Explicit and Implicit Code Coupling Schemes in Fluid Structure Interaction

In multi-physics numerical computations a good choice of code coupling schemes is required. Several methods are possible like: an explicit synchronous scheme an Euler implicit method and no interpolation on velocity pressure; an explicit asynchonous scheme using a Crank-Nicholson time integration scheme and interpolation on velocity and pressure; an implicit scheme using a fixed iterative method. In the present paper these different schemes are compared for application in fluid structure interaction field. In the first part numerical coupling schemes are presented. Then their capability to ensure energy conservation is discussed according to numerical results obtained in analytical test cases. Finally application of coupling process to fluid structure interaction problems is investigated and results are discussed in terms of added mass and damping induced by a fluid for a structure vibrating in fluid at rest.

Fluctuating Forces in U-Tubes Subjected to Internal Two-Phase Flow

Severe in-plane vibrations were observed in a series of 20-mm dia. PVC vertical U-tubes of different elbow geometries subjected to air-water internal flow. An experimental study was undertaken to investigate the excitation mechanism. Vibration response, excitation forces and fluctuating properties of two-phase flow were measured over a wide range of flow conditions. The experimental results show that the observed vibrations are due to a resonance phenomenon between periodic momentum flux fluctuations of two-phase flow and the first modes of U-tubes. The excitation forces consist of a combination of narrow-band and periodic components, with a predominant frequency that increases proportionally to flow velocity. For a given void fraction, the force spectra for various flow velocities and elbow geometries coincide generally well on a plot of the normalized power spectral density as a function of a dimensionless frequency. The predominant frequencies of excitation agree with recent results on the characteristics of periodic structures in two-phase flow.

Flow-Induced Vibration of a Large-Diameter Elbow Piping Based on Random Force Measurement Caused by Conveying Fluid: Visualization Test Results

A 1/3 scale flow-induced vibration test facility that simulates the hot-leg piping of the JNC sodium-cooled fast reactor (JSFR) is used to investigate the pressure fluctuations of the pipe, where the high velocity fluid flows inside the piping. By the measurement of the pressure drop in the elbow piping while changing the Reynolds number, the similarity law of this model is confirmed. To evaluate the flow-induced vibrations for the hot-leg and cold-leg pipes, the random force distributions along the pipe and their correlations are measured with pressure sensors in a water loop. It is found that a flow velocity-dependent periodic phenomenon in the rear region of the elbow, and the maximum flow-induced random vibration force in the pipe are observed in the region of flow separation downstream the elbow. Finally, a design method is proposed with power spectral densities of the pressure fluctuations classified into four sections, correlation lengths in the axial direction divided into three sections, and with correlation lengths in the tangential direction into four sections.

A 12 MM/S RMS Screening Vibration Velocity for Pipes Using ANSI-OM3 Standard and Regulatory Design Rules

ASME ANSI-OM3 standard is dedicated to the assessment of piping vibrations for nuclear power plants. It provides an allowable zero-to-peak velocity, which is derived from a stress/velocity relationship, where corrections factors (C1, C2K2, C3, C4 and C5) and an allowable stress σal are introduced. In the ANSI-OM3 standard, the C4 correction factor depends on the pipe layout and on its boundary conditions, and is calculated for a few cases. In a former work, it was proposed to extend this factor to a larger number of pipe setups. Besides, the correction factor C1, which stands for the effect of concentrated mass, is established on a given set-up: a clamped-clamped straight pipe span on its first vibrating mode. C1 is then supposed to be conservative on any piping layout. Finally, allowable velocities derived from the ANSI-OM3 stress/velocity relationship may be very conservative. One way to reduce this conservatism is to introduce regulatory design rules. For a larger set of pipe geometries, a new set of C1 and C4 correction factors are computed using weight and pressure designs. Using these numerical results, allowable velocities can be calculated. Then, we propose here to check if a screening vibration velocity of 12 mm/s rms is fulfilled. For the 181 geometries on 3708, which do not meet the criterion, a seismic design checking is applied. Finally, by this way, 99.7% of the tested geometries, which are supposed to be acceptable with respect to static and seismic designs, display allowable velocities above 12 mm/s rms and the minimum allowable vibration velocity is 11.2 mm/s. This screening vibration velocity of 12 mm/s commonly used for vibration monitoring of piping systems in EDF nuclear power plants is then supported.

Kevlar and Carbon Composite Body Armor: Analysis and Testing

Kevlar materials make excellent body armor due to their fabric-like flexibility and ultra-high tensile strength. Carbon composites are made up from many layers of carbon AS-4 material impregnated with epoxy. Fiber orientation is bidirectional, orientated at 0° and 90°. They also have ultra-high tensile strength but can be made into relatively hard armor pieces. Once many layers are cut and assembled they can be ergonomicically shaped in a mold during the heated curing process. Kevlar and carbon composites can be used together to produce light and effective body armor. This paper will focus on computer analysis and laboratory testing of a Kevlar/carbon composite cross-section proposed for body armor development. The carbon composite is inserted between layers of Kevlar. The computer analysis was performed with a Lagrangian transversely isotropic material model for both the Kevlar and Carbon Composite. The computer code employed is AUTODYN. Both the computer analysis and laboratory testing utilized different fragments sizes of hardened steel impacting on the armor cross-section. The steel fragments are right-circular cylinders. Laboratory testing was undertaken by firing various sizes of hardened steel fragments at square test coupons of Kevlar layers and heat cured carbon composites. The V50 velocity for the various fragment sizes was determined from the testing. This V50 data can be used to compare the body armor design with other previously designed armor systems. AUTODYN [1] computer simulations of the fragment impacts were compared to the experimental results and used to evaluate and guide the overall design process. This paper will include the detailed transversely isotropic computer simulations of the Kevlar/carbon composite cross-section as well as the experimental results and a comparison between the two. Conclusions will be drawn about the design process and the validity of current computer modeling methods for Kevlar and carbon composites.

Linear Stability Analysis and Validation of a Unified Solution Method for Fluid-Structure-Interaction on Structural Dynamic Problems

In the conventional approach for fluid-structure interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: Partitioned methods and monolithic methods. Both methods use two separate sets of equations for fluid and solid. A unified solution method has been presented [1], which is different from these methods. The new method treats both fluid and solid as a single continuum, thus the whole computational domain is treated as one entity discretised on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, 2 time marching and one spatial discretisation scheme, widely used for fluids’ equations, are applied for the solution of the equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps and beam sizes is also presented. For all cases examined the numerical solution was stable and robust and proved to be suitable for the next stage of application to full fluid-structure interaction problems.

Two-Phase Flow Modeling in a Pipe Related to Flow-Induced Vibration

To understand the fluid dynamic forces acting on a structure subjected to two-phase flow, it is essential to get detailed information about the characteristics of two-phase flow. The distributions of flow parameters across a pipe, such as gas velocity, liquid velocity and void fraction, may be assumed to follow a power law (Cheng 1998, Serizawa et al. 1975). The void fraction profile is, for example, uniform for bubbly flow while it is more or less parabolic for slug flow. In the present work, the average values of momentum flux, slip ratio, etc. are derived by integral analysis, based on approximate power law distributions. A parametric study with various distributions was performed. The existing empirical formulations for average void fraction, proposed by Wallis (1969), Zuber et al. (1967) and Ishii (1970), are considered to obtain the present results. In particular, the unsteady momentum flux for slug flow is approximated.

Sub-Scale Versus Full-Scale Testing of Jet Pump Vibration

Time-dependent fluid pressure forces on jet pump components have been observed to cause destructive mechanical vibrations at a number of BWR plants. A test has been proposed for the purpose of studying the fluid-structure interaction phenomena and to determine what design or operational modifications can be imposed to mitigate or remove the vibration problem. Due to multi-system interactions of this problem, a full-scale test of water flow through a jet pump at reactor conditions is recommended over a sub-scale test. Each system to be studied imposes additional constraints to the modeling laws. Acoustic effects, vortex shedding or shear layer instability, and the fundamental beam mode of the jet pump diffuser all have similar characteristics, or response times. The need to maintain the time scale ratios for all systems implies that a full size system at full size structural and fluid parameters is the most likely success path in obtaining accurate and relevant data.

FIV Characteristics of U-Tubes Due to Relocation of the Tube Support Plate

Fluid-elastic instability and turbulence excitation for an under developing steam generator are investigated numerically. The stability ratio and the amplitude of turbulence excitation are obtained by using the PIAT (Program for Integrity Assessment of Steam Generator Tube) code from the information on the thermal-hydraulic data of the steam generator. The aspect ratio, the ratio between the height of U-tube from the upper most tube support plate (h) and the width of two vertical portion of U-tube (w), is defined for geometric parameter study. Several aspect ratios with relocation of tube support plates are adopted to study the effects on the mode shapes and characteristics of flow-induced vibration. When the aspect ratio exceeds value of 1, most of the mode shapes at low frequency are generated at the top of U-tube. It makes very high value of the stability ratio and the amplitude of turbulent excitation as well. We can consider that the local mode shape at the upper side of U-tube will develop the wear phenomena between the tube and the anti-vibration bars such as vertical, horizontal, and diagonal strips. It turns out that the aspect ratio reveals very important parameter for the design stage of the steam generator. The appropriate value of the aspect ratio should be specified and applied.

Air Cooling Temperature Analysis of Spent Fuel

Spent nuclear fuel is currently being stored at nuclear reactor sites. The spent fuel removed from the reactor is first placed in a large water pool to remove the initial decay heat. After several years, when the decay heat has dropped below a set level, the fuel is moved into concrete storage casks where natural circulation continues the cooling process. The purpose of this report is to predict, using a simplified analysis, how hot the fuel rods get when cooled by air in the cask. The increase in temperature and the decrease in density cause a chimney effect in the cask. This paper presents an analytical method of obtaining maximum fuel clad temperature in the cask. A non-dimensional model is derived, which is used to calculate the entrance and exit air velocities of the cask. The relationship between these velocities and the temperature used to obtain the maximum fuel clad temperature. A numerical scheme used to predict the maximum temperature is presented here and the results are compared to the analytical model. Both methods yielded corroborating results for fuel placed in the casks after spending similar amounts of time in a spent fuel pool.