Ghost Fluid Research Articles

Unsteady mixed convection past a circular cylinder using ghost fluid cascaded lattice Boltzmann method (GF-CLBM)

This paper presents the transient hydrodynamic and heat transfer behaviour of a cross-flow over a heated circular cylinder under the influence of thermal buoyancy. The Reynolds number chosen for the present study is fixed as 100, and the Richardson number is varied from 0.1 to 2. A relatively new ghost fluid thermal lattice Boltzmann method (GF-TLBM) is used as the numerical solver. Cascaded collision model is incorporated into the code and validated successfully. As the Richardson number increases from 0.1 to 2, the buoyancy forces become dominant and tend to tilt the vortex shedding towards the vertical direction. The drag and lift coefficients as well as the Strouhal number and the average Nusselt number show an increasing trend with the increase in the Richardson number.

Finite volume Ghost Fluid Method implementation of interfacial forces in PISO loop

In this work, we implement interfacial forces (surface tension, hydrostatic and viscous forces) by enlisting the finite volume discretization of GFM (Ghost Fluid Method) using A-CLSVOF (Algebraic Coupled Level-Set/Volume-of-Fluid) method for the mass conservative, and smooth interface description. The widely used PISO momentum solution to resolve the pressure–velocity coupling is presented along with the present GFM discretization and its placement within the PISO loop. The pressure jump at the interface due to the interfacial forces is made sharp via direct calculation of the modified pressure matrix coefficients corresponding to targeted interfacial cells, and as a source term for the jump value itself. The Level-Set field is enlisted for curvature computation in A-CLSVOF and for the interpolation and weighting of the relative contribution of the capillary force in adjacent for the matrix coefficients in the FV framework. To assess the A-CLSVOF/GFM performance, four canonical cases were studied. In the case of a static droplet in suspension, A-CLSVOF/GFM produces a sharp and accurate pressure jump compared to the traditional CSF implementation of A-CLSVOF. The interaction of viscous and capillary forces is proven to be accurate and consistent with theoretical results for the classical capillary wave. For the linear two-layer shear flow, GFM sharp treatment of the viscosity captured the velocity gradient across the interface and removed the diffusion of the viscous stresses caused by the discontinuous material properties. Finally, the combination of all GFM improvements proposed in this study are compared to experimental findings of terminal velocity for a gaseous bubble rising in a viscous fluid. GFM outperforms CSF with errors of 4.6% and 14.0% respectively.

A coupled vaporization model based on temperature/species gradients for detailed numerical simulations using conservative level set method

This paper proposes a vaporization model for detailed numerical simulations of a reactive interface. The proposed model represents a preliminary attempt to combine vaporization models based on heat flux and species mass flux to take each model’s advantages concerning numerical accuracy, robustness and applicability. We utilize a conservative level set method to reduce unphysical mass loss in capturing the deformable interface, and the ghost fluid method to accurately impose various jump conditions across the interface. Four validations are conducted to demonstrate both the strengths and limitations of the two original models. Since the vapor mass fraction is relevant in realistic applications, we add the species solver to the heat flux based model and assess the coupling strategy in different situations. The feasibility of switching between the two frameworks in the coupled vaporization model is also demonstrated. Finally, the coupled model is applied to simulations of deformable/moving droplet under high-ambient-temperature conditions. The results of the simulations are consistent with analytical and experimental data. Although additional work is required, the coupled vaporization model exhibits potential as a means for modeling spray combustion.

Numerical Simulation of Fluid–Structure Interaction Problem Associated with Vertical Launching System

We develop a combined Lagrangian–Eulerian method for transient fluid–structure interaction problems. Based on the ghost fluid framework for improving interface tracking accuracy between a fluid (hot rocket exhaust plume) and a high strain rate deforming solid (rear cover of a vertical launch system), the numerical coupling between the two media ensures an accurate description of the flexible structure. A nine-node quadrilateral element based on total Lagrangian formulation is used, while the hydrodynamic finite difference method is used for the supersonic exhaust plume that forms a complex flow within the plenum. The Lagrangian, Eulerian, and fluid–structure interaction coupling methods are verified by ANSYS results and related theories. A two-dimensional simulation of the full vertical launch system operation mode is conducted. This requires an accurate reproduction of the complex flowfield generated by the rapid rear cover opening under a high-pressure plume during rocket launch. This fluid–structure interaction problem solution may be used for future design upgrades when a vertical launch system is exposed to unusually harsh interactive gas and structure conditions.

On Importance of the Surface Charge Transport Equation in Numerical Simulation of Drop Deformation in a Direct Current Field

In the present study, the deformation of a droplet is numerically modeled by considering the dynamic model for electric charge migration at the drop interface under the effect of a uniform electric field. The drop and its ambient are both considered behaving as leaky dielectric fluids. Solving the charge conservation equation at the interface, which is the most important part of this study, the effect of conduction and convection of charges on different deformation modes will be explored. In this work, the interface is followed by the level set method and the ghost fluid method (GFM) is used to model the jumps at the interface. Physical properties are also chosen in a way that solving the charge conservation equation becomes prominent. The small drop deformation is investigated qualitatively by changing various effective parameters. In cases, different patterns of charges and flows are observed indicating the importance of electric charges at the interface. It is also shown that the transient behavior of deformation parameter can be either a monotonic or a nonmonotonic approach toward the steady-state. Moreover, large drop deformations are studied in different ranges of capillary numbers. It will be shown that for the selected range of physical parameters, considering the dynamic model of electric charges strongly affects the oblate deformation. Nevertheless, for the prolate deformation, the results are approximately similar to those obtained from the static model.

A computational framework for interface-resolved DNS of simultaneous atomization, evaporation and combustion

A computational framework for interface-resolved direct numerical simulations (DNS) of simultaneous atomization, evaporation and combustion process is proposed. The present work utilizes a level set method to implicitly capture the gas–liquid interface and the ghost fluid method (GFM) to accurately address jump conditions across the interface. Specific care has been devoted to the discretization of the convective term and diffusive term for the species and energy equations. The level set method with a sub-cell resolution of the interface is employed and a semi-Lagrangian scheme for the discretization of the level set equation with an evaporation source term is proposed. The one-step global reaction model of n-heptane is used for the vapor combustion. To the best of our knowledge, this is the first computational framework that has the capability to simulate spray combustion with an interface-resolved method. The present framework has been validated in several cases, including the one-dimensional evaporation and the static droplet evaporation for low ambient temperature, the Stefan problem, the Sucking problem, the evaporation of static and moving droplet for high ambient temperature, and the combustion of static and moving droplet. Finally, the integrated simulation of droplet collision and combustion is performed to evaluate the accuracy and robustness of the present method.

Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

SummaryPartitioned procedures are appealing for solving complex fluid‐structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added‐mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin‐Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection‐based incompressible CFD and finite element–based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid‐structure interfaces embedded in structured non–body‐conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex‐dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, αf, on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler‐Bernoulli beam interacting with a two‐dimensional incompressible inviscid flow. Both studies reveal a trade‐off between stability and accuracy: smaller values of αf tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of αf that optimizes this trade‐off is derived and discussed.

High accuracy modeling of sharp wave fronts for hyperbolic problems

In this paper, the arbitrary order derivative (ADER) schemes based on the generalized Riemann problem are proposed to capture shock waves and contact discontinuities by coupling ghost fluid method (GFM). The reconstruction technique for spatial derivatives at cell boundaries is presented by piece-wise smooth WENO interpolations which are used as initial states of the Riemann problems. A level set function is used to keep track of the location of wave fronts. The shock waves are pushed forward by shock speeds which are obtained by the Rankine–Hugoniot conditions, whereas the contact discontinuities are advanced by local fluid velocities. Numerical examples show that the presented scheme is suitable for capturing fine flow structures and has an accuracy comparable to other methods designed for traditional contact discontinuity.

Application of the ghost fluid lattice Boltzmann method to moving curved boundaries with constant temperature or heat flux conditions

In this paper, for the first time, the ghost-fluid lattice Boltzmann method (GF-LBM) is combined with a refilling scheme to simulate the heat transfer from moving bodies with curved boundaries. Two thermal boundary conditions namely, the constant temperature and constant heat flux are considered at the moving curved boundaries. First, the Galilean invariance of the presented method is verified by comparing the results of the problem of heat transfer from a cylinder in a crossflow, in two different inertial references. Next, the sedimentation of a cold particle in a vertical channel is simulated and the results of the presented method are compared to those from the conventional numerical methods, available in the literature, and a good agreement is observed. To sum up, the results of this study showed that the presented GF-LBM with refilling was capable of simulating the thermal moving curved boundaries with excellent accuracy.

Flow structure of compound droplets moving in microchannels

Compound droplets can be used in substance encapsulation and material compartmentalization to achieve a precise control over the relevant processes in many applications, such as bioanalysis, pharmaceutical manufacturing, and material synthesis. The flow fields in compound droplets directly affect the performance of these applications, but it is challenging to measure them experimentally. In this study, the flow in compound droplets in axisymmetric microchannels is simulated using the finite volume method, and the interface is captured using the level set method with surface tension accounted for via the ghost fluid method. The combination of the level set method and the ghost fluid method reduces spurious currents that are produced unphysically near the interface and achieves a precise simulation of the complex flow field within compound droplets. The shape of compound droplets, the vortical patterns, the velocity fields, and the eccentricity are investigated, and the effects of the key dimensionless parameters, including the size of the compound droplet, the size of the core droplet, the capillary number, and the viscosity ratio, are analyzed. The flow structures in multi-layered compound droplets are also studied. This study not only unveils the complex flow structure within compound droplets moving in microchannels but can also be used to achieve a precise control over the relevant processes in a wide range of applications of compound droplets.

不可压缩多介质流动问题的数值模拟

本文将基于MAC (Marker and cell)交错网格上的半拉格朗日方法推广应用于求解不可压缩多介质流动问题。通过求解Level set方程捕捉界面的位置，利用NGFM (New Ghost Fluid Method)方法定义界面边界条件，将多介质问题转化为单介质问题进行计算。给出了一种求解不可压缩多介质流动问题的简单且高效的数值算法。本文针对多个经典算例进行数值试验，数值结果表明本文所给出的方法可以有效的模拟流体的运动细节。 In this work, the semi-Lagrangian method is extended to the simulation of incompressible mul-ti-medium flow on MAC staggered grid method. We track the fluid interface by solving the level set equation, and the NGFM is used to define the fluid interface condition such that the calculation can be carried out the same as that in the single medium flow. Several classic examples are simulated to test the algorithm given in this work. The numerical results show that the given algorithm can track the interface accurately and capture the physical details of the multi-medium flow.

CFD verification and validation of green sea loads

An extensive verification and validation for green sea load simulations is presented. The calculations are performed using the Naval Hydro pack, a library based on foam–extend, which is an open source Computational Fluid Dynamics software. The geometric Volume of Fluid method is used for interface advection, while the Ghost Fluid Method is employed to discretise the free surface boundary conditions at the interface. Pressure measured at the deck of a fixed structure is compared to experimental data for nine regular waves. Verification is performed using four refinement levels in order to reliably assess numerical uncertainties. A detailed uncertainty analysis comprises both numerical and experimental data. Comparable uncertainties are exhibited in simulations and experiments, with good agreement of results.

A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods

This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid (VOF) method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.

An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces

Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressure-correction approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.

On comparison of the sharp-interface and diffuse-interface level set methods for 2D capillary or/and gravity induced flows

The present work is on comparison of numerical-methodology as well as performance of the two types of level set methods (LSMs): sharp-interface and diffused-interface. The numerical-methodology along with mathematical-formulation are presented in-detail for relatively recent ghost fluid method based sharp-interface level-set-method (SI-LSM); and compared with the methodology for the traditional diffuse-interface level-set-method (DI-LSM) as well as an improved diffuse-interface dual-grid-level-set-method (DI-DGLSM). Two different types of surface models are considered: continuum surface force (CSF) and sharp surface force (SSF) model; CSF model for the DI-LSM and SSF model for the SI-LSM. The SI-LSM considers the physically realistic sudden variation of the thermo-physical property across the sharp-interface while DI-LSM considers a smoothened value of the properties across the numerically diffused-interface. For solving the pressure Poisson equation in the SI-LSM, a finite volume method based generic formulation is proposed and its implementation-details are presented. For the SI-LSM as compared to DI-LSM and DI-DGLSM, the relative performance study is presented on four reasonably different two-phase problems: surface-tension model induced unphysical flow for a static water droplet, collapse of a water-column in air, falling of a water-droplet in air, and coalescence of an ethanol-droplet over a pool of ethanol in air. For the performance study on various problems, a comparison of the results obtained by the three types of LSMs (SI-LSM, DI-LSM and DI-DGLSM) and various other numerical methods in the literature are presented. SI-LSM as compared to DI-LSM and DI-DGLSM is shown to substantially reduce the unphysical spurious velocity and results in better accuracy on the same grid size.

Gradient augmented level set method for phase change simulations

A numerical method for the simulation of two-phase flow with phase change based on the Gradient-Augmented-Level-set (GALS) strategy is presented. Sharp capturing of the vaporization process is enabled by: i) identification of the vapor–liquid interface, Γ(t), at the subgrid level, ii) discontinuous treatment of thermal physical properties (except for μ), and iii) enforcement of mass, momentum, and energy jump conditions, where the gradients of the dependent variables are obtained at Γ(t) and are consistent with their analytical expression, i.e. no local averaging is applied. Treatment of the jump in velocity and pressure at Γ(t) is achieved using the Ghost Fluid Method. The solution of the energy equation employs the sub-grid knowledge of Γ(t) to discretize the temperature Laplacian using second-order one-sided differences, i.e. the numerical stencil completely resides within each respective phase. To carefully evaluate the benefits or disadvantages of the GALS approach, the standard level set method is implemented and compared against the GALS predictions. The results show the expected trend that interface identification and transport are predicted noticeably better with GALS over the standard level set. This benefit carries over to the prediction of the Laplacian and temperature gradients in the neighborhood of the interface, which are directly linked to the calculation of the vaporization rate. However, when combining the calculation of interface transport and reinitialization with two-phase momentum and energy, the benefits of GALS are to some extent neutralized, and the causes for this behavior are identified and analyzed. Overall the additional computational costs associated with GALS are almost the same as those using the standard level set technique.

Three dimensional modeling of free surface flow and sediment transport with bed deformation using automatic mesh motion

This study presents the development of a 3D numerical code for flow-sediment interactions with associated bed changes in free surface flows. To capture the water-air interface, a novel volume of fluid (VOF) formulation is implemented using the ghost fluid method with one-side extrapolation for dynamic pressure. Equations for fluid flow and free surface motion are decoupled due to separation of time scales. Accordingly, time step size can be increased by a factor of 3-orders of magnitude and still preserve numerical stability and computational efficiency. A novel finite area method (FAM) is utilized to discretize Exner equation on irregular bed surface providing a 3D finite volume-like discretization on curved surfaces. The evolution of the water-sediment interface is captured by a novel vertex-based unstructured mesh dynamic motion solve using Laplace operator with variable diffusivity. The code is implemented in foam-extend and tested against two classical experiments. Good results are obtained with correct trends and lower absolute error compared to previous mobile bed models. This shows that the developed code has a good potential of being applied to mobile-bed hydraulic real problems.

Simulation of Underwater Explosions Initiated by High-Pressure Gas Bubbles of Various Initial Shapes

UNDerwater EXplosions (UNDEXs) are widely used in many areas of applied engineering including oil production and warship protection. However, the three-dimensional computations of UNDEXs, especially for explosives with complex initial shapes are still lacking, which is mainly due to the difficulty in capturing the multi-medium interface with high pressure ratio. In this study, we conducted a series of three-dimensional numerical simulations of UNDEXs with different initial shapes of a high-pressure gas bubble surrounded with water, to investigate the dynamics of the explosion caused by the shape change of the gas bubble. The movement of the interface was traced with the level-set method, and the conditions at the gas–water interface were treated using the Real Ghost Fluid Method (RGFM). As a result, the temporal evolution of the pressure field during the explosion and the pressure exerted at the boundaries of the computational domain in each simulation scenario were obtained. It was found that an initial shock wave is generated by the explosion and transmitted in the water, leading to an increase of the pressure and density. Meanwhile, inside the gas bubble, a rarefaction wave is formed, causing a pressure drop of the explosive gas. The results also show that if the initial shape of the bubble filled with the explosive gas is simple (e.g., spherical, cylindrical, cuboidal), the peak pressure of the shock wave is dominated by the cross-sectional area of the initial bubble along each direction. In addition, the duration of the high pressure phase of the shock wave is dictated by the thickness of the bubble. Moreover, the simulation of a bubble with an initially bullet-like shape revealed that this specific shape enables a concentration of the energy in a well-defined direction. The peak of the pressure generated by the gas bubble of this more complex shape is approximately twice than that of the other scenarios. However, the high pressure was found to drop more rapidly than that of the other cases, which might be attributed to the comparably small thickness of the initial bubble.

A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation

AbstractA second order Ghost Fluid method is proposed for the treatment of interface problems of elliptic equations with discontinuous coefficients. By appropriate use of auxiliary virtual points, physical jump conditions are enforced at the interface. The signed distance function is used for the implicit description of irregular domain. With the additional unknowns, high order approximation considering the discontinuity can be built. To avoid the ill-conditioned matrix, the interpolation stencils are selected adaptively to balance the accuracy and the numerical stability. Additional equations containing the jump restrictions are assembled with the original discretized algebraic equations to form a new sparse linear system. Several Krylov iterative solvers are tested for the newly derived linear system. The results of a series of 1-D, 2-D tests show that the proposed method possesses second order accuracy in L∞ norm. Besides, the method can be extended to the 3-D problems straightforwardly. Numerical results reveal the present method is highly efficient and robust in dealing with the interface problems of elliptic equations.

A Comparison Study of Numerical Methods for Compressible Two-Phase Flows

AbstractIn this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.