Hydroelastic Stability and Vibration of a Large Reactor Pendulum Structure

Author(s):  
Gregory A. Meyer ◽  
Gregory A. Banyay ◽  
Samuel A. Maeby ◽  
Scott E. Sidener ◽  
Richard E. Schwirian

Parallel-flow induced vibrations of both large and small reactor internal structures have been analyzed in the past for multiple reactor types. In parallel flows relating to annular and leakage flows, the possibility for significant wear issues can arise and need to be assessed as has been shown throughout the literature. With parallel flow induced vibration, a particular fluid-structure interaction known as hydroelastic instability can arise. If hydroelastic instability occurs, damage to components can be severe and/or catastrophic. This particular phenomenon has been studied in the literature and a few empirically derived methodologies have been published to evaluate the potential for hydroelastic instability to occur in both a limited number of specific geometries and some generic geometries. However, as structural components and their associated flow field characteristics can vary significantly and because of the potential for catastrophic damage to reactor components and the associated costs, a more detailed first principles approach may be warranted to further determine if hydroelastic instability is not only possible, but probable. A potential design for a reactor internals test in which part of the upper internals would exhibit significant annular parallel flow velocities is analyzed for the potential onset of hydroelastic instability. In particular, the upper core plate, which is attached to the rest of the upper internals via support columns in a pendulum setup with the attachment/pivot point at the upper pressure vessel head flange, is temporarily designed to carry a significant non-prototypic pressure drop causing significant upper core plate to core barrel gap flow velocities and potential instability issues. Due to the different geometry of this hardware configuration compared to those found in the literature, both an empirically-based stability analysis from the literature and a first-principles based hydroelastic stability analysis are conducted. The first-principles analysis derives and solves the time-dependent equations of motion and mass conservation for both the fluid and structure and compares the results proximity to stability limits found in the literature. A comparison of the empirically based stability assessment with the first-principles stability analysis is made. Furthermore, an assessment of the probability for the onset of hydroelastic instability of the upper internals assembly is made via a Monte Carlo simulation using the first-principles analysis methodology.

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 7446
Author(s):  
Adrian Kampa ◽  
Iwona Paprocka

The aim of this paper is to present a model of energy efficient scheduling for series production systems during operation, including setup and shutdown activities. The flow shop system together with setup, shutdown times and energy consumption are considered. Production tasks enter the system with exponentially distributed interarrival times and are carried out according to the times assumed as predefined. Tasks arriving from one waiting queue are handled in the order set by the Multi Objective Immune Algorithm. Tasks are stored in a finite-capacity buffer if machines are busy, or setup activities are being performed. Whenever a production system is idle, machines are stopped according to shutdown times in order to save energy. A machine requires setup time before executing the first batch of jobs after the idle time. Scientists agree that turning off an idle machine is a common measure that is appropriate for all types of workshops, but usually requires more steps, such as setup and shutdown. Literature analysis shows that there is a research gap regarding multi-objective algorithms, as minimizing energy consumption is not the only factor affecting the total manufacturing cost—there are other factors, such as late delivery cost or early delivery cost with additional storage cost, which make the optimization of the total cost of the production process more complicated. Another goal is to develop previous scheduling algorithms and research framework for energy efficient scheduling. The impact of the input data on the production system performance and energy consumption for series production is investigated in serial, parallel or serial–parallel flows. Parallel flow of upcoming tasks achieves minimum values of makespan criterion. Serial and serial–parallel flows of arriving tasks ensure minimum cost of energy consumption. Parallel flow of arriving tasks ensures minimum values of the costs of tardiness or premature execution. Parallel flow or serial–parallel flow of incoming tasks allows one to implement schedules with tasks that are not delayed.


Author(s):  
Ehsan Sarshari ◽  
Nastaran Vasegh ◽  
Mehran Khaghani ◽  
Saeid Dousti

Ziegler’s pendulum is an appropriate model of a non-conservative dynamic system. By considering gravity effect, new equations of motion are extracted from Newton’s motion laws. The instability of equilibriums is determined by linear stability analysis. Chaotic behavior of the model is shown by numerical simulations. Sliding mode controller is used for eliminating chaos and for stabilizing the equilibriums.


Author(s):  
Yu Wang

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.


Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra K Kakoty

Rotors supported on gas foil bearings have low damping characteristics, which limits its application. A possible solution could be an integration of a gas foil bearing with an electromagnetic actuator. This paper discusses the effect of electromagnetic actuators on the stability of a rotor supported on gas foil bearings. A coupled dynamic model combining the dynamics of gas foil bearing and electromagnetic actuator has been developed. The fluid film forces from the gas foil bearings and the electromagnetic forces from the electromagnetic actuators are integrated into the equations of motion of the rotor. The sub-synchronous vibration present in case of conventional gas foil bearings is reduced and the stability band of the rotor is increased due to the implementation of electromagnetic actuator.


Author(s):  
M. Kim ◽  
P. Hughes ◽  
R. A. Ainsworth

This paper provides an overview of International Atomic Energy Agency (IAEA) draft technical guidelines on Fluid-Structure Interaction (FSI), which is supporting document for IAEA Safety Standards aimed at providing method and practices. The technical guidelines are based on sections in codes and standards, more general documents on FSI and documents describing particular plant issues or problems. The technical guidelines recognise that FSI has led to a range of problems in a range of reactor types including: flow-induced vibration in light water reactor (LWR) steam generators under external loading including seismic loading; fretting of LWR heat exchangers with the fretting loading dependent on cross-flow velocity; seismic effects and fluid sloshing in liquid metal cooled faster breeder reactor (LMFBR); and water hammer. In addition to providing an overview description of the technical guidelines, the paper also describes the process followed to produce and obtain peer review of the document.


Author(s):  
Ram Turaga

The influence of deterministic surface texture on the sub-synchronous whirl stability of a rigid rotor has been studied. Non-linear transient stability analysis has been performed to study the stability of a rigid rotor supported on two symmetric journal bearings with a rectangular dimple of large aspect ratio. The surface texture parameters considered are dimple depth to minimum film thickness ratio and the location of the dimple on the bearing surface. Journal bearings of different Length to diameter ratios have been studied. The governing Reynolds equation for finite journal bearings with incompressible fluid has been solved using the Finite Element Method under isothermal conditions. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. When the dimple is located in the raising part of the pressure curve the positive rectangular dimple is seen to decrease the stability whereas the negative rectangular dimple is seen to improve the stability of the rigid rotor.


Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Masakazu Ono

In this paper, the dynamic stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper, the third part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on circumferential vibration, that is, the ovaling vibration of a shell. The coupled equations of motion between shell and liquid are obtained by using Donnell’s shell theory and the Navier-Stokes equation. The added mass, added damping and added stiffness in the coupled equations of motion are described by utilizing the unsteady fluid pressure acting on the shell. The relations between axial velocity and the unstable vibration phenomena are clarified concerning the circumferential vibration of a shell. Numerical parametric studies are done for various dimensions of a shell and an axial leakage flow.


Author(s):  
Miranda M. Tanouye ◽  
Vishesh Vikas

Traditional tensegrity mechanisms are comprised of compressive (rigid rods) and tensile members (strings). Compliant tensegrity mechanisms (CoTM) introduce springs alongside strings and rods, allowing these structures to be more adaptable and robust. The kinematic and stability analyses of such mechanisms will facilitate better behavioral understanding for control of such structures. Generally, the kinematic analysis assumes zero-free length (ZFL) springs which facilitates simplification of equations of motion. However, a general ZFL does not exist and the relaxation of ZFL assumption for a CoTM introduces computational complexities resulting from their non-linear nature. The research considers equilibrium and stability analysis of a planar CoTM mechanism consisting of two triangular platforms connected by a compressive member and two spring elements. For an assumed numerical example, the analysis illustrates the increase in computation complexity, and non-linear behavior of equilibrium and stable solutions as assumption is relaxed from 1) both spring ZFL, to 2) one spring ZFL, and 3) no spring ZFL.


1984 ◽  
Vol 148 ◽  
pp. 301-318 ◽  
Author(s):  
A. Biesheuvel ◽  
L. Van Wijngaarden

Equations of motion correct to the first order of the gas concentration by volume are derived for a dispersion of gas bubbles in liquid through systematic averaging of the equations on the microlevel. First, by ensemble averaging, an expression for the average stress tensor is obtained, which is non-isotropic although the local stress tensors in the constituent phases are isotropic (viscosity is neglected). Next, by applying the same technique, the momentum-flux tensor of the entire mixture is obtained. An equation expressing the fact that the average force on a massless bubble is zero leads to a third relation. Complemented with mass-conservation equations for liquid and gas, these equations appear to constitute a completely hyperbolic system, unlike the systems with complex characteristics found previously. The characteristic speeds are calculated and shown to be related to the propagation speeds of acoustic waves and concentration waves.


2013 ◽  
Vol 392 ◽  
pp. 156-160
Author(s):  
Ju Seok Kang

Multibody dynamics analysis is advantageous in that it uses real dimensions and design parameters. In this study, the stability analysis of a railway vehicle based on multibody dynamics analysis is presented. The equations for the contact points and contact forces between the wheel and the rail are derived using a wheelset model. The dynamics equations of the wheelset are combined with the dynamics equations of the other parts of the railway vehicle, which are obtained by general multibody dynamics analysis. The equations of motion of the railway vehicle are linearized by using the perturbation method. The eigenvalues of these linear dynamics equations are calculated and the critical speed is found.


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