Search results for: Frenet Equations

Authors: Arash Taheri

Abstract:

In this paper, Lagrangian coherent structure (LCS) concept is applied to wake flows generated in the up/down-stream of a swimming nematode C. elegans in an intermediate Re number range, i.e., 250-1200. It materializes Lagrangian hidden structures depicting flow transport barriers. To pursue the goals, nematode swimming in a quiescent fluid flow environment is numerically simulated by a two-way fluid-structure interaction (FSI) approach with the aid of immersed boundary method (IBM). In this regard, incompressible Navier-Stokes equations, fully-coupled with Lagrangian deformation equations for the immersed body, are solved using IB2d code. For all simulations, nematode’s body is modeled with a parametrized spring-fiber built-in case available in the computational code. Reverse von-Kármán vortex street formation and vortex shedding characteristics are studied and discussed in details via LCS approach, including grid resolution, integration time and Reynolds number effects. Results unveil presence of different flow regions with distinct fluid particle fates in the swimming animal’s wake and formation of so-called ‘mushroom-shaped’ structures in attracting LCS identities.

Keywords: Lagrangian coherent structure, nematode swimming, fluid-structure interaction, immersed boundary method, bionics.

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Authors: Mohsen Torabi, Nader Karimi, Kaili Zhang

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This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.

Keywords: Entropy generation, exothermicity, endothermicity, forced convection, local thermal non-equilibrium, analytical modeling.

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Authors: Vikas Tewari, Shivendra Tewari, K. R. Pardasani

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Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.

Keywords: Excess buffer approximation, Na+ influx, sodium calcium exchange protein, sarcolemmal calcium atpase pump, forward time centred space.

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Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

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This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: Non-stationary, BINARMA(1, 1) model, Poisson Innovations, CML

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Authors: Dong-Hyun Kim, Yoo-Han Kim

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In this study, aeroelastic response and performance analyses have been conducted for a 5MW-Class composite wind turbine blade model. Advanced coupled numerical method based on computational fluid dynamics (CFD) and computational flexible multi-body dynamics (CFMBD) has been developed in order to investigate aeroelastic responses and performance characteristics of the rotating composite blade. Reynolds-Averaged Navier-Stokes (RANS) equations with k-ω SST turbulence model were solved for unsteady flow problems on the rotating turbine blade model. Also, structural analyses considering rotating effect have been conducted using the general nonlinear finite element method. A fully implicit time marching scheme based on the Newmark direct integration method is applied to solve the coupled aeroelastic governing equations of the 3D turbine blade for fluid-structure interaction (FSI) problems. Detailed dynamic responses and instantaneous velocity contour on the blade surfaces which considering flow-separation effects were presented to show the multi-physical phenomenon of the huge rotating wind- turbine blade model.

Keywords: Computational Fluid Dynamics (CFD), Computational Multi-Body Dynamics (CMBD), Reynolds-averageNavier-Stokes (RANS), Fluid Structure Interaction (FSI), FiniteElement Method (FEM)

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Authors: P. G. Siddheshwar, R. K. Vanishree, C. Kanchana

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A local nonlinear stability analysis using a eight-mode expansion is performed in arriving at the coupled amplitude equations for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence of LTNE effects. Streamlines and isotherms are obtained in the two-dimensional unsteady finite-amplitude convection regime. The parameters’ influence on heat transport is found to be more pronounced at small time than at long times. Results of the Rayleigh-Bénard convection is obtained as a particular case of the present study. Additional modes are shown not to significantly influence the heat transport thus leading us to infer that five minimal modes are sufficient to make a study of RBBC. The present problem that uses rolls as a pattern of manifestation of instability is a needed first step in the direction of making a very general non-local study of two-dimensional unsteady convection. The results may be useful in determining the preferred range of parameters’ values while making rheometric measurements in fluids to ascertain fluid properties such as viscosity. The results of LTE are obtained as a limiting case of the results of LTNE obtained in the paper.

Keywords: Rayleigh-Bénard convection, heat transport, porous media, generalized Lorenz model, coupled Ginzburg-Landau model.

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Authors: Ibrahim Yakubu Seini, Oluwole Daniel Makinde

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MHD chemically reacting viscous fluid flow towards a vertical surface with slip and convective boundary conditions has been conducted. The temperature and the chemical species concentration of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the vertical surface. The governing differential equations are modeled and transformed into systems of ordinary differential equations, which are then solved numerically by a shooting method. The effects of various parameters on the heat and mass transfer characteristics are discussed. Graphical results are presented for the velocity, temperature, and concentration profiles whilst the skin-friction coefficient and the rate of heat and mass transfers near the surface are presented in tables and discussed. The results revealed that increasing the strength of the magnetic field increases the skin-friction coefficient and the rate of heat and mass transfers toward the surface. The velocity profiles are increased towards the surface due to the presence of the Lorenz force, which attracts the fluid particles near the surface. The rate of chemical reaction is seen to decrease the concentration boundary layer near the surface due to the destructive chemical reaction occurring near the surface.

Keywords: Boundary layer, surface slip, MHD flow, chemical reaction, heat transfer, mass transfer.

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar

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This paper presents the problem of modeling and simulating of transient phenomena in conveying pipeline systems based on the rigid column and full elastic methods. Transient analysis is important and one of the more challenging and complicated flow problem in the design and the operation of water pipeline systems. Transient can produce large pressure forces and rapid fluid acceleration into a water pipeline system, these disturbances may result in device failures, system fatigue or pipe ruptures, and even the dirty water intrusion. Several methods have been introduced and used to analyze transient flow, an accurate analysis and suitable protection devices should be used to protect water pipeline systems. The fourth-order Runge-Kutta method has been used to solve the dynamic and continuity equations in the rigid column method, while the characteristics method used to solve these equations in the full elastic method. The results obtained provide that the model is an efficient tool for flow transient analysis and provide approximately identical results by using these two methods. Moreover; using the simple surge tank ”open surge tank” reduces the unfavorable effects of transients.

Keywords: Elastic method, Flow transient, Open surge tank, Pipeline, Protection devices, Numerical model, Rigid column method.

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Authors: K. V. Pagalthivarthi, R. J. Visintainer

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Two-dimensional Eulerian (volume-averaged) continuity and momentum equations governing multi-size slurry flow through pump casings are solved by applying a penalty finite element formulation. The computational strategy validated for multi-phase flow through rectangular channels is adapted to the present study.   The flow fields of the carrier, mixture and each solids species, and the concentration field of each species are determined sequentially in an iterative manner. The eddy viscosity field computed using Spalart-Allmaras model for the pure carrier phase is modified for the presence of particles. Streamline upwind Petrov-Galerkin formulation is used for all the momentum equations for the carrier, mixture and each solids species and the concentration field for each species. After ensuring mesh-independence of solutions, results of multi-size particulate flow simulation are presented to bring out the effect of bulk flow rate, average inlet concentration, and inlet particle size distribution. Mono-size computations using (1) the concentration-weighted mean diameter of the slurry and (2) the D50 size of the slurry are also presented for comparison with multi-size results.

Keywords: Eulerian-Eulerian model, Multi-size particulate flow, Penalty finite elements, Pump casing, Spalart-Allmaras.

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Authors: Abhishek Agarwal, Manoj Sarda, Juhi Kaushik, Vatsal Sanjay, Arup Kumar Das

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Propagation of fire through a non-air conditioned railway compartment is studied by virtue of numerical simulations. Simultaneous computational fire dynamics equations, such as Navier-Stokes, lumped species continuity, overall mass and energy conservation, and heat transfer are solved using finite volume based (for radiation) and finite difference based (for all other equations) solver, Fire Dynamics Simulator (FDS). A single coupe with an eight berth occupancy is used to establish the numerical model, followed by the selection of a three coupe system as the fundamental unit of the locomotive compartment. Heat Release Rate Per Unit Area (HRRPUA) of the initial fire is varied to consider a wide range of compartmental fires. Parameters, such as air inlet velocity relative to the locomotive at the windows, the level of interaction with the ambiance and closure of middle berth are studied through a wide range of numerical simulations. Almost all the loss of lives and properties due to fire breakout can be attributed to the direct or indirect exposure to flames or to the inhalation of toxic gases and resultant suffocation due to smoke and soot. Therefore, the temporal stature of fire and smoke are reported for each of the considered cases which can be used in the present or extended form to develop guidelines to be followed in case of a fire breakout.

Keywords: Fire dynamics, flame propagation, locomotive fire, soot flow pattern.

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Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: Optimal control, ensemble Kalman Filter, topography reconstruction, data assimilation, shallow water equations.

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Authors: Thomas Rowan, Mohammed Seaid

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A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: Erosion, finite volume method, sediment transport, shallow water equations.

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Authors: S.H. Mirtalaie, M.A. Hajabasi

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In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.

Keywords: Free vibration, laminated composite beam, material coupling, state space.

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Authors: G. Sarojamma, K. Vendabai

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An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: Casson nanofluid, Boundary layer flow, Internal heat generation/absorption, Exponentially stretching cylinder, Heat transfer, Brownian motion, Thermophoresis.

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Authors: Bhanu Gupta

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In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.

Keywords: impulsive differential equations, Lyapunov function, eventual stability

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Authors: Jemai Rabeb, Benhmidene Ali, Hidouri Khaoula, Chaouachi Bechir

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The diffusion-absorption refrigeration cycle consists of a generator bubble pump, an absorber, an evaporator and a condenser, and usually operates with ammonia/water/ hydrogen or helium as the working fluid. The aim of this paper is to study the stability problem a bubble pump. In fact instability can caused a reduction of bubble pump efficiency. To achieve this goal, we have simulated the behaviour of two-phase flow in a bubble pump by using a drift flow model. Equations of a drift flow model are formulated in the transitional regime, non-adiabatic condition and thermodynamic equilibrium between the liquid and vapour phases. Equations resolution allowed to define void fraction, and liquid and vapour velocities, as well as pressure and mixing enthalpy. Ammonia-water mixing is used as working fluid, where ammonia mass fraction in the inlet is 0.6. Present simulation is conducted out for a heating flux of 2 kW/m² to 5 kW/m² and bubble pump tube length of 1 m and 2.5 mm of inner diameter. Simulation results reveal oscillations of vapour and liquid velocities along time. Oscillations decrease with time and with heat flux. For sufficient time the steady state is established, it is characterised by constant liquid velocity and void fraction values. However, vapour velocity does not have the same behaviour, it increases for steady state too. On the other hand, pressure drop oscillations are studied.

Keywords: Bubble pump, drift flow model, instability, simulation.

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Authors: M. Sadighi, H. Pouriayevali, M. Saadati

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This paper deals with analysis of flexural stiffness, indentation and their energies in three point loading of sandwich beams with composite faces from Eglass/epoxy and cores from Polyurethane or PVC. Energy is consumed in three stages of indentation in laminated beam, indentation of sandwich beam and bending of sandwich beam. Theory of elasticity is chosen to present equations for indentation of laminated beam, then these equations have been corrected to offer better results. An analytical model has been used assuming an elastic-perfectly plastic compressive behavior of the foam core. Classical theory of beam is used to describe three point bending. Finite element (FE) analysis of static indentation sandwich beams is performed using the FE code ABAQUS. The foam core is modeled using the crushable foam material model and response of the foam core is experimentally characterized in uniaxial compression. Three point bending and indentation have been done experimentally in two cases of low velocity and higher velocity (quasi-impact) of loading. Results can describe response of beam in terms of core and faces thicknesses, core material, indentor diameter, energy absorbed, and length of plastic area in the testing. The experimental results are in good agreement with the analytical and FE analyses. These results can be used as an introduction for impact loading and energy absorbing of sandwich structures.

Keywords: Three point Bending, Indentation, Foams, Composite laminated beam, Sandwich beams, Finite element

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Authors: Camelia Frigioiu, Katica (Stevanovic) Hedrih, Iulian Gabriel Birsan

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In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.

Keywords: Lagrange's equations, mechanical system, non-linear connection, rheonomic Lagrange space.

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Authors: N. Khatiashvili, Ch. Pirumova, V. Akhobadze

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In the paper the mathematical model of tumor growth is considered. New capillary network formation, which supply cancer cells with the nutrients, is taken into the account. A formula estimating a tumor growth in connection with the number of capillaries is obtained.

Keywords: Differential Equations, Mathematical Models, Vascular Endothelial, Tumor

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Authors: S. J. Matlan, M. Mukhlisin, M. R. Taha

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Characterization of the engineering behavior of unsaturated soil is dependent on the soil-water characteristic curve (SWCC), a graphical representation of the relationship between water content or degree of saturation and soil suction. A reasonable description of the SWCC is thus important for the accurate prediction of unsaturated soil parameters. The measurement procedures for determining the SWCC, however, are difficult, expensive, and timeconsuming. During the past few decades, researchers have laid a major focus on developing empirical equations for predicting the SWCC, with a large number of empirical models suggested. One of the most crucial questions is how precisely existing equations can represent the SWCC. As different models have different ranges of capability, it is essential to evaluate the precision of the SWCC models used for each particular soil type for better SWCC estimation. It is expected that better estimation of SWCC would be achieved via a thorough statistical analysis of its distribution within a particular soil class. With this in view, a statistical analysis was conducted in order to evaluate the reliability of the SWCC prediction models against laboratory measurement. Optimization techniques were used to obtain the best-fit of the model parameters in four forms of SWCC equation, using laboratory data for relatively coarse-textured (i.e., sandy) soil. The four most prominent SWCCs were evaluated and computed for each sample. The result shows that the Brooks and Corey model is the most consistent in describing the SWCC for sand soil type. The Brooks and Corey model prediction also exhibit compatibility with samples ranging from low to high soil water content in which subjected to the samples that evaluated in this study.

Keywords: Soil-water characteristic curve (SWCC), statistical analysis, unsaturated soil.

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

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In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in x and y directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors.

Keywords: Feedback control system, magnetostrictive nano-plate, modified couple stress theory, nonlocal elasticity theory, vibration analysis.

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Authors: Nizami Mustafa, C. Ardil

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In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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Authors: Edikan E. Akpanibah Obinichi C. Mandah Imoleayo S. Asiwaju

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In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.

Keywords: Defined contribution pension scheme, extended Hamilton Jacobi Bellman equations, optimal portfolio policies, refund of premium clauses, supplementary premium.

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Authors: W. Triampo, D. Baowan, I.M. Tang, N. Nuttavut, J. Wong-Ekkabut, G. Doungchawee

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In this work, we consider a deterministic model for the transmission of leptospirosis which is currently spreading in the Thai population. The SIR model which incorporates the features of this disease is applied to the epidemiological data in Thailand. It is seen that the numerical solutions of the SIR equations are in good agreement with real empirical data. Further improvements are discussed.

Keywords: Leptospirosis, SIR Model, Deterministic model, Thailand.

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

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The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: Control, limits cycle, robot, stability.

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Authors: Haydar Kepekçi, Baha Zafer, Hasan Rıza Güven

Abstract:

Noise disturbance is one of the major factors considered in the fast development of aircraft technology. This paper reviews the flow field, which is examined on the 2D NACA0015 and 3D NACA0012 blade profile using SST k-ω turbulence model to compute the unsteady flow field. We inserted the time-dependent flow area variables in Ffowcs-Williams and Hawkings (FW-H) equations as an input and Sound Pressure Level (SPL) values will be computed for different angles of attack (AoA) from the microphone which is positioned in the computational domain to investigate effect of augmentation of unsteady 2D and 3D airfoil region noise level. The computed results will be compared with experimental data which are available in the open literature. As results; one of the calculated Cp is slightly lower than the experimental value. This difference could be due to the higher Reynolds number of the experimental data. The ANSYS Fluent software was used in this study. Fluent includes well-validated physical modeling capabilities to deliver fast, accurate results across the widest range of CFD and multiphysics applications. This paper includes a study which is on external flow over an airfoil. The case of 2D NACA0015 has approximately 7 million elements and solves compressible fluid flow with heat transfer using the SST turbulence model. The other case of 3D NACA0012 has approximately 3 million elements.

Keywords: Aeroacoustics, Ffowcs-Williams and Hawkings equations, SST k-ω turbulence model, Noise Disturbance, 3D Blade Profile, 2D Blade Profile.

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Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

Abstract:

This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

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Authors: T. Yamaguchi, Y. Fujii, A. Takita, T. Kanai

Abstract:

To compute dynamic characteristics of nonlinear viscoelastic springs with elastic structures having huge degree-of-freedom, Yamaguchi proposed a new fast numerical method using finite element method [1]-[2]. In this method, restoring forces of the springs are expressed using power series of their elongation. In the expression, nonlinear hysteresis damping is introduced. In this expression, nonlinear complex spring constants are introduced. Finite element for the nonlinear spring having complex coefficients is expressed and is connected to the elastic structures modeled by linear solid finite element. Further, to save computational time, the discrete equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. In this report, the proposed method is applied to simulation for impact responses of a viscoelastic shock absorber with an elastic structure (an S-shaped structure) by colliding with a concentrated mass. The concentrated mass has initial velocities and collides with the shock absorber. Accelerations of the elastic structure and the concentrated mass are measured using Levitation Mass Method proposed by Fujii [3]. The calculated accelerations from the proposed FEM, corresponds to the experimental ones. Moreover, using this method, we also investigate dynamic errors of the S-shaped force transducer due to elastic mode in the S-shaped structure.

Keywords: Transient response, Finite Element analysis, Numerical analysis, Viscoelastic shock absorber, Force transducer.

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar, A. A. Saber

Abstract:

In water pipeline systems, the flow control is an integrated part of the operation, for instance, opening and closing the valves, starting and stopping the pumps, when these operations very quickly performed, they shall cause the hydraulic transient phenomena, which may cause pump and, valve failures and catastrophic pipe ruptures. Fluid transient analysis is one of the more challenging and complicated flow problems in the design and the operation of water pipeline systems. Transient control has become an essential requirement for ensuring safe operation of water pipeline systems. An accurate analysis and suitable protection devices should be used to protect water pipeline systems. The fourth-order Runge-Kutta method has been used to solve the dynamic and continuity equations in the rigid column method, while the characteristics method used to solve these equations in the full elastic methods. This paper presents the problem of modeling and simulating of transient phenomena in conveying pipeline systems based on the rigid column and full elastic methods. Also, it provides the influence of using the protection devices to protect the pipeline systems from damaging due to the gain pressure which occur in the transient state. The results obtained provide that the model is an efficient tool for flow transient analysis and provide approximately identical results by using these two methods. Moreover; using the closed surge tank reduces the unfavorable effects of transients.

Keywords: Flow transient, Pipeline, Air chamber, Numerical model, Protection devices, Elastic method, Rigid column method.

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