Multiphase Flow Handbook in the Liquid Static Pressure
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Multiscale Computational Fluid Dynamics
energies Review Multiscale Computational Fluid Dynamics Dimitris Drikakis 1,*, Michael Frank 2 and Gavin Tabor 3 1 Defence and Security Research Institute, University of Nicosia, Nicosia CY-2417, Cyprus 2 Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1UX, UK 3 CEMPS, University of Exeter, Harrison Building, North Park Road, Exeter EX4 4QF, UK * Correspondence: [email protected] Received: 3 July 2019; Accepted: 16 August 2019; Published: 25 August 2019 Abstract: Computational Fluid Dynamics (CFD) has numerous applications in the field of energy research, in modelling the basic physics of combustion, multiphase flow and heat transfer; and in the simulation of mechanical devices such as turbines, wind wave and tidal devices, and other devices for energy generation. With the constant increase in available computing power, the fidelity and accuracy of CFD simulations have constantly improved, and the technique is now an integral part of research and development. In the past few years, the development of multiscale methods has emerged as a topic of intensive research. The variable scales may be associated with scales of turbulence, or other physical processes which operate across a range of different scales, and often lead to spatial and temporal scales crossing the boundaries of continuum and molecular mechanics. In this paper, we present a short review of multiscale CFD frameworks with potential applications to energy problems. Keywords: multiscale; CFD; energy; turbulence; continuum fluids; molecular fluids; heat transfer 1. Introduction Almost all engineered objects are immersed in either air or water (or both), or make use of some working fluid in their operation. -
General@ Electric Space Sciences Laboratory Theoretical Fluid Physics Section
4 3 i d . GPO PRICE $ CFSTI PRICE(S) $ R65SD50 Microfiche (MF) , 7.3, We53 July85 THE STRUCTURE OF THE VISCOUS HYPERSONIC SHOCK LAYER SPACE SCIENCES LABORATORY . MISSILE AND SPACE DIVISION GENERAL@ ELECTRIC SPACE SCIENCES LABORATORY THEORETICAL FLUID PHYSICS SECTION THE STRUCTURE OF THE VISCOUS HYPERSONIC SHOCK LAYER BY L. Goldberg . Work performed for the Space Nuclear Propulsion Office, NASA, under Contract No. SNPC-29. f This report first appeared as part of Contract Report DIN: 214-228F (CRD), October 1, 1965. Permission for release of this publication for general distribution was received from SNPO on December 9, 1965. R65SD50 December, 1965 MISSILE AND SPACE DIVISION GENERAL ELECTRIC CONTENTS PAGE 1 4 I List of Figures ii ... Abstract 111 I Symbols iv I. INTRODUCTION 1 11. DISCUSSION OF THE HYPER NIC CO TTINUI 3 FLOW FIELD 111. BASIC RELATIONS 11 IV . BOUNDARY CONDITIONS 14 V. NORMALIZED SYSTEM OF EQUATIONS AND BOUNDARY 19 CONDITIONS VI. DISCUSSION OF RESULTS 24 VII. CONCLUSIONS 34 VIII. REFERENCES 35 Acknowledgements 39 Figures 40 1 LIST OF FIGURES 'I PAGE 1 1 1. Hypersonic Flight Regimes 40 'I 2. Coordinate System 41 3. Profiles Re = 15, 000 42 S 3 4. Profiles Re = 10 43 S 3 5. Profiles Re = 10 , f = -0.4 44 S W 2 6. Profiles Re = 10 45 S 2 7. Profiles Re = 10 , f = do. 4 46 S W Profiles Re = 10 47 8. s 9. Normalized Boundary Layer Correlations 48 10. Reduction in Skin Friction and Heat Transfer with Mass 49 Transfer 11. Normalized Heat Transfer 50 12. Normalized Skin Friction 51 13. -
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: Colombo, M and Fairweather, M (2015) Multiphase turbulence in bubbly flows: RANS simulations. International Journal of Multiphase Flow, 77. 222 - 243. ISSN 0301-9322 https://doi.org/10.1016/j.ijmultiphaseflow.2015.09.003 © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ 1 Multiphase turbulence in bubbly flows: RANS simulations 2 3 Marco Colombo* and Michael Fairweather 4 Institute of Particle Science and Engineering, School of Chemical and Process Engineering, 5 University of Leeds, Leeds LS2 9JT, United Kingdom 6 E-mail addresses: [email protected] (Marco Colombo); [email protected] 7 (Michael Fairweather) 8 *Corresponding Author: +44 (0) 113 343 2351 9 10 Abstract 11 12 The ability of a two-fluid Eulerian-Eulerian computational multiphase fluid dynamic model to 13 predict bubbly air-water flows is studied. -
Convective Boiling Heat Transfer and Two-Phase Flow Characteristics
International Journal of Heat and Mass Transfer 46 (2003) 4779–4788 www.elsevier.com/locate/ijhmt Convective boiling heat transfer and two-phase flow characteristics inside a small horizontal helically coiled tubing once-through steam generator Liang Zhao, Liejin Guo *, Bofeng Bai, Yucheng Hou, Ximin Zhang State Key Laboratory of Multiphase Flow in Power Engineering, XiÕan Jiaotong University, Xi’an Shaanxi 710049, China Received 15 February 2003; received in revised form 8 June 2003 Abstract The pressure drop and boiling heat transfer characteristics of steam-water two-phase flow were studied in a small horizontal helically coiled tubing once-through steam generator. The generator was constructed of a 9-mm ID 1Cr18Ni9Ti stainless steel tube with 292-mm coil diameter and 30-mm pitch. Experiments were performed in a range of steam qualities up to 0.95, system pressure 0.5–3.5 MPa, mass flux 236–943 kg/m2s and heat flux 0–900 kW/m2. A new two-phase frictional pressure drop correlation was obtained from the experimental data using ChisholmÕs B-coefficient method. The boiling heat transfer was found to be dependent on both of mass flux and heat flux. This implies that both the nucleation mechanism and the convection mechanism have the same importance to forced convective boiling heat transfer in a small horizontal helically coiled tube over the full range of steam qualities (pre-critical heat flux qualities of 0.1–0.9), which is different from the situations in larger helically coiled tube where the convection mechanism dominates at qualities typically >0.1. Traditional single parameter Lockhart–Martinelli type correlations failed to satisfactorily correlate present experimental data, and in this paper a new flow boiling heat transfer correlation was proposed to better correlate the experimental data. -
Experimental Research of Multiphase Flow with Cavitation in the Nozzle
EPJ Web of Conferences 114, 02 058 (2016 ) DOI: 10.1051/epjconf/201611004 2 58 C Owned by the authors, published by EDP Sciences, 2016 Experimental research of multiphase flow with cavitation in the nozzle Milada Kozubkova1, Marian Bojko1, Jana Jablonska1, Dorota Homa2,a and Jií T\ma3 1Department of Hydromechanics and Hydraulic Equipment, Faculty of Mechanical Engineering, VSB – Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic 2Institute of Power Engineering and Turbomachinery, Faculty of Energy and Environmental Engineering, Silesian University of Technology, Konarskiego Street 18, 44 100 Gliwice, Poland 3Department of Controls Systems and Instrumentations, Faculty of Mechanical Engineering, VSB – Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic Abstract. The paper deals with the problems of cavitation in water flow in the nozzle. The area of research is divided into two directions (experimental and numerical research). During the experimental research the equipment with the nozzle is under the measurement and basic physical quantities such as pressure and volume flow rate are recorded. In the following phase measuring of noise which is generated during flow through the nozzle in the area of cavitation is measured at various operating conditions of the pump. In the second part the appropriate multiphase mathematical model including the consideration of cavitation is defined. Boundary conditions for numerical simulation are defined on the basis of experimental measurements. Undissolved air in the flow is taken into account to obtain pressure distribution in accordance to measured one. Results of the numerical simulation are presented by means of basic current quantities such as pressure, velocity and volume fractions of each phase. -
Inertia-Less Convectively-Driven Dynamo Models in the Limit
Inertia-less convectively-driven dynamo models in the limit of low Rossby number and large Prandtl number Michael A. Calkins a,1,∗, Keith Julienb,2, Steven M. Tobiasc,3 aDepartment of Physics, University of Colorado, Boulder, CO 80309 USA bDepartment of Applied Mathematics, University of Colorado, Boulder, CO 80309 USA cDepartment of Applied Mathematics, University of Leeds, Leeds, UK LS2 9JT Abstract Compositional convection is thought to be an important energy source for magnetic field generation within planetary interiors. The Prandtl number, Pr, characterizing compositional convection is significantly larger than unity, suggesting that the inertial force may not be important on the small scales of convection as long as the buoyancy force is not too strong. We develop asymptotic dynamo models for the case of small Rossby number and large Prandtl number in which inertia is absent on the convective scale. The rele- vant diffusivity parameter for this limit is the compositional Roberts number, q = D/η, which is the ratio of compositional and magnetic diffusivities. Dy- namo models are developed for both order one q and the more geophysically relevant low q limit. For both cases the ratio of magnetic to kinetic energy densities, M, is asymptotically large and reflects the fact that Alfv´en waves have been filtered from the dynamics. Along with previous investigations of asymptotic dynamo models for Pr = O(1), our results show that the ratio M is not a useful indicator of dominant force balances in the momentum equa- tion since many different asymptotic limits of M can be obtained without changing the leading order geostrophic balance. -
Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer 1. Nusselt Number Average Nusselt Number: Nul = Convective
Jingwei Zhu http://jingweizhu.weebly.com/course-note.html Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer 1. Nusselt number Average Nusselt number: convective heat transfer ℎ퐿 Nu = = L conductive heat transfer 푘 where L is the characteristic length, k is the thermal conductivity of the fluid, h is the convective heat transfer coefficient of the fluid. Selection of the characteristic length should be in the direction of growth (or thickness) of the boundary layer; some examples of characteristic length are: the outer diameter of a cylinder in (external) cross flow (perpendicular to the cylinder axis), the length of a vertical plate undergoing natural convection, or the diameter of a sphere. For complex shapes, the length may be defined as the volume of the fluid body divided by the surface area. The thermal conductivity of the fluid is typically (but not always) evaluated at the film temperature, which for engineering purposes may be calculated as the mean-average of the bulk fluid temperature T∞ and wall surface temperature Tw. Local Nusselt number: hxx Nu = x k The length x is defined to be the distance from the surface boundary to the local point of interest. 2. Prandtl number The Prandtl number Pr is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. That is, the Prandtl number is given as: viscous diffusion rate ν Cpμ Pr = = = thermal diffusion rate α k where: ν: kinematic viscosity, ν = μ/ρ, (SI units : m²/s) k α: thermal diffusivity, α = , (SI units : m²/s) ρCp μ: dynamic viscosity, (SI units : Pa ∗ s = N ∗ s/m²) W k: thermal conductivity, (SI units : ) m∗K J C : specific heat, (SI units : ) p kg∗K ρ: density, (SI units : kg/m³). -
Experimental Study of the Fluid Drag on a Torus at Low Reynolds Number. Dharmaratne Amarakoon Louisiana State University and Agricultural & Mechanical College
Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1982 Experimental Study of the Fluid Drag on a Torus at Low Reynolds Number. Dharmaratne Amarakoon Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Amarakoon, Dharmaratne, "Experimental Study of the Fluid Drag on a Torus at Low Reynolds Number." (1982). LSU Historical Dissertations and Theses. 3743. https://digitalcommons.lsu.edu/gradschool_disstheses/3743 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality o f the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. t.The sign or “target” for pages apparently lacking from the document photographed is "Missing Page(s)” . If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. -
The Analogy Between Heat and Mass Transfer in Low Temperature Crossflow Evaporation
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by AUT Scholarly Commons The analogy between heat and mass transfer in low temperature crossflow evaporation Reza Enayatollahi*, Roy Jonathan Nates, Timothy Anderson Department of Mechanical Engineering, Auckland University of Technology, Auckland, New Zealand. Corresponding Author: Reza Enayatollahi Email Address: [email protected] Postal Address: WD308, 19 St Paul Street, Auckland CBD, Auckland, New Zealand Phone Number: +64 9 921 9999 x8109 Abstract This study experimentally determines the relationship between the heat and mass transfer, in a crossflow configuration in which a ducted airflow passes through a planar water jet. An initial exploration using the Chilton-Colburn analogy resulted in a coefficient of determination of 0.72. On this basis, a re-examination of the heat and mass transfer processes by Buckingham’s-π theorem and a least square analysis led to the proposal of a new dimensionless number referred to as the Lewis Number of Evaporation. A modified version of the Chilton-Colburn analogy incorporating the Lewis Number of Evaporation was developed leading to a coefficient of determination of 0.96. 1. Introduction Heat and mass transfer devices involving a liquid interacting with a gas flow have a wide range of applications including distillation plants, cooling towers and aeration processes and desiccant drying [1-5]. Many studies have gone through characterising the heat and mass transfer in such configurations [6-9]. The mechanisms of heat and mass transfer are similar and analogical. Therefore, in some special cases where, either the heat or mass transfer data are not reliable or may not be available, the heat and mass transfer analogy can be used to determine the missing or unreliable set of data. -
Introduction
On the use of Darcy's law and invasion‐percolation approaches for modeling large‐scale geologic carbon sequestration Curtis M. Oldenburg Sumit Mukhopadhyay Abdullah Cihan First published: 01 December 2015 https://doi.org/10.1002/ghg.1564 Cited by: 4 UC-eLinks Abstract Most large‐scale flow and transport simulations for geologic carbon sequestration (GCS) applications are carried out using simulators that solve flow equations arising from Darcy's law. Recently, the computational advantages of invasion‐percolation (IP) modeling approaches have been presented. We show that both the Darcy's‐law‐ and the gravity‐capillary balance solved by IP approaches can be derived from the same multiphase continuum momentum equation. More specifically, Darcy's law arises from assuming creeping flow with no viscous momentum transfer to stationary solid grains, while it is assumed in the IP approach that gravity and capillarity are the dominant driving forces in a quasi‐static two‐phase (or more) system. There is a long history of use of Darcy's law for large‐scale GCS simulation. However, simulations based on Darcy's law commonly include significant numerical dispersion as users employ large grid blocks to keep run times practical. In contrast, the computational simplicity of IP approaches allows large‐scale models to honor fine‐scale hydrostratigraphic details of the storage formation which makes these IP models suitable for analyzing the impact of small‐scale heterogeneities on flow. However, the lack of time‐dependence in the IP models is a significant disadvantage, while the ability of Darcy's law to simulate a range of flows from single‐phase‐ and pressure‐gradient‐driven flows to buoyant multiphase gravity‐capillary flow is a significant advantage. -
Multiphase Turbulent Flow
Multiphase Turbulent Flow Ken Kiger - UMCP Overview • Multiphase Flow Basics – General Features and Challenges – Characteristics and definitions • Conservation Equations and Modeling Approaches – Fully Resolved – Eulerian-Lagrangian – Eulerian-Eulerian • Averaging & closure – When to use what approach? • Preferential concentration • Examples • Modified instability of a Shear Layer • Sediment suspension in a turbulent channel flow • Numerical simulation example: Mesh-free methods in multiphase flow What is a multiphase flow? • In the broadest sense, it is a flow in which two or more phases of matter are dynamically interacting – Distinguish multiphase and/or multicomponent • Liquid/Gas or Gas/Liquid • Gas/Solid • Liquid/Liquid – Technically, two immiscible liquids are “multi-fluid”, but are often referred to as a “multiphase” flow due to their similarity in behavior Single component Multi-component Water Air Single phase Pure nitrogen H20+oil emulsions Steam bubble in H 0 Coal particles in air Multi-phase 2 Ice slurry Sand particle in H20 Dispersed/Interfacial • Flows are also generally categorized by distribution of the components – “separated” or “interfacial” • both fluids are more or less contiguous throughout the domain – “dispersed” • One of the fluids is dispersed as non- contiguous isolated regions within the other (continuous) phase. • The former is the “dispersed” phase, while the latter is the “carrier” phase. • One can now describe/classify the geometry of the dispersion: • Size & geometry • Volume fraction Gas-Liquid Flow -
Sedimentation of Finite-Size Spheres in Quiescent and Turbulent Environments
Under consideration for publication in J. Fluid Mech. 1 Sedimentation of finite-size spheres in quiescent and turbulent environments Walter Fornari1y, Francesco Picano2 and Luca Brandt1 1Linn´eFlow Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, SE-10044 Stockholm, Sweden 2Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padua, Italy (Received ?; revised ?; accepted ?. - To be entered by editorial office) Sedimentation of a dispersed solid phase is widely encountered in applications and envi- ronmental flows, yet little is known about the behavior of finite-size particles in homo- geneous isotropic turbulence. To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to account for the dispersed rigid spherical particles. The solid volume fractions considered are φ = 0:5 − 1%, while the solid to fluid density ratio ρp/ρf = 1:02. The par- ticle radius is chosen to be approximately 6 Komlogorov lengthscales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reduction with respect to a single particle in quiescent fluid is about 12% and 14% for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated to the intermittent fast sedimentation of particle pairs in drafting-kissing-tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable mag- nitude as a consequence of the highly intermittent behavior observed in the quiescent fluid.