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Chapter 2: Introduction

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Chapter 2: Introduction Chapter 2: Introduction 2.1 Multiphase flow. At first glance it may appear that various two or multiphase flow systems and their physical phenomena have very little in common. Because of this, the tendency has been to analyze the problems of a particular system, component or process and develop system specific models and correlations of limited generality and applicability. Consequently, a broad understanding of the thermo-fluid dynamics of two-phase flow has been only slowly developed and, therefore, the predictive capability has not attained the level available for single-phase flow analyses. The design of engineering systems and the ability to predict their performance depend upon both the availability of experimental data and of conceptual mathematical models that can be used to describe the physical processes with a required degree of accuracy. It is essential that the various characteristics and physics of two-phase flow should be modeled and formulated on a rational basis and supported by detailed scientific experiments. It is well established in continuum mechanics that the conceptual model for single-phase flow is formulated in terms of field equations describing the conservation laws of mass, momentum, energy, charge, etc. These field equations are then complemented by appropriate constitutive equations for thermodynamic state, stress, energy transfer, chemical reactions, etc. These constitutive equations specify the thermodynamic, transport and chemical properties of a specific constituent material. It is to be expected, therefore, that the conceptual models for multiphase flow should also be formulated in terms of the appropriate field and constitutive relations. However, the derivation of such equations for multiphase flow is considerably more complicated than for single-phase flow. The complex nature of two or multiphase flow originates the existence of multiple, deformable and moving interfaces and attendant significant discontinuities of fluid properties and complicated flow field near the interface. By focusing on the interfacial structure and transfer, it is noticed that many of two-phase systems have a common geometrical structure. It is recalled that single-phase flow can be classified according to the structure of flow into laminar, transitional and turbulent flow. In contrast, two-phase flow can be classified according to the structure of interface into several major groups which can be called flow regimes or patterns such as separated flow, transitional or mixed flow and dispersed flow, as it is shown inFig.2. 1. 7 Fig.2. 1: Two phase flow classification by Ishii (1976) When focusing on the dispersed flows and their subdivision by considering the phase of dispersion, we can distinguish three regimes: bubbly, droplet or mist, and particulate flow. In each regime the geometry of the dispersion can be spherical, sphereoidal, distorted, etc… [Ishii and Hibiki(2006)]. This work is focused on bubbly flow, as it will be seen deeply in the next chapter 8 2.1.1Flow patterns Now, focusing on the conditions of this work, for co-current upward flow gas and liquid in a vertical tube, the liquid and gas phases distribute themselves into several recognizable flow structures, that are referred as flow patterns and depicted in Fig.2. 2 and explained below. Fig.2. 2: Engineering data book III (2007). [John R. Thome (2007)] Bubbly flow: Numerous bubbles are observable as the gas is dispersed in the form of discrete bubbles in the continuous liquid phase. The bubbles may vary widely in size and shape but they are typically nearly spherical and are much smaller than the diameter of the tube itself. Slug flow: With increasing gas void fraction, the proximity of the bubbles is very close such that bubbles collide and coalesce to form larger bubbles, which are similar in size to the tube diameter and have a characteristic shape similar to a bullet with a hemispherical nose and a blunt tail. They are commonly referred to as Taylor bubbles. These bubbles are separated by slugs of liquid, which may include small entrained bubbles. Taylor bubbles have a thin liquid film between them and the tube wall, which may flow downward due to gravity, even though the net flow of fluid is upward. Churn flow: Increasing the velocity of the flow, the structure of the flow becomes unstable with the fluid travelling up and down in an oscillatory fashion but with a net upward flow. The instability is the result of the relative parity of the gravity and shear forces acting in opposing direction on the thin liquid film surrounding Taylor bubbles. This flow pattern is in fact an intermediate regime between the slug flow and annular flow regimes. Churn flow is typically a flow regime to be avoided in two-phase transfer 9 lines, such as those from a reboiler back to a distillation column or in refrigerant piping networks, because the slugs may have a destructive consequence on the piping system. Annular flow: Once the interfacial shear of the high velocity gas on the liquid film becomes dominant over gravity force, the liquid is expelled from the center of the tube and flows as a thin film on the wall (forming an annular ring of liquid) while the gas flows as a continuous phase up the center of the tube. The interface is disturbed by high frequency waves and ripples. In addition, liquid may be entrained in the gas core as small droplets, so much so that the fraction of liquid entrained may become similar to that in the film. This flow regime is particularly stable and is the desired flow pattern for two-phase pipe flows. Wispy annular flow: When the flow rate is further increased, the entrained droplets may form transient coherent structures as clouds or wisps of liquid in the central vapor core. Mist flow: At very high gas flow rates, the annular film is thinned by the shear of the gas core on the interface until it becomes unstable and is destroyed, such that all the liquid in entrained as droplets in the continuous gas phase, analogous to the inverse of the bubbly flow regime. Impinging liquid droplets intermittently wet the tube wall locally. The droplets in the mist are often too small to be seen without special lighting and/or magnification. [John R. Thome (2007)] The Fig.2.3 on the left shows the typical order of previous flow regimes that would be encountered from inlet to outlet of an evaporator tube. The flow pattern typically begins in the bubbly flow regime at the inlet at the onset of nucleate boiling in the tube. This onset of nucleate boiling may begin in the subcooled zone of the tube, where bubbles nucleate in the superheated thermal boundary layer on the heated tube wall but tend to condense in the subcooled central flow. After bubbly flow the slug flow regime is entered and then the annular flow regime with its characteristic annular film of liquid. This film eventually dries out or the film is entrained by the interfacial vapor shear, taking the flow into the mist flow regime. The entrained liquid droplets may persist in the flow past the point of complete vapor flow. Fig.2.3 Flow regimes in a vertical evaporator tube. [Collier and Thome (1994)]. 10 The differences among the flow patterns depending on the pipe diameter are also shown in Fig.2. 4 . Fig.2. 4 Typical air-water flow images in a 25.4 mm diameter pipe (above) compared to typical images in a 50.8 mm pipe (bottom). [Ishii and Hibiki (2006)] The flow regimes in both figures from the left are bubbly, cap-bubbly, slug, chum- turbulent, and annular flows, respectively. 11 2.1.2Bubbly flow development In vertical upward two phase flow, the small bubbles tend to move towards the wall, whereas the bigger bubbles do it towards the pipe centerline. Tomiyama [Tomiyama (1998)] observed this behavior for simple bubbles in his experiments, and other investigators have observed the same trend in cases where bubble groups or packs exist [Prasser (2002)]. In the case of air-water flow in standard conditions (atmospheric pressure and ambient temperature) a critical diameter, around 5-6 mm, at which the bubble changes its migration direction from the wall to the center, exists. This way the radial distribution of the gas phase depends strongly on the bubble size, being this the key phenomenon to determine transition between bubbly and slug flow [Lucas (2005)]. It may be said that the change of flow pattern depends on the forces acting on the bubble, and the interaction among themselves (breakup and coalescence). The structure of the flow in a cylindrical vertical section with upward flow is defined by a flow map. There are flow maps like Taitel’s or Ishii’s that depend exclusively on the superficial velocities of liquid and gas for completely developed flow. Determining the pattern and the transition zone is an extremely subjective task. Lucas divided the possible flow patterns for bubbly flow in 7 types [Lucas (2005)]: (1) Finely dispersed bubbly flow, (2) Bubbly flow with wall peak, (3) Bubbly Flow in transition zone, (4) Bubbly flow with core peak, (5) Bubbly flow with bimodal distribution of bubble size, (6) Slug flow, and (7) Annular flow, similar to what we have seen before in this chapter. The flow map usually used for this kind of flows in our conditions was given by [Taitel (1980)] and is showed below in Fig.2. 5. It can be observed the transition zones , not only from finely dispersed bubbly flow to bubbly, but also from bubbly to slug, this transitions were proposed by Sherizawa y Kataoka. 12 Fig.2. 5: Taitel’s flow map for bubbly-slug flow. [Taitel (1980)] Taitel establishes that the transition between slug and bubbly flow is determined by the expression: Eq.2.1 When the bubbles are smaller tan 5-6 mm diameter, the lift force pushes the bubbles against the wall producing the typical wall peak profiles.
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