Investigation of the Vibration Behavior of Fluidelastic Instability in Closely Packed Square Tube Arrays
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Abstract
Flow-induced vibrations in heat exchanger tubes have led to numerous accidents and economic losses in the past. Fluidelastic instability is the most critical flow-induced vibration mechanism in heat exchangers. Both experimental and computational studies conducted to determine fluidelastic instability were presented in this paper. In the experiment, a water channel was built, and a closely packed normal square tube array with a pitch-to-diameter ratio of 1.28 was tested, and significant fluidelastic instability was observed. A numerical model adopting large-eddy simulation and moving mesh was established using ANSYS CFX, and results showed good agreement with the experimental findings. The vibration behaviors of fluidelastic instability were discussed, and results showed that the dominant vibration direction of the tubes changed from streamwise to transverse beyond a critical velocity. A 180° phase lag between adjacent tubes was observed in both the experiment and simulations. Normal and rotated square array cases with pitch-to-diameter ratios of 1.28 and 1.5 were also simulated. The results of this study provide better insights into the vibration characteristics of a square tube array and will help improve the fundamental research and safety design of heat exchangers.
Keywords
Fluidelastic instability Dominant vibration direction Phase lag Square tube array Heat exchangerList of symbols
- A
Cross-sectional area
- d
Outer tube diameter
- k
Spring coefficient
- ω
Circular frequency of the tube
- m
Mass per length of the tube
- f_{c}
Coupled frequency, i.e., natural frequency of tube array in fluid, which is corresponding to certain coupled mode
- f_{a}
Tube frequency in air
- f_{v}
Tube vortex shedding frequency
- f_{w}
Tube frequency in water
- G
Flow rate
- m_{a}
Tube mass per length
- P
Array pitch
- V
Income velocity
- V_{p}
Gap velocity
- V_{c}
Critical velocity
- δ_{s}
Mass damping parameter, δ_{s} = m_{w}δ_{w}/ρ_{o}d^{2}
- δ_{w}
Logarithmic decrement in water
- ρ_{o}
Fluid density
- m_{w}
Total tube mass per length in water
Introduction
Fluidelastic instability is considered the most critical flow-induced vibration mechanism in tube and shell heat exchangers that can cause short-term failure of tubes. Such failures are often expensive and potentially dangerous. Fluidelastic instability results from coupling between fluid-induced dynamic forces and the motion of structures. Instability occurs when the flow velocity is sufficiently high so that the energy absorbed from the fluid forces exceeds the energy dissipated by damping. Fluidelastic instability usually leads to excessive vibration amplitudes. The minimum velocity at which instability occurs is called the critical velocity. To ensure the safety of facilities, the operating flow velocity should be strictly controlled below the critical velocity.
Fluidelastic instability in heat exchangers has been intensively researched over the past 60 years. Several theoretical models have been developed [1], and a number of important reviews on this topic have been published [2, 3, 4]. Fluidelastic instability is mainly attributed to two fluid–structure interaction mechanisms [5, 6]. The first mechanism, which is called the stiffness mechanism, is associated with the fluid coupling of neighboring tube vibrations and related to relative tube displacement. Here, the fluid forces are proportional to the displacements of the cylinders, and with the increasing velocity, the fluid-stiffness forces can reduce the modal damping. When the modal damping becomes negative, the cylinders become unstable. The second fluidelastic instability mechanism is associated with fluid force components in phase with the tube velocity and is called the damping mechanism. Here, the dominant fluid force is proportional to the velocity of the cylinders and may reduce the system damping when it acts as an excitation mechanism. Once the modal damping of a mode becomes negative, the cylinders lose stability [7]. A fully flexible array can become fluidelastically unstable due to either one or a combination of both mechanisms.
Numerous experiments [8] have been conducted in research on fluidelastic instability in tube arrays, and findings have helped develop a better understanding of the phenomenon. One of the earlier experiments conducted on square tube arrays was reported by Tanaka and Takahara [9], who tested a normal square array with a pitch ratio of 1.33 and concluded that unsteady fluid dynamic forces on a cylinder are mainly induced by the vibrations of the cylinder itself and its four neighboring cylinders. Tanaka et al. [10] measured tube arrays of P/d = 2.0 and P/d = 1.33, and clarified the characteristics of the critical velocity with respect to the pitch-to-diameter ratio. Weaver and Yeung [11] conducted experiments on a normal square array with a pitch ratio of 1.5 in water flow and showed that a single flexible tube in an array of rigid tubes becomes unstable at or near the same flow velocity as that found in a fully flexible array. Price and Paidoussis [12] conducted experiments on five-row and six-column normal square tube arrays of P/d = 1.5 in both air and water flows and concluded that the position of the flexible cylinder in the array has little effect on its stability in water flow but does influence its stability in air flow. Chen et al. [13] used water channels to perform a series of experiments measuring motion-dependent fluid force coefficients for normal square arrays with a pitch ratio of 1.35. 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. Al-Kaabi et al. [14] used a test rig to test square array of P/d = 1.45. Measurements were conducted to identify the flow-induced dynamic coefficients, the developed scheme was utilized to predict the onset of flow-induced vibrations in two configurations of tube bundles, and results were examined in light of Tubular Exchange Manufacturers Association (TEMA) predictions. Scott [15] conducted experiments on a normal square array with a pitch ratio of 1.33. In the case of fully flexible array, fluidelastic instability occurred at a point very close to the local peak in tube response, and the stability threshold was difficult to determine precisely. The response of a third-row tube, which was a single flexible tube in a rigid array, showed no fluidelastic instability behavior. Austermann and Popp [16] did not observe fluidelastic instability in their wind tunnel study of square arrays with a pitch ratio of 1.25.
In summary, most of the present research on normal square tube arrays is devoted to tube arrays with a relatively large pitch ratio, and little work has been done on tube arrays with small tube ratios. Available results show that a single flexible tube in a rigid array does not become unstable in both air and water for pitch ratios less than 1.33; thus, the stiffness mechanism appears to be the dominant mechanism for the fluidelastic instability of tubes with small pitch ratios. The vibration characteristics of tubes with small pitch ratios are also slightly different from those of tubes with large pitch ratios.
The development of computer technology has enabled the use of computation fluid dynamics in the engineering industry. This branch of fluid mechanics provides a new way for solving problems of fluid dynamics in tube arrays. Due to the complexity of actual tube array problems, most presented numerical simulations of the flow around tube array were limited to two dimensions based on the solution of Reynolds averaged Navier–stokes (RANS) equations. However, as RANS models cannot accurately predict the problems of fluid dynamics in tube arrays, they have not yet been widely employed in this regard. Pioneering direct numerical simulations (DNS) in tube array flows were reported by Moulinec et al. [17, 18]; in this work, the disappearance of wakes was presented and compared with theoretical asymptotic limits for laminar and turbulent strained flows. Although DNS is considered the most accurate solution for fluid analysis, it is not feasible for practical engineering problems involving high Reynolds number flows. Few computers can afford the high computational expense required by even a simple model.
In large-eddy simulations (LES), large eddies are resolved directly, while small eddies are modeled. Therefore, LES falls between DNS and RANS in terms of the fraction of the resolved scales. As momentum, mass, energy, and other passive scalars are mostly transported by large eddies in tube arrays, the LES technique is a promising approach for solving many complicated problems. Early simulations of LES were two-dimensional [19, 20, 21, 22], but some important mechanisms, such as vortex stretching, could not be reproduced by this technique. Rollet-Miet et al. [23] and Benhamadouche and Laurence [24] pioneered the use of 3D LES calculations in staggered tube arrays. In their papers, period elemental cells of tube arrays in a flow were simulated in both the streamwise and transverse directions, and improved predictions were compared with the RANS approach for mean and turbulence quantities. Liang and Papadakis [25] used LES to analyze a 3D staggered tube array at subcritical Reynolds number; in their computations, two distinct and independent shedding frequencies were detected behind the first two rows, but the high-frequency component vanished in downstream rows. The corresponding Strouhal numbers obtained agreed well with measurements available in the literature. Unsteady RANS calculations can provide consistent data for a tube undergoing forced displacement within a fixed bundle [26, 27, 28]. Attempts to fully capture the free motions of a single moving tube within a fixed array were proposed by Shinde et al. [29] using URANS and delayed detached eddy simulations (DDES). Similarly, a single tube in a fixed array at a moderate Reynolds number of 60000 using LES was achieved by Berland et al. [30]; here, good agreement with the experimental reference data was obtained.
Despite decades of intensive research, many important vibration characteristics of normal square tube arrays have not yet been fully understood, especially for tube arrays with a small pitch ratio. This paper intensively investigates the vibration behaviors of normal square tube arrays with a pitch-to-diameter ratio of 1.28 at different velocities using both experimental and numerical methods. The basic characteristics of fluidelastic instability are discussed, and the change in dominant vibration direction, phase lag between adjacent tubes, and tube vibration patterns related to the instability of tube arrays are analyzed in detail. The influence of tube arrangement and pitch ratio on the critical velocity and resulting vibration patterns is also discussed using simulation data. The results afford a better understanding of the vibration behavior of square tube arrays.
Experimental Setup
Water Channel
Test Section and Tube Array
Strain gauges are mounted on the rod end of the test tubes (Fig. 3a), which is free from water. Two sets of strain gauges are used on each tube to enable measurement in two perpendicular directions. The accuracy of the strain gauge is less than 1%, and a dynamic data acquisition system (DH5922, Dong Hua Testing Technology Co., Ltd., China) is used to obtain the data. As the dominant frequency is smaller than 20 Hz, the sample frequency is set to 200 Hz in the system. Tubes denoted by 1, 2, and 3 in Fig. 3b are measured in each test.
Velocity
In analyses of tube array systems, the mean gap velocity (or pitch velocity), which reflects the velocity between the gaps of adjacent tubes, is usually used as a reference. The gap velocity of normal and rotated square tube arrays can be expressed by Eqs. (2) and (3), respectively.
Note that V_{p} is the gap velocity, P is the pitch length, and d is the outer tube diameter.
Natural Frequency
- (a)
Tube frequency in air
- (b)
Tube frequency in water
Vibration Behaviors at Different Velocities
- (a)V_{p} = 0.65–0.89 m/s, irregular turbulent buffeting region (Fig. 6): Tube vibrations in this velocity range are mainly affected by random turbulent buffeting, in which tubes vibrate slightly under a range of coupled frequencies f_{c} of tube array.
- (b)V_{p} = 0.89–1.02 m/s, vortex shedding resonance region (Fig. 7): The vortex shedding frequency f_{v} corresponds to the f_{w} of the tubes in this region, and this relationship causes tube resonance. Significant vibrations occur in the front two rows of the tube array, and the dominant frequency is close to f_{w}.
- (c)V_{p}= 1.02–1.17 m/s, turbulence buffeting phase before fluidelastic instability (Fig. 8): With the increasing velocity, f_{v} deviates from f_{w}. A significant decrease in vibration amplitude occurs, and the vibration frequencies shift to a broader spectrum.
- (d)V_{p} = 1.17–1.41 m/s, fluidelastic instability region (Fig. 9): In this region, the vibration amplitude increases abruptly, and obvious tube instability occurs.
Numerical Model
Assumption
- (a)
Period boundary condition
- (b)
Rigid body movement
Modeling
Parameters of the model
P/d (m/m) | D (m) | M_{a} (kg/m) | ρ_{o} (kg/m^{3}) | f_{a} (Hz) |
---|---|---|---|---|
1.28 | 0.025 | 1.71 | 998 | 19.5 |
Computations are performed in an HP Z800 workstation (8 cores with 96 GB RAM) in the High-performance Computing Center of Tianjin University (12 CPUs allocated).
Results and Discussion
Comparison Between the Experiment and Numerical Simulations
According to the changes in the tube vibration spectra in Fig. 14, the tubes mainly respond in two regions of the spectra. The first region occurs around f_{w}. Significant vibrations at this frequency occur when f_{v} corresponds to f_{w} (Fig. 14a–d). As f_{v} varies with velocity, vibrations at this frequency decrease sharply when f_{v} deviates from f_{w}, and only a small influence of shedding frequency can be seen in the spectra (Fig. 14g–l). The second region involves a series of frequencies around 14 Hz. These frequencies are related to several values of f_{c} in the whole tube system and mainly affect turbulent buffeting and fluidelastic instability. Turbulent buffeting is a random vibration phenomenon in which the spectrum disperses over a broad range of f_{c} with relatively small amplitudes. Turbulent buffeting is affected by fluctuations in turbulent flow. The dominant frequency of fluidelastic instability also occurs within f_{c}. In contrast to the behavior of turbulent buffeting, the vibration of fluidelastic instability occurs in a narrow band of the spectrum with very large vibration amplitudes, corresponding to a single peak frequency. Typical spectra of fluidelastic instability are shown in Fig. 14e–j. According to the analysis above, a critical velocity of 1.06 m/s can be estimated from the transformations of the spectra.
Changes in the Dominant Vibration Direction
This same trend can be seen in Fig. 13. According to the response curves obtained, the increases in vibration amplitudes in the streamwise and transverse directions with respect to velocity do not occur at the same pace. The vibration amplitudes in the streamwise direction of tubes 2 and 3 increase at about 1.06 m/s, which is estimated as the critical velocity of the tube array. The vibration amplitudes in the transverse direction increase later but faster than those in the streamwise direction at about 1.2 m/s. As such, following this trend, we can predict that the dominant vibration direction for most tubes will change to the transverse direction.
Phase Lag Relationship Between Adjacent Tubes
As tube arrays in water flow always have a small mass damping parameter δ_{s} (the δ_{s} calculated in the experiment is about 0.283), fluidelastic instability is generally controlled by the damping mechanism. However, no fluidelastic instability is observed [14] when only a flexible tube in a rigid tube array with a P/d = 1.33 is present. In this case, instability is only affected by the damping mechanism. Thus, a fully flexible tube array becomes unstable only when the pitch ratio is relatively small, which means that the stiffness mechanism may be used to explain unstable behaviors despite a small δ_{s}. Fluidelastic instability in a tube array with a small pitch may be significantly affected by the interaction of neighboring tubes. As such, the relationship between vibrating tubes must be clarified to obtain a better understanding of the instability of tube arrays.
Influence of Pitch-to-Diameter Ratio and Array Pattern
On account of the staggered arrangement of the tubes, the flow paths of the rotated square array are quite complicated, which makes the vibration of the tubes much more chaotic. Figures 20c–d and 21c–d show some cases of the rotated square array. In a tube array, tubes feature their own special orientations, and most tubes show an angle of approximately 45° relative to the flow direction. Many small vortices are formed behind tubes even in a tube array with a pitch ratio of 1.28, but these vortices immediately collide with other tubes, causing large turbulences in the flow field. The critical velocities of P/d = 1.28 and P/d = 1.5 are 0.71 and 0.77 m/s, respectively (Fig. 22c–d).
Comparison of fluidelastic coefficients
f_{w} (Hz) | δ _{w} | δ _{s} | V_{c} (m/s) | K | |
---|---|---|---|---|---|
Experiment (simulation) | 16.5 | 0.075 | 0.283 | 1.06 | 4.83 |
Normal square P/d = 1.28 | 16.5 | 0.054 | 0.206 | 0.81 | 4.32 |
Normal square P/d = 1.5 | 16.8 | 0.055 | 0.203 | 0.88 | 4.65 |
Rotate square P/d = 1.28 | 16.1 | 0.048 | 0.193 | 0.71 | 4.02 |
Rotate square P/d = 1.5 | 16.4 | 0.05 | 0.193 | 0.77 | 4.27 |
Connors [32] | – | – | – | – | 9.9 |
ASME [33] | – | – | – | – | 3.3 or 2.4 |
Pettigrew and Taylor [34] | – | – | – | – | 3.3 or 3.0 |
Table 2 reveals that the K values obtained from formulas besides the Connors’ formula are smaller than the present results. The K in references is obtained by the mean value or low boundary of all published experimental data. Neither theory nor the data are sufficient to establish values of K for δ_{s} < 0.7, and a much more conservative value of K is usually chosen in this range to ensure design safety. This limitation explains why the results of this paper are generally larger than the reference values provided.
Conclusions
This paper investigated some characteristics of fluidelastic instability in square tube arrays using both experimental and numerical methods. A closely packed normal square array with a pitch ratio of 1.28 was tested under a range of flow velocities, and different ranges of tube responses were presented. A fluid–structure coupling model for fluidelastic instability was established, and calculation results were compared with experimental results. Predictions of the critical velocity and spectrum were in good agreement with the experimental findings, although poor predictions of the amplitude of tube vibrations were observed. Changes in dominant vibration direction under fluidelastic instability were observed in both the experiment and simulations. This transformation was related to changes in the vibration patterns of the whole tube system. The vibration direction of tubes in rows 2–4 pointed toward the central tube in a fully unstable tube array, which was different from the vibration pattern observed in tube arrays with a large pitch ratio. A phase lag of 180° between adjacent tubes was observed, which was consistent with the instability of the tube array; this phase lag can be used to estimate the critical velocity and only appeared when large-amplitude vibrations occur in time history. The influence of tube configuration and pitch ratio was also discussed in this paper, and the basic vibration patterns of normal and rotated square array were compared. In a normal square array, movement orbits of P/d =1.5 were more regular than those of P/d =1.28 and tubes in row vibrate in the same orientation. Tubes in a rotated square array feature special orientations, most of which showed an angle of approximately 45° relative to the flow direction. The coefficient K obtained from the Connors’ formula presented in this paper was compared with those obtained from other formulas, and the results enrich the data at δ_{s} < 0.7, especially for tube arrays with a small pitch ratio.
Notes
Acknowledgements
The authors gratefully acknowledge the support from High-performance Computing Center of Tianjin University. This work is supported by the Natural Science Foundation of China (No. 21606164).
References
- 1.Price SJ (1995) A review of theoretical-models for fluidelastic instability of cylinder arrays in cross-flow. J Fluids Struct 9(5):463–518CrossRefGoogle Scholar
- 2.Chen SS (1982) Flow induced vibration. In: Zamrik SY, Dietrich D (eds) Pressure vessel and piping: Design technology, 1982-a decade of progress. ASME, New York, pp 301–312Google Scholar
- 3.Paidoussis MP (1983) A review of flow induced vibrations in reactors and reactor components. J Nucl Eng Des 74:31–60CrossRefGoogle Scholar
- 4.Weaver DS, Fitzpatrick JA (1988) A review of cross-flow induced vibrations in heat exchanger tube arrays. J Fluids Struct 2(1):73–93CrossRefGoogle Scholar
- 5.Chen SS (1983) Instability mechanisms and stability criteria of a group of circular cylinders subjected to cross flow I: theory. J Vib Acoust Stress Reliab Des 105:51–58CrossRefGoogle Scholar
- 6.Chen SS (1983) Instability mechanisms and stability criteria of a group of circular cylinders subjected to cross flow II: numerical results and discussion. J Vib Acoust Stress Reliab Des 105:253–260CrossRefGoogle Scholar
- 7.Paidoussis MP, Price SJ (1988) The mechanisms underlying flow-induced instabilities of cylinder arrays in crossflow. J Fluid Mech 187:45–59CrossRefzbMATHGoogle Scholar
- 8.Khalifa A, Weaver D, Ziada S (2012) A single flexible tube in a rigid array as a model for fluidelastic instability in tube bundles. J Fluids Struct 34(4):14–32CrossRefGoogle Scholar
- 9.Tanaka H, Takahara S (1981) Fluid elastic vibrations of tube array in cross flow. J Sound Vib 77(1):19–37CrossRefGoogle Scholar
- 10.Tanaka H, Takahara S, Ohta K (1982) Flow-induced vibrations in tube arrays with various pitch-to-diameter ratios. ASME J Press Vessel Technol 104:168–174CrossRefGoogle Scholar
- 11.Weaver DS, Yeung HC (1983) Approach flow direction effects on the cross-flow induced vibrations of a square array of tubes. J Sound Vib 87(3):469–482CrossRefGoogle Scholar
- 12.Price SJ, Paidoussis MP (1989) The flow-induced response of a single flexible cylinder in an in-line array of rigid cylinders. J Fluids Struct 3(1):61–82CrossRefGoogle Scholar
- 13.Chen SS, Zhu S, Jendrzejczyk JA (1994) Fluid damping and fluid stiffness of a tube in crossflow. ASME J Press Vessel Technol 116(4):370–383CrossRefGoogle Scholar
- 14.Al-Kaabi SA, Khulief YA, Said SA (2009) Prediction of flow-induced vibrations in tubular heat exchangers-part II: experimental investigation. J Pressure Vessel Technol 131(1):011302CrossRefGoogle Scholar
- 15.Scott P (1987) Flow visualization of cross-flow induced vibrations in tube arrays. Dissertation, McMaster University, HamiltonGoogle Scholar
- 16.Austermann R, Popp K (1995) Stability behaviour of single flexible cylinder in a rigid array of different geometry subjected to cross flow. J Fluids Struct 9(3):303–322CrossRefGoogle Scholar
- 17.Moulinec C, Hunt JCR, Nieuwstadt FTM (2004) Disappearing wakes and dispersion in numerically simulated flows through tube bundles. Flow Turbul Combust 73:95–116CrossRefzbMATHGoogle Scholar
- 18.Moulinec C, Pourquié MJBM, Boersma BJ et al (2004) Direct numerical simulation on a Cartesian mesh of the flow through a tube bundle. Int J Comput Fluid Dyn 18(1):1–14CrossRefzbMATHGoogle Scholar
- 19.Hassan YA, Ibrahim WA (1997) Turbulence prediction in two-dimensional bundle flows using large eddy simulation. Nucl Technol J 119:11–28CrossRefGoogle Scholar
- 20.Barsamian HR, Hassan YA (1997) Large eddy simulation of turbulent crossflow in tube bundles. Nucl Eng Des J 172:103–122CrossRefGoogle Scholar
- 21.Hassan YA, Barsamian HR (1999) Turbulence simulation in tube bundle geometries using the dynamic subgrid-scale model. Nucl Technol J 128(1):58–74CrossRefGoogle Scholar
- 22.Bouris D, Bergeles G (1999) Two dimensional time dependent simulation of the subcritical flow in a staggered tube bundle using a subgrid scale model. Int J Heat Fluid Flow 20(2):105–114CrossRefGoogle Scholar
- 23.Rollet-Miet P, Laurence D, Ferziger JH (1999) LES and RANS of turbulent flow in tube bundles. Int J Heat Fluid Flow 20(3):241–254CrossRefGoogle Scholar
- 24.Benhamadouche S, Laurence D (2003) LES, coarse LES, and transient RANS comparisons on the flow across a tube bundle. Int J Heat Fluid Flow 24(4):470–479CrossRefGoogle Scholar
- 25.Liang C, Papadakis G (2007) Large eddy simulation of cross-flow through a staggered tube bundle at subcritical Reynolds number. J Fluids Struct 23(8):1215–1230CrossRefGoogle Scholar
- 26.Kevlahan NKR (2011) The role of vortex wake dynamics in the flow-induced vibration of tube arrays. J Fluids Struct 27(5–6):829–837CrossRefGoogle Scholar
- 27.Hassan M, El Bouzidi S (2012) Unsteady fluid forces and the time delay in a vibrating tube subjected to cross flow. In: Flow-induced vibration 2012, DublinGoogle Scholar
- 28.El Bouzidi S, Hassan M, Fernandez LL et al (2014). Numerical characterization of the area perturbation and time lag for a vibrating tube subjected to cross-flow. In: Proceedings of the ASME 2014 pressure vessels and piping division conference, AnaheimGoogle Scholar
- 29.Shinde V, Marcel T, Hoarau Y et al (2014) Numerical simulation of the fluid–structure interaction in a tube array under cross flow at moderate and high Reynolds number. J Fluids Struct 47(5):99–113CrossRefGoogle Scholar
- 30.Berland J, Deri E, Adobes A (2014) Large-eddy simulation of cross-flow induced vibrations of a single flexible tube in a normal square tube array. In: Proceedings of the ASME 2014 pressure vessels and piping division conference, AnaheimGoogle Scholar
- 31.Wu H, Tan W, Nie QD (2013) A numerical model for fluid-elastic instability of a square tube array. J Vib Shock 32(21):102–106Google Scholar
- 32.Connors HJ (1970) Fluidelastic vibration of tube arrays excited by cross flow. In: Proceeding of the ASME winter annual meet, vol 41, pp 93–107Google Scholar
- 33.Moore CV (1984) ASME boiler and pressure vessel code. American Society of Mechanical Engineers, New YorkGoogle Scholar
- 34.Pettigrew MJ, Taylor CE (1991) Fluidelastic instability of heat exchanger tube bundles: review and design recommendations. J Pressure Vessel Technol 113(2):242–256CrossRefGoogle Scholar
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