Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.

Mesoscale Simulation for Polymer Migration in Confined Uniform Shear Flow

The structure and dynamics of confined single polymer chain in a dilute solution, either in equilibrium or at different shear rates in the uniform shear flow fields, were investigated by means of dissipative particle dynamics simulations. The no-slip boundary condition without density fluctuation near the wall was taken into account to mimic the environment of a nanochannel. The dependences of the radius of gyration, especially in three different di- rections, and the density profile of the chain mass center on the strength of the confinement and the Weissenberg number（Wn） was studied. The effect of the interaction between polymer and solvent on the density profile was also investigated in the cases of moderate and strong Wn. In the high shear flow, the polymer migrates to the center of the channel with increasing Wn. There is only one density profile peak in the channel center in the uniform shear flow, which is in agreement with the results of the experiments and theory.

Gao's interacting shear flows( ISF) theory and its inferences and their applications

Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dynamics （CFD） are reviewed and some subjects worthy to be studied are pro- posed in this paper. The flow-field and motion law of ISF, mathematics definition of strong viscous shear layer flow in ISF, ISF equations, wall-surface compatibility criteria （Gao＇s criteria ）, space scale variety law of strong viscous shear layer reveals flow mechanism and local space small scale triggered by strong interaction that cause some abnormal severe local pneumatic heating phenomenon in hypersonic flow. Gao＇s ISF theory was used in near wall flow, free ISF flow simulation and design of computing grids, Gao＇s wall-surface criteria were used to verify calculation reliability and accuracy of near wall flows, ISF theory approximate analytical result of shock waves-boundary layer interac- tion and ISF equations were used to obtain the numerical exact solution of local area flow （ such as stationary point flow）. Some new subjects, such as, improving near-wall turbulent models according to the turbulent flow simulation satisfying the wall-criteria and illustrating relation between grid-con- vergence based on the wall criteria and other convergence tactics, are suggested. The necessity of applying Gao＇s ISF theory and wall criteria is revealed. Difficulties and importance of hypersonic vis- cous/in-viscid interaction phenomenon were also emphasized.

Conformational and Dynamical Evolution of Block Copolymers in Shear Flow

Conformation and dynamical evolution of block copolymers in shear flow is an important topic in polymer physics that underscores the forming process of various materials.We explored deformation and dynamics of copolymers composed of rigid or flexible blocks in simple shear flow by employing multiparticle collision dynamics integrated with molecular dynamics simulations.We found that compared with the proportion between rigid and flexible blocks,the type of the central blocks plays more important role in the conformational and dynamical evolution of copolymers.That is,if the central block is a coil,the copolymer chain takes end-over-end tumbling motion,while if the central block is a rod,the copolymer chain undergoes U-shape or S-shape deformation at mid shear rate.As the shear strength increases,all copolymers behave similar to flexible polymers at high shear rate.This can be attributed to the fact that shear flow is strong enough to overcome the buckling force of the rigid blocks.These results provide a deeper understanding of the roles played by rod and coil blocks in copolymers for phase interface during forming processing.

Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics(DPD)simulations.The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a perturbation method in Fourier-transformed space.The autocorrelation functions(ACFs)fromthe analyticalmethod are comparedwith results obtained fromDPD simulations under the same shear-flow conditions.Up to a moderate shear rate,various ACFs from the two approaches agree with each other well.At large shear rates,discrepancies between the two methods are observed,hence revealing strong additional coupling between different fluctuating variables,which is not considered in the analytical approach.In addition,the results at low and moderate shear rates can serve as benchmarks for developing multiscale algorithms for coupling of heterogeneous solvers,such as a hybrid simulation of molecular dynamics and fluctuating hydrodynamics solver,where thermal fluctuations are indispensable.

Molecular dynamics simulations of surfactant adsorption at oil/water interface under shear flow

Surfactants are extensively used in many chemical products to improve their stability, appearance, texture, and rheology. Precise control of the emulsion droplet size distribution, which depends on the characteristics of the surfactant used, is important for target-oriented product design. A complete understand! ng of the structures and dynamics of emulsion droplets at the reactor level requires coupling of two mesoscale physical constraints, that at the interfacial level, i.e., smaller than a single droplet (Mesoscale- 1), and that at the device level, i.e., larger than a single droplet (Mesoscale-2). In this work, the structures and adsorption kinetics of Mesoscale-1 surfactant molecules were studied via coarse-grained molecular dynamics. A non-equilibrium model that could introduce stable shear flow into the simulation box was used to investigate the interfacial structures at the droplet interface under different shear rates. The configurations of the surfactant molecules and adsorption amounts were compared with those obtained without flow. The adsorption kinetics for different shear rates were compared to determine the effects of hydrodynamic interactions. The dominant mechanisms governing the dynamic structures can thus be summarized as maximization of the adsorption density at the interface and minimization of flow resistance in the bulk phase (water and/or oil molecules). A scheme for coupling between Mesoscale-1 and Mesoscale-2 is proposed. This method is promising for the incorporation of interfacial structure effects into the hydrodynamics at the reactor device level for the manipulation of chemical products.

Effects of chain stiffness and shear flow on nanoparticle dispersion and distribution in ring polymer melts

The dispersion behavior and spatial distribution of nanoparticles(NPs)in ring polymer melts are explored by using molecular dynamics(MD)simulations.As polymer-NP interactions increase,three general categories of polymer-mediated NP organization are observed,namely,contact aggregation,bridging,and steric dispersion,consistent with the results of equivalent linear ones in previous studies.In the case of direct contact aggregation among NPs,the explicit aggregation-dispersion transition of NPs in ring polymer melts can be induced by increasing the chain stiffness or applying a steady shear flow.Results further indicate that NPs can achieve an optimal dispersed state with the appropriate chain stiffness and shear flow.Moreover,shear flow cannot only improve the dispersion of NPs in ring polymer melts but also control the spatial distribution of NPs into a well-ordered structure.This improvement becomes more evident under stronger polymer-NP interactions.The observed induced-dispersion or ordered distribution of NPs may provide efficient access to the design and manufacture of high-performance polymer nanocomposites(PNCs).

Probing relationship between structure and viscosity of unentangled polymers in steady shear flow

Structural responses of unentangled polymers of various architectures, including linear, ring, star, asymmetric star, and H-shaped polymers, in steady shear flow are investigated via nonequilibrium molecular dynamics simulations. As observed in our previous simulations, these polymers, when having an identical equilibrium mean-square radius of gyration 〈R2g0〉 exhibit the same viscosity curve in both the linear and nonlinear regimes. In this article, the polymer orientation and deformation and the rate of deformation are calculated as a function of shear rate. The differences between different architectures in most of these properties are found to be related to the polymer extensibility, the number of free ends and the ability of folding. The unique architecture-independent quantity is the gradient component 〈Gyy〉 of the radius of gyration tensor. We find that a simple relation η=C,〈RZg0〉（3〈Gyy〉/〈R2g0〉）3/2 gives a near-perfect fit to shear viscosity η/data, where C, is a constant. The results suggest that this relation between chain thickness and viscosity is universal for unentangled polymers of various architectures.

Numerical simulation of two-dimensional granular shearing flows and the friction force of a moving slab on the granular media

This paper studies some interesting features of two-dimensional granular shearing flow by using molecular dynamic approach for a specific granular system. The obtained results show that the probability distribution function of velocities of particles is Gaussian at the central part, but diverts from Gaussian distribution nearby the wall. The macroscopic stress along the vertical direction has large fluctuation around a constant value, the non-zero average velocity occurs mainly near the moving wall, which forms a shearing zone.. In the shearing movement, the volume of the granular material behaves in a random manner. The equivalent fl＇iction coefficient between moving slab and granular material correlates with the moving speed at low velocity, and approaches constant as the velocity is large enough.

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.

EXPERIMENTAL STUDY ON COHERENT VORTEX STRUCTURES IN DIFFERENTIALLY ROTATING QUASI TWO DIMENSIONAL ZONAL FLOW

An experimental system for forming a rotating paraboloid shaped shallow water with a free surface was conducted to study coherent vortex structures in a differentially rotating quasi two dimensional zonal flow.Flow visualization and laser light scattering techniques were used to obtain the information of spatial flow patterns.Experimental results show that the coexistence of Coriolis effect and strong shear in latitudinal zones may lead to formation of coherent vortices.Power spectra analysis and photographs which were taken in a reference frame rotating with the observed vortices also justified the emergence,drift and evolution of persistent vortices on the large scale.Locked vortex state manifests the cyclone and anticyclone asymmetry.

Flow Dynamics around Two Side by Side Circular Cylinders with Alternating Movements

The flow dynamics is analyzed through two-dimensional numerical simulations around two circular cylinders arranged side by side, with 4 combinations of alternating motions. All simulations are performed for Re = 1000, amplitude of oscillation (A) equal to 3, frequency ratio (fr) of 0.5, specific rotation (α) equal to 0.5 and different values of spacing ratio (L/D). It is verified that the combination of the type of movement, together with the position of one cylinder in relation to the other, exerts significant influence on the flow dynamics, as well as on the pressure distribution around the cylinder surface and on the average values of the fluid dynamics coefficients. The smallest value of the average pressure coefficient (Cp = -3.3), is obtained for the oscillating cylinder when placed side by side with the clockwise rotation cylinder, case 3 and L/D = 1.5. On the other hand, the lowest mean drag coefficient (Cd = 1.0788), is obtained for the cylinder with counterclockwise rotation, located in the lower position in relation to oscillating cylinder in the upper position, with spacing between them of 1.5. Furthermore, it is observed that the rotation movement is more effective in reducing drag than the rotation-oscillation movement, for the studied frequency ratio.

Investigation of scale efect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.

Effects of Airflow Field on Droplets Diameter inside the Corrugated Packing of a Rotating Packed Bed

Rotating packing bed(RPB) has a better mixing performance than traditional mixers and shows potential application in the petroleum industry. However, acquisition of information about the mixing process directly through experiments is difficult because of the compact structure and complex multiphase flow pattern in RPB. To study the mixing characteristic, Fluent, the computational fluid dynamics(CFD) software, was used to explore the effect of airflow field on droplet diameter. For conducting calculations, the gas-liquid two-phase flow inside the packing was simulated with the RNG k-ε turbulence model and the Lagrange Discrete Phase Model(DPM), respectively. The numerical calculation results showed that coalescence and breakup of droplets can take place in the gas phase flow inside the packing and can be strengthened with increased rotating speed, thereby leading to the enlargement of the average diameter.

Effects of symmetrically alternative rotating flow on flocculation

A symmetrically alternative rotating flow pattern was designed for flocculation process in order to produce large and dense flocs. The special effects of a symmetrically alternative rotating flow on the diameter and density of flocs were investigated. The results show that under the new fluid conditions, the primary particles on the outer part of the formed flocs may be cut down and the flocs contract at the end of the original rotating direction; then fluid changes its rotating direction, an opposite shearing is imposed to the flocs and makes some primary particles slide along the floc surface, leading to a denser floc; meanwhile, the broken and unflocculated particles on the trajectory may have opportunities to penetrate into or cohere to the flocs. Compared with the conventional rotating flow, the new-designed flow pattern can not only keep the floc size (even enlarge the floc diameter if a suitable flow is chosen) but also increase the floc density effectively.

CFD Simulation of Reactor Internal Flow in the Scaled APR＋

A series of 1/5 scale reactor flow model tests have been conducted in order to determine the hydraulic characteristics of the APR＋ （advanced power reactor plus）. The objective of test was to determine the core inlet flow field of the model reactor in order to provide input information required by the open core thermal margin analysis code such as TORC. In this study, in order to examine the validity of the results of reactor flow model tests and the applicability of CFD （computational fluid dynamics） in the simulation of reactor internal flow, CFD simulation was conducted with the commercial multi-purpose CFD software, ANSYSCFX V. 14. It was found that the velocity field in the downcomer had the inhomogeneous feature. Relative high velocity region was located in the core region. This result was different from measurement and this difference may result from the fact that some internal structures were not modeled with the real geometry but treated as the porous domain.

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensionM axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter β and the rotating parameter Ω. However, the lower branch solution breaks down at some moderate values of β The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β. The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.

CONSTITUTIVE EQUATION OF CO-ROTATIONAL DERIVATIVE TYPE FOR ANISOTROPIC-VISCOELASTIC FLUID

A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.

Improved similarity criterion for seepage erosion using mesoscopic coupled PFC–CFD model

Conventional model tests and centrifuge tests are frequently used to investigate seepage erosion. However, the centrifugal test method may not be efficient according to the results of hydraulic conductivity tests and piping erosion tests. The reason why seepage deformation in model tests may deviate from similarity was first discussed in this work. Then, the similarity criterion for seepage deformation in porous media was improved based on the extended Darcy-Brinkman-Forchheimer equation. Finally, the coupled particle flow code–computational fluid dynamics(PFC-CFD) model at the mesoscopic level was proposed to verify the derived similarity criterion. The proposed model maximizes its potential to simulate seepage erosion via the discrete element method and satisfy the similarity criterion by adjusting particle size. The numerical simulations achieved identical results with the prototype, thus indicating that the PFC-CFD model that satisfies the improved similarity criterion can accurately reproduce the processes of seepage erosion at the mesoscopic level.