Modified SIMPLE Algorithm Research Articles

A velocity-coefficient independent pressure correction equation for accelerated convergence of linear systems in incompressible flows

A velocity-coefficient independent pressure correction equation is proposed based on a modified SIMPLE algorithm for the solution of incompressible Navier-Stokes equations. In the conventional approach of SIMPLE, the central velocity coefficient of linearized momentum equation updates with every non-linear iteration within a time step. Since the pressure correction equation is coupled to the velocity coefficient term the pressure matrix coefficients obtained from the discretized pressure Poisson’s equation also get updated. As a consequence, the preconditioning step used to accelerate the convergence of pressure linear system becomes computationally expensive as the preconditioner is computed at every SIMPLE iteration. In the proposed approach this difficulty is circumvented wherein the velocity coefficient term in the pressure correction equation is repositioned with the velocity term such that the pressure matrix coefficients no longer depend on the same. Hence the preconditioner is computed only once at the first non-linear iteration that is stored and re-used for the subsequent iterations thereby reducing the overall CPU time of simulation.

Mixed Convective Flow in Horizontal Rectangular Enclosure with a Wall Heat Source: A Numerical Study

In this work, we have investigated the heat transfer of a mixed convective flow in horizontal rectangular enclosure having a wall heat source. For the purpose of computing stable and convergent numerical solutions of the flow variables, the governing equations along with the boundary conditions are solved by using the upwind finite volume scheme and a modified SIMPLE algorithm. For discussing the heat transfer from the bottom wall of the enclosure, the average Nusselt numbers are computed from relevant empirical correlations existing in the literature. These correlations are in the range of 1708 ≤ Ra ≤ 108 and 1708 ≤ Ra ≤ 3.5×109 in terms of different Rayleigh numbers for the Newtonian fluids such as air and water. Numerical solutions obtained from this study are compared with available benchmark solutions.

Development of thermal-hydraulic analysis code of a helically coiled once-through steam generator based on two-fluid model

A thermal-hydraulic analysis model, coupling the flow and heat transfer of the primary and secondary sides, is developed to describe the thermal hydraulic behavior of OTSG (helically coiled Once-Through Steam Generator). This numerical model is developed based on the two-fluid model with distributed parameters method to predict all flow variables at each position along the tube. Correlations, validated a lot, are adopted to consider the effect of helical structure on the flow and heat transfer of both the primary and secondary sides in OTSG. The computational code THOSG (Thermal-Hydraulic analysis code of Once-through Steam Generator) for OTSG is then developed based on the numerical model with the modified SIMPLE algorithm. To benchmark the developed physic model and computer code, steady-state simulation of OTSG of IRIS reactor is conducted. Results are compared with RELAP5 code with respect to the design parameters. Comparisons indicate that the THOSG code can predict the thermal-hydraulic characteristics of OTSG well. In order to investigate the effect of changes in the input conditions on the output of the OTSG, transient analysis has been performed. Simulations of change in feedwater flow rate and temperature are conducted to assess the performance of OTSG. Both steady-state and transient results indicate that the THOSG code can be utilized for the design and performance analysis of OTSG. However, further analysis, coupling with the thermal-hydraulic behavior of the reactor core, is required to comprehensively evaluate the safety and reliability of OTSG design in nuclear power plant.

Modification of SIMPLE algorithm to handle supercritical natural circulation in a loop

The conventional SIMPLE algorithm for the pressure–velocity coupling has been adopted by many commercial CFD codes. Since it encounters convergence problem when it is used for numerical analysis of a two-dimensional unsteady natural convection flow in a rectangular cavity with zero-isothermal compressibility, the modification of SIMPLE algorithm has been proposed for such a fluid. In this paper, differences between solutions for a one dimensional natural circulation of a super-critical carbon dioxide in a loop with a horizontal heater and a horizontal cooler configuration obtained by using the conventional SIMPLE algorithm and the modified version of the algorithm are investigated. The modification of the algorithm includes updating the density at each time step based on its value at the previous time step to satisfy the mass conservation. The differences of the velocity and temperature are relatively small comparing with the two-dimensional natural convection case. As an example of utilizing the modified SIMPLE algorithm, characteristics of the unsteady natural circulation of super-critical carbon dioxide in a rectangular loop are revealed.

Modification of SIMPLE algorithm to handle natural convection flows with zero-isothermal compressibility

The conventional SIMPLE algorithm for the pressure–velocity coupling has been adopted by many commercial and non-commercial CFD codes. It encounters convergence problem when it is used to solve unsteady natural convection flows with zero-isothermal compressibility. In this paper, a modified version of this algorithm is proposed to remedy this drawback. The modification includes updating of the density at each time step based on its value at the previous time step to satisfy the continuity equation. As an example of utilizing the modified SIMPLE algorithm, the unsteady natural convection in a rectangular cavity with isothermal vertical walls and adiabatic horizontal walls was computed. Physically consistent results were obtained.

A SIMPLE-based monolithic implicit method for strong-coupled fluid–structure interaction problems with free surfaces

Abstract A SIMPLE-based implicit method (SBMIM) for the strong coupling of fluid and structure is proposed. The SBMIM solves the Navier–Stokes (NS) equations of fluid by using a modified SIMPLE algorithm, which takes into account the structure governing equation. The free surfaces are reconstructed using the volume of fluid method (VOF), and the structure equation, embedded into the fluid solver, is processed with the widely used finite element method (FEM). We validate SBMIM by performing numerical simulations of a dam-breaking issue, a tank sloshing problem, and the free oscillation of a wash bulkhead in a liquid tank, and making comparisons against experimental measurements, theoretical results as well as other numerical solutions. The SBMIM is proved to be stable and robust under extreme simulation circumstances, and is applied to the strong coupling of wave impact on deck structure.

Two-fluid modeling of three-dimensional cylindrical gas–solid fluidized beds using the kinetic theory of granular flow

A highly efficient numerical scheme has been incorporated to solve a traditional two-fluid model for dense gas–solid flow in large scale fluidized beds. Difficulties associated with the numerical solution and boundary condition enforcement especially in the azimuthally direction and at the axis of the cylindrical domain are discussed in detail. Higher order discretization schemes with deferred correction approach have been implemented for the convection terms. The p–ε algorithm (Van der Hoef et al., 2006) has been implemented to deal with densely packed regions in the fluidized bed. A modified SIMPLE algorithm is used to solve the pressure and volume fraction corrections, and a projection method is used to obtain solutions of the momentum equations. The resulting semi-implicit method allows for using larger time steps and produces accurate results in a stable and efficient manner. Numerical tests on bubbling fluidized beds are undertaken and compared with experimental data reported by Laverman et al., 2012. The simulation results are found to be in good agreement. In addition a comparative study has been performed quantifying the effects of grid size, flux limiters, frictional model and coefficient of restitution.

Static characteristics of new type externally pressurized spherical air bearings

In order to provide some theoretical guideline for the structure design of the new type externally pressurized spherical air bearings, the static characteristics and the factors affecting the static characteristics of the air bearings were analyzed. A finite volume method was adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations, and a modified SIMPLE algorithm for compressible fluid was applied to solve the discretized governing equations. The pressure field and velocity field of the air bearings were obtained, and the factors and rules affecting the static characteristics were analyzed. The results show that the pressure of near air intakes can reach above 80% of air supply pressure, and there is a pressure steep fall around the air intakes. When the film thickness is greater than 20 μm, the bearing capacity rapidly decreases as film thickness increases. As the air supply pressure increases from 0.2 to 0.6 MPa, the maximum static stiffness increases by more than three times. The calculation method proposed well fits the general principle, which can be extended to the characteristic analysis of other air bearings.

A Simple Algorithm for the Estimation of Phase Difference Between Two Sinusoidal Voltages

A simple algorithm (SAL) and a modified SAL (MSAL) for the estimation of the phase difference between two sine-wave signals are proposed. The results obtained by SAL and MSAL in simulations and on real samples are given. A comparison between the phase difference results estimated by MSAL, quadrature delay estimator (QDE), unbiased QDE (UQDE), three-parameter sine-fitting algorithm (3PSF), four-parameter sine-fitting algorithm (4PSF), and seven-parameter sine-fitting algorithm (7PSF) is presented. The requirements for the application of SAL and MSAL are analyzed.

Numerical simulation of transient cuttings transport with foam fluid in horizontal wellbore

With considering the interlayer mass transfer and fluid influx from the reservoir, a one-dimensional two-layer hydraulic model was established to describe the mechanism of transient cuttings transport with foam fluid in horizontal well section. The model was numerically calculated based on the modified SIMPLE algorithm, and the height of cuttings bed was predicted by the trial-and-error method. Sensitivity analysis was conducted on the affecting factors on the cuttings transport performance. Results show that cuttings deposition moves along the horizontal wellbore from the drilling bit, and finally achieves a steady state with dynamic balance. Dimensionless cuttings bed height decreases with the increase of foam quality or foam flow rate, but increases with the increase of drillpipe eccentricity, cuttings size or drilling rate. The influx of water and gas from the reservoir is helpful to improve the cuttings transport efficiency with foam. The proposed model offers theoretical guidelines for hydraulic parameter design and hole cleaning control in foamed horizontal drilling.

Effect of Manufacturing Errors on Static Characteristics of Externally Pressurized Spherical Air Bearings

Externally pressurized spherical air bearings are the key component of the three-axis air bearing table, and the manufacturing errors of the bearing affects the performance of the air bearing table. However, the manufacturing errors are unavoidable, and the pursuit to enhance the manufacturing accuracy will increase the cost greatly. In order to provide some theoretical guideline for the tolerance choice in the design of the externally pressurized spherical air bearings with inherent compensation, the effects of several manufacturing errors on the static characteristics of the air bearing are studied. Due to the complex geometry of the computational domain, an unstructured meshing technology is used for mesh generation. A finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations. A modified SIMPLE algorithm which is suitable for compressible flows is applied to solve the discretized governing equations. The effects of the dimension error and the roundness error of the ball head and the ball socket on the static characteristics are investigated. The investigation result shows that the positive dimension error and the oblate spheroid-type roundness error of the ball head as well as the negative dimension error and the prolate spheroid-type roundness error of the ball socket can improve the bearing capacity and static stiffness of the air bearings by reducing the mass flow. The calculation method proposed in this paper fits well for the general principle, which can be extended to the characteristics analysis of other air bearings.

LIF 공초점 현미경을 이용한 Y-채널 마이크로믹서의 혼합 효율 평가

Mixing between two or more reagents is one of important processes in biochemical microfluidics. In efficient micromixer design, it is essential to analyze flow pattern and evaluate mixing efficiency with good precision. In this work, mixing efficiency for Y-channel micromixer is measured by fluorescence intensity using LIF(Laser Induced Fluorescence) Confocal Microscope. The Y-channel micromixers are fabricated with polydimethylsiloxane(PDMS) and those are bonded to glass plate through Plasma bonding. Nile Blue A is injected into the micromixer as a fluorescence dye for measuring of fluorescence intensity by He/Ne laser. For visualization of the flow pattern, dynamic image capturing is carried out using CAM scope. For the comparison with computer simulation, modified SIMPLE algorithm for incompressible flow equation is solved for the same geometry as in the experiment. Throughout the experiments and computer simulation, accurate mixing efficiency evaluation process for a PDMS Y-channel micromixer is established.

개량된 SIMPLE알고리듬을 이용한 비압축성 자유계면유동의 수치해석

While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipments or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented fur the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm.

FLOW AND HEAT TRANSFER CHARACTERISTICS IN FLAT TUBES OF A RADIATOR

The flow and heat transfer characteristics for three-dimensional mixed convection flows in a radiator flat tube with U-shaped grooves are analyzed numerically. The flow and temperature fields are calculated using the developed program that is a modified SIMPLE algorithm for irregular geometry. One tube specification among the various flat tube exchangers is recommended by first considering the heat transfer and pressure drop. The effects of variation of coolant flow conditions and external air conditions on the flow and the thermal characteristics for the selected tube are investigated also. The results will be used as fundamental data for tube design by suggesting optimal specifications for radiator tubes.

Numerical analysis and experiments on transferred plasma torches for finding appropriate operating conditions and electrode configuration for a waste melting process

Thermal plasma characteristics of transferred plasma torches are numerically and experimentally investigated under atmospheric conditions to find the effects of operating variables and electrode arrangements on them. A control volume method and a modified SIMPLER algorithm are used for numerical analysis, and the temperature distributions of argon plasma are calculated in different torch operating conditions of a typical transferred arc torch. Transferred plasma torches are designed and fabricated, which have six different electrode arrangements, respectively, consisting of a conical rod cathode and a nozzle in the torch, and a distant anode material. The dynamic behaviors of arc voltage are measured to obtain stable arc conditions, and a similarity criterion is determined to analyze static behaviors of arc voltage. For predicting the heat transfer rate to melted material from arc column, measurements are made for the heat loss at the anode material and fractions of input power transferred to the anode. Furthermore, thermal plasma temperatures are measured by the optical emission spectroscopy of an Ar I line. As a result of the present work, an appropriate electrode configuration and operating conditions for waste melting process are presented for the optimization of transferred plasma torches.

A Study of Natural Convection Heat Transfer in a Composed Rectangular-Parallelogrammic Enclosure with a Guide Vane

The present experimental and numerical study investigate flow and natural convection heat transfer characteristics of a composed rectangular-parallelogrammic enclosure with a guide vane. The governing equations for the two-dimensional, laminar, natural convection process in an enclosure are discretized by the control volume approach which insures the conservative characteristics to be satisfied in the calculation domain, and solved by a modified SIMPLE algorithm. The momentum and energy equations are coupled through the buoyancy term. In this results of experimental study, the natural convection heat transfer characteristics was well coincided with conclusions of other earlier experimental researches and numerical analysis.

A numerical study of natural convection heat transfer in a composed thermal diode

The effects of inclination on the steady natural convection local heat transfer characteristics in an air-filled enclosure, which is composed of rectangular and parallelogrammic portions, are studied numerically. In this investigation, two geometrical aspect ratios are introduced: one for a parallelogrammic portion of an enclosure, the other for a rectangular one. The governing equations for a two-dimensional, laminar, natural convection process in an enclosure are discretized by the control volume approach which ensures the conservative characteristics to be satisfied in the calculation domain, and then solved by a modified SIMPLE algorithm. The momentum and energy equations are coupled through the buoyancy term. Computations are carried out for Prandtl number Pr = 1 and Rayleigh number Ra = 2.7 x 10 8 . In order to obtain a greater understanding of the flow and heat transfer behaviors, flow patterns with streamlines and isotherms at different inclination angles are shown. Also, the effects of numbers of installed guide vanes in a composed enclosure are studied to consider the enhancement of heat transfer of the inner diode.

A numerical study of natural convection heat transfer in a composed thermal diode

The effects of inclination on the steady natural convection local heat transfer characteristics in an air-filled enclosure, which is composed of rectangular and parallelogrammic portions, are studied numerically. In this investigation, two geometrical aspect ratios are introduced: one for a parallelogrammic portion of an enclosure, the other for a rectangular one. The governing equations for a two-dimensional, laminar, natural convection process in an enclosure are discretized by the control volume approach which ensures the conservative characteristics to be satisfied in the calculation domain, and then solved by a modified SIMPLE algorithm. The momentum and energy equations are coupled through the buoyancy term. Computations are carried out for Prandtl number Pr = 1 and Rayleigh number Ra = 2.7 × 108. In order to obtain a greater understanding of the flow and heat transfer behaviors, flow patterns with streamlines and isotherms at different inclination angles are shown. Also, the effects of numbers of installed guide vanes in a composed enclosure are studied to consider the enhancement of heat transfer of the inner diode. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 573–582, 1999

Arc plasma jets of a nontransferred plasma torch

The plasma flow of a nontransferred plasma torch used for thermal plasma processings is produced by the arc-gas interactions between a cathode tip and an anode nozzle and expands as a jet through the nozzle. In this work, numerically calculated images of the are plasma characteristics are found over the entire plasma region, including both an arc-gas interacting region inside the torch and a jet expanding region outside the torch. A numerical model used assumes a local thermodynamic equilibrium (LTE) with near-electrode phenomena and compressible flow effects. The computational system is described by a two-dimensional (2-D) axisymmetric model which is solved for plasma temperature and velocity by a control volume approach with the modified SIMPLER algorithm in a real torch geometry.

A Numerical Study of Two-Dimensional High Rayleigh Number Natural Convection Between Two Reservoirs Connected by a Horizontal Duct

The phenomenon of natural convection between two enclosures communicating through small openings like windows, ducts, and cracks has important applications in the fields of energy conservation in buildings, indoor air quality, fire research, solar energy storage, and nuclear reactor core performance. A numerical solution of natural convection between two reservoirs connected by a two-dimensional horizontal duct was obtained using a modified SIMPLE algorithm. The emphasis of the numerical computation was on high Rayleigh numbers and small duct dimensions. A strong fluid stratification in both reservoirs was observed at high Rayleigh number. The volume exchange of fluid between the reservoirs takes place through counterflow streams in the connecting duct. The exchange of diffusive energy between the two streams is substantial at low Rayleigh number and small duct dimension. Correlation equations were derived for the Nusselt number and volume exchange rate. 23 refs., 5 figs.