Fluid–structure interaction with viscoelastic supports during waterhammer in a pipeline

Waterhammer modeling with fluid–structure interaction (FSI) in a pipeline with axial viscoelastic supports is the aim of this research. The viscoelastic materials of supports (or the pipe wall) were described using the generalized Kelvin–Voigt model. Hydraulic governing equations were solved by the method of characteristic (MOC) and axial vibration equation of the pipe wall was solved using the finite element method (FEM) in the time domain. For a typical case study, four different types for supporting the pipeline in the axial direction: fully free to move; fixed (rigid support); elastic and viscoelastic supports, subject to a waterhammer are analyzed and the results are scrutinized. The results quantitatively confirm that the use of supports with viscoelastic behavior in the axial direction of the pipeline can significantly reduce axial-pipe vibrations (displacements and stresses). The consequences of this structural damping on the attenuation of the internal fluid pressure are further demonstrated.     

Fluid–structure interaction in water-filled thin pipes of anisotropic composite materials

The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small.     

Modal parameter identification based on ARMAV and state–space approaches

An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the modal parameters from output-only data. This article presents the results of modal parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of modal parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical modal parameters in the case where the block Hankel matrix has full row rank. The time-domain modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in modal parameter identification using response data only.     

A time splitting fictitious domain algorithm for fluid–structure interaction problems (A fictitious domain algorithm for FSI)

A Finite Element Method in mixed Eulerian and Lagrangian formulation is developed to allow direct numerical simulations of dynamical interaction between an incompressible fluid and a hyper-elastic incompressible solid. A Fictitious Domain Method is applied so that the fluid is extended inside the deformable solid volume and the velocity field in the entire computational domain is resolved in an Eulerian framework. Solid motion, which is tracked in a Lagrangian framework, is imposed through the body force acting on the fluid within the solid boundaries. Solid stress smoothing on the Lagrangian mesh is performed with the Zienkiewicz–Zhu patch recovery method. High-order Gaussian integration quadratures over cut elements are used in order to avoid sub-meshing within elements in the Eulerian mesh that are intersected by the Lagrangian grid. The algorithm is implemented and verified in two spatial dimensions by comparing with the well validated simulations of solid deformation in a lid driven cavity and periodic elastic wall deformation driven by a time-dependent flow. It shows good agreement with the numerical results reported in the literature. In 3-D the method is validated against previously reported numerical simulations of 3-D rhythmically contracting alveolated ducts.     

Fluid–structure interaction of turbulent pulsatile flow within a flexible wall axisymmetric aortic aneurysm model

Pulsatile turbulent flow characteristics in an axisymmetric aortic aneurysm (AA) model were analyzed numerically using a simulated physiological waveform. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this work. We investigated the effects of turbulent flow characteristics on the distribution of wall stress and flow patterns in AA models. Wall stress distributions were calculated by computational solid stress (CSS) model, which ignores the effect of the blood flow, and the FSI model that takes into account flow and solid mechanics. Our results showed that peak wall stress and peak deformation were found to occur shortly after peak systolic flow in the FSI model and at the peak luminal pressure condition in the CSS model. Further, CSS model underestimated wall stress calculations when compared to the FSI model. There were also significant differences in the structure of flow fields between the flexible and rigid wall aneurysm models. Contour plots of kinetic energy dissipation and the application of the Kolmogorov microscale suggest that the conditions that result in red blood cell damage and platelet activation most likely occur in the near-wall region of AA during turbulent flow.     

Grid movement techniques and their influence on laminar fluid–structure interaction computations

The efficiency and accuracy of grid movement methods for a typical fluid–structure interaction configuration is investigated. The set-up consists of a thin elastic structure including one rotational degree of freedom fixed in a laminar channel flow. Two different cases are considered, i.e., small and large structural deformations. The comparison is carried out by using two algebraic methods, linear and transfinite interpolation, and two elliptic solution strategies also providing boundary orthogonality. A reference solution is obtained from a mixed approach. The evaluation of efficiency and accuracy is based on computation times, number of coupling steps, structural displacements and swiveling frequencies. All mesh movement techniques are employed in the frame of a partitioned solution procedure involving the block-structured finite-volume flow solver FASTEST, the finite-element structural solver FEAP, and the coupling interface MpCCI.     

Numerical modeling of current loads on a net cage considering fluid–structure interaction

In this paper we propose and discuss a numerical method to model the current loads on a net cage. In our numerical model, the fluid–structure interaction is taken into consideration. The net cage is modeled on the mass-spring model; the flow field is modeled by the finite volume method (FVM). A novel hybrid volume approach is used to add the resistance force of the net cage into the flow field for coupling the fluid and net. The net resistance to the flow is calculated directly by the net’s current load using Newton’s Third Law. The resistance force is discretized in the hybrid volume and represented in the source term of the Navier–Stokes equation. By using the hybrid volume method, the mesh grid is separated from the net shape, and sparse grid (0.1 m) can be used to calculate the flow field for computational efficiency. Based on the detailed flow field, we can predict the net’s current load more accurately. The final results are derived by the segregated iterative calculation of net shape and flow field. Current forces acting on both rigid and flexible net cages are simulated at water velocity from 0 to 1 m/s; the simulation results of proposed numerical method are compared with the existing experiments, good agreements are shown in both flow field and current force, the mean normalized absolute error of the current force between simulations and measurements is about 5%.     

Development of a hybrid model based on mesh and meshfree methods and its application to fluid–elastic structure interaction for free surface waves

In this paper, a hybrid scheme, Fluid–Fluid–Elastic Structure (FFES) model was developed in the time domain to address the wave breaking impact on the structure. The model is developed based on the partitioned approach with different governing equations that describe various regions of the model domain. The fluid–fluid model denotes that two different fluid models were used to describe fluid in the actual physical domain. The method is a physics-based approximation to reduce the computational time, i.e. in the far-field inviscid fluid (fully nonlinear potential flow theory model), and near to the structure, viscous fluid (Navier Stokes model) is used. The coupled model then interacts with the elastic structure (based on Euler–Bernoulli beam theory). The system of equations is strongly coupled both in space and time. The Fluid–Fluid coupling uses an implicit predictor–corrector scheme, and the fluid–structure coupling works based on an iterative scheme. This approach makes the method more robust and for future extension. Three different possibilities for introducing the coupling was identified and implemented. The model was validated against results from the analytical solution and literature. The method proposed is a reliable, robust, and efficient alternative for simulating fluid–structure interaction problems.     

Investigation on the effect of density ratio on the convergence behavior of partitioned method for fluid–structure interaction simulation

In order to investigate the effect of density ratio of fluid and solid on the convergence behavior of partitioned FSI algorithm, three strong-coupling partitioned algorithms (fixed-point method with a constant under-relaxation parameter, Aitken’s method and Quasi-Newton inverse least squares (QN-ILS) method) have been considered in the context of finite element method. We have employed the incompressible Navier–Stokes equations for a Newtonian fluid domain and the total Lagrangian formulation for a non-linear motion of solid domain. Linear-elastic (hyper-elastic) model has been employed for solid material with small (large) deformation. A pulsatile inlet-flow interacting with a 2D circular channel of linear-elastic material and a pressure wave propagation in a 3D flexible vessel have been simulated. Both linear-elastic and hyper-elastic (Mooney–Rivlin) models have been adopted for the 3D flexible vessel. From the present numerical experiments, we have found that QN-ILS outperforms the others leading to a robust convergence regardless of the density ratio for both linear-elastic and hyper-elastic models. On the other hand, the performances of the fixed-point method with a constant under-relaxation parameter and the Aitken’s method depend strongly on the density ratio, relaxation parameter selected for coupling iteration, and degree of deformation. Although the QN-ILS of this work is still slower than a monolithic method for serial computation, it has an advantage of easier parallelization due to the modularity of the partitioned FSI algorithm.     

Gas–liquid two phase flow measurement method based on combination instrument of turbine flowmeter and conductance sensor

In order to solve the flowrate measurement problem of gas–liquid two phase flow widely existing in gas wells of Daqing oil field in China, a new method has been developed, which is based on the combination instrument of turbine flowmeter and conductance sensor with petal type concentrating flow diverter. The turbine and conductance signals under 104 different flow conditions have been acquired through oil–gas–water three phase flow loop experimental facility. To determine the flow pattern in measurement channel, attractor morphologic characteristics are extracted from the conductance signals. For the total flowrate measurement, based on the turbine fluctuant signals of gas–liquid two phase flow, a statistical model with the average error of 7.9% is set up. With regard to the water cut measurement, the characteristics in time and frequency domains are extracted from the fluctuant conductance signals, and then employing the Support Vector Machine (SVM) soft measurement model used in high-dimension data fitting, the water cut prediction is realized with the average error of 0.038. The results show that the combination instrument of turbine flowmeter and conductance sensor with petal type concentrating flow diverter would be useful in measuring the total flowrate and water cut of gas–liquid two phase flow in gas production wells.     

A fluid–structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

Research on fish locomotion has made extensive progress towards a better understanding of how fish control their flexible body and fin for propulsion and maneuvering. Although the biologically flexible fish fins are believed to be one of the most important features to achieve optimal swimming performance, due to the limitations of the existing numerical modeling tool, studies on a deformable fin with a non-uniformly distributed stiffness are rare. In this work, we present a fully coupled fluid–structure interaction solver which can cope with the dynamic interplay between flexible aquatic animal and the ambient medium. In this tool, the fluid is resolved by solving Navier–Stokes equations based on the finite volume method with a multi-block grid system. The solid dynamics is solved by a nonlinear finite element method. A sophisticated improved IQN-ILS coupling algorithm is employed to stabilize solution and accelerate convergence. To demonstrate the capability of the developed Fluid–Structure-Interaction solver, we investigated the effect of five different stiffness distributions on the propulsive performance of a caudal peduncle-fin model. It is shown that with a non-uniformly distributed stiffness along the surface of the caudal fin, we are able to replicate similar real fish fin deformation. Consistent with the experimental observations, our numerical results also indicate that the fin with a cupping stiffness profile generates the largest thrust and efficiency whereas a heterocercal flexible fin yields the least propulsion performance but has the best maneuverability.     

On human–robot interaction of a 3-DOF decoupled parallel mechanism based on the design and construction of a novel and low-cost 3-DOF force sensor

This paper addresses the extension of a 3-degrees-of-freedom (3-DOF) decoupled parallel mechanism for human–robot interaction purposes. To this end, a low-cost 3-DOF force sensor for human–robot interaction applications is proposed, designed and constructed. In the latter force sensor, five load cells are placed in order to identify the amount of the applied force along each Cartesian direction. In addition, an experimental identification procedure based on least square method is carried out in order to obtain the first and third degree polynomial models of the sensor output model. From the practical tests it has been reveled that the force sensor has a reasonable precision of 0.1 N in both x and y-axes and 0.2 N in z-axis, within a range of 5 N which is suitable for human–robot interaction applications. Then, using the proposed force sensor, two control methods, namely “position control” and “speed control” are applied for human–robot interaction purposes and their performances are compared.     

Lump-type solution and breather lump–kink interaction phenomena to a ($$\mathbf{{3{\varvec{+}}1}}$$3+1)-dimensional GBK equation based on trilinear form

Nonlinear Dynamics - In this paper, the multivariate trilinear operators in the ($$3+1$$)-dimensional space are applied to a ($$3+1$$)-dimensional GBK equation. The resulting trilinear form is used...