Flow Distribution in Vertical Pipes

Only bubbles with volumes less than the critical bubble volume, Fbs, can be trapped on the upper surface of a circular cylinder. In a water-air system, the volume equivalent diameter of the trapped bubble was approximately 5 mm. As the critical bubble volume increases with of a solid body, larger bubbles can be trapped on the 

Considerable effort has been devoted to understanding the characteristics of gas-liquid two-phase flows in vertical and horizontal pipes. Such systems are used in a variety of engineering fields, including mechanical, chemical, and atomic 

Model experiments, therefore, are expected to be used, but it is difiicult to control and maintain the wettability of a pipe wall over a sufficiently long duration even in the model experiments. Surface treatment is commonly applied to change the wettability of the pipe wall. The advancing contact angle, which is used to represent the wettability quantitatively [26], rapidly decreases due to contamination and in most cases, the pipe becomes wet with liquid only for a relatively short time. Therefore, long-range experiments are difiicult except in very rare cases. 

Terauchi et al. [72] carried out model experiments on the flow pattern in a vertical circular pipe of poor wettability. 9 of an acrylic pipe was changed by coating a hydrophilic substance or liquid paraffin on the inner wall of the pipe. Three different values of were realized 0a = 36,77, and 104°. The flow pattern was observed with a still camera and a high-speed video camera to understand the effects of pipe wettability. The results of this study will be presented in the following. 

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Figure 11.13. Velocity and density distributions in vertical pipe flows at negligible gravity effect (from Soo, 1990) (a) NDF = 0.25 (b) NDF = 0.025.

The flow behaviour of suspensions of coarse particles is completely different in horizontal and vertical pipes. In horizontal flow, the concentration of particles increases towards the bottom of the pipe, the degree of non-uniformity increasing as the velocity of flow is decreased. In vertical transport, however, axial symmetry is maintained with the solids evenly distributed over the cross-section. The two cases are therefore considered separately. 

The term two-phase flow covers an extremely broad range of situations, and it is possible to address only a small portion of this spectrum in one book, let alone one chapter. Two-phase flow includes any combination of two of the three phases solid, liquid, and gas, i.e., solid-liquid, gas-liquid, solid-gas, or liquid-liquid. Also, if both phases are fluids (combinations of liquid and/or gas), either of the phases may be continuous and the other distributed (e.g., gas in liquid or liquid in gas). Furthermore, the mass ratio of the two phases may be fixed or variable throughout the system. Examples of the former are nonvolatile liquids with solids or noncondensable gases, whereas examples of the latter are flashing liquids, soluble solids in liquids, partly miscible liquids in liquids, etc. In addition, in pipe flows the two phases may be uniformly distributed over the cross section (i.e., homogeneous) or they may be separated, and the conditions under which these states prevail are different for horizontal flow than for vertical flow. 

Consider a dilute gas-solid flow in a horizontal rectangular pipe made of electrically conducting materials. The pipe is well grounded. The flow is fully developed. It is assumed that the particle volume fraction distribution in the vertical direction is the same as that in a circular pipe flow. Find out (a) the cross-sectionally averaged particle volume fraction in terms of the particle volume fraction at the centerline and (b) the vertical location at which the particle volume fraction represents the cross-sectionally averaged particle volume fraction. 

Consider a fully developed dilute gas-solid flow in a vertical pipe in which solid particles carry significant electrostatic charges. The particle charges vary radially. It is assumed that (a) the flow and the electrostatic field are axisymmetric and (b) the radial charge distribution C(r), defined as q(r)af(r), is known. Derive an expression for the radial volume fraction distribution of the particles. 

In a pioneering investigation, Serizawa [127, 128] measured the lateral void distribution as well as the turbulent axial liquid velocity fluctuations for bubbly air/water up-flows in a vertical pipe of diameter 60 (mm) inner diameter. They used electrical resistivity probes to measure the local void fraction, the bubble impaction rate, the bubble velocity and its spectrum. Turbulence quantities, such as the liquid phase mean velocity, and the axial turbulent fluctuations were measured using a hotfilm anemometer. A supplementary... 

Dilute transport fluidization The gas velocity is so large that all the particles are carried out of the bed with the gas. This solid transport by gas blowing through a pipe is named pneumatic conveying. In vertical pneumatic transport, particles are always suspended in the gas stream mainly because the direction of gravity is in line with that of the gas flow. The radial particle concentration distribution is almost uniform. No axial variation of solids concentration except i the bottom acceleration section [58]. 

Nasr-El-Din and Shook (58) studied solids distribution in a vertical pipe downstream of a 90° elbow. They tested sand-water slurries of various solid concentrations and particle sizes. The slurry flows were turbulent, and the particle Stokes number (inertia parameter) based on the pipe diameter and bulk velocity varied from 0.5 to 3. The solids distribution downstream of the elbow was found to be a function of the radius of curvature of the elbow, solids concentration, and particle size. 

Beck and co-workers (86, 87) placed the sensors on the pipe wall. As a result, their measurements give particle velocity averaged over the pipe cross-section. Mounting the sensors on the pipe wall is useful for vertical slurry flow where the velocity profile is uniform. This technique, however, is not so useful for the flow of settling slurries in horizontal pipelines. In this case, the solids are not uniformly distributed over the pipe cross-section, and, as a result, particle velocity is a strong function of position in the pipe. 

The IHX is a vertical, counter current flow, shell and tube heat exchanger (fig. 6). Each IHX has 3000 straight tubes (19 mm OD x 0.8 mm WT) with primary sodium on shell side and secondary sodium on the tube side. The tubes are arranged in circumferential pitch. A variable flow distribution is provided inside the IHX tubes with a higher flow on the outer rows to improve the thermohydraulic behaviour of the tube bundle. A mixing device is also provided at the secondary outlet to reduce the temperature differences between inner and outer shell of the secondary outlet header. Absence of flow induced vibration of tube bundle and the drain pipe in the downcomer have been verified by theoretical analysis. 

It is customary to divide suspensions into two broad categories - fine particle suspensions in which the particles are reasonably uniformly distributed in the liquid with little separation and coarse suspensions in which particles, if denser than the liquid, tend to separate out and to travel predominantly in the lower part of a horizontal pipe (at a lower velocity than the liquid) in a vertical pipe the solids may have an appreciably lower velocity than the liquid. Although, this is obviously not a very clear cut classification and is influenced by the flow rate and concentration of solids, it does nonetheless provide a convenient initial basis for classifying the flow behaviour of liquid-solid mixtures. 

The influence of a bend on the distribution of particles in a pipe cross-section of pneumatic conveying systems has been investigated numerically. The numerical model solved the finite-volume equations for the conservation of mass and momentum for two phases. It was evident that the cross-sectional concentration of the particles a few meters after a bend is not uniform and that the particles tend to concentrate around the pipe s wall. Various cross-sectional concentrations of particles were found for different pipe to bend radius ratios particles size and direction of gravity (i.e. horizontal to vertical flow, and horizontal to horizontal flow). Based on the (Efferent cross-sectional concentrations for different particle sizes, it was concluded that the paths taken by the particles after the bend were strongly dependent upon their sizes. As a consequence, segregation of particles downstream of a bend is expected. 

The five-point electro conductivity probe technique (FPECPT) has been used to measure time averaged bubble size (volume) distribution, absolute bubble velocity and gas volume fraction in gas-liquid dispersions like the two-phase bubble columns and vertical pipe flows. Other similar conductivity probes have also been used [88, 135]. 

Sensors of this kind were applied at FZR to an air-water flow test loop in a vertical pipeline (inner diameter D = 51.2mm) as well as to a cavitating flow behind a fast acting valve. The high resolution of the sensor allowed to obtain bubble size distributions and to study the evolution of the flow structure along the pipe [7]. The maximum time resolution available to perform these experiments was 1200 measurements per second. Recently, the measuring rate was increased to 10 000 frames per second with sensors of 16 x 16 measuring points. In the result it is possible to visualise and quantify individual bubbles or droplets at a much higher flow velocity, than before. 

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