Flow-structure Interaction Problems Research Articles

An improved impermeable solid boundary scheme for Meshless Local Petrov–Galerkin method

Meshless methods have become an essential numerical tool for simulating a wide range of flow–structure interaction problems. However, the way by which the impermeable solid boundary condition is implemented can significantly affect the accuracy of the results and computational cost. This paper develops an improved boundary scheme through a weak formulation for the boundary particles based on Pressure Poisson’s Equation (PPE). In this scheme, the wall boundary particles simultaneously satisfy the PPE in the local integration domain by adopting the Meshless Local Petrov–Galerkin method with the Rankine source solution (MLPG_R) integration scheme (Ma, 2005b) and the Neumann boundary condition, i.e., normal pressure gradient condition, on the wall boundary which truncates the local integration domain. The new weak formulation vanishes the derivatives of the unknown pressure at wall particles and is discretized in the truncated support domain without extra artificial treatment. This improved boundary scheme is validated by analytical solutions, numerical benchmarks, and experimental data in the cases of patch tests, lid-driven cavity, flow over a cylinder and monochromic wave generation. Second-order convergent rate is achieved even for disordered particle distributions. The results show higher accuracy in pressure and velocity, especially near the boundary, compared to the existing boundary treatment methods that directly discretize the pressure Neumann boundary condition.

An immersed boundary method with implicit body force for compressible viscous flow

We present a new immersed boundary method for the simulation of compressible viscous flow. The method is based on the singular source approach where the immersed boundary adds surface singularities to the governing equations. The strengths of the surface singularities are treated as algebraic variables under the framework of differential-algebraic equations and are implicitly calculated to enforce the corresponding boundary conditions. Discrete delta functions are used to approximate the surface singularities in the Eulerian grid and interpolate variables back to the surface mesh. A half-explicit Runge-Kutta method is used to achieve desired temporal accuracy. The method has been generalized from the well-known no-slip and isothermal condition to stress and heat flux conditions. The latter necessitates the introduction of further singularities in the stresses and heat flux, which is a new feature of the formulation. Furthermore, the approach has been extended to porous surfaces. The method is also applicable to flow-structure interaction problems. Two- and three-dimensional numerical tests are carried out to demonstrate accuracy. The results are compared with previous numerical and experimental studies or analytical solutions. Finally, a fully three-dimensional fluid-structure interaction simulation of a subsonic parachute is showcased to demonstrate applicability to a real problem.

Numerical investigation of non-Newtonian power law flows using B-spline material point method

• A weakly compressible BSMPM method for simulating non-Newtonian flow is proposed. • Complex free surface flow and fluid structure interaction problems for power law fluid are studied. • Shear thickening/thinning, jet buckling/splashing, and vortex whirling are well represented. • Results demonstrate the efficacy of the proposed method for non-Newtonian power law flow problems. Simulating the complex flow with free surface and large deformation of non-Newtonian fluid is a challenging problem and plays a significant role in many industrial areas. In this paper, a weakly compressible B-spline material point method (WC-BSMPM) is presented and extended to solve the complex free surface flow of non-Newtonian fluid with a power law rheology model. Numerical examples including two-dimensional problems of plane Poiseuille, dam break, and container filling flow as well as three-dimensional sphere water entry problems are adopted to demonstrate the effectiveness and capabilities of the proposed method. The simulated results show good agreements with analytical solutions or published experimental data. Moreover, significant flow features for non-Newtonian power law fluid, including shear thickening, shear thinning, jet buckling, jet splashing, vortex whirling, and fluid-structure interactions can be well captured. Meanwhile, the numerical noise of the traditional MPM can be eliminated by the proposed method, which confirms that the WC-BSMPM method is a promising alternative to simulate the complex free surface flow and fluid-structure interactions for the non-Newtonian power law fluid.

A remeshed vortex method for mixed rigid/soft body fluid–structure interaction

We outline a 2D algorithm for solving incompressible flow–structure interaction problems for mixed rigid/soft body representations, within a consistent framework based on the remeshed vortex method. We adopt the one-continuum formulation to represent both solid and fluid phases on an Eulerian grid, separated by a diffuse interface. Rigid solids are treated using Brinkman penalization while an inverse map technique is used to obtain elastic stresses in the hyperelastic solid phase. We test our solver against a number of benchmark problems, which demonstrate physical accuracy and first to second order convergence in space and time. Benchmarks are complemented by additional investigations that illustrate the ability of our numerical scheme to capture essential fluid–structure interaction phenomena across a variety of scenarios involving internal muscular actuation, self propulsion, multi-body contact, heat transfer and rectified viscous streaming effects. Through these illustrations, we showcase the ability of our solver to robustly deal with different constitutive models and boundary conditions, solve disparate multi-physics problems and achieve faster time-to-solutions by sidestepping CFL time step restrictions.

A target-fixed immersed-boundary formulation for rigid bodies interacting with fluid flow

We present an immersed boundary projection method for flow-structure interaction problems involving rigid bodies with complex geometries. Dynamics of a rigid body interacting with fluid flow and kinematics of other rigid bodies undergoing prescribed motions are coupled implicitly with the incompressible vorticity equations. In particular, the method is formulated in a frame of reference fixed on the rigid body under flow-structure interaction (the target) so that the coupled system can be solved non-iteratively, accurately, and efficiently. The implicit coupling of the fluid solver and dynamics and kinematics of rigid bodies ensures the method being stable for low solid-to-fluid mass ratios. The influence of fictitious fluid inside the rigid body is considered and the spurious oscillations in surface stresses are filtered to impose physically correct rigid body dynamics. Similar to many predecessors of the immersed boundary projection method, the resulting discrete system is solved efficiently using a block-LU decomposition. We then validate the method with two-dimensional test problems of a neutrally buoyant cylinder migrating in a planar Couette flow and a freely falling or rising cylindrical rigid body.

Stationary and flow-induced vibration of two elliptic cylinders in tandem by immersed boundary-MRT lattice Boltzmann flux solver

Numerical method, combining immersed boundary method and multi-relaxation-time lattice Boltzmann flux solver, is used to carry out flow-structure interaction problems in this paper. Without dynamic mesh technique and body fitted grid re-generation, the flow-structure interaction problems can be solved by Cartesian mesh in order to simplify calculation process and save computation time. The accuracy and rationality of this method are verified by comparison of force coefficients, vibration amplitudes and flow characteristics with previous numerical results. Numerical simulations of two stationary and flow-induced vibration elliptical cylinders in tandem are carried out in laminar flow. For two stationary elliptical cylinders, the existing of downstream elliptical cylinder effectively prevents the unsteady characteristic of upstream wake at small gap spacing. With the increase of aspect ratio, the critical gap augments. After reaching the critical gap, the upstream force coefficients decrease and the downstream ones increase as aspect ratio increasing. Flow characteristic presents three regimes, including steady flow, shear layer attachment and 2S shedding vortex and 2S or C(2S) shedding vortex. For two flow-induced vibration elliptical cylinders, in comparison with stationary simulations, upstream transverse vibration responses are strengthened and downstream ones are strengthened at larger gap spacing and aspect ratio. The in-line vibration responses are both weaken, especially for downstream bluff body. Flow characteristic show different flow-regimes: (a) shear layer attachment for upstream and 2S shedding vortex for downstream; (b) 2S shedding vortex for upstream and C(2S) shedding vortex for downstream; (c) 2S shedding vortex for upstream and vortex pair presenting in the downstream wake. Greater L/D and AR, the effects of upstream wakes on downstream elliptical cylinder are more intense.

An immersed boundary-lattice Boltzmann method combined with a robust lattice spring model for solving flow–structure interaction problems

• A hybrid IB-LBM-LSM for simulation of elastic body in fluid flow was developed. • A closed form formula for implicitly updating the body deformation was presented. • Steady flow and vortex-shedding in the presence of deformable body were examined. • Critical Reynolds number for initiation of vortex-shedding in the presence of deformable body was studied. • Effects of Capillary and Reynolds numbers on deformable plate were analyzed. An immersed boundary (IB)-lattice Boltzmann method (LBM) combined with a robust lattice spring model (LSM) was developed for modeling fluid–elastic body interactions. To include the effects of viscous flow forces on the deformation of a flexible body, rotational invariant springs were connected regularly inside the deformable body with square lattices. Fluid–solid interactions were due to an additional force density in the lattice Boltzmann equation enhanced by the split-forcing approach. To check the validity and accuracy of the numerical method, the flow over a rigid plate and the deformation of a cantilever beam were investigated. To demonstrate the capability of the new method, different test cases were examined. The deformation of a two-dimensional flexible vertical plate in a laminar cross-flow stream at different conditions was analyzed. The simulations were performed for different boundary conditions imposed on the elastic plate, namely, fixed-end corners and fixed middle point. Different flow conditions such as “steady flow regime”, “vortex shedding flow regime”, and the limit of “rigid body motion” were examined using the new IB-LBM-LSM approach. A general formulation for evaluating the deformation of the elastic body was also introduced, in which the position of the LSM nodes (inside the body) was updated implicitly at each time step. Two dimensionless groups, namely capillary number ( Ca ) and Reynolds number ( Re ), were used for parametric study of the behavior of the flow around the deformable plate. It was found that for low Reynolds numbers ( Re < 50) and when the middle of the plate was fixed, decreasing the capillary number led to a decrease in the drag coefficient. The fluctuation of the plate during the vortex shedding flow regime was also explored. It was found that when the middle of the plate was fixed, the critical Reynolds number for the initiation of vortex shedding increased. For Re > 100, the Strouhal number was observed to increase with the decrease in capillary number.

A strongly-coupled immersed-boundary formulation for thin elastic structures

We present a strongly-coupled immersed-boundary method for flow–structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with many strongly-coupled immersed-boundary methods, our method requires the solution of a nonlinear algebraic system at each time step. The system is solved through iteration, where the iterates are obtained by linearizing the system and performing a block-LU factorization. This restricts all iterations to small-dimensional subsystems that scale with the number of discretization points on the immersed surface, rather than on the entire flow domain. Moreover, the iteration procedure we propose does not involve heuristic regularization parameters, and has converged in a small number of iterations for all problems we have considered. We derive our method for general deforming surfaces, and verify the method with two-dimensional test problems of geometrically nonlinear flags undergoing large amplitude flapping behavior.

High-order fluid solver based on a combined compact integrated RBF approximation and its fluid structure interaction applications

In this study, we present a high-order numerical method based on a combined compact integrated RBF (IRBF) approximation for viscous flow and fluid structure interaction (FSI) problems. In the method, the fluid variables are locally approximated by using the combined compact IRBF, and the incompressible Navier-Stokes equations are solved by using the velocity-pressure formulation in a direct fully coupled approach. The fluid solver is verified through various problems including heat, Burgers, convection-diffusion equations, Taylor-Green vortex and lid driven cavity flows. It is then applied to simulate some FSI problems in which an elastic structure is immersed in a viscous incompressible fluid. For FSI simulations, we employ the immersed boundary framework using a regular Eulerian computational grid for the fluid mechanics together with a Lagrangian representation of the immersed boundary. For the immersed fibre/membrane FSI problems, although the order of accuracy of the present scheme is generally similar to FDM approaches reported in the literature, the present approach is nonetheless more accurate than FDM approaches at comparable grid spacings. The numerical results obtained by the present scheme are highly accurate or in good agreement with those reported in earlier studies of the same problems.

Computational Mechanics of a Coupled Flow-Structure Interaction Problem with Applications to Bio-Inspired Micro Air Vehicles

Computational Mechanics of a Coupled Flow-Structure Interaction Problem with Applications to Bio-Inspired Micro Air Vehicles

An Iterative Incompressible Immersed Boundary Method Applied to Biofluid-Structure Interaction Problems

This work reports on the development of a novel iterative coupling between the Immersed Boundary method (IBM)[1] and a modified projection-based pressure correction, under the assumption of global incompressibility; its validation using a problem of practical interest - flow past an obstacle; and its application on the simulation of an idealised physiological system - blood flowing past a thrombotic-filter. Indeed, the method presented in [2] was improved through a Lagrangian restoring force based correction of the post-projection residual IB-velocity, which is inherent in fractional-step methods[3], being more evident at high Reynolds numbers Re. Overall, the results have shown that the proposed approach is very promising to study complex flow-structure interaction problems under the assumption of global incompressibility, which are commonly found in biophysical systems. The number of iterations remains almost constant in relation to both mesh-spacing and time-step refinement, the iterative approach avoids linearised formulations commonly used in matrix resolutions, and it is driven by upper limits of residuals (L∞ norm) - Figure 1.View Large Image | View Hi-Res Image | Download PowerPoint Slide[1] C.S. Peskin, Acta Numerica,11,479-517(2002).[2] G. Pereira, Conf. Multiscale Modelling in Medicine and Biology, Nottingham, UK(2012).[3] R. Verzicco and P. Orlandi, J. Comput. Phys,123,402-414(1996).

Aerodynamics of knuckle ball: Flow-structure interaction problem on a pitched baseball without spin

In the game of baseball, the knuckleball—so-called because the baseball is gripped with the knuckles in a certain position—is pitched in a way that introduces nearly no rotation, resulting in erratic flight paths which confuse batters. The “knuckleball” effect is believed to be caused by asymmetric flow separation over the baseball, but little is known about its flow physics. In the experiment described in this paper, the flow near the seams of the baseball is visualized thoroughly and the velocity vector fields near the surface and in the wake are obtained with Digital Particle Image Velocimetry. Depending on its position, the seam is found to trigger the boundary layer transition thus delaying the separation, or to cause separation itself. Three-dimensional wake patterns associated with specific ball orientations are identified and related to the force variations on the ball.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

A Coupled Sharp-Interface Immersed Boundary-Finite-Element Method for Flow-Structure Interaction With Application to Human Phonation

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems

A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems

Optimal lift force coefficient databases from riser experiments

Significant past effort has gone into understanding the complicated flow–structure interaction problem of vortex-induced vibration (VIV) of long flexible cylindrical structures (e.g., risers, mooring lines, tendons, conductors) in the ocean environment. However, major challenges persist with regard to riser VIV modeling and response prediction. The existing prediction schemes are based on a number of hypotheses, experimental facts and data like strip theory, energy balance, correlation length and, most importantly, the use of lift force coefficient databases. Recent advances in observing the VIV motions on experimental risers with high confidence shows that some of these assumptions may not be valid. One important source of the discrepancies between theoretical estimates and experimental observations arise from the use of experimentally obtained lift coefficient databases. These databases were obtained under the laboratory conditions of limited Reynolds number , and under the assumption that the cross-flow motions are not influenced by restraining the in-line motions. In this paper we develop a method to improve the modeling capability of riser VIV by extracting empirical lift coefficient databases from field riser VIV measurements. The existing laboratory-based lift coefficient databases are represented in a flexible parameterized form using a set of carefully chosen parameters. Extraction of the lift coefficient parameters is posed as an optimization problem, where the objective is to minimize the error between the prediction using a theoretical model and the experimental data. Application of the method to data from the Norwegian Deepwater Programme experiments shows that the new optimal databases significantly reduce the error in estimating the riser VIV cross-flow response.

Flow in a multi-branching vessel with compliant walls

The problem of fluid flow in a compliant-walled channel which branches into two or more daughters is considered with the aim of understanding blood flow through arterio-venous malformations (AVMs) in the brain. The outer walls of the channel are assumed for definiteness to behave as spring-back plates, whilst the divider is taken as rigid. The fluid is assumed to be incompressible and inviscid. When the Strouhal number is small (as occurs in practice in the brain), there are two main axial length scales, one much longer than the vessel width and the other comparable with the vessel width. Also, in the case of small wall displacements, one can analyse the local flow-structure interaction problem using a complex variable method. The flow shows markedly different qualitative features downstream of the branching, depending on the wall stiffness.

An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers

We present a novel particle method, combining remeshed Smoothed Particle Hydrodynamics with Immersed Boundary and Level Set techniques for the simulation of flows past complex deforming geometries. The present method retains the Lagrangian adaptivity of particle methods and relies on the remeshing of particle locations in order to ensure the accuracy of the method. In fact this remeshing step enables the introduction of Immersed Boundary Techniques used in grid based methods. The method is applied to simulations of flows of isothermal and compressible fluids past steady and unsteady solid boundaries that are described using a particle Level Set formulation. The method is validated with two and three-dimensional benchmark problems of flows past cylinders and spheres and it is shown to be well suited to simulations of large scale simulations using tens of millions of particles, on flow-structure interaction problems as they pertain to self-propelled anguilliform swimmers.

An immersed-boundary method for flow–structure interaction in biological systems with application to phonation

A new numerical approach for modeling a class of flow–structure interaction problems typically encountered in biological systems is presented. In this approach, a previously developed, sharp-interface, immersed-boundary method for incompressible flows is used to model the fluid flow and a new, sharp-interface Cartesian grid, immersed-boundary method is devised to solve the equations of linear viscoelasticity that governs the solid. The two solvers are coupled to model flow–structure interaction. This coupled solver has the advantage of simple grid generation and efficient computation on simple, single-block structured grids. The accuracy of the solid-mechanics solver is examined by applying it to a canonical problem. The solution methodology is then applied to the problem of laryngeal aerodynamics and vocal fold vibration during human phonation. This includes a three-dimensional eigen analysis for a multi-layered vocal fold prototype as well as two-dimensional, flow-induced vocal fold vibration in a modeled larynx. Several salient features of the aerodynamics as well as vocal fold dynamics are presented.

2720 柔軟構造円柱の流体構造連成解析(J20-5 流体関連の騒音と振動(5) 流体連成振動の解析法,ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

In this study, a fully coupled methodology is developed for calculation of the flow-structure interaction problems with moving and deforming mesh systems. In order to confirm the applicability of our code, flow simulation around a flexible cantilever circular cylinder was performed. The characteristics of the response amplitude obtained by present calculations were similar to the experimental results, though these amplitudes were somewhat smaller than the experimental results. It was confirmed that the lock-in phenomena can be caused near the tip of the cylinder.