Gap Effect on the Random and Fluid-Elastic Forces Acting in the Vibration of a Loosely Supported Tube Under Cross-Flow

In degraded situations of heat-exchangers, tubes may become loosely supported while subjected to intense crossflow which generates both turbulent and fluid-elastic forces. The vibro-impacting regimes that result have been studied by the authors during these last few years, based on analytical experiments and numerical simulations. Taking advantage of this material, the paper aims at showing some dynamic effects that have been observed and drawing lessons concerning the vibration of tubes under cross-flow when they are linearly unstable. If the fluid-elastic damping drops until the total damping becomes negative when the flow reduced velocity increases, a non-linear gap-system escapes from instability by reinforcing the sequence of impacts and its apparent frequency. On the other hand, the turbulent excitation is characterized by broadband PSDs that decrease with frequency. Thus the vibro-impacting response of the tubes results from a competition between the turbulent and fluid-elastic forces, according to a process that depends on the gap size. The fluid-elastic coupling forces may be either stabilizing (positive damping) or destabilizing (negative one), and, in a more amazing way, the random forces may be dissipative. The paper illustrates the previous points from the tested experimental configuration which was mainly 1-DOF. Dimensionless results are given for this configuration. Extensions to more realistic tubes are discussed from numerical simulations of a straight beam with three loosely supports. The starting point of simulations is though experiments where the fluid-elastic forces would act, but not the turbulent ones, which would produce limit cycles in the phase space. Turbulence is then considered as perturbation of limit cycles, and as shown below by notably introducing a dimensionless “gap-turbulence” parameter, smaller the gap sizes are, larger the relative weight of turbulence is. The Rice frequency and the mean impact force are indicators of this relative weight and the competition between the fluid-forces. From this general understanding, and using preliminary results with the beam model, a few guidelines are finally evoked for determining allowable gaps sizes in degraded situations. But a lot of work has to be done with more sophisticated models to concretize these ideas.

Fluid Structure Interaction for Tubes Bundles: Different Homogenization Methods

ASTRID is a project for an industrial prototype of a 600 MWe sodium cooled Fast Reactor, led by CEA. An important program is in progress for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (of FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fluid Assemblies. The FA and the NS are slender structures, which may be considered as beams, form a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. Two main movements have to be considered: global horizontal movements under a seismic excitation, and opening of the core. The fluid leads to complex interactions between the structures in the whole core. The dynamic behavior of the core is also strongly influenced by contacts between the beams and by the sodium, which limit the relative displacements. Numerical methods and models are built to describe and simulate this dynamic behavior. The validation of the numerical tools is based on the results of different experimental programs, already performed or in progress. The paper is mainly devoted to the modeling of the Fluid Structure Interaction phenomena in the Fast Reactor cores. Tubes bundles immersed in a dense fluid are very common in the nuclear industry (reactor cores and steam generators). In the case of an external excitation (earthquake or shock) the presence of the fluid leads to “inertial effects” with lower natural frequencies, and “dissipative effects”, with higher damping. The geometry of a tubes bundle is complex, which may lead to very huge sizes for the numerical models. Many works have been made during the last decades to develop homogenization, in order to simplify the problem. Theoretical analyses are presented on different simplifications and assumptions which can be made in the homogenization approach. The accuracy of the different assumptions depends of the conditions of the system: fluid flow or fluid at rest, small or large displacements of the structure. In the general case, it is theoretically necessary to consider the Navier Stokes equations: the fluid flow is fully nonlinear. Models have been developed during the last years, based on the Euler linear equations, corresponding to a fluid at rest, with small displacements of the structure. Only the inertial effects are theoretically described but the dissipative effects may be taken into account by using a Rayleigh damping. Different theoretical analyses show that, even in the case of a nonlinear fluid flow, the linear potential flow models may be used as linear equivalent models. In the cases with an important head loss in the fluid flow through the tubes, the fluid movement is mainly driven by the important forces exchanged with the structure and by the pressure gradient. The global equations of the system are close to the equations used for porous media, like the Darcy equations. An important condition to get a relevant model is to describe globally the energy balance in the system. The energy given to the fluid by the solid correspond to a variation of kinetic energy in the fluid and to energy dissipation in the fluid. Attention will be paid to the cases where the tubes bundle is in interaction with free fluid, without tubes. The global equation of the system has to be accurate for the tubes bundle and for the free fluid also.

Natural Frequencies and Damping of a Full-Scale Pipe Loop in Air and Water

A full scale pipework system, typical of oil and gas installations located on the sea floor, was subjected to vibration tests in both dry and submerged conditions. The frequency range examined covered 10 Hz to 500 Hz. The objective of the tests was to provide experimental data so that computer simulations could be developed and validated. The method used to determine the vibration properties was that of an experimental modal analysis using an impact hammer. The hammer was modified for underwater use. In dry conditions the damping was found to be very small (damping ratio less than 0.0002) despite the construction being typical. When submerged the effect of the surrounding water was significant. The changes in the natural frequencies from the dry case to the wet case occurred in such a complex manner that it was not possible to identify a simple shift between wet and dry vibration modes. It was necessary to include appropriate added mass coefficients in the computer simulation for both the pipe and the support system. The effect of the surrounding water on the damping was measured but found to be insignificant. It was concluded that immersion in water does not add significant damping to oil and gas pipework.

Study on the Relation Between Side Ratios of Rectangular Cross Sections and Secondary Vortices at Trailing Edge in Motion-Induced Vortex Excitation

According to the results of conventional wind tunnel tests on rectangular cross sections with side ratios of B/D = 2–8 (B: along-wind length (m), D: cross-wind length (m)), motion-induced vortex excitation was confirmed. The generation of motion-induced vortex excitation is considered to be caused by the unification of separated vortices from the leading edge and secondary vortices at the trailing edge [1]. Spring-supported test for B/D = 1.18 was conducted in a closed circuit wind tunnel (cross section: 1.8 m high×0.9 m wide) at Kyushu Institute of Technology. Vibrations were confirmed in the neighborhoods of reduced wind speeds Vr = V/fD = 2 and Vr = 8 (V: wind speed (m/s), f: natural frequency (Hz)). Because the reduced wind speed in motion-induced vortex excitation is calculated as Vr = 1.67×B/D = 1.67×1.18 = 2.0 [1], vibrations around Vr = 2 were considered to be motion-induced vortex excitation. According to the smoke flow visualization result for B/D = 1.18 which was carried out by the authors, no secondary vortices at the trailing edge were formed, although separated vortices from the leading edge were formed at the time of oscillation at the onset wind speed of motion-induced vortex excitation, where aerodynamic vibrations considered to be motion-induced vortex excitation were confirmed. It was suggested that motion-induced vortex excitation might possibly occur in the range of low wind speeds, even in the case of side ratios where secondary vortices at trailing edge were not confirmed. In this study, smoke flow visualizations were performed for ratios of B/D = 0.5–2.0 in order to find out the relation between side ratios of rectangular cross sections and secondary vortices at trailing edge in motion-induced vortex excitation. The smoke flow visualizations around the model during oscillating condition were conducted in a small-sized wind tunnel at Kyushu Institute of Technology. Experimental Reynolds number was Re = VD/v = 1.6×103. For the forced-oscillating amplitude η, the non-dimensional double amplitudes were set as 2η/D = 0.02–0.15. Spring-supported tests were also carried out in order to obtain the response characteristics of the models.

Confinement Effects on Added Mass of Cylindrical Structures in a Potential Flow

Efficient modelling and accurate knowledge of the mechanical behaviour of the reactor core are needed to estimate the effects of seismic excitation on a nuclear power plant. The fuel assemblies (in the reactor core) are subjected to an axial water flow which modifies their dynamical behaviour. Several fluid-structure models simulating the response of the core to a seismic load has been developed in recent years; most of them require high computational costs. The work which is presented here is a first step in order to simplify the fluid forces modelling, and thus to be able to catch the main features of the mechanical behaviour of reactor core with low computational costs. The main assumption made in this work is to consider the fluid flow as an inviscid potential flow. Thus, the flow can be described only using one scalar function (velocity potential) instead of a vector field and strongly simplifies the fluid mechanics equations, avoiding the necessity to solve Navier-Stokes equations. The pressure distribution around a cylinder is first solved in Fourier space for different values of the parameters (wavenumber, confinement size). The method is applied to a simple geometry (cylinder in an axial flow with a variable confinement) in order to test its effectiveness. The empirical model is then compared to simulations and reference works in literature. The configuration with large confinement has been solved, and results were in agreement with Slender Body Theory. The dependency on the confinement size strongly depends on the wavenumber, but in any case added mass increases as the confinement size decreases. Finally, future perspectives to extend the model to a group of cylinders and to improve the model are discussed (i.e. add viscosity to the model).

Modeling of Hypervelocity Impact Experiments Using Gamma-SPH Technique

A series of experiments were performed to study plastic deformation of metallic plates under hypervelocity impact at the University of Nevada, Las Vegas (UNLV) Center for Materials and Structures using a two-stage light gas gun. In these experiments, cylindrical Lexan projectiles were fired at A36 steel target plates with velocities range of 4.5–6.0 km/s. Experiments were designed to produce a front side impact crater and a permanent bulging deformation on the back surface of the target without inducing complete perforation of the plates. Free surface velocities from the back surface of target plate were measured using the newly developed Multiplexed Photonic Doppler Velocimetry (MPDV) system. To simulate the experiments, a Lagrangian-based smooth particle hydrodynamics (SPH) is typically used to avoid the problems associated with mesh instability. Despite their intrinsic capability for simulation of violent impacts, particle methods have a few drawbacks that may considerably affect their accuracy and performance including, lack of interpolation completeness, tensile instability, and existence of spurious pressure. Moreover, computational time is also a strong limitation that often necessitates the use of reduced 2D axisymmetric models. To address these shortcomings, IMPETUS Afea Solver® implemented a newly developed SPH formulation that can solve the problems regarding spurious pressures and tensile instability. The algorithm takes full advantage of GPU Technology for parallelization of the computation and opens the door for running large 3D models (20,000,000 particles). The combination of accurate algorithms and drastically reduced computation time now makes it possible to run a high fidelity hypervelocity impact model.

An Experimental Investigation of the Dynamics of a Loosely Supported Tube Array

The integrity of tube bundles is very important especially when dealing with high-risk applications such as nuclear steam generators. A major issue to system integrity is the flow-induced vibration (FIV). FIV is manifested through several mechanisms including the most severe mechanism; fluidelastic instability (FEI). Tube vibration can be constrained by using tube supports. However, clearances between the tube and their support are required to allow for thermal expansion and for other manufacturing considerations. The clearance between tubes may allow frequent impact and friction between tube and support. This in turn may cause fatigue and wear at support and potential for catastrophic tube failure. This study aims to investigate the dynamics of loosely supported tube array subjected to cross-flow. The work is performed experimentally in an open-loop wind tunnel to address this issue. A loosely-supported single flexible tube in both triangle and square arrays subjected to cross-flow with a pitch-to-diameter ratio of 1.5 and 1.733, respectively were considered. The effect of the flow approach angle, as well as the support clearance on the tube response, are investigated. In addition, the parameters that affect tube wear such as impact force level are presented.

Nuclear Power Plant Fires and Explosions: Part IV — Water Hammer Explosion Mechanisms

Water hammers, or fluid transients, compress flammable gasses to their autognition temperatures in piping systems to cause fires or explosions. While this statement may be true for many industrial systems, the focus of this research are reactor coolant water systems (RCW) in nuclear power plants, which generate flammable gasses during normal operations and during accident conditions, such as loss of coolant accidents (LOCA’s) or reactor meltdowns. When combustion occurs, the gas will either burn (deflagrate) or explode, depending on the system geometry and the quantity of the flammable gas and oxygen. If there is sufficient oxygen inside the pipe during the compression process, an explosion can ignite immediately. If there is insufficient oxygen to initiate combustion inside the pipe, the flammable gas can only ignite if released to air, an oxygen rich environment. This presentation considers the fundamentals of gas compression and causes of ignition in nuclear reactor systems. In addition to these ignition mechanisms, specific applications are briefly considered. Those applications include a hydrogen fire following the Three Mile Island meltdown, hydrogen explosions following Fukushima Daiichi explosions, and on-going fires and explosions in U.S nuclear power plants. Novel conclusions are presented here as follows. 1. A hydrogen fire was ignited by water hammer at Three Mile Island. 2. Hydrogen explosions were ignited by water hammer at Fukushima Daiichi. 3. Piping damages in U.S. commercial nuclear reactor systems have occurred since reactors were first built. These damages were not caused by water hammer alone, but were caused by water hammer compression of flammable hydrogen and resultant deflagration or detonation inside of the piping.

Numerical Analysis of Flow-Induced Vibration of Large Diameter Pipe With Short Elbow

Japan Atomic Energy Agency is now conducting design study and R&D of an advanced loop-type sodium cooled fast reactor. The cooling system is planned to be simplified by employing a two-loop configuration and shortened piping with less elbows than a prototype fast reactor in Japan, Monju, in order to reduce construction costs and enhance economic performance. The design, however, increases flow velocity in the hot-leg piping and induces large flow turbulence around elbows. Therefore, flow-induced vibration (FIV) of a hot-leg piping is one of main concerns in the design. Numerical simulation is a useful method to deal with such a complex phenomenon. We have been developing numerical analysis models of the hot-leg piping using Unsteady Reynolds Averaged Navier-Stokes simulation with Reynolds stress model. In this study, numerical simulation of a 1/3 scaled-model of the hot-leg piping was conducted. The results such as velocity profiles and power spectral densities (PSD) of pressure fluctuations were compared with experiment ones. The simulated PSD of pressure fluctuation at the recirculation region agreed well with the experiment, but it was found some underestimation at other parts, especially in relatively high frequency range. Eigenvalue vibration analysis was also conducted using a finite element method. Then, stress induced by FIV was evaluated using pressure fluctuation data calculated by URANS simulation. The calculated stress generally agrees well the measurement values, which indicates the importance of precise evaluation of the PSD of pressure fluctuation at the recirculation region for evaluation of FIV of the hot-leg piping with a short elbow.

Bending-Torsional Flutter of a Slender Web in a Cross Flow

This paper presents a flutter analysis of a slender web in a cross air flow. In the flutter analysis, a Doublet-point method (DPM) [1] based on an unsteady lifting surface theory is used to calculate the unsteady fluid force acting on the sheet surface. The equation of motion of the web with tension is derived by using the finite element method (FEM). Flutter velocity, frequency and mode are examined through the root locus of the flutter determinant of the system with changing flow velocity of air. In this study, these flutter characteristics derived by flutter analysis are compared with wind-tunnel experiments. The influence of tension of the web on flutter velocity, frequency and mode is clarified. As tension of the web becomes higher, the flutter velocity and corresponding frequency increase. In any tension, coupled mode flutter of bending and torsional modes occurs. Then, local work done by the fluid force around the upstream end of the web is positive. On the other hand, near the downstream end of the web, the local work is negative.