Added Mass Model Research Articles

Validation of the added mass effect in the narrow gaps of nuclear reactor pressure vessels

Nuclear reactor pressure vessels (RPVs) must be robust to external environmental excitations such as seismic loads. Precise numerical models that predict the dynamic responses to external loads are crucial for evaluating the safety of RPVs. Notably, in RPVs submerged in reactor coolant, it is necessary to examine the added mass effect of the fluid via fluid-structure interaction (FSI) analysis, employing either an analytical approach or a numerical analysis. The present study focuses on modeling and analyzing the added mass effect in the narrow gaps associated with the dense structural layout in the reactor. In this context, this paper validates analytical and numerical models that accurately describe the added mass effect for two cases: (i) simple concentric cylinders with a narrow gap filled with fluid and (ii) a complex small-scale RPV with narrow gaps also filled with fluid. Initially, the analytical model, employing Lagrange's equation of motion and velocity potential, and the numerical model, utilizing FE modeling in acoustic FSI through ANSYS, were validated through experimental modal testing for the added mass effect in the narrow gap between simple concentric cylinders. The analytical model for the concentric cylinders indicates that the added mass diverges to infinity as the gap approaches zero, which should be examined carefully. Through experiments for the concentric cylinders, the analytical and FEM-based added mass effects were validated with a natural frequency error of 3 %. Subsequently, based on the results for the concentric cylinders, a complex numerical model of the small-scale reactor with complex boundary conditions was developed and cross-validated through corresponding experimental modal testing of the small-scale RPV. The added mass model for the narrow gaps in the RPV was validated by substantial agreement of eight representative modes, as demonstrated by a 5 % natural frequency error.

The added mass of a biaxial tensioned membrane in still air

It is well known that added mass significantly impacts the vibration of membrane structures in still air. Numerous theoretical, numerical, and experimental studies have been conducted on the added mass of axial tensioned membranes. However, the added mass of biaxial tensioned membranes subjected to different tensile forces in two directions in still air remains unclear. Therefore, this study focuses on investigating the added mass of biaxial tensioned membranes in still air. Firstly, this paper proposes a simplified theoretical model for the added mass of biaxial tensioned membranes in still air based on the energy conservation law. To validate the accuracy of the proposed model, a modal testing system for a rectangular membrane is designed to identify the frequencies of biaxial tensioned membranes in still air. In the experimental system, the utilization of a laser displacement sensor array is to obtain the time-displacement information of observation points. Then, a combination of Fast Fourier Transform (FFT) and Stochastic Subspace Identification (SSI) methods is employed for modal identification. Comparative analysis between the experimental and theoretical model results demonstrates an excellent agreement in frequencies. Additionally, the proposed added mass model is closer to the experimental added mass than other models, with a maximum deviation of only 4.77 %. This research provides a reference for the study of the impact of air on the ground vibration of membranes.

Inelastic Collision Influencing the Rotational Dynamics of a Non-Rigid Asteroid (of Rubble Pile Type)

We have considered here a novel particular model for dynamics of a non-rigid asteroid rotation, assuming the added mass model instead of the concept of Viscoelastic Oblate Rotators to describe the physically reasonable response of a ‘rubble pile’ volumetric material of asteroid with respect to the action of a projectile impacting its surface. In such a model, the response is approximated as an inelastic collision in which the projectile pushes the ‘rubble pile’ parts of the asteroid together to form a mostly solidified plug in the crater during the sudden impact on the asteroid’s surface. Afterwards, the aforementioned ‘solidified plug’ (having no sufficient adhesion inside the after-impact crater) will be pushed outside the asteroid’s surface by centrifugal forces, forming a secondary rotating companion around the asteroid. Thus, according to the fundamental law of angular momentum conservation, the regime of the asteroid’s rotation should be changed properly. Namely, changes in rotational dynamics stem from decreasing the asteroid’s mass (due to the fundamental law of angular momentum conservation). As the main finding, we have presented a new solving procedure for a semi-analytical estimation of the total mass of the aforementioned ‘solidified plug’, considering the final spin state of rotation for the asteroid with minimal kinetic energy reduced during a long time period by the inelastic (mainly, tidal) dissipation. The asteroid is assumed to be rotating mainly along the maximal inertia axis with a proper spin state corresponding to minimal energy with a fixed angular momentum.

The unsteady aerodynamics of insect wings with rotational stroke accelerations, a systematic numerical study

To generate aerodynamic forces required for flight, two-winged insects (Diptera) move their wings back and forth at high wing-beat frequencies. This results in exceptionally high wing-stroke accelerations, and consequently relatively high acceleration-dependent fluid forces. Quasi-steady fluid force models have reasonable success in relating the generated aerodynamic forces to the instantaneous wing motion kinematics. However, existing approaches model the stroke-rate and stroke-acceleration effects independently from each other, which might be too simplified for capturing the complex unsteady aerodynamics of accelerating wings. Here, we use computational-fluid-dynamics simulations to systematically explore how aerodynamic forces and flow dynamics depend on wing-stroke rate, wing-stroke acceleration and wing-planform geometry. Based on this, we developed and calibrated a novel unsteady aerodynamic force model for insect wings with stroke accelerations. This includes improved versions of the translational-force model and the added-mass force model, and we identify a third novel component generated by the interaction of the two. This term reflects the delay in bound-circulation build-up as the wing accelerates. The physical interpretation of this effect is analogous to the Wagner effect experienced by a wing starting from rest. Here, we show that this effect can be modelled in the context of flapping wings as a stroke-acceleration-dependent correction on the translational-force model. Our revised added-mass model includes a viscous force component, which is relatively small but not negligible. We subsequently applied our new model to realistic wing-beat kinematics of hovering Dipteran insects, in a quasi-steady approach. This revealed that stroke-acceleration-related aerodynamic forces contribute substantially to lift and drag production, particularly for high-frequency flapping mosquito wings.

A model for underwater shaking table tests on the basis of different similar criteria

Shaking table testing is still considered a reliable approach when examining the seismic performance of structures, however, for long-span and large-scale hydraulic structures, limited by the constraints of test equipment and the influence of water, during underwater shaking table testing, if the earthquakes input, water levels and similitude law obtained on the basis of the test model and the resulting similar relationship do not fall within the operating range of the shaking table, the obtained results cannot truly reflect the dynamic response of the tested structure. To solve this problem, the improved dimensional analysis method and the finite element software ANSYS are used to study similar relationships and derive the design model of a certain bridge. Within the elastic similarity criteria, effective and feasible test models are proposed. The distortion model is designed by increasing the added mass can reduce the time scale, guarantee that the test runs smoothly, and better reflect the dynamic response of the prototype structure after such modification, however, for the long and thin model structure, the appropriate added mass adopted to ensure that within the bearing capacity of the structure and the shaking table, the elastic similarity meets the design requirements of the structure model of irregular and regular cross-sections and is suitable for the model design requirements of long-span and large-scale structures. Within the elasticity-gravity similar criteria, the distortion model designed by added mass can reflect the dynamic response of the prototype structure, which needs to be configured with certain added masses, and the bearing capacity of the model itself and the shaking table needs to be considered. The elasticity-gravity similitude law is suitable for examining regular cross-sections and short-span and small-scale test models, but the fluid-structure coupling and failure mechanism of structures can be examined. The distinctive peak acceleration will not affect the error of the dynamic response of the lacking-artificial added mass model, the distortion model and the prototype. The reinforcement ratio will not affect the error of the dynamic response of the distortion model and the prototype structure, but it will affect the error of the dynamic response of the lacking-artificial added mass model and the prototype structure. The added mass of the water triggered by the flexible movement of the structure under the action of earthquake changes the dynamic characteristics of the structure and the rigid movement of the structure triggers the water to exert an external force on the structure, which affects the dynamic characteristics and responses of the structure. This paper can provide a reference for the examine of other hydraulic structures and is beneficial to the examine of applied ocean engineering problems.

Simplified Added-Mass Model for Evaluating the Response of Rectangular Hollow Bridge Piers under Earthquakes

Abstract A simplified added-mass model is proposed in this paper for evaluating the seismic response of rectangular hollow piers in deep water, which are widely used in railway bridges. For this pu...

Bubble cloud configuration effect on the added mass

Understanding the mechanisms that control the dynamics of bubble clouds is essential to many industrial processes in the energy and chemical realms. Due to the complexity of the two-phase flow configurations, modeling the physics of the phenomena driving the mixing of bubbles within a liquid matrix is still a major challenge. One of the weaknesses of most existing two-phase flow models is due to the incomplete handling of bubble dispersion. This difficulty comes from the fact that dispersion can be driven by numerous complex phenomena, such as turbulence, local pressure distribution, bubble to bubble interaction, etc. In this study, we introduce the effect of added mass fluctuations on the dispersion of small bubbles. Existing models based on the Euler–Euler approach do not take into account local flow variations due to bubble distributions. Therefore, these models do not correctly describe fine dispersion features. Solving the potential flow around N bubbles allows to take into account the effect of the added mass on bubble cloud distributions. To this aim, a complete added mass model, which includes local bubble configurations via the void fraction gradient, is developed. The void fraction gradient allows us to account for the asymmetry of the bubble cloud around a single central bubble. Consequently, the proposed model can only represent regular and irregular bubble cloud distributions. This methodology results in a more consistent consideration of the added mass effects as well as Meshchersky's force, which should be included in hydrodynamic two-phase flow models. The proposed approach can be implemented in Euler–Euler models intended to consider the dispersion of bubbles caused by the effect of added mass.

A substructure method for the transient response of vertical cylinders subjected to shock wave of underwater explosion

Vertical cylinders are widely used as supporting structures in ocean engineering applications. Shock waves due to underwater explosives (UNDEX) can cause serious damage to offshore structures, which has attracted the interest of many researchers. The propagation characteristics of shock waves produced by UNDEX across a cylinder are a complex physical phenomenon that involves fluid-structure dynamic interactions. For the shock wave produced by UNDEX, the total pressure on a cylinder consists of three parts, including the incident shock wave pressure, scattered wave pressure and radiation pressure due to the motion of the cylinder. This paper develops an improved method for obtaining the transient response of a vertical circular cylinder subjected to UNDEX. First, an empirical formula of the shock wave pressure for far-field UNDEX is adopted as the incident shock wave. Based on the continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient, an accurate model in the time domain for solving the scattered wave pressures on a cylinder is further developed. Then, the added mass model is used to replace the fluid-structure interaction caused by radiation wave. Finally, the vibration equation of a Euler-Bernoulli beam is utilized to evaluate the transient response of the cylinder subjected to UNDEX.

Added-Mass Based Efficient Fluid–Structure Interaction Model for Dynamics of Axially Moving Panels with Thermal Expansion

The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel displacement. Then, the panel displacement, accounting also for the fluid–structure interaction, is analyzed with the help of the weak form of the governing partial differential equation, using a Galerkin method. In the first part of this paper, we represent the traveling panel by a single partial differential equation in weak form, using an added-mass approximation of the exact fluid reaction. In the second part, we apply a Galerkin method for dynamic stability analysis of the panel, and present an analytical investigation of static stability loss (divergence, buckling) based on the added-mass model.

A CMUT-based gas density sensor with high sensitivity

In this paper, a gas density sensor based on capacitive microfabricated ultrasonic transducers (CMUTs) is developed. The working principle is based on the resonant frequency shift of the membrane by the change of gas density under the fluid-solid interaction. Due to the advantages of high frequency, the frequency shift will be larger, which also results in higher detection measuring sensitivity (DMS). Combined with the fluid added mass model and the electromechanical coupling reduced order model of a CMUT in vacuum, the relationship between gas density and resonant frequency is established. Furthermore, the influences of the structural parameters and the bias voltage on DMS are further analyzed. As a result, a good linearity is shown between gas density and resonant frequency of CMUTs in a certain density range. Simultaneously, the CMUT-based density sensor shows a high measuring sensitivity. After fabricating a sensor with the low-temperature direct wafer-bonding technique and building the gas density detection platform, the resonant frequency and phase-frequency curves of the CMUTs-based density sensor under different bias voltages are achieved by the experimental analysis in the different mixed gas. The results demonstrate the excellent capability of fabricated CMUTs for gas density measurement with a good linear relationship between gas density and resonant frequency and a higher DMS of 9760 Hz · kg−1 · m3, which make it a promising sensor.

Modeling and control of tethered undersea kites

The modeling and control of tethered undersea kites for power generation are discussed in this paper. In the first part, we apply the added mass model to underwater kite systems. In the second part, the stability of undersea kite systems is analyzed using two frameworks. The dissipative property of the hydrodynamic force is provided first. Based on this property, the input to state stability of the undersea kite dynamics is established. Moreover, based on the input to state stability, the ultimate boundedness of constrained undersea kite dynamics is also discussed. Finally, an input–output system is proposed, and a passivity-based control signal is designed. The proposed control signal is tested in a baseline simulation, which yields consecutive figure eight cycles with positive net power generation.

Study on added mass model for fluid-structure interaction of spent fuel storage rack

The spent fuel storage racks are placed freely inside a pool that is filled with water. Under seismic condition, the fluid in the gap between the racks will be forced to flow due to the movement of the racks. Inversely, the fluid may impose an added mass to the rack and affect the movement of the racks. The added mass imposed to the rack in this kind of fluid-structure interaction phenomenon (FSI) is very important for the dynamic analysis of racks. Previous researches on rack mainly focus on theoretical analysis and numerical simulation. Due to the complexity of the structure, application of the theoretical analysis is limited, while the effectiveness of numerical method need to be validated by experiments. In order to develop an added mass model for rack with end-tube-connection construction like CAP1400 spent fuel storage rack, in this paper, a two-dimensional model of the CAP1400 rack is established and added mass of rack were obtained by the numerical simulation. The numerical results are in good agreement with the experimental ones. Therefore, the effective of numerical method for the calculation of the added mass is validated. In order to study added mass of the multi-rack, the hydraulic mass matrix of double-rack is calculated by CFD. The results can provide added mass input for the design and analysis of the CAP1400 series rack.

An efficient numerical model for hydrodynamic added mass of immersed column with arbitrary cross - Section

Abstract The assessment of earthquake-induced hydrodynamic added mass is critical in the seismic design of structures supported by immersed columns. This paper developed an efficient potential-based numerical model to determine the hydrodynamic added mass for immersed column with arbitrary cross - section. General formulations of the hydrodynamic added mass for a column with general cross - section under horizontal earthquake were derived. The accuracy of the developed model for immersed columns was validated analytically and experimentally. The developed model was then applied to evaluate the hydrodynamic added mass of an immersed column with dumbbell cross - section. The hydrodynamic added mass of the example dumbbell column along various earthquake directions was determined and the directional-dependent added mass was expressed as an analytical function of the added mass along the major and minor axes of the column and the earthquake direction. The frequency- and time-domain seismic responses of the example dumbbell column were finally computed using both fluid-structure interaction (FSI) model and the developed hydrodynamic added mass model. The good agreement between seismic responses from the FSI and developed added mass model confirmed the high accuracy and efficiency of the developed model for the hydrodynamic added mass of immersed columns with arbitrary cross - section under earthquakes.

A simple added mass model for simulating elliptical cylinder vibrating in water under earthquake action

An accurate added mass model representation for a flexible elliptical cylinder vibrating in water is presented. To accomplish this, the analytical expressions for the hydrodynamic forces on elliptical cylinders are first derived in the elliptical coordinate system. Then, explicit expressions for computing the free vibration response of the elliptical cylinder vibrating in water like natural frequencies and mode shapes are given by solving the coupled differential equations. The expressions for calculating the forced vibration responses of a flexible cylinder surrounded by water are further given. However, the expressions of the exact model are too complicated and require the use of computer program to generate the results. Based on the fundamental frequency reduction rate, a simple formula for the added mass representation is proposed to simulate a flexible elliptical cylinder vibrating in water. The simple formula for evaluating the natural frequencies and the simple model for evaluating the seismic responses of the submerged cylinder are also presented in the study.

Effect of Added Mass on Wind-Induced Vibration of a Circular Flat Membrane by Wind Tunnel Tests

Flexible roof structures, such as membranes, are sensitive to wind action due to their flexibility and light weight. Previously, the effect of added mass on the vibration frequency of membrane structures has been experimentally tested. However, the effect of added mass on wind-induced vibration remains unclear. The purpose of this paper is to investigate the effect of added mass on the wind-induced vibration of a circular flat membrane based on wind tunnel tests. First, wind tunnel tests were conducted to obtain wind pressure distribution from the rigid model and wind-induced vibration from the aeroelastic model of a circular flat membrane. Secondly, a dynamic finite element analysis for the proposed added mass model was conducted to obtain the wind-induced vibration of the membrane structure. Then, with the wind pressure distribution obtained from the rigid model tests, dynamic analysis was conducted either with or without consideration of the effect of added mass. According to the dynamic analysis results and the wind tunnel test results, it is clear that considering the effect of added mass in dynamic analysis can significantly improve the accuracy of a wind-induced response. Such an effect is more significant at the windward than the central zone. The inclusion of added mass can result in a larger displacement response as wind velocity increases but a smaller response as the prestress level increases.

Dynamic characteristics assessment of reactor vessel internals with fluid-structure interaction

Abstract Improvement of numerical analysis methods has been required to solve complicated phenomena that occur in nuclear facilities. Particularly, fluid-structure interaction (FSI) behavior should be resolved for accurate design and evaluation of complex reactor vessel internals (RVIs) submerged in coolant. In this study, the FSI effect on dynamic characteristics of RVIs in a typical 1,000 MWe nuclear power plant was investigated. Modal analyses of an integrated assembly were conducted by employing the fluid-structure (F-S) model as well as the traditional added-mass model. Subsequently, structural analyses were carried out using design response spectra combined with modal analysis data. Analysis results from the F-S model led to reductions of both frequency and Tresca stress compared to those values obtained using the added-mass model. Validation of the analysis method with the FSI model was also performed, from which the interface between the upper guide structure plate and the core shroud assembly lug was defined as the critical location of the typical RVIs, while all the relevant stress intensities satisfied the acceptance criteria.

津波サージ力による1自由度系の弾性応答

Experiments using a reservoir discharge type flume with an orifice are conducted to investigate the dynamic characteristics of finite width wall structures attached to a flexible cantilever support subjected to surge forces. The surge acts as a step-like force with finite rise time in which the response is governed by the structure's vibrational properties. A structure vibrating under a single mode can be modeled as a single-degree-of-freedom(SDOF) system. When the structure is subjected to a surge, parts of its surface are submerged in water, giving rise to added intertial and hydrodynamic damping forces, which can be expressed as added masses and hydrodynamic damping coefficients. The focus of this research is to investigate and model the added mass and hydrodynamic damping coefficient for wall like structures subjected to surge forces. From potential theory, the added mass depends on the water density, inundation height, width of the structure, and their ratio. Assuming that the hydrodynamic damping has a form similar to aerodynamic damping, the hydrodynamic damping coefficient depends on the water density, water velocity, inundation height, width of the structure, and the ratio between inundation height and width of the structure. In order to investigate the added mass and hydrodynamic damping coefficient, finite width walls mounted on a flexible support are selected as the structural system. Three different materials and two different widths are selected as parameters for the wall. The first fundamental mode is translational in the direction of the flume. Two types of experiments are conducted. One in which the added mass and hydrodynamic damping coefficient is extracted from the system submerged in various inundation depths of still water, and the other in which they are extracted from the system subjected to surges resulting from 4 different initial reservoir heights. The former is conducted to obtain the ideal properties of the system when both sides of the plate are submerged in water as opposed to the latter which is to obtain actual properties of the system when only a single side is submerged. The time history of the measured response shear force of the structural system is decomposed into the quasi-static average force corresponding to the applied surge force and the oscillating dynamic force corresponding to the vibration of the structure, from which the added mass and hydrodynamic damping coefficient is obtained. From the stillwater experiments, a monotonic increase in added mass with respect to an increase in inundation depth was observed. By incorporating the mode of vibration and reduction of added mass due to the free water surface, the added mass can be modeled using the wall width, inundation height, and aspect ratio. From the surge experiments, a positive correlation between the added mass and inundation height is also observed, from which an added mass model similar to that for the stillwater case can be developed. The relationship between the total damping coefficient (material damping coeff. + hydrodynamic damping coeff.) and inundation depth obtained is dispersed but has a trend similar to the hydrodynamic damping model based on aerodynamic damping. Time history analysis is conducted, using the surge force, inundation height, and velocity time histories obtained from the experiments as input into the SDOF system with proposed added mass and hydrodynamic damping models. By using the proposed model, the decrease in fundamental frequency as well as the increase in damping observed in the experiments is adequately modeled. Though the damping is slightly overestimated for surges with smaller initial reservoir heights.

Investigation of the added mass method for seismic design of lock gates

During an earthquake, lock gates are subjected to additional pressure since the water contained in the chamber is put into motion by the earthquake. It is difficult to assess the level of this pressure because the system is affected by a fluid–structure interaction. The gate deformations have an effect on the water pressure, which in turn affects the gate vibrations. A common approach, referred to as the added mass method, consists of simulating the fluid action by distributing lumped masses over the gate. However, this method has been questioned, since the calculation of the lumped masses is usually based on the Westergaard formula, which was derived assuming a perfectly rigid structure. Consequently, fluid–structure interactions may not be captured correctly. This paper proposes to investigate the validity of this approach for such problems and to explain why it might not be conservative. The numerical solutions of an added mass model and a fluid–structure interaction model are confronted. The results indicate that the added mass method may eventually lead to conservative results depending on the type of damping used in the model. Based on these observations, some recommendations are suggested to improve the design of lock gates subjected to earthquakes.

Structural model updating of an offshore platform using the cross model cross mode method: An experimental study

The present paper validates a recently developed cross model cross mode (CMCM) model updating method for an offshore platform structure by using experimental data. First, the CMCM model updating method, where a modal expansion technique is used to overcome the spatial incompleteness problem, is briefly summarized. One particularly novel development is that a simplified added-mass model of the surrounding water is proposed, and the updating coefficients are directly incorporated into the CMCM procedure. Next, a small-scale offshore platform is fabricated. Model tests are experimentally conducted for four cases, including two cases in air with and without deck mass and two cases in water under hammer and wave excitation. Finally, the first three orders of modal parameters are identified. The CMCM method in combination with the modal expansion technique is used to update the structural models. The results demonstrate that the present method is effective for the model updating of offshore platform structures with a minimal amount of lower-order, spatially incomplete experimental modal data.

Dynamic Interaction between Reservoir and a High Concrete Face Rockfill Dam on Deep Alluvium Deposit

Potential-based fluid model and Westergaard added mass model were used to reflect the dynamic interaction of reservoir-CFRD(concrete face rockfill dam)-foundation coupling system. The deep alluvium deposit was treated as porous medium using Biot's dynamic consolidation theory. In the coupled analysis, the paper focused on hydrodynamic pressures in the reservoir zone, dynamic response and pore water pressure in the structure zone. The result shows that the dynamic response of added mass model is greater than that of potential-based fluid model. The porous medium of alluvium deposit is of great significance in performing soil liquefaction analysis and reservoir-dam-foundation system.