Search results for: Linear Flow Splitting

Authors: Kumaresh Selvakumar, Man Young Kim

Abstract:

Wet scrubbers have found widespread use in cleaning contaminated gas streams because of their ability to remove particulates and based on the applications of scrubbing of marine engine exhaust gases by spraying sea-water. In order to examine the flow characteristics inside the scrubber, the model is designated with flow properties of hot air and water sprayer. The flow dynamics of evaporation of hot air by the injection of water droplets is the key factor considered in this paper. The flow behavior inside the scrubber was investigated from the previous works and to sum up the evaporation rate with respect to the concentration of water droplets are predicted to bring out the competent modelling. The numerical analysis using CFD facilitates in understanding the problem better and empathies the behavior of the model over its entire operating envelope.

Keywords: Concentration of water droplets, Evaporation rate, Scrubber, Water sprayer.

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Authors: Satyavati Shukla, Lakhan V. Rathod, Mohan V. Khire

Abstract:

Rapid urbanization changes the land use/land cover pattern of a developing region. Due to these land surface changes, stream flow of the rivers also changes. It is important to investigate the factors affecting hydrological characteristics of the river basin for better river basin management planning. This study is aimed to understand the effect of Land Use/Land Cover (LU/LC) changes on stream flow of Upper Bhima River basin which is highly stressed in terms of water resources. In this study, Upper Bhima River basin is divided into two adjacent sub-watersheds: Mula-Mutha (urbanized) sub-watershed and Bhima (non-urbanized) sub-watershed. First of all, LU/LC changes were estimated over 1980, 2002, and 2009 for both Mula-Mutha and Bhima sub-watersheds. Further, stream flow simulations were done using Soil and Water Assessment Tool (SWAT) for the streams draining both watersheds. Results revealed that stream flow was relatively higher for urbanized sub-watershed. Through Sensitivity Analysis it was observed that out of all the parameters used, base flow was the most sensitive parameter towards LU/LC changes.

Keywords: Land Use/Land Cover, remote sensing, stream flow, urbanization.

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Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: Mohammad Ahmed Rehmatullah

Abstract:

The aim of this paper is to discuss a low-cost methodology that can predict traffic flow conflicts and quantitatively rank crash expectancies (based on relative probability) for various traffic facilities. This paper focuses on the application of statistical distributions to model traffic flow and Monte Carlo techniques to simulate traffic and discusses how to create a tool in order to predict the possibility of a traffic crash. A low-cost data collection methodology has been discussed for the heterogeneous traffic flow that exists and a GIS platform has been proposed to thematically represent traffic flow from simulations and the probability of a crash. Furthermore, discussions have been made to reflect the dynamism of the model in reference to its adaptability, adequacy, economy, and efficiency to ensure adoption.

Keywords: Heterogeneous traffic data collection, Monte CarloSimulation, Traffic Flow Modeling, GIS.

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Authors: Phool Singh, Ashok Jangid, N. S. Tomer, Deepa Sinha

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The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.

Keywords: Magneto hydrodynamics, stretching sheet, thermal radiation, unsteady flow.

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Authors: V. A. C. Vale, E. T. L. Cöuras Ford

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In view of the requirements of the current industrial processes, the instrumentation plays a critical role. In this context, this work aims to raise some the operating characteristics of the level and flow transmitters, in addition to observing their similarities and possible limitations configurations.

Keywords: Flow, level, instrumentation, configurations of meters, method of choice of the meters, instrumentation in the industrial processes.

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Authors: Soltani Amir, Wang Xuan

Abstract:

The advantage of using non-linear passive damping  system in vibration control of two adjacent structures is investigated  under their base excitation. The base excitation is El Centro  earthquake record acceleration. The damping system is considered as  an optimum and effective non-linear viscous damper that is  connected between two adjacent structures. A MATLAB program is  developed to produce the stiffness and damping matrices and to  determine a time history analysis of the dynamic motion of the  system. One structure is assumed to be flexible while the other has a  rule as laterally supporting structure with rigid frames. The response  of the structure has been calculated and the non-linear damping  coefficient is determined using optimum LQR algorithm in an  optimum vibration control system. The non-linear parameter of  damping system is estimated and it has shown a significant advantage  of application of this system device for vibration control of two  adjacent tall building.

Keywords: Structural Control, Active and passive damping, Vibration control, Seismic isolation.

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Authors: R.YadollahiFarsani, B. Ghasemi

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A magnetohydrodynamic mixed convective flow in a cavity was studied in this paper. The lower surface of cavity was heated from below whereas other walls of the cavity were thermally isolated. The governing two-dimensional flow equations have been solved by using finite volume code. The effects of magnetic field were studied on flow and temperature field and heat transfer performance at a wide range of parameters, Such as Hartmann (0≤Ha≤100) and Reynolds (1≤Re≤100) numbers. The results showed that as Hartman number increases the Nusselt number, representing heat transfer from the cavity decreases.

Keywords: Cavity, Magnetic Field, Mixed Convection, Magnetohydrodynamic

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Authors: John B. McQuillen, David F. Chao, Nancy R. Hall, Brian J. Motil, Nengli Zhang

Abstract:

Future space vehicles will require the use of non-toxic, cryogenic propellants, because of the performance advantages over the toxic hypergolic propellants and also because of the environmental and handling concerns. A prototypical capillary flow liquid acquisition device (LAD) for cryogenic propellants was fabricated with a mesh screen, covering a rectangular flow channel with a cylindrical outlet tube, and was tested with liquid oxygen (LOX). In order to better understand the performance in various gravity environments and orientations with different submersion depths of the LAD, a series of computational fluid dynamics (CFD) simulations of LOX flow through the LAD screen channel, including horizontally and vertically submersions of the LAD channel assembly at normal gravity environment was conducted. Gravity effects on the flow field in LAD channel are inspected and analyzed through comparing the simulations.

Keywords: Liquid acquisition device, cryogenic propellants, CFD simulation, vertically submerged screen channel, gravity effects.

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Authors: A.K.Jayanthy, N.Sujatha, M.Ramasubba Reddy

Abstract:

Microcirculation is essential for the proper supply of oxygen and nutritive substances to the biological tissue and the removal of waste products of metabolism. The determination of blood flow in the capillaries is therefore of great interest to clinicians. A comparison has been carried out using the developed non-invasive, non-contact and whole field laser speckle contrast imaging (LSCI) based technique and as well as a commercially available laser Doppler blood flowmeter (LDF) to evaluate blood flow at the finger tip and elbow and is presented here. The LSCI technique gives more quantitative information on the velocity of blood when compared to the perfusion values obtained using the LDF. Measurement of blood flow in capillaries can be of great interest to clinicians in the diagnosis of vascular diseases of the upper extremities.

Keywords: Blood flow, Laser Doppler flowmeter, LSCI, speckle

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Authors: Lukas Mocek, Alexandros Markopoulos

Abstract:

The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.

Keywords: Linear elasticity, fictitious domain method, Total-FETI, domain decomposition, saddle-point system.

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: Single-degree-of-freedom system, linear acceleration method, nonlinear excited system, equivalent displacement method.

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Authors: Rangoli Goyal, Rama Bhargava

Abstract:

The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, Thermophoresis, Diffusiophoresis, Brownian motion.

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Authors: Malika.D Kedir-Talha, Mohammed Mehenni

Abstract:

To improve the characterization of blood flows, we propose a method which makes it possible to use the spectral analysis of the Doppler signals. Our calculation induces a reasonable approximation, the error made on estimated speed reflects the fact that speed depends on the flow conditions as well as on measurement parameters like the bore and the volume flow rate. The estimate of the Doppler signal frequency enables us to determine the maximum Doppler frequencie Fd max as well as the maximum flow speed. The results show that the difference between the estimated frequencies ( Fde ) and the Doppler frequencies ( Fd ) is small, this variation tends to zero for important θ angles and it is proportional to the diameter D. The description of the speed of friction and the coefficient of friction justify the error rate obtained.

Keywords: Doppler frequency, Doppler spectrum, estimate speed, permanent flow.

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Authors: A. G. Pradeep, Gorantla Giridhar Kumar, Vijay Turaga, Vinod Srinivasa

Abstract:

The major problem in the flow control valve is of lower Flow Capacity (Cv) which will reduce overall efficiency of flow circuit. Designers are continuously working to improve the Cv of the valve, but they need to validate the design ideas they have regarding the improvement of Cv. Traditional method of prototype and testing take a lot of time, that is where CFD comes into picture with very quick and accurate validation along with the visualization which is not possible with traditional testing method. We have developed a method to predict Cv value using CFD analysis by iterating on various Boundary conditions, solver settings and by carrying out grid convergence studies to establish correlation between the CFD model and Test data. The present study investigates 3 different ideas put forward by the designers for improving the flow capacity of the valves like reducing the cage thickness, changing the port position, and using the parabolic plug to guide the flow. Using CFD, we analyzed all design changes using the established methodology that we developed. We were able to evaluate the effect of these design changes on the Valve Cv. We optimized the wetted surface of the valve further by suggesting the design modification to the lower part of the valve to make the flow more streamlined. We could find that changing cage thickness and port position has little impact on the valve Cv. Combination of optimized wetted surface and introduction of parabolic plug improved the Cv of the valve significantly.

Keywords: Flow control valves, flow capacity, CFD simulations, design validation.

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Authors: Vai Kuong Sin, Chon Kit Chio

Abstract:

In this paper, the two-dimensional reversed stagnationpoint flow is solved by means of an anlytic approach. There are similarity solutions in case the similarity equation and the boundary condition are modified. Finite analytic method are applied to obtain the similarity velocity function.

Keywords: reversed stagnation-point flow, similarity solutions, asymptotic solution

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Authors: Midiya Khademi, Ali Nikoo, Shabnam Rahimnezhad Baghche Jooghi

Abstract:

Cardiovascular diseases (CVDs) are the main cause of death globally. Most CVDs can be prevented by avoiding habitual risk factors. Separate from the habitual risk factors, there are some inherent factors in each individual that can increase the risk potential of CVDs. Vessel shapes and geometry are influential factors, having great impact on the blood flow and the hemodynamic behavior of the vessels. In the present study, the influence of bifurcation angle on blood flow characteristics is studied. In order to approach this topic, by simplifying the details of the bifurcation, three models with angles 30°, 45°, and 60° were created, then by using CFD analysis, the response of these models for stable flow and pulsatile flow was studied. In the conducted simulation in order to eliminate the influence of other geometrical factors, only the angle of the bifurcation was changed and other parameters remained constant during the research. Simulations are conducted under dynamic and stable condition. In the stable flow simulation, a steady velocity of 0.17 m/s at the inlet plug was maintained and in dynamic simulations, a typical LAD flow waveform is implemented. The results show that the bifurcation angle has an influence on the maximum speed of the flow. In the stable flow condition, increasing the angle lead to decrease the maximum flow velocity. In the dynamic flow simulations, increasing the bifurcation angle lead to an increase in the maximum velocity. Since blood flow has pulsatile characteristics, using a uniform velocity during the simulations can lead to a discrepancy between the actual results and the calculated results.

Keywords: Coronary artery, cardiovascular disease, bifurcation, atherosclerosis, CFD, artery wall shear stress.

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Authors: László Lengyel, Tihamér Levendovszky, Gergely Mezei, Hassan Charaf

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Graph rewriting-based visual model processing is a widely used technique for model transformation. Visual model transformations often need to follow an algorithm that requires a strict control over the execution sequence of the transformation steps. Therefore, in Visual Model Processors (VMPs) the execution order of the transformation steps is crucial. This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This paper introduces VCFL, discusses its termination properties and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual ModelTransformation, OCL, Termination Properties, UML.

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Authors: M. Khaing, A. V. Tkacheva

Abstract:

The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: Temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli.

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Authors: Manisha Dubey, Gaurav Gupta, Anoop Arya

Abstract:

The demand for power supply increases day by day in developing countries like India henceforth demand of reactive power support in the form of ancillary services provider also has been increased. The multi-line and multi-type Flexible alternating current transmission system (FACTS) controllers are playing a vital role to regulate power flow through the transmission line. Unified power flow controller and interline power flow controller can be utilized to control reactive power flow through the transmission line. In a restructured power system, the demand of such controller is being popular due to their inherent capability. The transmission pricing by using reactive power cost allocation through modified matrix methodology has been proposed. The FACTS technologies have quite costly assembly, so it is very useful to apportion the expenses throughout the restructured electricity industry. Therefore, in this work, after embedding the FACTS devices into load flow, the impact on the costs allocated to users in fraction to the transmission framework utilization has been analyzed. From the obtained results, it is clear that the total cost recovery is enhanced towards the Reactive Power flow through the different transmission line for 5 bus test system. The fair pricing policy towards reactive power can be achieved by the proposed method incorporating FACTS controller towards cost recovery of the transmission network.

Keywords: Inter line power flow controller, Transmission Pricing, Unified power flow controller, cost allocation.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: H. Barati, M. Wu, A. Kharicha, A. Ludwig

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A transient model for nozzle clogging has been developed and successfully validated against a laboratory experiment. Key steps of clogging are considered: transport of particles by turbulent flow towards the nozzle wall; interactions between fluid flow and nozzle wall, and the adhesion of the particle on the wall; the growth of the clog layer and its interaction with the flow. The current paper is to investigate the mesh (size and type) sensitivity of the model in both two and three dimensions. It is found that the algorithm for clog growth alone excluding the flow effect is insensitive to the mesh type and size, but the calculation including flow becomes sensitive to the mesh quality. The use of 2D meshes leads to overestimation of the clog growth because the 3D nature of flow in the boundary layer cannot be properly solved by 2D calculation. 3D simulation with tetrahedron mesh can also lead to an error estimation of the clog growth. A mesh-independent result can be achieved with hexahedral mesh, or at least with triangular prism (inflation layer) for near-wall regions.

Keywords: Clogging, nozzle, numerical model, simulation.

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Authors: Liu Zhiyuan, Sun Zongdi, Liu Zhiyuan, Sun Zongdi

Abstract:

Qingdao is a seaside city. Taking into account the characteristics of Qingdao, this article established a multiple linear regression model to analyze the impact of macroeconomic factors on housing prices. We used stepwise regression method to make multiple linear regression analysis, and made statistical analysis of F test values and T test values. According to the analysis results, the model is continuously optimized. Finally, this article obtained the multiple linear regression equation and the influencing factors, and the reliability of the model was verified by F test and T test.

Keywords: Housing prices, multiple linear regression model, macroeconomic factors, Qingdao City.

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Authors: A. Hasanpour, M. Farhadi, K.Sedighi, H.R.Ashorynejad

Abstract:

A numerical study of flow in a horizontally channel partially filled with a porous screen with non-uniform inlet has been performed by lattice Boltzmann method (LBM). The flow in porous layer has been simulated by the Brinkman-Forchheimer model. Numerical solutions have been obtained for variable porosity models and the effects of Darcy number and porosity have been studied in detail. It is found that the flow stabilization is reliant on the Darcy number. Also the results show that the stabilization of flow field and heat transfer is depended to Darcy number. Distribution of stream field becomes more stable by decreasing Darcy number. Results illustrate that the effect of variable porosity is significant just in the region of the solid boundary. In addition, difference between constant and variable porosity models is decreased by decreasing the Darcy number.

Keywords: Lattice Boltzmann Method, Porous Media, Variable Porosity, Flow Stabilization

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Authors: Artem Nuriev, Olga Zaitseva

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This paper is devoted to the study of a viscous incompressible flow around a circular cylinder performing harmonic oscillations, especially the steady streaming phenomenon. The research methodology is based on the asymptotic explanation method combined with the computational bifurcation analysis. The research approach develops Schlichting and Wang decomposition method. Present studies allow to identify several regimes of the secondary streaming with different flow structures. The results of the research are in good agreement with experimental and numerical simulation data.

Keywords: Oscillating cylinder, Secondary Streaming, Flow Regimes, Asymptotic and Bifurcation Analysis.

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Authors: Weihao Chung, Iau-Teh Wang, Yu-Hsi Hu

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This is the second part of the paper. It, aside from the core subroutine test reported previously, focuses on the simulation of turbulence governed by the full STF Navier-Stokes equations on a large scale. Law of the wall is found plausible in this study as a model of the boundary layer dynamics. Model validations proceed to include velocity profiles of a stationary turbulent Couette flow, pure sloshing flow simulations, and the identification of water-surface inclination due to fluid accelerations. Errors resulting from the irrotational and hydrostatic assumptions are explored when studying a wind-driven water circulation with no shakings. Illustrative examples show that this numerical strategy works for the simulation of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.

Keywords: potential flow theory, sloshing flow, space-timefiltering, order of accuracy.

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Authors: Akhilesh Khapre, Basudeb Munshi

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A computational fluid dynamics simulation is done for non-Newtonian fluid in a baffled stirred tank. The CMC solution is taken as non-Newtonian shear thinning fluid for simulation. The Reynolds Average Navier Stocks equation with steady state multi reference frame approach is used to simulate flow in the stirred tank. The turbulent flow field is modelled using realizable k-ε turbulence model. The simulated velocity profiles of Rushton turbine is validated with literature data. Then, the simulated flow field of CD-6 impeller is compared with the Rushton turbine. The flow field generated by CD-6 impeller is less in magnitude than the Rushton turbine. The impeller global parameter, power number and flow number, and entropy generation due to viscous dissipation rate is also reported.

Keywords: Computational fluid dynamics, non-Newtonian, Rushton turbine, CD-6 impeller, power number, flow number, viscous dissipation rate.

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Authors: Younes Matar, Fabien Candelier, Camille Solliec

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The aim of this study is to investigate the kinematics of undulatory elongated fish swimming against a velocity flow. We perform the experiments on European eel Anguilla Anguilla swimming in a hydrodynamic re-circulating tank with the velocity flow fixed at 0.2 m/s. We find that the undulating shape of overall eel body changes when it swims slantwise from the flow direction, by comparison to axial undulation shape. We examine this kinematics and we propose a general equation describing the lateral position of undulation body taking into account the direction of the eel-s swimming.

Keywords: Undulatory swimming, maneuver, eel Anguilla Anguilla, biomechanic.

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Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Nawin Raj, Zhenquan Li

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Streamtube is used to visualize expansion, contraction and various properties of the fluid flow. These are useful in fluid mechanics, engineering and geophysics. The streamtube constructed in this paper only reveals the flow expansion rate along streamline. Based on the mass conservative streamline, we will show how to construct the streamtube.

Keywords: Flow visualization, mass conservative, streamline, streamtube.

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