Uncertainty Quantification for Multi-Frequency Unsteady Flow and Fluid-Structure Interaction

An unsteady adaptive stochastic finite elements formulation for rigid-body fluid–structure interaction

The performance of radial diffusers in centrifugal compressor stages is influenced by the impeller exit flow characteristics as well as the vaneless and semi-vaneless space flow characteristics. Both steady and unsteady flow interactions are present due to the propagation of pressure fields upstream and downstream between the impeller and diffuser. Furthermore, unsteady flow interactions occur when the impeller moving wakes developed due to secondary and tip clearance flows propagate through the diffuser passages. The present study aims at presenting a model that describes the unsteady wake propagation in the centrifugal compressor diffuser using vorticity principles. 3D unsteady Reynolds-Averaged Navier Stokes simulations are performed for both a vaned and a vaneless diffuser centrifugal stage. The simulations are used to examine the mechanism for the unsteady wake flow interactions in the diffuser. The unsteady streamwise vortical structures present in the impeller wakes and their propagation through the diffuser flow field is presented. The effect of the unsteady flow on loss production in the compressor stage is investigated. The velocity perturbations due to these vortical structures are presented. The present study indicates that the impeller wake propagation in the diffuser can be represented by a series of unsteady streamwise vortices superimposed on a uniform flow field. These vortices result in velocity perturbations that take the form of both positive and negative jets in the diffuser.

The lifespan of a reinforced concrete (RC) structure can be greatly influenced by the spatial variability of its material characteristics which, in particular, explains the observed or measured reduction of the tensile strength at first crack when the volume under tension increases. This paper discusses the ability of accounting for the spatial variability of the tensile strength of concrete in RC structures using a stochastic finite element (SFE) method based on random field simulations. In this work, the generation of random fields on the concrete tensile strength aims at computing the force corresponding to the first crack occurrence, and the reduced tensile strength of the structure. The method can be applied in particular to large‐sized structures, which show a pronounced size effect, for different types of loading. The method consists of, first, estimating the mean of the random field, using the analytical approach of the weakest link and localization method (WL ). Then, the discretized random field is defined on a particular 2D or 3D grid, and it is finally projected on the finite element mesh of the studied structure. The study of the parameters that influence the prediction of the cumulative density functions (CDFs) of the rupture force or the tensile strength is highlighted using experimental series of concrete beams having different volumes and subjected to 4‐point bending loading. Moreover, the SFE method is applied to a RC tie‐beam under tensile loading, characterized by a weak stress gradient, which complicates the prediction of crack positions.

Full waveform inversion using a decomposed single frequency component from a spectrogram

Fluid–structure interactions provide design constraints in many fields, yet methods available for their analysis normally assume that the structural properties are exactly known. In this contribution, these properties are more realistically modeled using random fields. Stochastic finite element methods are applied to perform uncertainty and reliability analysis on fluid–structure interaction problems with random input parameters. As an example we consider panel divergence and panel flutter. Numerical simulations demonstrate the appropriateness of sensitivitybased methods for characterization of the statistical moments of the critical points as well as for the determination of the probability of occurrence of undesired phenomena

The subject of this work is the development of a nonlinear model of the interaction of an unsteady fluid flow with a structure and finding analytical solutions for the system of equations that correspond to the specified model. The convection effect of the fluid velocity field was already considered in the previous works of the authors of this paper. These studies are devoted to the water hammer without considering the "flow-structure" interaction. This work expands the possibilities of modeling and considers four equations instead of two equations of the theory of the water hammer (equations of conservation of mass and momentum), two of which relate to the motion of particles of a solid body (pipes or structures). The novelty of this work lies in the consideration of the model that describes the interaction of the flow with the structure, the convection in the velocity field, and the effect, together with the friction of the fluid against the solid wall, on the dynamics of the shock pulse propagation process both in the fluid and in the solid body. It should be noted that the solution of the nonlinear system of differential equations as a whole is carried out by an analytical method, which makes it possible to obtain an exact (rather than numerical) solution of the problem. Since the effects of various factors should be evaluated by comparison with the main components, dimensionless equations containing six parameters (dimensionless combinations) were obtained in this study. Two of these parameters were named after scientists – Darcy and Weisbach (steady friction) and Bruno (unsteady friction). Particular cases of the general (full) model were considered, and the effects of various factors on the dynamics of the interaction of the flow with the structure during the propagation of the shock pulse were determined. Research methods are purely theoretical. The concepts of a self-similar equation and a system of equations, balances of forces acting on particles of a fluid and a solid body, and a standard method of reducing a system of equations to a single equivalent equation are used. Conclusions. An extended model of the interaction between the unsteady fluid flow and the structure is proposed. The transition to a self-similar variable makes it possible to solve a nonlinear system of differential equations and obtain an analytical (exact) solution. The functions of longitudinal stress in a solid body, pressure disturbance, and velocity of motion of particles in a solid body (pipe) are linearly expressed by the velocity of shock pulse propagation in the fluid. It should also be noted that the results for the particular case of the linear model completely agree with the already known ones. The advantage of using a self-similar solution is that it is easy to obtain. The results of previous studies on the water hammer problem were qualitatively consistent. As the fluid viscosity increases, the shock pulse domain becomes more concentrative.

<sec>Fluid-structure interaction pipeline systems are extensively adopted to transfer matter, energy and momentum, which are widely used in various fields. Due to the fluid-structure interaction effect, the pipe wall proves to produce strong vibration and noise under fluid action, which has a serious influence on the safety and concealment of the equipment, even leading to serious damages. Therefore, it is of great significance to study the vibration characteristics of fluid-structure interaction pipeline and methods to reduce the vibration of pipeline both in theory and in practice. </sec><sec>Phononic crystal can suppress the propagation of elastic waves in a specific frequency range by their special band-gap characteristics, which have wide application prospects in the field of vibration and noise reduction. Especially, the band gap characteristics of phononic crystal pipeline used to design fluid-structure interaction pipeline system have been widely studied, thus providing a new technical approach to reducing the vibration and noise of the pipeline. </sec><sec>In this paper, based on the theory of phononic crystal, the vibration transfer characteristics of the Bragg phononic crystal pipeline under fluid-structure interaction are studied. Combining the transfer matrix method and the finite element method, the band structure and band gap characteristics are calculated. Using the finite element method, the vibration characteristics of the phononic crystal pipeline under fluid-structure interaction effect, the shock excitation of pipe wall and the shock excitation of the fluid are considered. The influence of the fluid-structure interaction on the vibration transmission characteristics of the phononic crystal pipeline is also analyzed. </sec><sec>The research results indicate that when the fluid velocity in the fluid-structure interaction pipeline system is small the Bragg phononic crystal pipeline has a good attenuation effect on the shock excitation of pipe wall in the band gap range, and that when the fluid velocity increases the fluid-structure interaction effect becomes significant, the attenuation effect becoming weaker. Bragg phononic crystal pipeline has a certain attenuation effect on the pipe wall vibration caused by the fluid shock excitation near the band gap. The research results are expected to be able to provide a technical reference for the vibration control of pipeline systems under fluid-structure interaction conditions. </sec>

We propose a non-intrusive numerical coupling method for transient fluid-structure interaction (FSI) problems simulated by means of different discretization methods: smoothed particle hydrodynamics (SPH) and finite element (FE) methods for the fluid and the solid sub-domains, respectively. As a partitioned coupling method, the present algorithm can ensure a zero interface energy during the whole period of numerical simulation, even in the presence of large interface motion. In other words, the time integrations of the two sub-domains (second order Runge---Kutta scheme for fluid and Newmark integrator for solid) are synchronized. Thanks to this energy-conserving feature, one can preserve the minimal order of accuracy in time and the numerical stability of the FSI simulations, which are validated with a 1D and a 2D trivial numerical test cases. Additionally, some other 2D FSI simulations involving large interface motion have also been carried out with the proposed SPH---FE coupling method. Finally, an example of aquaplaning problem is given in order to show the feasibility of such coupling method in multi-dimensional applications with complicated structural geometries.

Random fields and processes in mechanics of granular materials

A phase-field/ALE method for simulating fluid–structure interactions in two-phase flow

A strong-coupled method combined finite element method and lattice Boltzmann method via an implicit immersed boundary scheme for fluid structure interaction

Until recently, stochastic structural mechanics has addressed the issue of deterministic structures subjected to random loading. With the availability of more accurate analysis and design tools, however, quantifying the sensitivity of model predictions to uncertainty in the mechanical properties of structures has become possible. It has been observed, with the help of these tools, that this type of uncertainty can be more significant to the overall predictions of a particular structural model than the more traditional fluctuations attributed to external loads. In view of that, recent procedures have been developed for representing uncertainties in the parameters of a structural model, as well as, for propagating this uncertainty to obtain the associated uncertainty in the predicted response. The stochastic finite element method is a procedure for performing such an analysis, whereby the spatial extent of the structure has been represented within the context of the finite element method. This chapter describes a recent implementation of the stochastic finite element method that combines theoretical rigor with generality and efficiency of implementation. Specifically, the Spectral Stochastic Finite Element Method (SSFEM) presented in this chapter addresses the situation where the uncertain material properties are realizations of a spatially fluctuating random field. The formulation relies on discretizing the random processes using spectral expansions, thus eliminating the correlation between the requisite mesh size to meet energy-based convergence criteria, and the scales of fluctuation of the random material properties involved.

Gas foil journal bearings (GFJBs) have been widely employed in high-speed rotating machinery in the aviation industry. However, the role of fluid–structure interaction in the unsteady aerodynamic character of the gas film and the dynamic response of the elastic foils have not yet been clarified. In this study, an unsteady shearing flow interacting with an exciting deformation of the top or bump foils was investigated by means of a large eddy simulation with bidirectional fluid–structure interaction (BFSI). The result shows that the main frequencies and amplitudes of stable fluctuations of different flow field parameters at different positions are different. The oscillating duration in the solid domain is much less than that in the fluid domain. The main positions for the interaction between the gas film pressure and the elastic foil are on both sides of θ = π. Compared with the case without FSI, the presence of the elastic foil flattens the distribution of the pressure of the gas film. As the rotational speed increases, the main frequency and the amplitude of pressure in the fluid domain continuously increase. With FSI, there is no interference frequency near the main frequency, which improves the stability of the shearing flow. However, an interference frequency appears near the main frequency of total displacement in the solid domain. The analysis in this paper lays the foundation for unsteady fluid–structure interaction research.

This study tackles the issue of electromechanical modes identification through a measurement‐based methodology employing a novel signal decomposition theorem based upon the Hilbert transform. The methodology aims to answer in a simpler and more pragmatic manner to the main weaknesses of the Hilbert–Huang transform with respect to the major refinements in the relevant literature. These weak points are discussed with sufficient detailed degree in the study. The main contribution of this study consists in combining a recent signal decomposition theorem for separating an assigned signal into elemental ones, each of them characterised by a single frequency component and a robust preliminary non‐linear spectral analyser, named L p periodogram. This procedure's results are very appropriate for analysing some critical cases of electromechanical oscillations, because of the L p periodogram robustness against heavy‐tailed noise and also its intrinsic ability in estimating closely spaced frequency components. The proposed approach is found to be inherently simple, reliable and consistent in performance as well as characterised by low computational burden. Some numerical applications validate the methodology and assess its own performance on synthetic signals, near real‐life signals acquired by IEEE test networks and on a real measured signal from a wide‐area monitoring system currently in operation.

Dynamic response considering fluid structure interaction (FSI) is crucial in many engineering fields and the numerical methods to solve the FSI problems are keenly demanded in engineering field. Generally coupled phenomena can be simulated in either monolithic or partitioned methods, however the application of FSI analysis are limited because of its calculation costs. The partitioned method is now focused because it can re-use the existing flow and structural analysis solver without elaborated modification and it gives the same accuracy when iterative coupling approach is taken. When the partitioned method combined with the existing flow and structure solver which can solve large-scale analysis model, it is expected to solve realistic three dimensional complex FSI problems in acceptable durations. In this work, the partitioned FSI analysis system are developed using existing flow and structure solvers. The system is applied to several validation models and accuracy and efficiency of the solver are shown.