Modern Physics Letters B

A Detached-Eddy Simulation (DES) with moving boundaries has been developed and applied to synthetic jet flows. Complex unsteady flow patterns of the flows were revealed from the simulation. Comparisons between the simulation and experiments showed reasonably good agreements, which indicates that, as a hybrid RANS/LES method, DES is capable of handling unsteady separations with turbulent boundary layers and time-dependent moving boundary conditions.

The lift and power requirements of a model dragonfly in forward flight are studied, using the method of numerically solving the Navier-Stokes equations. The graph of power against flight speed is U-shaped, suggesting that a dragonfly might have a preferred cruising speed. Considerable variation in the relative phase between fore- and hindwings results in only very small change in power requirement. This suggests theat the forewing-hingwing interaction is weak and furthermore, might explain why phase angles ranging from to are employed by dragonflies in hovering and forward flight.

In this paper, the spectral volume (SV) method is experimented for the Navier-Stokes equations by treating the viscous terms with a mixed formulation named the local Discontinuous Galerkin approach. The formulation of the SV method for the two-dimensional compressible Navier-Stokes equations is described. The solver is used to solve several viscous flow problems to show its potential.

Direct numerical simulation (DNS) is carried out to study turbulence characteristics in a vertical rotating open-channel with the rotation number N_τ = 0-0.12 and the Reynolds number Re_τ = 180 based on the wall friction velocity of non-rotating case and the channel depth. Here, two typical rotation regimes are identified. As 0 < N_τ < 0.06, the turbulence statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. As N_τ > 0.06, the turbulence statistics are suppressed significantly because the effect of Coriolis force plays as a dominant role.

In this paper, an immersed membrane method (IMM) is proposed for the simulation of three-dimensional (3D) fluid-structure interaction phenomena in a mechanical heart valve (MHV).

The shock wave is reflected when it meets the boundary, and the boundary suffers an impulsive force simultaneously. The interaction between shock wave and boundary surface is related with their shapes. Many researches focused on the problems that a planar or a spherical shock wave is reflected by plate surface in the past. Recently, some researchers indicated that the interaction effect of spherical shock wave with a parabolic surface may be used for propulsion technique. But detailed work was not reported. In this paper, by using the numerical method, we study the interaction effect between a spherical shock wave and the parabolic surface. The propagation of reflected shock wave and the impulsive force that the parabolic surface sustains are computed.

In this paper we apply the unified coordinate system developed by Hui and his co-workers to the steady compressible flow computation in such a way that the grid is generated physically and automatically. At the beginning of computation one only needs to build a narrow layer of grids near the left boundary. It is demonstrated that by continuously injecting layers of grid in the inflow boundary, the grid will gradually fill up the entire flow domain.

In this paper, a solution-adaptive finite difference method is presented for the simulation of flow past a pair of side-by-side circular cylinders. The method consists of an adaptive 5-point stencil algorithm, a central-difference spatial discretization and an immersed boundary representation of complex geometry. Numerical results indicate that the method is capable of solving the flow problems with complex geometry in a multilevel manner.

The asymmetric vortex flows about slender bodies at high angle of attack are investigated numerically. 3D O-O type multi-block structured grids are adopted for the computation, and a series of small spatial disturbances are imposed on the leeward body surface near the tip to trigger the asymmetry. The unsteady Navier-Stokes equations are solved using a dual-time method based on the cell-centered finite-volume scheme. Comparisons between numerical results and experimental data demonstrate that the asymmetric vortex pattern observed in the experiment is successfully simulated. In a certain small perturbation level, the magnitude of the side-force is independent of the size of the spatial perturbation, but its direction is dependent on the direction of the spatial perturbation, i.e. a counterclockwise or clockwise circumferential angle from the leeward meridian. When perturbation is removed, the flow field returns to its original asymmetric shape after a period of oscillation.

In numerically solving a physical problem governed by partial differential equations with proper boundary condition, central-kind difference schemes can yield high-order accuracy in the interior of the computational domain. But near the boundary the stencil structure is limited to only upwind-kind schemes. This has led to a reduction of the accuracy that in turn pollutes the entire interior solution as a long-standing critical obstacle in developing high-order accuracy numerical PDE solvers. The root of this difficulty lies in the ignorance of the use of (discrete) PDE at boundary, which is essentially an ignorance of the key role of the boundary physics in the determination of the solution. In this paper we recover the boundary physics by applying the original PDE all the way to the boundary along with the original boundary condition, which can yield uniformly high-order discretisation.

Although the flapping oscillatory motion is organized, its effect on the mean flows of turbulent plane jets is similar to the effect of turbulence. Therefore, the close relation for the stress due to flapping-induced velocity components is assumed to be similar to the relation for the turbulent Reynolds stress, and the similarity theory applicable for mean flows of turbulent plane jets is extended to that of unstable flapping turbulent plane jets. The results show the effect of flapping motion on mean flows can be regarded as two folds: one is to enhance the mixing by flapping-induced Reynolds stress and the other is to modify the effective advection. The results from similarity analyses are in good agreement with the experimental data.

In this work, we show that the Ghost Fluid Method (GFM) has actually zero-order accuracy if the gas-liquid interface is not in normal motion initially. The modified GFM (MGFM) is found to overcome this problem well. Examples are given to support the present analysis and conclusions obtained, and the MGFM is then applied to simulate compressible fluid-structure interaction.

A generic two-fluid (water/air) numerical model has been developed and applied for the simulation of the complex fluid flow around a wave driven rotating vane near a shoreline in the context of a novel wave energy device OWSC (Oscillating wave surge converter). The underlying scheme is based on the solution of the incompressible Euler equations for a variable density fluid system for automatically capturing the interface between water and air and the Cartesian cut cell method for tracking moving solid boundaries on a background stationary Cartesian grid. The results from the present study indicate that the method is an effective tool for modeling a wide range of free surface flow problems.

A fully implicit unfactored algorithm for three-dimensional Euler equations is developed and tested on multi-block curvilinear meshes. The convective terms are discretized using an upwind TVD scheme. The large sparse linear system generated at each implicit time step is solved by GMRES* method combined with the block incomplete lower-upper preconditioner. In order to reduce the memory requirements and the matrix-vector operation counts, an approximate method is used to derive the Jacobian matrix, which only costs half of the computational efforts of the exact Jacobian calculation. The comparison between the numerical results and the experimental data shows good agreement, which demonstrates that the implicit algorithm presented is effective and efficient.

The turbulent flow in a reacting hydro turbine was simulated with large eddy simulation (LES) to investigate the spatial and temporal distributions of the turbulence in a 3D skew blade passage. The simulations show that the intrinsic features are quite complicated. LES can capture the details of the structures, and the results are generally agreeable with those by direct numerical simulation.

A new mesh free algorithm, which is both solution and geometry adaptive, is introduced and described in this paper to capture the physical features of inviscid flows modeled by the Euler equations. Only clouds of points instead of grids are distributed over the computational domain and the spatial derivatives of the Euler equations are estimated using a weighted least-square curve fit on local clouds of points. The adaptive approach is compared to traditional global refinement techniques using structured grids. In this procedure, unnecessary "grid" points in adjacent area are prevented from being generated by using mesh free local clouds refinement techniques. These techniques operate, in particular, in the vicinity of shock influencing regions and near large curvature regions including the boundary surface of the geometry. Several numerical experiments with Euler flow simulation around airfoils at transonic regimes will be presented to illustrate the potential of this methodology in terms of accuracy, efficiency and low computer memory requirement of the mesh free adaptive algorithm.

Numerical simulations of an oblique shock interacting with a compressible laminar boundary layer are reported. The Mach number ranges from 2 to 6.85, while the Reynolds number based on the distance to the impingement location is fixed at 3 × 10⁵. All the simulations are carried out with a constant wall temperature, equal to the adiabatic recovery temperature. At higher shock strength the evolved separation bubbles are taller and are biased towards the upstream side of the impingement location with an asymmetrical structure. Existing similarity scalings for the bubble length need to be modified for the high Mach number range. Introduction of small amplitude disturbances upstream of the separation bubble resulted in the growth of organised streamwise structures downstream of the bubble.

A simple and efficient moving grid technique is proposed for computing unsteady flow problems with geometrical deformation, relative body movement or shape changes due to aerodynamic optimisation and fluid-structure interaction. A Delaunay graph of the solution domain is first generated, which can be moved easily during the geometric dynamic deformation, even for very large distortion. A one to one mapping between the Delaunay graph and the computational grid is maintained during the movement. The new computational grid after the dynamic movement can be generated efficiently through the mapping while maintaining the primary qualities of the grid. While most dynamic grid deformation techniques are iterative based on the spring analogy, the present method is non-iterative and much more efficient. On the other hand, in comparison with dynamic grid techniques based on transfinite interpolation for structured grids, it offers both geometric and cell topology flexibility, which is crucial for many unsteady flow problems involving geometric deformation and relative motions. Comparison with the popular spring analogy method for a wing-body combination is demonstrated regarding their efficiency and grid quality.

Nonparallel stability of the compressible boundary layers for three-dimensional configurations having large curvature variation on the surface is investigated by using the parabolic stability equations, which are derived from the Navier-Stokes equations in the curvilinear coordinate system. The difference schemes with fourth-order accuracy can be used in the entire computational regions. The global method is combined with the local method using a new iterative formula, thus more precise eigenvalues are obtained, and fast convergences are achieved. Computed curves of the amplification factor and shape functions of disturbances show clearly variable process of the flow stability, and agree well with other available results.

The main objective of the present work is to solve the non-linear inviscid Burger equation using the second-order TVD scheme with the different TVD limiters. These limiters include Non-MUSCL (monotone upwind scalar conservation laws) Harten-Yee upwind limiters, Roe-Sweby upwind limiters and Davis-Yee symmetric TVD limiters. These limiters are then used in conjunction with the explicit finite difference second order TVD scheme to model the flow in which discontinuity is present. Non-linear Burger equation was solved for this purpose to capture a one dimensional traveling discontinuity. Every limiter was individually tested for its ability to resolve the discontinuity in as few mesh point as possible. In addition, each limiter's capability to eliminate spurious oscillations associated with numerical computation of discontinuities was investigated. The results showed that all the TVD limiters were able to completely eliminate the spurious oscillations except Roe-Sweby limiter that caused the solution to diverge.

The characteristics of Mach stem in steady and unsteady Mach reflections are important in supersonic vehicle design. In this paper we give an overview of the current status of the study on the height and shape characteristics of Mach stem. Notably, we will show that in many cases the shape of the Mach stem seems to be well approximated by a circular arc.

The Lattice Boltzmann methods are used to study the mixing enhancements by the electro-osmotic flow in microchannel. Three sets of lattice evolution methods are performed for the fluid flow, for the electrical potential distribution, and for the concentration propagation. The simulation results show that the electro-osmotic flow induces y-directional velocity which enhances the mixing in microchannels. The mixing enhancement is related with the surface zeta potential arrangement and the external electric field strength.

The static aeroelastic characteristics of a flexible V-tail airplane were studied by the analyses of the variations of aerodynamic derivatives and flight loads versus flight dynamic pressure. The results show that the variation trends of aerodynamic derivatives and flight loads of the flexible airplane are different from those of the rigid airplane. Therefore, it is necessary to consider the static aeroelastic effects during the flexible airplane design.

In this article, the combination of fictitious domain and domain decomposition has been presented. First, we construct an equivalent variational formulation for the Dirichlet problem of linear elliptic operators and discuss the space approximation. Then the approach is applied to the incompressible Navier-Stokes equations, including construction of the variational formulation and time discretization by operator splitting. Finally, some numerical results are presented to validate our approach.

The physical origin of severe low-frequency pressure fluctuation frequently observed in Francis hydraulic turbines under off-design conditions, which greatly damages the structural stability of turbines and even power stations, is analyzed based on the hydrodynamic stability theory and our Reynolds-averaged Navier-Stokes equation simulation (RANS) of the flow in the entire passage of a Francis turbine. We find that spontaneous unsteady vortex ropes, which induce severe pressure fluctuations, are formed due to the absolute instability of the swirling flow at the conical inlet of the turbine's draft tube.

The fluid flow and heat transfer in porous media has wide applications in oil industry and air conditioning system. In this study the momentum and energy transport processes in a porous medium are numerically simulated. The Brinkman-Forchheimer-extended Darcy equations and energy equation are solved using single lattice-Boltzmann method (LBM). As a first attempt, a benchmark problem is studied, i.e., momentum and energy transfer in a rectangular enclosure with differentially heated vertical walls. The effect of permeability on the critical Rayleigh numbers, the temperature distribution and flow field is discussed.

A new analytic model of the intense shock-wave decay is deduced in the paper based on self-consistent and well-defined assumptions. The shock wave attenuation in PMMA can be divided into two stages. In the initial decay, a spherical wave model is adopted because the dimension of the wave origin is too small to be neglected in comparison with the dimension of target. Due to overdamp at initial stage, the pressure gradient along the radial direction is expressed as dp/dr=f(∂p/∂t, du/dp) with the term (du/dp) deduced from the transient equation of wave front and the linear relation between the wave velocity and particle velocity at the wave rear. A temporal equicrural trapezoidal pressure profile applied to the target surface is used as the initial condition in order to obtain the pressure of ∂p/∂t. This pressure profile induces three stages of shock wave evolution: (1) The formation stage of "pressure increase"; (2) The plateau of "maximum pressure"; (3) The decay stage of "pressure decreases". According to the relation between the surge pressure of shock wave and laser power density, the character of laser-induced shock wave is described in detail. The above assumptions could not be applied in the final stage of propagation because the distorted "negative" pressure caused by the overdamp assumption would appear. In the final stage, the famous Taylor's equations of shock wave attenuation based on underdamp assumption are adopted. The theoretical model and the numerical results are in good agreement with the experiment.

The generation and the development of turbulent coherent structures in channel flows are investigated by using numerical simulation of Navier-Stokes equation and the theoretic model of turbulent coherent structures built up by the flow stability theories. The three-dimensional coupling compact difference scheme with high accuracy and resolution developed can be applied to the calculative region including points near the boundary. The results computed show nonlinear evolution process and characteristics of Reynolds stress, stream-wise vortices and span-wise vorticities, especially the nonlinear interactions between different coherent structures.

The present work shows that vortex breakdown may also occur in a bioreactor for animal cell or tissue culture. The aim is to study the effect of vortex breakdown on the fluid environment for cell growth, particularly hydrodynamic stress and mass transfer. A numerical simulation of the fluid flow and oxygen transfer in a cylindrical bioreactor is presented, in which a rotating base wall is used to generate the medium flow and mixing. The steady and laminar, axisymmetric Navier-Stokes and species equations are solved by the numerical model based on finite volume method. The hydrodynamic stress and oxygen transfer conditions are systematically studied by varying the two key parameters which determine the flow behavior: bioreactor aspect ratio H/R and a rotation Reynolds number Re=ΩR²/ν. It is found that the oxygen concentration at the attached breakdown vortex center is significantly higher than that at the main recirculation center but the hydrodynamic stress level is almost similar in the two regions. The results would provide guidance on choosing the proper operating parameters for cell or tissue culture.

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

Flows over two tandem cylinders are simulated numerically based on the lattice Boltzmann method. The pressure distribution on the cylinders for varying distance between the two cylinders at different Reynolds numbers is depicted. The results show that the minimum pressure on the front cylinder does not occur at the stagnation point because of the existence of the back cylinder. The distance between the point with minimum pressure and the stagnation point becomes large with increasing Re number. The minimum pressure on the back cylinder varies with the distance between the two cylinders. The effective distance of interaction between two cylinders is less than 4d with d being the diameter of the cylinder.

A new so-called truncation error reduction method (TERM) is developed in this work. This is an iterative process which initially uses a coarse grid (2h) to estimate the truncation error and then reduces the error on the original grid (h). The purpose of this method is to use multigrid technique to achieve high-order accuracy on simple stencils.

Surface roughness exists in most microfluidic devices due to the microfabrication technique or particle adhesion. In this study, a numerical model based on Finite Volume Method has been developed to simulate the mass transfer in a flat-plate microchannel bioreactor with semi-circular protrusions uniformly distributed on the bottom. The results show that the mass transfer in rough channel is enhanced, as shown by lower minimum species concentration in the rough channel compared with that in smooth channel. Non-dimensional parameters such as Peclet number (Pe), Damkohler number (Da) and the roughness size ratio (β) can influence the effect of roughness greatly. However, it is important to ensure that the minimum species concentration in the rough channel is adequate for cell growth. The results would provide guidance on the perfusion requirements to avoid solute depletion or toxicity during cell culture.

We construct a localized finite volume method by applying ENO (essentially non-oscillatory) reconstruction to solve hyperbolic conservation laws following the partitions of the spectral volume methods. The main idea is as follows: Firstly, separate the calculating domain into intervals, named main-cells, then divide the intervals into subintervals, named sub-cells. Secondly, use ENO methodology to reconstruct conservative variables in the main-cells by using the cell averages of proper sub-cells. After that, use the TVD Runge-Kutta time discrete method to obtain fully discrete scheme. Several classic numerical tests show that this scheme has capabilities to capture discontinuities in high resolution and robustness.

With fast development of microfluidic systems, fluid micro-mixing becomes a very important issue. In this paper, recent developments on various micromixers and their working mechanisms are reviewed, including the external agitation methods applied in active mixing and the channel geometries adopted in passive mixer design. The chaotic mixing and the influences of Re would be mainly discussed. At moderate and high Re, the fluid inertial effects usually facilitate the chaotic mixing. At low Re, generation of chaotic advection becomes more difficult but can still be achieved through fluid manipulations such as stretching and folding. Chaotic mixers can be characterized using dynamical system techniques, such as Poincaré plot, and Lyapunov exponent.

The wind tunnel experiments for high angle of attack aerodynamics were designed from the inspiration of understanding the mechanism and development of an innovative flow control technique. The side force, varying with the different rolling angle, is featured by bi-stable situation, and can be easily switched by a tiny disturbance. A miniature strake is attached to the nose tip of the model. When the strake is stationary, the direction of the side force can be controlled. When the nose tip strake, as an unsteady control means, is swung the flow pattern could be controlled. The results obtained from dynamic measurements of section side force indicate that when the strake swing at lower frequency the side force can follow the cadence of the swinging strake. With increasing frequency, the magnitude of the side force decreases. At still high frequency, the side force diminishes to zero. The side forces could be also changed proportionally. Based on the experimental factors, the mechanism of the asymmetry is discussed.

An effort is made to develop a new 3-component force-moment balance, which is capable of measuring lift force, drag force and pitching moment of a model mounted in the water tunnel. The concept used in the balance design is the bending- beam principle. The forces acting on the spring element cause strains on its surface, which are measured by strain gauges. Since strain yielded by the axial force is usually very small, therefore it is not practical to measure axial force using strain gauge directly to sense the strain in axial direction. The main idea of the new balance design is to translate all desired forces (lift and drag) in such a way that they yield bending strain at selected strain-gauge station. This is done by using a bending balance geometry. Under this apparatus, the model wing is mounted at one of its end to the bending balance. The corresponding Lift, Drag forces and Pitching moment are translated into moments at the other end of the balance, and can be measured from sets of strain gauges in bending mode (twisting mode for pitching moment). Example readings are presented in this paper.

Experimental observations and numerical simulations (based on the boundary element method) concerning an oscillating bubble near a flexible (thin) membrane are presented in this paper. The bubbles are created using an underwater electrical spark discharge. It is shown that the presence of a membrane can have a profound influence on the behavior of a bubble.

Energy components in the flow field at high angle of attack were analyzed by the dynamic measurement. The effect of the unsteadiness induced by these components on the flow was analyzed as well. The results showed that the flow itself at high angle of attack is a kind of "vortices behavior" and the effect of unsteadiness on the asymmetry of flow is relatively weak. The key factor that can essentially affect the flow at high angle of attack is the response of the dynamic unsteadiness of the vortices to the unpredictable micro-disturbance coming from near the nose of the model.

This study deals with the active control of T-S (Tollmien-Schlichting) wave in a two-dimensional boundary layer over a flat plate using a neural network and a flapping actuator. The flapping actuator consists of a thin aluminum plate and a piezoelectric element bonded together. Microphones were used as sensors to measure the pressure fluctuation in the boundary layer. A neural network was used to control the piezoelectric actuator based on the pressure signals from the sensors. The experimental results shows that the T-S wave in the boundary layer can be successfully suppressed even when its phase, amplitude and frequency change with time.

We experimentally investigate the breakup process of a circular oil film with a hole on water surface using PIV and flow visualization. The hole moves to the bound of the oil slick driven by surface tension, and then the slick breaks into smaller drops. Typical flow maps and velocity fields are given. It is shown that a pair of vortices forms at initial stage, the position of the vortices varies as the hole approaches the bound of the slick. Satellite drops arise when breakup occurs and the size of the satellite drops depend on the shape of the slick.

The wake of two circular cylinders in tandem arrangement is investigated by flow visualization and PIV experiments in a towing water tank. The two cylinders are spaced at L/d (spacing ratio) = 2.0 to 15.0 and the cross flow Reynolds number ranges from 60 to 120. The flow is seeded with fine Rilsan particles and illuminated by a 2 mm thick laser sheet. The PIV image analysis is done by a standard cross correlation scheme with a powerful validation algorithm followed by multi-pass adaptive cross correlation iterations. The main objective of the study is to investigate the characteristics of the downstream cylinder wake changing considerably with the spacing ratio of the two cylinders.

A novel framework of experimental studies on spatial dynamics of open flows has been put forward. The equivalence between global relations that bridge the relations in the momentum sense between two arbitrary points in a flow field and the NSE in the temporal Fourier series form has been proved mathematically. Furthermore, the global relations in the energy sense can be deduced.

Systematic experimental researches on reverse transition in the boundary layer on a heated plate are carried out, and the time-series of instantaneous velocity components and temperature fluctuation are measured, then the Reynolds stress, the production term and absorption term of turbulent energy are presented. From the experimental results, the characteristics and physics mechanism of reverse transition as well as statistical properties of turbulence during reversion are revealed.

An experimental and numerical study has been carried out on an indeterminate-origin V-notched jet to understand the pertinent vortex dynamics involved in the resultant flow. Laser cross-sections showed that outward-spreading streamwise vortices are formed at both peak and trough locations. The numerical simulation was also able to reproduce the general flow features observed in the same study by employing numerical dye-visualization. In view of the observations, a vortex flow model is proposed to account for the phenomenon.

Flow visualization experiments had been conducted using a water tunnel to investigate and study the effect of different hole geometries on lift-off and spreading characteristics on a jet in a cross flow stream. The relationships between the hydraulic diameters of the hole geometries and their lift-off and spreading characteristics were also investigated. Eight different hole geometries with the same cross-sectional area were used in the experiments. They are round, square, triangle, rectangular, "rect-circle", "peanut", "V-shaped" and "W-shaped". Dye release injection technique was used to visualize the characteristics of the jet trajectories from different hole geometries. From the results, the different geometries of cooling holes were found to have an effect on the trajectory of the jet. Hole geometries with "tongues" in them such as "W-shaped" and "V-shaped" holes produced jets with better flow adherence but poorer spreading. Hole geometries with lower hydraulic diameters also produced jets with better flow adherence but poorer spreading.

The experiment was carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The feature of the phenomenon was that the big amplitude axisymmetric surface wave frequency was typically about 1/50 of the excitation frequency. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we found the viscosity was important to achieve the low frequency water wave with the cooperation of hundreds of "finger" waves. Photographs were taken with stroboscopic lighting and thereafter relevant quantitative results were obtained based on the measurements with Polytec Scanning Vibrometer PSV 400.

The control mechanism of jet vectoring using synthetic jet actuators is investigated. The final deflection angle of the primary jet is a result of the primary jet controlled by synthetic jets at three different regions. The lower static pressure near the primary jet exit induced by the synthetic jet, the entrainment and absorption of the primary jet fluid by the synthetic jet during the blowing and the suction stroke, the coupling and interaction between the vortices of synthetic jet and the shear layer of the primary jet are the main control mechanisms for the synthetic jet actuator vectoring a primary jet. The main factors influencing jet vectoring are analyzed and summarized, and a preparatory model for jet vectoring using synthetic jet actuator is presented.

An experiment was performed to investigate the onset of turbulence in a flat plate boundary layer. The correlation dimension was calculated from the experimental data by means of chaos dynamics and the existence of the strange attractor was shown in the transitional processes. Therefore, the transitional processes to turbulence have been classified by not only the instability theory but also the nonlinear chaotic analysis. The relationship between the correlation dimension and the streamwise positions implies a natural connection between chaos dynamics and the onset of turbulence in a plate boundary layer, so transition is linked to the chaotic motion.

Both open and closed loop control algorithms have been developed for manipulating wake flows past a solid cylinder in an electrically low-conducting fluid. The intent is to avoid vortex shedding and flow separation from the body, which is achieved through the introduction of localized electromagnetic forces (Lorentz forces) in the azimuthal direction generated by an array of permanent magnets and electrodes on the surface of the circular cylinder. The array of actuators offers the advantage of making the Lorentz force time and space dependent. More specifically, one closed loop control method has been derived from the equations of motion capable of determining at all times the intensity of the Lorentz force in order to control the flow. This is accomplished first, independently of the flow (open loop algorithm) and second, based on some partial flow information measured on the surface of the solid body (closed loop algorithm).

An aircraft model was tested at the 3-meter low speed wind tunnel as it was oscillated with large amplitude. The unsteady aerodynamic behavior was acquired during the oscillation in yawing, rolling and yawing-rolling. The lateral-directional dynamic derivative was obtained using the mathematic model of unsteady aerodynamics and the dynamic derivative simulation. According to the principle of linear superposition, the unsteady aerodynamic parameters of the model about yaw-roll coupled motion can be obtained by the quasi-steady aerodynamic model and the result was compared with the experimental test. It was found that for the quasi-steady aerodynamic model the unsteady aerodynamic characteristic was in agreement with the test at the middle and large angle of attack (for example α ≤ 45°), but was opposite at the extremely large angle of attack (α > 45°).

A benchmark problem with air medium in a square cavity heated by a vertical side is studied in a Ra range near its critical value without using the usual model approximations, such as Boussinesq or low-Mach-number approximation. Two analysis methods of power spectrum and phase trajectory are adopted to distinguish the flow pattern in the cavity. It demonstrates how the flow evolves from transition to turbulent regimes with increasing Ra values.

This paper develops an efficient three-dimensional numerical procedure to predict incompressible flow in long microchannels. The major advantage of the present numerical procedure is its fast speed due to the parabolic character of the governing equations.

One of the functions of microvilli in the microvessel endothelial glycocalyx is molecular filtering. The microvillus behaves as a mechanosensory system which may sense the fluid shear and drag forces. The permeability of small particles in microvessel is crucial for drug design and drug delivery. Therefore a better understanding of flow field around microvillus is important to simulate accurately the particle penetration in microvessel. Since the dimension of the microvilli is about ~10 nm, the conventional Navier-Stokes equation may not be good enough to simulate the fluid flow in such microscale and nanoscale structures. Molecular dynamics (MD) simulation is a powerful method to simulate the fluid flow at the molecular level. As a first attempt, the microvillus is reduced as a two-dimensional cylinder which is in a cross flow. The detailed drag and lift together with flow field are obtained and compared with available data.

In this paper, a Newton-Multigrid method is presented to solve the numerical simulation of the slider air bearing. For each fixed attitude in the specified grid, the Newton method is used to achieve the pressure distribution of the slider by solving the generalized Reynolds equations discretized by the least square finite difference (LSFD) method. Between the different sizes of grids, full approximation multigrid method is used to accelerate the convergence rate by eliminating the dominating low frequency error mode in the late stages of convergence. From the case study of the slider air bearing, it shows that the Newton-Multigrid method is accurate and efficient for the numerical simulation problem.

Burgers equation is a fundamental partial differential equation of second order to describe the integrated process of convection-diffusion in physics. It occurs in various areas of applied mathematics and physics, such as modeling of turbulence, boundary layer behavior, shock wave formation, and mass transport. The convective and diffusive terms in Navier-Stokes equation are included in Burgers equation while the pressure term is neglected. A least-square point collocation meshless formula is proposed to discretize the Burgers equation. To verify the present meshless approach, the distributions of velocity for Burgers equation under different Reynolds numbers are investigated. Numerical results show that the proposed approach presents a good simulation of shock wave for Burgers equation with large Reynolds number.

Electro-osmotic flow can be used as an efficient pumping mechanism in microfluidic devices. For this type of flow, frictional losses at the entrance and exit can induce an adverse longitudinal pressure distribution that can lead to dispersive effects. The present study describes a numerical investigation of the influence of the electric double layer on the induced pressure field and the flow development length. The induced pressure gradient is affected by the volumetric flow rate, fluid viscosity and the channel height. When the electric double layer is small, the development length remains constant at 0.57 of the channel height but decreases as the double layer grows in thickness.

A set of governing equations for flows in the vegetated domain has been derived with the assumption that the vegetation is of straight and rigid cylinder. The effect of vegetation on flow motion is represented by the additional inertial and drag forces exerted by the vegetation on the ambient flow. The derived governing equations are incorporated into an existing 3D turbulent free surface flow model. The new model is validated by available experimental data for open channel flows passing through the vegetation with different vegetation size and density. The numerical results agree very well to the experiment data.

The aim of this paper is to show numerically the semi-ideal way of transferring energy in the non-steady supersonic mechanism. Energy can be transferred between two fluids in semi-ideal process if the two fluids are brought together for a direct contact. This paper shows the energy transfer between two fluids via the direct fluid-fluid interaction in a non-steady supersonic flow. This was shown by using two fluids one with higher energy than the other. Results including contour plots of static pressure, static temperature, and total pressure and velocity vectors show the structure of flow of the energy-transfer-mechanism in a supersonic flow.

This paper employs a thickness-averaged shallow water model to approximate periodical flows in a piezoelectric micropump. The fluid pressure equation is combined with the vibration equation of silicon diaphragm to construct a liquid-solid coupled equation. Numerical results of mode analysis of the coupled system indicate that the natural frequencies of coupled system are much lower than those of the non-coupled system. The relationships of the first order amplitude-frequency of the silicon diaphragm, and the flow rate-frequency of micropump are also given in this paper.

The steady-state force on the droplet released in another liquid subjected to the gravitational field and imposed thermal gradient in the case of vanishingly small Re and Ma is derived using the general solution given by Lamb. A solution to a transitional thermocapillary-type droplet migration is thereby obtained for the case of constant physical properties, which corresponds to the well known YGB result as t → ∞. These can be employed to investigate the interactions between droplets in a host solution under the gravitational and thermal influences, and further to explore deposition and migration of a droplet cluster in the corresponding fields.

When a thin flat pate is released in the still air, the plate may fall aslant and automatically set into a rotational motion. This phenomenon is called autorotation. In this state, the unsteady fluid-dynamic forces act on the plate due to the vortex shedding and the rotation of the body. In this study, we focused on the auto-rotating phenomenon of an elliptic cylinder and investigated the effect of the cylinder rotation on the unsteady fluid-dynamic forces by the comparison between the result of the complex velocity potential theory and the one of numerical simulation. It was found that the low drag occurring at -160 degree phase and the high lift at zero degree phase are caused by the cylinder rotation.

A fast algorithm for the boundary element method is developed to handle problems in underwater acoustics. The algorithm employs the multipole and local expansions to approximate far-field potentials, and exploits the discrete convolution nature of mapping multipole to local expansions to accelerate the potential evaluation process. The speedup in the solution process is achieved by fast Fourier transform on the multipole and local expansion coefficients on a regular grid. The method is demonstrated by a three-dimensional underwater acoustics scattering problem, and it is found to achieve accurate results with relatively low order of expansion.

In this proton exchange membrane fuel cell study, we present a transport equation for water molar concentration in the membrane; we also present a new equation for the membrane potential loss that strictly accounts for variable water content. Both 2-D and 3-D numerical simulations using our new membrane model are performed and compared with each other, and the 3-D numerical results are shown in good agreement with the experimentally acquired data.

In this paper, we experiment with city coal gas/air mixture in enclosed duct to investigate the acceleration mechanism of orifice plate obstacles on flame and its influence on explosion overpressure. Experimental results indicate that obstacle-induced turbulence can continually accelerate flame during its propagation and enhance explosion overpressure, and that flame acceleration is due to the unburned mixture heated by leading compression wave in front of flame front and the positive feedback of obstacle-induced turbulent zone to combustion process. Based on multi-material cell program, we adopt two-step chemical reaction model to simulate explosion process of city coal gas-air mixture in the duct, and the results agree well with the experimental ones.

Tourism is the major industry in the Huangshan city. This paper examines time series of tourism to Huangshan from 1979 to 2004. The yearly data set comprises the total arrivals of tourists and total income. A mathematical model which is based on the polynomial approximation and radial basis function is set up to model the tourist flow. The total income and expenditure per tourist are also modeled. The established mathematical models can be used to forecast the tourist flow so that proper planning and management can be arranged.

In this paper, an identification method is proposed for linear continuous time delay processes with unknown non-zero initial condition and disturbance from pulse tests. Multiple integral is used and integral intervals are specifically chosen to enable easy identification of the system parameters in one step. The effectiveness of the identification method is demonstrated through simulations.

Ink-jet technology is a novel method for rapid deposition of accurately measured material with high precision. Consequently it has been used for applications such as, deposition of light emitting polymers and more recently for fabricating 3D objects and micro-mechanical structures. Ink-jet technology is also being applied to produce tactile maps for the visually impaired. The efficiency of the tactile maps, as outlined by psychophysical and cartographic studies of haptics, depends on its 3D features. To comprehend and control these features, detailed understanding of interaction amongst micro-drops, which are typically 50μm in diameter, is imperative. Multiphase interaction takes place between each liquid drop at impact with liquid or solid cured drops (deposited previously) and the solid substrate in an envelop of air. The behavior of micro-drops with regards to surface tension, drop coalescence among liquid and solid drops, drop impact kinetics, wettability, surface energy and drop spread has been analyzed using a computational model.

In this paper, based on the idea of the homogeneous balance method, the special truncated expansion method is improved. The Burgers-KdV equation is discussed and its many exact solutions are obtained with the computerized symbolic computation system Mathematica. Our method can be applied to finding exact solutions for other nonlinear partial differential equations too.

Two new methods for correlating experimental data of Rayleigh-Bénard convection in a fluid layer dispersed with phase-change-material particles have been proposed. Instead of the conventional arithmetic mean temperature method, two new methods for evaluating the intensity of convection in a horizontal fluid layer with strongly temperature-dependent specific heat were given. One method is by introducing a modified Stefan number in a Nu-Ra correlation or using the integrally averaged specific heat across the layer for calculating the Rayleigh number. The other method is by using the supercriticality (Ra/Ra_c) as an intensity parameter, in which the critical Rayleigh number Ra_c can be calculated by using the linear stability theory. Two models of non-dimensionalized apparent specific heat functions with respect to temperature were introduced. Results show that the two proposed methods are more rational comparing with the convectional 1/2-height rule method.

Spherical oscillation of an acoustically levitated gas bubble in water was simulated numerically to elucidate the phenomenon of single-bubble sonoluminescence (SBSL). A refined hydro-chemical model was used, which took into account the processes of water vapor evaporation and condensation, mass diffusion, and chemical reactions. The numerical results show significant water vapor dissociations but rather low degrees of ionizations. A widely accepted weakly ionized gas model is then used to compute the light emission. Contrary to earlier predictions without chemical reactions, the present calculated light spectra are generally too small and the pulses are too short to fit to recent experimental results within stable SBSL range. To solve this contradiction, the electrostatic interactions of the ionized gases are included, which is shown to lower the ionization potentials of gas species in the bubble significantly.

This paper will explain the structure of the flow induction in a non-steady supersonic fluid in which steam is the working fluid. The ratio of the throat diameter is varied and the analyses related to the induction processes are studied. This ejector is used for compression applications. The work to be presented herein is a Computational Fluid Dynamics investigation of the complex fluid mechanisms that occur inside a non-steady, three-dimensional, steam supersonic pressure exchange ejector, specifically with regard to the pressure exchange mechanisms and the induction processes between a primary fluid and a secondary fluid and how this is related to the shape of the aerodynamic shroud-diffuser surface. The results will show the correct throat diameter ratio that is capable of producing the desire affect of the flow induction in a three-dimensional supersonic, non-steady, viscous flow. The calculated throat diameter ration is about 2.90.

In this work, a fixed-mesh method for general moving objects in fluid flow was developed and implemented into the commercial CFD software FLOW-3D. A general moving object is a rigid body with any type of six-degrees-of-freedom, fixed-point and fixed-axis motion which can be either user-prescribed or dynamically coupled with fluid flow. The method allows multiple general moving objects, and each of them can possess any different type of motion. Area and volume fractions to represent the objects in the fixed-grid are calculated at every time step to describe time-variation of object locations and orientations. Continuity and momentum equations for fluid are modified to account for the effects of object motion on fluid flow. A good agreement is achieved between computational and experimental results in an application to a valve problem.

An application of CFD model for the simulation of a strongly swirling and high speed flow in the vortex tube is presented in this paper. A partly modified standard K-ε turbulent model has been used to investigate the flow characteristics and energy separation effect in the vortex tube. It is found that there is an obvious energy separation effect in the vortex tube and the numerical solutions of the flow and temperature fields agree well with the experiments. More detailed flow features are obtained by the CFD calculation. Based on the validated numerical model, the influence of the cold flow fraction on the energy separation effect is also investigated and compared with experimental results.

Modeling flow and solute transport in the unsaturated zone requires specifying values for soil hydraulic conductivity. Fractal models describe hierarchical systems and are suitable to model soil structure and soil hydraulic properties. The objectives of the paper are to propose a parameter identification approach and to determine hydraulic parameters using inverse modeling. The inverse problem of parameter identification is formulated as an optimization problem. In order to identify hydraulic parameters of soils efficiently and in a robust manner, the genetic algorithm is presented for the parameter identification of the fractal models. The investigation shows that the proposed inversion procedure is more superior for applying to parameter identification of fractal model of mass transport for unsaturated soils.

One important function of the port is to protect ship or some other facilities from wave attack so as to stably handle cargoes. In current design codes, there are mainly two expressions of the tranquility standard of harbor basin: one is the acceptable wave height in front of wharf; the other is the tolerable amplitude of ship motion. However, ship motions are affected by some more factors simultaneously, such as wave frequency, wave height, incident wave direction, ship properties and wharf type. This paper presents some computed results of the wave-induced ship motions on the basis of a port case in China. First, the Simple Green Function method is employed to solve and compare the 2-dimension hydrodynamic coefficients in front of open or bulkhead wharf. The results show a great difference between them. Then, this paper computes and discusses the ship motions in front of open wharf at different wave frequencies and incident wave directions.

This paper presents the preliminary results of a modeling study on regional air pollutants transport over the Pearl River Delta (PRD) region of China in fall season (Nov. 2002) on the basis of compiled emission inventories. The advanced regional chemical transport model, STEM-2K1, driven by meso-scale meteorological model MM5, was employed with a nesting technique. Three weather patterns were found in the fall season. Numerical sensitive study indicated that external influence on air quality in PRD was significant and dependent on the transport pattern determined by weather situations.

This paper presents a numerical solution for the four-phase traveling dielectrophoresis (DEP) using a novel meshless method - weighted least square finite difference (LSFD) scheme. The exact boundary condition and nonuniform point distribution were used in the calculation. Numerical results including the electrical potential, electrical field, traveling DEP forces and particle behavior are presented. Although the LSFD scheme was originally proposed in solving incompressible viscous flow, it is further demonstrated in this paper that the method is also well suited for solving all kinds of DEP problems in which extremely high gradient of electric field exists in the computational domain, e.g. edges of the electrodes. The LSFD method enables the computational ease of free point/mesh distribution in these areas and hence save the computational efforts.

A three-dimension numerical wave model (3DWAVE) has been developed to simulate free surface flows. The model solves Navier-Stokes equations for two-phase flows of air and water. The level set method is employed to track water surfaces. The model is tested for water sloshing in a 3-D confined tank. The relative error in the mass and total energy computation is less than 1%. Excellent agreements between numerical results and analytical solution are obtained for free surface calculation. The nonlinearity in the 3-D fluid sloshing is analyzed. These have laid a foundation on research of breaking waves.

Pressure wave refrigerators (PWR) refrigerate the gas through periodical expansion waves. Due to its simple structure and robustness, PWR may have many potential applications if the efficiency becomes competitive with existing alternative devices. In order to improve the efficiency, the characteristics of wave propagation in a PWR are studied by experiment, numerical simulation and theoretical analysis. Based on the experimental results and numerical simulation, a simplified model is suggested, which includes the assumptions of flux-equilibrium and conservation of the free energy. This allows the independent analysis of the operation parameters and design specifics. Furthermore, the optimum operation condition can be deduced. Some considerations to improve the PWR efficiency are also given.