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Orbital motion of tube TV with 2 degrees of freedom, showing instability in the transverse direction (P/d=1.25, m r δ=26.7, U r =22.2), X 0 /d=8.6 × 10 −3 , Y 0 /d=5.9 × 10 −5 .
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A CFD methodology involving structure motion and dynamic re-meshing has been optimized and applied to simulate the unsteady flow through normal triangular cylinder arrays with one single tube undergoing either forced oscillations or self-excited oscillations due to damping-controlled fluidelastic instability. The procedure is based on 2D URANS comp...
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... Due to the large number of tubes in the heat exchanger, the cost of numerical calculation is significant, making it unrealistic to model and study the vibration of all tubes. It makes sense to reduce the number of tubes through reasonable simplification 34,35 . The three-dimensional model of the tube bundle is simplified into a (11) www.nature.com/scientificreports/ ...
A two-dimensional tube bundles fluid–structure coupling model was developed using the CFD approach, with a rigid body motion equation and the Newmark integral method. The numerical simulations were performed to determine the vibration coupling properties between various tube bundles of stiffness. Take the corner square tube bundles with a pitch ratio of 1.28 as the research object. The influence of adjacent tubes with different stiffness on the vibration of the central target tube was analyzed. The research results show that the vibration characteristic of tube bundles is affected by the flow field dominant frequency and the inherent frequency of tube bundles. The vibration of adjacent tube bundles significantly impacts the amplitude and frequency of the central target tube. The equal stiffness and large stiffness tubes upstream or downstream inhibit the vibration displacement of the target tube to some extent. The low-stiffness tubes upstream or downstream significantly enhanced the amplitude of the target tube. The findings can be used to provide a basis for reasonable design and vibration suppression of shell-and-tube heat exchangers.
... Literature review shows that the presence of large-scale oscillations in the tubes located in the final column of array. This is because the flow is uninterrupted until a new disturbance enters the channel, and there are no new disturbances in the final column of the tube (de Pedro et al., 2016). To prevent the formation of large-scale oscillations in the last column of the tube array, the side walls of the rectangular section are equipped with half tubes. ...
Purpose-The purpose of this paper is to present investigations on the significant influence of the tube material and fin density on fluid elastic instability and vortex shedding in a parallel triangular finned tube array subjected to water cross flow. Design/methodology/approach-The experiment was conducted on finned tube arrays with a fin height of 6 mm and fin density of 3 fins per inch (fpi) and 9 fpi. A dedicated setup has been developed to examine fluid elastic instability and vortex shedding. Nine parallel triangular tube arrays with a pitch to tube diameter ratio of 1.78 were considered. The plain tube arrays, coarse finned tube arrays and fine finned tube arrays each of steel, copper and aluminium materials were tested. Plain tube arrays were tested to compare the results of the finned tube arrays having an effective tube diameter same as that of the plain tube. Findings-A significant effect of fin density and tube material with a variable mass damping parameter was observed on the instability threshold. In the parallel triangular finned tube array subjected to water cross flow, a delay in the instability threshold was observed with an increase in fin density. For steel and aluminium tube arrays, the natural frequency is 9.77 Hz and 10.38 Hz, which is close to each other, whereas natural frequency of the copper tubes is 7.40 Hz. The Connors' stability constant K for steel and aluminium tube arrays is 4.78 and 4.87, respectively, whereas it is 5.76 for copper tube arrays, which increases considerably compared to aluminum and steel tube arrays. The existence of vortex shedding is confirmed by comparing experimental results with Owen's hypothesis and the Strouhal number and Reynolds number relationship. Originality/value-This paper's results contribute to understand the effect of tube materials and fin density on fluid elastic instability threshold of finned tube arrays subjected to water cross flow. Nomenclature A = Test section cross-sectional area (m 2); A g = Amplitude of vibration in terms of "g"; A m = Amplitude of vibration (mm); d i = Tube internal diameter (m); d b = Tube external diameter (m); d f = Fin diameter (m); d eff = Tube effective diameter (m); D e /D = Confinement factor; E = Young's modulus of elasticity (N/m 2); f n = Tube natural frequency in air (Hz); f w = Tube natural frequency in water (Hz); K = Connors' stability constant; m = Tube mass (kg/m); m t = Tube structural mass (kg/m); X p = Tube pitch ratio; m h = Tube hydrodynamic mass (kg/m); M r = Mass ratio; P = Pitch between the tube (m); P/D eff = Effective pitch ratio; p f = Fin pitch (mm); Q = Flow rate (m 3 /h); t f = Fin thickness (m); V f = Free stream velocity (m); V g = Gap velocity (m); V c = Critical gap velocity (m); d = Logarithmic decrement; r = Mass density of the tube (kg/m 3); r f = Mass density of the fluid (kg/m 3); a = Connors' exponential constant; and z = Damping factor.
... They concluded that the predicted critical velocity is too low with different eddy viscosity models. [6] performed URANS computations on a triangular configuration in 2D. They concluded that the predictions of the critical velocity are satisfactory with 1 and 2 degrees of freedom with an underprediction of the order of 5 to 10%, and 25 to 30%, respectively. ...
... It can be clearly observed that there was a region behind tube 2 with a large normal velocity. In conclusion, the distribution of velocities, whether lateral, streamwise, or normal, is asymmetric and does not resemble straight tube bundles (Paul et al., 2007;Pedro et al., 2016;Pettigrew et al., 2005;Shinde et al., 2018). This phenomenon occurs because the existence of a enhances the streamwise velocity of the gaps between the tubes and the coiling geometry of the tubes makes the distribution of lateral velocity more uneven. ...
... Zheng et al. [12] applied three-dimensional DNS study the fluid elastic instability of a single flexible pipe. Pedro et al. [13] studied a single elastic tube in a rigid tube bundle based on the one-way FSC method and dynamic grid technology. The unsteady flow field of self-oscillation of an equilateral triangular multicolumn array is simulated numerically by using the fluid-structure interaction [14]. ...
According to the needs generated by the industry, there is an urgent need to investigate the flow vibration response law of the elastic tube bundle of heat exchangers subjected to the coupling effect of shell and tube domain at different inlet flow velocities. In this paper, based on the continuity equation, momentum equation, turbulence model, and dynamic grid technology, the vibration response of the elastic tube bundle under the mutual induction of shell and tube fluids is studied by using pressure-velocity solver and two-way fluid-structure coupling (FSC) method. The results show that the monitoring points on the same connection block have the same vibration frequency, while the vibration amplitude is different. Monitoring point A is the most deformed by the impact of fluid in the shell and tube domain. When the inlet velocity( v shell = v tube = 0.15 , 0.4, 0.5 m/s) of shell and tube is low, the amplitude of tube bundle vibration in the Y direction is greater than that in X and Z direction, and the tube bundle produces periodic vibration in the vertical direction. The vibration equilibrium position of the tube bundle along the shell flow direction gradually moves up with the increase of the inlet velocity. The amplitude in the Y -direction of the elastic bundle decreases with the increase of shell-side and tube-side velocity. The relationship between the vibration amplitude in the Y direction and the entrance velocity is a linear function.
... The gap velocity refers to the velocity of the fluid impacting the coil tube vertically and is an important parameter in FIV analysis. In the present study, the gap velocity (i.e., the pitch velocity) in the shell-side of the straight tube bundle is defined as (de Pedro et al., 2016;Pettigrew and Taylor, 2003): ...
The coil tube bundle of Coil-wound heat exchanger (CWHE) is densely arranged, resulting in a complex flow domain in the shell. And Flow-induced vibration (FIV) is a common phenomenon in working situations where coil tubes are submerged in the oncoming flow. Understanding the flow and FIV characteristics of the shell-side plays a significant key in engineering issues, such as the design of coil tube bundle arrangements and safety verification of heat exchangers. This paper presented a detailed investigation of flow in the shell-side of the three-layer coil tube bundle with Detached eddy simulation (DES), whose validity was verified by comparison with the experimental results. Eight calculated cases of inlet flow rates from 0.01 m³/s to 0.15 m³/s with an interval of 0.02 m³/s were set up to determine that the flow domain of the shell-side is turbulent. The flow was found to form flow channels between adjacent layers, while variable eddy currents appeared around coil tubes. Subsequently, the gap transverse flow velocity was predicted and the calculation correlation was proposed. Furthermore, spectral and wavelet analyses were carried out to investigate the time-frequency data of fluctuating velocities in the flow, to bring to light vortex shedding frequencies and to capture St with respect to this tube bundle arrangement.
... Some real-life failures of heat exchanger components due to fluidelastic instability were reported in Jo and Shin (1999), Païdoussis (2006), and Blevins (2018), etc. Due to this instability's extremely destructive nature, considerable efforts have been made in this area in the last few decades. Fluidelastic instability has been extensively studied experimentally using wind/water tunnel tests (e.g., Connors, 1978;Rzentkowski and Lever, 1998;Inada et al., 2002;Meskell and Fitzpatrick, 2003;Sawadogo and Mureithi, 2014;Tan et al., 2018;Piteau et al., 2019), numerically using computational fluid dynamics simulations (e.g., Jafari and Dehkordi, 2013;de Pedro et al., 2016;Wang et al., 2019;Elbanhawy et al., 2020;Sadek et al., 2020;, and analytically using semi-analytically models (e.g., Chen, 1983;Lever and Weaver, 1986;Granger and Païdoussis, 1996;Tanaka et al., 2002;Wang et al., 2012;Li and Mureithi, 2017;Piteau et al., 2018;Jiang et al., 2019;Lai, 2019;Lai et al., 2019;Zhang and Øiseth, 2021). It is now well known that there exist at least two distinct instability mechanisms, i.e., fluidelastic damping-controlled and fluidelastic stiffness-controlled mechanisms. ...
Fluidelastic analysis of a tube array usually considers a transverse vibration mode and a streamwise vibration mode for each tube. The underlying effect of multimode coupling is often neglected. For an array of multi-span tubes with closely spaced modes exposed to nonuniform flow, the effect of multimode coupling on fluidelastic instability may be non-negligible but the effect remains unclear. To fill this gap, this paper analyzes the effect of multimode coupling on the fluidelastic instability of tube arrays in a nonuniform flow. The main purpose is to quantify the multimode coupling effect on the instability threshold and figure out conditions under which the multimode coupling effect becomes significant. Equations of motion for the fluidelastic vibrations of an array of multi-span tubes in general nonuniform flow are presented. A mode-by-mode tracing method is introduced to iteratively search for the critical mode (i.e., the mode that initiates the instability) and determine the critical flow velocity. Two case studies involving the fluidelastic analyses of different tube arrays demonstrate the effects of multimode coupling. It is concluded that the multimode coupling may affect the critical flow velocity and the vibration mode and hence the wear pattern due to fluidelastic vibrations. For the considered two case studies, the reductions of critical flow velocities due to multimode coupling can become as high as 40%. The overall effect depends on the mode that initiates the instability and the modal velocity integrals and frequency ratios of the coupling modes. For an array of flexible tubes, the multimode coupling effect on the critical flow velocity is insignificant if the tubes’ natural frequencies are perfectly tuned. However, the multimode coupling effect contributes to affect the critical flow velocity if there is a detuning between natural frequencies of respective tubes, and/or between the streamwise and transverse frequencies of every single tube. These conclusions highlight the necessity to consider the multimode coupling effect in fluidelastic analysis of tube arrays with closely spaced modes.
... A distance of 5.5 D is provided upstream of the array to the inlet boundary to allow for the free development of the flow. On the other hand, plates parallel to the flow are added downstream of the array to reduce the large-scale periodicities behind the tube array [19]. Although these periodicities may materialize behind the last row of tubes [20], they are not considered to be linked to FEI. ...
For decades, fluidelastic instability (FEI) has been known to cause dramatic mechanical failures in tube bundles. Therefore, it has been extensively studied to mitigate its catastrophic consequences. Most of these studies were conducted in controlled experiments where significant simplifications to the geometry and flow conditions were utilized. One of these simplifications is the assumption that all tubes have the same dynamic characteristics. However, in steam generators with U-bend tube configuration, the natural frequencies of tubes are nonuniform due to manufacturing tolerances and tubes' curvature in the U-bend region. Thus, this investigation aims to understand the rule of frequency variation (detuning) on FEI in two-phase flow. This includes investigating the effect of detuning on transverse and streamwise FEI for air-water mixture flow. The role of FEI damping and stiffness couplings was investigated over the entire range of air void fraction, or equivalently, the mass-damping parameter. It was found that frequency detuning could elevate the stability threshold caused by either coupling at high air void fraction in the case of transverse FEI. Furthermore, the frequency detuning had a marginal effect on the stability threshold for water flow. It was observed that the mass-damping parameter has a critical impact on FEI under detuning conditions.
... In the past decade many studies have utilized this approach for both single and twophase flows. Several studies utilized coupled computational fluid dynamics (CFD)/structural codes to directly simulate the flow-induced vibration of tube arrays (de Pedro et al., 2016;Mohany, 2012, 2016). A more pragmatic approach involved using CFD to extract the necessary parameters for any of the well-established FEI models to predict the threshold of instability (Anderson et al., 2014;de Pedro and Meskell, 2018;El Bouzidi and Hassan, 2015;Hassan et al., 2010). ...
... The downstream section also has a length of 5.5 D and is composed of channels made from baffle plates that reduce the flow periodicity downstream of the tubes. These plates were useful in obtaining a clearer time-signal of the lift and the drag forces (de Pedro et al., 2016;de Pedro and Meskell, 2018;Sadek et al., 2020). ...
The U-bend region in a typical steam generator is characterized by two-phase flow conditions and susceptible to damage due to fluidelastic instability excitation. To prevent such a destructive fluid-structure mechanism, numerous experimental and numerical works have been done to investigate, understand, and devise techniques to mitigate it. The effect of the flow approach angle on fluidelastic instability remains one of the topics which has not been fully resolved. This work aims to utilize flow numerical modeling techniques to gain an understanding of such an effect in a two-phase air-water flow. Various flow approach angles ranging from normal to parallel triangular arrays were investigated for various void fractions ranging from water to air flows. The results obtained revealed that the effect of a homogeneous air void fraction is very critical at very high values (99% and above). Moreover, at any intermediate flow approach angle between a normal and a parallel triangular array, the flow inside the array carries features of both normal and parallel triangular flow patterns. Based on this, a new FEI force-approach angle, semi analytical model is proposed to calculate the fluidelastic forces at any flow approach angle. The data obtained from this model were validated against information extracted from flow simulations and showed a good agreement.
... The half tubes as guide plates were placed along the sidewall of the test section. This helps to maintain constant pressure distribution along with the fluid flow over the tube bundle and to avoid large oscillations (de Pedro et al., 2016). This provides a constant outlet pressure along with the tube array. ...
A major cause of heat exchanger failure is fluid-elastic instability which leads to serious accidents and commercial losses. In this work, an experimentation program was carried out on a parallel triangular fin tube array pattern subjected to water crossflow. The experiment studied the effect of the fin geometry and the pitch ratio of the tube on the critical fluid velocity at which fluid-elastic instability occurs. Owing to additional surface area and increased turbulence, the increase in the number of fins on the heat exchanger tube increases the heat transfer rate affecting the fluid dynamics around the tube. As such, it is important to analyze the effect of fin height, fin pitch and tube pitch-to-diameter ratio on the instability threshold. In this paper, a total of five fully flexible tube arrays made of steel material having a length of 320 mm and an outer diameter of 19.05 mm were tested. Crimped helically wound fin tubes with coarse and fine fin density of 3fpi (8.47mm pitch) and 9 fpi (2.82mm pitch) respectively with 6mm and 3mm fin height along with plain tube were tested. Frequency response plots were recorded for the gradual increase in the water flow rate for each type of array. The experimental results obtained show that the critical velocity at which fluid-elastic instability occurs is greatly affected by fin pitch density and fin height. The finned tube results fit within the scatter of the existing data for fluid-elastic instability and the Karman vortex shedding occurred before the occurrence of instability in the tube array. By using the measured values of the shedding frequency of the vortex, gap velocity and the equivalent diameter, the Strouhal number
