mechanical6_11 (1).doc

Slug bubbles velocity the absolute rise velocity of

  • No School
  • AA 1
  • 16

This preview shows page 8 - 10 out of 16 pages.

Slug Bubbles Velocity: The absolute rise velocity of the dispersed gas bubbles ( U GLS ) is treated in the same way like the Taylor bubble. Many researchers recommended Harmathy's equation (as sighted in Collier &Thome (1994)) for the rise velocity of dispersed bubbles in a stagnant liquid, so: 5 . 0 25 . 0 2 ) 1 ( ) ( 53 . 1 LS L g L L LS GLS g U U (34) The Liquid Film Thickness: The liquid film thickness ( ) is related to ( TB )(Orell & Rembrand 1986) as: 2 2 2 ) 2 1 ( ris ris TB ris TB TB D D D A A (35) Several methods are found in literature to relate ( U film ) with ( δ ). The simple way that is adopted her is given by Orell & Rembrand (1986) which make force balance of the liquid film neglecting the interfacial shear force along the Taylor bubble and assuming no pressure drop across it: TB ris film L TB ris TB film L Z D U f Z D Z A g . . ). . . 2 1 ( . . . . . . 2 (36) Where friction factor ( f ) is a function of Reynolds number (based on hydraulic diameter) and pipe roughness (Darby, 2001): L ris film film L D U A . . . . . 4 Re (37) The explicit form for ( f ) given by the eq. (10) is used. Liquid Slug Void Fraction: 57
Image of page 8

Subscribe to view the full document.

AN APPROACH FOR MODELING THE PERFORMANCE Prof. Dr. Abdulwadood S. OF THERMAL BUBBLE PUMP Dr. Safaa H The basic difficulty in the slug flow modeling is concerned with the gas content in the liquid slug (Orell & Rembrand 1986, Abdul-Majeed & Al-Mashat 2000). In the absence of a predictive method, two limiting cases have been recognized (Orell & Rembrand 1986), namely ideal slug flow (α LS =0) and (α LS =0.3). The latter value represents the upper void fraction limit observed in the bubbly flow. In this study the maximum allowable void fraction is considered since it best describe the real situation. Slug-Unit Void Fraction: The slug unit void fraction is defined as the ratio of the gas volume in the Taylor bubble plus the liquid slug sections relative to the slug unit volume. The slug unit void fraction is assumed equal to the riser void fraction according to the principle of cell analysis Orell & Rembrand (1986), hence: ) 1 ( . LS TB tot (38) Slip Ratio: It is the ratio of the gas phase velocity (U g ) to the liquid phase velocity (U L ) (Collier & Thome 1994), i.e: L g U U S / (39) This term could be related to void fraction and dryness fraction(Collier & Thome 1994) as: 1 . . 1 g L x x S (40) 3.RESULTS AND DISCUSSION: The theoretical equations governing the performance of the bubble pump are solved to obtain the whole pump behavior based on water properties. The solution algorithm is shown in fig.(3) and the computer code is written by Engineering Equation Solver (EES) software. The inputs to the one dimensional slug model are the properties of the phases and the superficial velocities and the main output is the total void fraction. The "By-Section" numerical method was used in the major iteration while the inner iteration was solved by the usual try and errors method.
Image of page 9
Image of page 10
  • Fall '19
  • Fluid Dynamics, Iraqi Journal For Mechanical And Material Engineering

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern