Cut-cell Method Research Articles

A Sharp Interface Method for Compressible Multi-Phase Flows Based on the Cut Cell and Ghost Fluid Methods

AbstractA new sharp interface method with the combination of Ghost Fluid Method (GFM) and Cut Cell scheme is developed to study compressible multi-phase flows with clear interfaces. Straight-line cutting is applied on the cells passed by the interface. A new real-ghost mixing method is presented and applied around the cut cells to deal with very small cut cells. A cut face reconstruction method similar to volume of fluid is applied to deal with topological change problems. A high order Level Set (LS) method is applied to evolve the free interface, with the Level Set velocities from exact Riemann solver on the cut faces. Various 1D and 2D numerical examples are tested to show the robustness and ability of the present method in wide flow variable domains. This method benefits from cut cell on the sharp interface description, shows good conservation performance, and does not have the topological change difficulty of the full cut cell method presented in Chang, Deng & Theofanous, J. Comput. Phys., 242 (2013), pp. 946–990.

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.

Direct particle–fluid simulation of Kolmogorov-length-scale size particles in decaying isotropic turbulence

The modulation of decaying isotropic turbulence by 45 000 spherical particles of Kolmogorov-length-scale size is studied using direct particle–fluid simulations, i.e. the flow field over each particle is fully resolved by direct numerical simulations of the conservation equations. A Cartesian cut-cell method is used by which the exchange of momentum and energy at the fluid–particle interfaces is strictly conserved. It is shown that the particles absorb energy from the large scales of the carrier flow while the small-scale turbulent motion is determined by the inertial particle dynamics. Whereas the viscous dissipation rate of the bulk flow is attenuated, the particles locally increase the level of dissipation due to the intense strain rate generated near the particle surfaces due to the crossing-trajectory effect. Analogously, the rotational motion of the particles decouples from the local fluid vorticity and strain-rate field at increasing particle inertia. The high level of dissipation is partially compensated by the transfer of momentum to the fluid via forces acting at the particle surfaces. The spectral analysis of the kinetic energy budget is supported by the average flow pattern about the particles showing a nearly universal strain-rate distribution. An analytical expression for the instantaneous rate of viscous dissipation induced by each particle is derived and subsequently verified numerically. Using this equation, the local balance of fluid kinetic energy around a particle of arbitrary shape can be precisely determined. It follows that two-way coupled point-particle models implicitly account for the particle-induced dissipation rate via the momentum-coupling terms; however, they disregard the actual length scales of the interaction. Finally, an analysis of the small-scale flow topology shows that the strength of vortex stretching in the bulk flow is mitigated due to the presence of the particles. This effect is associated with the energy conversion at small wavenumbers and the reduced level of dissipation at intermediate wavenumbers. Consequently, it damps the spectral flux of energy to the small scales.

Effect of wave periods on added resistance and motions of a ship in head sea simulations

Given that the International Maritime Organization (IMO) recently introduced the Energy Efficiency Design Index (EEDI) for new ships and the Energy Efficiency Operational Indicator (EEOI) for ship operations, accurate prediction of the added resistance of ships advancing in waves has become necessary. In the present study, the open-source computational fluid dynamics library, OpenFOAM, was used to predict the added resistance with the motions of a ship. Unstructured grid using a hanging-node and cut-cell method was used to generate fine grid around a free-surface and ship. Five wavelengths from a short wavelength (λ/LPP=0.65) to a long wavelength (λ/LPP=1.95) were considered as head waves. The grid uncertainty was evaluated with respect to three grid systems for a wavelength of λ/LPP=1.15. The predicted added resistance and heave and pitch motions with various head waves were compared with the data from model experiments. The wave pattern around the ship and the motions of the ship were analyzed with respect to the wave encounter period. When the wavelength was similar to the ship length, the ship moved against the waves, and thus the added resistance was greater compared with other wavelengths.

Performance evaluation of RANS-based turbulence models in simulating a honeycomb heat sink

As well-known, there is not a universal turbulence model that can be used to model all engineering problems. There are specific applications for each turbulence model that make it appropriate to use, and it is vital to select an appropriate model and wall function combination that matches the physics of the problem considered. Therefore, in this study, performance of six well-known Reynolds-Averaged Navier–Stokes (RANS) based turbulence models which are the Standard $$k {\text{-}} \varepsilon$$ , the Renormalized Group $$k {\text{-}} \varepsilon$$ , the Realizable $$k {\text{-}} \varepsilon$$ , the Reynolds Stress Model, the $$k {\text{-}} \omega$$ and the Shear Stress Transport $$k {\text{-}} \omega$$ and accompanying wall functions which are the standard, the non-equilibrium and the enhanced are evaluated via 3D simulation of a honeycomb heat sink. The CutCell method is used to generate grid for the part including heat sink called test section while a hexahedral mesh is employed to discretize to inlet and outlet sections. A grid convergence study is conducted for verification process while experimental data and well-known correlations are used to validate the numerical results. Prediction of pressure drop along the test section, mean base plate temperature of the heat sink and temperature at the test section outlet are regarded as a measure of the performance of employed models and wall functions. The results indicate that selection of turbulence models and wall functions has a great influence on the results and, therefore, need to be selected carefully. Hydraulic and thermal characteristics of the honeycomb heat sink can be determined in a reasonable accuracy using RANS-based turbulence models provided that a suitable turbulence model and wall function combination is selected.

Development of Advanced Cut-Cell Method for Higher Accuracy in Mold Filling Simulation

Development of Advanced Cut-Cell Method for Higher Accuracy in Mold Filling Simulation

High resolution LES by using wall model and cut cell method based on uniform Cartesian grid

High resolution LES by using wall model and cut cell method based on uniform Cartesian grid

Модификация метода погруженных границ LS-STAG для моделирования течений вязкоупругих жидкостей

The LS-STAG immersed boundary cut-cell method modification for viscoelastic flow computations is presented. Rate type viscoelastic flow models (linear and quasilinear) are considered. Formulae for differential types of convected time derivatives the LS-STAG discretization was obtained. Normal non-newtonian stresses are computed at the centers of base LS-STAG mesh cells and shear non-newtonian stresses are computed at the cell corners. The LS-STAG-discretization of extra-stress equations for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson - Segalman fluids was developed. Time-stepping algorithm is defined by the following three steps. Firstly, a prediction of the velocity and pressure correction are computed by means of semi-implicit Euler scheme. Secondly, the provisional velocity is corrected to get a solenoidal velocity and the corresponding pressure field. After this the extra-stress equations are solved. Applications to popular benchmarks for viscoelastic flows with stationary boundaries and comparisons with experimental and numerical studies are presented. The results show that the developed LS-STAG method modification demonstrates an accuracy comparable to body-fitted methods. The obtained modification is implemented in the «LS-STAG» software package developed by the author. This software allows to simulate viscous incompressible flows around a moving airfoil of arbitrary shape or airfoils system with one or two degrees of freedom. For example, it allows to simulate rotors autorotation and airfoils system wind resonance. Intel ® Cilk™ Plus, Intel ® TBB and OpenMP parallel programming technologies are used in the «LS-STAG».

Simulation of compressible two-phase flows with topology change of fluid–fluid interface by a robust cut-cell method

We develop a robust cut-cell method for numerical simulation of compressible two-phase flows with topology change of the fluid–fluid interface. In cut cell methods the flows can be solved in the finite volume framework and the jump conditions at the interface are resolved by solving a local Riemann problem. Therefore, cut cell methods can obtain interface evolution with high resolution, and at the same time satisfactorily maintain the conservation of flow quantities. However, it remains a challenge for the cut cell methods to handle interfaces with topology change or very high curvature, where the mesh is not sufficiently fine to resolve the interface. Inappropriate treatment could give rise to either distorted interface advection or unphysical oscillation of flow variables, especially when the regularization process (e.g. reinitialization in the level set methods) is implemented. A robust cut-cell method is proposed here, with the interface being tracked by a level set function. The local unphysical oscillation of flow variables in the presence of topology change is shown to be greatly suppressed by using a delayed reinitialization. The method can achieve second-order accuracy with respect to the interface position in the absence of topology changes of interface, while locally degrading to first-order at the interface region where topology change occurs. Its performance is examined through a variety of numerical tests, such as Rayleigh collapse, shock-bubble interaction, and shock-induced bubble collapse in water. Numerical results are compared against either benchmark solutions or experimental observations, and good agreement has been achieved qualitatively and/or quantitatively. Finally, we apply the method to investigating the collapse process of two tandem bubbles in water.

Turbulent jet in crossflow analysis with LES approach

Purpose This study aims to investigate effects of sonic jet injection into supersonic cross-flow (JISC) numerically in different dynamic pressure ratio values and free stream Mach numbers. Design/methodology/approach Large Eddy simulation (LES) with dynamic Smagorinsky model is used as the turbulence approach. The numerical results are compared with the experimental data, and the comparison shows acceptable validation. Findings According to the results, the dynamic pressure ratio has critical effects on the zone related to barrel shock. Despite free stream Mach number, increasing dynamic pressure ratio leads to expansion of barrel shock zone. Consequently, expanded barrel shock zone would bring about more obstruction effect. In addition, the height of counter-rotating vortex pair increases, and the high-pressure area before jet and low-pressure area after jet will rise. The results show that the position of barrel shock is deviated by increasing free stream Mach number, and the Bow shock zone becomes stronger and close to barrel shock. Moreover, high pressure zone, which is located before the jet, decreases by high free stream Mach number. Practical implications In this study, LES with a dynamic Smagorinsky model is used as the turbulence approach. Effects of sonic JISC are investigated numerically in different dynamic pressure ratio values and free stream Mach numbers. Originality/value As summary, the following are the contribution of this paper in the field of JISC subjects: several case studies of jet condition have been performed. In all the cases, the flow at the nozzle exit is sonic, and the free stream static pressure is constant. To generate proper grid, a cut cell method is used for domain modelling. Boundary condition effect on the wall pressure distribution around the jet and velocity profiles, especially S shape profiles, is investigated. The results show that the relation between representing the location of Mach disk centre and at transonic regime is a function of second-order polynomial, whereas at supersonic regime, the relationship is modelled as a first-order polynomial. In addition, the numerical results are compared with the experimental data demonstrating acceptable validation.

Application of the LS-STAG Immersed Boundary/Cut-Cell Method to Viscoelastic Flow Computations

AbstractThis paper presents the extension of a well-established Immersed Boundary (IB)/cut-cell method, the LS-STAG method (Y. Cheny & O. Botella, J. Comput. Phys. Vol. 229, 1043-1076, 2010), to viscoelastic flow computations in complex geometries. We recall that for Newtonian flows, the LS-STAG method is based on the finite-volume method on staggered grids, where the IB boundary is represented by its level-set function. The discretization in the cut-cells is achieved by requiring that global conservation properties equations be satisfied at the discrete level, resulting in a stable and accurate method and, thanks to the level-set representation of the IB boundary, at low computational costs.In the present work, we consider a general viscoelastic tensorial equation whose particular cases recover well-known constitutive laws such as the Oldroyd-B, White-Metzner and Giesekus models. Based on the LS-STAG discretization of the Newtonian stresses in the cut-cells, we have achieved a compatible velocity-pressure-stress discretization that prevents spurious oscillations of the stress tensor. Applications to popular benchmarks for viscoelastic fluids are presented: the four-to-one abrupt planar contraction flows with sharp and rounded re-entrant corners, for which experimental and numerical results are available. The results show that the LS-STAG method demonstrates an accuracy and robustness comparable to body-fitted methods.

Numerical Analysis of the Impact of the Interior Nozzle Geometry on Low Mach Number Jet Acoustics

The flow and acoustic fields of subsonic turbulent hot jets exhausting from three divergent nozzles at a Mach number M=0.12 based on the nozzle exit velocity are conducted using a hybrid CFD-CAA method. The flow field is computed by highly resolved large-eddy simulations (LES) and the acoustic field is computed by solving the acoustic perturbation equations (APE) whose acoustic source terms are determined by the LES. The LES of the computational domain includes the interior of the nozzle geometry. Synthetic turbulence is prescribed at the inlet of the nozzle to mimic the exit conditions downstream of the last turbine stage. The LES is based on hierarchically refined Cartesian meshes, where the nozzle wall boundaries are resolved by a conservative cut-cell method. The APE solution is determined on a block structured mesh. Three nozzle geometries of increasing complexity are considered, i.e., the flow and acoustic fields of a clean geometry without any built-in components, a nozzle with a centerbody, and a nozzle with a centerbody plus struts are computed. Spectral distributions of the LES based turbulent fluctuated quantities inside the nozzle and further downstream are analyzed in detail. The noise sources in the near field are noticeably influenced by the nozzle built-in components. The centerbody nozzle increases the overall sound pressure level (OASPL) in the near field with respect to the clean nozzle and the centerbody-plus-strut nozzle reduces it compared to the centerbody nozzle due to the increased turbulent mixing. The centerbody perturbed nozzle configurations generate a remarkable spectral peak at S t=0.56 which also occurs in the APE findings in the near field region. This tone is generated by large scale vortical structures shed from the centerbody. The analysis of the individual noise sources shows that the entropy term possesses the highest acoustic contribution in the sideline direction whereas the vortex sound source dominates the downstream acoustics.

Parametric Study on Wave Interaction with a Porous Submerged Rubble Mound Breakwater Using Modified N-S Equations and Cut-Cell Method

Parametric Study on Wave Interaction with a Porous Submerged Rubble Mound Breakwater Using Modified N-S Equations and Cut-Cell Method

Numerical Analysis for Saving Fin Material in Helical Segmented-Tubes

A numerical analysis is carried out in a small finned tube bank for several cutoff angles (30°, 45°, 60°, and 90°) at the rear part of helical segmented-tubes. Numerical simulations are undertaken using the Reynolds Averaged Navier-Stokes Equations approach. The turbulence effect is modeled with the Re-Normalization Group k-ε model and the finned tube geometry is represented by means of cut-cell method. Numerical results of these proposals are compared to a benchmark case (uncut fin case). Predictions show transport properties (energy and momentum) similar for cutoff angles less than (or equal to) 60°, since flow separation occurs nearly at this angle. Variations in heat transfer are less than 1% for 45° cutoff angle (fin material is reduced 25%) and less than 3.37% for 60° cutoff angle (fin material is reduced 33%). Therefore, finned tubes with cutoff angles of either 60° or 45° are recommended because their heat transfer and aerodynamics are approximately equal to those of benchmark case.

Computational analysis of nozzle geometry variations for subsonic turbulent jets

Large-eddy simulations (LES) of turbulent hot jets emanating from realistic helicopter engine nozzle configurations at a Reynolds number of Re = 7.5 × 105 and a Mach number of M=0.341 are conducted. The numerical method is based on hierarchically refined Cartesian meshes. The nozzle wall boundaries are resolved by a conservative cut-cell method. Three nozzle geometries of increasing complexity are considered, i.e., the flow fields of a clean geometry without any built-in components, a nozzle with a centerbody, and a nozzle with a centerbody plus struts are computed. The numerical method is validated by solutions for a single, a coaxial, and a chevron nozzle jet problem. A grid convergence study shows that the essential flow characteristics due to the intricacy of the nozzle geometry are well resolved. The results evidence that the flow field in the region 35 nozzle radii downstream of the exit is dominated by flow structures induced by the geometry. Compared to the clean geometry, the other two configurations show enhanced turbulent mixing. The centerbody and centerbody-plus-strut nozzle configurations reveal a spectral peak in the near nozzle exit region at St=0.15 which is caused by the wake flow of the centerbody.

Numerical Analysis of Turbulent Flow in a Small Helically Segmented Finned Tube Bank

A full finned tube bank is represented as a small finned tube bank in order to analyze numerically mean properties behavior in the streamwise direction. The main goal is to obtain criteria for implementing periodic boundary conditions in a single isolated finned tube module. The simulation is carried out with the Reynolds Averaged Navier–Stokes method and the turbulence effect is modeled with the Renormalization Group k-ϵ model. The complex geometry of finned tube is represented by means of a cut-cell method. Numerical results are compared with experimental data, experimental visualizations, and semi-empirical correlations. Predictions show an adequate hydrodynamics and heat transfer representation. Additionally, mean properties in the streamwise direction show quasi-sinusoidal behavior, and the heat transfer presents approximately identical values in every finned tube in the fully developed flow zone. Therefore, periodic boundary conditions for turbulent kinetic energy and its dissipation rate and a constant wall heat flux condition in the fully developed flow are proposed in numerical simulations on a single isolated finned tube module.

A high-order adaptive Cartesian cut-cell method for simulation of compressible viscous flow over immersed bodies

A new adaptive finite volume conservative cut-cell method that is third-order accurate for simulation of compressible viscous flows is presented. A high-order reconstruction approach using cell centered piecewise polynomial approximation of flow quantities, developed in the past for body-fitted grids, is now extended to the Cartesian based cut-cell method. It is shown that the presence of cut-cells of very low volume results in numerical oscillations in the flow solution near the embedded boundaries when standard small cell treatment techniques are employed. A novel cell clustering approach for polynomial reconstruction in the vicinity of the small cells is proposed and is shown to achieve smooth representation of flow field quantities and their derivatives on immersed interfaces. It is further shown through numerical examples that the proposed clustering method achieves the design order of accuracy and is fairly insensitive to the cluster size. Results are presented for canonical flow past a single cylinder and a sphere at different flow Reynolds numbers to verify the accuracy of the scheme. Investigations are then performed for flow over two staggered cylinders and the results are compared with prior data for the same configuration. All the simulations are carried out with both quadratic and cubic reconstruction, and the results indicate a clear improvement with the cubic reconstruction. The new cut-cell approach with cell clustering is able to predict accurate results even at relatively low resolutions. The ability of the high-order cut-cell method in handling sharp geometrical corners and narrow gaps is also demonstrated using various examples. Finally, three-dimensional flow interactions between a pair of spheres in cross flow is investigated using the proposed cut-cell scheme. The results are shown to be in excellent agreement with past studies, which employed body-fitted grids for studying this complex case.

Comparison of Terrain-Following and Cut-Cell Grids Using a Nonhydrostatic Model

Abstract Terrain-following coordinates are widely used in operational models but the cut-cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite-volume model enables a like-for-like comparison of terrain-following and cut-cell grids. A series of standard two-dimensional tests using idealized terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain-following coordinate surfaces. These new tests present a challenge on cut-cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain-following velocity fields lead to errors on cut-cell grids. Because of semi-implicit time stepping and an upwind-biased, explicit advection scheme, there are no time step restrictions associated with small cut cells. In contradiction to other studies, no significant advantages of cut cells or smoothed coordinates are found.

An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows

A Cartesian cut-cell method for viscous flows interacting with freely moving boundaries is presented. The method enables a sharp resolution of the embedded boundaries and strictly conserves mass, momentum, and energy. A new explicit Runge-Kutta scheme (PC-RK) is introduced by which the overall computational time is reduced by a factor of up to 2.5. The new scheme is a predictor-corrector type reformulation of a popular class of Runge-Kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy. The structural motion is computed by an implicit scheme with good stability properties due to a strong-coupling strategy and the conservative discretization of the flow solver at the material interfaces. A new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted Taylor-series approach solved via singular-value decomposition. The efficiency and the accuracy of the new method are demonstrated for several three-dimensional cases of laminar and turbulent particulate flow. It is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid-solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed. The results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes. An efficient Cartesian cut-cell method for freely moving solid boundaries is presented.The new predictor-corrector Runge-Kutta scheme (PC-RK) enables simulation speedups of up to 2.5.Mass, momentum, and energy are strictly conserved at the sharply resolved solid-fluid interfaces.The method exhibits very good stability and accuracy properties even for large displacements of the boundaries.Spurious force oscillations inherent to this class of methods are suppressed.

直交格子法における埋め込み境界法とCut-Cell法の比較ー壁面近傍での圧力・せん断応力分布の検証ー

直交格子法における埋め込み境界法とCut-Cell法の比較ー壁面近傍での圧力・せん断応力分布の検証ー