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

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.

Drag Coefficient and Two-Phase Friction Multiplier on Tube Bundles Subjected to Two-Phase Cross-Flow

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
W. G. Sim ◽  
Njuki W. Mureithi
Keyword(s):  
Drag Coefficient ◽  
Void Fraction ◽  
Euler Number ◽  
Tube Bundle ◽  
Cross Flow ◽  
Water Mixture ◽  
Duct Flow ◽  
Two Phase ◽  
Mass Fluxes ◽  
Wide Range

An approximate analytical model, to predict the drag coefficient on a cylinder and the two-phase Euler number for upward two-phase cross-flow through horizontal bundles, has been developed. To verify the model, two sets of experiments were performed with an air–water mixture for a range of pitch mass fluxes and void fractions. The experiments were undertaken using a rotated triangular (RT) array of cylinders having a pitch-to-diameter ratio of 1.5 and cylinder diameter 38 mm. The void fraction model proposed by Feenstra et al. was used to estimate the void fraction of the flow within the tube bundle. An important variable for drag coefficient estimation is the two-phase friction multiplier. A new drag coefficient model has been developed, based on the single-phase flow Euler number formulation proposed by Zukauskas et al. and the two-phase friction multiplier in duct flow formulated by various researchers. The present model is developed considering the Euler number formulation by Zukauskas et al. as well as existing two-phase friction multiplier models. It is found that Marchaterre's model for two-phase friction multiplier is applicable to air–water mixtures. The analytical results agree reasonably well with experimental drag coefficients and Euler numbers in air–water mixtures for a sufficiently wide range of pitch mass fluxes and qualities. This model will allow researchers to provide analytical estimates of the drag coefficient, which is related to two-phase damping.

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

2010 ◽  
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.

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

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.

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

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.

Fluidelastic Instability and Work-Rate Measurements of Steam-Generator U-Tubes in Air–Water Cross-Flow

2005 ◽  
Vol 127 (1) ◽  
pp. 84-91 ◽  
Author(s):  
V. P. Janzen ◽  
E. G. Hagberg ◽  
M. J. Pettigrew ◽  
C. E. Taylor
Keyword(s):  
Tube Bundle ◽  
Cross Flow ◽  
Two Phase ◽  
Void Fractions ◽  
Wide Range ◽  
Fluidelastic Instability ◽  
Out Of Plane ◽  
Plane Direction ◽  
First Time ◽  
Support Work

The dynamic response of U-tubes to two-phase cross-flow has been studied in tests involving a simplified U-tube bundle with a set of flat-bar supports at the apex, subjected to air–water cross-flow over the mid-span region. Tube vibration and the interaction between tubes and supports were measured over a wide range of void fractions and flow rates, for three different tube-to-support clearances. The vibration properties and tube-to-support work-rates could be characterized in terms of the relative influence of fluidelastic instability and random-turbulence excitation. For the first time, in a U-bend tube bundle with liquid or two-phase flow, fluidelastic instability was observed both in the out-of-plane and in the in-plane direction. This raises the possibility of higher-than-expected tube-to-support work-rates for U-tubes restrained by flat bars, particularly if fluidelastic instability, random turbulence and loose supports combine adversely.

Random Excitation Forces in Heat Exchanger Tube Bundles

2000 ◽  
Vol 122 (4) ◽  
pp. 509-514 ◽  
Author(s):  
C. E. Taylor ◽  
M. J. Pettigrew
Keyword(s):  
Heat Exchangers ◽  
Vibration Analysis ◽  
Full Range ◽  
Cross Flow ◽  
Random Excitation ◽  
Fretting Wear ◽  
Liquid Region ◽  
Flow Conditions ◽  
Fluid Forces ◽  
Wide Range

Random excitation forces can cause low-amplitude tube motion that will result in long-term fretting-wear or fatigue. To prevent these tube failures in heat exchangers, designers and troubleshooters must have guidelines that incorporate random or turbulent fluid forces. Experiments designed to measure fluid forces were conducted at the Chalk River Laboratories and at other laboratories worldwide. The data from these experiments were studied and collated, to determine suitable guidelines for random excitation forces. In this paper, a guideline for random excitation forces in single-phase cross flow is presented in the form of normalized spectra that are applicable to a wide range of flow conditions and tube frequencies. In particular, the experimental results used in this study were conducted over the full range of flow conditions found in the liquid region of a nuclear steam generator. The proposed guidelines are applicable to steam generators, condensers, reheaters and other shell-and-tube heat exchangers. They may be used for flow-induced vibration analysis of new or existing components, as input to vibration analysis computer codes and as specifications in procurement documents. [S0094-9930(00)00603-X]

Experimental Study on the Dynamics of Four Flexible Cylinders in Square Arrangement Subjected to Uniform Cross-Flow

2012 ◽  
Author(s):  
Bijan Sanaati ◽  
Naomi Kato
Keyword(s):  
Amplitude Ratio ◽  
Lift Coefficient ◽  
Cross Flow ◽  
Mass Ratio ◽  
Drag Forces ◽  
Low Mass ◽  
Drag And Lift ◽  
Low Mass Ratio ◽  
Lift And Drag ◽  
Four Cylinders

Groups of cylinders can be found in many engineering fields such as marine and civil applications. The behaviors of the group cylinders can be very complex because it undergoes the mutual effects of adjacent cylinders arranged in different positions. In this paper, we present the results of a study on the dynamics of a group of flexible cylinders in square arrangements along with a single (isolated) cylinder subjected to uniform cross-flow (CF). Four cylinders of the same size, properties, and pretensions were tested in two configurations with different centre-to-centre separations. Horizontal and vertical separations were 2.75D & 2.75D and 5.50D & 2.75D for the first and second configurations, respectively. The tandem (horizontal) separations between the downstream and upstream cylinders, i.e., 2.75D and 5.5D, correspond to the reattachment and co-shedding regimes, respectively. Vertical separation, i.e., 2.75 was chosen in a range where the side-by-side cylinders can have proximity interference. Reynolds number ranged from 1400 to 20000 (subcritical regime). The parameter of reduced velocity reached up to 19. The aspect ratio of all the cylinders was 162 (length/diameter). Mass ratio (cylinders mass/displaced water) is 1.17, a low mass ratio. The amplitude ratio of the CF vibration of the downstream cylinders, hydrodynamic force coefficients including mean and fluctuating components of the drag and lift forces, and frequency responses for both CF and inline (IL) directions were analyzed. All the cylinders excited up to the second and fourth mode of vibrations for CF and IL directions, respectively. Mean drag coefficient of the upstream cylinders are almost twice those of the downstream cylinders at high reduced velocities. The mean lift coefficient is much higher for the upstream cylinders than the downstream cylinders with a negative value. Obvious IL and CF lock-in regions exist for all four cylinders at low reduced velocities. Among the four cylinders, the upper downstream cylinder shows the least and the most fluctuating lift and drag forces, respectively. The IL and CF frequencies of the downstream cylinders are much lower than those of the upstream ones and the single cylinder.

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

2005 ◽  
Author(s):  
C. Zhang ◽  
M. J. Pettigrew ◽  
N. W. Mureithi
Keyword(s):  
Tube Bundle ◽  
Cross Flow ◽  
Fretting Wear ◽  
Experimental Program ◽  
Force Measurements ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Drag Forces ◽  
Vibration Excitation ◽  
Excitation Force

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 vibration excitation force measurements in tube bundles subjected to two-phase cross flow are required to understand the underlying vibration excitation mechanisms. An experimental program was undertaken with a rotated-triangular array of cylinders subjected to air/water flow to simulate two-phase mixtures over a broad range of void fraction and mass fluxes. Both the dynamic lift and drag forces were measured with strain gage instrumented cylinders. The experiments revealed somewhat unexpected but significant quasi-periodic forces in both the drag and lift directions. The periodic forces appeared well correlated along the cylinder with the drag force somewhat better correlated than the lift forces. The periodic forces are also dependent on the position of the cylinder within the bundle.

scholarly journals Correlation Between Vibration Excitation Forces and the Dynamic Characteristics of Two-Phase Flow in a Rotated Triangular Tube Bundle

2006 ◽  
Author(s):  
C. Zhang ◽  
M. J. Pettigrew ◽  
N. W. Mureithi
Keyword(s):  
Void Fraction ◽  
Cross Flow ◽  
Main Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Drag Forces ◽  
Vibration Excitation ◽  
Tube Bundles ◽  
Lift Forces ◽  
Drag And Lift

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. Some of this work has already been done. The distributions of both void fraction and bubble velocity in rotated-triangular tube bundles were obtained. Somewhat unexpected but significant quasi-periodic forces in both the drag and lift directions were measured. The present work aims at understanding the nature of such unexpected drag and lift quasi-periodic forces. An experimental program was undertaken with a rotated-triangular array of cylinders subjected to air/water flow to simulate two-phase mixtures. Fiber-optic probes were developed to measure local void fraction. Both the dynamic lift and drag forces were measured with a strain gage instrumented cylinder. The investigation showed that the quasi-periodic drag and lift forces are generated by different mechanisms that have not been observed so far. The quasi-periodic drag forces appear related to the momentum flux fluctuations in the main flow path between the cylinders. The quasi-periodic lift forces, on the other hand, are mostly correlated to oscillations in the wake of the cylinders. The relationships between the lift or drag forces and the dynamic characteristics of two-phase flow are established through fluid mechanics momentum equations. The quasi-periodic lift forces are related to local void fraction measurements in the unsteady wake area between upstream and downstream cylinders. The quasi-periodic drag forces correlate well with similar measurements in the main flow stream between cylinders.

Correlation Between Vibration Excitation Forces and the Dynamic Characteristics of Two-Phase Cross Flow in a Rotated-Triangular Tube Bundle

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
C. Zhang ◽  
M. J. Pettigrew ◽  
N. W. Mureithi
Keyword(s):  
Void Fraction ◽  
Cross Flow ◽  
Main Flow ◽  
Experimental Program ◽  
Two Phase ◽  
Drag Forces ◽  
Vibration Excitation ◽  
Tube Bundles ◽  
Lift Forces ◽  
Drag And Lift

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. Some of this work has already been done. The distributions of both void fraction and bubble velocity in rotated-triangular tube bundles were obtained. Somewhat unexpected but significant quasiperiodic forces in both the drag and lift directions were measured. The present work aims at understanding the nature of such unexpected drag and lift quasiperiodic forces. An experimental program was undertaken with a rotated-triangular array of cylinders subjected to air/water flow to simulate two-phase mixtures. Fiber-optic probes were developed to measure local void fraction. Both the dynamic lift and drag forces were measured with a strain gage instrumented cylinder. The investigation showed that the quasiperiodic drag and lift forces are generated by different mechanisms that have not been previously observed. The quasiperiodic drag forces appear related to the momentum flux fluctuations in the main flow path between the cylinders. The quasiperiodic lift forces, on the other hand, are mostly correlated to oscillations in the wake of the cylinders. The quasiperiodic lift forces are related to local void fraction measurements in the unsteady wake area between upstream and downstream cylinders. The quasiperiodic drag forces correlate well with similar measurements in the main flow stream between cylinders.

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