP methods. The spatial dis-cretization is based on the finite volume scheme on a Marker and Cells (MAC) staggered grid. Furthermore, two different second-order time discretization schemes are investigated: the second-order Backward Difference Formula (BDF2) known also as Gear's scheme and the Crank-Nicolson scheme. We show that the VPP methods provide a second-order convergence rate for both velocity and pressure in space and time even in the presence of open boundary conditions with small values of the augmentation parameter r typically 0 ≤ r ≤ 1 and a penalty parameter e small enough typically e = 10 −10. The resulting constraint on the discrete divergence of velocity is not exactly equal to zero but is satisfied approximately as O(e δt) where e is the penalty parameter (taken as small as desired) and δt is the time step. The choice r = 0 requires a special attention to avoid the accumulation of round-off errors for very small values of e. Indeed, it is important in this case to directly correct the pressure gradient by taking account of the velocity correction issued from the vector penalty-projection step. Finally, the efficiency and the second-order accuracy of the method are illustrated by several numerical test cases including homogeneous or non-homogeneous given traction on the boundary.

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 modelling of pump-around jet mixing tanks: a discrepancy in concentration profiles

ABSTRACTJet mixing tanks are important in chemical processes. Over the past two decades or so, computational fluid dynamics (CFD) has been employed to study jet mixers. The shortfalls of the previous CFD models were the discrepancy in concentration profiles between simulation and experiment and the absence of exact inlet turbulence conditions. So, in our present work, the CFD model was developed to investigate the proper conditions for jet mixing tank simulation and improve the accuracy of concentration profile prediction by using an appropriate grid arrangement, a realizable k-epsilon model, and a second-order upwind discretization scheme. The results revealed that the CFD model with proper inlet conditions predicted the overall mixing time well and somewhat improved the predicted concentration profiles. Further, the reasons for discrepancies in concentration profiles were inappropriate inlet turbulence conditions and overprediction in total momentum available for mixing due to the flat top liquid surface assumption. In addition, this discrepancy may be caused by the dynamic response of concentration measuring device.

A second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing

This paper shows a second-order discretization scheme for expectations of stochastic differential equations. We introduce a smart Malliavin weight which is given by a sum of simple polynomials of Brownian motions as an improvement of the scheme of Yamada [J. Comput. Appl. Math., 2017, 321, 427–447]. A new quasi-Monte Carlo simulation is proposed to obtain an efficient option pricing scheme. Numerical examples for the SABR model are shown to illustrate the validity of the scheme.

CFD Modeling of Chamber Filling in a Micro-Biosensor for Protein Detection.

Tuberculosis (TB) remains one of the main causes of human death around the globe. The mortality rate for patients infected with active TB goes beyond 50% when not diagnosed. Rapid and accurate diagnostics coupled with further prompt treatment of the disease is the cornerstone for controlling TB outbreaks. To reduce this burden, the existing gap between detection and treatment must be addressed, and dedicated diagnostic tools such as biosensors should be developed. A biosensor is a sensing micro-device that consists of a biological sensing element and a transducer part to produce signals in proportion to quantitative information about the binding event. The micro-biosensor cell considered in this investigation is designed to operate based on aptamers as recognition elements against Mycobacterium tuberculosis secreted protein MPT64, combined in a microfluidic-chamber with inlet and outlet connections. The microfluidic cell is a miniaturized platform with valuable advantages such as low cost of analysis with low reagent consumption, reduced sample volume, and shortened processing time with enhanced analytical capability. The main purpose of this study is to assess the flooding characteristics of the encapsulated microfluidic cell of an existing micro-biosensor using Computational Fluid Dynamics (CFD) techniques. The main challenge in the design of the microfluidic cell lies in the extraction of entrained air bubbles, which may remain after the filling process is completed, dramatically affecting the performance of the sensing element. In this work, a CFD model was developed on the platform ANSYS-CFX using the finite volume method to discretize the domain and solving the Navier–Stokes equations for both air and water in a Eulerian framework. Second-order space discretization scheme and second-order Euler Backward time discretization were used in the numerical treatment of the equations. For a given inlet–outlet diameter and dimensions of an in-house built cell chamber, different inlet liquid flow rates were explored to determine an appropriate flow condition to guarantee an effective venting of the air while filling the chamber. The numerical model depicted free surface waves as promoters of air entrainment that ultimately may explain the significant amount of air content in the chamber observed in preliminary tests after the filling process is completed. Results demonstrated that for the present design, against the intuition, the chamber must be filled with liquid at a modest flow rate to minimize free surface waviness during the flooding stage of the chamber.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

This paper concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested with two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. At last, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).

Numerical Study on the Effect of Lambda Value (Oxygen/Fuel Ratio) on Temperature Distribution and Efficiency of a Flameless Oxyfuel Combustion System

The flameless oxyfuel combustion technology has been proven to be a promising new method to reduce the fuel consumption and pollutants in industrial applications [...]

Comparison of sharp and smoothed interface methods for simulation of particulate flows II: Inertial and added mass effects

This paper studies the robustness of the Smoothed Profile Method (SPM) in fluid-solid interaction problems where inertia and added mass effects are significant. The performance of SPM is compared with that of a Sharp Interface Method (SIM), which is constructed with second-order discretization schemes. The applicability of SPM is extended to the moderate Reynolds numbers regime where the boundary layer and wake dynamics are likely to be influenced by the thickness of the solid-fluid interface. It is shown that SPM is able to correctly predict the drag and surface vorticity forRe<O(104). In comparison with SIM, SPM is more robust on coarse grids for Re<O(104); however, SPM needs fine grids to produce accurate results when Re∼O(104). SPM and SIM are also applied to fluid structure interaction (FSI) problems using an implicit fluid-solid strong coupling framework. This allows computations of FSI problems with moderate inertia and low particle to fluid density ratios (high added mass effects). The effect of the smoothed interface on accuracy and robustness is assessed for such FSI problems. Results indicate that SPM is more robust than SIM when the density of the particle is comparable to the fluid, i.e. for high added mass effects.

New analytical solutions to the two-phase water faucet problem

The one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for code assessment, benchmark, and numerical verification. In this work, we present a new set of analytical solutions to the water faucet problem at the steady-state condition, with the gas-phase density’s effect on pressure distribution considered. This new set of analytical solutions is used in a rigorous numerical verification process from which the anticipated second-order spatial accuracy is achieved for a second-order spatial discretization scheme. On the contrary, the same anticipated order of accuracy could not be obtained using the Ransom solutions as the reference. In addition, extended Ransom transient solutions for the gas-phase velocity and pressure are derived with the assumption of decoupled liquid and gas pressures. Numerical benchmark on the extended Ransom solutions is also presented.

Flow Instability Detected by High-Resolution Computational Fluid Dynamics in Fifty-Six Middle Cerebral Artery Aneurysms.

Recent high-resolution computational fluid dynamics (CFD) studies have detected persistent flow instability in intracranial aneurysms (IAs) that was not observed in previous in silico studies. These flow fluctuations have shown incidental association with rupture in a small aneurysm dataset. The aims of this study are to explore the capabilities and limitations of a commercial cfd solver in capturing such velocity fluctuations, whether fluctuation kinetic energy (fKE) as a marker to quantify such instability could be a potential parameter to predict aneurysm rupture, and what geometric parameters might be associated with such fluctuations. First, we confirmed that the second-order discretization schemes and high spatial and temporal resolutions are required to capture these aneurysmal flow fluctuations. Next, we analyzed 56 patient-specific middle cerebral artery (MCA) aneurysms (12 ruptured) by transient, high-resolution CFD simulations with a cycle-averaged, constant inflow boundary condition. Finally, to explore the mechanism by which such flow instabilities might arise, we investigated correlations between fKE and several aneurysm geometrical parameters. Our results show that flow instabilities were present in 8 of 56 MCA aneurysms, all of which were unruptured bifurcation aneurysms. Statistical analysis revealed that fKE could not differentiate ruptured from unruptured aneurysms. Thus, our study does not lend support to these flow instabilities (based on a cycle-averaged constant inflow as opposed to peak velocity) being a marker for rupture. We found a positive correlation between fKE and aneurysm size as well as size ratio. This suggests that the intrinsic flow instability may be associated with the breakdown of an inflow jet penetrating the aneurysm space.

Numerical Study on Hydrodynamics and Heat Transfer Characteristics Around a Cylinder with Inclined Splitter Plates

In the current paper, the effect of length and angle of a splitter plate on hydro-thermal field in a range of Reynolds number from 40 to 1000 are numerically studied by solving the two-dimensional Navier-Stokes equations. For discretization of governing equations, PISO algorithm was imposed to segregate the pressure-velocity coupled equations, and second-order upwind discretization scheme was applied for momentum and energy values. A convergence criterion was set to 10-6. The influence of splitter plate attachment on the fluctuating drag forces, vortex shedding and heat transfer behavior was investigated. It was found that the drag force decreases as the splitter plate elongates and the vortices vanish. The average Nusselt number rises with increasing the angle of splitter plate. A reduction in drag force was observed at about 25o. The overall heat transfer increased due to surface enlargement resulting from the splitter plate. In addition, it was seen that by increasing the plate angle up to 25o the outflow temperature grows.

Numerical Computation and Analysis of the Numerical Scheme Order of the Two-Dimensional Temperature Field of Thermoelectric Coolers Cold Substrate

This paper presents a numerical computation and analysis of the numerical scheme order of the two-dimensional temperature distribution in cold substrate of thermoelectric coolers with the presence of a discrete heat source. The finite difference method is applied to obtain the linear system of equations and the temperature at each node of the domain. The numerical code is implemented in the free software package GNU Octave. In the first part, a mesh independency study is carried on in order to establish a relation between accuracy and computational cost, comparing the simulated results with results from an approximate analytical solution available in the literature. It is observed excellent agreement between numerical and the analytical results. In the second part, an analysis of the overall order of the numerical scheme is carried on by considering numerical solutions for three different meshes and different formulations of the boundary conditions. Results show that the overall order of the numerical scheme is first-order even if full second-order discretization scheme is applied for all grid points, due to the presence of the discrete heat source. Those results are observed for the considered discretization schemes and are confirmed after using a continuous formulation for the heat source term.

Design Optimization of an Oil-Air Catch Can Separation System

The Positive Crankcase Ventilation (PCV) system in a car engine is designed to lower the pressure in the crankcase, which otherwise could lead to oil leaks and seal damage. The rotation of crankshaft in the crankcase causes the churn up of oil which conducts to occurrence of oil droplets which in turn may end in the PCV exhaust air intended to be re-injected in the engine admission. The oil catch can (OCC) is a device designed to trap these oil droplets, allowing the air to escape from the crankcase with the lowest content of oil as possible and thus, reducing the generation and emission of extra pollutants during the combustion of the air-fuel mixture. The main purpose of this paper is to optimize the design of a typical OCC used in many commercial cars by varying the length of its inner tube and the relative position of the outlet from radial to tangential fitting to the can body. For this purpose, CFD parametric analysis is performed to compute a one-way coupled Lagrangian-Eulerian two-phase flow simulation of the engine oil droplets driven by the air flow stream running through the device. The study was performed using the finite volume method with second-order spatial discretization scheme on governing equations in the Solid Works-EFD CFD platform. The turbulence was modelled using the k-? model with wall functions. Numerical results have proved that maximum efficiency is obtained for the longest inner tube and the tangential position of the outlet; however, it is recommended further investigation to assess the potential erosion on the bottom of the can under such a design configuration.

FLOW PHYSICS OF 3-BLADED STRAIGHT CHORD H-DARRIEUS WIND TURBINE

Steady-state two-dimensional Computational Fluid Dynamics (CFD) simulations were performed using Fluent 6.0 software to analyze the flow physics of 3-bladed straight chord H-Darrieus wind turbine having blade twist of 300 for 10% of its chord at the trailing ends. The flow was simulated using finite volume method coupled with moving mesh technique to solve mass and momentum conservation equations. The standard k-ε turbulence model with enhanced wall condition was used. Second-order upwind discretization scheme was adopted for pressure-velocity coupling of the flow. Flow physics of the turbine was analyzed with the help of pressure and velocity contours. It was found that velocity magnitude decreases from upstream to downstream side across the turbine, which will cause overall lift for the turbine. Further, blade twist at the trailing ends creates circulations that interact with the blades in a direction opposite to the direction of rotation of the turbine which would enhance power production for the three bladed turbine.