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A new approach for predicting surge and swab pressures in open-ended pipes running in steady-state is proposed. In addition to the fluid flow through the annulus and drill pipe, the upper ends of drill pipe and annular space are assumed to be opened to the atmosphere, creating two free surfaces. The approach is based on the modified Bernoulli׳s equation applied to Bingham fluid flows. The pressure differences are not only due to viscous losses but also to fluid velocity differences, and to the fluid column weight differences. The model results are compared with measured data for a Newtonian fluid and the differences lie within an error range of 0% to +10%. A sensitivity analysis is conducted, depicting that the model depends on the Reynolds, Bingham and Froude numbers, and also on the pipe geometry (diameter ratios). [ABSTRACT FROM AUTHOR]

In this work, the natural convection of a viscoplastic fluid inside an enclosure filled with many obstacles is solved numerically. The enclosure is characterized by differentially heated vertical walls, while the obstacles are heat-conducting square blocks. Due to the nature of the viscoplastic material, it is seen that if the buoyancy force is not strong enough, the whole fluid can be unyielded, and the heat transfer takes place only by conduction. The Bingham constitutive equation is chosen to represent the yield-stress material. Steady-state velocity and temperature fields are obtained for a wide range of Rayleigh and Bingham numbers and several numbers of blocks. We show that increasing the yield-stress has a quantitative effect on reducing the fluid circulation, and consequently, the heat transfer rate. At a certain yield-stress level, the fluid motion is abruptly interrupted. The critical Bingham number for complete unyielding does not depend on the Rayleigh or Prandtl numbers. However, the obstacles' configuration has a significant effect on this transition. Flow vs. no-flow diagrams and average Nusselt number correlations are proposed as aid for thermal engineering of similar arrangements. [ABSTRACT FROM AUTHOR]

In this work, a scale analysis is applied over the two-dimensional steady flow of stable-stratified fluid in a lid-driven square cavity. Scales for the viscous and thermal boundary layers are pursuit, and adjusted with numerical results. The flow parameters investigated covers the range 10 3 ≤ G r < 10 6 , 100 ≤ R e ≤ 2500 , and 10 − 1 ≤ P r ≤ 10 2 . The outcome of the scale analysis is an expression for the surface-averaged Nusselt number which is capable of predicting the heat transfer within a 10% error range. [ABSTRACT FROM AUTHOR]

The gas–liquid slug flow pattern is characterized by the alternate succession of two structures: an aerated liquid slug and an elongated gas bubble, which together constitute that what is known as a unit cell . Computationally, the unit cell concept is used in modern slug tracking models in order to develop transient, lagrangian models capable of accurately predicting the flow behaviour with low computational costs, although early commercial packages using the unit cell concept did not offer slug tracking capabilities [3] . However, slug tracking models generally predict the hydrodynamic parameters only, whereas heat transfer is usually neglected. The present work couples heat transfer governing equations to a slug tracking model through energy balances in deformable, moving control volumes using the Reynolds transport theorem in its integral form, so as to achieve numerical simulations of heat transfer in developed, non-boiling, horizontal two-phase slug flows. In addition, a new expression for the calculation of the two-phase heat transfer coefficient is proposed. The numerical results were compared with data from the literature, and a good agreement was found. [ABSTRACT FROM AUTHOR]