DOCSLIB.ORG

[email protected] (T

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Colonius@Caltech.Edu (T International Journal of Multiphase Flow 37 (2011) 596–608 Contents lists available at ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow Numerical simulation of shock propagation in a polydisperse bubbly liquid ⇑ Keita Ando , Tim Colonius, Christopher E. Brennen Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States article info abstract Article history: The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically inves- Received 7 December 2010 tigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation Received in revised form 12 February 2011 laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly Accepted 7 March 2011 flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat trans- Available online 25 March 2011 fer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distri- bution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to Keywords: phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, Continuum bubbly flow the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged Bubble size distributions Shock dynamics shock profile is smoothed out. Bubble screen Ó 2011 Elsevier Ltd. All rights reserved. Finite volume method 1. Introduction 1988; Watanabe and Prosperetti, 1994; Kameda and Matsumoto, 1996; Kameda et al., 1998) reproduced averaged shock structures. Complex bubbly flows are ubiquitous in engineering flows, such The direct numerical simulations of shock propagation in bubbly liq- as underwater explosions, industrial piping systems and hydraulic uids (Delale et al., 2005; Delale and Tryggvason, 2008; Seo et al., machinery (Cole, 1948; Wylie and Streeter, 1993; Brennen, 1994). 2010) are an important step to quantify the effect of direct interac- Seawater near the sea surface contains fairly big bubbles due to tions between the neighboring bubbles. breaking waves. Even for liquid flows with small nuclei popula- A finite cloud of bubbles has been extensively studied as a tions, the interaction with structures often produces tension waves canonical example. One of the earliest attempts is the work of that can cause cavitation, and complex two-phase flow regimes are van Wijngaarden (1964) that considered the collapse of a bubbly encountered. The resulting gas or vapor bubbles lead to wave dis- layer near a wall. The study of the linearized dynamics of spherical persion; the dynamics of bubbly mixtures cannot be properly de- bubble clouds (d’Agostino and Brennen, 1989) identified the scribed by simple barotropic relations (Brennen, 1995, 2005). An natural frequencies of the cloud that can be much smaller than understanding of complex dynamics of such bubbly flows is still the natural frequency of individual bubble oscillations. The nonlin- inadequate for many engineering applications. ear computations of bubble clouds (Chahine, 1982; Omta, 1987; Theoretical and numerical models have been developed to inves- Wang and Brennen, 1999; Colonius et al., 2000) indicate that cloud tigate shock dynamics in bubbly flows. In the classic papers of van collapse can generate higher pressure than that predicted by Wijngaarden (1968, 1972), volume-averaged mixture quantities superposition of single-bubble calculations in the corresponding were defined in order to average out local scattering due to the one-way-coupling case (in which interactions among the bubbles dynamics of individual bubbles, and averaged conservation laws through the averaged field are ignored); this violent cloud collapse for bubbly flows were formulated based on heuristic reasoning. may account for cavitation noise and erosion. All of the above Zhang and Prosperetti (1994) developed an ensemble-averaging analyses were confined to the case of monodisperse mixtures. technique to derive the mixture-averaged equations. The computa- However, the computations of a spherical bubble cloud with a tions of the mixture-averaged equations coupled to a Rayleigh–Ples- distribution of equilibrium bubble sizes (Wang, 1999; Shimada set-type equation for single bubble dynamics (Nigmatulin et al., et al., 2000) suggest a profound impact of polydispersity on the averaged dynamics. The continuum models have been validated by experiments. In the pioneering work of Campbell and Pitcher (1958), shock propa- ⇑ Corresponding author. Present address: School of Electrical and Electronic gation in a bubbly liquid-filled, vertical tube was considered, and Engineering, Nanyang Technological University, Singapore 639798, Singapore. Tel.: +65 6790 6534. their results showed reasonable agreement with the steady shock E-mail addresses: [email protected] (K. Ando), [email protected] (T. Colo- relations derived from mixture-averaged equations. Subsequent nius), [email protected] (C.E. Brennen). experiments (Noordzij and van Wijngaarden, 1974; Beylich and 0301-9322/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2011.03.007 K. Ando et al. / International Journal of Multiphase Flow 37 (2011) 596–608 597 Gülhan, 1990; Kameda and Matsumoto, 1996; Kameda et al., 1998) where q is the mixture density, u is the mixture velocity, pl is the used a similar device with careful control of bubble sizes, and iden- averaged liquid pressure, I is the identity tensor, a is the void frac- tified oscillatory shock structures. Beylich and Gülhan (1990) re- tion, R is the bubble radius, and R_ is the bubble wall velocity. For di- ported on the polydisperse case in which the smoothed shock lute cases, the mixture density is well approximated by (1 À a)ql, structure was seen. Unfortunately, experimental observations on where ql is the liquid density. The averaged liquid pressure may the shock dynamics of polydisperse mixtures are rather limited. be described by the Tait equation of state (Thompson, 1972), The goals of this paper are to derive a continuum bubbly flow p þ B q m 1 q m model that incorporates a distribution of equilibrium bubble nuclei l ¼ l ¼ ; ð4Þ p B m 1 sizes and quantify the effect of polydispersity on averaged shock l0 þ ql0 ql0 À a dynamics. In Section 2, the continuum and single-bubble-dynamic where ql0 is the reference liquid density at the ambient pressure pl0, models with their limitations are presented. One-way-coupled and m and B denote stiffness and tensile strength of the liquid, flow computations are also considered in order to clarify some respectively. fundamental issues arising in polydisperse flows. Section 3 pro- The term p~ in the momentum flux in Eq. (2) represents pressure vides the numerical implementation and its verification with linear fluctuations due to the phase interactions, problems. In Section 4, one-dimensional shock propagation ! through a bubbly liquid and a bubble screen is computed, and R3p R3R_ 2 ~ bw the effect of polydispersity on the averaged shock dynamics is p ¼ a pl À À q ; ð5Þ R3 R3 investigated. Finally, we summarize the findings in Section 5. where pbw is the bubble wall pressure described by the dynamic 2. Physical model boundary condition (Brennen, 1995), 4l R_ 2Ç 2.1. Continuum bubbly flow model p ¼ p À l À : ð6Þ bw b R R 2.1.1. Ensemble-averaged equations Here, pb is the internal bubble pressure (sum of noncondensible gas With the ensemble-averaging technique of Zhang and Prosper- pressure pg and vapor pressure pv), ll is the liquid viscosity, and Ç is etti (1994), one may formally derive continuum models in order to the surface tension. evaluate the average mixture dynamics. The key concept is to sta- The overbar in Eqs. (3) and (5) denotes moments with respect to tistically treat the dynamical state of bubbly mixtures in which a the (normalized) distribution of equilibrium bubble sizes, f(R0), Z large number of realizations of spherical bubbles (or isotropic scat- 1 ters) exist. In other words, we discard any scattering effects in a u ðx; tÞ¼ uðx; t; R0Þf ðR0ÞdR0; ð7Þ specific realization, but explore the statistically averaged dynam- 0 ics. Even though direct interactions between the neighboring bub- where R0 is the equilibrium bubble radius corresponding to the bles are minimal, there can still appear indirect interactions among 2 _ 3 3 _ 2 3 ambient pressure and u represents any of R R; R pbw; R R or R . the bubbles through the averaged field; the problem is two-way- Note that the functional dependence of R0 on the distribution is as- coupled. In what follows, we present the ensemble-averaged con- sumed spatially uniform. This assumption is valid for all times due servation laws for polydisperse bubbly flows with the model to the no-slip assumption (d). For example, the void fraction is de- assumptions. The complete derivation can be found in Zhang and fined as Prosperetti (1994) and is also summarized in Ando (2010). 4p The continuum model assumes that (a) the bubbles are spheri- a ¼ nR3; ð8Þ cal; (b) mutual interactions among the bubbles are negligible ex- 3 cept through their effect on the mixture-averaged flow; (c) where n is the number of bubbles per unit volume of the mixture wavelengths in the mixture are large compared to the mean bubble and is conserved in time because of the assumption (a); namely spacing; (d) the bubbles advect with the ambient liquid velocity; @n and (e) density and velocity fluctuations in the liquid phase are þ r ðnuÞ¼0: ð9Þ uncorrelated. @t Assumption (a) implies that fission and coalescence of the bub- It should be noted that the phase interaction term p~ does not appear bles are not permitted, so that the bubble number is conserved in in the volume-averaged momentum equation of van Wijngaarden time. Assumption (c) is used for the model closure. Relative motion (1968, 1972).
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]
  • 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
    [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]