A Simplified Method for Determining Acoustic and Tube Eigenfrequencies in Heat Exchangers

1982 ◽  
Vol 104 (3) ◽  
pp. 175-179 ◽  
Author(s):  
J. Planchard ◽  
F. N. Remy ◽  
P. Sonneville
Keyword(s):  
Eigenvalue Problem ◽  
Sound Velocity ◽  
Heat Exchangers ◽  
Fluid Structure Interaction ◽  
Coupled System ◽  
Experimental Results ◽  
Structure Interaction ◽  
Experimental Apparatus ◽  
Tube Arrays ◽  
Simplified Method

A method of computation of eigenfrequencies of large tube arrays is presented, which is based on homogenization techniques. It is supposed that the fluid is compressible, at rest and contained in a cavity; the bundle geometry is assumed to be repetitive; an equivalent sound velocity through the tubes can then be calculated, and the fluid-structure interaction is taken into account. A new eigenvalue problem is so obtained, defined over a simpler domain, i.e., the region occupied by both fluid and tubes; it is then easy to solve it for computing the eigenfrequencies of the coupled system. Numerical and experimental results are presented and some details of the experimental apparatus are given.

Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D

2016 ◽  
Vol 32 (2) ◽  
pp. 207-219 ◽  
Author(s):  
Fande Kong ◽  
Xiao-Chuan Cai
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Coupled System ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Krylov Method ◽  
Fine Mesh ◽  
Processor Cores ◽  
Fully Coupled

Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier–Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.

Hydroelastic Modeling of a Compliant Offshore Tower: Formulation

2003 ◽  
Author(s):  
Jinzhu Xia ◽  
Quanming Miao ◽  
Nicholas Haritos ◽  
Beverley Ronalds
Keyword(s):  
Oil And Gas ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Coupled System ◽  
Dynamic Responses ◽  
Variation Principle ◽  
Diffraction Radiation ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Radiation Theory

Offshore oil and gas can be produced using a variety of platform types. One option, the compliant offshore tower, has proven to be an economic solution in moderately deep water (300–600m). In this paper, the wave-induced global dynamic responses of a compliant tower in wind, current and waves are studied in the context of fluid-structure interaction. A beam undergoing transverse and axial motion models the vertical member of the tower. The beam is supported by a linear-elastic torsional spring at the bottom end and a point mass and a buoyant chamber is located at the top free end. The fluid forces on the beam are modeled using the Morison equation while the hydrodynamic forces on the chamber are obtained based on the three-dimensional diffraction-radiation theory. By applying Hamilton’s variation principle, the equations of motion are derived for the coupled fluid-structure interaction system. The non-linear coupled system equations that emanate from this new approach can then be solved numerically in the time domain.

Natural Frequencies of Centrifugal Compressor Impellers for High Density Gas Applications

2008 ◽  
Author(s):  
Yohei Magara ◽  
Mitsuhiro Narita ◽  
Kazuyuki Yamaguchi ◽  
Naohiko Takahashi ◽  
Tetsuya Kuwano
Keyword(s):  
Centrifugal Compressor ◽  
Natural Frequencies ◽  
Fluid Structure Interaction ◽  
Mass Effect ◽  
Added Mass ◽  
High Density ◽  
Experimental Results ◽  
Density Condition ◽  
Fluid Structure ◽  
Structure Interaction

Characteristics of natural frequencies of an impeller and an equivalent disc were investigated in high-density gas to develop a method for predicting natural frequencies of centrifugal compressor impellers for high-density gas applications. The equivalent disc had outer and inner diameters equal to those of the impeller. We expected that natural frequencies would decrease with increasing the gas density because of the added-mass effect. However, we found experimentally that some natural frequencies of the impeller and the disc in high-density gas decreased but others increased. Moreover, we observed, under high-density condition, some resonance frequencies that we did not observe under low-density condition. These experimental results cannot be explained by only the added-mass effect. For simplicity, we focused on the disc to understand the mechanism of the behavior of natural frequencies. We developed a theoretical analysis of fluid-structure interaction considering not only the mass but also stiffness of gas. The analysis gave a qualitative explanation of the experimental results. In addition, we carried out a fluid-structure interaction analysis using the finite element method. The behavior of natural frequencies of the disc in high-density gas was predicted with errors less than 6%.

scholarly journals Interpolation-based solution of a nonlinear eigenvalue problem in fluid-structure interaction

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 633-634 ◽  
Author(s):  
Cedric Effenberger ◽  
Daniel Kressner ◽  
Olaf Steinbach ◽  
Gerhard Unger
Keyword(s):  
Eigenvalue Problem ◽  
Nonlinear Eigenvalue Problem ◽  
Fluid Structure Interaction ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Nonlinear Eigenvalue

Fluid Structure Interaction Study on Dynamic Response of a Capped Drilling Riser Filled With Mud

2014 ◽  
Author(s):  
K. W. Paczkowski ◽  
P. Zhang ◽  
R. Rogers ◽  
N. Richardson
Keyword(s):  
Fluid Structure Interaction ◽  
Coupled System ◽  
Fe Model ◽  
Drilling Mud ◽  
Offshore Drilling ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Linear Behavior ◽  
Computational Fluid Dynamics Cfd ◽  
Structural Parts

In the offshore drilling, during emergency disconnect scenario the drilling operation must not be maintained and forced LMRP disconnect procedure takes place [1,2]. Such procedure allows drilling mud to interact with seawater. The paper presents hydrodynamic behavior of a drilling riser when mud is retained and not interacted with seawater. A two-way coupled fluid-structure interaction (FSI) model between a simplified drilling riser structure and mud fluid was studied through techniques of computational fluid dynamics (CFD). The volume of fluid (VOF) hydrodynamics model was used with commercially available software STAR-CCM+ [3]. A 3D finite element (FE) model of a drilling riser was created in FE software ABAQUS [4] to determine the stress and deflection of structural parts of the model due to hydrodynamic loads. In the model, the compressibility [5] and non-linear behavior of the mud was included. The dynamic frequencies of the two domains and possible resonance of the coupled system were investigated. The aim of the study was to verify the dynamic behavior of a riser system with a drilling mud enclosed within the system. The authors of this paper know no similar study of such a problem.

The Natural Vibration of Fluid-Structure Interaction Systems Subject to the Sommerfeld Radiation Condition

2006 ◽  
Author(s):  
Jing T. Xing
Keyword(s):  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Fluid Structure Interaction ◽  
Complex Conjugate ◽  
Natural Vibrations ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Natural Modes

A fluid-structure interaction system subject to a Sommerfeld condition is defined as a Sommerfeld system in this paper. It is well known that the natural vibration of a dynamic system is defined by the eigenvalue problem of the corresponding idealized system with no material damping assumed and external forces. From the defined eigenvalue problem, the real natural frequencies and the corresponding natural modes of the system can be derived. What are the characteristics of natural vibrations of a Sommerfeld system? This paper intends to address this problem by investigating three selected fluid-structure interaction systems. The systems chosen involve the solid structures with one, two and infinite degrees of freedom coupling to an infinite fluid domain subject to a Sommerfeld condition, respectively. The governing equations describing these coupled systems are presented using the theory of continuum mechanics. The theoretical solution for each problem is derived and discussed. The analysis demonstrates that a Sommerfeld system undergoing a natural vibration behaves energy dissipative characteristics although there is no material damping in solid and fluid of the system. The natural vibrations of a Sommerfeld system are governed by a complex eigenvalue problem which has only pairs of complex conjugate natural frequencies. The number of the complex conjugate natural frequencies and corresponding natural modes of this Sommerfeld system equals to the number of the degrees of freedom of the dry solid structure in the system and it is independent of the infinite fluid domain. The natural vibration forms of the solid structure in natural vibrations do not satisfy the orthogonal relationship. The findings in this research reveal some common dynamic characteristics of Sommerfeld systems. An approach for the dynamic response analysis of a Sommerfeld system is proposed based on the orthogonal natural modes of the dry structure in the system which is more efficient for engineering analysis.

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