DOCSLIB.ORG

Numerical and Experimental Studies of a Double- Pipe

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Numerical and Experimental Studies of a Double- Pipe NUMERICAL AND EXPERIMENTAL STUDIES OF A DOUBLE­ PIPE HELICAL HEAT EXCHANGER Timothy J. Rennie Department of Bioresource Engineering McGill University, Montreal Suhmitted August 2004 A thesis suhmitted to McGill University in partial fulfillment of the requirements of the degree of Doctor of Philosophy © Timothy J. Rennie, 2004 Library and Bibliothèque et 1+1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de l'édition 395 Wellington Street 395, rue Wellington Ottawa ON K1A ON4 Ottawa ON K1A ON4 Canada Canada Your file Votre référence ISBN: 0-494-12936-0 Our file Notre référence ISBN: 0-494-12936-0 NOTICE: AVIS: The author has granted a non­ L'auteur a accordé une licence non exclusive exclusive license allowing Library permettant à la Bibliothèque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par télécommunication ou par l'Internet, prêter, telecommunication or on the Internet, distribuer et vendre des thèses partout dans loan, distribute and sell th es es le monde, à des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, électronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriété du droit d'auteur ownership and moral rights in et des droits moraux qui protège cette thèse. this thesis. Neither the thesis Ni la thèse ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent être imprimés ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission. ln compliance with the Canadian Conformément à la loi canadienne Privacy Act some supporting sur la protection de la vie privée, forms may have been removed quelques formulaires secondaires from this thesis. ont été enlevés de cette thèse. While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. ••• Canada ABSTRACT A double-pipe helical heat exchanger was studied numerically and experimentally for both heat transfer and hydrodynamic characteristics. Numerical studies were performed with the aid of a commercial computational fluid dynamics package. Two sizes of the heat exchanger were investigated; the difference between the two was the diameter of the inner tube. Simulations were performed using various flow rates (laminar regime) in the inner tube and in the annulus, as weIl as for parallel flowand counterflow. The results of the Nusselt number in the inner tube were compared to similar experiments reported in the literature. A second study used the same numerical model; however several Prandtl numbers were used by varying the thermal conductivity of the fluid. Furthermore, the effects of thermally dependent thermal conductivities on the heat transfer characteristics were investigated. A third numerical study was performed using thermally dependent viscosities and non-Newtonian fluids. The objective was to determine the effects ofthese fluid properties on the heat transfer and pressure drop in the heat exchanger. The final numerical study involved the determination of the uniformity of the residence time and temperature distributions, as weIl as the heatinglcooling uniformity. A method was developed based on the concept of thermal kill to estimate the heatinglcooling uniformity. Two physical models of the heat exchanger were designed, built, and instrumented for temperature measurements. Inlet and outlet temperatures were measured for a range of laminar flow velocities. Both parallel flow and counterflow configurations were tested. Overall heat transfer coefficients and Nusselt numbers were calculated and compared to the numerical results and to literature data. Results from the numerical trials show that the inner Nusselt numbers in the heat exchanger were similar to literature data, despite the different boundary conditions. Nusselt numbers in the annulus were correlated to a modified Dean number. It was shown that the thermal resistance in the annulus to be the greatest limiting factor for the heat transfer, and heat transfer rates could be increased by increasing the inner tube diameter. 11 The Prandtl number was shown to affect the inner Nusselt number; however the effects were much greater at low Dean numbers. These differences were attributed to the difference in the developing thermal and hydrodynamic boundary layers. The studies with the thermally dependent thermal conductivities showed that the Nusselt number correlated well with a modified Graetz number. Thermally dependent viscosity had little effect on the heat transfer; however it affected the pressure drop. Furthermore, it was shown that by keeping the flow rate in the inner tube or the annulus constant, the pressure drop in that section can be affected by changes in the flow rate in the opposite section, due to the change in the heat transfer rate and hence the average temperature and viscosity of the fluid. Non-Newtonian fluids showed little effect on the heat transfer rates, though they significantly affected the pressure drop relations. The uniformity of the residence time and the temperature distribution were both increased in the inner tube with increasing flow rates. It was shown that a smaller gap size in the annulus resulted in more uniform residence times. Temperature distributions in the inner tube and the annulus were affected by changes in the flow velocity in the opposite section, with lower flow rates resulting in more uniform temperature distributions. Implications of using parallel flow versus counterflow, heating versus cooling, and flow rate are discussed. Overall heat transfer coefficients and Nusselt numbers were calculated for the experimental data. The inner and annulus heat transfer coefficients were determined using Wilson plots. The results were compared to the numerical data and literature values and showed reasonable agreement. III RÉSUMÉ Un échangeur de chaleur hélicoïdal à double tubes a été étudié de façons numérique et expérimentale tant pour ses caractéristiques hydrodynamiques que de transfert de chaleur. Les études numériques ont été conduites à l'aide d'un logiciel commercial numérique de dynamique des fluides. Deux échangeurs de chaleur ont été étudiés, la différence entre les deux étant le diamètre du tube intérieur. Des simulations ont été pratiquées utilisant divers débits (régime laminaire) dans le tube interne et dans le tube annulaire, ainsi que pour un courant parallèle ou opposé. Les résultats du nombre de Nusselt dans le tube interne ont été comparés à des expériences similaires présentées dans la littérature. Une deuxième étude a été conduite utilisant le même modèle numérique; toutefois, plusieurs nombres de Prandtl ont été utilisés, en variant la conductivité thermique du fluide. De plus, les effets des conductivités thermiques, dépendantes de la terp-pérature, sur les caractéristiques de transfert de la chaleur ont été étudiées. Une troisième étude numérique a été conduite utilisant des viscosités dépendantes de la température et des fluides non Newtoniens. L'objectif était de déterminer les effets des propriétés de ces fluides sur le transfert de chaleur et sur la chute de pression dans l'échangeur de chaleur. L'étude numérique finale impliquait la détermination de l'uniformité du temps de résidence et la distribution de la température, ainsi que l'uniformité du réchauffement/refroidissement. Une méthode a été développée basée sur le concept de destruction thermique pour estimer l'uniformité du réchauffement. Deux modèles physiques d'échangeur de chaleur ont été construits et instrumentés pour mesurer la température. Les températures à l'entrée et à la sortie ont été mesurées pour un intervalle de vitesse de débits laminaires. Les configurations de courant parallèle et opposé ont toutes deux été testées. Les coefficients de transfert de chaleur et les nombres de Nusselt ont été calculés et comparés aux résultats numériques et aux données de la littérature. Les résultats des essais numériques démontrent que le nombre Nusselt interne dans l'échangeur de chaleur était similaire aux données de la littérature, malgré les différentes conditions aux limites. Les nombres de Nusselt dans le tube annulaire étaient corrélés à un nombre de Dean modifié. TI a été démontré que la résistance thermique dans IV le tube annulaire était le plus grand facteur limitant pour le transfert de chaleur et que les taux de transfert de chaleur pouvaient être accrus en augmentant le diamètre du tube interne. Il a aussi été démontré que le nombre de Prandtl affectait le nombre de Nusselt dans le tube intérieur; toutefois, les effets étaient plus bien importants lorsque le nombre de Dean était petit. Ces différences ont été attribuées à la différence dans le développement thermal et aux conditions aux limites hydrodynamiques. Les études avec les conductivités thermiques dépendantes de la température démontraient que le nombre de Nusselt avait une bonne corrélation avec un nombre de Graetz modifié. La viscosité dépendante de la température avait peu d'effet sur le transfert de chaleur; toutefois, elle affectait la chute de pression. De plus, il a été démontré qu'en gardant un débit constant dans le tube
Load more

Recommended publications
  • Static Mixing Spacers for Spiral Wound Modules
    Desalination and Water Purification Research and Development Program Report No. 161 Static Mixing Spacers for Spiral Wound Modules U.S. Department of the Interior Bureau of Reclamation Technical Service Center Denver, Colorado November 2012 Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To) November 2012 Final 2010-2012 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Static Mixing Spacers for Spiral Wound Modules Agreement No.R10AP81213 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER Glenn Lipscomb 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Chemical Engineering Task Identification Number University of Toledo Task IV: Expanding Scientific 3048 Nitschke Hall (MS 305) Understanding of Desalination Processes 1610 N Westwood Ave Subtask: Increase of rates of mass transfer Toledo, OH 43607 to membrane or to heat transfer surfaces.
    [Show full text]
  • Experimental Heat Transfer and Friction Factor of Fe3o4 Magnetic Nanofluids Flow in a Tube Under Laminar Flow at High Prandtl Numbers
    International Journal of Heat and Technology Vol. 38, No. 2, June, 2020, pp. 301-313 Journal homepage: http://iieta.org/journals/ijht Experimental Heat Transfer and Friction Factor of Fe3O4 Magnetic Nanofluids Flow in a Tube under Laminar Flow at High Prandtl Numbers Lingala Syam Sundar1*, Hailu Misganaw Abebaw2, Manoj K. Singh3, António M.B. Pereira1, António C.M. Sousa1 1 Centre for Mechanical Technology and Automation (TEMA–UA), Department of Mechanical Engineering, University of Aveiro, Aveiro 3810-131, Portugal 2 Department of Mechanical Engineering, University of Gondar, Gondar, Ethiopia 3 Department of Physics – School of Engineering and Technology (SOET), Central University of Haryana, Haryana 123031, India Corresponding Author Email: [email protected] https://doi.org/10.18280/ijht.380204 ABSTRACT Received: 15 February 2020 The work is focused on the estimation of convective heat transfer and friction factor of Accepted: 23 April 2020 vacuum pump oil/Fe3O4 magnetic nanofluids flow in a tube under laminar flow at high Prandtl numbers experimentally. The thermophysical properties also studied Keywords: experimentally at different particle concentrations and temperatures. The Fe3O4 heat transfer enhancement, friction factor, nanoparticles were synthesized using the chemical reaction method and characterized using laminar flow, high Prandtl number, magnetic X-ray powder diffraction (XRD) and vibrating sample magnetometer (VSM) techniques. nanofluid The experiments were conducted at mass flow rate from 0.04 kg/s to 0.208 kg/s, volume concentration from 0.05% to 0.5%, Prandtl numbers from 440 to 2534 and Graetz numbers from 500 to 3000. The results reveal that, the thermal conductivity and viscosity enhancements are 9% and 1.75-times for 0.5 vol.
    [Show full text]
  • Effect of Dean Number on Heating Transfer Coefficients in an Flat Bottom Agitated Vessel
    IOSR Journal of Engineering May. 2012, Vol. 2(5) pp: 945-951 Effect of Dean Number on Heating Transfer Coefficients in an Flat Bottom Agitated Vessel 1*Ashok Reddy K 2 Bhagvanth Rao M 3 Ram Reddy P 1*..Professor Dept. of Mechanical Engineering ,Prof Rama Reddy College of Engineering & Technology Nandigoan(V) Pantacheru(M) Greater Hyderabad A P 2. Director CVSR College of Engineering Ghatkesar(M) R R Dist A P 3 .Director Malla Reddy College of Engineering Hyderbad A P ABSTRACT Experimental work has been reviewed using non- Newtonian and Newtonian fluids like Sodium Carboxymethal Cellulose with varying concentrations 0.05%,0.1%,0.15% and 0.2% with two different lengths (L=2.82m,L=2.362m) and outer diameter do=6.4mm,inner diameter di=4.0mm in an mixing vessel completely submerged helical coil. In our present study, the effect impeller speed, discharge ,flow behavior index(n) and consistency index (K) of test fluids with dimensionless curvature of the helical coil based on characteristic diameter were presented.. Keywords: Dean Number, Curvature, Heating Rates, Agitated Vessel I. Introduction To improve the performance of heat transfer rates, the fundamental aspect of flow patterns is an essential and important criteria in the helical coil design theory. The helical coil silent features consists of a inner diameter di and mean coil diameter Dm which is also known as pitch circle diameter of the coil. The ratio of coil pipe diameter to the mean coil diameter is known as dimensionless curvature .The ratio of pitch of the helical coil to the developed length of one turn is called non dimensional pitch .The angle which makes with plane geometry perpendicular to the axis of the one turn of the coil dimensions ic defined as helix angle.
    [Show full text]
  • Introduction to Biofluid Mechanics Portonovo S
    To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd. It is not allowed to publish this proof online or in print. This proof copy is the copyright property of the publisher and is confidential until formal publication. CHAPTER 16 Introduction to Biofluid Mechanics Portonovo S. Ayyaswamy OUTLINE 16.1 Introduction e2 Exercises e71 16.2 The Circulatory System in the Acknowledgments e72 Human Body e2 Literature Cited e72 16.3 Modeling of Flow in Blood Vessels e18 Supplemental Reading e73 16.4 Introduction to the Fluid Mechanics of Plants e65 CHAPTER OBJECTIVES • To properly introduce the subject of biofluid • To review the parametric impact of the prop- mechanics including the necessary language erties of rigid, flexible, branched, and curved fl • To describe the components of the human cir- tubes on blood ow culation system and document their nominal • To provide an overview of fluid transport in characteristics plants • To present analytical results of relevant models of steady and pulsatile blood flow Fluid Mechanics http://dx.doi.org/10.1016/B978-0-12-405935-1.00016-2 e1 Copyright © 2016 Elsevier Inc. All rights reserved. To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd. It is not allowed to publish this proof online or in print.
    [Show full text]
  • Exact Solution of Boundary Value Problem Describing the Convective Heat Transfer in Fully-Developed Laminar Flow Through a Circular Conduit
    Songklanakarin J. Sci. Technol. 40 (4), 840-853, Jul - Aug. 2018 Original Article Exact solution of boundary value problem describing the convective heat transfer in fully-developed laminar flow through a circular conduit Ali Belhocine1* and Wan Zaidi Wan Omar2 1Faculty of Mechanical Engineering, University of Sciences and the Technology of Oran, L. P. 1505 El – Mnaouer, Oran, 31000 Algeria 2Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, UTM Skudai, Johor, 81310 Malaysia Received: 17 September 2016; Revised: 2 March 2017; Accepted: 8 May 2017 Abstract This paper proposes anexact solution in terms of an infinite series to the classical Graetz problem represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages are elaborated to reach the solution of the Graetz problem. MATLAB was used to compute the eigenvalues of the differential equation as well as the coefficient series. However, both the Nusselt number as an infinite series solution and the Graetz number are based on the heat transfer coefficient and the heat flux from the wall to the fluid. In addition, the analytical solution was compared to the numerical values obtained by the same author using a FORTRAN program, showing that the orthogonal collocation method gave better results. It is important to note that the analytical solution is in good agreement with published numerical data. Keywords:
    [Show full text]
  • Heat Transfer Data
    Appendix A HEAT TRANSFER DATA This appendix contains data for use with problems in the text. Data have been gathered from various primary sources and text compilations as listed in the references. Emphasis is on presentation of the data in a manner suitable for computerized database manipulation. Properties of solids at room temperature are provided in a common framework. Parameters can be compared directly. Upon entrance into a database program, data can be sorted, for example, by rank order of thermal conductivity. Gases, liquids, and liquid metals are treated in a common way. Attention is given to providing properties at common temperatures (although some materials are provided with more detail than others). In addition, where numbers are multiplied by a factor of a power of 10 for display (as with viscosity) that same power is used for all materials for ease of comparison. For gases, coefficients of expansion are taken as the reciprocal of absolute temper­ ature in degrees kelvin. For liquids, actual values are used. For liquid metals, the first temperature entry corresponds to the melting point. The reader should note that there can be considerable variation in properties for classes of materials, especially for commercial products that may vary in composition from vendor to vendor, and natural materials (e.g., soil) for which variation in composition is expected. In addition, the reader may note some variations in quoted properties of common materials in different compilations. Thus, at the time the reader enters into serious profes­ sional work, he or she may find it advantageous to verify that data used correspond to the specific materials being used and are up to date.
    [Show full text]
  • Extended Stokes Series for Dean Flow in Weakly Curved Pipes
    EXTENDED STOKES SERIES FOR DEAN FLOW IN WEAKLY CURVED PIPES A thesis presented for the degree of Doctor of Philosophy of Imperial College by Florencia Amalia Tettamanti Department of Mathematics Imperial College 180 Queen’s Gate, London SW7 2BZ June 24, 2012 2 I certify that this thesis, and the research to which it refers, are the product of my own work, and that any ideas or quotations from the work of other people, published or otherwise, are fully acknowledged in accordance with the standard referencing practices of the discipline. Signed: 3 Copyright Copyright in text of this thesis rests with the Author. Copies (by any process) either in full, or of extracts, may be made only in accordance with instructions given by the Author and lodged in the doctorate thesis archive of the college central library. Details may be obtained from the Librarian. This page must form part of any such copies made. Further copies (by any process) of copies made in accordance with such instructions may not be made without the permission (in writing) of the Author. The ownership of any intellectual property rights which may be described in this thesis is vested in Imperial College, subject to any prior agreement to the contrary, and may not be made available for use by third parties without the written permission of the University, which will prescribe the terms and conditions of any such agreement. Further information on the conditions under which disclosures and exploitation may take place is available from the Imperial College registry. 4 5 Abstract This thesis considers steady, fully-developed flows through weakly curved pipes using the extended Stokes series method.
    [Show full text]
  • (English Edition) a Review on the Flow Instability of Nanofluids
    Appl. Math. Mech. -Engl. Ed., 40(9), 1227–1238 (2019) Applied Mathematics and Mechanics (English Edition) https://doi.org/10.1007/s10483-019-2521-9 A review on the flow instability of nanofluids∗ Jianzhong LIN†, Hailin YANG Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China (Received Mar. 22, 2019 / Revised May 6, 2019) Abstract Nanofluid flow occurs in extensive applications, and hence has received widespread attention. The transition of nanofluids from laminar to turbulent flow is an important issue because of the differences in pressure drop and heat transfer between laminar and turbulent flow. Nanofluids will become unstable when they depart from the thermal equilibrium or dynamic equilibrium state. This paper conducts a brief review of research on the flow instability of nanofluids, including hydrodynamic instability and thermal instability. Some open questions on the subject are also identified. Key words nanofluid, thermal instability, hydrodynamic instability, review Chinese Library Classification O358, O359 2010 Mathematics Subject Classification 76E09, 76T20 1 Introduction Nanofluids have aroused significant interest over the past few decades for their wide applica- tions in energy, machinery, transportation, and healthcare. For example, low concentration of particles causes viscosity changes[1–2], decreases viscosity with increasing shear rate[3], changes friction factors and pressure drops[4–6], and improves heat transfer[7–9]. Moreover, the unique flow properties of nanofluids are determined by the flow pattern. Heat transfer[10] and pressure drop[11] are also much lower and higher, respectively, in laminar flow than in turbulent flow. By adding particles to the fluid, the thermal entropy generation and friction are of the same order of magnitude as in turbulent flow, while the effect of heat transfer entropy generation strongly outweighs that of the friction entropy generation in laminar flow.
    [Show full text]
  • Blood Flow in Arteries
    November 8, 1996 13:58 Annual Reviews KUTEXT.DOC AR23-12 Annu. Rev. Fluid Mech. 1997. 29:399–434 Copyright c 1997 by Annual Reviews Inc. All rights reserved BLOOD FLOW IN ARTERIES David N. Ku G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405 ABSTRACT Blood flow in arteries is dominated by unsteady flow phenomena. The cardiovas- cular system is an internal flow loop with multiple branches in which a complex liquid circulates. A nondimensional frequency parameter, the Womersley num- ber, governs the relationship between the unsteady and viscous forces. Normal arterial flow is laminar with secondary flows generated at curves and branches. The arteries are living organs that can adapt to and change with the varying hemo- dynamic conditions. In certain circumstances, unusual hemodynamic conditions create an abnormal biological response. Velocity profile skewing can create pock- ets in which the direction of the wall shear stress oscillates. Atherosclerotic dis- ease tends to be localized in these sites and results in a narrowing of the artery lumen—a stenosis. The stenosis can cause turbulence and reduce flow by means of viscous head losses and flow choking. Very high shear stresses near the throat of the stenosis can activate platelets and thereby induce thrombosis, which can totally block blood flow to the heart or brain. Detection and quantification of by CAPES on 04/01/09. For personal use only. stenosis serve as the basis for surgical intervention. In the future, the study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow.
    [Show full text]
  • Secondary Flow Structures Under Stent-Induced Perturbations for Cardiovascular Flow in a Curved Artery Model
    SECONDARY FLOW STRUCTURES UNDER STENT-INDUCED PERTURBATIONS FOR CARDIOVASCULAR FLOW IN A CURVED ARTERY MODEL Autumn L. Glenn, Kartik V. Bulusu, and Michael W. Plesniak Department of Mechanical and Aerospace Engineering The George Washington University 801 22 nd Street, N.W, Washington, D.C. 20052 [email protected] Fangjun Shu Department of Mechanical and Aerospace Engineering New Mexico State University MSC 3450, P.O. Box 30001, Las Cruces, NM 88003-8001 [email protected] ABSTRACT by the complex geometry and inherent forcing functions, as Secondary flows within curved arteries with unsteady well as changes due to disease. Strong evidence linking forcing are well understood to result from amplified cellular biochemical response to mechanical factors such as centrifugal instabilities under steady-flow conditions and are shear stress on the endothelial cells lining the arterial wall has expected to be driven by the rapid accelerations and received considerable interest (Berger and Jou, 2000; Barakat decelerations inherent in such waveforms. They may also and Lieu, 2003; White and Frangos, 2007; Melchior and affect the function of curved arteries through pro-atherogenic Frangos, 2010). Secondary flow structures may affect the wall shear stresses, platelet residence time and other vascular wall shear stress in arteries, which is known to be closely response mechanisms. related to atherogenesis (Mallubhotla et al., 2001; Evegren et Planar PIV measurements were made under multi-harmonic al., 2010). non-zero-mean and physiological carotid artery waveforms at In curved tubes, secondary flow structures characterized various locations in a rigid bent-pipe curved artery model. by counter-rotating vortex pairs (Dean vortices) are well- Results revealed symmetric counter-rotating vortex pairs that understood to result from amplified centrifugal instabilities developed during the acceleration phases of both multi- under steady flow conditions.
    [Show full text]
  • Similitude of Forced Convection Heat Transfer of Dowtherm a and of Li2bef4 Molten Salt in Cylindrical Tubes
    Similitude of forced convection heat transfer of Dowtherm A and of Li2BeF4 molten salt in cylindrical tubes By Dajie Sun A thesis submitted in partial satisfaction of the requirements for the degree of Master of Science in Nuclear Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Prof. Per Peterson, Chair Prof. Karl van Bibber Prof. Jasmina Vujic Summer 2017 The University of California Berkeley Department of Nuclear Engineering Content Symbols ......................................................................................................................................................................................... ii Abstract .......................................................................................................................................................................................... 1 Chapter 1 Introduction ............................................................................................................................................................. 1 Chapter 2 Description of Experiments ................................................................................................................................ 4 Chapter 3 Theoretical model for data reduction ............................................................................................................. 7 Chapter 4 Fitting Method .......................................................................................................................................................
    [Show full text]
  • On Dimensionless Numbers
    chemical engineering research and design 8 6 (2008) 835–868 Contents lists available at ScienceDirect Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd Review On dimensionless numbers M.C. Ruzicka ∗ Department of Multiphase Reactors, Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Rozvojova 135, 16502 Prague, Czech Republic This contribution is dedicated to Kamil Admiral´ Wichterle, a professor of chemical engineering, who admitted to feel a bit lost in the jungle of the dimensionless numbers, in our seminar at “Za Plıhalovic´ ohradou” abstract The goal is to provide a little review on dimensionless numbers, commonly encountered in chemical engineering. Both their sources are considered: dimensional analysis and scaling of governing equations with boundary con- ditions. The numbers produced by scaling of equation are presented for transport of momentum, heat and mass. Momentum transport is considered in both single-phase and multi-phase flows. The numbers obtained are assigned the physical meaning, and their mutual relations are highlighted. Certain drawbacks of building correlations based on dimensionless numbers are pointed out. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Dimensionless numbers; Dimensional analysis; Scaling of equations; Scaling of boundary conditions; Single-phase flow; Multi-phase flow; Correlations Contents 1. Introduction .................................................................................................................
    [Show full text]