Rajeev K. Jaiman

A stable second-order scheme for fluid-structure interaction with strong added-mass effects

Abstract In this paper, we present a stable second-order time accurate scheme for solving fluid–structure interaction problems. The scheme uses so-called Combined Field with Explicit Interface (CFEI) advancing formulation based on the Arbitrary Lagrangian–Eulerian approach with finite element procedure. Although loosely-coupled partitioned schemes are often popular choices for simulating FSI problems, these schemes may suffer from inherent instability at low structure to fluid density ratios. We show that our second-order scheme is stable for any mass density ratio and hence is able to handle strong added-mass effects. Energy-based stability proof relies heavily on the connections among extrapolation formula, trapezoidal scheme for second-order equation, and backward difference method for first-order equation. Numerical accuracy and stability of the scheme is assessed with the aid of two-dimensional fluid–structure interaction problems of increasing complexity. We confirm second-order temporal accuracy by numerical experiments on an elastic semi-circular cylinder problem. We verify the accuracy of coupled solutions with respect to the benchmark solutions of a cylinder-elastic bar and the Navier–Stokes flow system. To study the stability of the proposed scheme for strong added-mass effects, we present new results using the combined field formulation for flexible flapping motion of a thin-membrane structure with low mass ratio and strong added-mass effects in a uniform axial flow. Using a systematic series of fluid–structure simulations, a detailed analysis of the coupled response as a function of mass ratio for the case of very low bending rigidity has been presented.

A positivity preserving variational method for multi-dimensional convectiondiffusionreaction equation

A new positivity preserving variational (PPV) procedure is proposed to solve the convectiondiffusionreaction (CDR) equation. Through the generalization of stabilized finite element methods, the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection, diffusion and reaction effects. By means of Fourier analysis, we first review the shortcomings of the Galerkin/Least-Squares (GLS) and the Subgrid Scale (SGS) methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined GLS-SGS methodology. Discrete upwind operator with a solution-dependent nonlinear term is then introduced in high gradient regions, which enables the positivity preserving property in the variational formulation. Direct extension to multi-dimensions is carried out by considering the principle streamline and crosswind directions. The efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one- and two-dimensions. Results show the reduction of oscillations in the solution in one- and two-dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient. The proposed formulation provides a superior solution in the reaction-dominated as well as the convection-dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions.

Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel

This work presents a review and theoretical study of the added-mass and aeroelastic instability exhibited by a linear elastic plate immersed in a mean flow. We first present a combined added-mass result for the model problem with a mean incompressible and compressible flow interacting with an elastic plate. Using the Euler–Bernoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. A new compressibility correction factor is introduced in the incompressible added-mass force to account for the compressibility effects. We present a formulation for predicting the critical velocity for the onset of flapping instability. Our proposed new formulation considers tension effects explicitly due to viscous shear stress along the fluid-structure interface. In general, the tension effects are stabilizing in nature and become critical in problems involving low mass ratios. We further study the effects of the mass ratio and channel height on the aeroelastic instability using the linear stability analysis. It is observed that the proximity of the wall parallel to the plate affects the growth rate of the instability, however, these effects are less significant in comparison to the mass ratio or the tension effects in defining the instability. Finally, we conclude this paper with the validation of the theoretical results with experimental data presented in the literature.

Interaction dynamics of gap flow with vortex-induced vibration in side-by-side cylinder arrangement

A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61(3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenom...

Dynamics of simultaneously impinging drops on a dry surface: Role of impact velocity and air inertia.

Three dimensional simulations are performed to investigate the interaction dynamics between two drops impinging simultaneously on a dry surface. Of particular interest in this study is to understand the effects of impact velocity and surrounding gas density on droplet interactions. To simulate the droplet dynamics and morphologies, a computational framework based on the phase-field lattice Boltzmann formulation is employed for the two-phase flow computations involving high density ratio. Two different coalescence modes are identified when the impinging droplets have different impact speeds. When one of the droplet has a tangential impact velocity component, asymmetric ridge formation is observed. Influence of droplet impact angle on the interaction dynamics of the central ridge is further investigated. Traces of different fluid particles are seeded to analyse internal flow dynamics in oblique impact scenarios. Greater overlapping between the fluid particles is observed with increase in the impact angle. Finally, the present simulations indicate that the ambient gas density has a significant influence to determine the final outcome of the droplet interactions.

Homogenization and Stress Analysis of Multilayered Composite Offshore Production Risers

An approach for stress analysis of multilayered composite cylinders is proposed for the analysis of new composite risers used in deep-water oil production of offshore petroleum industries. Risers essentially comprise long cylindrical sections connected end-to-end. In the formulation, only stresses and strains that are continuous through the thickness of the multilayered composite risers are taken to be equal to reported solutions for homogenous orthotropic hollow cylinders using homogenized material properties. These stress and strain solutions are then used to calculate the remaining discontinuous stresses and strains from the material properties of individual layers of materials. The homogenized elastic constants of cylindrically orthotropic composite risers are derived from forcedeformation equivalence, taking into account the stress and strain distributions in each layer. Four typical loading conditions are considered in the stress analysis, namely, internal and external pressures, axial loading, bending, and torsion. Examples of homogenized elastic constants and stress analyses of composite cylindrical structures with different layups and materials are presented to demonstrate the application of the proposed method. The results compared very favorably with those from other solutions. This method provides practical benefits for the design and analysis of composite risers. Because there is no requirement to explicitly enforce interfacial continuity in this method, stress analyses of composite cylinders with many layers of different fiber angles or materials can be carried out efficiently. The homogenized elastic constants can greatly expedite the analysis of entire composite riser systems by replacing complex models of riser sections with homogenized riser sections. [DOI: 10.1115/1.4024695]

Global-Local Analysis of a Full-scale Composite Riser during Vortex-Induced Vibration

This paper presents a global-local analysis procedure to demonstrate the feasibility of a composite riser and its advantages over the traditional steel counterpart. This procedure starts from the local design of the sandwich tubular structure of riser section. The equivalent material properties of the sandwich tube are obtained using classic composite theory and they are used to parameterize the full-scale riser model in global analysis. The global analysis mainly focuses on the vortex-induced vibration (VIV). The methodology is first verified by comparison with experimental data and results produced by SHEAR 7. Four representative cases are then studied and the results show that the critical loads experienced by the composite riser are much lower than that of the steel one due to its lightweight. The lightweight composite riser requires lower top tension and fewer buoyancy cans, which is economically beneficial. The failure envelopes of both composite and steel riser sections are obtained by performing damage modelling techniques. The results show that composite riser yields larger safety margin. Overall, this paper demonstrates that composite riser is technically feasible and its high performance/weight ratio would make it a promising design for deepwater environment, where self-weight is a big challenge that is hindering the development of traditional steel riser.Copyright

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

Abstract We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen–Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen–Cahn phase-field equation with the incompressible Navier–Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen–Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace–Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

Coupled dynamics of vortex-induced vibration and stationary wall at low Reynolds number

The flow past an elastically mounted circular cylinder placed in proximity to a plane wall is numerically studied in both two dimensions (2D) and three dimensions (3D). This paper aims to explain the mechanism of the cylinder bottom shear layer roll-up suppression in the context of laminar vortex-induced vibration (VIV) of a cylinder placed in the vicinity of a plane stationary wall. In 2D simulations, VIV of a near-wall cylinder with structure-to-displaced fluid mass ratios of m* = 2 and 10 is investigated at the Reynolds number of Re = 100 at a representative gap ratio of e/D = 0.90, where e denotes the gap distance between the cylinder surface and the plane wall. First, the cylinder is placed at five different upstream distances, LU, to study the effects of the normalized wall boundary layer thickness, δ/D, on the hydrodynamic quantities involved in the VIV of a near-wall cylinder. It is found that the lock-in range shifts towards the direction of the higher reduced velocity Ur as δ/D increases and that the lock-in range widens as m* reduces. Second, via visualization of the vortex shedding patterns, four different modes are classified and the regime maps are provided for both m* = 2 and 10. Third, the proper orthogonal decomposition analysis is employed to assess the cylinder bottom shear layer roll-up suppression mechanism. For 3D simulations at Re = 200, the circular cylinder of a mass ratio of m* = 10 with a spanwise length of 4D is placed at a gap ratio of e/D = 0.90 and an upstream distance of LU = 10D. The 3D vortex patterns are investigated to re-affirm the vortex shedding suppression mechanism. The pressure distributions around the cylinder are identified within one oscillation cycle of VIV. The pressure and the shear stress distributions on the bottom wall are examined to demonstrate the effects of near-wall VIV on the force distributions along the plane wall. It is found that both the suction pressure and the shear stress right below the cylinder peak when the cylinder is located at its negative maximum transverse displacement. This study represents a step towards an improved understanding of the hydrodynamics involved in the subsea pipelines subject to ocean currents with different boundary layer flows.The flow past an elastically mounted circular cylinder placed in proximity to a plane wall is numerically studied in both two dimensions (2D) and three dimensions (3D). This paper aims to explain the mechanism of the cylinder bottom shear layer roll-up suppression in the context of laminar vortex-induced vibration (VIV) of a cylinder placed in the vicinity of a plane stationary wall. In 2D simulations, VIV of a near-wall cylinder with structure-to-displaced fluid mass ratios of m* = 2 and 10 is investigated at the Reynolds number of Re = 100 at a representative gap ratio of e/D = 0.90, where e denotes the gap distance between the cylinder surface and the plane wall. First, the cylinder is placed at five different upstream distances, LU, to study the effects of the normalized wall boundary layer thickness, δ/D, on the hydrodynamic quantities involved in the VIV of a near-wall cylinder. It is found that the lock-in range shifts towards the direction of the higher reduced velocity Ur as δ/D increases and tha...

Rebound suppression of a droplet impacting on an oscillating horizontal surface.

The behavior of a droplet impinging onto a solid substrate can be influenced significantly by the horizontal motion of the substrate. The coupled interactions between the moving wall and the impacting droplet may result in various outcomes, which may be different from the usual normal droplet impact on a stationary wall. In this paper, we present a method to suppress drop rebound on hydrophobic surfaces via transverse wall oscillations, normal to the impact direction. The numerical investigation shows that the suppression of droplet rebound has a direct relationship with the oscillation phase, amplitude, and frequency. For a particular range of oscillation frequencies and amplitudes, a lateral shifting of the droplet position is observed along the oscillating direction. While large oscillation amplitude favors the process of droplet deposition, a high frequency promotes droplet rebound from the oscillating wall. A linear trend in the transition region between deposition and rebound is observed from a scaled phase diagram of the oscillation amplitude versus frequency. We provide a systematic investigation of drop deposition and elucidate the mechanism of rebound suppression through the temporal evolution of the nonaxial kinetic energy and the velocity flow field.