“…Therefore, the mesh M3 is adequate for the present study. Furthermore, the adopted full-order solver and the numerical discretizations have been extensively validated in several earlier studies for both low Re (Miyanawala et al 2016;Jaiman et al 2016a) and moderate Re (Jaiman et al 2016a;Miyanawala & Jaiman 2018) flows. In the next section, the modal decomposition of the pressure field is presented for a representative reduced velocity of U r = 6.0 in the lock-in region at (Re, m * , ζ) = (100, 3.0, 0).…”
We present a dynamic decomposition analysis of the wake flow in fluid-structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational fluid-structure interaction solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Reynolds number (Re). The snapshot data from high-dimensional FSI simulations are projected to a low-dimensional subspace using the proper orthogonal decomposition (POD). We utilize each corresponding POD mode for detecting features of the organized motions namely the vortex street, the shear layer and the near-wake bubble. We find that the vortex shedding modes contribute solely to the lift force, while the near-wake and shear layer modes play a dominating role to the drag force. We further examine the fundamental mechanism of this dynamical behavior and propose a force decomposition technique via low-dimensional approximation. To elucidate the frequency lock-in, we systematically analyze the decomposed modes and their dynamical contributions to the force fluctuations for a range of reduced velocity at low Re laminar flow. We ascertain quantitatively that the shear layer feeds the vorticity flux to the wake vortices and the near-wake bubble during the wake-body synchronization. Based on the decomposition of wake dynamics, we suggest an interaction cycle for the frequency lock-in during the wake-body interaction, which provides the inter-relationship between the high amplitude motion and the dominating wake features. Through our investigation of wake-body synchronization below critical Re range, we discover that the bluff body can undergo a synchronized high-amplitude vibration due to flexibility-induced unsteadiness. Owing to the wake turbulence at a moderate Reynolds number of Re = 22, 000, a distorted set of POD modes and the broadband energy distribution are observed, while the interaction cycle for the wake-synchronization is found to be valid for the turbulent wake flow.
“…Therefore, the mesh M3 is adequate for the present study. Furthermore, the adopted full-order solver and the numerical discretizations have been extensively validated in several earlier studies for both low Re (Miyanawala et al 2016;Jaiman et al 2016a) and moderate Re (Jaiman et al 2016a;Miyanawala & Jaiman 2018) flows. In the next section, the modal decomposition of the pressure field is presented for a representative reduced velocity of U r = 6.0 in the lock-in region at (Re, m * , ζ) = (100, 3.0, 0).…”
We present a dynamic decomposition analysis of the wake flow in fluid-structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational fluid-structure interaction solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Reynolds number (Re). The snapshot data from high-dimensional FSI simulations are projected to a low-dimensional subspace using the proper orthogonal decomposition (POD). We utilize each corresponding POD mode for detecting features of the organized motions namely the vortex street, the shear layer and the near-wake bubble. We find that the vortex shedding modes contribute solely to the lift force, while the near-wake and shear layer modes play a dominating role to the drag force. We further examine the fundamental mechanism of this dynamical behavior and propose a force decomposition technique via low-dimensional approximation. To elucidate the frequency lock-in, we systematically analyze the decomposed modes and their dynamical contributions to the force fluctuations for a range of reduced velocity at low Re laminar flow. We ascertain quantitatively that the shear layer feeds the vorticity flux to the wake vortices and the near-wake bubble during the wake-body synchronization. Based on the decomposition of wake dynamics, we suggest an interaction cycle for the frequency lock-in during the wake-body interaction, which provides the inter-relationship between the high amplitude motion and the dominating wake features. Through our investigation of wake-body synchronization below critical Re range, we discover that the bluff body can undergo a synchronized high-amplitude vibration due to flexibility-induced unsteadiness. Owing to the wake turbulence at a moderate Reynolds number of Re = 22, 000, a distorted set of POD modes and the broadband energy distribution are observed, while the interaction cycle for the wake-synchronization is found to be valid for the turbulent wake flow.
“…With the help of all the updated fluid variables, the hydrodynamic force on the fluid‐structure interface Γ fs is evaluated by integrating the stress tensor over the structural surface. The force corrected by the NIFC procedure, at the fluid‐structure interface is equated with the structural force in the final step, thus satisfying the dynamic equilibrium (Equation ) at the fluid‐structure interface …”
Section: The Nonlinear Partitioned Iterative Couplingmentioning
Summary
We present a partitioned iterative formulation for the modeling of fluid‐structure interaction (FSI) in two‐phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz, an incompressible viscous fluid, a rigid or flexible structure, and a two‐phase indicator field. The fluid‐fluid interface between the two phases, which may have high density and viscosity ratios, is evolved by solving the conservative phase‐field Allen‐Cahn equation in the arbitrary Lagrangian‐Eulerian coordinates. While the Navier‐Stokes equations are solved by a stabilized Petrov‐Galerkin method, the conservative Allen‐Cahn phase‐field equation is discretized by the positivity preserving variational scheme. Fully decoupled implicit solvers for the two‐phase fluid and the structure are integrated by the nonlinear iterative force correction in a staggered partitioned manner and the generalized‐α method is employed for the time marching. We assess the accuracy and stability of the phase‐field/ALE variational formulation for two‐ and three‐dimensional problems involving the dynamical interaction of rigid bodies with free surface. We consider the decay test problems of increasing complexity, namely, free translational heave decay of a circular cylinder and free rotation of a rectangular barge. Through numerical experiments, we show that the proposed formulation is stable and robust for high density ratios across fluid‐fluid interface and for low structure‐to‐fluid mass ratio with strong added‐mass effects. Overall, the proposed variational formulation produces results with high accuracy and compares well with available measurements and reference numerical data. Using unstructured meshes, we demonstrate the second‐order temporal accuracy of the coupled phase‐field/ALE method via decay test of a circular cylinder interacting with the free surface. Finally, we demonstrate the three‐dimensional phase‐field FSI formulation for a practical problem of internal two‐phase flow in a flexible circular pipe subjected to vortex‐induced vibrations due to external fluid flow.
“…(1) represents the partial derivative ofū f with respect to time while the ALE referential coordinatex f is kept fixed. Based on the formulation in [38], the filtered Navier-Stokes equations (1)(2) in the weak form can be written as…”
Section: Incompressible Navier-stokes With Ale Formulationmentioning
confidence: 99%
“…where the derivation and the terms A f f and R N I are described in detail in [38]. The idea is to compute the iterative correction for the interface fluid force f I = Γ fs σ f ·ndΓ over the deformed ALE configuration as the structure moves.…”
Section: Interface Force Correction Schemementioning
confidence: 99%
“…The present force correction scheme can be interpreted as a generalization of Aitken's ∆ 2 extrapolation scheme [45,46] to provide convergent behavior to the interface force sequence generated through the nonlinear iterations between the fluid and the structure. The geometric extrapolations with the aid of dynamic weighting parameter allow to transform a divergent fixedpoint iteration to a stable and convergent iteration [38,25]. We next present the common-refinement scheme to transfer the fluid traction over the solid boundary across non-matching meshes.…”
Section: Interface Force Correction Schemementioning
We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid 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 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 cylindrical tubular elastic body. We demonstrate 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 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 benchmark 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. Finally, we demonstrate the 3D parallel implementation of common-refinement with NIFC scheme for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects.
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