Characterising the Heat and Mass Transfer Coefficients for a Crossflow
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Laws of Similarity in Fluid Mechanics 21
Laws of similarity in fluid mechanics B. Weigand1 & V. Simon2 1Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart, Germany. 2Isringhausen GmbH & Co KG, Lemgo, Germany. Abstract All processes, in nature as well as in technical systems, can be described by fundamental equations—the conservation equations. These equations can be derived using conservation princi- ples and have to be solved for the situation under consideration. This can be done without explicitly investigating the dimensions of the quantities involved. However, an important consideration in all equations used in fluid mechanics and thermodynamics is dimensional homogeneity. One can use the idea of dimensional consistency in order to group variables together into dimensionless parameters which are less numerous than the original variables. This method is known as dimen- sional analysis. This paper starts with a discussion on dimensions and about the pi theorem of Buckingham. This theorem relates the number of quantities with dimensions to the number of dimensionless groups needed to describe a situation. After establishing this basic relationship between quantities with dimensions and dimensionless groups, the conservation equations for processes in fluid mechanics (Cauchy and Navier–Stokes equations, continuity equation, energy equation) are explained. By non-dimensionalizing these equations, certain dimensionless groups appear (e.g. Reynolds number, Froude number, Grashof number, Weber number, Prandtl number). The physical significance and importance of these groups are explained and the simplifications of the underlying equations for large or small dimensionless parameters are described. Finally, some examples for selected processes in nature and engineering are given to illustrate the method. 1 Introduction If we compare a small leaf with a large one, or a child with its parents, we have the feeling that a ‘similarity’ of some sort exists. -
Influence of Nusselt Number on Weight Loss During Chilling Process
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Available online at www.sciencedirect.com Procedia Engineering 32 (2012) 90 – 96 I-SEEC2011 Influence of Nusselt number on weight loss during chilling process R. Mekprayoon and C. Tangduangdee Department of Food Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, 10140, Thailand Elsevier use only: Received 30 September 2011; Revised 10 November 2011; Accepted 25 November 2011. Abstract The coupling of the heat and mass transfer occurs on foods during chilling process. The temperature of foods is reduced while weight changes with time. Chilling time and weight loss involve the operating cost and are affected by the design of refrigeration system. The aim of this work was to determine the correlations of Nu-Re-Pr and Sh-Re-Sc used to predict chilling time and weight loss, respectively for infinite cylindrical shape of food products. The correlations were obtained by estimating coefficients of heat and mass transfer based on analytical solution method and regression analysis of related dimensionless numbers. The experiments were carried out at different air velocities (0.75 to 4.3 m/s) and air temperatures (-10 to 3 ÛC) on different sizes of infinite cylindrical plasters (3.8 and 5.5 cm in diameters). The correlations were validated through experiments by measuring chilling time and weight loss of Vietnamese sausages compared with predicted values. © 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of I-SEEC2011 Open access under CC BY-NC-ND license. -
Heat Transfer in Turbulent Rayleigh-B\'Enard Convection Within Two Immiscible Fluid Layers
This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics 1 Heat transfer in turbulent Rayleigh-B´enard convection within two immiscible fluid layers Hao-Ran Liu1, Kai Leong Chong2,1, , Rui Yang1, Roberto Verzicco3,4,1 and Detlef† Lohse1,5, ‡ 1Physics of Fluids Group and Max Planck Center Twente for Complex Fluid Dynamics, MESA+Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands 2Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, PR China 3Dipartimento di Ingegneria Industriale, University of Rome “Tor Vergata”, Via del Politecnico 1, Roma 00133, Italy 4Gran Sasso Science Institute - Viale F. Crispi, 7 67100 L’Aquila, Italy 5Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 G¨ottingen, Germany (Received xx; revised xx; accepted xx) We numerically investigate turbulent Rayleigh-B´enard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number Nu) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number Ra = 108, Prandtl number Pr =4.38, and Weber number We = 5. We vary the relative thickness of the upper layer between 0.01 6 α 6 0.99 and the thermal conductivity coefficient ratio of the two liquids between 0.1 6 λk 6 10. Two flow regimes are observed: In the first regime at 0.04 6 α 6 0.96, convective flows appear in both layers and Nu is not sensitive to α. -
Heat Transfer by Impingement of Circular Free-Surface Liquid Jets
18th National & 7th ISHMT-ASME Heat and Mass Transfer Conference January 4-6, 2006 Paper No: IIT Guwahati, India Heat Transfer by Impingement of Circular Free-Surface Liquid Jets John H. Lienhard V Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge MA 02139-4307 USA email: [email protected] Abstract Q volume flow rate of jet (m3/s). 3 Qs volume flow rate of splattered liquid (m /s). 2 This paper reviews several aspects of liquid jet im- qw wall heat flux (W/m ). pingement cooling, focusing on research done in our r radius coordinate in spherical coordinates, or lab at MIT. Free surface, circular liquid jet are con- radius coordinate in cylindrical coordinates (m). sidered. Theoretical and experimental results for rh radius at which turbulence is fully developed the laminar stagnation zone are summarized. Tur- (m). bulence effects are discussed, including correlations ro radius at which viscous boundary layer reaches for the stagnation zone Nusselt number. Analyti- free surface (m). cal results for downstream heat transfer in laminar rt radius at which turbulent transition begins (m). jet impingement are discussed. Splattering of turbu- r1 radius at which thermal boundary layer reaches lent jets is also considered, including experimental re- free surface (m). sults for the splattered mass fraction, measurements Red Reynolds number of circular jet, uf d/ν. of the surface roughness of turbulent jets, and uni- T liquid temperature (K). versal equilibrium spectra for the roughness of tur- Tf temperature of incoming liquid jet (K). bulent jets. The use of jets for high heat flux cooling Tw temperature of wall (K). -
Turbulent-Prandtl-Number.Pdf
Atmospheric Research 216 (2019) 86–105 Contents lists available at ScienceDirect Atmospheric Research journal homepage: www.elsevier.com/locate/atmosres Invited review article Turbulent Prandtl number in the atmospheric boundary layer - where are we T now? ⁎ Dan Li Department of Earth and Environment, Boston University, Boston, MA 02215, USA ARTICLE INFO ABSTRACT Keywords: First-order turbulence closure schemes continue to be work-horse models for weather and climate simulations. Atmospheric boundary layer The turbulent Prandtl number, which represents the dissimilarity between turbulent transport of momentum and Cospectral budget model heat, is a key parameter in such schemes. This paper reviews recent advances in our understanding and modeling Thermal stratification of the turbulent Prandtl number in high-Reynolds number and thermally stratified atmospheric boundary layer Turbulent Prandtl number (ABL) flows. Multiple lines of evidence suggest that there are strong linkages between the mean flowproperties such as the turbulent Prandtl number in the atmospheric surface layer (ASL) and the energy spectra in the inertial subrange governed by the Kolmogorov theory. Such linkages are formalized by a recently developed cospectral budget model, which provides a unifying framework for the turbulent Prandtl number in the ASL. The model demonstrates that the stability-dependence of the turbulent Prandtl number can be essentially captured with only two phenomenological constants. The model further explains the stability- and scale-dependences -
Chapter 5 Dimensional Analysis and Similarity
Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences. -
Analysis of Mass Transfer by Jet Impingement and Heat Transfer by Convection
Analysis of Mass Transfer by Jet Impingement and Study of Heat Transfer in a Trapezoidal Microchannel by Ejiro Stephen Ojada A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering University of South Florida Major Professor: Muhammad M. Rahman, Ph.D. Frank Pyrtle, III, Ph.D. Rasim Guldiken, Ph.D. Date of Approval: November 5, 2009 Keywords: Fully-Confined Fluid, Sherwood number, Rotating Disk, Gadolinium, Heat Sink ©Copyright 2009, Ejiro Stephen Ojada i TABLE OF CONTENTS LIST OF FIGURES ii LIST OF SYMBOLS v ABSTRACT viii CHAPTER 1: INTRODUCTION AND LITERATURE REVIEW 1 1.1 Introduction (Mass Transfer by Jet Impingement ) 1 1.2 Literature Review (Mass Transfer by Jet Impingement) 2 1.3 Introduction (Heat Transfer in a Microchannel) 7 1.4 Literature Review (Heat Transfer in a Microchannel) 8 CHAPTER 2: ANALYSIS OF MASS TRANSFER BY JET IMPINGEMENT 15 2.1 Mathematical Model 15 2.2 Numerical Simulation 19 2.3 Results and Discussion 21 CHAPTER 3: ANALYSIS OF HEAT TRANSFER IN A TRAPEZOIDAL MICROCHANNEL 42 3.1 Modeling and Simulation 42 3.2 Results and Discussion 48 CHAPTER 4: CONCLUSION 65 REFERENCES 67 APPENDICES 79 Appendix A: FIDAP Code for Analysis of Mass Transfer by Jet Impingement 80 Appendix B: FIDAP Code for Fluid Flow and Heat Transfer in a Composite Trapezoidal Microchannel 86 i LIST OF FIGURES Figure 2.1a Confined liquid jet impingement between a rotating disk and an impingement plate, two-dimensional schematic. 18 Figure 2.1b Confined liquid jet impingement between a rotating disk and an impingement plate, three-dimensional schematic. -
Stability of Swirling Flow in Passive Cyclonic Separator in Microgravity
STABILITY OF SWIRLING FLOW IN PASSIVE CYCLONIC SEPARATOR IN MICROGRAVITY by ADEL OMAR KHARRAZ Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Advisor: Dr. Y. Kamotani Department of Mechanical and Aerospace Engineering CASE WESTERN RESERVE UNIVERSITY January, 2018 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis dissertation of Adel Omar Kharraz candidate for the degree of Doctor of Philosophy*. Committee Chair Yasuhiro Kamotani Committee Member Jaikrishnan Kadambi Committee Member Paul Barnhart Committee Member Beverly Saylor Date of Defense July 24, 2017 *We also certify that written approval has been obtained for any proprietary material contained therein. ii Dedication This is for my parents, my wife, and my children. iii Table of Contents Dedication …………………………………………………..…………………………………………………….. iii Table of Contents ………………………………………..…………………………………………………….. iv List of Tables ……………………………………………………………………………………………………… vi List of Figures ……………………………………………………………………………………..……………… vii Nomenclature ………………………………………………………………………………..………………….. xi Acknowledgments ……………………………………………………………………….……………………. xv Abstract ……………………………………………….……………………………………………………………. xvi Chapter 1 Introduction ……………………………………………….…………………………………….. 1 1.1 Phase Separation Significance in Microgravity ……………………………………..…. 1 1.2 Effect of Microgravity on Passive Cyclonic Separators …………………………….. 3 1.3 Free Surface (Interface) in Microgravity Environment ……………………….……. 5 1.4 CWRU Separator …………………………………………………….………………………………. -
Turbulence, Entropy and Dynamics
TURBULENCE, ENTROPY AND DYNAMICS Lecture Notes, UPC 2014 Jose M. Redondo Contents 1 Turbulence 1 1.1 Features ................................................ 2 1.2 Examples of turbulence ........................................ 3 1.3 Heat and momentum transfer ..................................... 4 1.4 Kolmogorov’s theory of 1941 ..................................... 4 1.5 See also ................................................ 6 1.6 References and notes ......................................... 6 1.7 Further reading ............................................ 7 1.7.1 General ............................................ 7 1.7.2 Original scientific research papers and classic monographs .................. 7 1.8 External links ............................................. 7 2 Turbulence modeling 8 2.1 Closure problem ............................................ 8 2.2 Eddy viscosity ............................................. 8 2.3 Prandtl’s mixing-length concept .................................... 8 2.4 Smagorinsky model for the sub-grid scale eddy viscosity ....................... 8 2.5 Spalart–Allmaras, k–ε and k–ω models ................................ 9 2.6 Common models ........................................... 9 2.7 References ............................................... 9 2.7.1 Notes ............................................. 9 2.7.2 Other ............................................. 9 3 Reynolds stress equation model 10 3.1 Production term ............................................ 10 3.2 Pressure-strain interactions -
Huq, P. and E.J. Stewart, 2008. Measurements and Analysis of the Turbulent Schmidt Number in Density
GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L23604, doi:10.1029/2008GL036056, 2008 Measurements and analysis of the turbulent Schmidt number in density stratified turbulence Pablo Huq1 and Edward J. Stewart2 Received 18 September 2008; revised 27 October 2008; accepted 3 November 2008; published 3 December 2008. [1] Results are reported of measurements of the turbulent where rw is the buoyancy flux, uw is the Reynolds shear Schmidt number Sct in a stably stratified water tunnel stress. The ratio Km/Kr is termed the turbulent Schmidt experiment. Sct values varied with two parameters: number Sct (rather than turbulent Prandtl number) as Richardson number, Ri, and ratio of time scales, T*, of salinity gradients in water are used for stratification in the eddy turnover and eddy advection from the source of experiments. Prescription of a functional dependence of Sct turbulence generation. For large values (T* 10) values on Ri = N2/S2 is a turbulence closure scheme [Kantha and of Sct approach those of neutral stratification (Sct 1). In Clayson, 2000]. Here the buoyancy frequency N is defined 2 contrast for small values (T* 1) values of Sct increase by the gradient of density r as N =(Àg/ro)(dr/dz), and g is with Ri. The variation of Sct with T* explains the large the gravitational acceleration. S =dU/dz is the velocity scatter of Sct values observed in atmospheric and oceanic shear. Analyses of field, lab and numerical (RANS, DNS data sets as a range of values of T* occur at any given Ri. and LES) data sets have led to the consensus that Sct The dependence of Sct values on advective processes increases with Ri [see Esau and Grachev, 2007, and upstream of the measurement location complicates the references therein]. -
A Review of Models for Bubble Clusters in Cavitating Flows Daniel Fuster
A review of models for bubble clusters in cavitating flows Daniel Fuster To cite this version: Daniel Fuster. A review of models for bubble clusters in cavitating flows. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2018, 10.1007/s10494-018-9993-4. hal-01913039 HAL Id: hal-01913039 https://hal.sorbonne-universite.fr/hal-01913039 Submitted on 5 Nov 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Journal of Flow Turbulence and Combustion manuscript No. (will be inserted by the editor) D. Fuster A review of models for bubble clusters in cavitating flows Received: date / Accepted: date Abstract This paper reviews the various modeling strategies adopted in the literature to capture the response of bubble clusters to pressure changes. The first part is focused on the strategies adopted to model and simulate the response of individual bubbles to external pressure variations discussing the relevance of the various mechanisms triggered by the appearance and later collapse of bubbles. In the second part we review available models proposed for large scale bubbly flows used in different contexts including hydrodynamic cavitation, sound propagation, ultrasonic devices and shockwave induced cav- itation processes. -
Numerical Analysis of Droplet and Filament Deformation For
NUMERICAL ANALYSIS OF DROPLET AND FILAMENT DEFORMATION FOR PRINTING PROCESS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Muhammad Noman Hasan August, 2014 NUMERICAL ANALYSIS OF DROPLET AND FILAMENT DEFORMATION FOR PRINTING PROCESS Muhammad Noman Hasan Thesis Approved: Accepted: _____________________________ _____________________________ Advisor Department Chair Dr. Jae–Won Choi Dr. Sergio Felicelli _____________________________ _____________________________ Committee Member Dean of the College Dr. Abhilash J. Chandy Dr. George K. Haritos _____________________________ _____________________________ Committee Member Dean of the Graduate School Dr. Chang Ye Dr. George R. Newkome _____________________________ Date ii ABSTRACT Numerical analysis for two dimensional case of two–phase fluid flow has been carried out to investigate the impact, deformation of (i) droplets and (ii) filament for printing processes. The objective of this research is to study the phenomenon of liquid droplet and filament impact on a rigid substrate, during various manufacturing processes such as jetting technology, inkjet printing and direct-printing. This study focuses on the analysis of interface capturing and the change of shape for droplets (jetting technology) and filaments (direct-printing) being dispensed during the processes. For the investigation, computational models have been developed for (i) droplet and (ii) filament deformation which implements quadtree spatial discretization based adaptive mesh refinement with geometrical Volume–Of–Fluid (VOF) for the representation of the interface, continuum– surface–force (CSF) model for surface tension formulation, and height-function (HF) curvature estimation for interface capturing during the impact and deformation of droplets and filaments. An open source finite volume code, Gerris Flow Solver, has been used for developing the computational models.