Unsteady Fluid Force and Random Excitation Force Measurement of Triangular Array Tube Bundle in Steam-Water Two Phase Flow

Abstract The in-plane (stream-wise) fluid-elastic instability of triangular tube arrays caused tube-to-tube wear indications as observed in the U-bend regions of tube the bundles of San Onofre Unit-3 steam generators. To understand the in-plane FEI characteristics, stability analysis using unsteady fluid forces is quite helpful. However, taking measurements of unsteady fluid forces in the in-plane direction is quite challenging as the fluid coupling forces of the surrounding tubes must be measured simultaneously for the in-plane stability analysis. In particular, taking measurements under a high pressure and high temperature steam-water conditions, similar to an SG operating condition, is extremely difficult. Recently we have been able to successfully measure unsteady fluid force using a specially designed test equipment. In the meantime, random excitation forces acting on heat transfer tubes were also measured. We calculated the stability boundary of the in-plane FEI using the unsteady fluid force measurement with this special equipment.

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In-Plane Fluidelastic Instability Evaluation of Triangular Array Tube Bundle Using Fluid Force Measured Under Steam–Water Two-Phase Flow Condition

Journal of Pressure Vessel Technology ◽

10.1115/1.4049145 ◽

2020 ◽

Vol 143 (1) ◽

Author(s):

Shingo Nishida ◽

Seinosuke Azuma ◽

Hideyuki Morita ◽

Kazuo Hirota ◽

Ryoichi Kawakami ◽

...

Keyword(s):

Critical Velocity ◽

Tube Bundle ◽

Straight Tube ◽

Two Phase ◽

Fluid Force ◽

Stability Analyses ◽

Fluid Forces ◽

Fluidelastic Instability ◽

The Difference ◽

Unsteady Fluid

Abstract Recently, tube-to-tube wear indications of triangular tube bundle steam generators (SGs) caused by fluidelastic instability (FEI) in the in-plane direction of U-bend region (in-plane FEI) have been reported. Several experiments were conducted to investigate the characteristics of in-plane FEI by our research groups. In a series of experiments, particular characteristics of in-plane FEI were found. For example, there are the critical velocity difference between the in-plane and the out-of-plane directions, the difference between straight tube bundle tests and U-bend tube bundle tests, etc. To explain these characteristics, unsteady fluid force acting on tubes were measured. The experimental investigation was conducted under high temperature and high-pressure steam–water flow conditions close to the SGs. Stability analyses were conducted using the measured unsteady fluid forces as inputs. First, stability analyses were done to simulate straight tube bundle tests. Analysis results agreed well with experiments and it could explain the effect on critical velocity trend by number of flexible tubes and directions of vibration. Second, U-tube stability analyses were performed by applying unsteady fluid force coefficients for each location of U-bend tube finite element method (FEM) model. From the results, mechanisms of in-plane FEI were understood.

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Vibration Excitation Forces in a Normal Triangular Tube Bundle Subjected to Two-Phase Cross Flow

ASME 2011 Pressure Vessels and Piping Conference: Volume 4 ◽

10.1115/pvp2011-57102 ◽

2011 ◽

Author(s):

E. S. Perrot ◽

N. W. Mureithi ◽

M. J. Pettigrew ◽

G. Ricciardi

Keyword(s):

Tube Bundle ◽

Cross Flow ◽

Random Excitation ◽

Two Phase ◽

Constant Frequency ◽

Fluid Forces ◽

Drag Forces ◽

Wide Range ◽

Drag And Lift ◽

Lift And Drag

This paper presents test results of vibration forces in a normal triangular tube bundle subjected to air-water cross-flow. The dynamic lift and drag forces were measured with strain gage instrumented cylinders. The array has a pitch-to-diameter ratio of 1.5, and the tube diameter is 38 mm. A wide range of void fraction and fluid velocities were tested. The experiments revealed significant forces in both the drag and lift directions. Constant frequency and quasi-periodic fluid forces were found in addition to random excitation. These forces were analyzed and characterized to understand their origins. The forces were found to be dependent on the position of the cylinder within the bundle. The results are compared with those obtained with flexible cylinders in the same tube bundle and to those for a rotated triangular tube bundle. These comparisons reveal the influence of quasi-periodic forces on tube motions.

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Quasi-Static Forces and Stability Analysis in a Triangular Tube Bundle Subjected to Two-Phase Cross-Flow

Volume 4: Fluid-Structure Interaction ◽

10.1115/pvp2007-26017 ◽

2007 ◽

Cited By ~ 6

Author(s):

Soroush Shahriary ◽

Njuki W. Mureithi ◽

Michel J. Pettigrew

Keyword(s):

Stability Analysis ◽

Force Field ◽

Two Phase Flow ◽

Tube Bundle ◽

Mode Analysis ◽

Phase Flow ◽

Two Phase ◽

Fluid Force ◽

Flexible Tube ◽

Fluidelastic Instability

Although almost half of the process heat exchangers operate in two-phase flow, the complex nature of the flow makes the prediction of fluidelastic instability a challenging problem yet to be solved. In the work reported here, the quasi-static fluid force-field is measured in a rotated-triangle tube bundle for a series of void fractions and flow velocities. The forces are strongly dependent on void fraction, flow rates and relative tube positions. The fluid force field is employed along with quasi-steady models [1, 2], originally developed for single phase flows, to model the two-phase flow problem. Stability analysis is performed using the single flexible tube model [1] as well as constrained mode analysis [2]. The results are compared with dynamic stability tests [3] and show good agreement. The results of single flexible tube analysis and multiple flexible tubes tend to coincide at low structural damping as expected. The present work uncovers some of the complexities of the fluid force field in two-phase flows. The data are valuable since they are the necessary inputs to the class of quasi-static, quasi-steady and quasi-unsteady fluidelastic instability theoretical models. This database opens a new research avenue on the feasibility of applying quasi-steady models to two-phase flow.

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Vibration Excitation Forces in a Rotated Triangular Tube Bundle Subjected to Two-Phase Cross Flow

ASME 2010 7th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, and Flow-Induced Vibration and Noise: Volume 3, Parts A and B ◽

10.1115/fedsm-icnmm2010-30528 ◽

2010 ◽

Cited By ~ 2

Author(s):

H. Senez ◽

N. W. Mureithi ◽

M. J. Pettigrew

Keyword(s):

Steam Generator ◽

Tube Bundle ◽

Cross Flow ◽

Fretting Wear ◽

Experimental Program ◽

Phase Flow ◽

Flow Induced Vibration ◽

Two Phase ◽

Fluid Forces ◽

Vibration Excitation

Two-phase cross flow exists in many shell-and-tube heat exchangers. Flow-induced vibration excitation forces can cause tube motion that will result in long-term fretting wear or fatigue. Detailed flow and vibration excitation force measurements in tube bundles subjected to two-phase cross flow are required to understand the underlying vibration excitation mechanisms. Studies on this subject have already been done, providing results on flow regimes, fluidelastic instabilities, and turbulence-induced vibration. The spectrum of turbulence-induced forces has usually been expected to be similar to that in single-phase flow. However, a recent study, using tubes with a diameter larger than that in a real steam generator, showed the existence of significant quasi-periodic forces in two-phase flow. An experimental program was undertaken with a rotated-triangular array of cylinders subjected to air-water cross-flow, to simulate two-phase mixtures. The tube bundle here has the same geometry as that of a real steam generator. The quasi-periodic forces have now also been observed in this tube bundle. The present work aims to understand turbulence-induced forces acting on the tube bundle, providing results on drag and lift force spectra and their behaviour according to flow parameters, and describing their correlations. Detailed experimental test results are presented in this paper. Comparison is also made with previous measurements with larger diameter tubes. The present results suggest that quasi-periodic fluid forces are not uncommon in tube arrays subjected to two-phase cross-flow.

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Fluidelastic Instability and Periodic Fluid Forces in a Normal Triangular Tube Bundle Subjected to Air-Water Flow

ASME 2010 7th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, and Flow-Induced Vibration and Noise: Volume 3, Parts A and B ◽

10.1115/fedsm-icnmm2010-30143 ◽

2010 ◽

Author(s):

G. Ricciardi ◽

M. J. Pettigrew ◽

N. W. Mureithi

Keyword(s):

Two Phase Flow ◽

Tube Bundle ◽

Fatigue Cracks ◽

Cross Flow ◽

Fretting Wear ◽

Phase Flow ◽

Steam Generators ◽

Two Phase ◽

Fluid Forces ◽

Void Fractions

Two-phase flow in power plant steam generators can induce tube vibrations, which may cause fretting-wear and even fatigue cracks. It is therefore important to understand the relevant two-phase flow-induced vibration mechanisms. Fluidelastic instabilities in cross-flow are known to cause the most severe vibration response in the U-bend region of steam generators. This paper presents test results of the vibration of a normal triangular tube bundle subjected to air-water cross-flow. The test section presents 31 flexible tubes. The pitch-to-diameter ratio of the bundle is 1.5, and the tube diameter is 38 mm. Tubes were flexible in the lift direction. Seven tubes were instrumented with strain gauges to measure their displacements. A broad range of void fractions (from 10% to 90%) and fluid velocities (up to 13 m/s) were tested. Fluidelastic instabilities were observed for void fractions between 10% and 60%. Periodic fluid forces were also observed. The results are compared with those obtained with the rotated triangular tube bundle, showing that the normal triangular configuration is more stable than the rotated triangular configuration.

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A Method for Extracting the Time Delay From the Unsteady and Quasi-Steady Fluidelastic Forces in Two-Phase Flow

Volume 4: Fluid-Structure Interaction ◽

10.1115/pvp2013-97437 ◽

2013 ◽

Author(s):

Teguewinde Sawadogo ◽

Njuki Mureithi

Keyword(s):

Time Delay ◽

Two Phase Flow ◽

Phase Flow ◽

Two Phase ◽

Fluid Forces ◽

Void Fractions ◽

Fluidelastic Instability ◽

Measured Time ◽

Unsteady Fluid ◽

Theoretical Results

The time delay is a key parameter for modeling fluidelastic instability, especially the damping controlled mechanism. It can be determined experimentally by measuring directly the time lag between the tube motion and the induced fluid forces. The fluid forces may be obtained by integrating the pressure field around the moving tube. However, this method faces certain difficulties in two-phase flow since the high turbulence and the non-uniformity of the flow may increase the randomness of the measured force. To overcome this difficulty, an innovative method for extracting the time delay inherent to the quasi-steady model for fluidelastic instability is proposed in this study. Firstly, experimental measurements of unsteady and quasi-static fluid forces (in the lift direction) acting on a tube subject to two-phase flow were conducted. The unsteady fluid forces were measured by exciting the tube using a linear motor. These forces were measured for a wide range of void fraction, flow velocities and excitation frequencies. The experimental results showed that the unsteady fluid forces could be represented as single valued function of the reduced velocity (flow velocity reduced by the excitation frequency and the tube diameter). The time delay was determined by equating the unsteady fluid forces with the quasi-static forces. The results given by this innovative method of measuring the time delay in two-phase flow were consistent with theoretical expectations. The time delay could be expressed as a linear function of the convection time and the time delay parameter was determined for void fractions ranging from 60% to 90%. Fluidelastic instability calculations were also performed using the quasi-steady model with the newly measured time delay parameter. Previously conducted stability tests provided the experimental data necessary to validate the theoretical results of the quasi-steady model. The validity of the quasi-steady model for two-phase flow was confirmed by the good agreement between its results and the experimental data. The newly measured time delay parameter has improved significantly the theoretical results, especially for high void fractions (90%). However, the model could not be verified for void fractions lower or equal to 50% due to the limitation of the current experimental setup. Further studies are consequently required to clarify this point. Nevertheless, this model can be used to simulate the flow induced vibrations in steam generators’ tube bundles as their most critical parts operate at high void fractions (≥ 60%).

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Primitive Model for the Random Excitation of a Tube Under Two-Phase Cross Flow

Volume 4: Fluid-Structure Interaction ◽

10.1115/pvp2016-63241 ◽

2016 ◽

Author(s):

Laurent Borsoi ◽

Philippe Piteau ◽

Xavier Delaune ◽

Jose Antunes

Keyword(s):

Two Phase Flow ◽

Tube Bundle ◽

Cross Flow ◽

Interface Velocity ◽

Momentum Conservation ◽

Random Excitation ◽

Nuclear Industry ◽

Phase Flow ◽

Two Phase ◽

Primitive Model

Flow-induced vibration of heat-exchangers tubes is particularly studied in the nuclear industry for safety and cost reasons. It implies to have, among others, relevant characterizations of the random buffeting forces the cross-flow applies to the tube bundle. Work is still needed in this domain, particularly for two-phase flow, to improve the available data as the ones for PWR steam generator, currently very envelope. In parallel to get new experimental data, using “real” or substitutional mixtures (e.g. air-water instead of steam-water for PWR), it is essential to understand the basic excitation mechanisms which induce the vibrations under two-phase flow, as e.g. the influence of flow regimes. In this general framework, what can be learnt from deliberately simple models may be a contributive help. As a first attempt on this issue, the paper deals with the elementary case of a single rigid tube under air-water cross flow. This case is part of experiments carried out at CEA-Saclay with bundles where both tube support reactions and flow characteristics are measured, with respectively piezo-electrical sensors and bi-optical probes (BOP). The information provided by the BOP (mean interface velocity, statistical distribution, etc.) feeds a primitive model of water “droplet” impulses on the tube, based on a lot of crude assumptions about impact velocity, momentum conservation, impulse shape, statistical independence, etc., and which uses analytical results of random processes constructed from the superposition of random pulses. The “equivalent” excitation force, obtained in terms of dimensional PSD, is compared to the one measured in the drag and lift direction with an acceptable agreement, at least in order of magnitude. Comments and lessons are drawn from this first attempt, and some paths are advanced to improve this kind of primitive models, especially for treating rigid square bundles under air-water cross flow.

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Development of Experimental Active Magnetic Bearing Device for Measurement of Mechanical Seal Reaction Force Acting on Rotor

Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2018-85883 ◽

2018 ◽

Author(s):

Hiroki Manabe ◽

Shota Yabui ◽

Hideyuki Inoue ◽

Tsuyoshi Inoue

Keyword(s):

Force Measurement ◽

Reaction Force ◽

Magnetic Bearing ◽

Active Magnetic Bearing ◽

Mechanical Seal ◽

Rotating Shaft ◽

Fluid Force ◽

Fluid Forces ◽

Whirling Motion ◽

Measurement And Evaluation

In turbomachinery, seals are used to prevent fluid leakage. At seal part, rotordynamic fluid force (RD fluid force), which causes whirling motion of rotor, is generated. Under certain conditions, the RD fluid force may contribute to instability of the machine. There are several cases that the whirling is accompanied by eccentricity due to the influence of gravity, or the whirling orbit becomes elliptical due to the influence of the bearing support anisotropy. In these cases, mathematical modeling of the RD fluid forces becomes increasingly complex. As a result, the RD fluid force measurement is more preferable. To improve the measurement and evaluation technology of the RD fluid force, a method to arbitrarily control whirling of the orbit is required. In this paper, RD fluid force measurement by controlling the shape of the orbit using an active magnetic bearing (AMB) is proposed. A contact type mechanical seal is used as a test specimen. When the rotating shaft is whirling, the RD fluid force due to hydrodynamics lubrication and the frictional force due to contact occur on the sliding surface. The resultant force of these forces is taken as the reaction force of mechanical seal and the measurement is performed. The measured reaction force of the mechanical seal is compared with simulation results and the validity of the proposed measurement method is confirmed.

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