Solid Solver Research Articles

A full immersed boundary solution coupled to a Lattice–Boltzmann solver for multiple fluid–structure interactions in turbulent rotating flows

This paper presents a Fluid–Structure Interaction (FSI) model based on an Immersed Boundary Method (IBM) which is applied to the transport of rags in waste water pumps. The IBM is used both to handle the flow in presence of moving rigid solids with arbitrary geometries, and to couple the fluid equations with the structural dynamics of flexible slender solids. The whole FSI model involves the combination of four numerical blocks: (i) a Lattice–Boltzmann solver for the fluid equations, (ii) a solid solver to solve the structural dynamics (if flexible solids are considered), (iii) the IBM to perform the coupling fluid–solid, and (iv) collision models for the coupling solid–solid.The present IBM is based on a direct-forcing approach available in the open-source library Palabos. In the first part of this paper, the accuracy of the IBM is assessed for single-phase flow applications. Particular attention is paid to the prediction of integrated and averaged quantities. The results show good agreements with experimental data. The second part deals with the validation of the proposed FSI–IBM model for solving the interactions between the fluid and flexible slender structures. Quantitative and qualitative comparisons have been carried out against benchmark cases and have demonstrated the good stability and accuracy of the model. The proposed collision models are also assessed in terms of stability and relevance. Finally, simulations of the rag transport in a waste water pump have shown to give stable and consistent results, as well as good insight on the probability of occurrence of clogging.

A 3D SPH–FE coupling for FSI problems and its application to tire hydroplaning simulations on rough ground

A 3D fluid–structure coupling between Smoothed Particle Hydrodynamics (SPH) and Finite Element (FE) methods is proposed in this paper, with its application to complex tire hydroplaning simulations on rough ground. The purpose of this work is to analyze the SPH–FE coupling capabilities for modeling efficiently such a complex phenomenon. On the fluid side, the SPH method is able to handle the three complex interfaces of the hydroplaning phenomenon: free-surface, ground/fluid and fluid/tire interfaces. On the solid side, the FE method is used for its ability to treat tire–ground contact. A new algorithm dedicated to such SPH–FE coupling strategies is proposed to optimize the computational efficiency through the use of differed time steps between fluid and solid solvers. This way, the number of calls to the FE solver is minimized while maintaining the accuracy and stability of the coupling. The ratio between these respective time steps relies on a control procedure based on pressure loading. The present 3D SPH–FE model is first validated with different academic test cases and experimental data before considering the complex problem of the 3D hydroplaning simulations. Hydroplaning simulations are performed and analyzed on 3D configurations involving both smooth and rough grounds.

On the coupling of a direct-forcing immersed boundary method and the regularized lattice Boltzmann method for fluid-structure interaction

The present paper provides an analysis of the force model effect on the regularization procedure based on the Hermite expansion in regularized lattice Boltzmann method (RLBM). It is shown that, when using the 2nd-order accurate in time semi-implicit force model of Guo et al. [15] in RLBM, the reconstruction of the non-equilibrium part of the distribution function has to start from the 1st-order Hermite polynomial, because the new distribution function (after a change of variables) contains the body force effect. Based on this Hermite regularization, an immersed boundary-regularized lattice Boltzmann (IB-RLB) coupling method is proposed for simulating transient fluid-structure interactions (FSI) with rigid and deformable solid objects. The fluid and solid solvers are coupled in a non-staggered way so that the stability and accuracy are well preserved. The proposed IB-RLB coupling method is then validated with several numerical test-cases, such as impulsively started plate, vortex-induced vibrations and 3D flapping flag, for which good agreements are found with the references.

A fully partitioned Lagrangian framework for FSI problems characterized by free surfaces, large solid deformations and displacements, and strong added-mass effects

In this work a fully partitioned Lagrangian framework for the solution of fluid–structure interaction (FSI) problems involving free surfaces, large solid displacements and deformations, and strong added mass effects is presented. The fluid is simulated using the Particle Finite Element Method (PFEM), while Metafor, a large deformations nonlinear Finite Element code, is employed to simulate the solid part. The fully partitioned coupling is ensured through an Interface Quasi-Newton Inverse Least Squares (IQN-ILS) (Degroote et al., 2009) strategy to avoid added mass effects. The Lagrangian particle nature of the PFEM allows the simulation of problems involving free surfaces and very large solid displacements, usually difficult to achieve with traditional body-fitted CFD techniques. We show that owing to the generality of its formulation the PFEM can be used as is in the framework of fully partitioned FSI coupling schemes, where minimal information (i.e. loads and displacements at the FSI interface) is exchanged between the fluid and the solid solvers. More importantly, we demonstrate that a fully partitioned PFEM–FEM coupling based on the IQN-ILS strategy allows the simulation of a very large spectrum of FSI problems without incurring added-mass instabilities. The performance of the IQN-ILS coupling strategy in a fully Lagrangian framework is also assessed and compared to more traditional approaches such as Block-Gauss–Seidel (BGS) iterations with Aitken relaxation. An extensive work of verification and benchmarking is proposed, aiming to encompass all the combinations of physical and numerical parameters possibly leading to added-mass instabilities, and testing the IQN-ILS strategy on different benchmarks beyond those already proposed in the literature. The coupling is performed through CUPyDO (Thomas et al., 2019), a general Python framework for partitioned FSI coupling.

OpenIFEM: A High Performance Modular Open-Source Software of the Immersed Finite Element Method for Fluid-Structure Interactions.

We present a high performance modularly-built open-source software - OpenIFEM. OpenIFEM is a C++ implementation of the modified immersed finite element method (mIFEM) to solve fluid-structure interaction (FSI) problems. This software is modularly built to perform multiple tasks including fluid dynamics (incompressible and slightly compressible fluid models), linear and nonlinear solid mechanics, and fully coupled fluid-structure interactions. Most of open-source software packages are restricted to certain discretization methods; some are under-tested, under-documented, and lack modularity as well as extensibility. OpenIFEM is designed and built to include a set of generic classes for users to adapt so that any fluid and solid solvers can be coupled through the FSI algorithm. In addition, the package utilizes well-developed and tested libraries. It also comes with standard test cases that serve as software and algorithm validation. The software can be built on cross-platform, i.e., Linux, Windows, and Mac OS, using CMake. Efficient parallelization is also implemented for high-performance computing for large-sized problems. OpenIFEM is documented using Doxygen and publicly available to download on GitHub. It is expected to benefit the future development of FSI algorithms and be applied to a variety of FSI applications.

A Loosely Coupled Scheme for Fictitious Domain Approximations of Fluid-Structure Interaction Problems with Immersed Thin-Walled Structures

Fictitious domain approximations of fluid-structure interaction problems are generally discretized in time using strongly coupled schemes. This guarantees unconditional stability but at the price of solving a computationally demanding coupled system at each time-step. The design of loosely coupled schemes (i.e., methods that invoke the fluid and solid solvers only once per time-step) is of fundamental interest, especially for three-dimensional simulations, but the existing approaches are known to suffer from severe stability and/or time accuracy issues. We propose a new approach that overcomes these difficulties in the case of the coupling with immersed thin-walled structures.

Simulations of self-propelled anguilliform swimming using the immersed boundary method in OpenFOAM

This study extends the existing immersed boundary method (IBM) in the open source toolbox OpenFOAM for solving fluid-structure interactions involving the immersed structure with changeable shapes. To handle a changeable-shape problem, the existing discrete-forcing direct-imposition approach of IBM in OpenFOAM with a pressure-implicit split-operator (PISO) solver is used to solve the fluid domain with interpolated immersed boundary conditions. In the solved fluid domain, the interactions between the fluid domain and the immersed structure are calculated. Making use of these interactions, a user-defined solid solver is applied to compute and update the boundary conditions on the immersed structure. To validate this methodology, models of anguilliform swimming, a typical FSI problem with moving boundaries which has been well studied, is simulated. The accuracy of the present work is examined by comparing the numerical results with the published data. In simulations, anguilliform swimmers are modeled as deformable immersed boundaries. The immersed swimmers propagate in a path determined by the forces from the surrounding fluid acting upon their bodies, as generated by their prescribed changing shapes. The results including the velocity, the thrust, the wake morphology, and the force distribution along the immersed boundaries are presented and discussed. The good agreement of the computational results with reported works validates the extension of IBM in OpenFOAM.

CUPyDO - An integrated Python environment for coupled fluid-structure simulations

CUPyDO, a fluid-structure interaction (FSI) tool that couples existing independent fluid and solid solvers into a single synchronization and communication framework based on the Python language is presented. Each coupled solver has to be wrapped in a Python layer in order to embed their functionalities (usually written in a compiled language) into a Python object, that is called and used by the coupler. Thus a staggered strong coupling can be achieved for time-dependent FSI problems such as aeroelastic flutter, vortex-induced vibrations (VIV) or conjugate heat transfer (CHT). The synchronization between the solvers is performed with the predictive block-Gauss-Seidel algorithm with dynamic under-relaxation. The tool is capable of treating non-matching meshes between the fluid and structure domains and is optimized to work in parallel using Message Passing Interface (MPI). The implementation of CUPyDO is described and its capabilities are demonstrated on typical validation cases. The open-source code SU2 is used to solve the fluid equations while the solid equations are solved either by a simple rigid body integrator or by in-house linear/nonlinear Finite Element codes (GetDP/Metafor). First, the modularity of the coupling as well as its ease of use is highlighted and then the accuracy of the results is demonstrated.

An extended partitioned method for conservative solid-fluid coupling

We present a novel extended partitioned method for two-way solid-fluid coupling, where the fluid and solid solvers are treated as black boxes with limited exposed interfaces, facilitating modularity and code reusability. Our method achieves improved stability and extended range of applicability over standard partitioned approaches through three techniques. First, we couple the black-box solvers through a small, reduced-order monolithic system, which is constructed on the fly from input/output pairs generated by the solid and fluid solvers. Second, we use a conservative, impulse-based interaction term to couple the solid and fluid rather than typical pressure-based forces. We show that both of these techniques significantly improve stability and reduce the number of iterations needed for convergence. Finally, we propose a novel boundary pressure projection method that allows for the partitioned simulation of a fully enclosed fluid coupled to a dynamic solid, a scenario that has been problematic for partitioned methods. We demonstrate the benefits of our extended partitioned method by coupling Eulerian fluid solvers for smoke and water to Lagrangian solid solvers for volumetric and thin deformable and rigid objects in a variety of challenging scenarios. We further demonstrate our method by coupling a Lagrangian SPH fluid solver to a rigid body solver.

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O2 and CH4) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH4 oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH4 to the O2 streams at approximately 450 Hz, affecting the whole flame structure.

A 3D common-refinement method for non-matching meshes in partitioned variational fluid–structure analysis

We present a three-dimensional (3D) common-refinement method for non-matching unstructured meshes between non-overlapping subdomains of incompressible turbulent fluid flow and nonlinear hyperelastic structure. The fluid flow is discretized using a stabilized Petrov–Galerkin method, and the large deformation structural formulation relies on a continuous Galerkin finite element method. An arbitrary Lagrangian–Eulerian formulation with a nonlinear iterative force correction (NIFC) coupling is achieved in a staggered partitioned manner by means of fully decoupled implicit procedures for the fluid and solid discretizations. To begin, we first investigate the accuracy of common-refinement method (CRM) to satisfy the traction equilibrium condition along the fluid-elastic interface with non-matching meshes. We systematically assess the accuracy of CRM against the matching grid solution by varying grid mismatch between the fluid and solid meshes over a tubular elastic body. We demonstrate the second-order accuracy of CRM through uniform refinements of fluid and solid meshes along the interface. We then extend the error analysis to transient data transfer across non-matching meshes between the fluid and solid solvers. We show that the common-refinement discretization across non-matching fluid–structure grids yields accurate transfer of the physical quantities across the fluid–solid interface. We next solve a 3D fluid–structure interaction (FSI) problem of a cantilevered hyperelastic plate behind a circular bluff body and verify the accuracy of coupled solutions with respect to the available solution in the literature. By varying the solid interface resolution, we generate various non-matching grid ratios and quantify the accuracy of CRM for the nonlinear structure interacting with a laminar flow. We illustrate that the CRM with the partitioned NIFC treatment is stable for low solid-to-fluid density ratio and non-matching meshes for the 3D FSI problem. Finally, we demonstrate the 3D parallel implementation of the common-refinement with the NIFC method for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects and turbulent wake flow.

Coupling immersed method with node-based partly smoothed point interpolation method (NPS-PIM) for large-displacement fluid-structure interaction problems

The newly developed node-based partly smoothed point interpolation method (NPS-PIM) and immersed technique are coupled to simulate fluid-structure interaction (FSI) problems associated with largely deformable solid/structure. Under the framework of immersed method, the governing equations can be decomposed into three components based on fictitious fluid assumption, i.e. equations for incompressible viscous fluid, FSI conditions and nonlinear solid. The semi-implicit characteristic-based split algorithm is used to solve the Navier-Stokes equation of incompressible viscous fluid, and the fictitious fluid domain can be used to calculate the FSI force. Owing to the properly softened stiffness by the node-based partly strain smoothing operation, NPS-PIM can effectively solve the large deformation problem of solids discretized with the simplest linear triangular mesh. The immersed framework makes the present method avoid the troublesome re-meshing process and the triangular mesh further simplifies the preprocessing operation. In comparison with the models using FEM and node-based smoothed point interpolation method (NS-PIM) as solid solver, numerical results have shown that the present method using NPS-PIM can provide more accurate solutions for both steady and transient problems with regard to large-displacement FSI problems.

Assessment of Unsteadiness Modeling for Transient Natural Convection

Turbine flexible operations with faster startups/shutdowns are required to accommodate emerging renewable power generations. A major challenge in transient thermal design and analysis is the time scale disparity. For natural cooling, the physical process is typically in hours, but on the other hand, the time-step sizes typically usable tend to be very small (subseconds) due to the numerical stability requirement for natural convection as often observed. An issue of interest is: What time-step sizes can and should be used in terms of stability as well as accuracy? In this work, the impact of flow temporal gradient and its modeling is examined in relation to numerical stability and modeling accuracy for transient natural convection. A source term-based dual-timing formulation is adopted, which is shown to be numerically stable for very large time-steps. Furthermore, a loosely coupled procedure is developed to combine this enhanced flow solver with a solid conduction solver for solving unsteady conjugate heat transfer (CHT) problems for transient natural convection. This allows very large computational time-steps to be used without any stability issues, and thus enables to assess the impact of using different time-step sizes entirely in terms of a temporal accuracy requirement. Computational case studies demonstrate that the present method can be run stably with a markedly shortened computational time compared to the baseline solver. The method is also shown to be more accurate than the commonly adopted quasi-steady flow model when unsteady effects are non-negligible.

Modelling fluid-microstructure interaction on elasto-visco-plastic digital rocks

Flow simulators have become increasingly popular to compute permeability on digital porous rocks reconstructed from Computerised Tomography (CT) scan data as part of Digital Rock Physics workflows. Various schemes are being used that focus mainly on numerical efficiency but do not necessarily provide the flexibility to account for more complex couplings between other physical models than the flow itself, like irreversible mechanical deformation for instance. To overcome this limitation, we present a finite element implementation of an Eulerian flow solver that is coupled to a Lagrangian solid mechanics solver, both in a sequential or tight manner. The flow simulator is successfully benchmarked for permeability computation on a digital rock that has been previously used for other code validations. The need for a tightly coupled hydro-mechanical simulator is then highlighted by comparing the loose and tight coupling approaches, revealing that the tight approach is more accurate and more efficient computationally. Finally, the use of the simulator in real cases is illustrated by running a hydro-mechanical simulation on a digital rock sample, where plastic deformation and fluid flow in the porous space are resolved simultaneously.

1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application

AbstractThe equation of state (EOS) plays a crucial role in hyperbolic conservation laws for the compressible fluid. Whereas, the solid constitutive model with elastic-plastic phase transition makes the analysis of the solid Riemann problem more difficult. In this paper, one-dimensional elastic-perfectly plastic solid Riemann problem is investigated and its exact Riemann solver is proposed. Different from previous works treating the elastic and plastic phases integrally, we resolve the elastic wave and plastic wave separately to understand the complicate nonlinear waves within the solid and then assemble them together to construct the exact Riemann solver for the elastic-perfectly plastic solid. After that, the exact solid Riemann solver is associated with the fluid Riemann solver to decouple the fluid-solid multi-material interaction. Numerical tests, including gas-solid, water-solid high-speed impact problems are simulated by utilizing the modified ghost fluid method (MGFM).

Multiphase fluid-solid coupled analysis of shock-bubble-stone interaction in shockwave lithotripsy.

A novel multiphase fluid-solid-coupled computational framework is applied to investigate the interaction of a kidney stone immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The main objective is to elucidate the effects of a bubble in the shock path to the elastic and fracture behaviors of the stone. The computational framework couples a finite volume 2-phase computational fluid dynamics solver with a finite element computational solid dynamics solver. The surface of the stone is represented as a dynamic embedded boundary in the computational fluid dynamics solver. The evolution of the bubble surface is captured by solving the level set equation. The interface conditions at the surfaces of the stone and the bubble are enforced through the construction and solution of local fluid-solid and 2-fluid Riemann problems. This computational framework is first verified for 3 example problems including a 1D multimaterial Riemann problem, a 3D shock-stone interaction problem, and a 3D shock-bubble interaction problem. Next, a series of shock-bubble-stone-coupled simulations are presented. This study suggests that the dynamic response of a bubble to LSW varies dramatically depending on its initial size. Bubbles with an initial radius smaller than a threshold collapse within 1μs after the passage of LSW, whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (pmax =35.0MPa, pmin =-10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a noncollapsing bubble imposes a negative effect on stone fracture as it shields part of the LSW from the stone. On the other hand, a collapsing bubble may promote fracture on the proximal surface of the stone, yet hinder fracture from stone interior.

Aerodynamic simulations of offshore floating wind turbine in platform-induced pitching motion

Forfloating offshore wind turbines, rotors are under coupled motions of rotating and platform-induced motions because of hydrodynamics impacts. Notably, the coupled motion of platform pitching and rotor rotating induces unsteadiness and nonlinear aerodynamics in turbine operations; thus having a strong effect on the rotor performances including thrust and power generation. The present work aims at developing a computational fluid dynamics model for simulations of rotor under floating platform induced motions. The rotor motion is realized using arbitrary mesh interface, and wind flows are modelled by incompressible Navier-Stokes flow solver appended by the k − ω shear stress transport turbulence model to resolve turbulence quantities. In order to investigate the fully coupled motion of floating wind turbine, the six degree of freedom solid body motion solver is extended to couple with multiple motions, especially for the motion of rotor coupled with the prescribed surge-heave-pitch motion of floating platform. The detailed methodology of multiple motion coupling is also described and discussed in this work. Both steady and unsteady simulations of offshore floating wind turbine are considered in the present work. The steady aerodynamic simulation of offshore floating wind turbine is implemented by the multiple reference frames approach and for the transient simulation, the rotor motion is realized using arbitrary mesh interface. A rigorous benchmark of the present numerical model is performed by comparing to the reported literatures. The detailed elemental thrust and power comparisons of wind turbine are carried out by comparing with the results from FAST developed by National Renewable Energy Laboratory and various existing numerical data with good agreement. The proposed approach is then applied for simulations of National Renewable Energy Laboratory 5MW turbine in coupled platform motion at various wind speeds under a typical load case scenario. Transient effect of flows over turbines rotor is captured with good prediction of turbine performance as compared with existing data from FAST. Copyright © 2016 John Wiley & Sons, Ltd.

A natural framework for isogeometric fluid–structure interaction based on BEM–shell coupling

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of Stokes equations to model the surrounding flow, and a non linear Kirchhoff–Love shell theory to model the elastic behavior of the structure. We propose three different coupling strategies: a monolithic, fully implicit coupling, a staggered, elasticity driven coupling, and a novel semi-implicit coupling, where the effect of the surrounding flow is incorporated in the non-linear terms of the solid solver through its damping characteristics. The novel semi-implicit approach is then used to demonstrate the power and robustness of our method, which fits ideally in the isogeometric paradigm, by exploiting only the boundary representation (B-Rep) of the thin structure middle surface.

Conjugate heat transfer of a rib-roughened internal turbine blade cooling channel using large eddy simulation

This contribution focuses on the conjugate heat transfer computation of a rib-roughened internal turbine blade cooling channel with a blockage ratio of 0.3 and a Reynolds number of 40,000. The work considers the coupling between two numerical tools: a Large Eddy Simulation flow solver and a solid conduction solver. While interested in the thermal steady states of such problems, both solvers provide time dependent de-synchronized solutions. A novel weak coupling strategy, the hFFB method, is applied to solve the challenge of varying fluid and solid time scales. This method first computes the fluid domain until it reaches a statistically steady state, from which the mean temporal solution is obtained. Then, it solves the solid domain with the mean boundary conditions imposed from the fluid leading to an updated fluid boundary condition. This process is repeated until convergence of the coupled problem. The coupled convective-conductive solution shows that conjugate heat transfer is important for rib-roughened internal cooling ducts and has a large impact on the heat transfer at the solid-fluid interface. The results were validated against experimental data provided by the von Karman Institute for Fluid Dynamics.

Use of the method of manufactured solutions for the verification of conjugate heat transfer solvers

This paper demonstrates the use of the method of manufactured solutions to verify the implementation of tightly coupled conjugate heat transfer for fluid-solid solvers. The interface conditions in the prescribed manufactured solutions were implemented to mimic real effects such as no-slip, and temperature/heat flux match between the solid and fluid domains. The newly developed solid heat transfer solver was verified in standalone mode using this prescribed manufactured solution and was found to have no apparent coding errors. Our pre-existing in-house compressible fluid solver (Eilmer) was used to demonstrate the conjugate heat transfer implementation. Both the fluid and solid solvers showed an expected spatial order of convergence of 2.0 in the standalone mode. The coupled conjugate heat transfer mode also showed no coding errors and demonstrated that the spatial order of convergence was again 2.0. The one-sided spatial discretisation utilised to enforce the tight coupling for the interface conditions were effectively equivalent to a central difference. Hence, the overall spatial order of the error convergence for the entire domain, including the interface, was 2.0. The method prescribed in this work can be extended for verification of other conjugate heat transfer solvers, in particular for compressible flow scenarios where analytical solutions may not be readily available.