Drop Tower Experiment to Study the Capillary Flow in Symmetrical and Asymmetrical Channels: Experimental Set-up and Preliminary Results

Owing to the development of the space exploration activities, the in-orbit management of fluids such as the transportation of propellant liquid in microgravity becomes the important direction of microgravity fluid research, and one of main problems is the stability behaviors of free surface flow in capillary channel of PMD. In the present study, an experiment set-up of the fluid transport with two different capillary channels has been developed on the Beijing Drop Tower platform. Both symmetrical and asymmetrical flow channels, with the same cross-sectional areas and lengths and different cross-sectional geometries were used and HFE-7500 is chosen as test liquid. 10 times of the drop-down experiments were performed for investigation of the capillary flow characters in different volumetric flow rates, and the three main patterns of capillary flows: subcritical flow, critical flow and supercritical flow were found in experiments, these patterns are distinguished by the movement of the point of lowest surface over time. Meanwhile, the critical flow rates at which free surface becomes instable observed in our experiments are (1) 2.7 ±0.2ml/s for the critical flow rate of asymmetrical channel; and (2) 2.2 ±0.2ml/s for symmetrical channel flow, respectively.     

A three-dimensional panel method for nonlinear free surface waves on vector computers

A number of recent improvements in a higher-order three-dimensional (3D) panel method for highly nonlinear free surface wave simulations is discussed. Special attention is paid to grid evolution techniques, and stability of the time-dependent problem. Due to the improvements, stable and accurate results can be obtained for linear and highly nonlinear wave problems. Although no artificial smoothing is applied, even extreme problems like the development of breaking waves in a 3D configuration can be simulated. The computer code has been specially developed for implementation on a vector computer. The program is highly vectorized, and use is made of mathematical libraries for acceptable CPU-times.     

Parallel finite element fluid analysis on an element-by-element basis

A finite element fluid analysis code, which is based on an element-by-element scheme and the matrix-storage free formulation, is developed and implemented to the massively parallel computer; KSR1. Since the element-by-element scheme coupled with the CG-type iterative solver is suitable for parallel processing, the matrix-storage free formulation will enable the large-scale computation within a reasonable time.After the verification of the code by some numerical examples, the cavity flow and cyclinder flow, the parallel efficiency is discussed. In the analysis of cavity flow, the speed-up using 16 CPUs is 15.35, which corresponds to the parallel efficiency of 95.9%.     

The free surface fluid flow over a step of an arbitrary shape in a channel

A boundary integral technique has been developed for the two-dimensional, free surface fluid flow in an arbitrary shaped channel. For steady, ideal, irrotational fluid flow a system of boundary integral equations are derived which are based on the Riemann-Hilbert technique for mixed boundary value problems of an analytical function. The boundary integral equations are solved for the fluid speed on both the solid boundary and the free surface, the shape of the free surface and for the critical Froude number for which waves first occur.     

ANN approach to sorption hysteresis within a coupled hygro‐thermo‐mechanical FE analysis

Non‐linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN‐FE code has been developed and tested for 1‐D and 2‐D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary‐porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN‐FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro‐thermal behaviour of capillary‐porous materials. Copyright © 2001 John Wiley & Sons, Ltd.     

Analysis of steady free convection from an axisymmetric heat-generating body embedded in a semi-infinite porous medium

An analysis is presented for the steady state free convective flow and heat transfer from an axisymmetric heat-generating body that is embedded in a fluid-saturated, semi-infinite, porous medium. The porous medium is assumed to be rigid, homogeneous and isotropic, and be in thermal equilibrium with the fluid. The fluid is assumed to be incompressible, with the density changes contributing only towards the buoyancy forces via the Boussinesq approximation. The governing equations for the fluid consist of the equation of continuity, Darcy's law and the equation of energy. After introducing the stream function concept, the equations governing the stream function and pressure are derived. Using the non-dimensional variables, the non-dimensional equations governing the non-dimensional forms of the temperature, stream function and pressure are dervied and the appropriate boundary conditions are stated. The mathematical formulation contains two parameters; D, the non-dimensional depth of the body from the surface of the porous medium, and a product Raθ_s of Rayleigh number (Ra) and the non-dimensional surface temperature of the body (θ_s). The Galerkin finite element method, with linear, isoparametric, quadrilateral elements, is used to reduce the mathematical formulation into a set of algebraic equations. The expressions to calculate the non-dimensional surface temperature and Nusselt number of the body, and the non-dimensional velocity of the fluid, are derived. A computer code has been developed to solve the algebraic equations, using Gauss elimination procedure, in a banded matrix form. The computer code, in addition to the non-dimensional temperature, stream function and pressure, calculates the isothermal lines, non-dimensional surface temperature of the body, Nusselt number of the body, velocity field and isobars. To demonstrate the application of the code, a spherical heat-generating body is considered as an example. Numerical results are obtained for D = 3 and 6, and Raθ_s = 0.001, 0.1, 1 and 5, and presented.     

Stationary Two-dimensional Inviscid Flow with Flexible Boundaries Including the Effect of Surface Tension

Surface tension, which acts on free boundaries, can change considerably the configuration of a free boundary and influence the hydrodynamic characteristics of a deformable surface. The capillary film on the border of a fluid and gas can be regarded as a flexible momentless shell; however, the existence conditions of a flow of capillary fluid with a free boundary and a flow about a flexible shell with analogous geometry may differ considerably. In this paper problems of the two mentioned types with a single boundary condition are investigated and it is shown which flow corresponds to each mathematical solution     

Parallel implementation of the EFG Method for heat transfer and fluid flow problems

The parallel implementation of the element free Galerkin (EFG) method for heat transfer and fluid flow problems on MIMD type parallel computer is treated. A new parallel algorithm has been proposed in which parallelization is performed by row-wise data distribution among the processors. The codes have been developed in FORTRAN language using MPI message passing library. Two model (one each in heat transfer and fluid flow) problems have been solved to validate the proposed algorithm. The total time, communication time, user time, speedup and efficiency have been estimated for heat transfer and fluid flow problems. For eight processors, the speedup and efficiency are obtained to be 7.11 and 88.87% respectively in heat transfer problems for a data size of N=2,116 whereas 7.20 and 90.04% respectively in fluid flow problems for a data size of N=2,378.     

Free surface flow through rock-fill dams analyzed by FEM with level set approach

 A stabilized-finite element formulation is coupled with a level set technique for computations of incompressible non-linear flow with interfaces between two immiscible fluids. An interface capturing formulation (ICF) for non-linear, free surface, seepage flow in rock-fill dams is proposed. The formulation is derived for two- and three-dimensional flow within a fixed mesh domain. The resulting formulation is general and applicable for various steady and transient two-phase flow problems. FE-refinement is processed for the entire fixed mesh domains. A general solver is also reviewed for large and non-symmetric non-positive definite linear system of equations with the GMRES-update technique based on a Newton-iterative method. The computational procedure has been implemented in MATLAB. A comparison is performed between the 2-D computed test problem for coarse and refined meshes together with some proposed analytical solutions for nonlinear seepage flow with free surface in rock-fill dams. An expansion of the 2-D program code to a 3-D one for a rectangular rock-fill dam is also developed and simulated in MATLAB. The performance of the computations in 3-D is very promising and its opening the future for possible industrial applications using the same simple technique. Computations for a simple 3-D seepage flow problem with free surface in rock-fill dam are included in present paper. A general mesh generator and solver for large scale and complex 3-D flow problems in a real embankment dam is also under construction in C++.     

Numerical analysis of heat-induced transients in forced flow helium cooling systems

This work investigates theoretically the consequences of a space and time dependent energy input into the cooling system of a forced flow cooled superconducting magnet. Based on a proved computer code for calculation of instationary fluid flows, a new program was developed which is able quantitatively to calculate pressure and temperature transients caused by heat pulses. The program was checked by comparing the results with those of a simulation experiment. A further test was made by comparison with stationary flow results calculated from a well know program. In combination with computer programs, which are able to calculate the quench propagation in a current loaded superconductor, the numerical procedure allows for the investigation of the influence of transient helium flow processes on the stability of the superconductor. Our program is proposed as a good tool for the design of forced flow cooling systems of large superconducting magnets.     

A finite element method with a hybrid lagrange line for fluid mechanics problems involving large free surface motion

In this paper, free surface flow problems involving large free surface motion are analysed using finite element techniques. In solving these problems a spatially fixed Eulerian mesh is employed, in conjunction with a moving Lagrangian free surface line. The coupling, between the equations valid on the free surface and the equations valid on the fluid domain, is carried out using hybrid finite element techniques. Physical problems involving solitary wave propagation, sloshing dynamics and porous media flow are analysed to demonstrate the developed technique.     

Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part II: Experimental validation

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of capillary tube–suction line heat exchangers considering metastable region and separated flow has been developed in Part I of this paper. The developed numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions and metastable region. The accuracy of the detailed simulation model is demonstrated in this part (Part II) of the paper by comparing simulation results with a wide range of steady state experimental data from the technical literature, which include the refrigerant mass flow rate, outlet suction line temperature, and temperature profile along concentric and lateral capillary tube–suction line heat exchangers. Of the 196 data points evaluated for mass flow rate 96.4% are within an error of ±15%, 81.1% are within ±10% with a mean deviation of ±6.3%. Of the 143 data points evaluated for outlet suction line temperature 89.5% are within an error of ±2 °C, with a mean deviation of ±0.98 °C.The numerical results obtained are used to understand the refrigerant flow behavior inside non-adiabatic capillary tubes. Some divergence problems in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the heat exchanger zone; this aspect needs special attention while modeling the non-adiabatic capillary tube flow. Other important parameter to be evaluated experimentally with special care is the capillary tube internal diameter due to its strong influence on the refrigerant flow results (results of any study based on the nominal diameter are to be used with caution).     

Use of an extremal functional in solving for an unknown bottom surface given a free surface profile

In this paper the free surface fluid flow is induced by an obstacle on the bottom of the channel whose exact shape and location are unknown a priori. The inviscid fluid flow is assumed to be steady, incompressible and irrotational under the influence of gravity. A boundary integral technique, which is based on the combination of the boundary integral method (BIM), the variational principle technique (VPT) and the application of a minimization technique (MT) is developed. Two minimization techniques, namely the extremal pressure method (EPM) and the extremal energy method (EEM), are extensively used in identifying the unknown bottom surfaces. To illustrate these techniques the free surface profile to be applied in the inverse analysis has been generated following a direct formulation when the solid bottom boundary is monotonically decreasing, monotonically increasing, when it possesses a single hump and when it possesses a single depression. It is found that in all four cases both extremum techniques can be very accurately used to identify the shape and position of the solid obstacle.     

The crush analysis of vehicle structures

In recent years, there has been a gradual development of a variety of numerical methods for treating vehicle component crush behavior. A significant portion of these methodologies involves the utilization of finite-element computer programs, while finite-difference techniques have generally received less attention. However, recent advances in finite-difference technology may change this picture. The present survey paper reports on the application of the MENTOR-III finite-difference computer program to a variety of vehicle crush analysis problems, many of which have not proven to be analyzable in any rigorous sense by alternate predictive methods.     

An efficient parallel computation of unsteady incompressible viscous flow with elastic moving and compliant boundaries on unstructured grids

This paper presents the development and validation of a parallel unstructured‐grid fluid–structure interaction (FSI) solver for the simulation of unsteady incompressible viscous flow with long elastic moving and compliant boundaries. The Navier–Stokes solver on unstructured moving grid using the arbitrary Lagrangian Eulerian formulation is based on the artificial compressibility approach and a high‐order characteristics‐based finite‐volume scheme. Both unsteady flow and FSI are calculated with a matrix‐free implicit dual time‐stepping scheme. A membrane model has been formulated to study fluid flow in a channel with an elastic membrane wall and their interactions. This model can be employed to calculate arbitrary wall movement and variable tension along the membrane, together with a dynamic mesh method for large deformation of the flow field. The parallelization of the fluid–structure solver is achieved using the single program multiple data programming paradigm and message passing interface for communication of data. The parallel solver is used to simulate fluid flow in a two‐dimensional channel with and without moving membrane for validation and performance evaluation purposes. The speedups and parallel efficiencies obtained by this method are excellent, using up to 16 processors on a SGI Origin 2000 parallel computer. A maximum speedup of 23.14 could be achieved on 16 processors taking advantage of an improved handling of the membrane solver. The parallel results obtained are compared with those using serial code and they are found to be identical. Copyright © 2005 John Wiley & Sons, Ltd.     

Electroosmotic and pressure-driven flow in open and packed capillaries: velocity distributions and fluid dispersion

The flow field dynamics in open and packed segments of capillary columns has been studied by a direct motion encoding of the fluid molecules using pulsed magnetic field gradient nuclear magnetic resonance. This noninvasive method operates within a time window that allows a quantitative discrimination of electroosmotic against pressure-driven flow behavior. The inherent axial fluid flow field dispersion and characteristic length scales of either transport mode are addressed, and the results demonstrate a significant performance advantage of an electrokinetically driven mobile phase in both open-tubular and packed-bed geometries. In contrast to the parabolic velocity profile and its impact on axial dispersion characterizing laminar flow through an open cylindrical capillary, a pluglike velocity distribution of the electroosmotic flow field is revealed in capillary electrophoresis. Here, the variance of the radially averaged, axial displacement probability distributions is quantitatively explained by longitudinal molecular diffusion at the actual buffer temperature, while for Poiseuille flow, the preasymptotic regime to Taylor-Aris dispersion can be shown. Compared to creeping laminar flow through a packed bed, the increased efficiency observed in capillary electrochromatography is related to the superior characteristics of the electroosmotic flow profile over any length scale in the interstitial pore space and to the origin, spatial dimension, and hydrodynamics of the stagnant fluid on the support particles' external surface. Using the Knox equation to analyze the axial plate height data, an eddy dispersion term smaller by a factor of almost 2.5 than in capillary high-performance liquid chromatography is revealed for the electroosmotic flow field in the same column.     

Three-dimensional computer code for dynamic response of solids to intense impulsive loads

Earlier publications demonstrated the capability of the EPIC-3 code to perform high velocity impact computations in three dimensions.^1,2 These capabilities were demonstrated with simplified material and sliding surface models in a core-contained computer program. This paper presents recent developments which include more comprehensive material and sliding surface formulations, and an expanded computer program which can handle problems of unlimited size by beffering data between disc files and core. The EPIC-3 code is based on an explicit, finite element, Lagrangian formulation which uses constant strain tetrahedral elements.     

Simulation of 3D gas–solid fluidized bed reactor hydrodynamics

In this article, an attempt is made to develop a 3D gas–solid fluidized bed reactor (FBR). Basically, it deals with simulation of a FBR in computational fluid dynamics (CFD) using the software, Ansys Fluent v14. The simulation of gas–solid flow is carried out using Eulerian multifluid model which is integrated with the solid particle kinetic theory. The coefficients of exchange momentum are estimated using the Syamlal & O'Brien, Gidaspow, Wen-Yu, and Huilin–Gidaspow drag functions. The results of the simulation have been validated with the experimental data available in literature and had proven that the model is capable to predict the hydrodynamics of FBR. The variation in kinetic energy of the solid phase is calculated by varying the restitution coefficient (RC) from 0.90 to 0.99. The predictions of pressure drop compare excellently with the experimental data. Finally, the effect of particle diameter on the expanded bed height has been studied for FBR.     

A free-front tracking algorithm for a control-volume-based Hele–Shaw method

With free surface flow problems the position of the free front at a particular time step needs to be predicted. When simulating the flow of hot molten polymer in injection moulds this position is essential for the prediction of the position of the weld lines on the final product. Weld lines are important in that they indicate positions of diminished strength and spoil the aesthetics of the product. A code using a finite volume approach on the thin gap Hele–Shaw flow equations to simulate the filling stage of the injection moulding process has been developed which requires a suitable algorithm for the free-front tracking. The Volume of Fluid (VOF) method was implemented in this study for the tracking of the free front. The discretization and various formulations of the VOF equation are presented as well as the results obtained. The impact on the existing equations is also investigated as well as the development of a packing routine that is used to eliminate the diffusive nature of the VOF equation. © 1998 John Wiley & Sons, Ltd.