Multiphase Problems Research Articles

Optimal Trajectory Planning for Multiphase Lunar Landing

Lunar landing problem is formulated as an optimal control problem and has been solved by Legendre Pseudospectral method. The landing problem is split into various stages to take into account various mission constraints. Based on These constraints, the problem is split into three stages Hough Braking, Attitude Hold and Retargeting Legendre Pseudospectral method is used for solving this multiphase lunar landing problem. The idea of this method is to discretize the trajectory optimization as a nonlinear programming problem. Legendre Pseudospectral method was applied to approximate the state and the state differential equations as algebraic constraints. Optimal solutions of the above problem are those control variables which dynamically satisfy all mission constraints. The cost function considered is minimum fuel satisfying all mission constraints envisaged. The method guarantees a null (Mann fuel solution which satisfies terminal mission constraints in each stage as part of the formulation. The mission constraints considered in studying this problem are desired altitude, attitude and velocity while reaching the desired landing site from a specified perilune height. At touchdown, the lander orientation should be vertical favoring landing leg of the Lander to touch the Moons surface as desired. The commanded acceleration should be within the limit of the main engine thruster capability (saturation limit) which enforces maximum and minimum thrust constraints. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Lattice Boltzmann simulation of the droplet impact onto liquid film

The process of the droplet impact onto the liquid film, as one of the basic multiphase problems, is very important in many fields of science and engineering. On the other hand, the problem is also very complicated since there are many parameters that may influence the process of the droplet impact on the liquid film. To clearly understand the physical phenomena appearing in the process droplet impact on the liquid film, a parametric study on this problem is conduced based on a recently developed lattice Boltzmann method in which a lattice Boltzmann model is used to solve the Navier-Stokes equations, and the other is adopted to solve the Cahn-Hilliard equation that is used to depict the interface between different phases. In this paper, we mainly focus on the effects of the Reynolds number (Re), the Weber number (We), the relative thickness of film (h) and the surface tension () on the dynamic behavior of interface between different phases, and the velocity and pressure fields are also presented. It is found that with the increase of Re and We, the phenomena of crown and entrainment can be observed obviously during the process of droplet impact onto the liquid film, and the radius of the crown seems not dependent on the We and Re where the relative thickness of film and surface tension are fixed to be 0.5 and 0.003. However, when Re becomes much larger, the splashing phenomenon is produced, and the small droplets caused by the splashing can fall and then impact onto the liquid film again. We also find that if the relative thickness of film is small, the surface tension, Re and We are set to be 0.003, 480 and 500, the film can break up during the process of the droplet impact onto the liquid film, while with the increase of relative thickness, although more liquid are induced in the splashing process, the film cant break up. In addition, with the increase of surface tension, the resistance which prevents the change of interface becomes large, and thus the change of interface is not large when the droplet impacts onto liquid film, as expected. And finally, a quantitative study on the relation between the radius of crown (formed by droplet impact onto liquid film) and the time is also performed, and the expression r/(2R) Ut/(2R) where the parameter is about 1.0 and is also independent of We and Re, can be used to describe the relation.

Lattice Boltzmann simulation of droplet dynamics in a bifurcating micro-channel

The droplet dynamic in a bifurcating micro-channel, as one of the basic multiphase problems, is frequently encountered in the fields of science and engineering. Due to its great relevance to many important applications and also its fascinating physical phenomena, it has attracted the increasing attention in the past decades. However, this problem is still not fully understood since it is very complicated:the droplet behaviors may be influenced by several physical factors. To clearly elucidate the physics governing droplet dynamics in a bifurcating micro-channel, a detailed numerical study on this problem is conducted. The present investigation is based on our recently developed phase-field-based lattice Boltzmann multiphase model, in which one distribution function is used to solve the Cahn-Hilliard equation, and the other is adopted to solve the Navier-Stokes equations. In this paper, we mainly focus on the effects of the surface wettability, capillary number and outlet flux ratio on the droplet dynamics, and the volume of the generated daughter droplet is also presented. The numerical results show that when the capillary number is large enough, the droplet behaviors depend critically on surface wettability. For the nonwetting case, the main droplet breaks up into two daughter droplets, which then completely suspend in the branched channels and flow towards the outlet. While for the wetting case, the main droplet also breaks up into two daughter droplets at first, and then different behaviors can be observed. The daughter droplet undergoes a secondary breakup, which results in part of droplet adhering to the wall, and the remaining flowing to the outlet. The volume of the generated daughter droplet is also measured, and it is shown that it increases linearly with contact angle increasing. When the capillary number is small enough, the droplet remains at the bifurcating position, which does not break up. Finally, we also find that the outlet flux ratio affects the rupture mechanism of the droplet. When the outlet flux ratio is 1, the droplet is split into two identical daughter droplets. When the outlet flux ratio increases, an asymmetric rupture resulting in the generation of two different daughter droplets, will be observed. However, if the outlet flux ratio is larger enough, the droplet does not breakup, and flows into the branched channel where the fluid velocity is larger. Here we define a critical outlet flux ratio, below which the droplet breakup occurs, and above which the droplet does not break up. The relationship between the capillary number and the critical outlet flux ratio is examined, and it is found that the critical outlet flux ratio increases with capillary number increasing.

Solving 2-D water entry problems with a CIP method and a parallel computing algorithm

Two-dimensional water entry problems have been solved by a constrained interpolation profile (CIP) method. This paper presents the further development of this numerical method using staggered grids and a parallel computing algorithm. In this work, the multi-phase problem governed by the Navier–Stokes equations was solved by a CIP-based finite difference method. The interfaces between different phases (solid, water and air) were captured using density functions. A parallel computing algorithm based on the message passing interface method and a domain decomposition scheme were implemented to speed up the computations. The effect of the domain decomposition scheme on the solution and the speedup performance were studied. Validation studies were carried out for the water entry of a wedge, a ship section and a circular cylinder. The predicted slamming forces and pressure distribution were compared with experimental results and other numerical solutions.

A Methodology for the Reduction of Numerical Diffusion in Sloshing Analyses through Automated Mesh Adaptation

The paper proposes a methodology to improve the accuracy of Volume of Fluid (VoF) multiphase problems involving liquid/gas sloshing in fuel/lubricant tanks without penalizing the computational cost of the simulations. In order to correctly track the complex trajectory of the liquid/gas interface and the presence of liquid droplets in the gas phase, the VoF method requires a fine mesh at each interface location to reduce modeling errors.The investigated case is a lubricant tank of a sport car subject to typical race track maneuvers. Due to the geometrical extent and the complexity of the computational domain and to the relevant accelerations, resulting in dispersed liquid structures within the gas phase, the use of a generalized fine mesh would result in computational costs far beyond the industrial practice.A methodology is then proposed to reduce the overall number of computational cells through a combination of local interface tracking and mesh refinement, which is combined with an active control of the time step to comply with Courant-Friedrichs-Lewy number limits.The methodology is at first validated against experimental measurements for a simplified test case, and then applied to the actual oil tank sloshing case, showing a relevant reduction of the numerical diffusion and a consequent higher accuracy.

Reduced relative entropy techniques fora posteriorianalysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal. , 46 , 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Experimental and Numerical Analysis of Filament Front Deformation for Direct-Print

The purpose of this research is to perform an investigation of continuously dispensed material (or filament) deformation during dispensing. Depending on the material properties, and the process parameters the deformation behavior of the filament changes, so as the formation of the filament front (the front face of the filament, i.e., dispensing material). The focus of this investigation is the study of the evolution of the filament shape for Newtonian fluid experimentally and computationally. The experimental analysis has been performed with commercially available monomers with the help of a screw driven micro dispensing system installed on a high precision xyz translation stage. The imaging system consists of a high resolution CMOS camera. The developed computational model utilizes an adaptive quadtree spatial discretization with piecewise–linear geometrical volume–of–fluid (VOF) method for calculating the volume fraction for this multiphase problem. The model employs the continuum–surface–force model for formulating the surface tension, whereas the height function (HF) to estimate the curvature for tracking the evolution of the filament shape during the deformation. The computational model has been developed using an open source solver, Gerris Flow Solver. The considered governing and process parameters for this investigation are Froude number (Fr), Reynolds number (Re), gap ratio (GR), and velocity ratio (VR). The VR is the ratio of travel velocity to dispensing velocity. The GR is the ratio of filament height to filament diameter. Results have been presented as the interface contour for the filament front. The investigation shows that the results found from the developed model have a good agreement with experimental results, and the deformation phenomena is greatly influenced by the variation of the governing parameters.

Validation of robust SPH schemes for fully compressible multiphase flows

The present study examines the ability of the SPH number-density scheme to treat multiphase problems of the fully compressible regime. The number-density scheme is extended to the fully compressible regime, using the standard variational SPH framework and incorporate artificial diffusion coming from a generic formula. Aiming at robust schemes, we adopt the differential form of mass conservation. The performance of this scheme is studied with the help of two benchmark tests. It is shown that the standard variational framework of SPH may treat multiphase processes in the fully compressible regime, without reverting to non-standard formulations. The SPH solutions are compared to solutions coming from the Arbitrary Lagrangian Eulerian method and are validated against exact solutions.

The hole-filling method and the multiscale computation for the wave equations in perforated domains

In this paper we discuss the multiscale computation of the wave equations with rapidly oscillating coefficients in a perforated domain. The hole-filling method through filling all holes with a very compliant material is introduced. As the material parameters of the weak phase go to zero, the proof of this limiting process is derived. Based on the above hole-filling method, the multiscale asymptotic method and the convergence results for the associated multiphase problem in a domain without holes are presented. The numerical experiments are carried out to validate the theoretical results.

단파장 영역에서의 부가저항 해석

In this study, the added resistance of ships in short waves is systematically studied by using two different numerical methods - Rankine panel method and Cartesian grid method – and existing asymptotic and empirical formulae. Analysis of added resistance in short waves has been preconceived as a shortcoming of numerical computation. This study aims to observe such preconception by comparing the computational results, particularly based on two representative three-dimensional methods, and with the existing formulae and experimental data. In the Rankine panel method, a near-field method based on direct pressure integration is adopted. In the Cartesian grid method, the wave-body interaction problem is considered as a multiphase problem, and volume fraction functions are defined in order to identify each phase in a Cartesian grid. The computational results of added resistance in short waves using the two methods are systematically compared with experimental data for several ship models, including S175 containership, KVLCC2 and Series 60 hulls (C_B = 0.7, 0.8). The present study includes the comparison with the established asymptotic and empirical formulae in short waves.

On the application of higher‐order elements in the hierarchical interface‐enriched finite element method

SummaryThis article introduces a new algorithm for evaluating enrichment functions in the higher‐order hierarchical interface‐enriched finite element method (HIFEM), which enables the fully mesh‐independent simulation of multiphase problems with intricate morphologies. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along materials interfaces that are in close proximity, in contact, and even intersecting with one another using nonconforming finite element meshes for discretizing the problem. We study different approaches for creating higher‐order HIFEM enrichments corresponding to six‐node triangular elements and analyze the advantages and shortcomings of each approach. The preferred method, which yields the lowest computational cost and highest accuracy, relies on a special mapping between the local and global coordinate systems for evaluating enrichment functions. A comprehensive convergence study is presented to show that this method yields similar convergence rate and precision as those of the standard FEM with conforming meshes. Finally, we demonstrate the application of the higher‐order HIFEM for simulating the thermal and deformation responses of several materials systems and engineering problems with complex geometries. Copyright © 2015 John Wiley & Sons, Ltd.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in [Gie14]. We prove optimal bounds for the strain in an appropriate norm and suboptimal bounds for the velocity.

Incompressible multiphase flow and encapsulation simulations using the moment‐of‐fluid method

SummaryA moment‐of‐fluid method is presented for computing solutions to incompressible multiphase flows in which the number of materials can be greater than two. In this work, the multimaterial moment‐of‐fluid interface representation technique is applied to simulating surface tension effects at points where three materials meet. The advection terms are solved using a directionally split cell integrated semi‐Lagrangian algorithm, and the projection method is used to evaluate the pressure gradient force term. The underlying computational grid is a dynamic block‐structured adaptive grid. The new method is applied to multiphase problems illustrating contact‐line dynamics, triple junctions, and encapsulation in order to demonstrate its capabilities. Examples are given in two‐dimensional, three‐dimensional axisymmetric (R–Z), and three‐dimensional (X–Y–Z) coordinate systems. Copyright © 2015 John Wiley & Sons, Ltd.

3D hierarchical interface-enriched finite element method: Implementation and applications

A hierarchical interface-enriched finite element method (HIFEM) is proposed for the mesh-independent treatment of 3D problems with intricate morphologies. The HIFEM implements a recursive algorithm for creating enrichment functions that capture gradient discontinuities in nonconforming finite elements cut by arbitrary number and configuration of materials interfaces. The method enables the mesh-independent simulation of multiphase problems with materials interfaces that are in close proximity or contact while providing a straightforward general approach for evaluating the enrichments. In this manuscript, we present a detailed discussion on the implementation issues and required computational geometry considerations associated with the HIFEM approximation of thermal and mechanical responses of 3D problems. A convergence study is provided to investigate the accuracy and convergence rate of the HIFEM and compare them with standard FEM benchmark solutions. We will also demonstrate the application of this mesh-independent method for simulating the thermal and mechanical responses of two composite materials systems with complex microstructures.

Multi-scale Kinetic Modeling and Experimental Investigation of Syngas Production from Coal Gasification in Updraft Gasifiers

Gasification is a thermochemical process devoted to the production of syngas, starting from a solid fuel such as coal, biomass, or refuse-derived fuel (RDF). The gasification efficiency and the chemical composition of the produced syngas are strongly affected by the feedstock and the operating conditions of the process. Besides the direct use as a fuel for power generation, downstream applications of syngas for chemical production demand specific H2/CO ratios, as extensively reported in the literature. For this reason, in the present work, a comprehensive mechanistic approach is applied to the description of the coal gasification process, highlighting the sensitivity of key operating parameters on syngas quality. The solution of this multi-scale, multi-phase, and multi-component problem requires careful attention to the kinetics in the solid and the gas phase as well as the heterogeneous gas–solid reactions. The kinetic model is validated with experimental data obtained in updraft gasifiers (including the...

On the derivation of SPH schemes for shocks through inhomogeneous media

Smoothed Particle Hydrodynamics (SPH) is typically used for the simulation of shock propagation through solid media, commonly observed during hypervelocity impacts. Although schemes for impacts into monolithic structures have been studied using SPH, problems occur when multimaterial structures are considered. This study begins from a variational framework and builds schemes for multiphase compressible problems, coming from different density estimates. Algorithmic details are discussed and results are compared upon three one-dimensional Riemann problems of known behavior.

Proper generalized decomposition of a geometrically parametrized heat problem with geophysical applications

SummaryThe solution of a steady thermal multiphase problem is assumed to be dependent on a set of parameters describing the geometry of the domain, the internal interfaces and the material properties. These parameters are considered as new independent variables. The problem is therefore stated in a multidimensional setup. The proper generalized decomposition (PGD) provides an approximation scheme especially well suited to preclude dramatically increasing the computational complexity with the number of dimensions. The PGD strategy is reviewed for the standard case dealing only with material parameters. Then, the ideas presented in [Ammar et al., “Parametric solutions involving geometry: A step towards efficient shape optimization.” Comput. Methods Appl. Mech. Eng., 2014; 268:178–193] to deal with parameters describing the domain geometry are adapted to a more general case including parametrization of the location of internal interfaces. Finally, the formulation is extended to combine the two types of parameters. The proposed strategy is used to solve a problem in applied geophysics studying the temperature field in a cross section of the Earth crust subsurface. The resulting problem is in a 10‐dimensional space, but the PGD solution provides a fairly accurate approximation (error ≤1%) using less that 150 terms in the PGD expansion. Copyright © 2015 John Wiley & Sons, Ltd.

Towards numerical simulations of supersonic liquid jets using ghost fluid method

A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid jets.

Mechanical properties of irradiated multi-phase polycrystalline BCC materials

Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility, resulting from irradiation-induced defects such as vacancies, interstitials and dislocation loops, etc. In this paper, we develop an elastic–viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored. At the microscopic grain scale, we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop, which facilitates the analysis of the defect loop evolutions and dislocation-defect interactions. At the macroscopic polycrystal scale, the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties. Based on the proposed model, we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops, and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors. At the polycrystalline scale, numerical results for pure Fe match well with the irradiation experiment data. The model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan bowing. The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials. Comparison of numerical modeling results (solid lines) with experimental results (square lines) for the polycrystalline BCC iron. We develop an elastic–viscoplastic model for irradiated multiphase polycrystalline BCC materials, based on a dislocation-based model at the grain scale, and the self-consistent scheme at the macroscopic scale. This model can be easily applied to predict the hardening behaviors of irradiated multi-phase polycrystalline materials.

Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying

Dried plant food products are increasing in demand in the consumer market, leading to continuing research to develop better products and processing techniques. Plant materials are porous structures, which undergo large deformations during drying. For any given food material, porosity and other cellular parameters have a direct influence on the level of shrinkage and deformation characteristics during drying, which involve complex mechanisms. In order to better understand such mechanisms and their interrelationships, numerical modelling can be used as a tool. In contrast to conventional grid-based modelling techniques, it is considered that meshfree methods may have a higher potential for modelling large deformations of multiphase problem domains. This work uses a meshfree based microscale plant tissue drying model, which was recently developed by the authors. Here, the effects of porosity have been newly accounted for in the model with the objective of studying porosity development during drying and its influence on shrinkage at the cellular level. For simplicity, only open pores are modelled and in order to investigate the influence of different cellular parameters, both apple and grape tissues were used in the study. The simulation results indicated that the porosity negatively influences shrinkage during drying and the porosity decreases as the moisture content reduces (when open pores are considered). Also, there is a clear difference in the deformations of cells, tissues and pores, which is mainly influenced by the cell wall contraction effects during drying.