U-bend Region Research Articles

Investigations of In-Plane Fluidelastic Instability in a Multispan U-Bend Tube Array—Part I: Tests in Air Flow

Abstract The tubes in the U-bend region of a recirculating type of nuclear steam generator are subjected to cross-flow of a two-phase mixture of steam and water. There is a concern that these tubes may experience flow-induced vibration, including the damaging effects of fluidelastic instability. This two-part series of papers presents the results of flow-induced vibration experiments performed by Canadian Nuclear Laboratories for the Electric Power Research Institute (EPRI) using the Multi-Span U-Bend test rig. The tube bundle is made of 22 U-bend tubes of 12.7 mm (0.5 in.) diameter, arranged in a rotated triangular configuration with a pitch-to-diameter ratio of 1.5. The test rig was equipped with variable clearance flat bar supports at two different locations to investigate a variety of tube and flat-bar support configurations. The primary purpose of the overall project was to study the occurrence of in-plane (or streamwise) fluidelastic instability in a U-tube bundle with flat-bar tube supports with clearances or preloads. Initially, the test rig was configured for tests in air-flow using an industrial air blower. Then tests with two-phase refrigerant (R-134a) were performed. Part I of this two-part series describes the test rig, experimental setup and some of the challenges encountered, and the results of experiments with air flows. Part II will present results of tests using refrigerant two-phase flows.

Experimental and Numerical Study on Flow-Induced Vibration of PWR Steam Generator U-Tubes

The flow-induced vibration (FIV) of steam generators (SGs) in pressurized water reactors (PWRs) is a significant problem in the design process. This problem contains issues such as two-phase flow, nonlinear dynamics and fretting wear. In this paper, an experimental setup was established to study the FIV of a newly designed U-tube SG. Numerical simulations, including computational fluid dynamics (CFD) and vibration studies were performed to reveal the detailed mechanisms of FIV. To study the U-bend region of the tube bundles, the experiments were carried out under 23 experimental conditions containing void fractions of 70%, 80%, 90 and 95%. The flow fields of the tested model in each condition were calculated to reveal the causes of the vibration phenomenon, and the vibration results were calculated through structure dynamics. The experimental results showed that the vibration amplitudes of the U-tube increased with increasing inlet velocity, flow rate and bending radius. It decreased with increasing void fraction under the same inlet velocity, while it increased with increasing void fraction under the same flow rate. Along with the out-of-plane vibration, the in-plane vibration also featured high amplitude vibration of the U-tubes due to lack of support by the anti-vibration bars (AVBs). The simulation results show the same variation trends of the vibration responses as the above experiments. The prototype SG can be fluid-elastic stable in given working conditions, and the main vibration mechanism of this model is turbulence buffeting. The experiment and simulation methods and data can be used in the design process of new SGs similar to this prototype.

Migration–deposition coupling characteristics and influence of corrosion products on heat transfer in steam generators

• A coupled model of impurity migration-deposition considering boiling is developed. • A critical time step is proposed to realize the simulation time to the real scale. • The whole lifetime fouling characteristics are predicted in steam generators. • The effects of fouling on heat transfer of steam generator is investigated. Fouling on tube surfaces degrades the heat transfer characteristics of heat exchangers. The objective of this study was to predict the distribution of deposits on the surface of heat transfer tubes and assess its influence on heat transfer characteristics. For this purpose, a comprehensive model of impurity migration and deposition, which considered deposition and removal processes under boiling conditions, was established to simulate the fouling characteristics of steam generators. A critical time step was determined to solve the problems at a large time-scale span between the fluid flow and long-term deposition time in actual operation. Then, the deposit distribution was used to propose a fouling thermal resistance model based on the Maxwell model to study the influence of fouling on the heat transfer performance of steam generators. The results showed that the corrosion products were mainly deposited on the hot side and in the U-bend region. The deposition rate on the hot side gradually decreased with time, whereas the deposition mass on the cold side linearly increased with time. Fouling had an evident effect on the overall heat transfer efficiency and distribution of steam generators. This study is relevant for the prediction of operating conditions during the life cycle of heat exchangers in industry.

The Flow-Structure Couplings of Fluidelastic Instability and the Effect of Frequency Detuning in Triangular Tube Bundles Subjected to a Two-Phase Flow

Abstract 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.

The prediction of fluidelastic forces in triangular tube bundles subjected to a two-phase flow: The effect of the flow approach angle

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.

In-Plane Fluidelastic Instability Evaluation of Triangular Array Tube Bundle Using Fluid Force Measured Under Steam–Water Two-Phase Flow Condition

Abstract Recently, tube-to-tube wear indications of triangular tube bundle steam generators (SGs) caused by fluidelastic instability (FEI) in the in-plane direction of U-bend region (in-plane FEI) have been reported. Several experiments were conducted to investigate the characteristics of in-plane FEI by our research groups. In a series of experiments, particular characteristics of in-plane FEI were found. For example, there are the critical velocity difference between the in-plane and the out-of-plane directions, the difference between straight tube bundle tests and U-bend tube bundle tests, etc. To explain these characteristics, unsteady fluid force acting on tubes were measured. The experimental investigation was conducted under high temperature and high-pressure steam–water flow conditions close to the SGs. Stability analyses were conducted using the measured unsteady fluid forces as inputs. First, stability analyses were done to simulate straight tube bundle tests. Analysis results agreed well with experiments and it could explain the effect on critical velocity trend by number of flexible tubes and directions of vibration. Second, U-tube stability analyses were performed by applying unsteady fluid force coefficients for each location of U-bend tube finite element method (FEM) model. From the results, mechanisms of in-plane FEI were understood.

Numerical simulation of the effects of trefoil tube support plates on the flow and heat transfer characteristics of a steam generator

A three-dimensional coupled model of heat transfer tube and trefoil tube support plate (TSP) is developed based on a full-size steam generator (SG). The CFX thermal phase change model is adopted to numerically investigate the flow and heat transfer behaviors of the secondary side fluid. And the effects of trefoil TSPs and inlet subcooling on the thermal-hydraulic characteristics of tube bundle are obtained. The calculation model reasonably reveals the distributions of the flow and heat transfer parameters in the SG, especially in trefoil TSP regions. Based on the across flow velocity and density of the secondary side fluid in U-bend region, the most severe flow-induced vibration damage is predicted at the angles of 110° on the hot leg and 60° on the cold leg, respectively. Due to the effects of trefoil TSPs, vortexes are induced, the outer wall temperature in the circumferential direction shows periodic characteristic in TSP regions, which increases the possibility of aggressive solutes deposition and U-tubes rupture. In addition, inlet subcooling of the secondary side fluid has significant effects on the SG. As inlet subcooling decreases, the heat transfer is enhanced. The numerical simulation results obtained may provide guidance to facilitate the optimal design and in-depth thermal-hydraulic analysis of TSPs and SGs.

Numerical investigation of the thermal-hydraulic characteristics of AP1000 steam generator U-tubes

Steam generators (SGs) are vital heat exchangers that connect the primary and secondary sides in power plant systems. Based on the AP1000 SG, a numerical model of SG U-tubes is developed. The interior flow and heat transfer behaviors of the SG are simulated using CFX thermal phase change model. The numerical model reasonably predicts the distributions of the thermal-hydraulic behaviors, including the velocity, temperature, steam quality, void fraction and heat transfer coefficient. The slip-ratio of the secondary side increases and then decreases slowly along the axial direction. The simulated heat transfer coefficient agrees with the calculation of the Rohsenow formula. The most serious flow-induced vibration (FIV) damage is expected at the angles of θ = 60° in cold leg and θ = 110° in hot leg according to the fluid density and velocity of the secondary side in U-bend region, and the simulated results agree with the drift-flux model. The current simulation results may provide useful technical information for the optimal structural design of SGs.

Prediction of Streamwise Fluidelastic Instability of a Tube Array in Two-Phase Flow and Effect of Frequency Detuning

Experimental measurements of the steady forces on a central cluster of tubes in a rotated triangular array (P/D=1.5) subjected to two-phase air–water cross-flow have been conducted. The tests were done for a series of void fractions and a Reynolds number (based on the pitch velocity), Re=7.2×104. The forces obtained and their derivatives with respect to the static streamwise displacement of the central tube in the cluster were then used to perform a quasi-steady fluidelastic instability analysis. The predicted instability velocities were found to be in good agreement with the dynamic stability tests. Since the effect of the time delay was ignored, the analysis confirmed the predominance of the stiffness-controlled mechanism in causing streamwise fluidelastic instability. The effect of frequency detuning on the streamwise fluidelastic instability threshold was also explored. It was found that frequency detuning has, in general, a stabilizing effect. However, for a large initial variance in a population of frequencies (e.g., σ2=7.84), a smaller sample drawn from the larger population may have lower or higher variance resulting in a large scatter in possible values of the stability constant, K, some even lower than the average (tuned) case. Frequency detuning clearly has important implications for streamwise fluidelastic instability in the steam generator U-bend region where in-plane boundary conditions, due to preload and contact friction variance, are poorly defined. The present analysis has, in particular, demonstrated the potential of the quasi-steady model in predicting streamwise fluidelastic instability threshold in tube arrays subjected to two-phase cross-flows.

Evaluation of the Integrity of Steam Generator Tubes Subjected to Flow Induced Vibrations

Flow-induced vibrations (FIV) continue to affect the operations of nuclear power plant components such as heat exchanger tube bundles. The negative effect of FIV is in the form of tube fatigue, cracking, and fretting wear at the supports. Fretting wear at the supports is the result of tube/support impact and friction. Fluidelastic and turbulence forces are the two main excitation mechanisms that feed energy into the system causing these violent vibrations. To minimize this effect all support clearances must be kept at a very small value. This paper investigates the consequences of losing the effectiveness of a particular support as a result of corrosion or excessive fretting wear. A full U-bend tube subjected to both fluidelastic and turbulence forces is utilized in this work. The performance of countermeasures such as the installation of additional flat bars in the U-bend region is thoroughly investigated. The investigation utilized both deterministic and probabilistic techniques.

Study on secondary side flow of steam generator with coupled heat transfer from primary to secondary side

Thermohydraulics characteristics in the secondary side of AP1000 steam generator (SG) are simulated based on the porous media models. The drift flux two-phase flow model coupled with a simplified flow boiling model is utilized. The heat transfer from primary side fluid to secondary side fluid is calculated three-dimensionally during iterations. The resistances caused by downcomer, tube bundle, support plates and primary separators are considered. Three-dimensional distributions of velocity, temperature, pressure, enthalpy, density, void fraction and flow vapor quality are obtained from the calculation by using the CFD code ANSYS FLUENT. Flow-induced vibration (FIV) damage is analyzed based on the cross flow velocity over the U-bend region of the outmost U-tube. The most severe FIV damages occur at the angles of −0.544 rad on the cold side and 0.353 rad on the hot side with maximum cross flow energies of 1145.2 J/m3 and 658.9 J/m3, respectively. Fouling is expected to deposit at the bottom of tube bundle since the velocity there is close to zero. The flow vapor qualities of mixture flowing into separators vary from each other significantly, with the maximum and minimum flow vapor quality in separators of 0.659 and 0.073, which is a severe challenge to the capacity design of separators.

Numerical investigation of thermal–hydraulic characteristics in a steam generator using a coupled primary and secondary side heat transfer model

A coupled primary and secondary side heat transfer and thermal phase change model is used to investigate the thermal–hydraulic characteristics of a steam generator (SG) at Daya Bay Nuclear Power Plant (DBNPP). The simulation results reasonably reveal the ununiform boiling behavior in the secondary hot and cold legs. Vapor velocity is slightly higher than that of water and the corresponding slip-ratio first increases rapidly before gradually decreasing in the secondary hot leg and cold leg regions, a result which agrees with predictions using the drift-flux model. Cross-flow energy, which accounts for flow-induced vibration (FIV) at the U-bend tubes, is determined with the aid of localized thermal–hydraulic distributions, and the resulting FIV damage is predicted to be most severe at 0.35m on the cold leg side and −0.2m on the hot leg side of the U-bend region, respectively. These FIV damage predictions agree with measured plant data for the prototypical SG, showing that this model can provide the use information to improve thermal–hydraulic characteristics and help alleviate FIV damage in a SG.

Test Results of a 100 kA NbTi CICC

For the secondary winding of the flux pump (super- conducting transformer) of the EDIPO test facility at CRPP Villigen, a NbTi cable-in-conduit conductor (CICC) was designed at CRPP and procured at the industry. From a left section of the CICC a SULTAN sample, nicknamed TRASEK, has been assembled and tested. In the conductor design, high Cu:non-Cu ratio in the strand (no copper segregation), low void fraction and SnAg5 coating of the strand surface are selected to allow smooth current redistribution and enhance the take-off voltage. The DC tests are carried out be- fore and after solder filling the sample termination and current sharing is observed up to 80 kA. Eventually, the DC conductor performance is limited by the self field of the sample in the U-bend region. In normal operation, the secondary coil of the transformer is not exposed to significant magnetic field sweeps. The AC loss is expected to be large according to the design choices (tin coating, low void fraction). The AC loss characterization in SULTAN includes over 400 load cycles. The pressure drop vs. mass flow rate is measured in SULTAN to complement the data base for friction factor of CICC's.

Effect of Preferential Flexibility Direction on Fluidelastic Instability of a Rotated Triangular Tube Bundle

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.

Prediction of Fretting Wear Depth for Steam Generator Tubes Based on Various Types of Wear Scars

Calculations of fretting wear depth due to the turbulence excitation around steam generator tubes, for various wear scars, are carried out numerically. Four typical wear topologies, namely, round-, crescent-, flat-, and oblique-shaped wear scars, are adopted to represent the configuration of the wear volume. Oblique wear shows the most severe case for the wear time history, whereas both round- and crescentshaped wears have smaller increasing rates of wear histories than flat- or oblique-shaped wears. It can be estimated that a high cross flow, around the U-bend region of the steam generator tube, significantly enhances the wear phenomena because the basic wear scar, at the contact point between the tube and its support, is flat or oblique. Parametric studies on the inclined angle and radial clearance are also carried out for oblique and crescent wear shapes.

EFFECTS OF SUPPORT STRUCTURE CHANGES ON FLOW-INDUCED VIBRATION CHARACTERISTICS OF STEAM GENERATOR TUBES

Fluid-elastic instability and turbulence-induced vibration of steam generator U-tubes of a nuclear power plant are studied numerically to investigate the effect of design changes of support structures in the upper region of the tubes. Two steam generator models, Model A and Model B, are considered in this study. The main design features of both models are identical except for the conditions of vertical and horizontal support bars. The location and number of vertical and horizontal support bars at the middle of the U-bend region in Model A differs from that of Model B. The stability ratio and the amplitude of turbulence-induced vibration are calculated by a computer program based on the ASME code. The mode shape with a large modal displacement at the upper region of the U-tube is the key parameter related to the fretting wear between the tube and its support structures, such as vertical, horizontal, and diagonal support bars. Therefore, the location and the number of vertical and horizontal support bars have a great influence on the fretting wear mechanism. The variation in the stability ratios for each vibrational mode is compared with respect to Model A and Model B. Even though both models satisfy the design criteria, Model A shows substantial improvements over Model B, particularly in terms of having greater amplitude margins in the turbulence-excited vibration (especially at the inner region of the tube bundle) and better stability ratios for the fluid-elastic instability.

Prediction of Fretting Wear Depth for Steam Generator Tubes Based on Various Types of Wear Scars

Calculations of fretting wear depth due to the turbulence excitation around steam generator tubes, for various wear scars, are carried out numerically. Four typical wear topologies, namely, round-, crescent-, flat-, and oblique-shaped wear scars, are adopted to represent the configuration of the wear volume. Oblique wear shows the most severe case for the wear time history, whereas both round- and crescentshaped wears have smaller increasing rates of wear histories than flat- or oblique-shaped wears. It can be estimated that a high cross flow, around the U-bend region of the steam generator tube, significantly enhances the wear phenomena because the basic wear scar, at the contact point between the tube and its support, is flat or oblique. Parametric studies on the inclined angle and radial clearance are also carried out for oblique and crescent wear shapes.

Two-Phase Flow-Induced Vibration of Parallel Triangular Tube Arrays With Asymmetric Support Stiffness

Laboratory experiments were conducted to determine the flow-induced vibration response and fluidelastic instability threshold of model heat exchanger tube bundles subjected to a cross-flow of refrigerant 11. Tube bundles were specially built with tubes cantilever-mounted on rectangular brass support bars so that the stiffness in the streamwise direction was about double that in the transverse direction. This was designed to simulate the tube dynamics in the U-bend region of a recirculating-type nuclear steam generator. Three model tube bundles were studied, one with a pitch ratio of 1.49 and two with a smaller pitch ratio of 1.33. The primary intent of the research was to improve our understanding of the flow-induced vibrations of heat exchanger tube arrays subjected to two-phase cross-flow. Of particular concern was to compare the effect of the asymmetric stiffness on the fluidelastic stability threshold with that of axisymmetric stiffness arrays tested most prominently in literature. The experimental results are analyzed and compared with existing data from literature using various definitions of two-phase fluid parameters. The fluidelastic stability thresholds of the present study agree well with results from previous studies for single-phase flow. In two-phase flow, the comparison of the stability data depends on the definition of two-phase flow velocity.

Effect of channel-to-channel cross-flow on local flooding in serpentine flow-fields

Serpentine flow-fields have long been used in polymer electrolyte membrane (PEM) fuel cells for effective transportation of reactants from the flow-field to the reaction sites. It has been observed in the literature that localized flooding near the U-bend region of serpentine flow-fields occurs at high current densities. This has been attributed to the boundary layer separation and recirculation of flow in the U-bend. In the present study, it is established, using computational fluid dynamics (CFD) simulations, that this is due to lower channel-to-channel cross-flow in the electrodes between consecutive serpentine channels rather than to the flow-field in the gas distribution channels.

Limit Loads for Circumferential Cracks in the Steam Generator Tube under Combined Pressure and Bending Loads

Steam generator in a nuclear power plant is huge heat exchanger that transfers heat from reactor to make steam to drive turbine-generator. Failure of the steam generator tubes can result in the release of fission products to the secondary side. Therefore, accurate integrity assessment of the cracked steam generator tubes is of great importance for maintaining the safety of the nuclear power plant. This paper provides limit loads for circumferential through-wall cracks in steam generator tubes under combined internal pressure and bending loads. Such limit loads are developed on the basis of three dimensional finite element analyses assuming elastic-perfectly plastic material behavior. As for the crack location, both the top of the tubesheet and U-bend regions are considered. The analysis results can be directly applied to the practical integrity assessment of cracked steam generator tubes, because the comparison between experimental data and FE results shows a very good agreement.