Search results for: Stokes theorem

Authors: Samuel Ahamefula

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Turbulent motion is a highly nonlinear and complex phenomenon, and its modelling is still very challenging. In this study, we developed a hybrid computational approach to accurately simulate fluid turbulence phenomenon. The focus is coupling and transitioning between Direct Numerical Simulation (DNS) and Large Eddy Simulating Wall Models (LES-WM) regions. In the framework, high-order fidelity fluid dynamical methods are utilized to simulate the unsteady compressible Navier-Stokes equations in the Eulerian format on the unstructured moving grids. The coupling and transitioning of DNS and LES-WM are conducted through the linearly staggered Dirichlet-Neumann coupling scheme. The high-fidelity framework is verified and validated based on namely, DNS ability for capture full range of turbulent scales, giving accurate results and LES-WM efficiency in simulating near-wall turbulent boundary layer by using wall models.

Keywords: computational methods, turbulence modelling, turbulence entropy, navier-stokes equations

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Authors: Judith Stein, Elfriede Friedmann

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The injection of a drug into the vitreous body for the treatment of retinal diseases like wet aged-related macular degeneration (AMD) is the most common medical intervention worldwide. We develop mathematical models for drug transport in the vitreous body of a human eye to analyse the impact of different rheological models of the vitreous on drug distribution. In addition to the convection diffusion equation characterizing the drug spreading, we use porous media modeling for the healthy vitreous with a dense collagen network and include the steady permeating flow of the aqueous humor described by Darcy's law driven by a pressure drop. Additionally, the vitreous body in a healthy human eye behaves like a viscoelastic gel through the collagen fibers suspended in the network of hyaluronic acid and acts as a drug depot for the treatment of retinal diseases. In a completely liquefied vitreous, we couple the drug diffusion with the classical Navier-Stokes flow equations. We prove the global existence and uniqueness of the weak solution of the developed initial-boundary value problem describing the drug distribution in the healthy vitreous considering the permeating aqueous humor flow in the realistic three-dimensional setting. In particular, for the drug diffusion equation, results from the literature are extended from homogeneous Dirichlet boundary conditions to our mixed boundary conditions that describe the eye with the Galerkin's method using Cauchy-Schwarz inequality and trace theorem. Because there is only a small effective drug concentration range and higher concentrations may be toxic, the ability to model the drug transport could improve the therapy by considering patient individual differences and give a better understanding of the physiological and pathological processes in the vitreous.

Keywords: coupled PDE systems, drug diffusion, mixed boundary conditions, vitreous body

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Authors: A. U. Haque, W. Asrar, A. A Omar, E. Sulaeman, J. S. M. Ali

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Buoyancy force applied on deformable symmetric bodies can be estimated by using Archimedes Principle. Such bodies like ellipsoidal bodies have high volume to surface ratio and are isometrically scaled for mass, length, area and volume to follow square cube law. For scaling up such bodies, it is worthwhile to find out the scaling relationship between the other physical quantities that represent thermodynamic, structural and inertial response etc. So, dimensionless similarities to find an allometric scale can be developed by using Bukingham π theorem which utilizes physical dimensions of important parameters. Base on this fact, physical dependencies of buoyancy system are reviewed to find the set of physical variables for deformable bodies of revolution filled with expandable gas like helium. Due to change in atmospheric conditions, this gas changes its volume and this change can effect the stability of elongated bodies on the ground as well as in te air. Special emphasis was given on the existing similarity parameters which can be used in the design of experiments of such bodies whose shape is affected by the external force like a drag, surface tension and kinetic loads acting on the surface. All these similarity criteria are based on non-dimensionalization, which also needs to be consider for scaling up such bodies.

Keywords: Bukhigham pi theorem, similitude, scaling, buoyancy

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Authors: Medine Demir, Volker John

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Fluid equations in a rotating frame of reference have a broad class of important applications in meteorology and oceanography, especially in the large-scale flows considered in ocean and atmosphere, as well as many physical and industrial applications. The Coriolis and the centripetal forces, resulting from the rotation of the earth, play a crucial role in such systems. For such applications it may be required to solve the system in complex three-dimensional geometries. In recent years, the Navier--Stokes equations in a rotating frame have been investigated in a number of papers using the classical inf-sup stable mixed methods, like Taylor-Hood pairs, to contribute to the analysis and the accurate and efficient numerical simulation. Numerical analysis reveals that these classical methods introduce a pressure-dependent contribution in the velocity error bounds that is proportional to some inverse power of the viscosity. Hence, these methods are optimally convergent but small velocity errors might not be achieved for complicated pressures and small viscosity coefficients. Several approaches have been proposed for improving the pressure-robustness of pairs of finite element spaces. In this contribution, a pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. However, this approach might come with a modification of the meshes, like the use of barycentric-refined grids in case of Scott--Vogelius pairs. However, this strategy requires the finite element code to have control on the mesh generator which is not realistic in many engineering applications and might also be in conflict with the solver for the linear system. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples illustrate the theoretical results. The idea of pressure-robust method could be cast on different types of flow problems which would be considered as future studies. As another future research direction, to avoid a modification of the mesh, one may use a very simple parameter-dependent modification of the Scott-Vogelius element, the pressure-wired Stokes element, such that the inf-sup constant is independent of nearly-singular vertices.

Keywords: navier-stokes equations in a rotating frame of refence, coriolis force, pressure-robust error estimate, scott-vogelius pairs of finite element spaces

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Authors: Yuyang Cheng, Marcos Escobar-Anel

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This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in Grasselli (2017). Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market.

Keywords: stochastic covariance process, 4/2 stochastic volatility model, stochastic co-volatility movements, characteristic function, expected utility theory, verication theorem

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Wu Di, Yeo Khoon Seng, Lim Tee Tai

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The typical insects employ a flapping-wing mode of flight. The numerical simulations on free flight of a model fruit fly (Re=143) including hovering and are presented in this paper. Unsteady aerodynamics around a flapping insect is studied by solving the three-dimensional Newtonian dynamics of the flyer coupled with Navier-Stokes equations. A hybrid-grid scheme (Generalized Finite Difference Method) that combines great geometry flexibility and accuracy of moving boundary definition is employed for obtaining flow dynamics. The results show good points of agreement and consistency with the outcomes and analyses of other researchers, which validate the computational model and demonstrate the feasibility of this computational approach on analyzing fluid phenomena in insect flight. The present modeling approach also offers a promising route of investigation that could complement as well as overcome some of the limitations of physical experiments in the study of free flight aerodynamics of insects. The results are potentially useful for the design of biomimetic flapping-wing flyers.

Keywords: free hovering flight, flapping wings, fruit fly, insect aerodynamics, leading edge vortex (LEV), computational fluid dynamics (CFD), Navier-Stokes equations (N-S), fluid structure interaction (FSI), generalized finite-difference method (GFD)

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Authors: Terrance Charles, Zhiyin Yang, Yiling Lu

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Heavy trucks are aerodynamically inefficient due to their un-streamlined body shapes, leading to more than of 60% engine power being required to overcome the aerodynamics drag at 60 m/hr. There are many aerodynamics drag reduction devices developed and this paper presents a study on a drag reduction device called Cross Vortex Trap Device (CVTD) deployed in the gap between the tractor and the trailer of a simplified tractor-trailer model. Numerical simulations have been carried out at Reynolds number 0.51×10⁶ based on inlet flow velocity and height of the trailer using the Reynolds-Averaged Navier-Stokes (RANS) approach. Three different configurations of CVTD have been studied, ranging from single to three slabs, equally spaced on the front face of the trailer. Flow field around three different configurations of trap device have been analysed and presented. The results show that a maximum of 12.25% drag reduction can be achieved when a triple vortex trap device is used. Detailed flow field analysis along with pressure contours are presented to elucidate the drag reduction mechanisms of CVTD and why the triple vortex trap configuration produces the maximum drag reduction among the three configurations tested.

Keywords: aerodynamic drag, cross vortex trap device, truck, Reynolds-Averaged Navier-Stokes, RANS

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Authors: Hashem Sazegar

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Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Zhuoneng Li, Zeeshan A. Rana, Karl W. Jenkins

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In industry, to validate a case, often a multitude of simulation are required and in order to demonstrate confidence in the process where users tend to use a coarser mesh. Therefore, it is imperative to establish the coarsest mesh that could be used while keeping reasonable simulation accuracy. To date, the two most reliable, affordable and broadly used advanced simulations are the hybrid RANS (Reynolds Averaged Navier Stokes)/LES (Large Eddy Simulation) and wall modelled LES. The potentials in these two simulations will still be developed in the next decades mainly because the unaffordable computational cost of a DNS (Direct Numerical Simulation). In the wall modelled LES, the turbulence model is applied as a sub-grid scale model in the most inner layer near the wall. The RANS turbulence models cover the entire boundary layer region in a hybrid RANS/LES (Detached Eddy Simulation) and its variants, therefore, the RANS still has a very important role in the state of art simulations. This research focuses on the turbulence model mesh sensitivity analysis where various turbulence models such as the S-A (Spalart-Allmaras), SSG (Speziale-Sarkar-Gatski), K-Omega transitional SST (Shear Stress Transport), K-kl-Omega, γ-Reθ transitional model, v2f are evaluated within the OpenFOAM. The simulations are conducted on a fully developed turbulent flow over a flat plate where the skin friction coefficient as well as velocity profiles are obtained to compare against experimental values and DNS results. A concrete conclusion is made to clarify the mesh sensitivity for different turbulence models.

Keywords: mesh sensitivity, turbulence models, OpenFOAM, RANS

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Authors: Ross Calvert, Colin Whittaker, Alison Raby, Alistair G. L. Borthwick, Ton S. van den Bremer

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Large concentrations of plastic have polluted the seas in the last half century, with harmful effects on marine wildlife and potentially to human health. Plastic pollution will have lasting effects because it is expected to take hundreds or thousands of years for plastic to decay in the ocean. The question arises how waves transport plastic in the ocean. The predominant motion induced by waves creates ellipsoid orbits. However, these orbits do not close, resulting in a drift. This is defined as Stokes drift. If a particle is infinitesimally small and the same density as water, it will behave exactly as the water does, i.e., as a purely Lagrangian tracer. However, as the particle grows in size or changes density, it will behave differently. The particle will then have its own inertia, the fluid will exert drag on the particle, because there is relative velocity, and it will rise or sink depending on the density and whether it is on the free surface. Previously, plastic pollution has all been considered to be purely Lagrangian. However, the steepness of waves in the ocean is small, normally about α = k₀a = 0.1 (where k₀ is the wavenumber and a is the wave amplitude), this means that the mean drift flows are of the order of ten times smaller than the oscillatory velocities (Stokes drift is proportional to steepness squared, whilst the oscillatory velocities are proportional to the steepness). Thus, the particle motion must have the forces of the full motion, oscillatory and mean flow, as well as a dynamic buoyancy term to account for the free surface, to determine whether inertia is important. To track the motion of a floating inertial particle under wave action requires the fluid velocities, which form the forcing, and the full equations of motion of a particle to be solved. Starting with the equation of motion of a sphere in unsteady flow with viscous drag. Terms can added then be added to the equation of motion to better model floating plastic: a dynamic buoyancy to model a particle floating on the free surface, quadratic drag for larger particles and a slope sliding term. Using perturbation methods to order the equation of motion into sequentially solvable parts allows a parametric equation for the transport of inertial finite-sized floating particles to be derived. This parametric equation can then be validated using numerical simulations of the equation of motion and flume experiments. This paper presents a parametric equation for the transport of inertial floating finite-size particles by ocean waves. The equation shows an increase in Stokes drift for larger, less dense particles. The equation has been validated using numerical solutions of the equation of motion and laboratory flume experiments. The difference in the particle transport equation and a purely Lagrangian tracer is illustrated using worlds maps of the induced transport. This parametric transport equation would allow ocean-scale numerical models to include inertial effects of floating plastic when predicting or tracing the transport of pollutants.

Keywords: perturbation methods, plastic pollution transport, Stokes drift, wave flume experiments, wave-induced mean flow

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Authors: Mohamed Abdelwahed

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We propose an optimization algorithm for the geometric control of fluid flow. The used approach is based on the topological sensitivity analysis method. It consists in studying the variation of a cost function with respect to the insertion of a small obstacle in the domain. Some theoretical and numerical results are presented in 2D and 3D.

Keywords: sensitivity analysis, topological gradient, shape optimization, stokes equations

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Authors: Emmanuel Ophel Gilbert, Williams Speret

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The control for fluid flow behaviours of viscous fluids and heat transfer occurrences within heated mini-channel is considered. Heat transfer and flow characteristics of different viscous liquids, such as engine oil, automatic transmission fluid, one-half ethylene glycol, and deionized water were numerically analyzed. Some mathematical applications such as Fourier series and Laplace Z-Transforms were employed to ascertain the behaviour-wave like structure of these each viscous fluids. The steady, laminar flow and heat transfer equations are reckoned by the aid of numerical simulation technique. Further, this numerical simulation technique is endorsed by using the accessible practical values in comparison with the anticipated local thermal resistances. However, the roughness of this mini-channel that is one of the physical limitations was also predicted in this study. This affects the frictional factor. When an additive such as tetracycline was introduced in the fluid, the heat input was lowered, and this caused pro rata effect on the minor and major frictional losses, mostly at a very minute Reynolds number circa 60-80. At this ascertained lower value of Reynolds numbers, there exists decrease in the viscosity and minute frictional losses as a result of the temperature of these viscous liquids been increased. It is inferred that the three equations and models are identified which supported the numerical simulation via interpolation and integration of the variables extended to the walls of the mini-channel, yields the utmost reliance for engineering and technology calculations for turbulence impacting jets in the near imminent age. Out of reasoning with a true equation that could support this control for the fluid flow, Navier-stokes equations were found to tangential to this finding. Though, other physical factors with respect to these Navier-stokes equations are required to be checkmated to avoid uncertain turbulence of the fluid flow. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme via numerical simulation method that takes into account certain terms in the full Navier-Stokes equations. However, this resulted in dropping out in the approximation of certain assumptions. Concrete questions raised in the main body of the work are sightseen further in the appendices.

Keywords: frictional losses, heat transfer, laminar flow, mini-channel, number simulation, Reynolds number, turbulence, viscous fluids

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Nazneen Khan, Vakeel A. Khan

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In this article we introduce the Paranorm Zweier I-convergent sequence spaces, for a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem and study some inclusion relations on these spaces.

Keywords: ideal, filter, I-convergence, I-nullity, paranorm

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Authors: Ganiyat Soliu, Glen Bright, Chiemela Onunka

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Performance optimization plays a key role in controlling the waiting time during manufacturing in an advanced manufacturing environment to improve productivity. Queuing mathematical modeling theory was used to examine the performance of the multi-stage production line. Robotics as a disruptive technology was implemented into a virtual manufacturing scenario during the packaging process to study the effect of waiting time on productivity. The queuing mathematical model was used to determine the optimum service rate required by robots during the packaging stage of manufacturing to yield an optimum production cost. Different rates of production were assumed in a virtual manufacturing environment, cost of packaging was estimated with optimum production cost. An equation was generated using queuing mathematical modeling theory and the theorem adopted for analysis of the scenario is the Newton Raphson theorem. Queuing theory presented here provides an adequate analysis of the number of robots required to regulate waiting time in order to increase the number of output. Arrival rate of the product was fast which shows that queuing mathematical model was effective in minimizing service cost and the waiting time during manufacturing. At a reduced waiting time, there was an improvement in the number of products obtained per hour. The overall productivity was improved based on the assumptions used in the queuing modeling theory implemented in the virtual manufacturing scenario.

Keywords: performance optimization, productivity, queuing theory, robotics

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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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: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Jayme R. T. Silva, Paulo G. P. Toro, Angelo Passaro, Giannino P. Camillo, Antonio C. Oliveira

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An in-house C++ code has been developed, at the Prof. Henry T. Nagamatsu Laboratory of Aerothermodynamics and Hypersonics from the Institute of Advanced Studies (Brazil), to estimate the aerothermodynamic properties around the Hypersonic Vehicle Integrated to the Scramjet. In the future, this code will be applied to the design of the Brazilian Scramjet Technological Demonstrator 14-X B. The first step towards accomplishing this objective, is to apply the in-house C++ code at the leading edge of a flat plate, simulating the leading edge of the 14-X Hypersonic Vehicle, making possible the wave phenomena of oblique shock and boundary layer to be analyzed. The development of modern hypersonic space vehicles requires knowledge regarding the characteristics of hypersonic flows in the vicinity of a leading edge of lifting surfaces. The strong interaction between a shock wave and a boundary layer, in a high supersonic Mach number 4 viscous flow, close to the leading edge of the plate, considering no slip condition, is numerically investigated. The small slip region is neglecting. The study consists of solving the fluid flow equations for unstructured meshes applying the SIMPLE algorithm for Finite Volume Method. Unstructured meshes are generated by the in-house software ‘Modeler’ that was developed at Virtual’s Engineering Laboratory from the Institute of Advanced Studies, initially developed for Finite Element problems and, in this work, adapted to the resolution of the Navier-Stokes equations based on the SIMPLE pressure-correction scheme for all-speed flows, Finite Volume Method based. The in-house C++ code is based on the two-dimensional Navier-Stokes equations considering non-steady flow, with nobody forces, no volumetric heating, and no mass diffusion. Air is considered as calorically perfect gas, with constant Prandtl number and Sutherland's law for the viscosity. Solutions of the flat plate problem for Mach number 4 include pressure, temperature, density and velocity profiles as well as 2-D contours. Also, the boundary layer thickness, boundary conditions, and mesh configurations are presented. The same problem has been solved by the academic license of the software Ansys Fluent and for another C++ in-house code, which solves the fluid flow equations in structured meshes, applying the MacCormack method for Finite Difference Method, and the results will be compared.

Keywords: boundary-layer, scramjet, simple algorithm, shock wave

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Authors: Saeed Poormoaied

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Perishability and developing an intelligent control policy for perishable items are the major concerns of marketing managers in a supply chain. In this study, we address a two-echelon supply chain problem for perishable items with a single vendor and a single buyer. The buyer adopts an aged-based continuous review policy which works by taking both the stock level and the aging process of items into account. The vendor works under the warehouse framework, where its lot size is determined with respect to the batch size of the buyer. The model holds for a positive and fixed lead time for the buyer, and zero lead time for the vendor. The demand follows a Poisson process and any unmet demand is lost. We provide exact analytic expressions for the operational characteristics of the system by using the renewal reward theorem. Items have a fixed lifetime after which they become unusable and are disposed of from the buyer's system. The age of items starts when they are unpacked and ready for the consumption at the buyer. When items are held by the vendor, there is no aging process which results in no perishing at the vendor's site. The model is developed under the centralized framework, which takes the expected profit of both vendor and buyer into consideration. The goal is to determine the optimal policy parameters under the service level constraint at the retailer's site. A sensitivity analysis is performed to investigate the effect of the key input parameters on the expected profit and order quantity in the supply chain. The efficiency of the proposed age-based policy is also evaluated through a numerical study. Our results show that when the unit perishing cost is negligible, a significant cost saving is achieved.

Keywords: two-echelon supply chain, perishable items, age-based policy, renewal reward theorem

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Minho Kwak, Suhwan Yun, Choonsoo Park

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Nose shape optimizations of high-speed train are performed for the improvement of aerodynamic characteristics. Based on the commercial train, KTX-Sancheon, multi-objective optimizations are conducted for the improvement of the side wind stability and the micro-pressure wave following the optimization for the reduction of aerodynamic drag. 3D nose shapes are modelled by the Vehicle Modeling Function. Aerodynamic drag and side wind stability are calculated by three-dimensional compressible Navier-Stokes solver, and micro pressure wave is done by axi-symmetric compressible Navier-Stokes solver. The Maxi-min Latin Hypercube Sampling method is used to extract sampling points to construct the approximation model. The kriging model is constructed for the approximation model and the NSGA-II algorithm was used as the multi-objective optimization algorithm. Nose length, nose tip height, and lower surface curvature are design variables. Because nose length is a dominant variable for aerodynamic characteristics of train nose, two optimization processes are progressed respectively with and without the design variable, nose length. Each pareto set was obtained and each optimized nose shape is selected respectively considering Honam high-speed rail line infrastructure in South Korea. Through the optimization process with the nose length, when compared to KTX Sancheon, aerodynamic drag was reduced by 9.0%, side wind stability was improved by 4.5%, micro-pressure wave was reduced by 5.4% whereas aerodynamic drag by 7.3%, side wind stability by 3.9%, micro-pressure wave by 3.9%, without the nose length. As a result of comparison between two optimized shapes, similar shapes are extracted other than the effect of nose length.

Keywords: aerodynamic characteristics, design variable, multi-objective optimization, train nose shape

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Authors: Keltoum Bouherine, Olivier Leroy

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The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.

Keywords: electron density, electric field, microwave plasma reactor, gas velocity, non-equilibrium plasma

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Authors: Mahbod Seyednia, Shidvash Vakilipour, Mehran Masdari

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Computations for two-dimensional flow past a stationary and harmonically pitching wind turbine airfoil at a moderate value of Reynolds number (400000) are carried out by progressively increasing the angle of attack for stationary airfoil and at fixed pitching frequencies for rotary one. The incompressible Navier-Stokes equations in conjunction with Unsteady Reynolds Average Navier-Stokes (URANS) equations for turbulence modeling are solved by OpenFOAM package to investigate the aerodynamic phenomena occurred at stationary and pitching conditions on a NACA 6-series wind turbine airfoil. The aim of this study is to enhance the accuracy of numerical simulation in predicting the aerodynamic behavior of an oscillating airfoil in OpenFOAM. Hence, for turbulence modelling, k-ω-SST with low-Reynolds correction is employed to capture the unsteady phenomena occurred in stationary and oscillating motion of the airfoil. Using aerodynamic and pressure coefficients along with flow patterns, the unsteady aerodynamics at pre-, near-, and post-static stall regions are analyzed in harmonically pitching airfoil, and the results are validated with the corresponding experimental data possessed by the authors. The results indicate that implementing the mentioned turbulence model leads to accurate prediction of the angle of static stall for stationary airfoil and flow separation, dynamic stall phenomenon, and reattachment of the flow on the surface of airfoil for pitching one. Due to the geometry of the studied 6-series airfoil, the vortex on the upper surface of the airfoil during upstrokes is formed at the trailing edge. Therefore, the pattern flow obtained by our numerical simulations represents the formation and change of the trailing-edge vortex at near- and post-stall regions where this process determines the dynamic stall phenomenon.

Keywords: CFD, moderate Reynolds number, OpenFOAM, pitching oscillation, unsteady aerodynamics, wind turbine

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Authors: Kejal Khatri, Vishnu Narayan Mishra

Abstract:

We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Stéphanie Pellerin, Bérengére Podvin, Luc Pastur

Abstract:

In aerovehicles context, the flow around an Ahmed body profile is simulated using the velocity-vorticity formulation of the Navier-Stokes equations, associated to a penalization method for solids and Large Eddy Simulation for turbulence. The study focuses both on the ground influence on the flow and on the dissymetry of the wake, observed for a ground clearance greater than 10% of the body height H. Unsteady and mean flows are presented and analyzed. POD study completes the analysis and gives information on the most energetic structures of the flow.

Keywords: Ahmed body, bi-stability, LES, near wake

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Authors: Timur S. Zaripov, Artur K. Gilfanov, Sergei S. Sazhin, Steven M. Begg, Morgan R. Heikal

Abstract:

The calculation of the concentration of inertial droplets in complex flows is encountered in the modelling of numerous engineering and environmental phenomena; for example, fuel droplets in internal combustion engines and airborne pollutant particles. The results of recent research, focused on the development of methods for calculating concentration and their implementation in the commercial CFD code, ANSYS Fluent, is presented here. The study is motivated by the investigation of the mixture preparation processes in internal combustion engines with direct injection of fuel sprays. Two methods are used in our analysis; the Fully Lagrangian method (also known as the Osiptsov method) and the Eulerian approach. The Osiptsov method predicts droplet concentrations along path lines by solving the equations for the components of the Jacobian of the Eulerian-Lagrangian transformation. This method significantly decreases the computational requirements as it does not require counting of large numbers of tracked droplets as in the case of the conventional Lagrangian approach. In the Eulerian approach the average droplet velocity is expressed as a function of the carrier phase velocity as an expansion over the droplet response time and transport equation can be solved in the Eulerian form. The advantage of the method is that droplet velocity can be found without solving additional partial differential equations for the droplet velocity field. The predictions from the two approaches were compared in the analysis of the problem of a dilute gas-droplet flow around an infinitely long, circular cylinder. The concentrations of inertial droplets, with Stokes numbers of 0.05, 0.1, 0.2, in steady-state and transient laminar flow conditions, were determined at various Reynolds numbers. In the steady-state case, flows with Reynolds numbers of 1, 10, and 100 were investigated. It has been shown that the results predicted using both methods are almost identical at small Reynolds and Stokes numbers. For larger values of these numbers (Stokes — 0.1, 0.2; Reynolds — 10, 100) the Eulerian approach predicted a wider spread in concentration in the perturbations caused by the cylinder that can be attributed to the averaged droplet velocity field. The transient droplet flow case was investigated for a Reynolds number of 200. Both methods predicted a high droplet concentration in the zones of high strain rate and low concentrations in zones of high vorticity. The maxima of droplet concentration predicted by the Osiptsov method was up to two orders of magnitude greater than that predicted by the Eulerian method; a significant variation for an approach widely used in engineering applications. Based on the results of these comparisons, the Osiptsov method has resulted in a more precise description of the local properties of the inertial droplet flow. The method has been applied to the analysis of the results of experimental observations of a liquid gasoline spray at representative fuel injection pressure conditions. The preliminary results show good qualitative agreement between the predictions of the model and experimental data.

Keywords: internal combustion engines, Eulerian approach, fully Lagrangian approach, gasoline fuel sprays, droplets and particle concentrations

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