Search results for: stokes equations

Authors: Amal Machtalay

Abstract:

In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

Procedia PDF Downloads 82

Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

Procedia PDF Downloads 354

Authors: Anamika Paul, Sudipto Sarkar

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The flow behaviour of non-Newtonian fluid is quite complicated, although both the pseudoplastic (n < 1, n being the power index) and dilatant (n > 1) fluids under this category are used immensely in chemical and process industries. A limited research work is carried out for flow over a bluff body in non-Newtonian flow environment. In the present numerical simulation we control the vortices of a square cylinder by placing an upstream vertical splitter plate for pseudoplastic (n=0.8), Newtonian (n=1) and dilatant (n=1.2) fluids. The position of the upstream plate is also varied to calculate the critical distance between the plate and cylinder, below which the cylinder vortex shedding suppresses. Here the Reynolds number is considered as Re = 150 (Re = U∞a/ν, where U∞ is the free-stream velocity of the flow, a is the side of the cylinder and ν is the maximum value of kinematic viscosity of the fluid), which comes under laminar periodic vortex shedding regime. The vertical plate is having a dimension of 0.5a × 0.05a and it is placed at the cylinder centre-line. Gambit 2.2.30 is used to construct the flow domain and to impose the boundary conditions. In detail, we imposed velocity inlet (u = U∞), pressure outlet (Neumann condition), symmetry (free-slip boundary condition) at upper and lower domain. Wall boundary condition (u = v = 0) is considered both on the cylinder and the splitter plate surfaces. The unsteady 2-D Navier Stokes equations in fully conservative form are then discretized in second-order spatial and first-order temporal form. These discretized equations are then solved by Ansys Fluent 14.5 implementing SIMPLE algorithm written in finite volume method. Here, fine meshing is used surrounding the plate and cylinder. Away from the cylinder, the grids are slowly stretched out in all directions. To get an account of mesh quality, a total of 297 × 208 grid points are used for G/a = 3 (G being the gap between the plate and cylinder) in the streamwise and flow-normal directions respectively after a grid independent study. The computed mean flow quantities obtained from Newtonian flow are agreed well with the available literatures. The results are depicted with the help of instantaneous and time-averaged flow fields. Qualitative and quantitative noteworthy differences are obtained in the flow field with the changes in rheology of fluid. Also, aerodynamic forces and vortex shedding frequencies differ with the gap-ratio and power index of the fluid. We can conclude from the present simulation that fluent is capable to capture the vortex dynamics of unsteady laminar flow regime even in the non-Newtonian flow environment.

Keywords: CFD, critical gap-ratio, splitter plate, wake-wake interactions, dilatant, pseudoplastic

Procedia PDF Downloads 92

Authors: Rawhy Ismail

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Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity.

Keywords: curl operator, fractional calculus, fractional curl operators, Maxwell equations

Procedia PDF Downloads 453

Authors: Jiahui You, Kyung Jae Lee

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Hydraulic fracturing fluid (HFF) is widely used in shale reservoir productions. HFF contains diverse chemical additives, which result in the dissolution and precipitation of minerals through multiple chemical reactions. In this study, a new pore-scale Darcy–Brinkman–Stokes (DBS) model coupled with Level Set Method (LSM) is developed to address the microscopic phenomena occurring during the iron–HFF interaction, by numerically describing mass transport, chemical reactions, and pore structure evolution. The new model is developed based on OpenFOAM, which is an open-source platform for computational fluid dynamics. Here, the DBS momentum equation is used to solve for velocity by accounting for the fluid-solid mass transfer; an advection-diffusion equation is used to compute the distribution of injected HFF and iron. The reaction–induced pore evolution is captured by applying the LSM, where the solid-liquid interface is updated by solving the level set distance function and reinitialized to a signed distance function. Then, a smoothened Heaviside function gives a smoothed solid-liquid interface over a narrow band with a fixed thickness. The stated equations are discretized by the finite volume method, while the re-initialized equation is discretized by the central difference method. Gauss linear upwind scheme is used to solve the level set distance function, and the Pressure–Implicit with Splitting of Operators (PISO) method is used to solve the momentum equation. The numerical result is compared with 1–D analytical solution of fluid-solid interface for reaction-diffusion problems. Sensitivity analysis is conducted with various Damkohler number (DaII) and Peclet number (Pe). We categorize the Fe (III) precipitation into three patterns as a function of DaII and Pe: symmetrical smoothed growth, unsymmetrical growth, and dendritic growth. Pe and DaII significantly affect the location of precipitation, which is critical in determining the injection parameters of hydraulic fracturing. When DaII<1, the precipitation uniformly occurs on the solid surface both in upstream and downstream directions. When DaII>1, the precipitation mainly occurs on the solid surface in an upstream direction. When Pe>1, Fe (II) transported deeply into and precipitated inside the pores. When Pe<1, the precipitation of Fe (III) occurs mainly on the solid surface in an upstream direction, and they are easily precipitated inside the small pore structures. The porosity–permeability relationship is subsequently presented. This pore-scale model allows high confidence in the description of Fe (II) dissolution, transport, and Fe (III) precipitation. The model shows fast convergence and requires a low computational load. The results can provide reliable guidance for injecting HFF in shale reservoirs to avoid clogging and wellbore pollution. Understanding Fe (III) precipitation, and Fe (II) release and transport behaviors give rise to a highly efficient hydraulic fracture project.

Keywords: reactive-transport , Shale, Kerogen, precipitation

Procedia PDF Downloads 144

Authors: E. Manikandan, C. Chilambarasan, M. Sulthan Ariff Rahman, S. Kanagaraj, V. R. Sanal Kumar

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The noise regulations around the major airports and rocket launching stations due to the environmental concern have made jet noise a crucial problem in the present day aero-acoustics research. The three main acoustic sources in jet nozzles are aerodynamics noise, noise from craft systems and engine and mechanical noise. Note that the majority of engine noise is due to the jet noise coming out from the exhaust nozzle. The previous studies reveal that the potential of chevron nozzles for aircraft engines noise reduction is promising owing to the fact that the jet noise continues to be the dominant noise component, especially during take-off. In this paper parametric analytical studies have been carried out for optimizing the number of chevron lobes, the lobe length and tip shape, and the level of penetration of the chevrons into the flow over a variety of flow conditions for various aerospace applications. The numerical studies have been carried out using a validated steady 3D density based, SST k-ω turbulence model with enhanced wall functions. In the numerical study, a fully implicit finite volume scheme of the compressible, Navier–Stokes equations is employed. We inferred that the geometry optimization of an environmental friendly chevron nozzle with a suitable number of chevron lobes with aerodynamically efficient tip contours for facilitating silent exit flow will enable a commendable sound reduction without much thrust penalty while comparing with the conventional supersonic nozzles with same area ratio.

Keywords: chevron nozzle, jet acoustic level, jet noise suppression, shape optimization of chevron nozzles

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Authors: W. Meron Mebrahtu, R. Absi

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Velocity distribution in turbulent open-channel flows is organized in a complex manner. This is due to the large spatial and temporal variability of fluid motion resulting from the free-surface turbulent flow condition. This phenomenon is complicated further due to the complex geometry of channels and the presence of solids transported. Thus, several efforts were made to understand the phenomenon and obtain accurate mathematical models that are suitable for engineering applications. However, predictions are inaccurate because oversimplified assumptions are involved in modeling this complex phenomenon. Therefore, the aim of this work is to study velocity distribution profiles and obtain simple, more accurate, and predictive mathematical models. Particular focus will be made on the acceptable simplification of the general transport equations and an accurate representation of eddy viscosity. Wide rectangular open-channel seems suitable to begin the study; other assumptions are smooth-wall, and sediment-free flow under steady and uniform flow conditions. These assumptions will allow examining the effect of the bottom wall and the free surface only, which is a necessary step before dealing with more complex flow scenarios. For this flow condition, two ordinary differential equations are obtained for velocity profiles; from the Reynolds-averaged Navier-Stokes (RANS) equation and equilibrium consideration between turbulent kinetic energy (TKE) production and dissipation. Then different analytic models for eddy viscosity, TKE, and mixing length were assessed. Computation results for velocity profiles were compared to experimental data for different flow conditions and the well-known linear, log, and log-wake laws. Results show that the model based on the RANS equation provides more accurate velocity profiles. In the viscous sublayer and buffer layer, the method based on Prandtl’s eddy viscosity model and Van Driest mixing length give a more precise result. For the log layer and outer region, a mixing length equation derived from Von Karman’s similarity hypothesis provides the best agreement with measured data except near the free surface where an additional correction based on a damping function for eddy viscosity is used. This method allows more accurate velocity profiles with the same value of the damping coefficient that is valid under different flow conditions. This work continues with investigating narrow channels, complex geometries, and the effect of solids transported in sewers.

Keywords: accuracy, eddy viscosity, sewers, velocity profile

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Authors: Y. M. Aiyesimi, G. T. Okedayo, O. W. Lawal

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The analysis has been carried out to study unsteady MHD thin film flow of a third grade fluid down an inclined plane with heat transfer when the slippage between the surface of plane and the lower surface of the fluid is valid. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved analytically using method of separation of variable and eigenfunctions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the slip and magnetic field parameter depends on time.

Keywords: non-Newtonian fluid, MHD flow, thin film flow, third grade fluid, slip boundary condition, heat transfer, separation of variable, eigenfunction expansion

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Mohammadreza Nezamirad, Sepideh Amirahmadian, Nasim Sabetpour, Azadeh Yazdi, Amirmasoud Hamedi

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Cavitation inside diesel injector nozzle is investigated using Reynolds-Stress-Navier Stokes equations. Schnerr-Sauer cavitation model is used for modeling cavitation inside diesel injector nozzle. The carrying fluid utilized in the current study is diesel fuel. The flow is verified at the beginning by comparing with the previous experimental data, and it was found that K-Epsilon turbulent model could lead to a better accuracy comparing to K-Omega turbulent model. Moreover, the mass flow rate obtained numerically is compared with the experimental value, and the discrepancy was found to be less than 5 percent which shows the accuracy of the current results. Finally, a real-size four-hole nozzle is investigated, and the flow inside it is visualized based on velocity profile, discharge coefficient, and cavitation number. It was found that the mesh density could be reduced significantly by utilizing periodic boundary conditions. Velocity contour at the mid nozzle showed that the maximum value of velocity occurs at the end of the needle before entering the orifice area. Last but not least, at the same boundary conditions, when different needle heights were utilized, it was found that as needle height increases with an increase in cavitation number, discharge coefficient increases, while the mentioned increases are more tangible at smaller values of needle heights.

Keywords: cavitation, diesel fuel, CFD, real size nozzle, mass flow rate

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Authors: Said Algarni

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The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

Procedia PDF Downloads 275

Authors: Minas Balyan

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In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

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Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Nkemjika Chinenye-Kanu, Mamdud Hossain, Ghazi Droubi

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Prediction of multiphase flow induced forces, void fraction and pressure is crucial at both design and operating stages of practical energy and process pipe systems. In this study, transient numerical simulations of upward slug-churn flow through a vertical 90-degree elbow have been conducted. The volume of fluid (VOF) method was used to model the two-phase flows while the K-epsilon Reynolds-Averaged Navier-Stokes (RANS) equations were used to model turbulence in the flows. The simulation results were validated using experimental results. Void fraction signal, peak frequency and maximum magnitude of void fraction fluctuation of the slug-churn flow validation case studies compared well with experimental results. The x and y direction force fluctuation signals at the elbow control volume were obtained by carrying out force balance calculations using the directly extracted time domain signals of flow properties through the control volume in the numerical simulation. The computed force signal compared well with experiment for the slug and churn flow validation case studies. Hence, the present numerical simulation technique was able to predict the behaviours of the one-way flow induced forces and void fraction fluctuations.

Keywords: computational fluid dynamics, flow induced vibration, slug-churn flow, void fraction and force fluctuation

Procedia PDF Downloads 136

Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

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In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: elastic foundation, impact, moving load, thick plate

Procedia PDF Downloads 281

Authors: Anuar Ishak

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The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

Procedia PDF Downloads 384

Authors: Bouabdellah Abed, Mohamed Bouzit, Lakhdar Bouarbi

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The objective of this study is to investigate numerically the effect of roof shaped on wind flow and pollutant dispersion in a street canyon with one row of trees of pore volume, Pvol = 96%. A three-dimensional computational fluid dynamics (CFD) model for evaluating air flow and pollutant dispersion within an urban street canyon using Reynolds-averaged Navier–Stokes (RANS) equations and the k-Epsilon EARSM turbulence model as close of the equation system. The numerical model is performed with ANSYS-CFX code. Vehicle emissions were simulated as double line sources along the street. The numerical model was validated against the wind tunnel experiment. Having established this, the wind flow and pollutant dispersion in urban street canyons of six roof shapes are simulated. The numerical simulation agrees reasonably with the wind tunnel data. The results obtained in this work, indicate that the flow in 3D domain is more complicated, this complexity is increased with presence of tree and variability of the roof shapes. The results also indicated that the largest pollutant concentration level for two walls (leeward and windward wall) is observed with the upwind wedge-shaped roof. But the smallest pollutant concentration level is observed with the dome roof-shaped. The results also indicated that the corners eddies provide additional ventilation and lead to lower traffic pollutant concentrations at the street canyon ends.

Keywords: street canyon, pollutant dispersion, trees, building configuration, numerical simulation, k-Epsilon EARSM

Procedia PDF Downloads 327

Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: Chun-Lin Chiang, Che-Yen Lee, Yu-Shan Yeh, Jiunn-Haur Shaw

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Wafer fabrication is a critical part of the semiconductor process, when the finest linewidth with the improvement of technology continues to decline and the structure development from 2D towards to 3D. The nanoparticles contained in the slurry or in the ultrapure water which used for cleaning have a large influence on the manufacturing process. Therefore, semiconductor industry is hoping to find a viable method for on-line detection the nanoparticles size and concentration. The resistive pulse sensing technology is one of the methods that may cover this question. As we know that nanoparticles properties of material differ significantly from their properties at larger length scales. So, we want to clear that the metal and non-metal nanoparticles translocation dynamic when we use the resistive pulse sensing technology. In this study we try to use the finite element method that contains three governing equations to do multiphysics coupling simulations. The Navier-Stokes equation describes the laminar motion, the Nernst-Planck equation describes the ion transport, and the Poisson equation describes the potential distribution in the flow channel. To explore that the metal nanoparticles and the non-metal nanoparticles in different concentration electrolytes, through the nanochannel caused by ion current changes. Then the reliability of the simulation results was verified by resistive pulse sensing test. The existing results show that the lower ion concentration, the greater effect of nanoparticles on the ion concentration in the nanochannel. The conductive spikes are correlated with nanoparticles surface charge. Then we can be concluded that in the resistive pulse sensing technique, the ion concentration in the nanochannel and nanoparticle properties are important for the translocation dynamic, and they have the interactions.

Keywords: multiphysics simulations, resistive pulse sensing, nanoparticles, nanochannel

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Authors: Nima Farshidfar, Navid Daryasafar

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In this paper, the seismic stability of reinforced soil slopes is studied using pseudo-dynamic analysis. Equilibrium equations that are applicable to the every kind of failure surface are written using Horizontal Slices Method. In written equations, the balance of the vertical and horizontal forces and moment equilibrium is fully satisfied. Failure surface is assumed to be log-spiral, and non-linear equilibrium equations obtained for the system are solved using Newton-Raphson Method. Earthquake effects are applied as horizontal and vertical pseudo-static coefficients to the problem. To solve this problem, a code was developed in MATLAB, and the critical failure surface is calculated using genetic algorithm. At the end, comparing the results obtained in this paper, effects of various parameters and the effect of using pseudo - dynamic analysis in seismic forces modeling is presented.

Keywords: soil slopes, pseudo-dynamic, genetic algorithm, optimization, limit equilibrium method, log-spiral failure surface

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Authors: Mustapha Kamel Mihoubi, Hocine Dahmani

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The purpose of work is to study the phenomenon of agitation of storm waves at basin caused by different directions of waves relative to the current provision thrown numerical model based on the equation in shallow water using Boussinesq model MIKE 21 BW. According to the diminishing effect of penetration of a wave optimal solution will be available to be reproduced in reduced model. Another alternative arrangement throws will be proposed to reduce the agitation and the effects of the swell reflection caused by the penetration of waves in the harbor.

Keywords: agitation, Boussinesq equations, combination, harbor

Procedia PDF Downloads 365

Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

Procedia PDF Downloads 482

Authors: Teng lin, Li Yuxing, Han Hui, Zhao Pengfei, Zhang Datong

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With the development of carbon capture and storage (CCS), the flow assurance of CO2 transportation becomes more important, particularly for supercritical CO2 pipelines. The relieving system using the choke valve is applied to control the pressure in CO2 pipeline. However, the temperature of fluid would drop rapidly because of Joule-Thomson cooling (JTC), which may cause solid CO2 form and block the pipe. In this paper, a Computational Fluid Dynamic (CFD) model, using the modified Lagrangian method, Reynold's Stress Transport model (RSM) for turbulence and stochastic tracking model (STM) for particle trajectory, was developed to predict the deposition characteristic of solid carbon dioxide. The model predictions were in good agreement with the experiment data published in the literature. It can be observed that the particle distribution affected the deposition behavior. In the region of the sudden expansion, the smaller particles accumulated tightly on the wall were dominant for pipe blockage. On the contrary, the size of solid CO2 particles deposited near the outlet usually was bigger and the stacked structure was looser. According to the calculation results, the movement of the particles can be regarded as the main four types: turbulent motion close to the sudden expansion structure, balanced motion at sudden expansion-middle region, inertial motion near the outlet and the escape. Furthermore the particle deposits accumulated primarily in the sudden expansion region, reattachment region and outlet region because of the four type of motion. Also the Stokes number had an effect on the deposition ratio and it is recommended for Stokes number to avoid 3-8St.

Keywords: carbon capture and storage, carbon dioxide pipeline, gas-particle flow, deposition

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Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

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The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Anna Avramenko, Heikki Haario

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This paper reports the development and application of a 2D depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. K-E and 2D LES turbulence models were consider in this article. 2D CFD simulations for one hill was done to check the depth-averaged model in practise.

Keywords: depth-averaged equations, numerical modeling, CFD, wind park model

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: DucTho Le, Duy Kien Dao, Quoc Tinh Bui, Haidang Phan

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The article is concerned with the motion of ultrasonic guided waves in a unidirectional fiber-reinforced composite plate under acoustic sources. Such unidirectional composite material has orthotropic elastic properties as it is very stiff along the fibers and rather compliant across the fibers. The dispersion equations of free Lamb waves propagating in an orthotropic layer are derived that results in the dispersion curves. The connection of these equations to the Rayleigh-Lamb frequency relations of isotropic plates is discussed. By the use of reciprocity in elastodynamics, closed-form solutions of elastic wave motions subjected to time-harmonic loads in the layer are computed in a simple manner. We also consider the problem of Lamb waves generated by a set of time-harmonic sources. The obtained computations can be very useful for developing ultrasound-based methods for nondestructive evaluation of composite structures.

Keywords: lamb waves, fiber-reinforced composite plates, dispersion equations, nondestructive evaluation, reciprocity theorems

Procedia PDF Downloads 115

Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

Abstract:

In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: Funda Erdem Şahnali, Ş. Özgür Atayılmaz, Tolga N. Aynur

Abstract:

Almost all of the domestic refrigerators operate on the principle of the vapor compression refrigeration cycle and removal of heat from the refrigerator cabinets is done via one of the two methods: natural convection or forced convection. In this study, airflow and temperature distributions inside a 375L no-frost type larder cabinet, in which cooling is provided by forced convection, are evaluated both experimentally and numerically. Airflow rate, compressor capacity and temperature distribution in the cooling chamber are known to be some of the most important factors that affect the cooling performance and energy consumption of a refrigerator. The objective of this study is to evaluate the original temperature distribution in the larder cabinet, and investigate for better temperature distribution solutions throughout the refrigerator domain via system optimizations that could provide uniform temperature distribution. The flow visualization and airflow velocity measurements inside the original refrigerator are performed via Stereoscopic Particle Image Velocimetry (SPIV). In addition, airflow and temperature distributions are investigated numerically with Ansys Fluent. In order to study the heat transfer inside the aforementioned refrigerator, forced convection theories covering the following cases are applied: closed rectangular cavity representing heat transfer inside the refrigerating compartment. The cavity volume has been represented with finite volume elements and is solved computationally with appropriate momentum and energy equations (Navier-Stokes equations). The 3D model is analyzed as transient, with k-ε turbulence model and SIMPLE pressure-velocity coupling for turbulent flow situation. The results obtained with the 3D numerical simulations are in quite good agreement with the experimental airflow measurements using the SPIV technique. After Computational Fluid Dynamics (CFD) analysis of the baseline case, the effects of three parameters: compressor capacity, fan rotational speed and type of shelf (glass or wire) are studied on the energy consumption; pull down time, temperature distributions in the cabinet. For each case, energy consumption based on experimental results is calculated. After the analysis, the main effective parameters for temperature distribution inside a cabin and energy consumption based on CFD simulation are determined and simulation results are supplied for Design of Experiments (DOE) as input data for optimization. The best configuration with minimum energy consumption that provides minimum temperature difference between the shelves inside the cabinet is determined.

Keywords: air distribution, CFD, DOE, energy consumption, experimental, larder cabinet, refrigeration, uniform temperature

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