In numerical simulations of hydroturbine systems, the fluid in the draft tube keeps alternating between the free surface flow condition and the pressured flow condition. This combination of free surface flow model and pressured flow model has been a focus of researchers. Because of the huge difference in pressure wave speed, the two models differ much in terms of meshing even in the same method. To track the interaction point between free surface flow and pressured flow, a type of interaction point tracking method (IPTM) is proposed, which is based on the method of characteristics. Using a controllable iteration to solve the controlling equations of the boundary conditions, the concrete interaction point can be tracked accurately at each time-step. The method is validated in an actual turbine draft tube and compared with experimentally measured data. The results show that IPTM is equipped with high reliability and offers some advantages compared to the other existing methods.

This paper describes a test program that was developed to measure the dynamic response of a bundle of steam generator U-tubes with anti-vibration bar (AVB) supports, subjected to Freon two-phase cross-flow. The tube bundle geometry is similar to the geometry used in preliminary designs for future CANDU steam generators. This test program is one of the initiatives that Atomic Energy of Canada Limited (AECL) is undertaking to demonstrate that the tube support design for future CANDU steam generators meets the stringent requirements associated with a 60-year lifetime. In particular, the tests will address issues related to in- and out-of-plane fluidelastic instability and random turbulent excitation of a U-tube bundle with AVB supports. Therefore, the measurements include tube vibration amplitudes and frequencies, work-rate due to impacting and sliding motion of the tubes against their supports, bulk process conditions and local two-phase flow properties. Details of the test rig setup and the measurement techniques are described in the paper. Moreover, a numerical prediction of the U-tube vibration response to flow was performed with AECL’s pipo-fe code. A summary of the numerical results is presented.

Predictive computations of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation have been the subject of active research. Nevertheless, experimental results are still necessary for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting relevant information from the actual vibratory response data. Although at the present time such analysis is overambitious, as far as the multisupported tube bundles of real-life components are concerned, the same instrumentation difficulties frequently apply in the case of laboratory test rigs. Therefore, the subject of this paper is of practical significance even in the more modest realm of laboratory experiments. The knowledge of the dynamical contact/impact (vibro-impact) forces is of paramount significance, and also the tube/support gaps. Following our previous studies in this area using wave-propagation techniques (De Araújo et al., 1998; Antunes et al., 1998; Paulino et al., 1999), we recently applied modal methods for extracting such information. Based on numerically simulated time-domain vibro-impact responses, the dynamical support forces, as well as the vibratory responses at the support locations, were identified from one or several vibratory responses at remote locations, from which the support gaps could also be inferred (Delaune et al., 2010). Also recently, for the related problem of friction force identification on bowed strings, preliminary experiments have shown the feasibility of these identification techniques (Debut et al., 2010). In the present paper, the modal identification techniques developed by Delaune et al. (2010) and Debut et al. (2010) are tested using an experimental rig built at Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA/Saclay), consisting of a randomly excited clamped-free beam which impacts on an intermediate gap-support. Identification of the impact force, as well as of the beam motion at the gap-support, is achieved based on remote measurements of the beam response provided by two accelerometers. A significant feature of the experimental identifications presented in this paper is that, beyond the results obtained under a point-force shaker excitation, we test here an original technique to identify the gap-supported reactions in flow-excited systems, which was recently introduced by Delaune et al. (2010). As for most inverse problems, the identification results may prove sensitive to both noise and modeling errors. Therefore, regularization techniques discussed by Delaune et al. (2010) are used to mitigate the effects of unmeasured noise perturbations. Overall, the experimentally identified results compare reasonably well with the measured contact forces and motions at the gap-supports. Actually, even if our identifications are not immaculate at the present time, they remain nevertheless quite usable.

The aim of the present study is to predict the impact force applied by an individual transient liquid slug on an elbow at the end of a horizontal and initially empty pipeline. The liquid slug is driven by pressurized air in a tank located upstream of the pipeline. The time dependent pressure distribution along the elbow and a vertical extension segment after the elbow are solved with a 1D numerical approach along a curved line mesh. An assumed and calibrated axial turbulent velocity profile function with 3D skewed shape for the slug is also used in the solution. The impact pressures and the transient forces at the elbow are computed and also compared with those obtained experimentally and numerically from previous studies. Comparisons indicate that the new method developed in the present study predict the peak pressures and/or forces with higher accuracy than the previous method proposed by other researchers.

This paper is the second part of the two-part review article presenting an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers were described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes were discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations were considered. The first part was closed by conclusions highlighting resolved and nonresolved controversies reported in the literature. The second part will address the problem of fluidelastic instability in single- and two-phase flows and fretting wear in process equipment, such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluidelastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting-wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.

An experimental program was conducted to examine fluidelastic instability in in-line and rotated square finned tube arrays. Three arrays of each geometry type were studied: two with serrated, helically wound finned tubes of different fin densities and the third is a bare tube, which had the same base diameter as the finned tubes. The finned tubes under consideration were commercial finned tubes of a type typically used in the fossil and process industries. The addition of fins to tubes in heat exchangers enhances heat transfer due to the increased surface area and the turbulence produced by the flow moving over the fins. The resulting flow pattern/distribution due to the fins is, therefore, more complex than in bare tube arrays. Previous research has shown that an effective diameter of a finned tube is useful in the prediction of vortex shedding. This concept is used to compare the finned tube results with the existing bare tube array guidelines for fluidelastic instability. All of the tube arrays in the present study have the same tube pitch and have been scaled to have the same mass ratio. The results for rotated square arrays suggest that the use of an effective diameter is beneficial in the scaling of fluidelastic instability and the finned tube results are found to fit within the scatter of the existing data for fluidelastic instability. For in-line square arrays, the results indicate that fins significantly increase the stability threshold. An earlier version of this paper appeared at the ASME 2007 PVP Division Conference, PVP2007-26597.

In operating shell-and-tube heat exchangers, tube vibration induced by cross-flow can be a serious problem. The region of concern in steam generators is the upper most U-bend region where the flow crosses a large number of tubes, which also cause significant hydraulic resistance. This hydraulic resistance forces the flow to change direction. From a fluidelastic instability point of view, the tube bundle is excited by oblique cross-flow. A secondary consequence of change in flow direction is a change in the flexibility direction of the tubes relative to the oncoming flow direction at different locations within the U-bend region. It is this somewhat simpler problem that is studied in this work. The effect of array flexibility direction on the fluidelastic instability phenomenon in a rotated-triangular tube bundle is investigated for single phase flow as a starting point. The study consists of both experiments and theoretical analysis of a simplified single-flexible-tube array. Experimental tests are conducted in a wind tunnel on a reconfigurable tube bundle. The results show that fluidelastic instability is strongly dependent on the flexibility angle. The results also show that, generally, the elimination of bundle flexibility in the direction transverse to the flow has a strong stabilizing effect on the tube bundle. The effect is, however, nonlinearly related to flexibility angle. In the second part of this work, the quasi-steady fluidelastic analysis is adapted for a single tube (within a rigid array), flexible in a single but arbitrary direction relative to the flow and subjected to cross-flow. The fluid-force expressions are rewritten to account for an arbitrary tube flexibility direction relative to the approaching flow. In the process, a simplified, flexibility direction dependent, one degree-of-freedom equation is obtained. The model is then evaluated against measured experimental data. This evaluation shows that the predicted critical flow velocity for fluidelastic instability is in qualitative agreement with experimental results, at least in the trend on the effect of varying the flexibility angle. At the same time, the model sheds some light on the role played by the flexibility angle in determining the overall fluid-structure damping underlying the observed stability behavior.

Acoustic resonance or acoustic vibration, which develops in flow channels containing a tube bank, is caused by vortex shedding generated by crossflow over the tube bank. Transverse acoustic modes are excited, which are perpendicular to the direction of flow and of the tube axes. For the excitation of the acoustic modes resulting in acoustic resonance, two conditions must be met: (a) The frequency of vortex shedding must coincide with the frequency of the particular acoustic mode to be excited, and (b) there must be sufficient energy available to initiate the vibration. If the frequency coincidence is not satisfied or if the excitation energy is insufficient, the acoustic resonance will not be possible. It is important to define the criteria, which need to be met for the initiation of the acoustic resonance. In this paper, new criteria are developed on the basis of the acoustic particle velocity for the onset of acoustic resonance in steam generator and tubular heat exchanger tube banks.

This study investigates unsteady flow in tube bundles and fluid forces, which can lead to large tube vibration amplitudes, in particular, amplitudes associated with fluidelastic instability (FEI). The fluidelastic forces are approximated by the coupling of the unsteady flow model (UFM) with computational fluid dynamics (CFD). The CFD model employed solves the Reynolds averaged Navier–Stokes equations for unsteady turbulent flow and is cast in an arbitrary Lagrangian–Eulerian form to handle any motion associated with tubes. The CFD solution provides time domain forces that are used to calculate added damping and stiffness coefficients employed with the UFM. The investigation demonstrates that the UFM utilized in conjunction with CFD is a viable approach for calculating the stability map for a given tube array. The FEI was predicted for in-line square and normal triangle tube arrays over a mass damping parameter range of 0.1– 100. The effect of the P / d ratio and the Reynolds number on the FEI threshold was also investigated.

Two-phase flow occurs in many situations in industry. Under certain circumstances, it can be a source of flow-induced vibrations. The forces generated can be sufficiently large to affect the performance or efficiency of an industrial device. In the worst-case scenario, the mechanical forces that arise may endanger structural integrity. Thus, it is important to take these forces into account in designing industrial machinery to avoid problems during operation. Although the occurrence of such forces is well known, not much is known about their magnitudes because, unfortunately, the amount of experimental data available in literature are rather limited. This paper describes the experiments performed to measure forces in 6 mm diameter tubing containing a bend. Experiments are performed on bends of different radii, with the bend positioned horizontally or vertically. The experimental results are analyzed based on flow regime and bend configuration. A comparison with available experimental results for bigger internal pipe diameter shows a general good agreement. To improve future predictions, a simple model based on momentum exchange is proposed to estimate the forces generated by multiphase flow. The proposed model shows a good agreement with the experimental data.

The offshore oil and gas industry uses corrugated pipes because of their flexibility. Gas flowing within these pipes interacts with the corrugations and generates noise. This noise is of concern because it is of sufficient amplitude to cause pipework vibration with the threat of fatigue and pipe breakages. This paper examines the conditions that give rise to the large noise levels. These conditions, for the occurrence of noise, are investigated using an eigenvalue approach, which involves the effect of damping due to losses from the pipe boundaries and pipe friction. The investigation is conducted in terms of reflection conditions and shows why only few of the very many possible natural frequencies are selected. The conditions for maximum noise response are also investigated by means of a nonlinear model of vortex shedding. Here, an approach is developed in which the net power generated by each wavelength is calculated.

This two-part review article presents an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis, and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers are described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes will be discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations are considered. This part will be closed by conclusions highlighting resolved and nonresolved controversies reported in literature. The second part will address the problem of fluid-elastic instability in single- and two-phase flows and fretting wear in process equipment such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluid-elastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.

Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, experimental results are still very important, for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information that is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this area using wave-propagation techniques ( De Araújo, Antunes, and Piteau, 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 1—Basic Theory and Experiments,” J. Sound Vib., 215, pp. 1015–1041 ; Antunes, Paulino, and Piteau, 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 2—Complex Vibro-Impact Motions,” J. Sound Vib., 215, pp. 1043–1064 ; Paulino, Antunes, and Izquierdo, 1999, “Remote Identification of Impact Forces on Loosely Supported Tubes: Analysis of Multi-Supported Systems,” ASME J. Pressure Vessel Technol., 121, pp. 61–70 ), we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results may prove quite sensitive to noise and modeling errors. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of nonmeasured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The extensive identification results presented are based on realistic numerical simulations of gap-supported tubes subjected to flow turbulence excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is thoroughly addressed elsewhere ( Debut, Delaune, and Antunes, 2009, “Identification of Nonlinear Interaction Forces Acting on Continuous Systems Using Remote Measurements of the Vibratory Responses,” Proceedings of the Seventh EUROMECH Solids Mechanics Conference (ESMC2009), Lisbon, Portugal, Sept. 7–11 ). Nevertheless, identifications are performed in this paper based on both the exact modes and also on randomly perturbed modal parameters. Our results show that, for the system addressed here, deterioration of the identifications is moderate when realistic errors are introduced in the modal parameters. In all cases, the identified results compare reasonably well with the real contact forces and motions at the gap-supports.

We experimentally studied the propagation of coupled fluid stress waves and tube flexural waves generated through projectile impact along the axis of a water-filled tube. We tested mild steel tubes, 38–40 mm inner diameter and wall thicknesses of 0.8 mm, 6.4 mm, and 12.7 mm. A steel impactor was accelerated using an air cannon and struck a polycarbonate buffer placed on top of the water surface within the tube. Elastic flexural waves were observed for impact speeds of 5–10 m/s and plastic waves appeared for impact speeds approaching 20 m/s for a 0.8 mm thickness tube. We observed primary wave speeds of 1100 m/s in a 0.8 mm thickness tube, increasing to the water sound speed with 6.4 mm and 12.7 mm thickness tubes. Comparison of our measurements in the 0.8 mm thickness tube with Skalak’s water hammer theory indicates reasonable agreement between the predicted and measured peak strains as a function of the impact buffer speed ( 1956, “An Extension to the Theory of Water Hammer,” Trans. ASME, 78, pp. 105–116 ). For thick-walled tubes, the correlation between the experimentally determined peak pressures and strains reveals the importance of corrections for the through-wall stress distribution.

Temperature gradients in the thermally stratified fluid flowing through a pipe may cause undesirable excessive thermal stresses at the pipe wall in the axial, circumferential, and radial directions, which can eventually lead to damages such as deformation, support failure, thermal fatigue, cracking, etc., to the piping systems. Several nuclear power plants have so far experienced such unwelcome mechanical damages to the pressurizer surgeline, feedwater nozzle, high pressure safety injection lines, or residual heat removal lines at a pressurized water reactor (PWR). In this regard, determining with accuracy the transient temperature distributions in the wall of a piping system subjected to internally thermal stratification is the essential prerequisite for the assessment of the structural integrity of such a piping system. In this study, to realistically predict the transient temperature distributions in the wall of an actual PWR pressurizer surgeline with a complex geometry of three-dimensionally bent piping, three-dimensional transient computational fluid dynamics (CFD) calculations involving the conjugate heat transfer analysis are performed for the PWR pressurizer surgeline subjected to either out- or in-surge flows using a commercial CFD code. In addition, the wall temperature distributions obtained by taking into account the existence of wall thickness are compared with those by neglecting it to identify some requirements for a realistic and conservative thermal analysis from a safety viewpoint.

Erosion-corrosion failures frequently found in piping systems can lead to the leakage of pipes, or even damage of the whole system. Erosion-corrosion is a form of material degradation that involves electrochemical corrosion and mechanical wear processes encountered on the surface of metal pipes. Fluid-structure interactions have a profound influence on such erosion-corrosion phenomena. This paper is focused on the multiphase flow-induced erosion-corrosion phenomena in pipes, with multiscale analysis, to study the interactions between the flow and the protective film inside the piping system. The shear stress and the pressure of the flow in a pipe with a step were first obtained using a multiphase flow dynamic analysis. The erosion-corrosion rules of the pipes under the multiphase flow were then summarized. Using the microscale flow simulation method, the fluid-structure interaction between the flow and the protective film at the critical position was modeled. The deformation of the protective films was shown to vary with the flow velocity and the corresponding flow regime. According to the simulation results of the fluid-structure interaction, the location, rate, and extent of the erosion-corrosion on pipe surfaces can be predicted. The prediction was also proven by actual instances. Moreover, the method can be used in optimizing the design of the inner sleeves of pipes.

This paper presents the results of a test series to study the vibration behavior of a normal triangular tube bundle subjected to two-phase Freon cross flow. A normal triangular tube bundle of pitch over diameter ratio of 1.5 was tested over a broad range of void fractions and mass fluxes. Fluidelastic instabilities, random turbulence excitation, and damping were investigated. The results were compared with those obtained for a similar tube bundle tested in an air-water cross flow and to those for a rotated triangular bundle similarly tested in Freon.

The flow-acoustic coupling mechanism in a T -junction, which combines flows from two branches, forming the “cross-bar” of the T -junction, into one pipe, forming the “stem” of the T -junction, is investigated experimentally. The T -junction has a step pipe expansion at its inlets. The shear layer separating from this step expansion is found to excite intense acoustic resonances over multiple ranges of flow velocity. The excited acoustic mode is confined to the branch pipes and has an acoustic pressure node at the centerline of the T -junction. The length of the expansion section of the T -junction is found to control the frequency of the shear layer oscillation and therefore determines the ranges of flow velocity over which acoustic resonances are excited. Introducing asymmetry in the T -junction expansion length has shown little influence on the excitation of acoustic resonance. An additional T -junction arrangement made of rectangular cross-sectional ducts is also investigated to facilitate a flow visualization study of unsteady flow structures in the T -junction during acoustic resonance, and thereby improve understanding of the acoustic resonance mechanism and the nature of the aero-acoustic sources in the T -junction.

Fluid-elastic instability characteristics of a U-tube bundle were experimentally investigated in air-water two-phase flow. A total of 39 U-tubes were arranged in a rotated square array with a pitch-to-diameter ratio of 1.633. Vibration responses of four U-tubes were measured with three-axis accelerometers. Two sets of experiments were performed to investigate the onset of fluid-elastic instability, and the damping and hydrodynamic mass of the U-tube. The experiments were performed for a void fraction of 70–95%. Fluid-elastic instability was clearly observed in an out-of-plane mode vibration. The effect of a primary side flow on the vibration of U-tube was investigated separately. The damping ratio of the present U-tube was higher than the damping ratio of the cantilever tubes in the literature. The hydrodynamic mass of the U-tube was generally in accordance with the hydrodynamic mass of the cantilever tubes in the literature. The instability constant ( K ) of the Connors equation was assessed with a simplified effective gap velocity, and the fluid-elastic instability constant was 8.5.

A parametric study has been performed to investigate the effect of cylinder diameter on the acoustic resonance mechanism of two tandem cylinders exposed to cross-flow in a duct. Three spacing ratios corresponding to different flow regimes inside the “proximity interference” region are considered, L ∕ D = 1.5 , 1.75, and 2.5, where L is the spacing between the cylinders and D is the diameter. For each spacing ratio, six cylinder diameters in the range of D = 7.6 – 27.5 mm have been tested. For small diameter cylinders, the acoustic resonance mechanism of the tandem cylinders seems to be similar to that observed for single cylinders; i.e., it occurs near frequency coincidence as the vortex shedding frequency approaches that of an acoustic resonance mode. However, for larger diameter cylinders, the resonance of a given acoustic mode occurs over two different ranges of flow velocity. The first resonance range, the precoincidence resonance, occurs at flow velocities much lower than that of frequency coincidence. The second resonance range, the coincidence resonance, is similar to that observed for single and small diameter tandem cylinders. Interestingly, the observed precoincidence resonance phenomenon is similar to the acoustic resonance mechanism of in-line tube bundles. It is shown that increasing the diameter of the tandem cylinders affects several flow parameters such that the system becomes more susceptible to the precoincidence resonance phenomenon. The occurrence and the intensity of the precoincidence resonance are therefore strongly dependent on the diameter of the cylinders.