Semi-implicit Method For Pressure-linked Equations Consistent Research Articles

Study on Internal Flow Characteristics and Abrasive Wear of Pelton Turbine in Sand Laden Water

When a Pelton turbine operates in sand laden water, the abrasive wear of its overflow components by high-speed jets is serious. Based on the VOF (volume of fluid) multiphase flow model, the SST (shear stress transfer) k-ω turbulence model, the particle motion Lagrangian model, the generic wear model, and the SIMPLEC (Semi-Implicit Method for Pressure Linked Equations Consistent) algorithm, the liquid–air–solid three-phase flow in the key overflow components of a Pelton turbine were simulated, the abrasive wear was predicted, and the internal sand-water flow characteristics and the abrasive wear of the overflow components were analyzed. The results show that the trailing edge at the root of the runner bucket, the leading face of the bucket near the root, the notch, and the splitter are severely worn. The abrasive wear of the splitter and the notch is more severe than that of the leading face of the bucket. The wear rate from the splitter to the trailing edge increases first and then decreases. The wear pattern of the needle tip is mainly “dotted”, while that of the nozzle opening is “flaky”, and the abrasive wear of the nozzle opening is more severe than that of the needle. The predicted results are consistent with the actual conditions at the site of the power station. This study provides a technical method for the prediction of abrasive wear of the Pelton turbine and a technical basis for the operation and maintenance of the power station.

Performance Analysis of a Phase Changing Material Based Thermocycler for Nucleic Acid Amplification

Abstract Modeling, simulation, and thermal performance analysis of a thermocycler for the continuous-flow polymerase chain reaction (CF-PCR), with a phase changing material (PCM)-laden annealing flow path, is presented. The incessant threat of microorganisms such as viruses, bacteria, and fungi has fostered effective, quick, and miniature detection devices in order to curtail the wide-spreading of infections. Microfluidics-based CF-PCR systems are compact and ideal for faster response. The thermal cycling process involves a sequential exposure of a given liquid sample to various temperature conditions when it is taken through the continuous-flow path. As a result, a prescribed periodic change of temperature suitable for deoxyribonucleic acid (DNA) amplification is achieved. A rapid temperature reduction and maintenance of isothermal conditions to facilitate the annealing phase of CF-PCR process by a PCM-assisted cooling is envisaged in the present study. Unsteady, two-dimensional, incompressible fluid flow, and internal convection heat transfer in a microchannel annealing path with melting of tetracosane (C24H50) boundary has been simulated using semi-implicit method for pressure linked equations-consistent (SIMPLEC) algorithm based finite volume solver. Solver validation is carried out against the experimental data on internal convection heat transfer in a rectangular microchannel. A detailed numerical study has been performed to assess the spatiotemporal heat transfer characteristics of internal convection in the microfluidic path when the flow triggers the melting of encapsulated PCM. A minimum sample flowrate with PCM encapsulation of less than 600 μm is found to be ideal for achieving desired thermal performance. The present study evidences the swift temperature reduction and management of isothermal conditions congenial for the annealing process in the CF-PCR system for various sample flowrates and PCM masses. The study offers valuable design input for the development of a microfluidic thermocycler for CF-PCR applications.

Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method

The flow analysis of the forebay of a lateral intake pumping station with asymmetrical operating pumps was carried out with a realizable k-ε turbulent model and SIMPLEC (Semi Implicit Method for Pressure Linked Equations Consistent) algorithm. The Pressure Inlet boundary condition was adopted and the pressure between the top surface and the bottom surface was linear with the height of the inlet section. The Mass Flow Outlet boundary condition was also adopted to ensure the accuracy and precision of the CFD (Computational Fluid Dynamics) simulation. The diversion pier was selected as the optimization strategy based on the flow parameters. The layout of the diversion piers was designed with four parameters which are the relative length, relative height, width, and straight-line distance of the piers’ tail. Each parameter had three values. Based on the orthogonal test, nine groups of the numerical simulation on different layouts of diversion piers were analyzed with the uniformity of axial flow velocity and weighted average angle of the flow velocity of the inlet cross-section of each pump, reducing the number of tests from 64 (43) groups to 9 groups, improving work efficiency. The results show that the diversion piers had a significant adjustment of uniformity of axial flow velocity and weighted average angle of flow velocity. After optimization of the forebay, the uniformity of axial flow velocity of intake of No.1 pump was 80.26% and the weighted average angle of flow velocity was 77.68°. The above values of the No.2 pump were 98.74% and 87.84°, respectively. The values of the No.4 pump were 93.41% and 77.28°. The results of numerical simulation, which was carried out to estimate the rectification effect under the operation combination of the No.1, No.3, and No.4 pumps, showed that the uniformity and the angle of the No.1 pump were 92.65% and 72.66°, respectively, the uniformity and the angle of No.3 pump were 94.54% and 85.14°, and the uniformity and the angle of the No.4 pump were 75.81% and 78.21°. This research proves that the orthogonal test method, in a reasonable and convenient way, can be applied in hydraulic optimization for a lateral intake pumping station.

Micro-macro model for the transient heat and fluid transport in solidification structure evolution during static casting processes

The current work used micro-macro model to study the transient fluid flow patterns, heat transfer and solute segregation during the solidification of eutectic binary Al-4%Cu alloy in a static casting process. Custom codes in the form of user defined functions (UDFs) for Nucleation and growth kinetics, thermo-physical properties, and other transport terms including boundary conditions specifically developed for this study were interfaced to ANSYS Fluent. Solidification kinetics was coupled to macroscopic heat transfer equation through the latent heat evolution. The pressure-velocity coupling in the momentum equations were handled by Semi-Implicit Method for Pressure-Linked Equations Consistent (SIMPLEC). The energy and species conservation equations were also solved with similar algorithm. The transient terms of the transport equations were evaluated using fully implicit scheme. Three cases were simulated to evaluate the effect of cooling conditions on the transient evolution of fluid flow, heat transfer and macro-segregation. The results obtained show significant variations in the pattern of fluid flow, heat transport and solute segregation for the three cases. Different thermal regions were reported for the three cases studied. Thickness of the slurry region was observed to be a function of cooling condition. Severity of macro-segregation varied significantly due to imposed boundary conditions. The results obtained provide evidence that choosing cooling orientations arbitrarily can lead to either overestimation or underestimation of casting defects. Therefore, thermal design and process parameters should be optimized for improved product quality and production output.

Improvement of heat-transfer correlations for supercritical methane coolant in rectangular channel

In this article, the conjugate heat transfer of the methane coolant inside a rectangular channel is studied and the related Nusselt correlations are improved. The compressible methane flow enters the cooling channel at supercritical pressure and subcritical temperature. The coolant flow absorbs heat from the heated walls and exits the channel with a supercritical temperature. An in-house solver is developed employing Semi-Implicit Method for Pressure-Linked Equations-Consistent (SIMPLEC) algorithm accompanied by the appropriate thermodynamic and transport property relations for the supercritical conditions of the methane coolant. The solver is validated with the experimental data found in the open literature. The behavior of pseudo-critical temperature and density versus pressure are studied and new relations are proposed. The accuracy of different Nusselt relations for estimating heat transfer coefficient of methane at supercritical pressures is evaluated. The variation of thermo-fluidic parameter correction factors (i.e. non-dimensional density, temperature, isobaric specific heat, viscosity, and thermal conductivity) through the cooling channel is investigated. Further, the current Nusselt relations are developed, and improved correlations are proposed for methane at the supercritical pressure inside a rectangular channel. The accuracy of the modified correlations is studied at different outlet pressures, heat transfer, and mass flow rates.

Thermal–Hydrodynamic Behaviour of Coated Pivoted Pad Thrust Bearings: Comparison between Babbitt, PTFE and DLC

The hydrodynamic lubrication and thermal analysis of tilting pad thrust bearings has been a major subject for many studies in the field of tribology. There is only a limited number of studies regarding thrust bearings with coated surfaces. The purpose of this study is to build a parametric, iterative algorithm in order to perform a complete thermal and hydrodynamic lubrication analysis for pivoted pad thrust bearings with coatings. The analytical model is mainly based on the energy, continuity and Navier–Stokes equations, which are solved numerically with the Semi-Implicit Method for Pressure Linked Equations Consistent (SIMPLEC) method. The analysis focuses on a single pivoted pad of the thrust bearing. The thermal properties of the coating material are taken into account and the resulting thermal and flow fields are solved. The basic hydrodynamic and tribological characteristics are calculated for an uncoated, a Babbitt coated, a PTFE coated and a diamond like carbon (DLC) coated pivoted pad thrust bearing. The pressure and the film thickness distribution, as well as the load capacity and the frictional forces, are determined for several pad positions and velocities of the rotor. A mineral oil lubricant is used to estimate the shear thinning or thickening effects on the pad tribological performance. The results indicate that pads coated with PTFE and DLC show lower friction forces compared to the common steel and Babbitt applications. At the same time, the DLC coating seems to affect the bearing’s flow and thermal fields less than the PTFE, making it more suitable for thrust bearings applications.

Geometric optimization for thermal–hydraulic performance of dimpled enhanced tubes for single phase flow

Enhanced surfaces have larger heat transfer surface area and offer increased turbulence level hence allowing higher heat exchange performance. In this study, numerical simulations are conducted to simulate geometric design optimization of enhanced tubes for optimal thermal–hydraulic performance. The simulations are validated with experimental data. Two and three dimensional steady incompressible turbulent flow in dimpled enhanced tube is numerically studied using realizable k–ε method. The pressure–velocity coupling is solved by Semi-Implicit Method for Pressure Linked Equations Consistent (SIMPLEC) algorithm. Results show that dimples on tube surface present high heat transfer performance. Compared to staggered configuration, the in-line dimples arrangement provided better overall heat exchange characteristics. The geometric parameters like dimple shape, depth, pitch and starts are found to have significant effects on overall heat exchange performance while the dimple diameter has insignificant effect on thermal performance.

Fluid Flow and Heat Transfer Characteristic of Outer and Inner Half Coil Jackets

The physical models of the outer and inner half coil jackets were simplified to two types of coiled ducts. The mathematic models of incompressible fluid at the condition of laminar flow and heat transfer in the two types of jackets for cooling process reactor were set up and solved by the semi-implicit method for pressure linked equations consistent (SIMPLEC) algorithm based on a control volume method. The flow and temperature fields were given and the effects of Dean and Prandtl numbers on flow and heat transfer were studied. The results show that flow in the inner half coil jacket is found to exhibit transition of secondary flow pattern from two vortices to four vortices when the Dean number increases, but that in the outer half coil jacket is not found. The critical Dean number is about 96. The inner half coil jacket has stronger heat transfer ability than the outer half coil jacket and this superiority is more evident with larger Prandtl number. However, as the Dean number is greater than 105, the flow resistance enhances more severely in the inner jacket than the outer jacket. For both jackets, the centers of the heated wall are the poorest for heat transfer.

FLOW FIELD AND TOPOLOGICAL ANALYSIS OF HEMISPHERICAL PARACHUTE IN LOW ANGLES OF ATTACK

For analyzing the flow field and topological structure of hemispherical parachute in low angles of attack, a fluid-structure interaction (FSI) simulation technique is established to decide the shape of the hemispherical parachute during terminal descent. In the fluid simulation, the semi-implicit method for pressure-linked equations consistent (SIMPLEC) algorithm is introduced to solve shear stress transport (SST) k–ω turbulence Navier–Stokes (N–S) Equations. This method is proved to be efficient and stable by the experiment and corresponding numerical simulation. After obtaining the stable shape of the canopy, the parachute in different angles and velocities are considered.

Computational fluid dynamics modeling of a solid oxide electrolyzer cell for hydrogen production

Abstract A 2D computational fluid dynamics (CFD) model was developed to study the performance of a planar solid oxide electrolyzer cell (SOEC) for hydrogen production. The governing equations for mass continuity, momentum conservation, energy conservation and species conservation were discretized with the finite volume method (FVM). The coupling of velocity and pressure was treated with the SIMPLEC (Semi-Implicit Method for Pressure Linked Equations – Consistent) algorithm. Simulations were performed to investigate the effects of operating/structural parameters on heat/mass transfer and the electric characteristics of a planar SOEC. It is found that the gas velocity at the cathode increases significantly along the main flow channel, as the increase in H2 molar fraction decreases the density and viscosity of the gas mixture at the cathode. It is also found that increasing the inlet gas velocity can enhance the SOEC performance. Another important finding is that the electrode porosity has small effect on SOEC performance. The results of this paper provide better understanding on the coupled heat/mass transfer and electrochemical reaction phenomena in an SOEC. The model developed can serve as a useful tool for SOEC design optimization.

Extended two-fluid model applied to analysis of bubbly flow in multiphase rotodynamic pump impeller

This paper presents an extended two-fluid model based on the Navier-Stokes equations and the standard κ — e turbulence model, to simulate the threedimensional air-water bubbly flow in turbo machinery. In the governing equations, the drag force and added mass force are added and the additional source terms arising from fluctuations of gas volume fraction are considered. The discrete equations are solved using a developed twophase semi-implicit method for pressure-linked equations, consistent (SIMPLEC) algorithm in body-fitted coordinates with a staggered grid system. Simulation is then carried out for the pure liquid flow and air-water two-phase flow with the inlet gas volume fraction being 15% in a multiphase rotodynamic pump impeller and the pump head performance is predicted. Comparison with experimental results shows the reliability and commonality of the numerical model.

Numerical simulation of interphase mass transfer with the level set approach

A level set approach is applied for simulating the interphase mass transfer of single drops in immiscible liquid with resistance in both phases. The control volume formulation with the SIMPLEC (semi-implicit method for pressure-linked equations consistent) algorithm incorporated is used to solve the governing equations of incompressible two-phase flow with deformable free interface on a staggered Eulerian grid. The solution of convective diffusion equation for interphase mass transfer is decoupled with the momentum equations. Different spatial discretization schemes including the fifth-order WENO (weighted essentially nonoscillatory), second-order ENO (essentially nonoscillatory) and power-law schemes, are tested for the solution of mass transfer to or from single drops. The conjugate cases with different equilibrium distribution coefficients are simulated successfully with the transformation of concentrations, molecular diffusivities, mass transfer time and velocities. The predicted drop concentration, overall mass transfer coefficient and flow structure are compared with the reported experimental data of a typical extraction system, i.e., n-butanol–succinic acid–water, and good agreement is observed.

A comparison study of the convergence characteristics and robustness for four variants of SIMPLE‐family at fine grids

A comparative study is performed to reveal the convergence characteristics and the robustness of four variants in the semi‐implicit method for pressure‐linked equations (SIMPLE)‐family: SIMPLE, SIMPLE revised (SIMPLER), SIMPLE consistent (SIMPLEC), and SIMPLE extrapolation (SIMPLEX). The focus is concentrated in the solution at fine grid system. Four typical fluid flow and heat transfer problems are taken as the numerical examples (lid‐driven cavity flow, flow in an axisymmetric sudden expansion, flow in an annulus with inner surface rotating and the natural convection in a square enclosure). It is found that an appropriate convergence condition should include both mass conservation and momentum conservation requirements. For the four problems computed, the SIMPLEX always requires the largest computational time, the SIMPLER comes the next, and the computational time of SIMPLE and SIMPLEC are the least. As far as the robustness is concerned, the SIMPLE algorithm is the worst, the SIMPLER comes the next and the robustness of SIMPLEX and SIMPLEC are superior to the others. The SIMPLEC algorithm is then recommended, especially for the computation at a fine grid system. Brief discussion is provided to further reveal the reasons which may account for the difference of the four algorithms.

Fluid dynamic modelling and simulation of circulating fluidized bed reactors: importance of the interface turbulence transfer

The main objective of this work is to analyze the importance of the gas-solid interface transfer of the kinetic energy of the turbulent motion on the accuracy of prediction of the fluid dynamic of Circulating Fluidized Bed (CFB) reactors. CFB reactors are used in a variety of industrial applications related to combustion, incineration and catalytic cracking. In this work a two-dimensional fluid dynamic model for gas-particle flow has been used to compute the porosity, the pressure, and the velocity fields of both phases in 2-D axisymmetrical cylindrical co-ordinates. The fluid dynamic model is based on the two fluid model approach in which both phases are considered to be continuous and fully interpenetrating. CFB processes are essentially turbulent. The model of effective stress on each phase is that of a Newtonian fluid, where the effective gas viscosity was calculated from the standard k-epsilon turbulence model and the transport coefficients of the particulate phase were calculated from the kinetic theory of granular flow (KTGF). This work shows that the turbulence transfer between the phases is very important for a better representation of the fluid dynamics of CFB reactors, especially for systems with internal recirculation and high gradients of particle concentration. Two systems with different characteristics were analyzed. The results were compared with experimental data available in the literature. The results were obtained by using a computer code developed by the authors. The finite volume method with collocated grid, the hybrid interpolation scheme, the false time step strategy and SIMPLEC (Semi-Implicit Method for Pressure Linked Equations - Consistent) algorithm were used to obtain the numerical solution.

Numerical simulation of solid-liquid phase change phenomena

Abstract A two-dimensional numerical simulation of the thermal behaviour of a solid-liquid phase change material (PCM), confined in a rectangular domain, has been carried out. A numerical coupling between the PCM enclosure and two heat exchangers forming a thermal storage device has been made. The natural convection in the fluid and the conduction in the solid are both considered. The enthalpy-porosity approach proposed by Voller et al. has been applied to formulate the governing equations. A fixed grid and the semi-implicit method for pressure-linked equations consistent (SIMPLEC) are used to obtain the numerical solution of the governing equations. Numerical results corresponding to three different PCMs under different work conditions are presented. The numerical predictions have been compared with experimental data found in the literature.