Strongly Implicit Procedure Research Articles

SPRAYING PROCESS FOR Cr<sub>3</sub>C<sub>2</sub>-NiCr COATING

In this paper, the theoretical research of Cr3C2-NiCr coating for zirconia substrate is discussed. To obtain this coating, one of the multi-efficiency methods high velocity oxygen-fuel thermal spraying (HVOF) was investigated. The coatings were processed by different thicknesses of zirconia substrate sample of 3–5 mm also with length of 20 mm and width of 30 mm, at spraying speed of 600–700 m/s. The temperature during HVOF spraying is about 3000 ºC and the cooling temperature is 27 ºC. Investigating the theoretical data of Cr3C2-NiCr coatings, the development and thermal stresses after HVOF treatment were determined using Stone's method and Brenner-Senderoff equations with a coating thickness not exceeding 0.6 mm for carbide coatings. According to the results of theoretical research, the deposition efficiency values were found by the method proposed by Kosaku Shinoda. According to the theoretical and mathematical calculations, the deposition efficiency for Cr3C2-NiCr coating with zirconia substrate is in the range of 59.5%–69.4%. Thus, it was found that the deposition efficiency for the coatings depends on the thickness of the substrate, the powder feed rate, and the mass of the applied material and consequently the number of spraying passes.

Darcy–Brinkman–Forchheimer forced convective pseudo-plastic nanofluid flow through annular sector duct

In this research paper, we numerically analyze the flow and heat transfer rate of non-Newtonian pseudo-plastic nanofluid with variable apparent viscosity and thermal conductivity effects, respectively, through annular sector duct. Concentric pipes annular sector duct of an apex angle, [Formula: see text] and ratio of radii, [Formula: see text], is filled with saturated porous media. For this purpose, we utilize the power law Darcy–Brinkman flow model along with Forchheimer term. Also, the contribution of nanoparticles is accounted in carboxy methyl cellulose (CMC)-water, which has been taken as base fluid. Finite volume method (FVM) is utilized to discretize the governing mathematical model, whereas algebraic equations are solved numerically by using strongly implicit procedure (SIP). With the help of graphs, the impacts of nanoparticles’ contribution and porosity factor have been discussed by giving physical interpretation. Results are also found in the limiting sense and show the good agreement with already published data. At [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], we can observe down in [Formula: see text] and Nu upto [Formula: see text] and [Formula: see text], respectively, when n decreases from 1 to [Formula: see text], whereas [Formula: see text] and [Formula: see text], respectively, by decreasing the value of n from 1 to [Formula: see text]. For both cases of nanoparticles’ contribution, the downs in Nu have been observed same by decreasing the value of n.

Forced convective power-law fluid flow through porous annular sector duct

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than [Formula: see text] has been observed in [Formula: see text], whereas maximum decrease in dilatant fluid is around [Formula: see text], when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k.

Viscous dissipation and Joule heating effects on hydro-thermal power law nanofluid through annular duct

This study presents a mathematical model along with numerical simulation to investigate the viscous dissipation and Joule heating effects on electrically conducting magnetohydrodynamics (MHD) forced convection non-Newtonian power law nanofluid flow through annular sector duct. Hydro-thermal power law nanofluid flow through annular sector duct is not investigated in the presence of Joule heating and viscous dissipation effects. The consideration of Joule heating and viscous dissipation effects makes it very much novel in its own right. The main objective of this work is to explore the Joule heating and viscous dissipation effects on hydro-thermal power law nanofluid. Both Copper, Cu/Titanium oxide, TiO2 nanoparticles with base fluid water have been taken as a power law model. Numerically simulation is carried out for viscous, incompressible and steady laminar fully developed fluid flow with constant properties, by using the finite volume method (FVM) and strongly implicit procedure (SIP). It has been observed that viscous dissipation effect on temperature profiles is enhanced in the absence of magnetic field/at lower value of Ha, however, when nanoparticles’ concentration is increased, the effect of magnetic field slightly decreases. Furthermore, by adding Cu nanoparticles from 0% to 5%, we observe the increment in average Nusselt number, Nu up to 16.01% and 16.07% in pseudo-plastic and dilatant fluids, respectively, at [Formula: see text].

Simulation of pollutant dispersion in urban street canyons using hybrid rans-les method with two-phase model

In this study, to simulate the pollution treatment as a separated phase a 3D incompressible turbulence model under isothermal conditions was considered. The hybrid RANS-LES method with a sub-grid scale(SGS) technique within the framework of two-phase flow was used to study pollution distribution in urban street canyons. An area source of pollutant with a constant concentration, located in the ground of the street canyon, was used to simulate vehicular emissions. The near-wall regions were simulated using the RANS(k-ε) turbulence model and the rest of the domain was simulated with the LES model. To measure the effect of building height on pollutant dispersion, the parameter AR(Aspect Ratio) was calculated. Also to determine the effect of street width, a new parameter SWV(Street Width Value) was introduced. Governing equations were discretized using the well-known finite volume method on a staggered grid. To increase the accuracy, the second-order Van Leer Method(VLM) was applied and the Volume of Fluid(VOF) method was employed for the description of the interfaces. The Iterative line-by-line TDMA solution procedure and the Strongly Implicit Procedure(SIP) was used for the Pressure Correction Equation. A fine comparison of the results revealed that by increasing SWV, the number of vertical vortices in the canyon streets generally decreased and the vortices grew larger. In addition, increasing AR caused a rise in the pollution volume fraction in the first canyon street. The current numerical results indicate that the AR and SWV influence the flow field and volume fraction of phases inside an isolated street canyon, significantly.

An input-output model in a balanced multi-layer framework

Production or consumption processes can be seen as a transformation of inputs into outputs. Some of these flows may have a market value, therefore they have a price and can be accounted in monetary units. Some others, for example, might only be accounted in mass units, or in energy units or even in some other metrics, such as hours,items and so forth. Therefore, a framework that uses many metrics is necessary for describing the complexity of reality.Secondly, there are unquestionable laws that rule our world, such as the laws of Thermodynamics. Production or consumption processes also obey to these laws. In practice, this means that for any input there must always be outputs that obey these laws.Given these preconditions, the paper introduces a multi-layer supply and use framework, where each layer is balanced and accounted in a single metric. Then an input-output model is built upon this multi-layer framework. The model adopts the Stone's method, which is more known as the by-product technology assumption. Furthermore, endogenous matrices of technical coefficients are presented. This means that technical coefficients are not predetermined and kept fixed when running a simulation. Rather, they are endogenous variables that change according to the implemented analysis. Finally, the model makes use of linear programming techniques instead of implementing the Leontief inverse.

Current Profile Reconstruction Using Motional Stark Effect Polarimeter Data on HL-2A Tokamak

In order to reconstruct the plasma current density, the Current Profile Fitting (CPF) code has been successfully developed on the HL-2A tokamak. A seven-channel motional Stark effect (MSE) diagnostic based on dual photoelastic modulators is installed to measure the pitch angle of the magnetic field, which can be used as an internal magnetic field constraint for the CPF code. Recently, the MSE polarimeter was upgraded with a real-time wavelength matching system to improve the signal-to-noise ratio. The magnetic field angle (γpitch) with a temporal resolution of 10 ms can be provided. In the CPF code, the plasma current density is described as a polynomial, and the Least-Squares method is used to determine the coefficients of the polynomial. The Finite Difference method and the Strongly Implicit Procedure method are used to solve the Grad-Shafranov equation. The code operation is stable. With the improved-quality MSE data, the CPF calculation result of shot 30782 suggests that the safety factor q profile is monotonic. The minimum q value is less than 1 on-axis during sawtooth oscillations in shot 30782. And, the position of the q = 1 surface is consistent with the sawtooth inversion radius measured by electron cyclotron emission and soft X-ray diagnostics.

MHD power law fluid flow and heat transfer analysis through Darcy Brinkman porous media in annular sector

We have investigated the influence of uniform transverse magnetic field on the forced convective power law fluid flow through the annular sector duct, filled with Darcy Brinkman porous media. A system of equations are obtained from the law of conservation of momentum and energy are transformed into dimensionless form with the help of dimensionless parameter and discretized on the base of control volume method. Algebraic equations are solved with the help of strongly implicit procedure (SIP) or successive over relaxation (SOR) method, depending on the value of flow behaviour index. Characteristics of power law fluid flow and heat transfer rate are studied numerically and graphically against different parameters such as Hartman number, porosity factor, sector angle and ratio of radii of concentric pipes. Limiting case results are obtained for the Newtonian fluid and compared with the literature.

Heat transfer analysis of CNT suspended nanofluid through annulus sector duct

In this paper, we have numerically analysed the effects of single and multi-walled carbon nanotubes on the base fluid water through the vertical annulus sector duct, under the influence of Buoyancy force. A discretized form of governing dimensionless momentum and energy equation obtain with the help of finite volume based method and uses strongly implicit procedure (SIP) to solve the algebraic system. It has been observed that volume fraction of carbon nanotubes has direct relationship with the heat transfer coefficient and friction factor. Furthermore, limiting case results obtained in this study, are comparable with the published data in the absence of carbon nanotubes and Buoyancy force.

Numerical investigation of oscillating conjugate heat transfer in pulse tubes

This paper is aimed to investigate the influence of axial heat conduction on conjugate heat transfer for oscillating flow at the pulse tube section of Pulse Tube Cryocoolers (PTCs) via a numerical approach. Finite volume technique with collocated arrangement of grids has been employed to discretize momentum and energy equations. The well-established SIMPLE algorithm was followed for handling the pressure–velocity coupling. The set of individual algebraic equations was solved by the Strongly Implicit Procedure (SIP). Strouhal number (St), wall thickness and solid to fluid conductivity ratio (ksf) are three important parameters which affect the conjugate heat transfer in oscillating flow in pulse tubes. It is shown that the overall Nusselt number (Nu) increases from 5.97 to 28.45 by increasing St from 0.02 to 1. In addition, by increasing ksf from 0.5 to 15, Nu decreases almost 27%, however, for ksf>15, increasing the solid to fluid conductivity ratio has no influence on the Nusselt number. Furthermore, the cycle averaged friction coefficient at fully developed region increases almost 73% at St=1 in comparison to St=0.02.

An Improved Phase Correlation Method Based on 2-D Plane Fitting and the Maximum Kernel Density Estimator

In this letter, an improved phase correlation (PC) method based on 2-D plane fitting and the maximum kernel density estimator (MKDE) is proposed, which combines the idea of Stone's method and robust estimator MKDE. The proposed PC method first utilizes a vector filter to minimize the noise errors of the phase angle matrix and then unwraps the filtered phase angle matrix by the use of the minimum cost network flow unwrapping algorithm. Afterward, the unwrapped phase angle matrix is robustly fitted via MKDE, and the slope coefficients of the 2-D plane indicate the subpixel shifts between images. The experiments revealed that the improved method can effectively avoid the impact of outliers on the phase angle matrix during the plane fitting and is robust to aliasing and noise. The matching accuracy can reach 1/50th of a pixel using simulated data. The real image sequence tracking experiment was also undertaken to demonstrate the effectiveness of the proposed PC method with a registration accuracy of root-mean-square error better than 0.1 pixels.

Assessing Item-Level Fit for the DINA Model.

This research focuses on developing item-level fit checking procedures in the context of diagnostic classification models (DCMs), and more specifically for the "Deterministic Input; Noisy 'And' gate" (DINA) model. Although there is a growing body of literature discussing model fit checking methods for DCM, the item-level fit analysis is not adequately discussed in literature. This study intends to take an initiative to fill in this gap. Two approaches are proposed, one stems from classical goodness-of-fit test statistics coupled with the Expectation-Maximization algorithm for model estimation, and the other is the posterior predictive model checking (PPMC) method coupled with the Markov chain Monte Carlo estimation. For both approaches, the chi-square statistic and a power-divergence index are considered, along with Stone's method for considering uncertainty in latent attribute estimation. A simulation study with varying manipulated factors is carried out. Results show that both approaches are promising if Stone's method is imposed, but the classical goodness-of-fit approach has a much higher detection rate (i.e., proportion of misfit items that are correctly detected) than the PPMC method.

Towards a finite volume model on a many-core platform

This article presents a study of porting the finite volume model, caffa3d.MB, to GPU in order to improve its computational efficiency. In particular, we evaluated all the stages of the aforementioned model and implemented on GPU the most costly one, the linear systems resolution by means of the strongly implicit procedure (SIP) method. The experimental evaluation of the proposed implementation of the solver demonstrates that a significant runtime reduction can be attained (acceleration values up to 18×) when compared with a CPU version, and this improvement significantly reduces the total runtime of the model. This results evidence a promising prospect for a full GPU-based implementation of finite volume flow solvers like caffa3d.MB.

Finite volume method analysis of heat transfer problem using adapted strongly implicit procedure

In most issues representing physical problems, the complex geometry cannot be represented by a Cartesian grid. The multi-block grid technique allows artificially reducing the complexity of the geometry by breaking down the real domain into a number of sub-domains with simpler geometry. The main aim of this article is to show the usefulness of simple solvers in complex geometry problems, when using curvilinear coordinates combined with multi-block grids. This requires adapted solvers to a nine nodes computational cell instead of the five nodes computational cell used with Cartesian coordinates for two-dimensional cases. These developments are presented for the simple iterative methods Jacobi and Gauss-Seidel and also for the incomplete factorization method strongly implicit procedure (SIP). These adapted solvers are tested in two cases: a simple geometry (heat transfer in a circular cross-section) and a complex geometry (solidification case). Results of the simple geometry case show that all the adapted solvers have good performance with a slight advantage for the SIP solver. For increasing the complexity of the geometry, the results showed that Jacobi and Gauss-Seidel solvers are not suitable. However, the SIP method has a reasonable performance. A conclusion could be drawn that the SIP method could be used in complex geometry problems using multi-block grid technique when high precision results are not required.

Laminar Confined Impinging Jet into a Porous Layer

This work aims at studying laminar impinging jets on surfaces covered with a layer of a porous material. This contribution may provide insight into the design and optimization of heat and mass transfer processes over surfaces. Numerical simulations are presented and the porous substrate is treated as a rigid, homogeneous, and isotropic medium. Macroscopic transport equations are written for a representative elementary volume (REV), yielding a set of equations that is valid for the entire computational domain, including both the porous layer attached to the surface and the fluid layer over the porous substrate. These equations are discretized using the control-volume method and the resulting system of algebraic equations is relaxed using the Strongly Implicit Procedure (SIP) methods. The SIMPLE algorithm is used to handle the pressure–velocity coupling. Results for flow, in both clear and porous flow domains, are given in terms of streamlines patterns, velocity profiles, pressure contours, and friction coefficient along the impinging wall. The influence of porosity on the flow pattern is shown to be very low in comparison to the effects caused by varying permeability, fluid-layer height, and porous-layer thickness. These finding could be used to advantage when designing engineering equipment, since the use of selected porous materials could reduce undesirable recirculation zones, promote quick flow redistribution, and adjust pressure to required levels.

A two-dimensional finite volume hydrodynamic model for coastal areas: Model development and validation

A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases.

A Note on Stone's Conjecture of Blind Signal Separation

Stone's method is one of the novel approaches to the blind source separation (BSS) problem and is based on Stone's conjecture. However, this conjecture has not been proved. We present a simple simulation to demonstrate that Stone's conjecture is incorrect. We then modify Stone's conjecture and prove this modified conjecture as a theorem, which can be used a basis for BSS algorithms.

Mixed convection in rectangular cavities at various aspect ratios with moving isothermal sidewalls and constant flux heat source on the bottom wall

Mixed convection heat transfer in a two-dimensional rectangular cavity with constant heat flux from partially heated bottom wall while the isothermal sidewalls are moving in the vertical direction is studied numerically. The enclosure represents a practical system such as an air-cooled electronic device, where cooling from the sides is expected to be an efficient electronic cooling option. The heat source represents a heater or an electronic component located at the bottom in such an enclosure. Several different values of the heat source length, the aspect ratio of the cavity, as well as symmetric and asymmetric placement of the heat source are considered. All computations are done for a range of Richardson number from 0.1 to 10. The influence of the Richardson number, heat source length, placement of the heat source, and aspect ratio of the cavity, on the maximum temperature and the Nusselt number at the heat source surface is investigated. Results are presented in the form of streamline and isotherm plots as well as the variation of the maximum temperature and Nusselt number at the heat source surface under different conditions. The pressure–velocity coupling in the governing equations is achieved using the well-known SIMPLE method for numerical computation. The computational procedure is based on finite volume collocated mesh. The linear algebraic system of equations is solved sequentially using the strongly implicit procedure (SIP).

Laminar free convection and entropy generation inside an inclined wavy enclosure

We investigate numerically the heat transfer and fluid flow characteristics inside a wavy walled enclosure. Second law of thermodynamics is also applied to predict the nature of irreversibility in terms of entropy generation. Finite-volume method is used to discretize the governing differential equations with non-staggered variable arrangement. SIP (strongly implicit procedure) solver solves the linear equation systems with full multigrid (FMG) acceleration. Simulation was carried out for a range of wave ratio (defined by amplitude/average width) λ=0.0–0.4, aspect ratio (defined by height/average width) A=1.0–2.0, Rayleigh number Ra=10 0–10 7 for a fluid having Prandtl number equal to 0.7. The angle of inclination ( θ) is varied from 0° to 360° with 15° interval. Streamlines and isothermal lines represent the corresponding flow and thermal fields. Local and global Nusselt number distributions express the rate of heat transfer. Contour of Bejan number is plotted. Volume averaged entropy generation rate is also presented.

NUMERICAL STUDY OF TURBULENT NATURAL CONVECTION IN A SIDE-HEATED SQUARE CAVITYAT VARIOUS ANGLES OF INCLINATION

Turbulent natural convection at a moderately high Rayleigh number (4.9 2 10 10 ) in a two-dimensional side-heated square cavity at various angles of inclination is studied numerically. Initially, the performance of the low Reynolds number k - y model of Wilcox (1994) and the low Reynolds number k m l turbulence model of Lam and Bremhorst (1981), in predicting buoyancy-driven flow in a noninclined enclosure, is evaluated against experimental measurements. The evaluation is focused on the prediction of the flow patterns and convective heat transfer in the boundary layer and corner regions. The performance of the Wilcox k m y model is found to be superior in capturing the flow physics such as the strong streamline curvature in the corner regions. The Lam and Bremhorst k m l model is not capable of predicting these features but provides reasonable predictions away from the corners. None of these models, however, is capable of predicting the boundary-layer transition from laminar to turbulent. In order to study the effect of the inclination of the square cavity on the heat transfer and flow patterns, computations are then performed using the Wilcox k m y model for a range of inclination angles from 0° through 90°, keeping other parameters fixed. The computed flow patterns, isotherms, convection strengths, variation of the local Nusselt numbers along the heated walls, and the average Nusselt number for various inclination angles of the square cavity are reported. It is noticed that the flow fields and heat transfer characteristics become significantly different for inclinations greater than45°. The computational procedure is based on finite-volume collocated mesh. The pressure-velocity coupling in the governing equations is achieved using the well-known SIMPLE method for numerical computation. The linear algebraic system of equations is solved sequentially using the strongly implicit procedure (SIP).