Search results for: Rotating Fluid.

Authors: T. Parra, R. Z. Szasz, C. Duwig, R. Pérez, V. Mendoza, F. Castro

Abstract:

The POD makes possible to reduce the complete high-dimensional acoustic field to a low-dimensional subspace where different modes are identified and let reconstruct in a simple way a high percentage of the variance of the field.

Rotating modes are instabilities which are commonly observed in swirling flows. Such modes can appear under both cold and reacting conditions but that they have different sources: while the cold flow rotating mode is essentially hydrodynamic and corresponds to the wellknown PVC (precessing vortex core) observed in many swirled unconfined flows, the rotating structure observed for the reacting case inside the combustion chamber might be not hydrodynamically but acoustically controlled. The two transverse acoustic modes of the combustion chamber couple and create a rotating motion of the flame which leads to a self-sustained turning mode which has the features of a classical PVC but a very different source (acoustics and not hydrodynamics).

Keywords: Acoustic field, POD, swirling flames.

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Authors: T. Chammem, H. Mhiri, O. Vauquelin

Abstract:

The present study was provided to examine the vortical structures generated by two inclined impinging jets with experimental and numerical investigations. The jets are issuing with a pitch angle α=40° into a confined quiescent fluid. The experimental investigation on flow patterns was visualized by using olive particles injected into the jets illuminated by Nd:Yag laser light to reveal the finer details of the confined jets interaction. It was observed that two counter-rotating vortex pairs (CVPs) were generated in the near region. A numerical investigation was also performed. First, the numerical results were validates against the experimental results and then the numerical model was used to study the effect of section ratio on the evolution of the CVPs. Our results show promising agreement with experimental data, and indicate that our model has the potential to produce useful and accurate data regarding the evolution of CVPs.

Keywords: Inclined impinging jets, counter-rotating vortex pair, CFD, experimental investigation, section ratio.

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Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee

Abstract:

Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: Rotating shaft, flexible blades, centrifugal stiffening, stability.

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Authors: G. R. Rameshkumar, B. V. A Rao, K. P. Ramachandran

Abstract:

Misalignment and unbalance are the major concerns in rotating machinery. When the power supply to any rotating system is cutoff, the system begins to lose the momentum gained during sustained operation and finally comes to rest. The exact time period from when the power is cutoff until the rotor comes to rest is called Coast Down Time. The CDTs for different shaft cutoff speeds were recorded at various misalignment and unbalance conditions. The CDT reduction percentages were calculated for each fault and there is a specific correlation between the CDT reduction percentage and the severity of the fault. In this paper, radial basis network, a new generation of artificial neural networks, has been successfully incorporated for the prediction of CDT for misalignment and unbalance conditions. Radial basis network has been found to be successful in the prediction of CDT for mechanical faults in rotating machinery.

Keywords: Coast Down Time, Misalignment, Unbalance, Artificial Neural Networks, Radial Basis Network.

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Authors: V. G. Rajesh, M. V. Rajesh

Abstract:

In rotating machinery one of the critical components that is prone to premature failure is the rolling bearing. Consequently, early warning of an imminent bearing failure is much critical to the safety and reliability of any high speed rotating machines. This study is concerned with the application of Recurrence Quantification Analysis (RQA) in fault detection of rolling element bearings in rotating machinery. Based on the results from this study it is reported that the RQA variable, percent determinism, is sensitive to the type of fault investigated and therefore can provide useful information on bearing damage in rolling element bearings.

Keywords: Bearing fault detection, machine vibrations, nonlinear time series analysis, recurrence quantification analysis.

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Authors: O. Mahian, A. B. Rahimi, A. Kianifar, A. Jabari Moghadam

Abstract:

In this study, the numerical solution of unsteady flow between two concentric rotating spheres with suction and blowing at their boundaries is presented. The spheres are rotating about a common axis of rotation while their angular velocities are constant. The Navier-Stokes equations are solved by employing the finite difference method and implicit scheme. The resulting flow patterns are presented for various values of the flow parameters including rotational Reynolds number Re , and a blowing/suction Reynolds number Rew . Viscous torques at the inner and the outer spheres are calculated, too. It is seen that increasing the amount of suction and blowing decrease the size of eddies generated in the annulus.

Keywords: Concentric spheres, numerical study, suction andblowing, unsteady flow, viscous torque.

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Authors: R. Usubamatov

Abstract:

The velocity of a moving point in a general path is the vector quantity, which has both magnitude and direction. The magnitude or the direction of the velocity vector can change over time as a result of acceleration that the time rate of velocity changes. Acceleration analysis is important because inertial forces and inertial torques are proportional to rectilinear and angular accelerations accordingly. The loads must be determined in advance to ensure that a machine is adequately designed to handle these dynamic loads. For planar motion, the vector direction of acceleration is commonly separated into two elements: tangential and centripetal or radial components of a point on a rotating body. All textbooks in physics, kinematics and dynamics of machinery consider the magnitude of a radial acceleration at condition when a point rotates with a constant angular velocity and it means without acceleration. The magnitude of the tangential acceleration considered on a basis of acceleration for a rotating point. Such condition of presentation of magnitudes for two components of acceleration logically and mathematically is not correct and may cause further confusion in calculation. This paper presents new analytical expressions of the radial and absolute accelerations of a rotating point with acceleration and covers the gap in theoretical study of acceleration analysis.

Keywords: acceleration analysis, kinematics of mechanisms.

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Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

Abstract:

The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure interaction, one-way method, two-way method.

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Authors: Risto Pöykiö, Olli Dahl, Hannu Nurmesniemi

Abstract:

The highest extractable concentration in the artificial sweat fluid was observed for Ba (120mg/kg; d.w.). The highest extractable concentration in the artificial gastric fluid was observed for Al (9030mg/kg; d.w.). Furthermore, the extractable concentrations of Ba (550mg/kg; d.w.) and Zn (400mg/kg: d.w.) in the bottom ash using artificial gastric fluid were elevated. The extractable concentrations of all heavy metals in the artificial gastric fluid were higher than those in the artificial sweat fluid. These results are reasonable in the light of the fact that the pH of the artificial gastric fluid was extremely acidic both before (pH 1.54) and after (pH 1.94) extraction, whereas the pH of the artificial sweat fluid was slightly alkaline before (pH 6.50) and after extraction (pH 8.51).

Keywords: Ash, artificial fluid, heavy metals, in vitro, waste.

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Authors: S. Sendhil Kumar, M. Senthil Kumar

Abstract:

Maintenance and design engineers have great concern for the functioning of rotating machineries due to the vibration phenomenon. Improper functioning in rotating machinery originates from the damage to rolling element bearings. The status of rolling element bearings require advanced technologies to monitor their health status efficiently and effectively. Avoiding vibration during machine running conditions is a complicated process. Vibration simulation should be carried out using suitable sensors/ transducers to recognize the level of damage on bearing during machine operating conditions. Various issues arising in rotating systems are interlinked with bearing faults. This paper presents an approach for fault diagnosis of bearings using neural networks and time/frequencydomain vibration analysis.

Keywords: Bearing vibration, Condition monitoring, Fault diagnosis, Frequency domain.

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Authors: F.Saadi, A.Aboudi Asl

Abstract:

In this paper, the dynamic analysis of fuel storage tanks has been studied and some equations are presented for the created fluid waves due to storage tank motions. Also, the equations for finite elements of fluid and structure interactions, and boundary conditions dominant on structure and fluid, were researched. In this paper, a numerical simulation is performed for the dynamic analysis of a storage tank contained a fluid. This simulation has carried out by ANSYS software, using FSI solver (Fluid and Structure Interaction solver), and by considering the simulated fluid dynamic motions due to earthquake loading, based on velocities and movements of structure and fluid according to all boundary conditions dominant on structure and fluid.

Keywords: fluid and structure interactions, finite elementmethod, ANSYS – FSI

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Authors: S. Jani, M. Mahmoodi, M. Amini

Abstract:

Magnetohydrodynamic free convection fluid flow and heat transfer in a square cavity filled with an electric conductive fluid with Prandtl number of 0.7 has been investigated numerically. The horizontal bottom wall of the cavity was kept at Th while the side and the top walls of the cavity were maintained at a constant temperature Tc with Th>Tc. The governing equations written in terms of the primitive variables were solved numerically using the finite volume method while the SIMPLER algorithm was used to couple the velocity and pressure fields. Using the developed code, a parametric study was performed, and the effects of the Rayleigh number and the Hartman number on the fluid flow and heat transfer inside the cavity were investigated. The obtained results showed that temperature distribution and flow pattern inside the cavity depended on both strength of the magnetic field and Rayleigh number. For all cases two counter rotating eddies were formed inside the cavity. The magnetic field decreased the intensity of free convection and flow velocity. Also it was found that for higher Rayleigh numbers a relatively stronger magnetic field was needed to decrease the heat transfer through free convection.

Keywords: Free Convection, Magnetic Field, Square Cavity, Numerical Simulation.

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Authors: S. Venkateswaran, C. Mallika Parveen

Abstract:

The fluid flow and the properties of the hydraulic fluid inside a torque converter are the main topics of interest in this research. The primary goal is to investigate the applicability of various viscous fluids inside the torque converter. The Taguchi optimization method is adopted to analyse the fluid flow in a torque converter from a design perspective. Calculations are conducted in maximizing the pressure since greater the pressure, greater the torque developed. Using the values of the S/N ratios obtained, graphs are plotted. Computational Fluid Dynamics (CFD) analysis is also conducted.

Keywords: Hydraulic fluid, Taguchi's method, optimization, pressure, torque.

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Authors: Paras Ram, Vikas Kumar

Abstract:

An attempt has been made to study the effect of rotation on incompressible, electrically non-conducting ferrofluid in porous medium on Axi-symmetric steady flow over a rotating disk excluding thermal effects. Here, we solved the boundary layer equations with boundary conditions using Neuringer-Rosensweig model considering the z-axis as the axis of rotation. The non linear boundary layer equations involved in the problem are transformed to the non linear coupled ordinary differential equations by Karman's transformation and solved by power series approximations. Besides numerically calculating the velocity components and pressure for different values of porosity parameter with the variation of Karman's parameter we have also calculated the displacement thickness of boundary layer, the total volume flowing outward the z-axis and angle between wall and ferrofluid. The results for all above variables are obtained numerically and discussed graphically.

Keywords: Ferrofluid, magnetic field porous medium, rotating disk.

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Authors: Carmen D. Pricinâ, E. Corina Cipu, Victor Ţigoiu

Abstract:

The flow of a third grade fluid in an orthogonal rheometer is studied. We employ the admissible velocity field proposed in [5]. We solve the problem and obtain the velocity field as well as the components for the Cauchy tensor. We compare the results with those from [9]. Some diagrams concerning the velocity and Cauchy stress components profiles are presented for different values of material constants and compared with the corresponding values for a linear viscous fluid.

Keywords: Non newtonian fluid flow, orthogonal rheometer, third grade fluid.

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Authors: A. Chandrashekar, H. N. Reddappa, B. S. Ajaykumar

Abstract:

A Friction stir welding tool is a critical component to the success of the process. The tool typically consists of a rotating round shoulder and a threaded cylindrical pin that heats the work piece, mostly by friction, and moves the softened alloy around it to form the joint. In this research work, an attempt has been made to investigate the relationship between FSW variables mainly tool profile, rotating speed, welding speed and the mechanical properties (tensile strength, yield strength, percentage elongation, and micro hardness) of friction stir welded aluminum alloy 5083 joints. From the experimental details, it can be assessed that the joint produced by using Triflute profile tool has contribute superior mechanical and structural properties as compared to Tapered unthreaded & Threaded tool for 1000rpm.

Keywords: Friction stir welding, Tool profile, Rotating speed, Strength, Speed ratio.

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

Abstract:

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Axially moving beam, Galerkin method, non-linear vibration, super harmonic resonances.

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Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

Abstract:

This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: Fluid-structure coupling, inverse methods, naval, vibrations.

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Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

Abstract:

The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: Creep, isotropic, steady-state, thermal gradient.

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Authors: F. Roger, A. Traidia, B. Reynier

Abstract:

Arc welding creates a weld pool to realize continuity between pieces of assembly. The thermal history of the weld is dependent on heat transfer and fluid flow in the weld pool. The metallurgical transformation during welding and cooling are modeled in the literature only at solid state neglecting the fluid flow. In the present paper we associate a heat transfer – fluid flow and metallurgical model for the 16MnD5 steel. The metallurgical transformation model is based on Leblond model for the diffusion kinetics and on the Koistinen-Marburger equation for Marteniste transformation. The predicted thermal history and metallurgical transformations are compared to a simulation without fluid phase. This comparison shows the great importance of the fluid flow modeling.

Keywords: Arc welding, Weld pool, Fluid flow, Metallurgical transformations.

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Authors: Remigijus Janulionis, Marijus Šeporaitis, Aleksandra Legha, Raimundas Ručys

Abstract:

All types of farms have a waste problem. Livestock farms have huge amounts of manure and vegetable farms have to deal with inedible parts of vegetables or rotten, damaged and unacceptable vegetable waste. All of this waste needs to be disposed of safely, ecologically, and as quickly as possible. One of the options is composting using bioreactors, which are rotating drum composters. This type of composting allows biodegradable waste to be disposed of quickly and in an environmentally friendly manner, turning it into a useful product such as soil fertilizer or livestock bedding. This paper presents the fatigue and stiffness analysis of a rotating drum composter. The analysis was performed using a 3D finite element model. It was found that the analyzed composter design has good mechanical strength, good fatigue strength for a cylinder, and acceptable fatigue strength for tire rings. The deformation analysis of the cylinder indicated that the front and rear door support mechanisms should allow the positioning angle to be changed to ensure tightness.

Keywords: 3D modeling, fatigue, Finite Element Method, Goodman’s diagram.

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Authors: Pankaj K. Gupta, Krishnan V. Pagalthivarthi

Abstract:

The present work compares the performance of three turbulence modeling approach (based on the two-equation k -ε model) in predicting erosive wear in multi-size dense slurry flow through rotating channel. All three turbulence models include rotation modification to the production term in the turbulent kineticenergy equation. The two-phase flow field obtained numerically using Galerkin finite element methodology relates the local flow velocity and concentration to the wear rate via a suitable wear model. The wear models for both sliding wear and impact wear mechanisms account for the particle size dependence. Results of predicted wear rates using the three turbulence models are compared for a large number of cases spanning such operating parameters as rotation rate, solids concentration, flow rate, particle size distribution and so forth. The root-mean-square error between FE-generated data and the correlation between maximum wear rate and the operating parameters is found less than 2.5% for all the three models.

Keywords: Rotating channel, maximum wear rate, multi-sizeparticulate flow, k −ε turbulence models.

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Authors: Donna M. G. Comissiong, Tyrone D. Dass, Harold Ramkissoon, Alana R. Sankar

Abstract:

The B'enard-Marangoni thermal instability problem for a viscoelastic Jeffreys- fluid layer with internal heat generation is investigated. The fluid layer is bounded above by a realistic free deformable surface and by a plane surface below. Our analysis shows that while the internal heat generation and the relaxation time both destabilize the fluid layer, its stability may be enhanced by an increased retardation time.

Keywords: Viscoelastic fluid, Jeffreys' model, Maxwell model, internal heat generation, retardation time, relaxation time.

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Authors: R. Manimaran

Abstract:

CFD simulations are carried out in arterial stenoses with 48 % areal occlusion. Non-newtonian fluid model is selected for the blood flow as the same problem has been solved before with Newtonian fluid model. Studies on flow resistance with the presence of surface irregularities are carried out. Investigations are also performed on the pressure drop at various Reynolds numbers. The present study revealed that the pressure drop across a stenosed artery is practically unaffected by surface irregularities at low Reynolds numbers, while flow features are observed and discussed at higher Reynolds numbers.

Keywords: Blood flow, Roughness, Computational fluid dynamics, Bio fluid mechanics.

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Authors: D. Šedivý, S. Fialová

Abstract:

The main purpose of this study is to show differences between the numerical solution of the flow through the artificial heart valve using Newtonian or non-Newtonian fluid. The simulation was carried out by a commercial computational fluid dynamics (CFD) package based on finite-volume method. An aortic bileaflet heart valve (Sorin Bicarbon) was used as a pattern for model of real heart valve replacement. Computed tomography (CT) was used to gain the accurate parameters of the valve. Data from CT were transferred in the commercial 3D designer, where the model for CFD was made. Carreau rheology model was applied as non-Newtonian fluid. Physiological data of cardiac cycle were used as boundary conditions. Outputs were taken the leaflets excursion from opening to closure and the fluid dynamics through the valve. This study also includes experimental measurement of pressure fields in ambience of valve for verification numerical outputs. Results put in evidence a favorable comparison between the computational solutions of flow through the mechanical heart valve using Newtonian and non-Newtonian fluid.

Keywords: Computational modeling, dynamic mesh, mechanical heart valve, non-Newtonian fluid, SDOF.

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Authors: Guorong Yan, Subhash Rakheja

Abstract:

The liquid cargo contained in a partly-filled road tank vehicle is prone to dynamic slosh movement when subjected to external disturbances. The slosh behavior has been identified as a significant factor impairing the safety of liquid cargo transportation. The laboratory experiments have been conducted for analyzing fluid slosh in partly filled tanks. The experiment results measured under forced harmonic excitations reveal the three-dimensional nature of the fluid motion and coupling between the lateral and longitudinal fluid slosh at resonance. Several spectral components are observed for the transient slosh forces, which can be associated with the excitation, resonance, and beat frequencies. The peak slosh forces and moments in the vicinity of resonance are significantly larger than those of the equivalent rigid mass. Due to the nature of coupling between sloshing fluid and vehicle body, the issue of the dynamic fluid-structure interaction is essential in the analysis of tank-vehicle dynamics. A dynamic pitch plane model of a Tridem truck incorporated the fluid slosh dynamics is developed to analyze the fluid-vehicle interaction under the straight-line braking maneuvers. The results show that the vehicle responses are highly associated with the characteristics of fluid slosh force and moment.

Keywords: Braking performance, fluid induced vibration, fluidslosh, fluid structure interaction, tank trucks, vehicle dynamics.

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Authors: M. M. Rahman

Abstract:

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: T. D. Kothalawala, A. Gatto, L. Wrobel

Abstract:

An exploratory computational investigation using RANS & URANS was carried out to understand the aerodynamics around an isolatedsingle rotating wheel with decreasing ground proximity. The wheel was initially modeled in free air conditions, then with decreasing ground proximity and increased yaw angle with rotational speeds. Three speeds of rotation were applied to the wheel so that the effect of different angular velocities can be investigated. In addition to rotation, three different yaw angles were applied to the rotating wheel in order to understand how these two variables combined affect the aerodynamic flow field around the wheel.

Keywords: Aerodynamics, CFD, Ground Proximity, Landing Gear, Wheel, Rotation, Yaw.

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Authors: I. Mahdavi, R. Janamiri, A. Sinkakarimi, M. Safdari, M. H. Sedaghat, A. Zamani, A. Hoseini, M. Karimi

Abstract:

In this work, study the location of interface in a stirred vessel with Rushton impeller by computational fluid dynamic was presented. To modeling rotating the impeller, sliding mesh (SM) technique was used and standard k-ε model was selected for turbulence closure. Mean tangential, radial and axial velocities and also turbulent kinetic energy (k) and turbulent dissipation rate (ε) in various points of tank was investigated. Results show sensitivity of system to location of interface and radius of 7 to 10cm for interface in the vessel with existence characteristics cause to increase the accuracy of simulation.

Keywords: CFD, Interface, Rushton impeller, Turbulence model.

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Authors: P. Parvasi, R. Janamiri, A. Sinkakarimi, I. Mahdavi, M. Safdari, M. H. Sedaghat, A. Hosseini, M. Karimi

Abstract:

In this work study the location of interface in a stirred vessel with a Concave impeller by computational fluid dynamic was presented. To modeling rotating the impeller, sliding mesh (SM) technique was used and standard k-ε model was selected for turbulence closure. Mean tangential, radial and axial velocities and also turbulent kinetic energy (k) and turbulent dissipation rate (ε) in various points of tank was investigated. Results show sensitivity of system to location of interface and radius of 7 to 10cm for interface in the vessel with existence characteristics cause to increase the accuracy of simulation.

Keywords: CFD, Interface, Concave impeller, turbulence model.

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