Motion-Dependent Fluid Force Coefficients for Tube Arrays in Crossflow

2001 ◽  
Vol 123 (4) ◽  
pp. 429-436 ◽  
Author(s):  
S. S. Chen ◽  
G. S. Srikantiah
Keyword(s):  
Excitation Amplitude ◽  
Steam Generators ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Stiffness Coefficients ◽  
Tube Arrays ◽  
Fluidelastic Instability ◽  
Fluid Damping ◽  
Series Of Experiments

Fluidelastic instability of tube arrays in crossflow is interesting academically and important in steam generators and heat exchangers. The key elements necessary to accurately predict fluidelastic instability of tube arrays in crossflow are motion-dependent fluid force coefficients. This paper presents several series of experiments that measure motion-dependent fluid forces for various tube arrays. Fluid damping and stiffness coefficients based on the unsteady flow theory were obtained as a function of reduced flow velocity, excitation amplitude, and Reynolds number, and the characteristics of motion-dependent fluid force coefficients were applied to provide some additional insights into fluidelastic instability.

Fluid Damping and Fluid Stiffness of a Tube Row in Crossflow

1994 ◽  
Vol 116 (4) ◽  
pp. 370-383 ◽  
Author(s):  
S. S. Chen ◽  
S. Zhu ◽  
J. A. Jendrzejczyk
Keyword(s):  
Flow Velocity ◽  
Water Channel ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Design Guideline ◽  
Fluid Forces ◽  
Tube Arrays ◽  
Fluidelastic Instability ◽  
Fluid Damping ◽  
Reliable Design

Motion-dependent fluid forces acting on a tube array were measured as a function of excitation frequency, excitation amplitude, and flow velocity. Fluid-damping and fluid-stiffness coefficients were obtained from measured motion-dependent fluid forces as a function of reduced flow velocity and excitation amplitude. The water channel and test setup provide a sound facility for obtaining key coefficients for fluidelastic instability of tube arrays in crossflow. Once the motion-dependent fluid-force coefficients have been measured, a reliable design guideline, based on the unsteady flow theory, can be developed for fluidelastic instability of tube arrays in crossflow.

Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Koya Yamada ◽  
Atsushi Ikemoto ◽  
Tsuyoshi Inoue ◽  
Masaharu Uchiumi
Keyword(s):  
Perturbation Analysis ◽  
Flow Analysis ◽  
Flow Theory ◽  
Bulk Flow ◽  
Design Stage ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Static Eccentricity ◽  
Harmonic Components

Rotor-dynamic fluid force (RD fluid force) of turbomachinery is one of the causes of the shaft vibration problem. Bulk flow theory is the method for analyzing this RD fluid force, and it has been widely used in the design stage of machine. The conventional bulk flow theory has been carried out under the assumption of concentric circular shaft's orbit with a small amplitude. However, actual rotating machinery's operating condition often does not hold this assumption, for example, existence of static load on the machinery causes static eccentricity. In particular, when such a static eccentricity is significant, the nonlinearity of RD fluid force may increase and become non-negligible. Therefore, conventional bulk flow theory is not applicable for the analysis of the RD fluid force in such a situation. In this paper, the RD fluid force of the annular plain seal in the case of circular whirling orbit with static eccentricity is investigated. The case with both the significant static eccentricity and the moderate whirling amplitude is considered, and the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in such cases. In this analysis, the assumption of the perturbation solution is extended to both static terms and whirling terms up to the third order. Then, the additional terms are caused by the coupling of these terms through nonlinearity, and these three kinds of terms are considered in the extended perturbation analysis of the bulk flow theory. As a result, a set of nonlinear analytical equations of the extended perturbation analysis of the bulk flow theory, for the case with both the significant static eccentricity and the moderate whirling amplitude, is deduced. The RD fluid force for such cases is analyzed, and the occurrence of constant component, backward synchronous component, and super-harmonic components in the RD fluid force is observed in addition to the forward synchronous component. The representation of RD fluid force coefficients (RD coefficients) are modified for the case with significant static eccentricity, and the variation of RD fluid force coefficients for the magnitude of static eccentricity is analyzed. These analytical results of RD fluid force and its RD coefficients are compared with the numerical results using finite difference analysis and experimental results. As a result, the validity of the extended perturbation analysis of the bulk-flow theory for the case with both the significant static eccentricity and the moderate whirling amplitude is confirmed.

An Analysis of In-Flow Fluidelastic Instability Based on a Physical Insight

2014 ◽  
Author(s):  
Tomomichi Nakamura
Keyword(s):  
Flow Velocity ◽  
Flow Instability ◽  
Pressure Sensors ◽  
Measured Data ◽  
Critical Flow ◽  
Nonlinear Phenomenon ◽  
Critical Flow Velocity ◽  
Fluid Force ◽  
Tube Arrays ◽  
Fluidelastic Instability

Fluidelastic vibration of tube arrays caused by cross-flow has recently been highlighted by a practical event. There have been many studies on fluidelastic instability, but almost all works have been devoted to the tube-vibration in the transverse direction to the flow. For this reason, there are few data on the fluidelastic forces for the in-flow movement of the tubes, although the measured data on the stability boundary has gradually increased. The most popular method to estimate the fluidelastic force is to measure the force acting on tubes due to the flow, combined with the movement of the tubes. However, this method does not give the physical explanation of the root-cause of fluidelastic instability. In the work reported here, the in-flow instability is assumed to be a nonlinear phenomenon with a retarded or delayed action between adjacent tubes. The fluid force acting on tubes are estimated, based on the measured data in another paper for the fixed cylinders with distributed pressure sensors on the surface of the cylinders. The fluid force acting on the downstream-cylinder is assumed in this paper to have a delayed time basically based on the distance between the separation point of the upstream-cylinder to the re-attachment point, where the fluid flows with a certain flow velocity. Two models are considered: a two-cylinder and three–cylinder models, based on the same dimensions as our experimental data to check the critical flow velocity. Both models show the same order of the critical flow velocity and a similar trend for the effect of the pitch-to-diameter ratio of the tube arrays, which indicates this analysis has a potential to explain the in-flow instability if an adequate fluid force is used.

Numerical Estimation of Fluidelastic Instability in Staggered Tube Arrays

2009 ◽  
Author(s):  
H. Omar ◽  
M. Hassan ◽  
A. Gerber
Keyword(s):  
Moving Boundary ◽  
Tube Bundle ◽  
Navier Stokes ◽  
Numerical Estimation ◽  
Arbitrary Lagrangian Eulerian ◽  
Fluid Forces ◽  
Damping Parameter ◽  
Tube Arrays ◽  
Fluidelastic Instability ◽  
Reynolds Average

This study investigates the unsteady flow and the resulting fluidelastic forces in a tube bundle. Numerical simulations are presented for normal triangle tube arrays with pitch-to-diameter (P/d) ratios of 1.35, 1.75, and 2.5 utilizing a 2-dimensional model. In this model a single tube was forced to oscillate within an otherwise rigid array. Fluid forces acting on the oscillating tube and the surrounding tubes were estimated. The predicted forces were utilized to calculate fluid force coefficients for all tubes. The numerical model solves the Reynolds-Average Navier-Stokes (RANS) equations for unsteady turbulent flow, and is cast in an Arbitrary Lagrangian-Eulerian (ALE) form to handle mesh the motion associated with a moving boundary. The fluidelastic instability (FEI) was predicted for both single and fully flexible tube arrays over a mass damping parameter (MDP) range of 0.1 to 200. The effect of the P/d ratio and the Reynolds number on the FEI threshold was investigated in this work.

Fluid Elastic Whirling of Tube Rows and Tube Arrays

1977 ◽  
Vol 99 (3) ◽  
pp. 457-460 ◽  
Author(s):  
R. D. Blevins
Keyword(s):  
Experimental Data ◽  
Control Volume ◽  
Fluid Force ◽  
Force Coefficients ◽  
Tube Arrays

Models are developed for the fluid force coefficients that determine the onset of whirling of tube rows and tube arrays. A control volume momentum analysis is employed. The results are in agreement with the available experimental data.

Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude

2018 ◽  
Author(s):  
K. Yamada ◽  
A. Ikemoto ◽  
M. Uchiumi ◽  
T. Inoue
Keyword(s):  
Perturbation Analysis ◽  
Flow Analysis ◽  
Flow Theory ◽  
Bulk Flow ◽  
Design Stage ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Static Eccentricity ◽  
Harmonic Components

Rotor-dynamic fluid force (RD fluid force) of turbo-machinery is one of the causes of the shaft vibration problem. Bulk flow theory is the method for analyzing this RD fluid force, and it has been widely used in the design stage of machine. Conventional bulk flow theory has been carried out under the assumption of concentric circular shaft’s orbit with small amplitude. However, actual rotating machinery’s operating condition often does not hold this assumption, for example, existence of static load on the machinery causes static eccentricity. In particular, when such a static eccentricity is significant, the nonlinearity of RD fluid force may increase and become non-negligible. Therefore, conventional bulk flow theory is not applicable for the analysis of RD fluid force in such situation. In this paper, RD fluid force of the annular plain seal in the case of circular whirling orbit with static eccentricity is investigated. The case with both the significant static eccentricity and the moderate whirling amplitude is considered, and the perturbation analysis of the bulk-flow theory is extended to investigate RD fluid force in such cases. In this analysis, the assumption of the perturbation solution is extended to both static terms and whirling terms up to the third order. Then, the additional terms are caused by the coupling of these terms through nonlinearity, and these three kinds of terms are considered in the extended perturbation analysis of the bulk flow theory. As a result, a set of nonlinear analytical equations of the extended perturbation analysis of the bulk flow theory, for the case with both the significant static eccentricity and the moderate whirling amplitude, is deduced. RD fluid force for such cases are analyzed, and the occurrence of constant component, backward synchronous component and super-harmonic components in RD fluid force is observed in addition to the forward synchronous component. The representation of RD fluid force coefficients (RD coefficients) are modified for the case with significant static eccentricity, and the variation of RD fluid force coefficients for the magnitude of static eccentricity is analyzed. These analytical results of RD fluid force and its RD coefficients are compared with the numerical results using finite difference analysis and experimental results. As a result, the validity of the extended perturbation analysis of the bulk-flow theory for the case with both the significant static eccentricity and the moderate whirling amplitude is confirmed.

scholarly journals Flow-Induced Vibration of Tubes in Cross-Flow

1996 ◽  
Vol 118 (4) ◽  
pp. 253-258 ◽  
Author(s):  
S. S. Chen ◽  
Y. Cai ◽  
S. Zhu
Keyword(s):  
Unsteady Flow ◽  
Mathematical Models ◽  
Cross Flow ◽  
Flow Theory ◽  
General Description ◽  
Flow Induced Vibration ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces

This paper presents an unsteady-flow theory for flow-induced vibration of tubes in cross-flow. It includes a general description of motion-dependent fluid forces, characteristics of fluid-force coefficients, and mathematical models. Detailed results are presented for the constrained mode in the lift direction for various tube arrangements.

Analytical Investigation on the Rotational Speed Dependence of the Rotordynamic Fluid Force: The Case of Concentric Circular Whirl in the Annular Plain Seal

2016 ◽  
Author(s):  
Atsushi Ikemoto ◽  
Kazukiyo Sakamoto ◽  
Tsuyoshi Inoue ◽  
Masaharu Uchiumi
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
Quadratic Function ◽  
Analytical Investigation ◽  
Experimental Unit ◽  
Rotating Shaft ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Speed Dependence

Rotordynamic (RD) fluid forces of various kinds of seals has been investigated and reported by Childs [1], Iwatsusbo [2][3] and so on, because it has significant influence on the stability of rotating machinery. Those studies were carried out at lower speeds than the actual machines because of various restrictions such as the limitations of the experimental unit. Then, extrapolation approximations using the obtained results were used to predict the RD fluid force of the actual machines. However, when the rotor vibration is analyzed for the high speed rotating shaft such as a rocket turbopump, a more accurate evaluation of the rotational speed dependence of the derived RD fluid force is desired. In this study, the rotational speed dependence of RD fluid forces in the case of the concentric circular whirl in the annular plain seal is investigated. As a result, the characteristics of these fluid forces vary with the rotational speed significantly. In addition, the strong dependencies of RD fluid force coefficients calculated from these fluid forces on the rotational speed are observed. It is revealed that the changes of the RD fluid force coefficients to rotational speed were modeled by using the quadratic function.

Investigation of Fluid-Elastic Instability in Tube Arrays at Low Mass Damping Parameters in Cross-Flow

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Kai Guo ◽  
Wei Xu ◽  
Zhanbin Jia ◽  
Wei Tan
Keyword(s):  
Critical Velocity ◽  
Transverse Direction ◽  
Cfd Simulation ◽  
Triangular Array ◽  
Elastic Instability ◽  
Streamwise Direction ◽  
Fluid Force ◽  
Force Coefficients ◽  
Tube Arrays ◽  
Low Mass

Abstract Fluid-elastic instability (FEI) is the most dangerous vibration mechanism in tube arrays. As the research shows in the recent years, the mechanism of FEI turns to be clear, but threshold prediction in low mass damping parameter (MDP) tube arrays is still not accurate because of the complexity of the instability mechanism. In this work, computational fluid dynamics (CFD) simulation is first validated by comparison with the water tunnel experiments in four kinds of tube arrangements and then extended to two-phase flow to get more data in low MDP range. Using fluid force coefficients calculated by CFD simulation, unsteady modeling of the tube model is established and the critical velocities match well with experiment and CFD simulation results. The effect of tube arrangement and Reynolds number on the fluid force coefficients and the predicted critical velocity is studied according to the unsteady flow theory. The results show that instability critical velocity of the normal triangular array can be underestimated at MDP lower than 1. When the frequency ratio (streamwise direction to transverse direction) decreases to below 0.8 in the rotated triangular array, the streamwise instability occurs earlier than transverse instability. The methods and conclusions in this paper can be used in FEI analysis in both streamwise direction and transverse direction.

Streamwise Fluidelastic Instability of Tube Arrays in Two-Phase Cross Flow

2014 ◽  
Author(s):  
Stephen Olala ◽  
Njuki W. Mureithi
Keyword(s):  
Nuclear Power ◽  
Single Phase ◽  
Cross Flow ◽  
Force Measurements ◽  
Two Phase Flows ◽  
Two Phase ◽  
Fluid Force ◽  
Void Fractions ◽  
Tube Arrays ◽  
Fluidelastic Instability

In-plane instability of tube arrays has not been a major concern to steam generator designers until recently following observations of streamwise tube failure in a nuclear power plant in U.S.A. However, modeling of fluidelastic instability in two-phase flows still remains a challenge. In the present work, detailed steady fluid force measurements for a kernel of an array of tubes in a rotated triangular tube array of P/D=1.5 subjected to air-water two-phase flows for a series of void fractions and a Reynolds number (based on the pitch velocity), Re = 7.2 × 104 has been conducted. The measured steady fluid force coefficients and their derivatives, with respect to streamwise static displacements of the central tube, are employed in the quasi-steady model [1, 2], originally developed for single phase flows, to analyze in-plane fluidelastic instability of multiple flexible arrays in two-phase flows. The results are consistent with dynamic stability tests [3].

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