Added Mass Effect Research Articles

Correction to: Seismic and stress qualification of LMFR fuel rod and simple method for the determination of LBE added mass effect

Correction to: Seismic and stress qualification of LMFR fuel rod and simple method for the determination of LBE added mass effect

내부 유체에 의한 고유진동수 분리 효과를 고려한 배관계의 적절한 시간이력 해석 방법론

In this study, the natural frequency separation phenomena found in the dynamic analysis of piping systems with internal fluids were identified, and methods for efficient seismic time history analysis were studied. We conducted a dynamic analysis of a piping system with consideration for the effect of its internal fluids using the coupled model, which incorporates the fluid-structure interaction effect. Owing to the mode separation effect, modes were divided into the fluid mass added (FMA) mode, generated by the added mass effect of the fluid, and coupled mode, which is created by the resonance of the internal fluid. The response contribution of the FMA and coupled modes was confirmed to be effective for efficient seismic time history analysis.

Collinear velocity relaxation of two spheres in a viscous incompressible fluid.

Collinear velocity relaxation of two spheres immersed in a viscous incompressible fluid is studied on the basis of an approximate expression for the retarded hydrodynamic interaction. After a sudden impulse applied to one sphere, the other one instantaneously starts to move as well, with amplitude determined by the added mass effect. The velocities of both spheres eventually decay with a t^{-3/2} long-time tail, but the relative velocity decays with a t^{-5/2} long-time tail. The three relaxation functions are approximated by simple expressions involving only a small number of poles in the complex square root of frequency plane.

Fluid Added-Mass Effect on Flexural Vibration of Hemispherical Shell Structure

In this hydroelasticity study, the fluid added-mass effect on a hemispherical shell structure under flexural vibration is investigated. The vibration response of the hemisphere is solved by using a commercial finite element software (ABAQUS) coupled with an in-house boundary element code that models the fluid as potential flow. The fluid-structure interaction is solved as a fully-coupled system by modal superposition to reduce the number of degrees of freedom. The need for an iterative scheme to pass displacement/force information between the two solvers is avoided by direct coupling between the fluid and structure equations. The numerical results on the downward shift in natural frequencies due to added-mass effect compare well with vibration measurements conducted on a stainless-steel bowl with interior and exterior fluid. For water and soap-water solution used in the experiments, the fluid viscosity (varying over a wide range) did not have any significant effect on the wet natural frequencies. This is due to the small viscous boundary layer (milimetre scale) compared to the nominal size of the bowl in centimetres. For such cases, the fluid-added mass only depends on the density of the fluid and the use of potential flow in the numerical model is applicable.

The Added Mass Effect and the Higgs Mechanism

A rigid body accelerated through an inviscid, incompressible fluid appears to gain mass, which is encoded in an added mass tensor. Swimmers, air bubbles, submarines and airships are slowed down by the associated `added mass' force proportional to their acceleration, which is distinct from viscous drag and buoyancy. In particle physics, otherwise massless electrons, quarks, $W$ and $Z$ bosons, moving through the Higgs scalar field acquire masses encoded in a mass matrix. In this expository article we give an introduction to the fluid mechanical added mass effect through examples of potential flows in various dimensions and exploit a correspondence with the Higgs mechanism [introduced in Proc. R. Soc. A471: 20140803 (2015)] to relate this to how the $W$ and $Z$ bosons can get their masses, while leaving the photon massless. The correspondence relates the Higgs scalar field to the fluid, the vacuum expectation value of the Higgs field to a constant fluid density and quantum fluctuations around the Higgs condensate to compressional waves in the fluid. The shape of the rigid body encodes the pattern of gauge symmetry breaking through the eigenvalues of the corresponding mass matrices. Possible directions of acceleration of the rigid body are related to directions in the gauge Lie algebra with a `flat' direction in the body corresponding to a massless photon. Moreover, symmetries of the body are related to those of the scalar vacuum manifold. The Higgs boson may be viewed as the analog of a long wavelength fluid mode around an accelerated body.

On the high-frequency response of unsteady lift and circulation: A dynamical systems perspective

In this paper, we consider the unsteady aerodynamics of a two-dimensional airfoil as a dynamical system whose input is the angle of attack (or airfoil motion) and output is the lift force. Based on this view, we discuss the evolution of lift and circulation from a purely dynamical perspective through step response, frequency response, transfer function, etc. In particular, we point to the relation between the high-frequency gain of the transfer function and the physics of the development of lift and circulation. Based on this view, we show that the circulatory lift dynamics is different from the circulation dynamics. That is, we show that the circulatory lift is not lift due to circulation. In fact, we show that the circulatory–non-circulatory classification is arbitrary. By comparing the steady and unsteady thin airfoil theory, we show that the circulatory lift possesses some acceleration (added-mass) effects. Finally, we perform simulations of Navier–Stokes equations to show that a non-circulatory maneuver in the absence of a free stream induces viscous circulation over the airfoil.

Auxiliary bearing squeeze film dampers for magnetic bearing supported rotors

Auxiliary bearings (AB) support the rotor and protect the magnetic bearing (AMB) system when the AMB is disabled due to power loss or excessive loads. The paper demonstrates that installing a damping device along with the AB can yield extended AB fatigue life, protect the AMB, and reduce vibration, contact force and AB heating. A squeeze film damper (SFD) is an energy dissipation device that has been widely used in the turbo-machinery industry, and as demonstrated in the paper can also work effectively in combination with an AB. Usually, the SFD implements a supply groove to ensure adequate lubricant flow into the film lands. The supply groove can provide significant added mass coefficients and significantly influence the overall impedance of the SFD. Past literature has analyzed the transient response of the rotor dropping onto AB's with squeeze film dampers, none though have considered the influence of the SFD's center groove and its added mass effect on rotor's drop behavior. This paper develops a high fidelity finite element grooved SFD model considering the fluid inertia, and an effective groove clearance is used following the practice appearing in the literature. SFD force coefficients are benchmarked with results of a linear fluid inertia, bulk-flow model developed in the literature, before including them in the rotor – AB system model. The SFD model is integrated into a high fidelity nonlinear auxiliary bearing (angular contact ball bearing) model, which considers the movements, contact force, stress, and temperature of bearing balls, the inner race and outer race. The instantaneous reaction forces from the SFD are calculated with a finite element based solution of Reynold equation at each time step due to the intermittent and large sudden loads. The flexibility of the rotor is included utilizing a Timoshenko beam, finite element model. The fatigue life of the auxiliary bearing when integrated into the SFD is also calculated based on the rain flow counting method. The influence of the added mass of the SFD on the rotor's drop behavior is demonstrated showing that the added mass increases the contact force and peak temperature and reduces the fatigue life of the AB. Therefore, the added mass effect of the SFD should be considered to avoid over predicting the AB fatigue life. The influence of the SFD clearance on the rotor's drop behavior is also studied showing that an optimal clearance exists for increasing the AB fatigue life. Too small of a clearance will yield excessive damping making the effective stiffness too large, and causing high contact forces. Too large of a clearance lowers damping which may lead to a destructive backward whirl. This paper provides key guidelines for auxiliary bearing damper system design.

Cephalopod-inspired robot capable of cyclic jet propulsion through shape change

The compliance and conformability of soft robots provide inherent advantages when working around delicate objects or in unstructured environments. However, rapid locomotion in soft robotics is challenging due to the slow propagation of motion in compliant structures, particularly underwater. Cephalopods overcome this challenge using jet propulsion and the added mass effect to achieve rapid, efficient propulsion underwater without a skeleton. Taking inspiration from cephalopods, here we present an underwater robot with a compliant body that can achieve repeatable jet propulsion by changing its internal volume and cross-sectional area to take advantage of jet propulsion as well as the added mass effect. The robot achieves a maximum average thrust of 0.19 N and maximum average and peak swimming speeds of 18.4 cm s−1 (0.54 body lengths/s) and 32.1 cm s−1 (0.94 BL/s), respectively. We also demonstrate the use of an onboard camera as a sensor for ocean discovery and environmental monitoring applications.

Optimized Schwarz Methods for Spherical Interfaces With Application to Fluid-Structure Interaction

In this work we consider the optimized Schwarz method designed for computational domains that feature spherical or almost spherical interfaces. In the first part, we consider the diffusion-reaction problem. We provide a convergence analysis of the generalized Schwarz method and, following [G. Gigante and C. Vergara, Numer. Math., 131 (2015), pp. 369--404], we discuss an optimization procedure for constant interface parameters leading to a Robin--Robin scheme. Finally, we present some numerical results both in spherical and in ellipsoidal domains. In the second part of the work, we address the fluid-structure interaction problem. Again, we provide a convergence analysis and discuss optimized choices of constant interface parameters. Finally, we present three-dimensional numerical results inspired by hemodynamic applications, to validate the proposed choices in the presence of large added mass effect. In particular, we consider numerical experiments both in an ideal spherical domain and in a realistic abdominal aortic aneurysm.

Seismic and stress qualification of LMFR fuel rod and simple method for the determination of LBE added mass effect

In this study, two different designs of liquid metal fast reactor (LMFR) fuel rods wire-wrapped and non-wire-wrapped (bare) are compared with respect to different parameters as a means of considering the optimum fuel design. Nuclear seismic rules require that systems and components that are important for safety must be capable of bearing earthquake effects, and that their integrity and functionality should be guaranteed. Mode shapes, natural frequencies, stresses on cladding, and seismic aspects are considered for comparison using ANSYS. Modal analysis is compared in a vacuum and in lead–bismuth eutectic (LBE) using potential flow theory by considering the added mass effect. A simple and accurate approach is suggested for the determination of the LBE added mass effect and is verified by a manually calculated added mass, which further proved the usefulness of potential flow theory for the accurate estimation of the added mass effect. The verification of the hydrodynamic function (τ) over the entire frequency range further validated the finite element method (FEM) modal analysis results. Stresses obtained for fuel rods against different loading combinations revealed that they were within the allowable limits with maximum stress ratios of 0.25 (bare) and 0.74 (wire-wrapped). In order to verify the structural integrity of cladding tubes, stresses along the cladding length were determined during different transients and were also calculated manually for static pressure. The manual calculations could be roughly compared with the ANSYS results, and the two showed a close agreement. Contact analysis methodology was selected, and the most appropriate analysis options were suggested for establishing contact between the wire and cladding for the wire-wrapped design grid independence analysis, which proved the accuracy of the results, confirmed the selection of the appropriate procedure, and validated the use of the ANSYS mechanical APDL code for LMFR fuel rod analysis. The results provided detailed insight into the structural design of LMFR fuel rods by considering different structural configurations (i.e., bare and wire-wrapped) in the seismic loading; this not only provides a FEM procedure for LMFR fuel with complex configuration, but also guides the reference design of LMFR fuel rods.

Vibration of a plate coupled with fluid considering the effects of stress and deformation under hydrostatic load

Abstract The effects of inner stress and geometric deformation caused by hydrostatic load on the vibration of a bottom plate-fluid coupled system are studied in detail. The Von Karman nonlinear strain displacement relationship and the Hamilton's principle are utilized to formulate the two sets of governing equations: nonlinear static equations under hydrostatic load and linear vibration equations of the plate-fluid coupled system considering the hydrostatic load effect at the nonlinear static position. A two-step theoretical approach is developed based on the equations. Experimental and numerical researches are carried out to validate the theoretical approach, and the natural frequencies derived by the three approaches coincide well. The results show that with the fluid height increasing, the natural frequencies of the plate decrease sharply at the very beginning, then increase constantly except that the fundamental frequency continues to decrease slowly. That means the added mass effect is the dominating effect when the fluid height is low, and the stiffening effect of the hydrostatic load plays a more important role with the fluid getting higher. The stress and deformation effects are considered respectively and compared in detail. Models with different fluid-plate size ratios are studied. Moreover, the hydrostatic load effect on the hydroelastic vibration responses of the plate is also analyzed.

Dynamic response analysis of polyoxymethylene hydrofoils using the hybrid pitch mode FSI method

In this paper, the objective is to analyze the dynamic responses of 2D pitching polyoxymethylene (POM) hydrofoils in the uniform flow using the hybrid coupling Fluid-Structure Interaction (FSI) method, which takes account of added mass effects and show its robustness by comparing with the experiments. First, FSI analysis using the empirical formula of hydrodynamic forces around hydrofoils was performed and validated by comparing the analysis results of the weak coupling FSI method and the hybrid coupling FSI method with the analytic solution. Next, The FSI method with Computational Fluid Dynamics (CFD) was implemented in the framework of OpenFOAM, the open-source CFD code. Flow analysis and structural analysis were performed for every time step in the calculations. Here, the flow analysis was performed using Large Eddy Simulation (LES) scheme and the structural analysis was performed by solving the equation which considered the pitch mode of deformable hydrofoils. Dynamic responses of 2D NACA0015 POM hydrofoils using the hybrid coupling FSI method well matched with the experimental results qualitatively, where dynamic responses without the hybrid coupling FSI method showed numerical instability. It is shown that the hybrid coupling FSI method considering added mass effects should be considered for analysis of deformable hydrofoils.

A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flow

A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems coupling viscous incompressible flow and compressible elastic solids. The hyperbolic system governing the solid is integrated using an explicit upwind (Godunov) scheme. The equations for the fluid are integrated using an implicit-explicit (IMEX) fractional-step scheme whereby the velocity is advanced in one step, treating the viscous terms implicitly, and the pressure is computed in a second step. The AMP interface conditions for the fluid arise from the outgoing characteristic variables in the solid, and they are partitioned into a Robin (mixed) interface condition for the pressure and interface conditions for the velocity. The latter conditions include an impedance-weighted average between fluid and solid velocities using a fluid impedance of a special form. A similar impedance-weighted average is used to define interface values for the solid. Deforming composite grids are used to effectively handle the evolving geometry and large deformations. The new algorithm is verified for accuracy and stability on a number of useful benchmark problems in two space dimensions, including a radial-piston problem for which exact solutions for radial and azimuthal motions are found and tested. Exact traveling wave solutions for a solid disk surrounded by an annular region of fluid are also derived and used to verify the AMP scheme. Fluid flow in a channel past a deformable solid annulus is computed, and the errors are estimated from a self-convergence grid refinement study. The AMP scheme is found to be stable and second-order accurate, without sub-time-step iterations, even for very difficult cases of very light solids when added-mass and added-damping effects are large.

The charmed string: self-supporting loops through air drag

The string shooter experiment uses counter-rotating pulleys to propel a closed string forward. Its steady state exhibits a transition from a gravity-dominated regime at low velocity towards a high-velocity regime where the string takes the form of a self-supporting loop. Here we show that this loop of light string is not suspended in the air due to inertia, but through the hydrodynamic drag exerted by the surrounding fluid, namely air. We investigate this drag experimentally and theoretically for a smooth long cylinder moving along its axis. We then derive the equations describing the shape of the string loop in the limit of vanishing string radius. The solutions present a critical point, analogous to a hydraulic jump, separating a supercritical zone where the wave velocity is smaller than the rope velocity, from a subcritical zone where waves propagate faster than the rope velocity. This property could be leveraged to create a white hole analogue similar to what has been demonstrated using surface waves on a flowing fluid. Loop solutions that are regular at the critical point are derived, discussed and compared to the experiment. In the general case, however, the critical point turns out to be the locus of a sharp turn of the string, which is modelled theoretically as a discontinuity. The hydrodynamic regularisation of this geometrical singularity, which involves non-local and added mass effects, is discussed on the basis of dimensional analysis.

Francis-99: Coupled simulation of the resonance effects in runner channels

A resonance phenomenon is observed experimentally in the runner channels of the Francis-99 model turbine runner. An incompressible CFD simulation is unable to simulate this. Two different coupled physics schemes are therefore presented to investigate if such effects can be replicated through simulations. The first procedure is a fully coupled acoustic-structural simulation, where the surrounding fluid is modelled using acoustic theory. This includes added mass effects and pressure propagation, but not advective and viscous effects. The second procedure is a quasi two-way coupled Fluid-Structure approach based on modal decomposition of the structural domain. In this procedure, the incompressible Navier-Stokes equations are solved along with the structural deformation.The fully coupled acoustic-structural approach does successfully exhibit a magnification of the pressure through the runner channels, indicating a resonance effect. The exact values of the acoustic pressure amplitudes are highly sensitive to the damping, the blade connection to the shroud close to the trailing edge, and more.The second procedure manages to simulate the structural deformation with the correct nodal diameters excited by the Rotor Stator Interaction, all inside the fluid solver. The pressure amplitudes however, does not exhibit the desired resonance effect, likely due to the assumption of incompressible fluid.

FSI analysis of francis-99 hydrofoil employing SBES model to adequately predict vortex shedding

The added effects from the fluid on a structure submerged in water significantly affect its dynamic response. Since the hydraulic turbine runner is geometrically complex and involves complicated flow phenomena, the research on simple hydrofoil offers a unique opportunity to investigate added effects and mutual interaction of the elastic structure and vortical flow. For this purpose, the fluid structure interaction of Francis-99 hydrofoil was analysed using the Stress Blended Eddy Simulation (SBES). Advantage of this hybrid RANS-LES turbulence model over RANS models is shown by its enhanced ability to represent vortex shedding. The results of modal sensitivity analysis showed, that fillets of the fixed hydrofoil have negligible influence on the natural frequencies of the hydrofoil and therefore the simplified geometry was used. The modal analysis of fully fixed hydrofoil both in the air and submerged in water were carried out to investigate the added mass effect. Moreover, the hydrodynamic damping for various flow velocities was also investigated for the first bending mode. Overall results are complemented by sensitivity analysis of time step size and mesh for both structural and fluid domains. The results showed that the computed damping ratio above the lock-in and vortex shedding frequency at lock-in are largely underestimated. Therefore, the geometry with blunt trailing edge was additionally tested.

Velocity Field Around a Rigid Flapping Wing with and Without Winglet in Quiescent Water

In the present paper velocity field around a rigid flapping wing is obtained to study the effect of winglet. Two dimensional particle image velocimetry (PIV) measurements are carried out to capture the velocity field. The experiments have been performed in quiescent water. A comparison between wing with and without winglet has been carried out at two flapping frequencies, namely, 1.5 and 2.0 Hz. It is observed that wing with winglet has a nontrivial effect on evolution of wingtip vortex, added mass and residual flow from previous stroke. At the beginning of downstroke, wingtip vortex does not form clearly for winglet case which is in contrast to without winglet case, while during upstroke wingtip vortex is well defined for both with and without winglet cases. Added mass is found to be lesser in winglet case in comparison with no winglet case. Residual flow in the beginning of downstroke is spread close to wing tip for winglet case over a distance of approximately unit span at same level as wingtip while for no winglet case it is spread over twice wing span with an angular orientation. During the beginning of upstroke the residual flow orientation in either case found to be nearly horizontal. Residual flow for winglet case is found to be lesser than that of no winglet case due to added mass effect. With increase in flapping frequency, added mass and velocity magnitudes in the flow field have been increased which is quite intuitive.

Fluid-structure interaction problem of hydrodynamic motion of an independent escape capsule under variable constraint conditions

Abstract Hydrodynamic behavior of an independent escape capsule from a disabled submarine is a complex six-degrees-of-freedom motion, in which added-mass effect is strong and variable constraint conditions happen. In this paper, loosely (or weakly) coupled scheme is adopted to solve this fluid-structure interaction problem. Flow field is simulated by Fluent (version 13.0.1) and motion equations are solved by the fourth-order Runge-Kutta method separately. Unstructured dynamic mesh technology is used to trace the trajectory of capsule. Hydrodynamic force is decomposed into resistance and added mass force, and new motion equations are derived in order to handle the huge added mass. The surfaces of capsule and its chamber come into contact randomly. The variable constraint conditions are analyzed and their corresponding kinematical equations are introduced. This loosely coupled scheme is applied to study the hydrodynamic behavior of a two-dimensional capsule from a narrow space into an open domain under different ocean currents. Hydrodynamic force, motion characteristics and trajectory are obtained. The simulation indicates that the velocity and direction of flow strongly affect the motion of capsule, and the contact force leads to the jamming problem of capsule during its ejection process.

Unsteady hydrodynamics of tidal turbine blades

Tidal turbines encounter a range of unsteady flow conditions, some of which may induce severe load fluctuations. Rotor blades can experience stall delay, load hysteresis and dynamic stall. Yet, the range of flow conditions which cause these effects for a full-scale axial-flow turbine are unclear. In this work we carry out a parameter study across a range of flow conditions by modelling root bending moment responses. We show how unsteadiness manifests along the span of the blade, the unsteady phenomena occurring and the conditions which induce the most significant load fluctuations. We find that waves and turbulence are the main sources of unsteadiness, and that extreme waves dominate over extreme turbulence. A yaw misalignment increases the load fluctuations but reduces the maximum peak. Large yaw angles, low tip-speed ratios, and very large waves lead to dynamic stall increasing the mean loads. Conversely, added mass effects mostly attenuate the loadings.

Numerical Modeling of Free-Surface Wave Effects on Flexural Vibration of Floating Structures

To investigate flexural vibration of structures in a fluid, a numerical algorithm was developed to relate the added mass and damping effects of the fluid to each mode of vibration. These are separate from the traditional added mass associated with rigid body motion, such as the translational motion along Cartesian axes. In this formulation, small-amplitude free surface waves were accounted for by using a nonsingular implementation of the free-surface Green’s function for a potential flow solver based on Boundary Element Method. The formulation was applied to the forced vibration of structures, namely, a hemispherical shell and a reinforced half cylinder with typical dimensions of ships and offshore structures, to obtain their dynamic response at various excitation frequencies. It is observed that resonance frequency of the structure, in contact with water, decreases due to the added mass effect. The influence of the free-surface wave on the fluid loading was investigated for large structures. It is simpler to relate the fluid added mass to mode shapes rather than distribution of fluid load over wetted surface of the structure in engineering simulations. Moreover, it is found that the vibration energy radiated away by the fluid surface wave has little influence on the vibration response of the shell structures.