IHMTC EULER-EULER TWO-FLUID MODEL BASED CODE DEVELOPMENT FOR TWO-PHASE FLOW SYSTEMS
|
|
- Lynette Little
- 5 years ago
- Views:
Transcription
1 Proceedings of the 24th National and 2nd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2017), December 27-30, 2017, BITS-Pilani, Hyderabad, India IHMTC EULER-EULER TWO-FLUID MODEL BASED CODE DEVELOPMENT FOR TWO-PHASE FLOW SYSTEMS Sanjeev Kumar Dept. of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India. Arun K Saha Dept. of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India. aksaha@iitk.ac.in Prabhat Munshi Dept. of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India. pmunshi@iitk.ac.in ABSTRACT The flow regimes of gas-liquid two-phase flow in a vertical pipe depend upon the drag as well as non-drag (Lift, Virtual mass, turbulent dispersion, wall lubrication, etc.) forces. The effect of these forces in a code is incorporated by the closure models of the interphase forces for the momentum exchange between the continuous and dispersed phases. In the present work, different drag models with and without the effect of bubbles swarm and shear rate of continuous phase are investigated in the in-house code. The code is based on the Euler-Euler twofluid model. The code is validated against the experimental data of Monros-Andreu et al. (2013, EPJ Web Conf. 45, 01105). The radial distribution of the volume fraction, gas velocity and slip velocity has been presented for different gas and liquid flow rates. The predictions from the sets of inter-phase closure models presented in this paper yielded satisfactory results. It has been found that a set of Ishii-Zuber drag coefficient model with bubble swarm effect by Roghair and shear effect by Magnaudet model, Tomiyama lift coefficient model, Hosokawa and Tomiyama wall force model, and Lopez de Bertodano turbulent dispersion force model was found to provide the best agreement with the experimental data. NOMENCLATURE 2D Two-dimensional α Void fraction ε Turbulent dissipation rate σ Surface tension c/d Continuous/Dispersed phase d b Bubble diameter C D Overall Drag coefficient C D Drag coefficient of single bubble D Pipe diameter E o Eotvos number g Gravitational acceleration H Pipe height Corresponding Author k Turbulent kinetic energy p Pressure r/z Radial/Axial co-ordinates Re Pipe Reynolds number Re b Bubble Reynolds number t Time U Velocity vector Relative velocity U r INTRODUCTION A large number of flows encountered in nature and technology are a mixture of phases. Multi-phase processes are commonly used in many industrial fields, e.g. nuclear reactors and chemical reactors [1, 2]. The distribution of phases and how they interact with each other is still a field of research. Bubble columns are commonly used among the equipments for such type of processes. They are inexpensive reactors and easy to operate. An axis-symmetric code is developed to analyze the twophase pipe flow systems with bubbly flow regime. This code is based on Euler-Euler two-fluid model. Governing equations in 2D cylindrical co-ordinates system (r, z) are considered. Navier- Stokes equations have been solved using modified Marker and Cell (MAC) method [3]. Explicit schemes are used to solve the transport equations. Standard wall function k ε turbulence model is used to incorporate the turbulent phenomena. Model is validated against the experimental work performed by Andreu et al., 2013 [4]. They have studied the water temperature effect on upward air-water flow in a vertical pipe. They have presented the local void fraction distribution, interfacial velocity, turbulent kinetic energy and turbulent dissipation energy profiles for different flow conditions of bubbly flow regime and at different axial locations of the cylindrical pipe. In the present work, an in-house code is used to simulate the experimental work done by Andreu et al., 2013 [4]. Different correlations of drag and nondrag (lift, virtual mass, turbulent dispersion and wall lubrication) forces are tested and there effects are discussed. It is found that present model predicts the results with reasonable accuracy. In 1
2 future this code will be coupled with the nuclear kinetics code to analyze the core of the Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) in detail. MATHEMATICAL MODEL Model equations rely on the Euler-Euler two-fluid methodology are described in this section. The local instantaneous equations of each phase are ensemble averaged to obtain an Euler- Euler two-phase flow description. The averaging process introduces the phase fraction α and unclosed terms M representing the interphase forces term. These unclosed terms must be modeled as these terms are crucial to the prediction of the two-phase flow. Both (continuous and dispersed) phases are assumed to be incompressible. For a monodisperse flow, i.e. for a flow with equally sized bubbles of diameter d B, and without mass transfer between the phases, these equations can be written as: U ϕ α ϕ ( τϕ + U ϕ U ϕ + R ϕ ) + α ϕ α ϕ ( τϕ ρ ϕ + R ϕ + (α ϕ U ϕ ) = 0, (1) + ρ ϕ ) = p ρ ϕ + g + M ϕ α ϕ ρ ϕ where U, τ, R, p, g, α and ρ are the velocity, laminar stress tensor, Reynolds stress tensor, pressure, gravity, volume fraction and density respectively. The subscript ϕ = c stands for the carrier phase (liquid) and ϕ = d for the dispersed phase (gas). The first term on the left side of Equation (2) is the transient term, second term represents the convective term, and the third and fourth terms represent the diffusion due to the laminar and turbulent stresses. The first, second and third terms on the right side of Equation (2) represents the pressure force, gravitational force and the inter phase momentum transfer terms respectively. Interfacial models The interphase force term or interfacial momentum transfer term is given by the sum of various (drag and non-drag) forces as given below M d = M c = M d,d + M d,v M + M d,l + M d,wl + M d,t D, (3) where M d,d, M d,v M, M d,l, M d,wl and M d,t D are the momentum exchange terms due to the drag force, the virtual mass force, the lift force, the wall lubrication force and the turbulent dispersion force respectively. The Basset force comes into the picture due to the formation of the boundary layer around the bubble. The Basset force is relevant only for the unsteady flows. In the present work, we have considered the cases with steady state flows and hence the magnitude of the Basset force is negligible and hence it is not considered in the present work. All these forces are described below in detail. (2) Drag force: The drag force exerted by the fluid on a bubble or droplet determines the relative velocity between the phases. The drag force is the function of slip velocity (U r = U d U c ). It can be calculated for spherical bubbles of uniform size by the following correlation [5]: M d,d = 3 4 α C D ρ c d U r U r, (4) d B where C D and d B are the drag coefficient and bubble diameter respectively. Hosokawa and Tomiyama (2009) [6] studied the effect of bubble swarm on the drag coefficient. They suggested a correction factor (C f,swarm ) with respect to the drag coefficient of single bubble (C D, ). Magnaudet and Legendre (1998) [7] suggested a correction factor (C f,shear ) for shear rate effect. The overall drag coefficient with the inclusion of both the above effects is given as: C D = C D, C f,swarm C f,shear, (5) Three different correlations of several distinct Reynolds number regions for individual bubbles proposed by Ishii and Zuber (1979), Tomiyama et al. (1998) [8] and Zhang and Banderheyde (2002) are tested in the present work. A drag correlation was derived by Ishii and Zuber (1979) for a spherical bubble as a function of the Eotvos number, C D, = 2 3 E0.5 o. (6) where E O = g(ρ c ρ d )db 2 σ is the Eotvos number. Tomiyama et al. (1998) [8] proposed another drag coefficient model. { [ 16 C D, = max mini ( Reb ), 48 ] Re b Re b E O },, 8 3 E O + 4 (7) Zhang and Banderheyde (2002) proposed another expression for C D, as: C D, = Re b 1 + Re 0.5 b Roghair et al. (2013) [9] proposed a correlation to take into account the effect of bubble swarm on drag coefficient. They uses DNS simulation to see the effect of the Eotvos number. This correlation is valid for high volume fraction cases. The expression is given below: (8) [ ( ] 22 C f,swarm = (1 α d ) 1 + )α d. (9) E O Magnaudet and Legendre (1998) [7] studied the effect of shear rate on the drag coefficient and proposed the following correction coefficient: C f,shear = ( Sr 2 ), (10) 2
3 where Sr = d bω U is the shear rate. Sr attains a very high value, r usually in the first cell near the wall. It is limited to 2 in the absence of evidence about the effect of the drag force above this value (Hosokawa and Tomiyama, 2009) [6]. Lift force: The bubble in a continuous phase with velocity gradient feels a lateral force and moves laterally with relative velocity related to the velocity gradient. This lateral force acting on a bubble due to the velocity gradient is called the lift force. The effect of the lateral force due to the lift was first modeled by Auton et al. (1988) [10]: M d,l = α d ρ c C L U r U c, (11) where C L is the lift coefficient and it should be modeled. Tomiyama et al., 2002 [11] proposed a form of the lift coefficient that take into account the interaction between the distorted bubble and the shear field of the liquid phase and is given as: min[0.288 tanh(0.121re b ), f (E Ohd )], for E Ohd < 4 C L = f (E Ohd ), for 4 E Ohd , for E Ohd > 10 (12) where E Ohd is the modified Eotvos number, given in terms of the maximum horizontal dimension of the bubble d hb. It is given as: E Ohd = g(ρ c ρ d )dhb 2 3, with d hb = d B EO 0.757, (13) σ and f (E Ohd ) = E 3 O hd E 2 O hd E Ohd (14) Virtual Mass force: The virtual mass (VM) force comes into picture when secondary (dispersed) phase accelerates relative to the primary (continuous) phase. The inertia of the primary phase mass encountered by the accelerating bubbles exerts a VM force on the particles. It is given as: M d,v M = α d ρ c C V M ( DUc Dt DU ) d, (15) Dt where C V M is the VM force coefficient and Dt D represents the phase material time derivative. The amplitude of the virtual mass force is very small at steady state in comparison with the amplitude of the other drag and non-drag forces and hence this force is not considered in the present work. Wall lubrication force: The liquid speed between bubble and the wall is lower than between the bubble and the main flow. This results in a hydrodynamic pressure difference. The force corresponding to this pressure difference is called the wall lubrication force. It drive bubble away from the wall. The expression for wall lubrication force was first modeled by Antal et al., (1991), for Re b < 1500 and α d < 0.1. Tomiyama et al., (1995b) [12] modified Antal et al. s (1991) wall force model: [ ] d b 1 M d,wl = α d ρ c C W 2 y 2 1 (D y) 2 U r n z 2 n r, (16) where C W is the wall lubrication force coefficient, n z is the unit vector parallel to the wall and n r is the unit vector normal to the wall. Hosokawa and Tomiyama (2009) [6] proposed the following model: [ max(6log10 M O + 24,4.4) C W = max Re 1.9 b where M O is the Morton number.,0.0217e O ], (17) Turbulent dispersion force: The turbulence of the phases helps to redistribute the dispersed phase from the regions of high concentration of void fraction to the regions of low concentration. This effect is called the turbulent dispersion effect and corresponding force is the turbulent dispersion force. There is a variety of models proposed by the researchers for the turbulent dispersion force. The model proposed by Antal et al., (1991b) [13] has been considered in this work. This model considers the effect of the turbulent fluctuations in the continuous phase on the dispersed phase and is given as: M d,t D = ρ c C T D k α d, (18) where k is the turbulent kinetic energy of the continuous phase and C T D is the turbulent dispersion force coefficient. Lopez de Bertodano (1998) [14] proposed a correlation for C T D : C T D = C1/4 µ St(1 + St), (19) St = τ d τ c, (20) where the coefficient C µ is 0.09, St is the Stokes number, τ d is the relaxation time of bubble and τ c is the relaxation time of flow. These relaxation times are given as [6]: τ d = 4d b 3C D U r ; τ c = Cµ 3/4 k ε where ε is the turbulent dissipation rate. (21) Turbulence model A standard wall function k ε turbulence model (Launder and Spalding, 1974 [15]) is used to model the effect of turbulent fluctuations in the continuous phase. The equations for the 3
4 turbulent kinetic energy kc and turbulent dissipation rate (εc ) for continuous phase are given as: kc + (Uc kc ) = νc + νt,c σk A proper drag coefficient determines the slip velocity of the two-phase flow system. The axial relative velocity profiles for Ishii-Zuber, Tomiyama and Zhang drag correlations are shown in Figure 1. It is clear that the slip velocity prediction by different models vary widely. kc + Pk εc + Sk, (22) νt,c εc + (Uc εc ) = νc + σε (23) εc εc + (C1ε Pk C2ε εc ) + Sε, kc The near wall region is modeled using the wall functions approach of Launder and Spalding, 1974 [15]. The bubble induced turbulence is modeled by the addition of a bubble-induced source term to the transport equations of the turbulence model. Lee et el., (1989) [16] proposed the following correlations for these source terms: Sk = αd C1k p Ur, z εc Sε = C3ε Sk, kc (24) Figure 1. SLIP VELOCITY COMPARISON WITH DIFFERENT DRAG CORRELATIONS. (25) where C1k = ( Re), 1 + e(re 60000)/2000 The wall swarm effect and shear rate effect corrections are included in the drag correlation of Ishii-Zuber. The axial slip velocity with and without all these corrections are shown in Figure 2. It is clear that Ishii-Zuber drag model with the correction of bubble swarm and shear rate effect predicts the slip velocity which is close to the experimental data. (26) where Re is the continuous phase Reynolds number. The model constants Cµ, C1ε, C2ε, C3ε, σk and σε are 0.09, 1.44, 1.92, 1.92, 1.0 and 1.3 respectively. PROBLEM DESCRIPTION The experimental work done by Andreu et al., 2013 [4] is considered to validate the developed code. The test section was a 52mm diameter pipe of 5.5m length. The test section was maintained at adiabatic conditions with air and water at superficial velocity ranges of 0.05m/s-0.30m/s and 0.5m/s-2.0m/s respectively. The experiments have been performed at three different temperatures (T 15 C, 24 C and 36 C). The radial profiles are provided at three different heights (H/D = 22.4, 61 and 98.7). The radial porfiles have been compared at (H/D = 22.4) in the present work. SENSITIVITY ANALYSIS The strong dependence between the different closure models makes it difficult to consider each model separately. The approach adopted to first neglected all the non-drag forces and bubble induced turbulence force to predict a realistic slip velocity. Once the drag model is finalized, non-drag forces will also be considered. Figure 2. SLIP VELOCITY COMPARISON WITH BUBBLE SWARM AND SHEAR RATE EFFECT. 4
5 velocities (0.05m/s and 0.3m/s) are considered and the superficial liquid velocity is 1.0m/s. It is clear from Figure 3 that the predicted radial void fraction profiles by the present model is closely matching with the experimental profiles. The predicted data lies within the maximum error involved (±15%) in the experiment [4]. The near wall peak is resolved accurately, except the peak position is a little closer to the wall than the experimental profile peak. The radial gas velocity profiles at three different temperatures are shown in Figure 4. It is clear from Figure 4 that the predicted radial gas velocity profiles by the present model is closely matching with the experimental profiles, for the low superficial gas velocity (J G = 0.05m/s) case. It is over predicted in the case of high superficial gas velocity (J G = 0.3m/s). But, the predicted data lies within the maximum error involved (±15%) in the experiment [4]. CONCLUSIONS An Euler-Euler multiphase model based code is developed and validated against the experimental data available for airwater bubbly flow in adiabatic vertical pipe. The effect of different closure models is shown and a suitable set of closure models have been identified. The developed code successfully predicts the radial profiles of gas velocity and void fraction for different flow conditions. Figure 3. THE VOID FRACTION PROFILES COMPARISON WITH EXPERIMENTAL DATA AT H/D=22.4, J L =1.0m/s, J G =0.05, 0.3m/s AT TEMPERATURES (A) 15 C, (B) 24 C and (C) 36 C. RESULTS AND DISCUSSION The radial void fraction profiles at three different temperatures are shown in Figure 3. The two different superficial gas 5 REFERENCES [1] Fabris, G., and Hantman, R. G., Fluid dynamic aspects of liquid-metal gas two-phase magnetohydrodynamic power generators. Proceedings of the 1976 Heat Transfer and Fluid Mechanics Institute, pp [2] Gutierrez-Miravete, E., and Xiaole, X., A study of fluid flow and heat transfer in a liquid metal in a backwardfacing setup under combined electric and magnetic fields. Proceedings of the 2011 COMSOL Conference in Boston. [3] Harlow, F. H., and Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 12(8), pp [4] Monros-Andreu, G., C. S. M.-C. R. T. S. J. J. E. H. L., and Mondragon, R., Water temperature effect on upward air-water flow in a vertical pipe: Local measurements database using four-sensor conductivity probes and lda. EPJ Web of Conferences, 45(01105). [5] Ishii, M., and Mishima, K., Two-fluid model and hydrodynamic constitutive relations. Nuclear Engineering and Design, 82, pp [6] Hosokawa, S., and Tomiyama, A., Multi-fluid simulation of turbulent bubbly pipe flows. Chemical Engineering Science, 84, pp [7] Magnaudet, J., and Legendre, D., Some aspects of the lift force on a spherical bubble. Applied Scientific Research, 58, pp [8] Tomiyama, A., K. I. Z. I., and Sakaguchi, T., Drag coefficients of single bubbles under normal and micro gravity conditions. JSME International Journal, 41(2), pp [9] Roghair, I., A. M. V. S., and Kuipers, H. J. A. M., 2013.
6 Drag force and clustering in bubble swarms. American Institute of Chemical Engineers, 59(5), pp [10] Auton, T. R., H. J. C. R., and Prud Homme, M., The force exerted on a body in inviscid unsteady nonuniform rotational flow. Journal of Fluid Mechanics, 197, pp [11] Tomiyama, A., T. H. Z. I., and Hosokawa, S., Transverse migration of single bubbles in simple shear flows. Chemical Engineering Science, 57, pp [12] Tomiyama, A., S. A. Z. I. K. N., and Sakaguchi, T., Effects of eotvos number and dimensionless liquid volumetric flux on lateral motion of a bubble in a laminar duct flow. Advances in Multiphase Flow, pp [13] Antal, S. P., L. R. T., and Flaherty, J. E., Analysis of phase distribution and turbulence in dispersed particle/liquid flows. Chemical Engineering Communications, 174, pp [14] Lopez de Bertodano, M. A., Two fluid model for two-phase turbulent jets. Nuclear Engineering and Design, 179, pp [15] Launder, G. E., and Spalding, D. B., The numerical computation of turbulent flows. Computer Methods in Applied mechanics and Engineering, 3(2), pp [16] Lee, S. L., and Lahey, R. T., J. O. C., The prediction of two-phase turbulence and phase distribution phenomena using a k ε model. Japanese Journal of Multiphase Flow, 3(4), pp Figure 4. THE GAS VELOCITY PROFILES COMPARISON WITH EXPERIMENTAL DATA AT H/D=22.4, J L =1.0m/s, J G =0.05, 0.3m/s AT TEMPERATURES (A) 15 C, (B) 24 C and (C) 36 C. 6
Modelling of Gas-Liquid Two-Phase Flows in Vertical Pipes using PHOENICS
Modelling of Gas-Liquid Two-Phase Flows in Vertical Pipes using PHOENICS Vladimir Agranat, Masahiro Kawaji, Albert M.C. Chan* Department of Chemical Engineering and Applied Chemistry University of Toronto,
More informationModeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics!
http://www.nd.edu/~gtryggva/cfd-course/! Modeling Complex Flows! Grétar Tryggvason! Spring 2011! Direct Numerical Simulations! In direct numerical simulations the full unsteady Navier-Stokes equations
More informationINTRODUCTION OBJECTIVES
INTRODUCTION The transport of particles in laminar and turbulent flows has numerous applications in engineering, biological and environmental systems. The deposition of aerosol particles in channels and
More informationDEVELOPMENT OF A MULTIPLE VELOCITY MULTIPLE SIZE GROUP MODEL FOR POLY-DISPERSED MULTIPHASE FLOWS
DEVELOPMENT OF A MULTIPLE VELOCITY MULTIPLE SIZE GROUP MODEL FOR POLY-DISPERSED MULTIPHASE FLOWS Jun-Mei Shi, Phil Zwart 1, Thomas Frank 2, Ulrich Rohde, and Horst-Michael Prasser 1. Introduction Poly-dispersed
More informationThis is a repository copy of Multiphase turbulence in bubbly flows: RANS simulations.
This is a repository copy of Multiphase turbulence in bubbly flows: RANS simulations. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/90676/ Version: Accepted Version Article:
More informationUnsteady Flow of a Newtonian Fluid in a Contracting and Expanding Pipe
Unsteady Flow of a Newtonian Fluid in a Contracting and Expanding Pipe T S L Radhika**, M B Srinivas, T Raja Rani*, A. Karthik BITS Pilani- Hyderabad campus, Hyderabad, Telangana, India. *MTC, Muscat,
More informationModelling of Break-up and Coalescence in Bubbly Two-Phase Flows
Modelling of Break-up and Coalescence in Bubbly Two-Phase Flows Simon Lo and Dongsheng Zhang CD-adapco, Trident Park, Didcot OX 7HJ, UK e-mail: simon.lo@uk.cd-adapco.com Abstract Numerical simulations
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationFundamentals 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 informationFluid 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 informationCFD analysis of the transient flow in a low-oil concentration hydrocyclone
CFD analysis of the transient flow in a low-oil concentration hydrocyclone Paladino, E. E. (1), Nunes, G. C. () and Schwenk, L. (1) (1) ESSS Engineering Simulation and Scientific Software CELTA - Rod SC-41,
More informationEuler-Euler Modeling of Mass-Transfer in Bubbly Flows
Euler-Euler Modeling of Mass-Transfer in Bubbly Flows Roland Rzehak Eckhard Krepper Text optional: Institutsname Prof. Dr. Hans Mustermann www.fzd.de Mitglied der Leibniz-Gemeinschaft Overview Motivation
More informationDifferential 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 informationChapter 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 informationCFD modelling of multiphase flows
1 Lecture CFD-3 CFD modelling of multiphase flows Simon Lo CD-adapco Trident House, Basil Hill Road Didcot, OX11 7HJ, UK simon.lo@cd-adapco.com 2 VOF Free surface flows LMP Droplet flows Liquid film DEM
More informationJOURNAL REVIEW. Simulation of Buoyancy Driven Bubbly Flow: Established Simplifications and Open Questions
FLUID MECHANICS AND TRANSPORT PHENOMENA JOURNAL REVIEW Simulation of Buoyancy Driven Bubbly Flow: Established Simplifications and Open Questions A. Sokolichin and G. Eigenberger Institut für Chemische
More informationCorresponding Author: Kandie K.Joseph. DOI: / Page
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 13, Issue 5 Ver. 1 (Sep. - Oct. 2017), PP 37-47 www.iosrjournals.org Solution of the Non-Linear Third Order Partial Differential
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible
More informationINTERACTION OF AN AIR-BUBBLE DISPERSED PHASE WITH AN INITIALLY ISOTROPIC TURBULENT FLOW FIELD
3rd Workshop on Transport Phenomena in Two-Phase Flow Nessebar, Bulgaria, 2-7 September 1998, p.p. 133-138 INTERACTION OF AN AIR-BUBBLE DISPERSED PHASE WITH AN INITIALLY ISOTROPIC TURBULENT FLOW FIELD
More informationTurbulent 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 informationShell 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 informationVALIDATION OF CFD-BWR, A NEW TWO-PHASE COMPUTATIONAL FLUID DYNAMICS MODEL FOR BOILING WATER REACTOR ANALYSIS
VALIDATION OF CFD-BWR, A NEW TWO-PHASE COMPUTATIONAL FLUID DYNAMICS MODEL FOR BOILING WATER REACTOR ANALYSIS V.Ustineno 1, M.Samigulin 1, A.Ioilev 1, S.Lo 2, A.Tentner 3, A.Lychagin 4, A.Razin 4, V.Girin
More informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
More informationTable of Contents. Preface... xiii
Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...
More informationDetailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces
Detailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces D. Darmana, N.G. Deen, J.A.M. Kuipers Fundamentals of Chemical Reaction Engineering, Faculty of Science and Technology,
More informationCONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 3 LAMINAR BOUNDARY LAYER FLOW LAMINAR BOUNDARY LAYER FLOW Boundary
More informationHEAT TRANSFER IN A RECIRCULATION ZONE AT STEADY-STATE AND OSCILLATING CONDITIONS - THE BACK FACING STEP TEST CASE
HEAT TRANSFER IN A RECIRCULATION ZONE AT STEADY-STATE AND OSCILLATING CONDITIONS - THE BACK FACING STEP TEST CASE A.K. Pozarlik 1, D. Panara, J.B.W. Kok 1, T.H. van der Meer 1 1 Laboratory of Thermal Engineering,
More informationCFD SIMULATION OF SOLID-LIQUID STIRRED TANKS
CFD SIMULATION OF SOLID-LIQUID STIRRED TANKS Divyamaan Wadnerkar 1, Ranjeet P. Utikar 1, Moses O. Tade 1, Vishnu K. Pareek 1 Department of Chemical Engineering, Curtin University Perth, WA 6102 r.utikar@curtin.edu.au
More informationFLUID MECHANICS. Chapter 9 Flow over Immersed Bodies
FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1
More informationCHAPTER 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 informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress
More informationContents. 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 informationCENG 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 informationFiltered Two-Fluid Model for Gas-Particle Suspensions. S. Sundaresan and Yesim Igci Princeton University
Filtered Two-Fluid Model for Gas-Particle Suspensions S. Sundaresan and Yesim Igci Princeton University Festschrift for Professor Dimitri Gidaspow's 75th Birthday II Wednesday, November 11, 2009: 3:15
More informationModelling multiphase flows in the Chemical and Process Industry
Modelling multiphase flows in the Chemical and Process Industry Simon Lo 9/11/09 Contents Breakup and coalescence in bubbly flows Particle flows with the Discrete Element Modelling approach Multiphase
More informationChapter 6: Incompressible Inviscid Flow
Chapter 6: Incompressible Inviscid Flow 6-1 Introduction 6-2 Nondimensionalization of the NSE 6-3 Creeping Flow 6-4 Inviscid Regions of Flow 6-5 Irrotational Flow Approximation 6-6 Elementary Planar Irrotational
More informationResearch Article CFD Modeling of Boiling Flow in PSBT 5 5Bundle
Science and Technology of Nuclear Installations Volume 2012, Article ID 795935, 8 pages doi:10.1155/2012/795935 Research Article CFD Modeling of Boiling Flow in PSBT 5 5Bundle Simon Lo and Joseph Osman
More informationMultiphase Flow and Heat Transfer
Multiphase Flow and Heat Transfer ME546 -Sudheer Siddapureddy sudheer@iitp.ac.in Two Phase Flow Reference: S. Mostafa Ghiaasiaan, Two-Phase Flow, Boiling and Condensation, Cambridge University Press. http://dx.doi.org/10.1017/cbo9780511619410
More informationTutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace
Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace Adapted from Publisher: John S. Wiley & Sons 2002 Center for Scientific Computation and
More informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationContents. Microfluidics - Jens Ducrée Physics: Laminar and Turbulent Flow 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More information- Marine Hydrodynamics. Lecture 4. Knowns Equations # Unknowns # (conservation of mass) (conservation of momentum)
2.20 - Marine Hydrodynamics, Spring 2005 Lecture 4 2.20 - Marine Hydrodynamics Lecture 4 Introduction Governing Equations so far: Knowns Equations # Unknowns # density ρ( x, t) Continuity 1 velocities
More informationLaminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition
Sādhanā Vol. 40, Part 2, April 2015, pp. 467 485. c Indian Academy of Sciences Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition RAMBIR BHADOURIYA,
More informationInvestigation of Three-Dimensional Upward and Downward Directed Gas-Liquid Two-Phase Bubbly Flows in a 180 o -Bent Tube
Investigation of Three-Dimensional Upward and Downward Directed Gas-Liquid Two-Phase Bubbly Flows in a 180 o -Bent Tube Th. Frank, R. Lechner, F. Menter CFX Development, ANSYS Germany GmbH, Staudenfeldweg
More informationLectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6
Lectures on Nuclear Power Safety Lecture No 6 Title: Introduction to Thermal-Hydraulic Analysis of Nuclear Reactor Cores Department of Energy Technology KTH Spring 2005 Slide No 1 Outline of the Lecture
More informationPairwise Interaction Extended Point-Particle (PIEP) Model for droplet-laden flows: Towards application to the mid-field of a spray
Pairwise Interaction Extended Point-Particle (PIEP) Model for droplet-laden flows: Towards application to the mid-field of a spray Georges Akiki, Kai Liu and S. Balachandar * Department of Mechanical &
More informationFluid Mechanics. Spring 2009
Instructor: Dr. Yang-Cheng Shih Department of Energy and Refrigerating Air-Conditioning Engineering National Taipei University of Technology Spring 2009 Chapter 1 Introduction 1-1 General Remarks 1-2 Scope
More informationDetailed Outline, M E 320 Fluid Flow, Spring Semester 2015
Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous
More informationWall Effects in Convective Heat Transfer from a Sphere to Power Law Fluids in Tubes
Excerpt from the Proceedings of the COMSOL Conference 9 Boston Wall Effects in Convective Heat Transfer from a Sphere to Power Law Fluids in Tubes Daoyun Song *1, Rakesh K. Gupta 1 and Rajendra P. Chhabra
More informationFluid Flow, Heat Transfer and Boiling in Micro-Channels
L.P. Yarin A. Mosyak G. Hetsroni Fluid Flow, Heat Transfer and Boiling in Micro-Channels 4Q Springer 1 Introduction 1 1.1 General Overview 1 1.2 Scope and Contents of Part 1 2 1.3 Scope and Contents of
More informationNumerical Simulation of the Gas-Liquid Flow in a Square Crosssectioned
Numerical Simulation of the as-iquid Flow in a Square Crosssectioned Bubble Column * N.. Deen, T. Solberg and B.H. Hjertager Chem. Eng. ab., Aalborg Univ. Esbjerg, Niels Bohrs Vej 8, DK-6700 Esbjerg; Tel.
More information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
More informationInterpreting Differential Equations of Transport Phenomena
Interpreting Differential Equations of Transport Phenomena There are a number of techniques generally useful in interpreting and simplifying the mathematical description of physical problems. Here we introduce
More informationModel Studies on Slag-Metal Entrainment in Gas Stirred Ladles
Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Anand Senguttuvan Supervisor Gordon A Irons 1 Approach to Simulate Slag Metal Entrainment using Computational Fluid Dynamics Introduction &
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationMOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow
TRANSPORT PHENOMENA MOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow Introduction to Turbulent Flow 1. Comparisons of laminar and turbulent flows 2. Time-smoothed equations of change for incompressible
More informationCFD in COMSOL Multiphysics
CFD in COMSOL Multiphysics Mats Nigam Copyright 2016 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective
More informationFluid 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 informationOn the validity of the twofluid model for simulations of bubbly flow in nuclear reactors
On the validity of the twofluid model for simulations of bubbly flow in nuclear reactors Henrik Ström 1, Srdjan Sasic 1, Klas Jareteg 2, Christophe Demazière 2 1 Division of Fluid Dynamics, Department
More informationANALYSIS AND APPLICATIONS OF A TWO-FLUID MULTI-FIELD HYDRODYNAMIC MODEL FOR CHURN-TURBULENT FLOWS
Proceedings of the 2013 21st International Conference on Nuclear Engineering ICONE21 July 29 - August 2, 2013, Chengdu, China ICONE21-16297 ANALYSIS AND APPLICATIONS OF A TWO-FLUID MULTI-FIELD HYDRODYNAMIC
More informationEFFECT OF LIQUID PHASE COMPRESSIBILITY ON MODELING OF GAS-LIQUID TWO-PHASE FLOWS USING TWO-FLUID MODEL
EFFECT OF LIQUID PHASE COMPRESSIBILITY ON MODELING OF GAS-LIQUID TWO-PHASE FLOWS USING TWO-FLUID MODEL Vahid SHOKRI 1*,Kazem ESMAEILI 2 1,2 Department of Mechanical Engineering, Sari Branch, Islamic Azad
More informationAIRLIFT BIOREACTORS. contents
AIRLIFT BIOREACTORS contents Introduction Fluid Dynamics Mass Transfer Airlift Reactor Selection and Design 1 INTRODUCTION airlift reactor (ALR) covers a wide range of gas liquid or gas liquid solid pneumatic
More informationAvailable 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 informationConvective Mass Transfer
Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface
More informationFINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE
Proceedings of the International Conference on Mechanical Engineering 2011 (ICME2011) 18-20 December 2011, Dhaka, Bangladesh ICME11-TH-014 FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT
More informationResearch Article Innovation: International Journal of Applied Research; ISSN: (Volume-2, Issue-2) ISSN: (Volume-1, Issue-1)
Free Convective Dusty Visco-Elastic Fluid Flow Through a Porous Medium in Presence of Inclined Magnetic Field and Heat Source/ Sink 1 Debasish Dey, 2 Paban Dhar 1 Department of Mathematics, Dibrugarh University,
More informationInter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows. UPMC Univ Paris 06, CNRS, UMR 7190, Paris, F-75005, France a)
Inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows Y. Ling, 1 S. Balachandar, 2 and M. Parmar 2 1) Institut Jean Le Rond d Alembert, Sorbonne Universités, UPMC Univ Paris
More informationOpenFOAM 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 informationModelling of dispersed, multicomponent, multiphase flows in resource industries. Section 3: Examples of analyses conducted for Newtonian fluids
Modelling of dispersed, multicomponent, multiphase flows in resource industries Section 3: Examples of analyses conducted for Newtonian fluids Globex Julmester 017 Lecture # 04 July 017 Agenda Lecture
More informationUNIT 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 informationEulerian model for the prediction of nucleate boiling of refrigerant in heat exchangers
Advanced Computational Methods and Experiments in Heat Transfer XI 51 Eulerian model for the prediction of nucleate boiling of refrigerant in heat exchangers D. Simón, M. C. Paz, A. Eirís&E.Suárez E.T.S.
More informationCFD Simulation of Sodium Boiling in Heated Pipe using RPI Model
Proceedings of the 2 nd World Congress on Momentum, Heat and Mass Transfer (MHMT 17) Barcelona, Spain April 6 8, 2017 Paper No. ICMFHT 114 ISSN: 2371-5316 DOI: 10.11159/icmfht17.114 CFD Simulation of Sodium
More informationNumerical study of stochastic particle dispersion using One-Dimensional-Turbulence
ILSS-mericas 29th nnual Conference on Liquid tomization and Spray Systems, tlanta, G, May 217 Numerical study of stochastic particle dispersion using One-Dimensional-Turbulence Marco Fistler *1, David
More informationV (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
More informationChapter 9: Differential Analysis
9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control
More informationComputational Fluid Dynamics 2
Seite 1 Introduction Computational Fluid Dynamics 11.07.2016 Computational Fluid Dynamics 2 Turbulence effects and Particle transport Martin Pietsch Computational Biomechanics Summer Term 2016 Seite 2
More informationNUMERICAL SIMULATION OF SUDDEN-EXPANSION PARTICLE-LADEN FLOWS USING THE EULERIAN LAGRANGIAN APPROACH. Borj Cedria, 2050 Hammam-Lif, Tunis.
NUMERICAL SIMULATION OF SUDDEN-EXPANSION PARTICLE-LADEN FLOWS USING THE EULERIAN LAGRANGIAN APPROACH Mohamed Ali. MERGHENI,2, Jean-Charles SAUTET 2, Hmaied BEN TICHA 3, Sassi BEN NASRALLAH 3 Centre de
More information1 Introduction to Governing Equations 2 1a Methodology... 2
Contents 1 Introduction to Governing Equations 2 1a Methodology............................ 2 2 Equation of State 2 2a Mean and Turbulent Parts...................... 3 2b Reynolds Averaging.........................
More informationBERNOULLI EQUATION. The motion of a fluid is usually extremely complex.
BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over
More informationWelcome to MECH 280. Ian A. Frigaard. Department of Mechanical Engineering, University of British Columbia. Mech 280: Frigaard
Welcome to MECH 280 Ian A. Frigaard Department of Mechanical Engineering, University of British Columbia Lectures 1 & 2: Learning goals/concepts: What is a fluid Apply continuum hypothesis Stress and viscosity
More informationOE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004
OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie
More informationInternational Journal of Scientific & Engineering Research, Volume 6, Issue 5, May ISSN
International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 28 CFD BASED HEAT TRANSFER ANALYSIS OF SOLAR AIR HEATER DUCT PROVIDED WITH ARTIFICIAL ROUGHNESS Vivek Rao, Dr. Ajay
More informationComputational model for particle deposition in turbulent gas flows for CFD codes
Advanced Computational Methods and Experiments in Heat Transfer XI 135 Computational model for particle deposition in turbulent gas flows for CFD codes M. C. Paz, J. Porteiro, A. Eirís & E. Suárez CFD
More informationCFD simulation of gas solid bubbling fluidized bed: an extensive assessment of drag models
Computational Methods in Multiphase Flow IV 51 CFD simulation of gas solid bubbling fluidized bed: an extensive assessment of drag models N. Mahinpey 1, F. Vejahati 1 & N. Ellis 2 1 Environmental Systems
More informationarxiv: v1 [physics.flu-dyn] 16 Nov 2018
Turbulence collapses at a threshold particle loading in a dilute particle-gas suspension. V. Kumaran, 1 P. Muramalla, 2 A. Tyagi, 1 and P. S. Goswami 2 arxiv:1811.06694v1 [physics.flu-dyn] 16 Nov 2018
More informationProbability density function (PDF) methods 1,2 belong to the broader family of statistical approaches
Joint probability density function modeling of velocity and scalar in turbulence with unstructured grids arxiv:6.59v [physics.flu-dyn] Jun J. Bakosi, P. Franzese and Z. Boybeyi George Mason University,
More informationBefore 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 information1 One-dimensional analysis
One-dimensional analysis. Introduction The simplest models for gas liquid flow systems are ones for which the velocity is uniform over a cross-section and unidirectional. This includes flows in a long
More informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 19 Turbulent Flows Fausto Arpino f.arpino@unicas.it Introduction All the flows encountered in the engineering practice become unstable
More informationChapter 9: Differential Analysis of Fluid Flow
of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known
More informationModeling of dispersed phase by Lagrangian approach in Fluent
Lappeenranta University of Technology From the SelectedWorks of Kari Myöhänen 2008 Modeling of dispersed phase by Lagrangian approach in Fluent Kari Myöhänen Available at: https://works.bepress.com/kari_myohanen/5/
More informationLecture 9 Laminar Diffusion Flame Configurations
Lecture 9 Laminar Diffusion Flame Configurations 9.-1 Different Flame Geometries and Single Droplet Burning Solutions for the velocities and the mixture fraction fields for some typical laminar flame configurations.
More informationCOMPUTATIONAL STUDY OF PARTICLE/LIQUID FLOWS IN CURVED/COILED MEMBRANE SYSTEMS
COMPUTATIONAL STUDY OF PARTICLE/LIQUID FLOWS IN CURVED/COILED MEMBRANE SYSTEMS Prashant Tiwari 1, Steven P. Antal 1,2, Michael Z. Podowski 1,2 * 1 Department of Mechanical, Aerospace and Nuclear Engineering,
More informationChapter 2 Mass Transfer Coefficient
Chapter 2 Mass Transfer Coefficient 2.1 Introduction The analysis reported in the previous chapter allows to describe the concentration profile and the mass fluxes of components in a mixture by solving
More informationLIQUID FILM THICKNESS OF OSCILLATING FLOW IN A MICRO TUBE
Proceedings of the ASME/JSME 2011 8th Thermal Engineering Joint Conference AJTEC2011 March 13-17, 2011, Honolulu, Hawaii, USA AJTEC2011-44190 LIQUID FILM THICKNESS OF OSCILLATING FLOW IN A MICRO TUBE Youngbae
More informationLecture 30 Review of Fluid Flow and Heat Transfer
Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in
More informationLaplace 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 informationPrediction of Minimum Fluidisation Velocity Using a CFD-PBM Coupled Model in an Industrial Gas Phase Polymerisation Reactor
Journal of Engineering Science, Vol. 10, 95 105, 2014 Prediction of Minimum Fluidisation Velocity Using a CFD-PBM Coupled Model in an Industrial Gas Phase Polymerisation Reactor Vahid Akbari and Mohd.
More informationLecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)
Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) The ABL, though turbulent, is not homogeneous, and a critical role of turbulence is transport and mixing of air properties, especially in the
More informationLiquid Metal Flow Control Simulation at Liquid Metal Experiment
Modestov DOI:10.1088/1741-4326/aa8bf4 FIP/P4-38 Liquid Metal Flow Control Simulation at Liquid Metal Experiment M. Modestov 1,2, E. Kolemen 3, E. P. Gilson 3, J. A. Hinojosa 1, H. Ji 3, R. P. Majeski 3,
More information