DOCSLIB.ORG

A Volume-Of-Fluid Type Algorithm for Compressible Two-Phase Flows

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Volume-Of-Fluid Type Algorithm for Compressible Two-Phase Flows A VolumeOfFluid Typ e Algorithm for Compressible TwoPhase Flows KehMing Shyue Abstract We present a simple approach to the computation of a simplied twophase ow mo del involving gases and liquids separated by interfaces in multiple space dimensions In contrast to the many p opular techniques which are mainly concerned with the incompressible ow we consider a compress ible version of the mo del equations without the eect of surface tension and viscosity We use the law and the Tait equation of state for approximating the material prop erty of the gas and the liquid in a resp ective manner The algorithm uses a volumeofuid formulation of the equations together with a stiened gas equation of state that is derived to give an approximate mo del for the mixture of more than one phase of the uids within grid cells A stan dard highresolution sho ck capturing metho d based on a wavepropagation viewp oint is employed to solve the prop osed mo del We show results of some preliminary calculations that illustrate the viability of the metho d to practical application without the o ccurrence of any spurious oscillation in the pressure near the interfaces This includes results of a planar sho ck wave in water over a bubble of air Intro duction We are interested in a twophase ow problem with interfaces that separate regions of two dierent uid comp onents consisting of gases and liquids We consider a twodimensional ow as an example and use the compressible Euler equations to mo deling the motion of the gases u v 2 C C C B B B u u p uv C C C B B B 2 A A A v uv v p t x y E E pu E pv Here is the density u and v are the velo cities in the x and y direction resp ec tively p is the pressure and E is the total energy p er unit mass We assume that This work was supp orted in part by National Science Council of Republic of China Grants NSC M and NSCM KM Shyue the equation of the state for the gas satises the law where is the ratio of sp ecic heats Then the internal energy is p e 2 2 and E e u v We note that the four comp onents of Eqs express the conservation of mass momenta in the x and y direction and energy resp ec tively As it is often the case we take the liquids to b e baratropic that the pressure p is a function of the density only and in particular it fullls the Tait equation of state of the form p A B where A and B are materialdep endent constants these two parameters along with give a fundamental characterization of the uid prop erties of interest and can b e obtained from a tting pro cedure of lab oratory data Typical set of values are for water A atm and B atm and for human blo o d A MPa and B MPa approximately It is imp ortant to note that b ecause of the mere dep endency of the pressure p on the density the energy equation of the Euler Eqs plays no active role to the determination of this ow b ehavior and hence can b e neglected For completeness we write down the equations of motion for the liquid as follows u v 2 A A A u u p uv t x y 2 v uv v p where the pressure p is governed by We want to use a stateoftheart sho ckcapturing metho d on a uniform rect angular grid for the computation For convenience let us supp ose that for each grid cell we have a volumefraction function Z representing the typ e of uid within the cell For example for the liquid only cells we may take Z and therefore for the gas only cells we may set Z In case there are some cells cut by the interfaces where Z we then have b oth of the gas and liquid comp onents in the cells in which the liquid and the gas are o ccupied by the volume fractions Z and Z resp ectively It is clear that when Z or Z there is no problem in describing the motion of each of the gas and liquid ows individually see Eqs The principle problem in the current application and also in the other multicomp onent problems cf is however directed to the development of an ecient and yet accurate way that is capable of dealing with the uidmixture case when Z Motivated by the previous work by the author the algorithm we employed uses a mixture mo del based on a volumefraction or called a volume ofuid formulation of the equations that is devised to mo del the mixture of the two dierent equations of state and by the socalled stiened gas equation of state see Section Then from the energy equation of we cho ose VolumeOfFluid Algorithm for TwoPhase Flows conditions that should b e satised to ensure the pressure in equilibrium for these cells see Section Numerical results to b e presented in Section show that this is a viable approach for practical problems without any spurious oscillations in the pressure near the interfaces when we approximate the mo del equations in a consistent manner by a uctuationandsignal typ e of sho ck capturing metho d It is true that for real applications the eect of surface tension as well as viscosity are two imp ortant elements to the solutions of a twophase ow problem under studied Among many of the approaches develop ed over the years to deal with these situations cf the metho d based on the level set formulation has shown to b e quite eective for an incompressible version of the problem where the uids are mostly in a low Mach numb er regime Here in contrast to the work just mentioned we consider a class of problems where the inuence of compressibility of the uids to the solutions is vital but not the surface tension and viscosity Examples of this kind cover a family of sho ck wave problems with interfaces Our goal here is to establish a basic solution strategy for the problem cf for other approaches Realization of this approach that couples with adaptive grid pro cedures such as front tracking and adaptive mesh renement is in progress cf In a future work we will take more physical factors into account and also lo ok at metho ds that are ecient for problems with low and high Mach numb er ow where the time step restriction is an imp ortant issue to b e addressed This pap er is organized as follows In Section we remark and discuss the equations of state that are used in our mo del twophase ow problems with gases and liquids In Section we review the derivation of the mo del system based on a volumeofuid formulation of the equations Numerical results for some sample problems are shown in Section Equations of State It is known that in gases the sp ecic entropy denoted by S has great inuence to the b ehavior of the pressure p while in liquids the inuence of its changes is negligible to the pressure In fact b ecause of this little dep endency of the pressure on the entropy and a consequence of the rst law of thermo dynamics we may write the internal energy of a liquid as a separable energy of the form (1) (2) e e e S where with the Tait equation of state we nd p B (1) e From this it is easy to observe strong resemblance of the equation of state of a liquid to that of an ideal gas With this in mind it should b e sensible to use KM Shyue a generalized version of Eq namely the stiened gas equation of state p B e without the explicitly dep endence on the density to the pressure p to mo deling mixtures of the comp onents of gases and liquids within a grid cell Note that a stiened gas reduces to a law gas when B and to a baratropic gas of the form when the pressure p is indep endent of the entropy S Oftentimes the equation of state has b een used in other applications to mo del materials including compressible liquids and solids Here we nd it is suitable for the current application when combining with a twophase ow algorithm describ ed in the next section see results shown in Section for numerical verication of this statement VolumeOfFluid Algorithm We now discuss the basic idea of our approach to mo deling cells that contain b oth of the gas and liquid phases We use the Euler Eqs as a mo del system that describ es the motion of the mixtures of conserved variables such as u v and E in a gasliquid co existent grid cell Then with the use of the equation of state the pressure p in the equations can b e set by 2 2 u v B p E when the mixture of materialdep endent parameters and B are dened and known a priori It is imp ortant to note that in our approach the conditions for and B are chosen so that the pressure p in retains in equilibrium for a gas liquid mixture cell The derivation of the evolution equations for and B in the current case follows directly from pro cedures develop ed in However to make the pap er selfcontained a brief overview of this approach is undertaken b elow We b egin by considering a mo del twophase ow problem that the pressure p and the velo city eld u v are constant in the domain while the other vari ables such as the density and the equation of state parameters and B are having jumps across a gasliquid interface We write Eqs in the following nonconservative form v u u v t x y x y u p u u u v t x y x p v v v u v t x y y v u e eu ev p t x y x y VolumeOfFluid Algorithm for TwoPhase Flows and obtain easily equations describing the motion of the gasliquid interface as u v t x y e u e v e t x y To see how the pressure p would keep in equilibrium as it should b e for this mo del problem we insert the equation of state into and have p B p B p B u v t x y Then with the volumefraction function Z dened previously in Section the total
Load more

Recommended publications
  • V- T of COMPRESSED LIQUIDS at HIGH PRESSURES
    INVESTIGATION of the CORRELATIONS P- V- T of COMPRESSED LIQUIDS at HIGH PRESSURES A Thesis Submitted to the College of Engineering of Al-Nahrain University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Chemical Engineering by NOOR SABEH MAJIED AL-QAZAZ (B.Sc. in Chemical Engineering 2002) Rbee el- awal 1426 April 2005 ABSTRACT Prediction of the accurate values of molar volume of compressed liquids is very important in process design calculation and other industrial applications. Experimental measurements of molar volume V for compressed fluids are very expensive , so in order to obtain accurate V values, attention has been turned to calculate it from equation of state Alto and Kiskinen[1] equation for pure non polar component, using correlations to Tait equation for polar component, and modification of Rackett equation are used for mixtures. In this study five types of equations of state were used to calculate molar volume V for pure non polar compressed liquid, they are Alto and Kiskinen, Tait, Peng- Robinson, Soave- Redlich- Kowng, Lee- Kesler. These equations were tested against 241 experimental data points of pure non polar compressed liquids and it was found that Aalto and Kiskinen equation is the best compared with the other equations. The results of Alto and Kiskinen gives the average absolute percent deviation of 11 pure components was 0.6276. For pure polar compound using four equations of state, Soave- Redlich- Kowng, Peng- Robinson, Alto and Kiskinen, Tait. These equations were tested against 63 experimental data points of polar compressed liquids and it was found that Tait equation is the best compared with the other equations.
    [Show full text]
  • Results for Two Phase Flows with Phase Transition Results for Two Phase Flows with Phase Transition
    Results for Two Phase Flows with Phase Transition Results for Two Phase Flows with Phase Transition Dissertation zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) von Dipl.-Math. Ferdinand Thein geb. am 22:04:1986 in Magdeburg, Deutschland genehmigt durch die Fakultät für Mathematik der Otto-von-Guericke-Universität Magdeburg Gutachter: PD Dr.in Maren Hantke Prof. Dr. Christian Rohde eingereicht am: 17.01.2018 Verteidigung am: 08.05.2018 Zusammenfassung Kompressible Zweiphasenströmungen sind von großem Interesse, sowohl in vielen Anwendung wie Wasserturbinen oder der chemischen Industrie, als auch in verschiedenen Forschungsgebieten wie der Meteorologie, den Ingenieurwissenschaften oder der Physik. Wir betrachten hier Strömungen von flüssigen und gasförmigen Phasen derselben Substanz und berücksich- tigen dabei auch Phasenübergänge, d.h. Kondensation und Verdampfung. Bedingt durch die hohe Komplexität des betrachteten Problems ist es nötig Ergebnisse verschiedener Forschungsgebiete miteinander zu kombinieren, um weitere Erkenntnisse zu gewinnen. Deshalb berücksichtigen wir in die- ser Arbeit die physikalische Modellierung, die mathematische Analysis und die numerische Behandlung von Zweiphasenstömungen. Der erste Teil der Arbeit stellt die benötigten Grundlagen zur Verfügung, Teil zwei behandelt ein isothermes Modell und abschließend wird in Teil drei ein adiabates Mo- dell diskutiert. Die drei Hauptresultate dieser Arbeit sind ein allgemeines Existenzresul- tat für ein Gleichungssystem, welches isotherme Zweiphasenstömungen modelliert, eine numerische Methode zum Lösen dieser Gleichungen, wel- che auch das Entstehen von Phasen behandeln kann und ein Resultat zur Nichtexistenz von Lösungen im Fall adiabater Zweiphasenströmungen. Die Ergebnisse für den isothermen Fall werden in Teil zwei gezeigt und das Re- sultat für die Nichtexistenz in Teil drei. Um die verschiedenen Fragestellungen zu verstehen und mögliche Ant- worten zu erarbeiten, benötigen wir Resultate der Thermodynamik und ein Verständnis der beschreibenden Bilanzgleichungen.
    [Show full text]
  • Tait Equation Revisited from the Entropic and Fluctuational Points Of
    Noname manuscript No. (will be inserted by the editor) Tait equation revisited from the entropic and fluctuational points of view E.B. Postnikov · A.L. Goncharov · V.V. Melent’ev Received: date / Accepted: date Abstract We consider the possibilities for prediction of liquids’ density un- der pressure basing on the inverse reduced fluctuations parameter, which is directly connected with the isothermal compressibility. This quantity can be determined basing on the thermodynamical properties of saturated liquid and it consists of only two constant parameters within a relatively wide region close to the melting points. It is confirmed by the comparison with the experimental data on n-alkanes that the derived expression is a quite reasonable estimator without a necessity to fit data along some parts of isotherms for different tem- peratures. At the same time the obtained formula: i) can be reduced to the form of the Tait equation and ii) the resulting Tait’s parameters in this rep- resentation have a clear physical meaning as functions of the excess entropy, which determines the mentioned reduced fluctuations. Keywords Excess entropy · Tait equation · Volume fluctuations E.B. Postnikov Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000 Kursk, Russia Tel.: +7-4712-56-14-39 Fax: +7-4712-56-14-39 E-mail: [email protected] A.L. Goncharov Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000 Kursk, Russia V.V. Melent’ev Laboratory of Molecular Acoustics, Kursk State University, Radishcheva st., 33, 305000 Kursk, Russia arXiv:1406.7688v1 [cond-mat.stat-mech] 30 Jun 2014 2 E.B.
    [Show full text]
  • Pvtx Properties of Saline Aqueous Fluids at High PT Conditions From
    Research Collection Doctoral Thesis PVTx properties of saline aqueous fluids at high P-T conditions from acoustic velocity measurements using Brillouin scattering spectroscopy Author(s): Mantegazzi, Davide Publication Date: 2012 Permanent Link: https://doi.org/10.3929/ethz-a-007582357 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library DISS. ETH NO. 20358 PVTx properties of saline aqueous uids at high P-T conditions from acoustic velocity measurements using Brillouin scattering spectroscopy A dissertation submitted to ETH ZURICH for the degree of Doctor of Sciences presen ted by Davide Mantegazzi Diplom in Naturwissenschaften ETH ETH Zürich born on January 8, 1983 citizen of Riva San Vitale (TI) accepted on the recommendation of examiner Prof. Dr. C. Sanchez-Valle ETH Zurich co-examiner PD Dr. T. Driesner ETH Zurich co-examiner Prof. Dr. R.J. Bodnar Virginia Tech. (VA) co-examiner Prof. Dr. L.W. Diamond UNI Bern 2012 Abstract Saline aqueous fluids play a fundamental role in several geological processes. Despite the great importance of these fluids for the heat and mass transport i for their contribution to geodynamical cycles, their thermodynamic data are limited to low pressure conditions, typically below 0.5 GPa (ca. 15 km depth). The lack of PVTx properties for saline aqueous fluids at higher pressure considerably limits the quantitative modelling of fluid-rock interactions at pressure and t crust and the upper mantle. The goal of this study was to determine experimentally the equation of state and thermodynamic properties of several model saline aqueous fluids at elevated pressure and temperature conditions.
    [Show full text]
  • Eosfit7c and a Fortran Module (Library) for Equation of State Calculations
    DOI 10.1515/zkri-2013-1711 Z. Kristallogr. 2014; 229(5): 405–419 Ross J. Angel*, Javier Gonzalez-Platas and Matteo Alvaro EosFit7c and a Fortran module (library) for equation of state calculations Abstract: The relationship between linear elasticity theo- and expansion. Equations of state therefore provide not ry of solids and their equations of state (EoS) is reviewed, only fundamental thermodynamic data that is required, along with the commonly-used types of isothermal EoS, for example, for the calculation of equilibrium phase dia- thermal expansion models, and P-V-T EoS. A new con- grams (e.g. Berman, 1988; Gottschalk, 1997; Holland & sole program, EosFit7c, is presented. It performs EoS cal- Powell, 1998; Stixrude & Lithgow-Bertelloni, 2005; Hol- culations and fitting for both volume and linear isother- land & Powell, 2011) but also give insights in to the de- mal data, isobaric data and P-T data. Linear data is tails of interatomic interactions within the solid state, as handled by cubing the quantities and treating them as it is these that resist the externally-applied compressive volumes in all EoS formulations. Least-squares fitting of stresses (e.g. Brown, Klages & Skowron, 2003; Zhao, EoS to data incorporates the option to weight the fit with Ross & Angel, 2004; Fabbiani & Pulham, 2006) and con- the measurement uncertainties in P, V and T simulta- trol the dynamics that lead to thermal expansion (e.g. neously. The EosFit7c program is built with a new library Willis & Pryor, 1975). of subroutines for EoS calculations and manipulation, The majority of equation of state studies measure the written in Fortran.
    [Show full text]
  • Experimental Determination and Equation of State Modeling of High-Pressure Fluid Behavior
    Virginia Commonwealth University VCU Scholars Compass Theses and Dissertations Graduate School 2013 Experimental Determination and Equation of State Modeling of High-Pressure Fluid Behavior Yue Wu Virginia Commonwealth University Follow this and additional works at: https://scholarscompass.vcu.edu/etd Part of the Engineering Commons © The Author Downloaded from https://scholarscompass.vcu.edu/etd/3237 This Dissertation is brought to you for free and open access by the Graduate School at VCU Scholars Compass. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of VCU Scholars Compass. For more information, please contact [email protected]. Experimental Determination and Equation of State Modeling of High-Pressure Fluid Behavior A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University. by Yue Wu, Doctor of Philosophy, Virginia Commonwealth University, 2013 Director: Mark A. McHugh, Professor, Department of Chemical and Life Science Engineering Virginia Commonwealth University Richmond, Virginia November, 2013 Acknowledgment I thank my advisor, Professor Mark A. McHugh for his support, encouragement, and guidance throughout this research over the years. He will always be given my respect for guiding me through the ocean of chemical engineering. His devotion to the science, great personality, and sense of humor impress me a lot. I do enjoy working in Professor McHugh’s Lab and I am very grateful to have such a great advisor. I appreciate my PhD committee members, Professor Everett Carpenter, Professor Stephen Fong, Professor Vamsi Yadavalli, and Professor Hu Yang for their time and efforts. I acknowledge Dr.
    [Show full text]
  • Particle-Based Fluids With
    Particle-Based Fluids COMS6998 – Problem Solving for Physical Simulation SPH - 1996 SPH – 2003 SPH – 2010 From mass-springs to fluids How might we move from a mass-spring model towards simulating fluids? Lennard-Jones potentials A method from molecular dynamics: • Forces depend on inter-particle distances Navier-Stokes equations Instead of starting from a collection of discrete liquid molecules, consider fluid as a continuum. Navier-Stokes equations are basically “F=ma” for continuum fluids. F=ma For a small parcel of fluid: • Mass = density(휌) x volume 퐷풖 • Acceleration = rate of change of velocity, 퐷푡 Per unit volume: Material 퐷풖 Derivative 휌퐷푡 = net force on fluid Material Derivative Consider how a quantity (eg. temp.) at a fixed point in a body of fluid can change: 1) Forces local to the point may cause changes, independent of the flow’s velocity. – eg. heating will increase temperature 2) The quantity has a higher or lower value upstream, so the point’s value changes as the flow goes past. Material Derivative (1) (2) 퐷휑 휕휑 = + 푢 ∙ 훻휑 퐷푡 휕푡 Advection In SPH, quantities are stored on moving particles, that travel with the flow. – advection is effectively automatic. Navier-Stokes equations Forces on fluid: • Pressure • Viscosity • Gravity • Surface tension • Any other external forces… Gravity Simple: Just a constant downward force. (At least on Earth, at scales we typically care about...) 푓푟푎푣푖푡푦 = 휌푔 Pressure Most fluids we encounter are effectively incompressible – they resist volume change. Pressure Gives a constraint, 훻 ∙ 풖 = 0. Pressure is the force that opposes compression (and expansion). Pressure differences yield changes in velocity, so force is the gradient of pressure: 푓푝푟푒푠푠푢푟푒 = −훻푝 Viscosity Loss of energy due to internal friction.
    [Show full text]
  • Density and Compressibility of Multicomponent N-Alkane Mixtures up to 463 K and 140 Mpa
    Downloaded from orbit.dtu.dk on: Oct 05, 2021 Density and Compressibility of Multicomponent n-Alkane Mixtures up to 463 K and 140 MPa Regueira, Teresa; Glykioti, Maria-Lito; Stenby, Erling Halfdan; Yan, Wei Published in: Journal of Chemical and Engineering Data Link to article, DOI: 10.1021/acs.jced.7b00803 Publication date: 2017 Document Version Peer reviewed version Link back to DTU Orbit Citation (APA): Regueira, T., Glykioti, M-L., Stenby, E. H., & Yan, W. (2017). Density and Compressibility of Multicomponent n- Alkane Mixtures up to 463 K and 140 MPa. Journal of Chemical and Engineering Data, 63(4), 1072-1080. https://doi.org/10.1021/acs.jced.7b00803 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Density and compressibility of multicomponent n-alkane mixtures up to 463 K and 140 MPa Teresa Regueira, Maria-Lito Glykioti, Erling H. Stenby, Wei Yan* Center for Energy Resources Engineering (CERE), Department of Chemistry, Technical University of Denmark, DK-2800 Kgs.
    [Show full text]
  • 1983 02 Calculation of Liquid Densities and Their
    ' Main Index Norske Sivilingeniorers Foreoing NORTH SEA FLOW METERING WOR..'T{SHOP Stavanger 30 Aug. - l Sept. 1983 Calculation of Liquid Densities and Their Mixtures D. IC. Petree G. R. Thomson R. W. 11.imk.inson Phillips Petroleum Compa~y El IEJtl'R?ICK kt1N ETIEB. SXRIYILIG Tn.LATE.LS! m NI.F OG FOll'AT.ra:REN THE CALCULATION OF LIQUID DENSITIES AND THEIR MIXTURES Douald X. Petree* George B. Thomson** • Risden W. Hankinson* Phillips Pet~oleuz::i Ccmpany Bartlesville, OK · 74004 *Corporate Enginee~ing - Proce•s Division **Ill.formation Services - Technical Systems Division 1.0 METHODOLOGY T~e~e are three physical phenocena that m~st be taken into ac~ounc ;y any valid model of the density behavior of pure liquids and their mixtures. The intentional and, hope fully, vell-infor.:ied neglect of any of these phenomena places we 11 defined 1 imitations on t~e po cen­ tial application of the :-esulting model. The intentional omission o: the so called ''di lat ion effect" from the list of phenomena considered, automatically limits the scope of this :paper to liquids ~.1ell-reII!oved from their critical region. TEMPERATURE EF:ECT The expansion and contraction of the vol\ll?le o: a fixed mass of constant composition liquid is the most significant departure ter~ that must be quanti tative1y described. The change in spec:i fie voltlI!le with a cl.~nge in te:upet"ature is defined by the the:-:odynamical ly • fundamental ter::i known as the coefficient of ther:ual expansion. 1 dv (1) c:: = -v -ct '!be final form of any model relating alpha to easily cbta~nable measu~ements depends upon the integration of this basic definiti~n.
    [Show full text]
  • Water Density and Polarizability Deduced from the Refractive Index Determined by Interferometric Measurements up to 250
    Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa Laurent Weiss, Abdel Tazibt, Albert Tidu, Michel Aillerie To cite this version: Laurent Weiss, Abdel Tazibt, Albert Tidu, Michel Aillerie. Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa. Journal of Chemical Physics, American Institute of Physics, 2012, 136 (12), pp.124201. 10.1063/1.3698481. hal-00699507 HAL Id: hal-00699507 https://hal.archives-ouvertes.fr/hal-00699507 Submitted on 21 May 2012 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. Ycvgt"fgpukv{"cpf"rqnctk¦cdknkv{"fgfwegf"htqo"vjg"tghtcevkxg"kpfgz fgvgtokpgf"d{"kpvgthgtqogvtke"ogcuwtgogpvu"wr"vq"472"ORc N0"Ygkuu."C0"Vc¦kdv."C0"Vkfw."cpf"O0"Cknngtkg Ekvcvkqp<"L0"Ejgo0"Rj{u0"358."346423"*4234+="fqk<"320328513058;:6:3 Xkgy"qpnkpg<"jvvr<11fz0fqk0qti1320328513058;:6:3 Xkgy"Vcdng"qh"Eqpvgpvu<"jvvr<11ler0ckr0qti1tguqwteg131LERUC81x3581k34 Rwdnkujgf"d{"vjg"Cogtkecp"Kpuvkvwvg"qh"Rj{ukeu0 Cffkvkqpcn"kphqtocvkqp"qp"L0"Ejgo0"Rj{u0 Lqwtpcn"Jqogrcig<"jvvr<11ler0ckr0qti1 Lqwtpcn"Kphqtocvkqp<"jvvr<11ler0ckr0qti1cdqwv1cdqwvavjgalqwtpcn Vqr"fqypnqcfu<"jvvr<11ler0ckr0qti1hgcvwtgu1oquvafqypnqcfgf Kphqtocvkqp"hqt"Cwvjqtu<"jvvr<11ler0ckr0qti1cwvjqtu Downloaded 02 Apr 2012 to 194.57.150.232.
    [Show full text]
  • Density and Viscosity Measurement of Diesel Fuels at Combined High Pressure and Elevated Temperature
    Processes 2013, 1, 30-48; doi:10.3390/pr1020030 OPEN ACCESS processes ISSN 2227-9717 www.mdpi.com/journal/processes Article Density and Viscosity Measurement of Diesel Fuels at Combined High Pressure and Elevated Temperature Carl Schaschke 1,*, Isobel Fletcher 1 and Norman Glen 2 1 Department of Chemical and Process Engineering, University of Strathclyde, Glasgow G1 1XJ, UK; E-Mail: [email protected] 2 TUV NEL Ltd., East Kilbride, Glasgow, G75 0QF, UK; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +44-0-141-548-2371. Received: 20 May 2013; in revised form: 24 June 2013 / Accepted: 2 July 2013 / Published: 19 July 2013 Abstract: We report the measurement of the viscosity and density of various diesel fuels, obtained from British refineries, at elevated pressures up to 500 MPa and temperatures in the range 298 K to 373 K. The measurement and prediction procedures of fluid properties under high pressure conditions is of increasing interest in many processes and systems including enhanced oil recovery, automotive engine fuel injection, braking, and hydraulic systems. Accurate data and understanding of the fluid characteristic in terms of pressure, volume and temperature is required particularly where the fluid is composed of a complex mixture or blend of aliphatic or aromatic hydrocarbons. In this study, high pressure viscosity data was obtained using a thermostatically-controlled falling sinker-type high pressure viscometer to provide reproducible and reliable viscosity data based on terminal velocity sinker fall times. This was supported with density measurements using a micro-pVT device.
    [Show full text]
  • MODELLING the PRESSURE and TEMPERATURE DEPENDENCE of VISCOSITY and VOLUME for HYDRAULIC FLUIDS 1 Introduction
    International Journal of Fluid Power 11 (2010) No. 2 pp. 37-42 MODELLING THE PRESSURE AND TEMPERATURE DEPENDENCE OF VISCOSITY AND VOLUME FOR HYDRAULIC FLUIDS Scott Bair1 and Paul Michael2 1Georgia Institute of Technology, Center for High-Pressure Rheology, George W. Woodruff School of Mechanical Engineering, Atlanta, GA 30332-0405, USA 2Corresponding author: Fluid Power Institute, Milwaukee School of Engineering, 1025 N. Broadway, Milwaukee, WI, 53202-3109, USA Abstract Viscosity and compressibility have a major impact upon the efficiency and dynamic response of fluid power sys- tems. The viscosity and compressibility of five hydraulic fluids have been measured for temperatures to 150 ºC and pressures to 350 MPa. A new correlation of viscosity with temperature and pressure based on the thermodynamic scal- ing rule of Roland et al. is offered. This correlation provides a means to model elastohydrodynamic effects in fluid power components and extends the accuracy of fluid power system models to higher pressure. The role of phase change and the resulting thixotropy in mineral based fluids is experimentally investigated. Keywords: hydraulics, elastohydrodynamics, rheology, high-pressure, viscosity, equation of state 1 Introduction There is a desire to make hydraulic machinery more of film thickness, to a quantitative field were the real compact and efficient. Typically, mobile fluid power measurable viscosity is used to calculate both film systems routinely operate at a pressure of 35 MPa. thickness and friction (Liu et al., 2007). Increasing the operating pressure of the hydraulic me- In hydraulic fluid power systems, an increased vis- dium is an obvious means to improve power density. cosity at the working pressure leads to viscous dissipa- However, efficiency losses may result from the proper- tion in hydraulic lines, valves and connectors (Manring, ties of the working fluid at higher pressures.
    [Show full text]