STRUCTURAL EXCITATION RESPONSE OF A STRAIGHT PIPE SUBJECTED TO AIR-WATER INTERNAL FLOW

3º Encontro Brasileiro sobre Ebulição, Condensação e Escoamentos Multifásicos Curitiba, 7 - 8 de Maio de 2012

STRUCTURAL EXCITATION RESPONSE OF A STRAIGHT PIPE SUBJECTED TO AIR-WATER INTERNAL FLOW Luis Enrique Ortiz Vidal1,*,°, Oscar Mauricio Hernandez Rodriguez2,*, Njuki Mureithi3,° *Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo (USP), 13566-970, São Carlos (SP) - Brazil, Email: [email protected] / [email protected], [email protected] ° BWC/AECL/NSERC Chair of Fluid-Structure Interaction, Department of Mechanical Engineering, Ecole Polytechnique Montreal, QC, Canada, H3C 3A7, [email protected]

ABSTRACT Gas-liquid flow in piping is a potential source of structural excitation, where the pipe response is very dependent on the flow characteristics, i.e. flow pattern, mixture velocity and void fraction. Although several studies on the excitation response due to gas-liquid pipe flow have been recently reported, e.g. forces in bends, the information available on this topic is quite scanty. In this paper, the excitation response of a straight pipe subjected to air-water internal flow is investigated. A set of 32 two-phase horizontal flow conditions was collected, including bubbly, slug and dispersed flow-patterns. The homogeneous mixture velocity J was in the range of 0.5 to 25 m/s, with homogeneous void fractions of β = 10%, 25%, 50%, 75% and 95%. Signals of acceleration and deformation were acquired as possible response parameters to obtain information on the two-phase flow. Results show higher acceleration levels in slug and dispersed than in bubbly flow. We also find that the acceleration frequency response contains useful information on the flow. Comparisons with single-phase flow are also presented. This is an exploratory attempt to develop a non-intrusive technique to determine important two-phase parameters, e.g. flow pattern.

INTRODUCTION Gas-liquid pipe flow is common in nuclear, refrigeration, gas and oil industries, where gas-liquid mixtures are transported in piping systems. The mixture flows in different flow patterns, such as bubbly, slug and annular, generating dynamic fluid forces which may induce structural vibration. Flow-induced vibrations (FIV), when excessive, may lead to structural component failures. For this reason, proper knowledge of FIV phenomena has a significant impact on the design and operation of piping systems. These factors have motivated significant research over the last three decades, mainly in the nuclear industry where two-phase cross flow is predominant, as cited by [1-7]. Overall, these studies found important dependence of the excitation response on the twophase flow parameters, i.e. flow pattern, mixture velocity and void fraction. The knowledge evolution and the characteristics of the mechanical vibrations due to two-phase pipe flow can be found in Ortiz-Vidal and Rodriguez [8]. In many industrial cases, the vibration of the piping systems is not enough to cause damage; however, it is present as an intrinsic part of the operation. The main goal of our research is to use this vibration response to obtain information about two-phase flow inside the pipe. In 2004 Evans et al. [9] showed that this is possible for single-phase water flow. From signals of an accelerometer installed on the external wall of a pipe, these authors obtained the flow rate. In a more recent study, based on the artificial-intelligence approach, Hua et al. [10] reported the possibility of obtaining the flow pattern in a horizontal two-phase flow also from accelerometer signals. In this paper, we present an exploratory experimental investigation on the excitation response of a straight pipe subjected to air-water internal flow. Acceleration patterns as a function of velocity, homogeneous void fraction and flow pattern were found. The results suggest that such patterns

could be used for the development of a nonintrusive technique to obtain information about important two-phase flow conditions. EXPERIMENTAL WORK The experimental work has been conducted at the FluidStructure Interaction Laboratory of the BWC/AECL/NSERC Industrial Research Chair, Ecole Polytechnique, Montreal. Table 1. Components of the two-phase test loop Letter A B C D E F G H I J K

Component Air regulation valve Water reservoir Water centrifugal pump Frequency shifter Water centrifugal pump Water regulation valve Air-Water mixer Heavy clamp Test section Heavy clamp High speed camera

Table 2. Measurement instruments of the two-phase test loop Number 1 2 3 4 5 6 7

Component Pressure regulator Air flowmeter Air flowmeter Pressure gage Water flowmeter Pressure transducer Pressure trasnducer

Range 0 to 100 psig 0 to 75 slpm 0 to 1000 slpm 0 to 100 psig 10.18 to 424.18 lpm 0 to 50 psig 0 to 50 psig

Accuracy --1% FS 1.5% FS 3% FS 0.25% RD 0.05% FS 0,05% FS

3º Encontro Brasileiro sobre Ebulição, Condensação e Escoamentos Multifásicos Curitiba, 7 - 8 de Maio de 2012

Figure 1. Schematic representation of the two-phase test loop.

The two-phase pipe test loop shown in Figure 1 was specifically constructed to measure the two-phase flowinduced vibration (2-FIV), where the main components and measurement instruments are designated by letters and numbers and listed in Tables 1 and 2, respectively. The test section (I, Figure 1) consists of a transparent PVC pipe schedule 40 with 3/4-in of nominal diameter and a span of 60in. Water at room temperature and atmospheric pressure was pumped from the reservoir B by the centrifugal pumps C and D and its flow rate was measured upstream by the flowmeter 5. From an independent line, air at high pressure was supplied and its pressure controlled by the regulator 1, which maintained a steady pressure. The air flow rate was measured and regulated by the flowmeters 2 and 3 and the valve A, respectively. Water and air were mixed in mixer G and twophase mixture flowed, in several flow patterns, through the test section I. Then, the fluids were separated in the atmospheric tank B. Accelerometer and strain gages sensors were used to monitor the vibration response in the test section. The sensors were located at the midspan position and the pipe entrance, respectively. Pressure transducers (6 and 7, Figure 1) were also installed in order to estimate the air pressure for each two-phase flow condition. A homemade program developed in LabVIEWTM was used for acquiring and processing the signals. The sampling rate of 5000 Hz was chosen to ensure the accuracy of the sensors and avoid the aliasing effect. Also, images of the two-phase flow patterns, for their correct characterization, were taken using the high speed camera system K. Two parameters were used to specify the two-phase flow conditions: the homogeneous mixture velocity, referred simply as velocity in this paper, J, and homogeneous void fraction (referred simply as void fraction), β,

J

QL  QG A

(1)



QG QG  QL

(2)

where QL, QG and A represent liquid and gas flow rate (m3/s) and cross-sectional area of the pipe (m2), respectively. Every flow condition was set for the midspan position of the test section, i.e. in-situ values. For this, the readings of the air flowmeters were corrected from the pressure values downstream and upstream (7 and 6, Fig. 1), assuming a linear pressure variation along the test section. RESULTS AND DISCUSSION Acceleration signal for single-phase flow Acceleration time signals for water single-phase flow were collected from a triaxial accelerometer. Although it is not the main topic of this paper, these experiments were performed to evaluate our experimental setup. Calculations of aRMS (root mean square of resultant acceleration) versus water velocity are shown in Fig. 2. Furthermore, a concave-up quadratic trend between these two variables can be observed, which is in agreement with Evans’ et al. [9] quadratic relationship between standard deviation and flow rate. It should be noted that this agreement is valid because the mean of the accelerometer signal is almost zero. Thus, the aRMS could be considered equal to the standard deviation. We also analyzed the influence of velocity on frequency response. Figure 3 shows frequency domain results (using a Fast Fourier Transform) for the z and y axes, where both axes are perpendicular to pipe axis and z-axis lies in the gravity direction. The x-axis is parallel to the direction of the flow. The differences between Fig. 3 a) and b) would be caused by the gravity field. Two effects for the same velocity can be noted: (i) larger values of y-axis vibration response and (ii) slightly lower values of frequency (respect to main peak) in yaxis. The fluid mass would be acting in z-axis as a natural damper and an added-mass, respectively. On the other hand, for each figures independently, a decrease in frequency due to the increase in velocity is observed (also see Long (1955 apud Ibrahim [11])). Although there is some influence of velocity on shift frequency it is negligible compared to the velocity variation, e.g. a factor of 10 for our case. This is the reason why Evans et al. [9] do not use frequency shifts for developing their technique. Finally, in spite of Evans’ et al.

[9] demonstration of a proportional relationship between flow rate and standard deviation, the characteristics of such relationship not was discussed. For example, why not adopting a third-grade fit as it had better results (dashed-line, R2 = 0.998, Fig. 2)? Therefore, phenomenological approaches to explain the physics behind that relationship, including the squared fit and effect of fluid mass, are needed.

Figure 2. aRMS as a function of velocity J for water single-phase flow. The solid and dashed line represent the quadratic and third-grade trend line, respectively. R2 is their coefficient of determination.

[12], was tested. In general, it was possible to observe values of two-phase aRMS higher than those for single-phase at the same velocity. Table 3 shows these results for each flow condition. The aRMS values indicate increments with increasing velocity for constant homogeneous void fractions. However, the trends for two-phase flow are different from single-phase flow. For low homogeneous void fractions, β = 10% and 25%, fit curves with linear and quadratic trends could be obtained (see Fig. 4 (a)), differently from single-phase flow where a suitable linear fit is impossible. For the others void fractions, experimental data were plotted and fit curves were constructed (see Fig. 4 (b)). Also, Differently from single-phase and lowvoid-fraction two-phase flow, concave-down curves of quadratic trend were found. Furthermore, only for β = 95% it was observed a proper quadratic fit. Based on these results, it can be noted that (i) there is a proportional relationship between aRMS and velocity, (ii) it is dependent on superficial void fraction and (iii) for two-phase flow a simple approach, similar to Evans et al. [9], is not plausible. An important parameter in two-phase flow is the flow pattern. This indicates the morphological arrangement of the phases inside the pipe and contains spatial and temporal information about the flow. Fundamental studies have shown the importance of the flow pattern on FIV [1-3]. Chen [1] noted that, for axial confined two-phase flow, vibration amplitude depends on the flow pattern and velocity. Hence, flow pattern could also be relevant for two-phase pipe flow due to the similarity between both kinds of flow. Figure 5 shows the experimental flow pattern map by Mandhane et al. [12] including our aRMS experimental data. It is noted that acceleration values are largest for dispersed and slug flow (refer also to Table 3), which can be attributed to the intense turbulence and periodic changes in the system’s mass, respectively. Table 3. RMS acceleration for tested two-phase flow conditions.

Figure 3. Frequency response, using a Fast Fourier Transform, for water single-phase flow and several J velocities. (a) z-axis and (b) yaxis are perpendicular to pipe axis. The z-axis lies in the gravity direction.

Acceleration signal for two-phase flow A set of 32 two-phase mixture conditions, including bubbly, slug and dispersed flow, according to Mandhane et al.

Condition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

β (%) 10 10 10 10 10 10 10 25 25 25 25 25 25 25 50 50 50 50 50 50 50 75 75 75 75 75 75 95 95 95 95 95

J (m/s) 0.5 1 2 3 4 5 7 0.5 1 2 3 4 5 7 0.5 1 2 3 5 7 10 1 2 5 10 15 17.5 5 10 15 20 25

aRMS (g) 0.01620 0.03215 0.04113 0.06328 0.08804 0.11028 0.16275 0.00999 0.03438 0.06761 0.08478 0.10651 0.13026 0.18033 0.00905 0.02932 0.07370 0.10809 0.19582 0.16735 0.21751 0.01980 0.10723 0.31181 0.52295 0.48876 0.54629 0.20771 0.34559 0.46837 0.54422 0.59243

3º Encontro Brasileiro sobre Ebulição, Condensação e Escoamentos Multifásicos Curitiba, 7 - 8 de Maio de 2012

Figure 4. Two-phase aRMS as a function of velocity J for (○) β = 10%, (■) β = 25%, (□) β = 50%, (♦) β = 75% and (●) β = 95%. The solid and dashed lines represent the linear and quadratic trend line, respectively. R2 is their coefficient of determination.

Figure 5. aRMS value in function of two-phase flow pattern.

Flow-induced vibrations could present recursive effects, i.e. flowing fluid generates vibrations on the structure and subsequently these vibrations induce perturbations on the flow; there is an interactive process. According to experimental observations and results (see Fig. 5), the recursive effect caused by bubbly flow could be negligible because the vibration level is low. On the other hand, intermittent (e.g. slug) and dispersed flows have a medium or high vibration level; however, the recursive effect could also be negligible. It is because (i) the arregement of velocityrange and clamp-clamp pipe does not present excessive vibrations, i.e. static or dynamic instabilities; and (ii) since two-phase fluctuations are natural in intermittent and dispersed flows, these flow patterns remain essentially the same in the presence of recursive effects (slight perturbations). From the discussion above, we could assume that the vibration response caused by flow pattern is in one way, i.e. without recursive effects. According to Table 3 and Fig. 5, flow pattern transitions have influence on aRMS results. Experimental data for β = 50% and 75% show a shift on velocity up-trend for the conditions 20 and 26 (see Fig. 4), respectively. These two conditions are located at the transition between slug and dispersed flow, as showed in Fig. 5. Also, for these two homogeneous void

fractions, higher aRMS-factor increases were measured in the bubbly-slug boundary (transitions 16-17 and 22-23, Table 3). In the case of bubbly-dispersed boundary transition, there are not significant changes. This could be because the flowpattern for β = 10% and 25% changes gradually. The analysis of the flow pictures will be crucial to deepen the understanding of the impact of flow pattern and transitions on FIV two-phase pipe flow. Frequency domain results of acceleration signal, using a Fast Fourier Transform, are shown in Fig. 6. The results are presented as a function of flow pattern for y and z axes, Figs. 6 (a-c) and (d-f), respectively. Each axis lies in the same direction as for single-phase flow. As expected, flow pattern has influence on frequency response. For example, the perturbations in low frequencies observed in Figs. 6 (a) and (b) can be related with flowing bubbles; furthermore, depending on the intensity of the response the flow pattern could be recognized, bubbly or slug flow. For the dispersed flow-pattern, an absence of bubbles would be determined for a regular increment (not perturbations) of frequency response (e.g. C27, Fig. 6(c)). Based on these observations, two-phase models and picture analysis could be relevant tools to determine the bubble frequencies, and consequently the flow pattern.

3º Encontro Brasileiro sobre Ebulição, Condensação e Escoamentos Multifásicos Curitiba, 7 - 8 de Maio de 2012

Figura 6. Frequency response (from Fast Fourier Transform) for several two-phase flow conditions, including bubbly, slug and dispersed flow. (a-c) z-axis and (d-f) y-axis are perpendicular to pipe axis. The z-axis lies in the gravity direction. C# corresponds to the flow condition (Table 3 and Fig. 5).

A shift in homogeneous void fraction determines changes of density of the flowing fluid. Besides, density is related to added-mass (see [2; 3]), and consequently to shifts on the predominant frequency. Then, void fraction affects directly the predominant frequency. It is can be observed Fig. 6 (see graphs independently), where increases in void fraction determines decreases of flowing fluid density. Respect to the influence of velocity, in general, increase in frequency response is accompanied by velocity increase (see Fig. 6). However, the opposite is not always true. Fig. 6 (b) shows an increase of the frequency response, from condition 24 to 28, caused by a void fraction increase at constant velocity. Thus, it is important to note that any analysis should be done considering the void fraction. The effect of gravity on frequency response is also analyzed. Figs. 6 (a)-(d), (b)-(e) and (d)-(f) represent graphs for bubbly, slug and dispersed flow, respectively, for the z and y axes. These results show that the frequency responses of yaxis are larger than z-axis. These findings are in disagreement with single-phase flow, and could be related to the dynamics of two-phase flow: density shifts affect z-axis more aggressively than y-axis. It was also observed that gravity affects the main peak frequency: frequency response for y-axis larger than z-axis in bubbly and dispersed flows (according to single-phase flow), the opposite occurs for slug flow. In general, the effect of gravity on frequency response and main peak frequency is usually not strong. Furthermore, the shape of frequency response is notorious and could be more

relevant. In-depth analysis of collected data will be needed for better understanding the phenomena. Deformation signals Both quarter and half bridge strain gages were tested, aiming for finding patterns for axial stress and bending moment as a function of two-phase flow parameters. The relationship between forces (caused by two-phase flow) and deformations (measured from strain gages) would be obtained from static-load tests. Initially, readings from the quarterbridge sensors for static loads were collected. We found drifting of data attributed to pipe material (poor heat sink) and level of excitation voltage. Although the voltage was set again, the drift continued. Then, half-bridge strain gages were installed on the pipe. Experimental points for static-load test were collected and a proper linear fit was obtained. At the flowing flow tests, strong drifts were noted, especially from the pressurized air. This time caused by the temperature of the fluids. Next, several unsuccessful attempts were made to reduce the effect of temperature. The principal difficulties of the drift were: (i) the deformation readings did not return to the reference level and (ii) it was not possible to separate the effect of temperature shift and stress (caused by fluids). On the other hand, cooling and heating systems could solve the temperature problem. However, this possible solution was not implemented because our goal is to obtain information about two-phase flow from simple vibration sensor in not-controlled systems.

CONCLUSION

REFERENCES

An experimental investigation of flow-induced vibrations subjected to two-phase pipe flow has been presented, where our goal was to obtain two-phase flow information from vibration response. Results of resultant acceleration response showed higher levels in slug and dispersed than in bubbly flow, depending on velocity, homogeneous void fraction and two-phase flow pattern transitions. Furthermore, it was not possible to analyze the vibration response as a function of only one of these parameters. Frequency response of acceleration shows information that could be related to flowing bubbles, and consequently flow pattern. After a detailed discussion, it was showed that the vibration response caused by flow pattern is preponderantly in one way, i.e. without recursive effects. Then, flow pattern is relevant and not depend on the vibration response. Single-phase flow experimental data were also collected and compared with a non-intrusive flow rate measurement technique available in the literature, obtaining good agreement. The use of deformation signals has also been tried, but problems with the temperatures of fluids did not allow their use as a predictive technique. Finally, it is suggested that flow pattern, mixture velocity and homogeneous void fraction are responsible for the patterns of acceleration response. Two-phase models and picture analysis should be relevant tools to determine the bubble frequencies, and consequently the flow pattern. The proposed non-intrusive technique to determine two-phase flow parameters seems promising.

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[8]

ACKNOWLEDGMENT The authors are grateful to Benedict Besner, Thierry Lafrance and Cedric Beguin for their support in the experimental facilities and discussions, and to Irma Consuelo Aguilar Avila for helping in data collect. Luis Enrique Ortiz Vidal gratefully acknowledges the support of the FAPESP (São Paulo Research Foundation, proc. 2009/17424-2) and of BWC/AECL/NSERC Chair of Fluid-Structure Interaction, Ecole Polytechnique Montréal.

[9] [10]

[11]

NOMENCLATURE aRMS A J Q β

resultant acceleration RMS cross-sectional area of the pipe homogeneous mixture velocity volumetric flow rate volumetric quality

Subscripst G gas L liquid

g m2 m/s m3 nondimensional

[12]

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