A numerical method for two phase flows with insoluble surfactants

In many practical multiphase flow problems, i.e. treatment of gas emboli and various microfluidic applications, the effect of interfacial surfactants, or surface reacting agents, on the surface tension between the fluids is important. The surfactant concentration on an interface separating the fluids can be modeled with a time dependent differential equation defined on the moving and deforming interface. The equations for the location of the interface and the surfactant concentration on the interface are coupled with the Navier–Stokes equations. These equations include the singular surface tension forces from the interface on the fluid, which depend on the interfacial surfactant concentration.A new accurate and inexpensive numerical method for simulating the evolution of insoluble surfactants is presented in this paper. It is based on an explicit yet Eulerian discretization of the interface, which for two dimensional flows allows for the use of uniform one dimensional grids to discretize the equation for the interfacial surfactant concentration. A finite difference method is used to solve the Navier–Stokes equations on a regular grid with the forces from the interface spread to this grid using a regularized delta function. The timestepping is based on a Strang splitting approach.Drop deformation in shear flows in two dimensions is considered. Specifically, the effect of surfactant concentration on the deformation of the drops is studied for different sets of flow parameters.     

Behavior analysis of air bubbles in the oil lubricant of FDBs at low speed operating conditions

This paper investigated the behavior of the air bubbles and the air–oil interface of FDBs at low speed operating conditions by using a two-phase flow analysis of air and oil to study the expelling mechanism of air bubbles in the operation of FDBs. The two-phase flow of air and oil was analyzed using the three-dimensional Navier–Stokes equation and the volume of fluid method of multi-phase flow. The proposed numerical method was verified by the experimental results. The effects of the depth and area of the groove near the outlet on the behavior of the air bubbles and the air–oil interface were also studied. This research shows that the groove near the outlet is responsible for the concave shape of the air–oil interface as a result of surface tension, and that air bubbles are expelled into the outside air when an air bubble meets the concave air–oil interface.     

Numerical simulation of structure response outfitted with a tuned liquid damper

An integrated fluid–structure numerical model has been developed to simulate the response of a single degree of freedom (SDOF) structure outfitted with a Tuned Liquid Damper (TLD). The structure is exposed to random external excitations. A non-linear, two-dimensional, flow model has been developed using the finite-difference method. Unlike most existing flow models, the present model does not include any linearization assumptions; it rather solves the entire nonlinear, moving boundary, flow problem under conditions leading to large interfacial deformations. The free surface has been reconstructed using the volume of fluid method and the donor–acceptor algorithm. The Duhamel integral method has been used to determine the response of the structure. The effectiveness and accuracy of the flow model has been validated using a set of benchmark problems and experimental data. The numerical results of this model have been compared with results of an equivalent TMD model. The present fluid–structure model can be used as a valuable tool for performance evaluation and design of more effective tuned liquid dampers.     

高速列车动模型车载数据采集系统

利用高速列车动模型试验研究高速列车实车运行时空气动力学问题是一种可行的方法。介绍一种车载数据采集系统,利用80C196KC单片机的外部事务服务器PTS功能,在动模型车外表面上多个测量点并行采集动模型车表面在运行时的空气压力波数据,实现高速、大容量数据采集和存储,同时利用光电传感器和80C196KC单片机的HIS事件捕捉功能实现动模型车的全程运行速度测量,并解决了数据采集触发启动问题。测量结果与实际情况相符,可建立动模型车各种运行情况时的路程、速度和其表面空气压力间关系,在实际应用中是可行的。     

Modeling of web conveyance systems for multivariable control

A distributed parameter model of the lateral dynamic behavior of a moving web in an n-roller system is proposed. A span of web moving longitudinally and under tension is modeled as a beam with shear flexibility (Timoshenko beam). A quasistatic simplification of the model is made on the basis of spectral separation. Boundary conditions at the web-roller interface are considered. Actuator dynamics are introduced through the formulation of the boundary conditions. Closed-loop simulations using a state-space version of the simplified model are in agreement with experimental results     

Similarity solutions for axisymmetric plane radial power law fluid flows through a porous medium

This paper investigates the unsteady flow of non-Newtonian fluids of power low behavior through a porous medium in a plane radial geometry. The equation governing the flow is a nonlinear parabolic partial differential equation with a source term whose solution satisfies certain fixed and moving boundary conditions. The attention is focused on the finding of similarity solution when the fixed boundary condition and the source term satisfy certain restrictions. In this case similarity transformations are determined and the resulting ordinary differential equations are deduced. For shear thinning fluids the existence of a pressure disturbance front moving with finite velocity is shown and expression for its location as a function of time is determined. The solutions in closed form have been given for certain particular cases where the resulting differential equations can be analytically solved. A numerical procedure has also been presented.     

Numerical simulation of molecularly thin lubricant film flow due to the air bearing slider in hard disk drives

In this paper we numerically study the evolution of depletion tracks on molecularly thin lubricant films due to a flying head slider in a hard disk drive. Here the lubricant thickness evolution model is based on continuum thin film lubrication theory with inter-molecular forces. Our numerical simulation involves air bearing pressure, air bearing shear stress, Laplace pressure, the dispersive component of surface free energy and disjoining pressure, a polynomial modeled polar component of surface free energy and disjoining pressure and shear stress caused by the surface free energy gradient. Using these models we perform the lubricant thickness evolution on the disk under a two-rail taper flat slider. The results illustrate the forming process of two depletion tracks of the thin lubricant film on the disk. We also quantify the relative contributions of the various components of the physical models. We find that the polar components of surface free energy and disjoining pressure and the shear stress due to the surface free energy gradient, as well as other physical models, play important rolls in thin lubricant film thickness change.     

Numerical analysis of dual-phase-lag heat transfer in a layered cylinder with nonlinear interface boundary conditions

To accommodate the micro-structural effect, this work analyzes the heat transfer induced by a pulsed surface heating in a two-layered solid cylinder with the dual-phase-lag model. The interface thermal resistance is specified with the radiation boundary condition model. Due to the difference in the relaxation times between two dissimilar materials, the strong nonlinearity of the interfacial boundary condition, and the singularity at the center axis, it introduces the complexity and causes some mathematical difficulties to analyze the present problem. Thus a numerical scheme is developed. Results show the lagging thermal behavior is affected with the geometry effect and the interface thermal resistance and depends on the magnitude of the relaxation times more than the ratio value between the relaxation times. The microstructure effect would destroy the structure of thermal wave. The propagation speed of thermal wave is independent of the interface thermal resistance and the microstructure effect.     

Coupling of two- and three-dimensional hydrodynamic numerical models for simulating wind-induced currents in deep basins

The main interest of the present study is the simulation of wind-induced currents in closed water bodies with shallow and deep regions. This paper describes a low time consumption numerical modelling technique for the simulation of free-surface flow over a geometrically complex bed. To achieve this, a technique employing coupled two- and three-dimensional flow solvers is developed for simulation of the flow. The conjunctive model consists of an upper part 2D Shallow Water Flow Solver (2D-SWFS) coupled with a 3D pseudo-compressible flow solver (3D-PCFS) for the deep regions with a proper interface boundary condition. The 2D-SWFS and 3D-PCFS solvers are coupled via an interfacial shear stress gradient and pressure effects. Time stepping is performed for the 2D solver, and an iterative procedure is employed by the 3D solver to satisfy the equilibrium constraints for the interfacial boundary. The model is able to consider 2D wetting and drying shallow regions without any underlying deep water. Both the 2D and 3D models use nodal based Galerkin finite volume method (GFVM) for solving the governing equations on the unstructured meshes. The accuracy of both models in solving the effective phenomena is examined by comparing the results of simulated test cases with readily available analytical solutions and experimental measurements. Finally, the accuracy of the conjunctive model is assessed by comparing its results for test cases with analytical solutions and experimental measurements from the literature. The new simulation method is then used to solve a wind-induced flow problem in a basin with deep water surrounded by shallow water parts.     

Measurement of dynamic surface tension using helical flow of a viscous liquid in a pool of another viscous liquid inside a micro-channel

Measurement of surface tension (s.t.) and critical micelle concentration (c.m.c.) of a surfactant in dynamic condition is important for several engineering applications, for which, the interface between two or more different phases does not remain constant but alters and replenishes continuously with flow of the fluids so that equilibrium may not be reached between the bulk and the interface. There are however not many methods for measuring these quantities in dynamic experiments which mimics the real dynamic situations. In this report, we present a novel two-phase flow pattern inside a triple-helical micro-channel using which, we show that it may be possible to measure the dynamic s.t. of a liquid. When two immiscible liquids such as oil and water are pumped into it, at a certain range of flow rates, oil flows as the continuous phase, whereas water remains in it as a wavy filament, the wavelength of which varies with the flow rates of oil and water but also on the interfacial tension between these two liquids. We show that wavelength decreases with increase in concentration of a solute attaining a minima at the c.m.c. A simple scaling analysis captures most experimental observations.     

CFD mesh generation for biological flows: Geometry reconstruction using diagnostic images

A new thrust in the use of CFD techniques for simulation of biological flows has necessitated the demand for robust grid generation techniques to characterize the complex geometries. While the techniques of image manipulation required are simple, most researchers in this field use proprietary 3rd party software for image manipulation and grid generation. In the current study, we propose a simple MATLAB based grid generation techniques suitable for CFD studies of external and internal biological flows such as blood flow and respiration and flows around the human body. As an example, the flow inside two specific intracranial aneurysms is modeled by generating CFD grids from 3D rotational angiography images. Specific issues of modeling, such as boundary conditions and location of flow inlets and outlets, in relation to the reconstructed geometry are discussed. The reconstructed arterial geometry including the aneurysm matches the visual representation generated by the angiogram software (Leonardo software). The calculated CFD flow patterns also show a good correlation to the flow visualization presented by the Leonardo software. Areas of high pressure and wall shear stress are identified. The same technique is also used to generate the CFD grid of a human trachea to study the particle dispersion patterns during a human cough cycle. The fluid is modeled using an actual human cough signal with the particles simulating the influenza virus. The flow pattern out of the mouth along with the dispersion pattern of the particles is validated against similar human experimental studies to track the spread of the disease through cough. Work is also currently underway to use the present grid generation program to construct a superficial mesh of the human body from MRI/CAT scan images of cadavers. The goal is to build an accurate and scalable model of the human body surface with articulate joints which can be posed in any environment to model the air flow patterns around the body.     

Development of a MEMS-based control system for compressible flow separation

A MEMS-based sensor and actuator system has been designed and fabricated for separation control in the compressible flow regime. The MEMS sensors in the system are surface-micromachined shear stress sensors and the actuators are bulk-micromachined balloon vortex generators (VGs). A three-dimensional (3-D) wing model embedded with the shear stress sensors and balloon VGs was tested in a transonic wind tunnel to evaluate the performance of the control system in a range of Mach number between 0.2 and 0.6. At each Mach number tested, the shear stress sensors quantify the boundary layer on the surface of the wing model while the balloon VGs interact with the boundary layer in an attempt to provide flow control. The shear stress measurements indicate the presence of a separated flow on the trailing ramp section of the wing model at all Mach numbers tested when the balloon VGs are not activated. This result is confirmed by total pressure measurements downstream from the wing model where a wake profile is observed. When the balloon VGs are activated, the shear stress level on the trailing ramp increases with the Mach number. At the highest Mach number tested, this increase elevates the shear stress on the ramp to almost the same level as the unseparated flow, suggesting the possibility of a boundary layer reattachment. This result is supported by the downstream pressure measurements which show a large pressure recovery when the balloon VGs are activated. The wind tunnel experiment successfully demonstrated two aspects of the MEMS flow control system: the effectiveness of the microshear stress sensors in measuring the separation characteristics of a high-speed compressible flow and the ability of the microballoons in positively enhancing the aerodynamic performance of a high-speed wing through boundary layer modification.     

Numerical modelling of interfacial soil erosion with viscous incompressible flows

The aim of this study is to develop a numerical model for simulating surface erosion occurring at a fluid/soil interface subject to a flow process. Balance equations with jump relations are used. A penalization procedure including a fictitious domain method is used to compute the Stokes flow around obstacles, in order to avoid body-fitted unstructured meshes and instead use fast and efficient finite volume approximations on Cartesian meshes. The evolution of the water/soil interface is described by using a level set function. The ability of the model to predict the interfacial erosion of soils is confirmed by several numerical simulations.     

Static Friction in Polysilicon Surface Micromachines

Surface micromachines of polycrystalline silicon were used to investigate the dependence of static friction in microelectromechanical systems on the external load, apparent contact area, and environmental conditions. An analytical model of the micromachine at the inception of sliding was used to determine the normal load consisting of the restoring and levitation forces exerted by the micromachine's comb-drive actuators. The apparent shear strength at the contact interface(s) exhibited a nonlinear dependence on the apparent contact pressure. Relatively higher static coefficient of friction and interfacial shear strength were obtained in room air than vacuum ambient. The static coefficient of friction was found to depend on the normal load, apparent contact area, and ambient conditions (i.e., relative humidity). Electrical contact resistance measurements indicated that sliding in room air promoted thickening of the native oxide film at asperity contacts. The experimental evidence suggests that modification of the surface topography occurred at the asperity level. However, these submicroscopic changes in the surface topography did not affect the overall static friction behavior, for the test cycles simulated in the friction experiments.$hfillhbox[1225]$     

Flux-based level-set method for two-phase flows on unstructured grids

In this paper we deal with the application of the flux-based level set method to moving interface computations on unstructured grids. The focus lies on the overcoming of the known difficulties of level set methods, e.g. accurate computations of important geometric properties, reliable and precise reinitialization of the level set function and the adaption of standard discretization methods to the moving boundary case. The basic building block of our approach is the high-resolution flux-based level set method for general advection equation (Frolkovi? and Mikula in SIAM J Sci Comput 29(2):579–597, 2007, Frolkovi? and Wehner in Comput Vis Sci 12(6):626–650, 2009). We extend this method for the problem of reinitialization of the level set function on unstructured grids by using quadratic interpolation to compute distances for nodes close to the interface. To realize numerical simulation for some applications with moving boundaries, we adapt the approach of ghost fluid method (Gibou and Fedkiw in J Comput Phys 202:577–601, 2005) for unstructured grids. The idea is to describe the development of the moving boundary with a level set formulation while the computational grid remains fixed and the boundary conditions are enforced using some extrapolation. Our main motivation is the numerical solution of two-phase incompressible flow problems. Additionally to previously mentioned steps, we introduce further numerical schemes in the framework of finite volume discretization for the flow. Possible jumps of the pressure and the directional derivative of velocity at the interface are modeled directly within the method using the approach of extended approximation spaces. Besides that, an algorithm for the computations of curvature is considered that exhibits the second order accuracy for some examples. Numerical experiments are provided for the presented methods.     

CFD simulations of wave-current-body interactions including greenwater and wet deck slamming

A numerical method for the solution of unsteady Navier-Stokes equations has been employed in conjunction with an interface-preserving level-set method for the simulation of greenwater effect on offshore structures and ships. In this method, the free surface flows are modeled as immiscible air-water two-phase flows and the free surface itself is represented by the zero level-set function. The Navier-Stokes equations for both the water and air flows are formulated in moving curvilinear coordinate system and discretized using the finite-analytic method on a non-staggered multi-block grid system. Large eddy simulation (LES) approach is used with Smagorinsky model to account for the effects of turbulence induced by violent free surface motions. A chimera domain decomposition approach is implemented using overlapping, embedding, or matching grids to facilitate the simulation of complex flow around practical configurations. The overset grid system also greatly simplified the simulation of arbitrary translational and rotational motions among various computational blocks. Calculations were performed first for dam-breaking flow and free jet problems involving violent free surface motions. The level-set Navier-Stokes method was then employed for the simulation of slamming of a hemisphere, greenwater on offshore structure and ships, and wet deck slamming of an X-Craft in pitch and heave motions. The numerical results clearly demonstrated the capability of the level-set method to deal with violent free surface flows involving breaking waves, water droplets, trapped air bubbles, and wave-current-body interactions.     

Co-surge in bi-turbo engines: Measurements,analysis and control

In parallel turbocharged V-engines, with two separate air paths connected before the throttle, an oscillation in the flow can occur. If the compressor operates close to the surge line, typically during low speed and high load, and a disturbance alters the mass flow balance, the compressors can begin to alternately go into surge. This phenomenon is called co-surge and is unwanted due to high noise and risk of turbocharger destruction. Co-surge is measured on a test vehicle in a chassis dynamometer and the system analyzed and modeled using a mean value engine model. The investigation shows that alternating compressor speeds have an important role in the prolonged oscillation. A reconstruction of the negative flow from measurements is made and compared to simulation results, showing similar amplitudes, and supports the model validation. A new co-surge detection algorithm is presented, suitable for a pair of sensors measuring either mass flow, boost pressure or turbo speed in the two air paths. Furthermore, a new controller is proposed that uses a model based feedforward for the throttle, together with wastegate actuation to force the compressor speeds together and improve balance at the recovery point. This has been shown to be sufficient for moderate to high pressure ratios over the throttle, and only for zero or very low pressure drop the use of bypass valves is necessary. The advantage of not opening the bypass valves is a smaller drop in boost pressure which also reduces the torque disturbance. The performance of the controller is evaluated both in simulation and in the test vehicle.     

Subdivision elements for large deformation of liquid capsules enclosed by thin shells

This paper presents a numerical method for studying the large deformation of a liquid capsule enclosed by a thin shell in a simple shear flow. An implicit immersed boundary method is employed for calculating the hydrodynamics and fluid–structure interaction effects. A thin-shell model for computing the forces acting on the shell middle surface during the deformation is described within the framework of the Kirchhoff–Love theory of thin shells. This thin-shell model takes full account of finite-deformation kinematics which allows thickness stretching as well as large deflections and bending strains. The interpolation of the reference and deformed surfaces of the shell is accomplished through the use of Loop's subdivision surfaces. The resulting limit surface is C¹-continuous which significantly improves the ability of the method in simulating capsules enclosed by hyperelastic thin shells with different physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, oblate spheroidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, tumbling and transition from tumbling to tank-treading have been studied over a range of shear rates and viscosity ratios.     

Incompressible moving boundary flows with the finite volume particle method

Mesh-free methods offer the potential for greatly simplified modeling of flow with moving walls and phase interfaces. The finite volume particle method (FVPM) is a mesh-free technique based on interparticle fluxes which are exactly analogous to intercell fluxes in the mesh-based finite volume method. Consequently, the method inherits many of the desirable properties of the classical finite volume method, including implicit conservation and a natural introduction of boundary conditions via appropriate flux terms. In this paper, we describe the extension of FVPM to incompressible viscous flow with moving boundaries. An arbitrary Lagrangian–Eulerian approach is used, in conjunction with the mesh-free discretisation, to facilitate a straightforward treatment of moving bodies. Non-uniform particle distribution is used to concentrate computational effort in regions of high gradients. The underlying method for viscous incompressible flow is validated for a lid-driven cavity problem at Reynolds numbers of 100 and 1000. To validate the simulation of moving boundaries, flow around a translating cylinder at Reynolds numbers of 20, 40 and 100 is modeled. Results for pressure distribution, surface forces and vortex shedding frequency are in good agreement with reference data from the literature and with FVPM results for an equivalent flow around a stationary cylinder. These results establish the capability of FVPM to simulate large wall motions accurately in an entirely mesh-free framework.     

Incompressible flow computations over moving boundary using a novel upwind method

In this paper a novel method for simulating unsteady incompressible viscous flow over a moving boundary is described. The numerical model is based on a 2D Navier–Stokes incompressible flow in artificial compressibility formulation with Arbitrary Lagrangian Eulerian approach for moving grid and dual time stepping approach for time accurate discretization. A higher order unstructured finite volume scheme, based on a Harten Lax and van Leer with Contact (HLLC) type Riemann solver for convective fluxes, developed for steady incompressible flow in artificial compressibility formulation by Mandal and Iyer (AIAA paper 2009-3541), is extended to solve unsteady flows over moving boundary. Viscous fluxes are discretized in a central differencing manner based on Coirier’s diamond path. An algorithm based on interpolation with radial basis functions is used for grid movements. The present numerical scheme is validated for an unsteady channel flow with a moving indentation. The present numerical results are found to agree well with experimental results reported in literature.