AC & DC Magnetic Levitation and Semi-Levitation Modelling

Size: px
Start display at page:

Download "AC & DC Magnetic Levitation and Semi-Levitation Modelling"

Transcription

1 International Scientific Colloquium Modelling for Electromagnetic Processing Hannover, March 24-26, 2003 AC & DC Magnetic Levitation and Semi-Levitation Modelling V. Bojarevics, K. Pericleous Abstract This work presents computational analysis of levitated liquid thermal and flow fields with free surface oscillations in AC and DC magnetic fields. The volume electromagnetic force distribution is continuously updated with the shape and position change. The oscillation frequency spectra are analysed for droplets levitated against gravity in AC and DC magnetic fields at various combinations. For larger volume liquid metal confinement and melting the semi-levitation induction skull melting process is simulated with the same numerical model. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions. Introduction Magnetic levitation is a well known technique for treating liquid metals without or with an absolute minimum contact at crucible solid walls [1-4]. AC magnetic field can be used to support, stir, heat, melt and evaporate electrically conducting liquid at high temperatures. DC magnetic field can be added to this in order to stabilize [5] the liquid motion, improve the heat-mass transfer characteristics or even to levitate a poorly conducting liquid material [6]. These techniques allow for reactive high temperature materials treatment, the material properties measurements [7] and energy saving processes development. Typically the material is solid at the beginning of the process, then it heats up owing to the induced currents Joule heating, gradually melts and assumes the shape dictated by the balance of forces acting on the liquid volume. The numerical modelling for the magnetic semi-levitation involving coupling of the electromagnetic field, liquid shape change, fluid velocities and the temperature field during the time evolution was introduced in [8].The generated fluid flow easily becomes turbulent and the 2-equation k-omega time dependent turbulence model [9] is used to predict the efficient viscosity and turbulent heat transport. The simulation model is validated against measurements of velocity and turbulent kinetic energy in the cylindrical liquid metal experiment [9] and measurements of temperature and heat losses in the commercial size cold-crucible [10]. The same model can be applied for small levitated droplets to test skin-layer approximation accuracy [11] and to predict surface oscillations for ideal fluid, laminar viscous and with dynamically varying effective turbulent viscosity. 1. Mathematical Model The present modelling approach is based on the turbulent momentum and heat transfer equations for an incompressible fluid: 1 T 1 t v + ( v ) v = ρ p + ( ν e ( v + v )) + ρ f + g, (1) v = 0, (2) 99

2 * 1 2 C p ( tt + v T ) = ( C pα e T ) + ρ J / σ, (3) where v is the velocity vector, p - the pressure, ρ - the density, ν e = ν T + ν (summ of turbulent and laminar viscosity) is the effective viscosity which is variable in time and position, f is the electromagnetic force, g - the gravity vector, T - the temperature, α e = α T + α (summ of turbulent and laminar) is the effective thermal diffusivity, C p - the specific heat, C * p - the solid fraction modified specific heat function which accounts for latent 2 heat effects (see [8] for details), and J / σ is the Joule heat. The momentum equation (1) contains the nonlinear term in the convective (in difference to the rotational) form which, according to our tests, gives greater stability for the long time development problems. The boundary conditions used for the fluid flow problem are: at the free surface normal stress is compensated by the surface tension only, tangential stress is zero, and the kinematic condition which states that the new interface location moves with material fluid particles. The no-slip condition is applied for the velocity at solid walls (if any). For the temperature boundary conditions we adopt the radiation and the effective heat transfer at solid walls. The respective expressions in co-ordinate representation are given in [8]. The temperature boundary conditions depend on the local turbulent thermal diffusion coefficient α e, which is proportional to the effective turbulent viscosity ν e determined from the numerical k-ω turbulence model [9]. The k-ω model used is a low Re number version which resolves the flow from laminar to developed turbulent states, and therefore is considered suitable for turbulent flow evolution simulations. The ω variable is related to the reciprocal turbulent time scale (frequency of vorticity fluctuations) and the k variable is the turbulence kinetic energy per unit mass. In the present work we apply the k-ω model within the pseudospectral framework [9,11]. The computation follows in detail the time development of the turbulent characteristics determined by the coupled non-linear transport equations accounting for a continuous generation and destruction of the turbulent energy. For the Navier-Stokes and the heat transfer equations (1-3), and also the k-ω model equations, the pseudo-spectral spatial representation and the implicit time stepping with iterative linearisation for the non-linear terms is used [9]. The electromagnetic force distribution is highly sensitive to the shape of liquid metal free surface and is recalculated at every time step. The computational procedure for the electromagnetic field is implemented with the same grid as the fluid dynamic equations, which ensures a high resolution within the surface boundary layer because of the dense grid in this region. The electromagnetic force f is computed by the previously tested [8, 9] accurate integral equation based algorithm. In the AC case the time-average force in the fluid is concentrated in the skin layer and it is variable along the layer. This means that, however small the skin layer depth is, the force is always rotational and drives the fluid flow. 2. Modelling Results 2.1. AC and DC field Levitation in Normal Gravity For the tests of AC magnetic levitation under normal gravity conditions we chose the levitation coil configuration from the surface tension measurement experimental setup [12]. It is shown in Figure 1, where the additional DC coil is our modification to the original setup. Electric current of a fixed effective magnitude 195 A flows in the positive azimuthal direction in the bottom four turns of the coil and in the negative direction at the top two turns. The coil current frequency is f ν = 450 khz, therefore one can expect a very small penetration depth for the electromagnetic field in a well conducting material like liquid aluminium with the 100

3 electrical conductivity 6 1 σ = ( Ω m) used for the tests. Indeed, the skin layer depth 1/ 2 3 according to the classical expression for a flat surface δ = ( µ 0σ 2πf ν ) = m. For the levitated droplet of initial diameter m, the penetration depth, which is numerically computed and analytically confirmed for the conducting sphere [8], is apparently larger, and it is quite non-uniform because of the coil configuration (Figure 2). From the Figure 2 we can see that the magnetic field behaves in a similar manner, being tangential over most of the external boundary (as expected from the asymptotic theories), yet there is a significant penetration into the material, and at the bottom part the field is entering normally into the droplet. There is also a closed loop of the secondary magnetic field lines enclosing the induced current in the metal. An external DC magnetic field can be added using a coaxial coil surrounding the AC coil as shown in Figure 1. Passing 200 A DC current in the 8 turn external coil creates an almost uniform additional DC magnetic field inside the droplet. T Liquid levitation DC coil Z (m) AC coil Figure 1. Perspective view of the AC levitation coil similar to the experimental [12] (a sectioned half of the full arrangement) and the additional DC coil. The computed typical velocity and the temperature field are shown at the end of 4 seconds physical time simulation. Magnetic field and electric current t=4. s 0.02 T J(A/m**2) z E E E E E E E E E E E E+07 Figure 2. The typical instantaneous induced AC electric current (level lines) and the magnetic field distribution (arrows) in the section of the deformed levitated Al droplet. 101

4 Let us consider the oscillations generated in the droplet, which is assumed initially of spherical shape and in molten quiescent state at an initial temperature of 700 o C for liquid aluminium. The droplet is positioned relative to the coil so that the initial total electromagnetic force balances the weight of the droplet. However, there is an initial transient time during which the droplet assumes the shape imposed by the force balance, and an intense fluid flow develops. The initial oscillations are damped significantly after some time, and a new non-decaying quasi-stationary oscillation pattern is established in 3-4 seconds time (Figure 3a). The final oscillation pattern is of a slightly distorted sinusoidal shape. The centre of mass for the droplet is subject to vertical oscillating motion affecting the flow and the surface oscillations. The final oscillation pattern does not show damping, which suggests a net energy transfer from the external field to the droplet mechanical motion. It is quite instructive to consider the numerically calculated Fourier power spectra for the simulated oscillations (Figure 3c). For the liquid aluminium properties the computed dominant frequency is Hz, corresponding closely to the ideal fluid nearly spherical droplet Rayleigh capillary oscillation frequency Hz of the l=2 mode [7,11,12]. The computed secondary frequency is Hz resulting from nonlinear interaction in presence of the varying electromagnetic field, which is still very close to the l=3 mode Rayleigh frequency Hz. There is also the translational motion frequency at 8.76 Hz for the electromagnetically excited droplet. The exact mechanism of the translational and normal mode oscillation interaction needs a further analysis. a) Amplitude (m) Al droplet oscillations d=8 mm, I=195 A, γ = R top b) Amplitude (m) t(s) Al droplet oscillations d=8 mm, I=195 A, γ =0.94 Idc=200 A Idc=200 A c) Power t(s) F ourier power spectra 10-8 R top Idc=20 0 A γ = f(h z) Figure 3. Oscillations of the levitated liquid Al droplet in normal gravity: a) by means of AC field only, b) with the additional presence of DC magnetic field, c) the computed Fourier power spectra. 102

5 When the DC magnetic field is added to the aluminium droplet oscillation in the presence of the same AC coil, the droplet stability is greatly enhanced, and the resulting oscillation amplitude is significantly reduced after a 2 second damping interval (Figure 3b). However for the case of 200 A DC in the coil, the oscillation still reaches a quasi-stationary state, and the power spectra in Figure 3c exhibit essentially the same frequencies as without the DC field. The remaining oscillation can be completely suppressed when 500 A current is supplied in the DC coil. The oscillations generated depend on the material properties of the liquid metal. When the surface tension coefficient in the numerical experiment is increased by a factor of two, the motion of the droplet is dominated by the centre of mass translational vertical oscillation. Apart from the oscillation mode interaction, there is a considerable influence also of the intense circulation flow (see Figure 1) consisting of two vortices, the intensity of which changes with the oscillation phase. The lower, smaller vortex is particularly affected by the bottom oscillation. The turbulent viscosity is mainly generated in this bottom part and then transported to the rest of the volume. The maximum magnitude for the time dependent turbulent viscosity is about times the laminar value, and it greatly enhances overall flow stability by limiting the velocity magnitude to below m/s. Attempts to simulate the flow with only the laminar viscosity failed when the flow velocities started to increase in a persistent continuous way. 2.2 Semi-Levitation in Cold Crucible (Induction Scull Melting ISM) In the ISM process the coil is positioned behind the water cooled sectioned copper walls (see Figure 4). If the initial charge is of cylindrical shape, there is usually a gap at the sidewall. After the melting starts the temperature is highest in the surface film zone and the heat is slowly penetrating the rather thick cylindrical charge in the radial direction. At the following few seconds the gravity driven flow is directed mainly downwards, waving and filling the bottom gap. After the initial stage, when the bottom is filled, the largest Joule heating concentration is shifted to the bottom part of the side skin layer, which is now closer to the source coil and the segmented wall induced electric currents. Subsequently the melting front progresses slowly radially inwards. The heat conduction coefficient within the solid part is small compared to the turbulent flow region, and the phase change from solid to liquid consumes significant energy. The bottom water-cooled wall takes away the heat efficiently when the bottom gap is filled. Therefore the optimisation for the coil and crucible design are of prime importance if the resulting superheat must be increased. At the final stage shown in Figure 4 the arrangement of the bottom made of a special Ti alloy permits rather good semilevitation containing the melt away from the side-walls. The electric current and the heating are induced in the side layer, from where the intense turbulent mixing distributes the heat. The wall adherent mushy zone damps the turbulence efficiently. No significant destruction of the turbulence occurs at the top free surface with the zero stress boundary condition. The flow and the temperature distribution changes dramatically when the electric current is switched off in preparation to pouring of the molten metal into a casting mould. See more detailed comparisons to experimental measurements in [10]. Conclusion The presented model calculations permit to analyse flow patterns, free surface behaviour and to estimate the energy consumption of the magnetically levitated and confined liquid metal. A detailed time history and the clear physical insight to the driving forces and the sequence of events are available from the simulations. The modelling procedure can be extended to other generally unsteady flows with the moving melting fronts and free surfaces. 103

6 t=718 s z 4 coil turns TIAl melting: coil current 6700 A and Ti bottom segmented crucible wall copper base 0.5 m/s Z Y T X x Figure 4. Computed final quasi-steady stage of the ISM semi-levitation with AC coil similar to the experimental [10]. y References [1] E. Okress et al.: J. Appl. Phys., Vol. 23, 1952, pp [2] A. D. Sneyd and H. K. Moffatt: J. Fluid Mech., Vol. 117, 1982, pp [3] J. Szekely and E. Schwartz: Proc. Int. Symp. On Electromagnetic Processing of Materials, Nagoya, 1994, pp [4] C. H. Winstead, P. C. Gazzerro and J. F. Hoburg: Metall. Materials Trans., Vol. 29B, 1998, pp [5] J. Priede, G. Gerbeth, A. Mikelsons and Y. Gelfgat: Proc. 3 rd Int. Symp. on Electromagnetic Processing of Materials, Nagoya, 2000, pp [6] P. Gillon: Proc. 3 rd Int. Symp. on Electromagnetic Processing of Materials, Nagoya, 2000, pp [7] I. Egry, A. Diefenbach, W. Dreier and J. Piller: Int. J. Thermophys., Vol. 22, 2001, pp [8] V. Bojarevics, K. Pericleous and M. Cross: Metall. Materials Trans., Vol. 31B, 2000, pp [9] A. Bojarevics, V. Bojarevics, J. Gelfgat and K. Pericleous: Magnetohydrodynamics, Vol. 35, 1999, pp [10] V. Bojarevics et al.: Proc. 5 th Int. Conf. on Fundamental and Applied MHD, Ramatuelle, 2002, Vol. 2, pp [11] V.Bojarevics, K.Pericleous: Magnetohydrodynamics, Vol. 37, 2001, pp [12] R. F. Brooks and A. P. Day: Int. J. Thermophys., Vol. 20, 1999, pp Authors Dr. Bojarevics, Valdis Prof. Pericleous, Koulis School of Computing and Mathematics School of Computing and Mathematics University of Greenwich University of Greenwich 30 Park Row 30 Park Row London SE10 9LS, UK London SE10 9LS, UK v.bojarevics@gre.ac.uk k.pericleous@gre.ac.uk 104

Magnetic Levitation of a Large Mass of Liquid Metal

Magnetic Levitation of a Large Mass of Liquid Metal Paper 75 Magnetic Levitation of a Large Mass of Liquid Metal V. Bojarevics, A. Roy and K.A. Pericleous School of Computing and Mathematical Sciences University of Greenwich, London, England Civil-Comp

More information

MODELLING THE DYNAMICS OF ELECTROMAGNETICALLY AGITATED METALLURGICAL FLOWS: LEVITATION, COLD CRUCIBLE, ALUMINIUM ELECTROLYSIS, ETC.

MODELLING THE DYNAMICS OF ELECTROMAGNETICALLY AGITATED METALLURGICAL FLOWS: LEVITATION, COLD CRUCIBLE, ALUMINIUM ELECTROLYSIS, ETC. MODELLING THE DYNAMICS OF ELECTROMAGNETICALLY AGITATED METALLURGICAL FLOWS: LEVITATION, COLD CRUCIBLE, ALUMINIUM ELECTROLYSIS, ETC. V.Boarevics 1, K.Pericleous 1 and J.Freibergs 1 University of Greenwich,

More information

Numerical model of EIGA

Numerical model of EIGA The current issue and full text archive of this journal is available at www.emeraldinsight.com/332-1649.htm Numerical model of electrode induction melting for gas atomization Valdis Bojarevics, Alan Roy

More information

LES modeling of heat and mass transfer in turbulent recirculated flows E. Baake 1, B. Nacke 1, A. Umbrashko 2, A. Jakovics 2

LES modeling of heat and mass transfer in turbulent recirculated flows E. Baake 1, B. Nacke 1, A. Umbrashko 2, A. Jakovics 2 MAGNETOHYDRODYNAMICS Vol. 00 (1964), No. 00, pp. 1 5 LES modeling of heat and mass transfer in turbulent recirculated flows E. Baake 1, B. Nacke 1, A. Umbrashko 2, A. Jakovics 2 1 Institute for Electrothermal

More information

Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas )

Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Yasutomo ISHII and Andrei SMOLYAKOV 1) Japan Atomic Energy Agency, Ibaraki 311-0102, Japan 1) University

More information

Electromagnetic Levitation White-noise Measurement Protocol for Modulated Calorimetry

Electromagnetic Levitation White-noise Measurement Protocol for Modulated Calorimetry Int. J. Microgravity Sci. Appl. Vol. 30 No. 1 2013 (50 55) Theorization and Modeling Ⅲ (Review) Electromagnetic Levitation White-noise Measurement Protocol for Modulated Calorimetry Jacqueline ETAY Abstract

More information

Nonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 4,

Nonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 4, Nonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 4, 513 524 Effects of Temperature Dependent Thermal Conductivity on Magnetohydrodynamic (MHD) Free Convection Flow along a Vertical Flat Plate

More information

STABILITY ANALYSIS FOR BUOYANCY-OPPOSED FLOWS IN POLOIDAL DUCTS OF THE DCLL BLANKET. N. Vetcha, S. Smolentsev and M. Abdou

STABILITY ANALYSIS FOR BUOYANCY-OPPOSED FLOWS IN POLOIDAL DUCTS OF THE DCLL BLANKET. N. Vetcha, S. Smolentsev and M. Abdou STABILITY ANALYSIS FOR BUOYANCY-OPPOSED FLOWS IN POLOIDAL DUCTS OF THE DCLL BLANKET N. Vetcha S. Smolentsev and M. Abdou Fusion Science and Technology Center at University of California Los Angeles CA

More information

Numerical Study of the Moving Boundary Problem During Melting Process in a Rectangular Cavity Heated from Below

Numerical Study of the Moving Boundary Problem During Melting Process in a Rectangular Cavity Heated from Below American Journal of Applied Sciences 4 (4): 25-256, 2007 ISSN 546-9239 2007 Science Publications Corresponding Author: Numerical Study of the Moving Boundary Problem During Melting Process in a Rectangular

More information

Free Surface Controlled by Magnetic Fields

Free Surface Controlled by Magnetic Fields Review Free Surface Controlled by Magnetic Fields ISIJ International, Vol. 43 (2003), No. 6, pp. 801 806 Yves FAUTRELLE, Damien PERRIER and Jacqueline ETAY INPG/CNRS/EPM-Madylam, ENSHMG BP 95, 38402 St

More information

Electrically Induced Instabilities of Liquid Metal Free Surfaces

Electrically Induced Instabilities of Liquid Metal Free Surfaces International Scientific Colloquium Modelling for Material Processing Riga, June 8-9, 2006 Electrically Induced Instabilities of Liquid Metal Free Surfaces D. Schulze, Ch. Karcher, V. Kocourek, J.U. Mohring

More information

Numerical Studies of Droplet Deformation and Break-up

Numerical Studies of Droplet Deformation and Break-up ILASS Americas 14th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2001 Numerical Studies of Droplet Deformation and Break-up B. T. Helenbrook Department of Mechanical and

More information

Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Bénard Cell

Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Bénard Cell Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows Lyon, July 2007 Paper reference : ISAIF8-00130 Analysis of Turbulent Free Convection

More information

Joule Heating Effect on the Coupling of Conduction with Magnetohydrodynamic Free Convection Flow from a Vertical Flat Plate

Joule Heating Effect on the Coupling of Conduction with Magnetohydrodynamic Free Convection Flow from a Vertical Flat Plate Nonlinear Analysis: Modelling and Control, 27, Vol. 12, No. 3, 37 316 Joule Heating Effect on the Coupling of Conduction with Magnetohydrodynamic Free Convection Flow from a Vertical Flat Plate M. A. Alim

More information

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

More information

Continuous Casting - Comparison between Numerical Simulation and Experimental Measurement

Continuous Casting - Comparison between Numerical Simulation and Experimental Measurement International Scientific Colloquium Modelling for Electromagnetic Processing Hannover, March 24-26, 3 Continuous Casting - Comparison between Numerical Simulation and Experimental Measurement Y. Delannoy,

More information

Flow patterns and heat transfer in square cavities with perfectly conducting horizontal walls: the case of high Rayleigh numbers ( )

Flow patterns and heat transfer in square cavities with perfectly conducting horizontal walls: the case of high Rayleigh numbers ( ) Advances in Fluid Mechanics VII 391 Flow patterns and heat transfer in square cavities with perfectly conducting horizontal walls: the case of high Rayleigh numbers (10 6 10 9 ) R. L. Frederick & S. Courtin

More information

The behaviour of high Reynolds flows in a driven cavity

The behaviour of high Reynolds flows in a driven cavity The behaviour of high Reynolds flows in a driven cavity Charles-Henri BRUNEAU and Mazen SAAD Mathématiques Appliquées de Bordeaux, Université Bordeaux 1 CNRS UMR 5466, INRIA team MC 351 cours de la Libération,

More information

Fundamentals of Fluid Dynamics: Elementary Viscous Flow

Fundamentals of Fluid Dynamics: Elementary Viscous Flow Fundamentals of Fluid Dynamics: Elementary Viscous Flow Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research

More information

Turbulence Model Affect on Heat Exchange Characteristics Through the Beam Window for European Spallation Source

Turbulence Model Affect on Heat Exchange Characteristics Through the Beam Window for European Spallation Source International Scientific Colloquium Modelling for Material Processing Riga, September 16-17, 2010 Turbulence Model Affect on Heat Exchange Characteristics Through the Beam Window for European Spallation

More information

Oscillatory MHD Mixed Convection Boundary Layer Flow of Finite Dimension with Induced Pressure Gradient

Oscillatory MHD Mixed Convection Boundary Layer Flow of Finite Dimension with Induced Pressure Gradient Journal of Applied Fluid Mechanics, Vol. 9, No., pp. 75-75, 6. Available online at www.jafmonline.net, ISSN 75-57, EISSN 75-65. DOI:.8869/acadpub.jafm.68.5.876 Oscillatory MHD Mixed Convection Boundary

More information

Simulation Study on the Generation and Distortion Process of the Geomagnetic Field in Earth-like Conditions

Simulation Study on the Generation and Distortion Process of the Geomagnetic Field in Earth-like Conditions Chapter 1 Earth Science Simulation Study on the Generation and Distortion Process of the Geomagnetic Field in Earth-like Conditions Project Representative Yozo Hamano Authors Ataru Sakuraba Yusuke Oishi

More information

Natural convection adjacent to a sidewall with three fins in a differentially heated cavity

Natural convection adjacent to a sidewall with three fins in a differentially heated cavity ANZIAM J. 48 (CTAC2006) pp.c806 C819, 2007 C806 Natural convection adjacent to a sidewall with three fins in a differentially heated cavity F. Xu 1 J. C. Patterson 2 C. Lei 3 (Received 31 August 2006;

More information

UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

More information

Laplace Technique on Magnetohydrodynamic Radiating and Chemically Reacting Fluid over an Infinite Vertical Surface

Laplace Technique on Magnetohydrodynamic Radiating and Chemically Reacting Fluid over an Infinite Vertical Surface International Journal of Engineering and Technology Volume 2 No. 4, April, 2012 Laplace Technique on Magnetohydrodynamic Radiating and Chemically Reacting Fluid over an Infinite Vertical Surface 1 Sahin

More information

Boundary-Layer Theory

Boundary-Layer Theory Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22

More information

Stability of Liquid Metal Interface Affected by a High-Frequency Magnetic Field

Stability of Liquid Metal Interface Affected by a High-Frequency Magnetic Field International Scientific Colloquium Modelling for Electromagnetic Processing Hannover, March 4-6, 3 Stability of Liquid Metal Interface Affected by a High-Frequency Magnetic Field J-U Mohring, Ch Karcher,

More information

Chapter 1: Basic Concepts

Chapter 1: Basic Concepts What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms

More information

Study on Non-Uniqueness of Taylor Vortex Flow Changing Inner Cylinder Acceleration Time

Study on Non-Uniqueness of Taylor Vortex Flow Changing Inner Cylinder Acceleration Time World Journal of Mechanics, 2018, 8, 301-310 http://www.scirp.org/journal/wjm ISSN Online: 2160-0503 ISSN Print: 2160-049X Study on Non-Uniqueness of Taylor Vortex Flow Changing Inner Cylinder Acceleration

More information

6. Basic basic equations I ( )

6. Basic basic equations I ( ) 6. Basic basic equations I (4.2-4.4) Steady and uniform flows, streamline, streamtube One-, two-, and three-dimensional flow Laminar and turbulent flow Reynolds number System and control volume Continuity

More information

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,

More information

Absorption of gas by a falling liquid film

Absorption of gas by a falling liquid film Absorption of gas by a falling liquid film Christoph Albert Dieter Bothe Mathematical Modeling and Analysis Center of Smart Interfaces/ IRTG 1529 Darmstadt University of Technology 4th Japanese-German

More information

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic

More information

SHALLOW WATER MODEL FOR ALUMINIUM ELECTROLYSIS CELLS WITH VARIABLE TOP AND BOTTOM

SHALLOW WATER MODEL FOR ALUMINIUM ELECTROLYSIS CELLS WITH VARIABLE TOP AND BOTTOM SHALLOW WATER MODEL FOR ALUMINIUM ELECTROLYSIS CELLS WITH VARIABLE TOP AND BOTTOM Valdis Boarevics and Koulis Pericleous University of Greenwich, School of Computing and Mathematical Sciences, 30 Park

More information

Fluctuation dynamo amplified by intermittent shear bursts

Fluctuation dynamo amplified by intermittent shear bursts by intermittent Thanks to my collaborators: A. Busse (U. Glasgow), W.-C. Müller (TU Berlin) Dynamics Days Europe 8-12 September 2014 Mini-symposium on Nonlinear Problems in Plasma Astrophysics Introduction

More information

Heat Transfer Enhancement using Synthetic Jet Actuators in Forced Convection Water Filled Micro-Channels

Heat Transfer Enhancement using Synthetic Jet Actuators in Forced Convection Water Filled Micro-Channels Heat Transfer Enhancement using Synthetic Jet Actuators in Forced Convection Water Filled Micro-Channels V. Timchenko 1, J.A. Reizes 1, E. Leonardi 1, F. Stella 2 1 School of Mechanical and Manufacturing

More information

Flow Field and Oscillation Frequency of a Rotating Liquid Droplet

Flow Field and Oscillation Frequency of a Rotating Liquid Droplet Flow Field and Oscillation Frequency of a Rotating Liquid Droplet TADASHI WATANABE Center for Computational Science and e-systems Japan Atomic Energy Agency (JAEA) Tokai-mura, Naka-gun, Ibaraki-ken, 319-1195

More information

Effect of Static Magnetic Field Application on the Mass Transfer in Sequence Slab Continuous Casting Process

Effect of Static Magnetic Field Application on the Mass Transfer in Sequence Slab Continuous Casting Process , pp. 844 850 Effect of Static Magnetic Field Application on the Mass Transfer in Sequence Slab Continuous Casting Process Baokuan LI and Fumitaka TSUKIHASHI 1) Department of Thermal Engineering, The School

More information

Numerical 2D Modelling of Turbulent Melt Flow in CZ System with AC Magnetic Fields

Numerical 2D Modelling of Turbulent Melt Flow in CZ System with AC Magnetic Fields International Scientific Colloquium Modelling for Electromagnetic Processing Hannover, March 24-26, 2003 Numerical 2D Modelling of Turbulent Melt Flow in CZ System with AC Magnetic Fields A. Krauze, A.

More information

Differential relations for fluid flow

Differential relations for fluid flow Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow

More information

Active Control of Separated Cascade Flow

Active Control of Separated Cascade Flow Chapter 5 Active Control of Separated Cascade Flow In this chapter, the possibility of active control using a synthetic jet applied to an unconventional axial stator-rotor arrangement is investigated.

More information

Enhancement of Heat Transfer by an Electric Field for a Drop Translating at Intermediate Reynolds Number

Enhancement of Heat Transfer by an Electric Field for a Drop Translating at Intermediate Reynolds Number Rajkumar Subramanian M. A. Jog 1 e-mail: milind.jog@uc.edu Department of Mechanical, Industrial, and Nuclear Engineering, University of Cincinnati, Cincinnati, OH 45221-0072 Enhancement of Heat Transfer

More information

CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION

CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION 7.1 THE NAVIER-STOKES EQUATIONS Under the assumption of a Newtonian stress-rate-of-strain constitutive equation and a linear, thermally conductive medium,

More information

DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT

DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT 10 th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT Bing-Chen Wang Department

More information

The shallow water approximation applied to the aluminium electrolysis process

The shallow water approximation applied to the aluminium electrolysis process The shallow water approximation applied to the aluminium electrolysis process L Leboucher, V. Bojarevics, K Pericleous Centre for Numerical Modelling and Process Analysis, University of Greenwich, Wellington

More information

DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING

DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING Yukinori Kametani Department of mechanical engineering Keio

More information

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Published in Phys. Fluids 14, L73-L76 (22). Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Koji Fukagata, Kaoru Iwamoto, and Nobuhide Kasagi Department of Mechanical

More information

The Role of Splatting Effect in High Schmidt Number Turbulent Mass Transfer Across an Air-Water Interface

The Role of Splatting Effect in High Schmidt Number Turbulent Mass Transfer Across an Air-Water Interface Turbulence, Heat and Mass Transfer 4 K. Hanjalic, Y. Nagano and M. Tummers (Editors) 3 Begell House, Inc. The Role of Splatting Effect in High Schmidt Number Turbulent Mass Transfer Across an Air-Water

More information

Applied Mathematics and Mechanics (English Edition)

Applied Mathematics and Mechanics (English Edition) Appl. Math. Mech. -Engl. Ed., 39(9), 1267 1276 (2018) Applied Mathematics and Mechanics (English Edition) https://doi.org/10.1007/s10483-018-2364-7 Direct numerical simulation of turbulent flows through

More information

PHYSICAL MECHANISM OF CONVECTION

PHYSICAL MECHANISM OF CONVECTION Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter

More information

Analysis of the flow and heat transfer characteristics for MHD free convection in an enclosure with a heated obstacle

Analysis of the flow and heat transfer characteristics for MHD free convection in an enclosure with a heated obstacle Nonlinear Analysis: Modelling and Control, 2011, Vol. 16, No. 1, 89 99 89 Analysis of the flow and heat transfer characteristics for MHD free convection in an enclosure with a heated obstacle S. Parvin,

More information

Shell Balances in Fluid Mechanics

Shell Balances in Fluid Mechanics Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell

More information

The Madison Dynamo Experiment: magnetic instabilities driven by sheared flow in a sphere. Cary Forest Department of Physics University of Wisconsin

The Madison Dynamo Experiment: magnetic instabilities driven by sheared flow in a sphere. Cary Forest Department of Physics University of Wisconsin The Madison Dynamo Experiment: magnetic instabilities driven by sheared flow in a sphere Cary Forest Department of Physics University of Wisconsin February 28, 2001 Planets, stars and perhaps the galaxy

More information

Turbulent Boundary Layers & Turbulence Models. Lecture 09

Turbulent Boundary Layers & Turbulence Models. Lecture 09 Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects

More information

COMSOL Conference 2010

COMSOL Conference 2010 Presented at the COMSOL Conference 2010 Boston COMSOL Conference 2010 Understanding Ferrofluid Spin-Up Flows in Rotating Uniform Magnetic Fields Shahriar Khushrushahi, Prof. Markus Zahn Massachusetts Institute

More information

Fluid Dynamics Exercises and questions for the course

Fluid Dynamics Exercises and questions for the course Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r

More information

Hartmann Flow in a Rotating System in the Presence of Inclined Magnetic Field with Hall Effects

Hartmann Flow in a Rotating System in the Presence of Inclined Magnetic Field with Hall Effects Tamkang Journal of Science and Engineering, Vol. 13, No. 3, pp. 243 252 (2010) 243 Hartmann Flow in a Rotating System in the Presence of Inclined Magnetic Field with Hall Effects G. S. Seth, Raj Nandkeolyar*

More information

Self-Excited Vibration in Hydraulic Ball Check Valve

Self-Excited Vibration in Hydraulic Ball Check Valve Self-Excited Vibration in Hydraulic Ball Check Valve L. Grinis, V. Haslavsky, U. Tzadka Abstract This paper describes an experimental, theoretical model and numerical study of concentrated vortex flow

More information

Before we consider two canonical turbulent flows we need a general description of turbulence.

Before we consider two canonical turbulent flows we need a general description of turbulence. Chapter 2 Canonical Turbulent Flows Before we consider two canonical turbulent flows we need a general description of turbulence. 2.1 A Brief Introduction to Turbulence One way of looking at turbulent

More information

Chapter 10. Solids and Fluids

Chapter 10. Solids and Fluids Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the

More information

Unsteady MHD Couette Flow with Heat Transfer in the Presence of Uniform Suction and Injection

Unsteady MHD Couette Flow with Heat Transfer in the Presence of Uniform Suction and Injection Mechanics and Mechanical Engineering Vol. 12, No. 2 (2008) 165 176 c Technical University of Lodz Unsteady MHD Couette Flow with Heat Transfer in the Presence of Uniform Suction and Injection Hazem A.

More information

A new approach for local similarity solutions of an unsteady hydromagnetic free convective heat transfer flow along a permeable flat surface

A new approach for local similarity solutions of an unsteady hydromagnetic free convective heat transfer flow along a permeable flat surface International Journal of Advances in Applied Mathematics and Mechanics Volume, Issue : (3) pp. 39-5 Available online at www.ijaamm.com IJAAMM ISSN: 347-59 A new approach for local similarity solutions

More information

Application of Viscous Vortex Domains Method for Solving Flow-Structure Problems

Application of Viscous Vortex Domains Method for Solving Flow-Structure Problems Application of Viscous Vortex Domains Method for Solving Flow-Structure Problems Yaroslav Dynnikov 1, Galina Dynnikova 1 1 Institute of Mechanics of Lomonosov Moscow State University, Michurinskiy pr.

More information

Chapter 5. The Differential Forms of the Fundamental Laws

Chapter 5. The Differential Forms of the Fundamental Laws Chapter 5 The Differential Forms of the Fundamental Laws 1 5.1 Introduction Two primary methods in deriving the differential forms of fundamental laws: Gauss s Theorem: Allows area integrals of the equations

More information

Available online at ScienceDirect. Procedia Engineering 90 (2014 )

Available online at   ScienceDirect. Procedia Engineering 90 (2014 ) Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 9 (214 ) 599 64 1th International Conference on Mechanical Engineering, ICME 213 Validation criteria for DNS of turbulent heat

More information

Point Vortex Dynamics in Two Dimensions

Point Vortex Dynamics in Two Dimensions Spring School on Fluid Mechanics and Geophysics of Environmental Hazards 9 April to May, 9 Point Vortex Dynamics in Two Dimensions Ruth Musgrave, Mostafa Moghaddami, Victor Avsarkisov, Ruoqian Wang, Wei

More information

meters, we can re-arrange this expression to give

meters, we can re-arrange this expression to give Turbulence When the Reynolds number becomes sufficiently large, the non-linear term (u ) u in the momentum equation inevitably becomes comparable to other important terms and the flow becomes more complicated.

More information

Effect of an adiabatic fin on natural convection heat transfer in a triangular enclosure

Effect of an adiabatic fin on natural convection heat transfer in a triangular enclosure American Journal of Applied Mathematics 2013; 1(4): 78-83 Published online November 10, 2013 (http://www.sciencepublishinggroup.com/j/ajam) doi: 10.11648/j.ajam.20130104.16 Effect of an adiabatic fin on

More information

COMBINED EFFECTS OF RADIATION AND JOULE HEATING WITH VISCOUS DISSIPATION ON MAGNETOHYDRODYNAMIC FREE CONVECTION FLOW AROUND A SPHERE

COMBINED EFFECTS OF RADIATION AND JOULE HEATING WITH VISCOUS DISSIPATION ON MAGNETOHYDRODYNAMIC FREE CONVECTION FLOW AROUND A SPHERE Suranaree J. Sci. Technol. Vol. 20 No. 4; October - December 2013 257 COMBINED EFFECTS OF RADIATION AND JOULE HEATING WITH VISCOUS DISSIPATION ON MAGNETOHYDRODYNAMIC FREE CONVECTION FLOW AROUND A SPHERE

More information

Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders

Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders A. Jugal M. Panchal, B. A M Lakdawala 2 A. M. Tech student, Mechanical Engineering Department, Institute

More information

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

More information

If there is convective heat transfer from outer surface to fluid maintained at T W.

If there is convective heat transfer from outer surface to fluid maintained at T W. Heat Transfer 1. What are the different modes of heat transfer? Explain with examples. 2. State Fourier s Law of heat conduction? Write some of their applications. 3. State the effect of variation of temperature

More information

Flow analysis in centrifugal compressor vaneless diffusers

Flow analysis in centrifugal compressor vaneless diffusers 348 Journal of Scientific & Industrial Research J SCI IND RES VOL 67 MAY 2008 Vol. 67, May 2008, pp. 348-354 Flow analysis in centrifugal compressor vaneless diffusers Ozturk Tatar, Adnan Ozturk and Ali

More information

12.1 Viscous potential flow (VPF)

12.1 Viscous potential flow (VPF) 1 Energy equation for irrotational theories of gas-liquid flow:: viscous potential flow (VPF), viscous potential flow with pressure correction (VCVPF), dissipation method (DM) 1.1 Viscous potential flow

More information

Experimental and numerical investigation on particle-induced liquid metal flow using Lorentz force velocimetry

Experimental and numerical investigation on particle-induced liquid metal flow using Lorentz force velocimetry IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Experimental and numerical investigation on particle-induced liquid metal flow using Lorentz force velocimetry To cite this article:

More information

Application of Reconstruction of Variational Iteration Method on the Laminar Flow in a Porous Cylinder with Regressing Walls

Application of Reconstruction of Variational Iteration Method on the Laminar Flow in a Porous Cylinder with Regressing Walls Mechanics and Mechanical Engineering Vol. 21, No. 2 (2017) 379 387 c Lodz University of Technology Application of Reconstruction of Variational Iteration Method on the Laminar Flow in a Porous Cylinder

More information

Global magnetorotational instability with inflow The non-linear regime

Global magnetorotational instability with inflow The non-linear regime Global magnetorotational instability with inflow The non-linear regime Evy Kersalé PPARC Postdoctoral Research Associate Dept. of Appl. Math. University of Leeds Collaboration: D. Hughes & S. Tobias (Dept.

More information

Numerical Simulation of MHD Processes in the Technology of Non-crucible Induction Melting of Titanium Alloys

Numerical Simulation of MHD Processes in the Technology of Non-crucible Induction Melting of Titanium Alloys Numerical Simulation of MHD Processes in the Technology of Non-crucible Induction Melting of Titanium Alloys V Demidovich, M Khatsayuk, V Timofeev, A Maksimov, I Rastvorova To cite this version: V Demidovich,

More information

ON VARIABLE LAMINAR CONVECTIVE FLOW PROPERTIES DUE TO A POROUS ROTATING DISK IN A MAGNETIC FIELD

ON VARIABLE LAMINAR CONVECTIVE FLOW PROPERTIES DUE TO A POROUS ROTATING DISK IN A MAGNETIC FIELD ON VARIABLE LAMINAR CONVECTIVE FLOW PROPERTIES DUE TO A POROUS ROTATING DISK IN A MAGNETIC FIELD EMMANUEL OSALUSI, PRECIOUS SIBANDA School of Mathematics, University of KwaZulu-Natal Private Bag X0, Scottsville

More information

ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS

ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS Karsten Lindegård Jensen 1, B. Mutlu Sumer 1, Giovanna Vittori 2 and Paolo Blondeaux 2 The pressure field in an oscillatory boundary layer

More information

Passive, Active and Feedback Stabilization of Thick, Flowing Liquid Metal Walls

Passive, Active and Feedback Stabilization of Thick, Flowing Liquid Metal Walls 21 st MHD Control Workshop, San Diego, CA, November 7-9, 2016 Passive, Active and Feedback Stabilization of Thick, Flowing Liquid Metal Walls Francesco A. Volpe, S.M.H. (Taha) Mirhoseini Dept. Applied

More information

Improving reliability of modelling heat and fluid flow in complex gas metal arc fillet welds part II: application to welding of steel

Improving reliability of modelling heat and fluid flow in complex gas metal arc fillet welds part II: application to welding of steel INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 38 (005) 7 34 doi:0.088/00-377/38//00 Improving reliability of modelling heat and fluid flow in complex gas

More information

OpenFOAM selected solver

OpenFOAM selected solver OpenFOAM selected solver Roberto Pieri - SCS Italy 16-18 June 2014 Introduction to Navier-Stokes equations and RANS Turbulence modelling Numeric discretization Navier-Stokes equations Convective term {}}{

More information

Physical Properties of Fluids

Physical Properties of Fluids Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel

More information

Boundary Layer Flow and Heat Transfer due to an Exponentially Shrinking Sheet with Variable Magnetic Field

Boundary Layer Flow and Heat Transfer due to an Exponentially Shrinking Sheet with Variable Magnetic Field International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 78 088 Volume 4, Issue 6, June 05 67 Boundary ayer Flow and Heat Transfer due to an Exponentially Shrinking Sheet with

More information

MYcsvtu Notes HEAT TRANSFER BY CONVECTION

MYcsvtu Notes HEAT TRANSFER BY CONVECTION www.mycsvtunotes.in HEAT TRANSFER BY CONVECTION CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in

More information

Suppression of Temperature Fluctuations by Rotating Magnetic Field in a Large Scale Rayleigh-Bénard Cell

Suppression of Temperature Fluctuations by Rotating Magnetic Field in a Large Scale Rayleigh-Bénard Cell International Scientific Colloquium Modelling for Material Processing Riga, September 16-17, 2010 Suppression of Temperature Fluctuations by Rotating Magnetic Field in a Large Scale Rayleigh-Bénard Cell

More information

Simulation of Liquid Jet Breakup Process by Three-Dimensional Incompressible SPH Method

Simulation of Liquid Jet Breakup Process by Three-Dimensional Incompressible SPH Method Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July 9-13, 212 ICCFD7-291 Simulation of Liquid Jet Breakup Process by Three-Dimensional Incompressible SPH

More information

Effects of Variation of the Flame Area and Natural Damping on Primary Acoustic Instability of Downward Propagating Flames in a Tube

Effects of Variation of the Flame Area and Natural Damping on Primary Acoustic Instability of Downward Propagating Flames in a Tube 5 th ICDERS August 7, 015 Leeds, UK Effects of Variation of the Flame Area and Natural Damping on Primary Acoustic Instability of Downward Propagating Flames in a Tube Sung Hwan Yoon and Osamu Fujita Division

More information

Turbulent boundary layer

Turbulent boundary layer Turbulent boundary layer 0. Are they so different from laminar flows? 1. Three main effects of a solid wall 2. Statistical description: equations & results 3. Mean velocity field: classical asymptotic

More information

4.2 Concepts of the Boundary Layer Theory

4.2 Concepts of the Boundary Layer Theory Advanced Heat by Amir Faghri, Yuwen Zhang, and John R. Howell 4.2 Concepts of the Boundary Layer Theory It is difficult to solve the complete viscous flow fluid around a body unless the geometry is very

More information

Turbulent Rotating Rayleigh-Bénard Convection: DNS and SPIV Measurements

Turbulent Rotating Rayleigh-Bénard Convection: DNS and SPIV Measurements Turbulent Rotating Rayleigh-Bénard Convection: DNS and SPIV Measurements Rudie Kunnen 1 Herman Clercx 1,2 Bernard Geurts 1,2 1 Fluid Dynamics Laboratory, Department of Physics Eindhoven University of Technology

More information

Numerical Analysis of MHD Flow of Fluid with One Porous Bounding Wall

Numerical Analysis of MHD Flow of Fluid with One Porous Bounding Wall Numerical Analysis of MHD Flow of Fluid with One Porous Bounding Wall Ramesh Yadav 1 & Vivek Joseph 2 1Assistant Professor, Department of Mathematics BBDNITM Lucknow U P 2Professor, Department of Mathematics

More information

PHYS 432 Physics of Fluids: Instabilities

PHYS 432 Physics of Fluids: Instabilities PHYS 432 Physics of Fluids: Instabilities 1. Internal gravity waves Background state being perturbed: A stratified fluid in hydrostatic balance. It can be constant density like the ocean or compressible

More information

A boundary-layer model of thermocapillary flow in a cold corner

A boundary-layer model of thermocapillary flow in a cold corner PHYSICS OF FLUIDS VOLUME 14, NUMBER 9 SEPTEMBER 2002 A boundary-layer model of thermocapillary flow in a cold corner D. Canright Mathematics Department, Code MA/Ca, Naval Postgraduate School, Monterey,

More information

PIV study for the analysis of planar jets in cross-flow at low Reynolds number

PIV study for the analysis of planar jets in cross-flow at low Reynolds number PIV study for the analysis of planar jets in cross-flow at low Reynolds number Vincenti I., Guj G., Camussi R., Giulietti E. University Roma TRE, Department of Ingegneria Meccanica e Industriale (DIMI),

More information

UNIVERSITY of LIMERICK

UNIVERSITY of LIMERICK UNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH Faculty of Science and Engineering END OF SEMESTER ASSESSMENT PAPER MODULE CODE: MA4607 SEMESTER: Autumn 2012-13 MODULE TITLE: Introduction to Fluids DURATION OF

More information

J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and

J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and turbulent, was discovered by Osborne Reynolds (184 191) in 1883

More information

Chapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI.

Chapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Chapter 10: Boiling and Condensation 1 1 Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Objectives When you finish studying this chapter, you should be able to: Differentiate between evaporation

More information