Mathematical and Physical Modeling of Three-Phase Gas-Stirred Ladles

2016 ◽  
Vol 1812 ◽  
pp. 29-34
Author(s):  
Juan A. López ◽  
Marco A. Ramírez-Argáez ◽  
Adrián M. Amaro-Villeda ◽  
Carlos González
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Stokes Equations ◽  
Steel Slag ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Steel Ladle ◽  
Phase System ◽  
Navier Stokes Equations ◽  
Three Phase

ABSTRACTA very realistic 1:17 scale physical model of a 140-ton gas-stirred industrial steel ladle was used to evaluate flow patterns measured by Particle Image Velocimetry (PIV), considering a three-phase system (air-water-oil) to simulate the argon-steel-slag system and to quantify the effect of the slag layer on the flow patterns. The flow patterns were evaluated for a single injector located at the center of the ladle bottom with a gas flow rate of 2.85 l/min, with the presence of a slag phase with a thickness of 0.0066 m. The experimental results obtained in this work are in excellent agreement with the trends reported in the literature for these gas-stirred ladles. Additionally, a mathematical model was developed in a 2D gas-stirred ladle considering the three-phase system built in the physical model. The model was based on the Eulerian approach in which the continuity and the Navier Stokes equations are solved for each phase. Therefore, there were three continuity and six Navier-Stokes equations in the system. Additionally, turbulence in the ladle was computed by using the standard k-epsilon turbulent model. The agreement between numerical simulations and experiments was excellent with respect to velocity fields and turbulent structure, which sets the basis for future works on process analysis with the developed mathematical model, since there are only a few three-phase models reported so far in the literature to predict fluid dynamics in gas-stirred steel ladles.

Influences of Recess Geometry and Restrictor Dimension on Flow Patterns and Pressure Distribution of Hydrostatic Bearings

2007 ◽  
Author(s):  
Cheng-Hsien Chen ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
De-Xing Peng ◽  
Ding-Wen Yang
Keyword(s):  
Pressure Distribution ◽  
Stokes Equations ◽  
Flow Patterns ◽  
Lubricant Film ◽  
Navier Stokes ◽  
Width Ratio ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Lubricant Flow ◽  
Land Width

This paper studies the influences of recess geometry and restrictor dimensions on the flow patterns and pressure distribution of lubricant film, which are coupled effects of hybrid characteristics of a hydrostatic bearing. The lubricant flow is described by using the Navier-Stokes equations. The Galerkin weighted residual finite element method is applied to determine the lubricant velocities and pressure in the bearing clearance. The numerical simulations will evaluate the effects of the land-width ratio and restriction parameter as well as the influence of modified Reynolds number and the jet-strength coefficient on the flow patterns in the recess and pressure distribution in lubricant film. On the basis of the simulation drawn from this study, the simulated results are expected to help engineers make better use of the design of hydrostatic bearing and its restrictors.

Mathematical study of a single leukocyte in microchannel flow

2018 ◽  
Vol 13 (5) ◽  
pp. 43 ◽  
Author(s):  
S. Boujena ◽  
O. Kafi ◽  
A. Sequeira
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Microchannel Flow ◽  
Navier Stokes Equations ◽  
Coupled Problem ◽  
Inflammatory Drugs ◽  
The Mathematical Model ◽  
Rate Type

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

Modeling of Cell Motion in Micro-Scale Hydrodynamic-Electrical Field

2009 ◽  
Vol 74 ◽  
pp. 139-142
Author(s):  
Ting Ye ◽  
Hua Li
Keyword(s):  
Stokes Equations ◽  
Elastic Shell ◽  
Practical Significance ◽  
Cell Manipulation ◽  
Navier Stokes ◽  
Phase System ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Maxwell Stress Tensor ◽  
Cell Motion

A modeling of two-phase system is presented for investigation of the cell motion and deformation in the microchannel subject to the mechanical and electrical coupled forces. In order to evaluate the mechanical force developed by cell membrane, it is treated as an incompressible and elastic shell with uniform thickness capable of shearing and bending deformation. Due to the irregular and complex cell configuration after deformation, the Maxwell stress tensor (MST) method is successfully employed to analyze the dielectrophoretic force. The modified particle binary level set (MPBLS) method is presented to accurately track the moving interface between the two phases, which is vital for a modeling of two-phase system. Afterwards the modified SIMPLER coupled with SIMPLEC is used to numerically solve the incompressible Navier-Stokes equations governing the entire flow field. On basis of the series of methods, the motion and deformation of red blood cell (RBC) in the microchannel under the mechanical and electrical forces are simulated to demonstrate the deformation process and the moving trajectory of RBC. The present study is not only of great value for deeper understanding of some diseases caused by cell abnormality, but also of practical significance for cell manipulation and separation.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

scholarly journals Experimental study and numerical simulation of dam reservoir sediment release

Water SA ◽  
2020 ◽  
Vol 46 (4 October) ◽  
Author(s):  
Marzieh Fadaee ◽  
Mohammad Zounemat-Kermani
Keyword(s):  
Numerical Simulation ◽  
Sediment Transport ◽  
Relative Error ◽  
Water Wave ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Navier Stokes Equations ◽  
Water And Sediment ◽  
Three Phase

In this research, experimental and numerical modelling of three-phase air, water, and sediment transport flow, due to the opening of a sluice gate was conducted in two scenarios, i.e., with and without a triangular obstacle. Numerical simulation was conducted using the Navier-Stokes equations with the aid of the volume of fluid method (VOF) to track the free surface of the fluid. For the experimental model, a glass-enclosed flume with 150 × 30 × 50 cm dimensions was used. The experiment was performed for an initial height of the water column at 20 cm and 10 cm sediment column. To evaluate the numerical model's performance, the simulation results were compared with the experimental observations using the average relative error %. The amount of relative error between experimental observations and numerical simulations, for the position and height of the wave flow for the three-phase air, water, and sediment flow, were obtained as 2.64% and 4.51% for the position and height of the water wave, and 2.23% and 2.82% for the position and height of the sediment transport, respectively, for the ‘without obstacle’ scenario, and 3.77% and 5.25% for the position and height of the water wave, and 2% and 7.23% for the position and height of the sediment transport, respectively, for the ‘with obstacle’ scenario. The findings of the study indicate the appropriate performance of the numerical model in the simulation of water and sediment wavefront advance, and also its weakness in the estimation of wave height.

II. Analysis of regular and singular motions

1965 ◽  
Vol 285 (1402) ◽  
pp. 400-412 ◽  
Keyword(s):  
Stokes Equations ◽  
Separated Flow ◽  
Fluid Flows ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Weakly Singular ◽  
Simultaneous Existence ◽  
Additional Explanation

An eigenmotion analysis of viscous fluid flows around dihedral angles presented in part I of this paper revealed the simultaneous existence of regular and weakly singular motions which are characterized by finite and infinite pressures at the edge of a wedge. Since the derivation of the Navier-Stokes equations is based on the finiteness of the velocity and pressure, the physical meaning of an infinite pressure in the region of operation requires an additional explanation. The present investigations analyse the flow properties of regular and weakly singular motions past a semi-infinite flat plate under symmetric and asymmetric attack. Particular attention is directed to the attached and separated flow patterns which can develop around a sharp edge. The duality of regular and weakly singular motions is shown to exist for most of the typical flow patterns which can be observed in published photographs. The qualitative agreement with photographs is especially satisfactory for regular motions. A brief summary of the essential flow properties of both types is given.

Effect of Slag on Mixing Time in Gas-Stirred Ladles Assisted with a Physical Model

2012 ◽  
Vol 1485 ◽  
pp. 101-106 ◽  
Author(s):  
Adrián M. Amaro-Villeda ◽  
A. Conejo ◽  
Marco A. Ramírez-Argáez
Keyword(s):  
Physical Model ◽  
Mixing Time ◽  
Steel Slag ◽  
Slag Layer ◽  
Process Conditions ◽  
Steel Ladle ◽  
Phase System ◽  
Mixing Times ◽  
Two Phase ◽  
Energy Dissipated

ABSTRACTA 1/6th water physical model of a 140 tons gas-stirred steel ladle is used to evaluate mixing times (τm at 95% of chemical uniformity) in a two phase system without slag (air-water) and in a more realistic three phase system (air-water-oil) to simulate the argon-steel-slag system and quantify the effect of the slag layer on the mixing time. Slag layer is kept constant at 0.004 m. Mixing times are estimated through measured changes in pH due to the addition of a tracer (NaOH 1 M). The effect of the following variables on the mixing time is evaluated for a single injector: gas flow rate (7, 17 y 37 l/min) and the injector position (R/r= 0, 1/3, ½, 2/3 and 4/5). Experimental results obtained in this work show good agreement when compared against mixing time correlations reported by Mazumdar for the two phase air-water case (no slag considered). Another comparison is done using the new concept called “effective bath height” proposed by Barati, where the mixing time is a function of the size of the slag layer since this layer dissipates part of the total amount of stirring energy introduced into the ladle by the injection of gas. Agreement is not good in this case. Finally, an estimation of the percentage of the stirring energy dissipated by the slag is computed, including other factors that govern the dissipation of stirring energy. Percentage of energy dissipated by the slag is found to be between 2.7 to 12 % depending on the process conditions.

Study of Maneuverability of Container Ship With Nonlinear and Roll-Coupled Effects by Numerical Simulations Using RANSE-Based Solver

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
R. Rajita Shenoi ◽  
P. Krishnankutty ◽  
R. Panneer Selvam
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Container Ship ◽  
Navier Stokes Equations ◽  
Hydrodynamic Derivatives ◽  
Computational Fluid Dynamics Cfd ◽  
Experimental Values ◽  
The Mathematical Model

The examination of maneuvering qualities of a ship is necessary to ensure its navigational safety and prediction of trajectory. The study of maneuverability of a ship is a three-step process, which involves selection of a suitable mathematical model, estimation of the hydrodynamic derivatives occurring in the equation of motion, and simulation of the standard maneuvering tests to determine its maneuvering qualities. This paper reports the maneuvering studies made on a container ship model (S175). The mathematical model proposed by Son and Nomoto (1981, “On Coupled Motion of Steering and Rolling of a High Speed Container Ship,” J. Soc. Nav. Arch. Jpn., 150, pp. 73–83) suitable for the nonlinear roll-coupled steering model for high-speed container ships is considered here. The hydrodynamic derivatives are determined by numerically simulating the planar motion mechanism (PMM) tests in pure yaw and combined sway–yaw mode using an Reynolds-Averaged Navier–Stokes Equations (RANSE)-based computational fluid dynamics (CFD) solver. The tests are repeated with the model inclined at different heel angles to obtain the roll-coupled derivatives. Standard definitive maneuvers like turning tests at rudder angle, 35 deg and 20 deg/20 deg zig-zag maneuvers are simulated using the numerically obtained derivatives and are compared with those obtained using experimental values.

Mathematical and Experimental Investigation of Liquid-Gas Interfaces in Porous Wicks

2002 ◽  
Author(s):  
Yuelei Yang ◽  
Frank M. Gerner ◽  
H. Thurman Henderson
Keyword(s):  
Mathematical Model ◽  
Experimental Investigation ◽  
Stokes Equations ◽  
Small Diameter ◽  
Flow In Porous Media ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vapor Interface ◽  
Porous Plastic ◽  
Capillary Pore

This paper focuses on the investigation of the liquid-gas (or vapor) interface, which occurs in very small diameter pores. A mathematical model is built to formulate the movements of a liquid column trapped in a capillary pore. The Navier-Stokes equations are applied to the liquid side with assumed no-slip conditions, while the Young-Laplace equation is used to formulate the shape of the interface. This theoretical model calculates both velocity profiles in the liquid side and transient profiles of the interface itself; and of particular interest, it predicts the pressure difference, oscillation frequency and amplitude required to burst this interface. These predicted parameters are examined by the experiments with both oscillating Coherent Porous Silicon (CPS) wicks and porous plastic wicks. This research helps better understanding the phenomena such as multiphase flow in porous media or de-watering process that happens in vibro-separators.

Fluid Flow Characteristics Around a Pair of Diamond-Shaped Cylinders in Side-by-Side and Tandem Arrangements

2011 ◽  
Author(s):  
Shuichi Torii ◽  
Noritugu Ueda ◽  
Zijie Lin
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Time History ◽  
Flow Patterns ◽  
Separation Distance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Spacing

The present study deals with unsteady laminar fluid flow phenomena around a pair of diamond-shaped cylinders in free stream. Emphasis is placed on the effects of the Reynolds number, Re, and the ratio of cylinder separation distance to length of diamond-shaped cylinder, s/d, on the flow patterns in side-by-side and tandem arrangements. The Navier-Stokes equations are discretized using finite difference method to determine the time history of velocity vector in the flow field. The Reynolds numbers, Re, is ranged from 30 to 300 and gap spacing, s/d, is varied from 0.0 to 2.5 for side-by-side and 0.0 to 5.0 for tandem, respectively. The results are compared with the experimental results with the aid of flow visualization method. The study discloses that (i) the generations of Karman vortex streets behind the diamond-shaped cylinders are intensified with an increase in the Reynolds number, (ii) the categorized flow patterns in the wake region of the diamond-shaped islands are affected by s/d, and (iii) the vortex shedding frequency in the wake of diamond-shaped cylinders depends on both the gap spacing and the formation of the vortices.

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