Two Ideal Flow Models: Plug Flow and Mixed Flow

2011 ◽  
pp. 27-34
Author(s):  
Octave Levenspiel
Keyword(s):  
Plug Flow ◽  
Mixed Flow ◽  
Flow Models ◽  
Ideal Flow

scholarly journals Application of Tanks-in-Series Model to Characterize Non-Ideal Flow Regimes in Continuous Casting Tundish

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 208
Author(s):  
Dong-Yuan Sheng ◽  
Zongshu Zou
Keyword(s):  
Model Experiment ◽  
Plug Flow ◽  
Flow Regimes ◽  
Dead Volume ◽  
Water Model ◽  
Flow Volume ◽  
Mixed Flow ◽  
Inclusion Removal ◽  
Ideal Flow ◽  
In Series

This study describes a new tanks-in-series model for analyzing non-ideal flow regimes in a single-strand tundish. The tundish was divided into two interconnected tanks, namely an inlet tank and an outlet tank. A water model experiment was carried out to separately measure the residence-time distribution (RTD) of the two tanks. Drift beads were adopted in the water model experiment to simulate the non-metallic inclusions in molten steel. Dead volume fraction was evaluated by analyzing measured RTD curves. The ratio between mixed flow volume and plug flow volume was proposed as a new criterion to evaluate the inclusion removal. In the inlet tank, a higher mixed flow fraction was preferred to effectively release turbulent kinetic energy and enhance inclusion collision growth. In the outlet tank, a higher plug flow fraction was preferred to facilitate inclusion removal by flotation. The optimal positions of the weir were recommended based on the RTD analysis and the inclusion removal from the results of water model experiments. A theoretical equation was derived based on the tanks-in-series model, providing a good fitting function to analyze the experimental data. The confirmation test was performed by applying computational fluid dynamics simulations of liquid steel flow in the real tundish.

scholarly journals A numerical study of glacier advance over deforming till

2010 ◽  
Vol 4 (3) ◽  
pp. 359-372 ◽  
Author(s):  
G. J.-M. C. Leysinger Vieli ◽  
G. H. Gudmundsson
Keyword(s):  
Effective Viscosity ◽  
Numerical Study ◽  
Thickness Distribution ◽  
Plug Flow ◽  
Linear Wave ◽  
Sediment Layer ◽  
Mixed Flow ◽  
Model Experiments ◽  
Non Linear ◽  
Glacier Advance

Abstract. The advance of a glacier over a deforming sediment layer is analysed numerically. We treat this problem as a contact problem involving two slowly-deforming viscous bodies. The surface evolution of the two bodies, and of the contact interface between them, is followed through time. Using various different non-linear till rheologies, we show how the mode of advance depends on the relative effective viscosities of ice and till. Three modes of advances are observed: (1) overriding, where the glacier advances through ice deformation only and without deforming the sediment; (2) plug-flow, where the sediment is strongly deformed, the ice moves forward as a block and a bulge is built in front of the glacier; and (3) mixed-flow, where the glacier advances through both ice and sediment deformation. For the cases of both overriding and mixed-flow, an inverse depth-age relationship within the ice is obtained. A series of model experiments show the contrast in effective viscosity between ice and till to be the single most important model parameter defining the mode of advance and the resulting thickness distribution of the till. Our model experiments indicate that the thickness of the deforming till layer is greatest close to the glacier front. Measurements of till thickness taken in such locations may not be representative of deforming till thickness elsewhere. Given sufficiently large contrast in effective viscosity between ice and till, a sediment bulge is formed in front of the glacier. During glacier advance, the bulge quickly reaches a steady state form strongly resembling single-crested push moraines. Inspection of particle paths within the sediment bulge, shows that particles within the till travel at a different speed from the bulge itself, and the push moraine to advance as a form-conserving non-linear wave.

Reactor Design for Complex Reactions

2001 ◽  
Author(s):  
L. K. Doraiswamy
Keyword(s):  
Batch Reactor ◽  
Plug Flow ◽  
Reaction Network ◽  
Reactor Design ◽  
Batch Reactors ◽  
Complex Reaction ◽  
Mixed Flow ◽  
Flow Reactors ◽  
Design Procedures ◽  
Reactor Types

Procedures were formulated in Chapter 5 for treating complex reactions. We now turn to the design of reactors for such reactions. Continuing with the ethylation reaction, we consider the following reactor types for which design procedures were formulated earlier in Chapter 4 for simple reactions: batch reactors, continuous stirred reactors (or mixed-flow reactors), and plug-flow reactors. However, we use the following less formal nomenclature: A = aniline, B = ethanol, C = monoethyaniline, D = water, E = diethylaniline, F = diethyl ether, and G = ethylene. The four independent reactions then become Using this set of equations as the basis, we now formulate design equations for various reactor types. Detailed expositions of the theory are presented in a number of books, in particular Aris (1965, 1969) and Nauman (1987). Consider a reaction network consisting of N components and M reactions. A set of N ordinary differential equations, one for each component, would be necessary to mathematically describe this system. They may be concisely expressed in the form of Equation 5.5 (Chapter 5), or . . . d(cV)/dt = vrV (11.1) . . . The use of this equation in developing batch reactor equations for a typical complex reaction is illustrated in Example 11.1.

An Experimental Study of Cavitation in a Mixed Flow Pump Impeller

1960 ◽  
Vol 82 (4) ◽  
pp. 929-940 ◽  
Author(s):  
G. M. Wood ◽  
J. S. Murphy ◽  
J. Farquhar
Keyword(s):  
Experimental Study ◽  
Static Pressure ◽  
Hydraulic Performance ◽  
Mixed Flow ◽  
Pump Impeller ◽  
Flow Models ◽  
Cavitation Performance ◽  
Pressure Profiles ◽  
Closed Water ◽  
Flow Pump

A mixed flow impeller design was tested with six, five, and four vanes in a closed water loop to study the effects of cavitation on hydraulic performance and the results were compared with the work of other investigators. Two idealized flow models for incipient cavitation were derived to illustrate limits of cavitation design. It was found that both vane blockage and solidity effects are important when designing for optimum cavitation performance. Data showing incidence and speed effects plus the tip static pressure profiles in cavitating and noncavitating flow are also presented.

A Capillary Electrophoresis Platform With “On-Chip” Electrochemical Detection: Experimental and Computational Flow Studies

2001 ◽  
Author(s):  
Thomas J. Roussel ◽  
Robert S. Keynton ◽  
Kevin M. Walsh ◽  
Mark M. Crain ◽  
John F. Naber ◽  
...  
Keyword(s):  
Capillary Electrophoresis ◽  
Electrochemical Detection ◽  
Power Supply ◽  
Electroosmotic Flow ◽  
Plug Flow ◽  
Finite Element Models ◽  
Separation Channel ◽  
Flow Models ◽  
On Chip ◽  
Electrochemical Potentials

Abstract The purpose of this study was to compare experimental electrokinetic plug flow velocities to computational flow models of microfabricated capillaries. Electroosmotic flow studies of dichlorofluorescein and electrophoretic separation of dopamine and catechol in a microfabricated capillary electrophoresis (CE) system were performed both experimentally and computationally. A “balanced cross design” consisting of a bent 2 cm long injection channel and a straight 2 cm long separation channel was used. The geometry of the capillary was 65 μm wide and 20 μm deep. For the fluorescein study, separation voltages ranging between 0.25 kV and 1 kV were applied, while voltages ranging from 100 V to 550 V were used in the separation studies. Laser Induced Fluorescent (LIF) images were obtained for flow visualization and qualitative analysis in the electroosmotic flow studies, while electrochemical potentials were acquired using “on-chip” electrodes interfaced to a custom-designed power supply and electrochemical detection (ECD) circuit. Finite element models of the experimental device were generated and flows were simulated using commercially available software. For the electroosmotic flow studies, the computational results were found to be within ± 11% of the experimentally obtained values. Similarly, the results of the computational separations of catechol and dopamine predicted plug velocities that were within ± 7.6% of the experimentally determined values.

Comparison of mixed and plug flow reactor for enhancing the cell concentration of Haematococcus pluvialis growth

2021 ◽  
Vol 16 (11) ◽  
pp. 141-146
Author(s):  
K. Vasumathi ◽  
Raja Vadivu G. Nadana ◽  
E.M. Nithiya ◽  
K. Sundar ◽  
M. Premalatha
Keyword(s):  
Carbon Dioxide ◽  
Carbon Dioxide Emissions ◽  
Flow Reactor ◽  
Cell Concentration ◽  
Haematococcus Pluvialis ◽  
Plug Flow ◽  
Basal Medium ◽  
Optimum Combination ◽  
Plug Flow Reactor ◽  
Mixed Flow

Photo bioreactions are employed for abating carbon dioxide emissions. The economics depends upon the choice of the type of the reactor. Photo bioreactions can be explained similarly to an autocatalytic reaction. A combined reactor mixed flow reactor followed by plug flow reactor could be the best choice. Using the data on cell concentration of Haematococcus pluvialis with respect to time in 2x concentration of Kobayashi’s basal medium available in the literature, it has been proved that the combined reactor could be the best choice. The optimum combination was also determined.

Ozone mass transfer in water treatment: hydrodynamics and mass transfer modeling of ozone bubble columns

2001 ◽  
Vol 1 (2) ◽  
pp. 123-130 ◽  
Author(s):  
M.G. El-Din ◽  
D.W. Smith
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Liquid Phase ◽  
Plug Flow ◽  
Axial Dispersion ◽  
Bubble Columns ◽  
Algebraic Equations ◽  
Mixed Flow ◽  
Back Flow ◽  
Linear Algebraic Equations

Most of the mathematical models that are employed to model the performance of bubble columns are based on the assumption that either plug flow or complete mixing conditions prevail in the liquid phase. Although due to the liquid-phase axial dispersion, the actual flow pattern in bubble columns is usually closer to being mixed flow rather than plug flow, but still not completely mixed flow. Therefore, the back flow cell model (BFCM), that hypothesises both back flow and exchange flow to characterise the liquid-phase axial dispersion, is presented as an alternative approach to describe the hydrodynamics and mass transfer of ozone bubble columns. BFCM is easy to formulate and solve. It is an accurate and reliable design model. Transient BFCM consists of NBFCM ordinary-first-order differential equations in which NBFCM unknowns (Yj) are to be determined. That set of equations was solved numerically as NBFCM linear algebraic equations. Steady-state BFCM consists of 3 × NBFCM non-linear algebraic equations in which 3 × NBFCM unknowns (qG,j, Xj, and Yj) are to be determined. Those non-linear algebraic equations were solved numerically using Newton–Raphson technique. Steady-state BFCM was initially tested using the pilot-scale experimental data of Zhou. BFCM provided excellent predictions of the dissolved ozone profiles under different operating conditions for both counter and co-current flow modes.

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