Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

Starting Nozzle Flow Simulation Using K-G Two-Equation Turbulence Model

The starting process of two-dimensional nozzle flows has been simulated with Euler, laminar and k - g two-equation turbulence Navier-Stokes equations. The flow solver is based on a combination of LUSGS subiteration implicit method and five spatial discretized schemes, which are Roe, HLLE, MHLLE upwind schemes and AUSM+, AUSMPW schemes. In the paper, special attention is for the flow differences of the nozzle starting process obtained from different governing equations and different schemes. Two nozzle flows, previously investigated experimentally and numerically by other researchers, are chosen as our examples. The calculated results indicate the carbuncle phenomenon and unphysical oscillations appear more or less near a wall or behind strong shock wave except using HLLE scheme, and these unphysical phenomena become more seriously with the increase of Mach number. Comparing the turbulence calculation, inviscid solution cannot simulate the wall flow separation and the laminar solution shows some different flow characteristics in the regions of flow separation and near wall.

Transport phenomena in radial flow MOCVD reactor with three concentric vertical inlets

Transport phenomena in radial flow metalorganic chemical vapor deposition (MOCVD) reactor with three concentric vertical inlets are studied by two-dimensional numerical modeling. By varying the parameters such as gas pressure, flow rates combination of multi-inlets, geometric shapes and sizes of reactor and flow distributor, temperatures of susceptor and ceiling, and susceptor rotation, the corresponding velocity, temperature, and concentration fields inside the reactor are obtained; the onset and change of flow recirculation cells under influences of those parameters are determined. It is found that recirculation cells, originated from flow separation near the bend of reactor inlets, are affected mainly by the reactor height and shape, the operating pressure, the flow rates combination of multi-inlets, and the mean temperature between susceptor and ceiling. By increasing the flow rate of mid-inlet and the mean temperature, decreasing the pressure, maintaining the reactor height below certain criteria, and trimming the bends of reactor wall and flow distributor to streamlined shape, the recirculation cells can be minimized so that smooth and rectilinear flow prevails in the susceptor region, which corresponds to smooth and rectilinear isotherms and larger reactant concentration near the susceptor. For the optimized reactor shape, the reactor size can be enlarged to diameter D = 40 cm and height H = 2 cm without flow recirculation. The susceptor rotation over a few hundred rpm around the reactor central axis will induce the recirculation cell near the exit and deflect the streamlines near the susceptor, which is not the case for vertical reactors. (c) 2006 Elsevier B.V. All rights reserved.

Extraction kinetics of thorium(IV) with primary amine N1923 in sulfate media using a constant interfacial cell with laminar flow

Extraction kinetics of thorium(IV) with primary amine N1923 in sulfate media has been investigated by a constant interfacial cell with laminar flow. Studies of interfacial tension and effects of the stirring rate, temperature, and specific interfacial area on mass transfer rate show that the most probable reaction zone takes place at the liquid-liquid interface. According to the experimental data correlated as a function of the concentration of the relevant species involved in the extraction reaction, the rate equation of extracting thorium has been obtained as follows: -d[Th(IV)]((o))/dt = 10(-3.10)center dot[Th(IV)](0.89)center dot[(RNH3)(2)SO4](0.74).

Domain decomposition hybrid method for numerical simulation of bluff body flows:theoretical model and application

The discrete vortex method is not capable of precisely predicting the bluff body flow separation and the fine structure of flow field in the vicinity of the body surface. In order to make a theoretical improvement over the method and to reduce the difficulty in finite-difference solution of N-S equations at high Reynolds number, in the present paper, we suggest a new numerical simulation model and a theoretical method for domain decomposition hybrid combination of finite-difference method and vortex method. Specifically, the full flow. field is decomposed into two domains. In the region of O(R) near the body surface (R is the characteristic dimension of body), we use the finite-difference method to solve the N-S equations and in the exterior domain, we take the Lagrange-Euler vortex method. The connection and coupling conditions for flow in the two domains are established. The specific numerical scheme of this theoretical model is given. As a preliminary application, some numerical simulations for flows at Re=100 and Re-1000 about a circular cylinder are made, and compared with the finite-difference solution of N-S equations for full flow field and experimental results, and the stability of the solution against the change of the interface between the two domains is examined. The results show that the method of the present paper has the advantage of finite-difference solution for N-S equations in precisely predicting the fine structure of flow field, as well as the advantage of vortex method in efficiently computing the global characteristics of the separated flow. It saves computer time and reduces the amount of computation, as compared with pure N-S equation solution. The present method can be used for numerical simulation of bluff body flow at high Reynolds number and would exhibit even greater merit in that case.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Modeling and optimization for separation of ionic solutes in pressurized flow capillary electrochromatography

By manipulation of applied pressure or voltage, pressurized flow capillary electrochromatography (P-CEC) permits unique control of selectivity for ionic solutes. A simple mathematical model has been developed to describe the quantitative relationship between the electrochromatographic retention factor (k(*)) of charged solutes and the applied voltage and pressure. The validity of the model was verified experimentally with hydrophilic interaction mode CEC (HI-CEC). On the basis of the model developed, it was found that the value of k(*) could be predicted accurately using only a limited number of data points from the initial experiments at different voltages or pressures. Correlation between the experimentally measured and calculated k(*) was excellent, with a correlation coefficient greater than 0.999. Optimization for the separation of peptides by P-CEC was also performed successfully on the basis of the proposed model.

Numerical Simulation of Particle Separation in An Oil-Sand Separator

The gathering systems of crude oil are greatly endangered by the fine sand and soil in oil. Up to now , how to separate sand from the viscid oil is still a technical problem for oil production home or abroad. Recently , Institute of Mechanics in Chinese Academy of Sciences has developed a new type of oil-sand separator , which has been applied successfully in oil field in situ. In this paper, the numerical method of vortex-stream function is used to predict the liquid-solid separating course and the efficiency for this oil-sand separator. Results show that the viscosity and particle diameter have much influence on the particle motion. The calculating separating efficiency is compared with that of experiment and indicates that this method can be used to model the complex two-phase flow in the separator.

Oil-Water Two-Phase Flow Inside T-Junction

The oil/water two-phase flow inside T-junctions was numerically simulated with a 3-D two-fluid model, and the turbulence was described using the mixture k - epsilon model. Some experiments of oil/water flow inside a single T-junction were conducted in the laboratory. The results show that the separating performance of T-junction largely depends oil the inlet volumetric fraction and flow patterns. A reasonable agreement is reached between the numerical simulation and the experiments for both the oil fraction distribution and the separation efficiency.

Effects of Mach number on turbulent separation behaviours induced by blunt fin

An experimental study of the interaction between shock wave and turbulent boundary layer induced by blunt fin has been carried out at M-infinity = 7.8 using oil flow visualization and simultaneous measurements of fluctuating wall pressure and heat transfer. This paper presents the effects of Mach number on turbulent separation behaviours induced by blunt fin.

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made.

Multiscale Method for Turbulent-Flow Computations

A main method of predicting turbulent flows is to solve LES equations, which was called traditional LES method. The traditional LES method solves the motions of large eddies of size larger than filtering scale An while modeling unresolved scales less than Delta_n. Hughes et al argued that many shortcomings of the traditional LES approaches were associated with their inabilities to successfully differentiate between large and small scales. One may guess that a priori scale-separation would be better, because it can predict scale-interaction well compared with posteriori scale-separation. To this end, a multi-scale method was suggested to perform scale-separation computation. The primary contents of the multiscale method are l) A space average is used to differentiate scale. 2) The basic equations include the large scale equations and fluctuation equations. 3) The large-scale equations and fluctuation equations are coupled through turbulent stress terms. We use the multiscale equations of n=2, i.e., the large and small scale (LSS) equations, to simulate 3-D evolutions of a channel flow and a planar mixing layer flow Some interesting results are given.

NUMERICAL AND EXPERIMENTAL STUDY ON LIQUID-SOLID FLOW IN A HYDROCYCLONE

Hydrocyclones are widely used in industry, of which the geometrical design using CFD techniques is gaining more popularity in recent years. In this study, the Euler-Euler approach and the Reynolds stress model are applied to simulate the liquid-solid flowfield in a hydrocyclone. The methodology is validated by a good agreement between experimental data and numerical results. Within the research range, the simulation indicates that the liquid-solid separation mainly occurs in the conical segment, and increasing conical height or decreasing cylindrical height helps to improve the grade efficiencies of solid particles. Based on these results, two of the same hydrocyclones are designed and installed in series to establish a liquid-solid separation system. Many experiments are then conducted under different conditions, in which the effects of the water cut and the second hydrocyclone on the separation are investigated. The results also confirm that smaller solid particles are more susceptible to the inlet conditions, and the second hydrocyclone plays a more important role as the water cut reduces.

Simultaneous determination of chromium(VI) and chromium(III) of bioavailable fraction in bottom mud by flow injection-atomic absorption spectroscopy

A rapid and sensitive method for separation and determination of Cr(VI) and Cr(III) in bottom mud of lake by flow injection on-line preconcentrtion system and GFAAS was developed. The available Cr(VI) and Cr(III) were extracted by HOAc or EDTA + NH4 NO3 and adsorbed simultaneously by an anion and a cation resin microclummn and then eluted simultaneously by 2 mol/L NH4 NO3 + 0.05 mol/L ascorbate and 2 mol/L H2SO4, respectively. The elution was performed for 50 s after adsorption for 2 min, and the efficiencies of elution were 85.4% - 94.8% and 96.7% - 106% for Cr(VI) and Cr(M) respectively. The detection limits of the method were 0.9 mu g/L and 2.7 mu g/L with relative standard deviations of 3.5% and 6.4% for the determination of Cr(VI) and Cr(III) in sample, respectively.

Separation of acidic and basic compounds in capillary electrochromatography with polymethacrylate-based monolithic columns

Methacrylate-based monolithic columns with electroosmotic flow (EOF) or very weak EOF are prepared by in situ copolymerization in the presence of a porogen in fused-silica capillaries pretreated with a bifunctional reagent. Satisfactory separations of acidic and basic compounds on the column with EOF at either low or high pH are achieved, respectively. With sulfonic groups as dissociation functionalities, sufficient EOF mobility still remains as high as 1.74 x 10(-4) cm(2) s(-1) V-1 at low pH. Under this condition, seven acidic compounds are readily separated within 5.7 min. Moreover, at high pH, the peak shape of basic compounds is satisfactory without addition of any masking amines into running mobile phase since the secondary interaction between the basic compounds and the monolithic stationary phase are minimized at high pH. Reversed-phase mechanism for both acidic and basic compounds is observed under investigated separation conditions. In addition, possibilities of acidic and basic compound separations on a monolithic column with extremely low EOF are discussed. (C) 2004 Elsevier B.V. All rights reserved.