Simulation of single‐ and two‐phase flows on sliding unstructured meshes using finite volume method

The paper presents an efficient finite volume method for unstructured grids with rotating sliding parts composed of arbitrary polyhedral elements for both single‐ and two‐phase flows. Mathematical model used in computations is based on the ensemble averaged conservation equations. These equations are solved for each phase and in case of single‐phase flow reduce to the transient Reynolds‐averaged Navier–Stokes (TRANS) equations. Transient flow induced by rotating impellers is thus resolved in time. The use of unstructured grids allows an easy and flexible meshing for the entire flow domain. Polyhedral cell volumes are created on the arbitrary mesh interface placed between rotating and static parts. Cells within the rotating parts move each time step and the new faces are created on the arbitrary interfaces only, while the rest of the domain remain ‘topologically’ unchanged. Implicit discretization scheme allows a wide range of time‐step sizes, which further reduce the computational effort. Special attention is given to the interpolation practices used for the reconstruction of the face quantities. Mass fluxes are recalculated at the beginning of each time step by using an interpolation scheme, which enhances the coupling between the pressure and velocity fields. The model has been implemented into the commercially available CFD code AVL SWIFT (AVL AST, SWIFT Manual 3.1, AVL List GmbH, Graz, Austria, 2002). Single‐phase flow in a mixing vessel stirred by a six‐bladed Rushton‐type turbine and two‐phase flow in aerated stirred vessel with the four‐blade Rushton impeller are simulated. The results are compared with the available experimental data, and good agreement is observed. The proposed algorithm is proved to be both stable and accurate for single‐phase as well as for the two‐phase flows calculations. Copyright 2004 John Wiley & Sons, Ltd.     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

低速二维流动的粒子仿真研究

本文运用信息保存法对低速二维的流动现象进行模拟，考察了低速条件下的有限平板绕流以及微槽道气体流动问题。研究表明：在对低速流动的模拟过程中，运用IP法在能够获得较好的结果的同时，具有比DSMC方法更高的计算效率。     

Temperature factor effect on the structure of the separated flow within a supersonic gas stream

The effect of the temperature factor, that is, the ratio of the body temperature to the freestream stagnation temperature, on the structure of the separated flow formed in the presence of a concave corner in a supersonic stream is studied. The strong influence of the temperature factor on the separation zone length and the flow-generated aerodynamic characteristics is established. It is shown that for fairly large deflection angles this flow cannot be described by free interaction, or triple deck, theory.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003     

Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A new approach to potential flow around axisymmetric bodies

A new method is introduced to solve potential flow problems around axisymmetric bodies. The approach relies on expressing the infinite series expansion of the Laplace equation solution in terms of a finite sum which preserves the Laplace solution for the potential function under a Neumann-type boundary condition. Then the coefficients of the finite sum are calculated in a least squares approximation sense using the Gram-Schmidt orthonormalization method. Sample benchmark problems are presented and discussed in some detail. The solutions are accurate and converged faster when a rather small number of terms were used. The method is simple and can be easily programmed.     

Cationic poly(methacryl oxyethyl trimethylammonium) and its poly(ethylene glycol)‐grafted analogue as capillary coating materials in electrophoresis

Cationic polyelectrolytes were synthesized and used as semipermanent coating materials for capillaries in electrophoresis. The polyelectrolytes used were a homopolymer of poly(methacryl oxyethyl trimethylammonium chloride) (PMOTAC) and its poly(ethylene glycol) (PEG)‐grafted analogue. Two PMOTAC polyelectrolytes, with molar masses of 85,000 and 300,000 g/mol, and PEG‐grafted PMOTAC with a molar mass of 280,000 g/mol were synthesized and then characterized by size exclusion chromatography (SEC) and nuclear magnetic resonance (NMR) spectroscopy. Attachment of the polyelectrolytes to the wall of the fused silica capillary for electrophoresis caused the electroosmotic flow (EOF) to reverse. The polyelectrolyte coatings were tested over the pH range 2–11 at different buffer ionic strengths, and the most stable and strongest anodic EOFs were obtained at acidic pH values with low ionic strength buffers. Between runs the capillary is merely rinsed for 2 or 3 min with the background electrolyte solution. With the PMOTAC coatings at pH values ≤5, the RSDs of the EOFs were less than 2.9% after 60 injections. The effects of the molar mass of the polycation and of PEGylation of PMOTAC on the interactions between the polycations and basic proteins were studied at acidic pH values. The differences in the effective electrophoretic mobilities, resolution values, and plate numbers of the proteins with the different coatings were due to the EOF, as demonstrated through calculations of reduced mobilities, relative resolution values, and relative plate numbers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2655–2663, 2007