J. Antunes

Random excitation of heat exchangertubes by cross-flows

This paper investigates the random excitation mechanism of tube arrays in cross-flow, also often called “turbulent buffeting”. It summarizes the experimental data obtained so far at CEA-Saclay on various tube bundles subjected to single and to two-phase flows. An attempt is made to put them into an appropriate theoretical framework. The formalism used to reduce the force spectra produced by single-phase cross-flow is first reviewed. It allows the determination of a reduced force spectrum which is found to be fairly independent of the tube array geometry. On the other hand, the situation in two-phase flow still remains insufficiently documented. Based on the restricted data set obtained at Saclay in the high void fraction range, random forces produced by air-water and by steam-water mixtures would be of the same order of magnitude. Only a crude estimate of it can be produced by using the single-phase force spectrum together with the homogeneous two-phase flow model without slip. Further investigations are still clearly required to confirm such preliminary conclusions and to derive the physically relevant scaling factors to reduce conveniently the two-phase data.

Coulomb friction modelling in numericalsimulations of vibration and wear work rate of multispan tube bundles

The working life of heat exchanger multispan tube bundless, and similar components subjected to flow-induced virabtion, is heavily dependent on nonlinear interaction between the loosely supported tubes and their supports. Therefore, reliable wear prediction techniques must account for a number of factorscontrolling impact-sliding tube response, such as tube support gap, contact stiffness impact damping, Coulomb friction and squeeze film effect at supports. Tube fretting wear potential risk may then be adequately quantified by an equivalent wear work rate. In this paper, a simple model is presented which accounts for the key aspects of dry friction and is well suited to the efficient explicit numerical integration schemes, specifically through nonlinear modal superposition. Extensive parametric two-dimensional simulations, under random vibration induced byflow turbulence, are presented. Also, the effect of permanent tube-support preload, arising from cross flow drag, tube-support masalignment and thermal expansion, is investigated. Results show that frictional forces consistently reduce wear work rates, which decreasefor higher values of the coefficient of friction. Indeed, such reductions may be extremely important for the limiting case when preload and frictional forces rate of sufficient magnitude to overcome dynamic forces, preventing tube-support relative motion.

Flexural vibrations of rotors immersed in dense fluids part I: Theory

Abstract In this paper, the linear vibrations arising in rotating shafts immersed in a dense annular fluid are analyzed from a theoretical point of view. It is found that even at relatively slow rotating speeds fluid elastic forces induced by the co-rotating flow surrounding the shaft significantly affect the transverse natural modes of vibration of the shaft: each transverse mode related to the shaft at rest gives rise to a forward whirl or direct mode and to a backward whirl or retrograde mode. Linear stability of such modes is also analyzed.

Flexural vibrations of rotors immersed in dense fluids Part II: Experiments

Abstract This paper describes experimental work carried out on a homogeneous rotating shaft partially immersed in an annular space of water. Experimental results concerning the natural frequencies and reduced damping of the first pair of transverse modes are found to agree fairly well with the analytical model presented in Part I, at least in a rotating velocity range below the buckling instability of the retrograde mode.

Remote Identification of Impact Forces on Loosely Supported Tubes: Analysis of Multi-Supported Systems

Impact forces are useful information in field monitoring of many industrial components, such as heat exchangers, condensers, etc. In two previous papers we presented techniques-based on vibratory measurements remote from the actual impact locations-for the experimental identification of isolated impacts (Araujo et al., 1996) and complex rattling forces (Antunes et al., 1997). In both papers a single gap support was assumed. Those results concern systems which are simpler than the actual multi-supported tube bundles found in heat exchangers. Impact force identification is a difficult problem for such systems, because 1) when sensed by the remote motion transducers, the traveling waves generated at several impact supports are mixed, and there is no obvious way to isolate the contribution of each support; 2) multi-supported tubes may be quite long, with significant dissipative effects (by interacting flows or by frictional phenomena at the clearance supports), leading to some loss of the information carried by the traveling waves; 3) in multi-supported systems, some of the supports are often in permanent contact, leading to nonimpulsive forces which are difficult to identify. In this paper, we move closer towards force identification under realistic conditions. Only the first problem of wave isolation is addressed, assuming that damping effects are small and also that all clearance supports are impacting. An iterative multiple-identification method is introduced, which operates in an alternate fashion between the time and frequency domains. This technique proved to be effective in isolating the impact forces generated at each gap support. Experiments were performed on a long beam with three clearance supports, excited by random forces. Beam motions were planar, with complex rattling at the supports. Experimental results are quite satisfactory, as the identified impact forces compare favorably with the direct measurements.

Nonlinear analysis of the orbital motions of immersed rotors using a spectral/Galerkin approach

Abstract We recently developed a symbolic-numerical formulation for the nonlinear planar motion of rotors under fluid confinement, based on a spectral/Galerkin approach, for gap geometries of about δ = H / R ≈0.1––where H is the average annular gap and R is the rotor radius. Results showed a quite good agreement between the class of approximate models generated, the corresponding analytical exact planar model and experiments. This methodology can be almost entirely automated on a symbolic computing environment. In the present paper this symbolic-numerical spectral/Galerkin procedure is extended in order to deal with nonlinear orbital motions–– X ( t ) and Y ( t ) taking place in orthogonal directions. Numerical simulations performed over a centered rotor configuration maintained by nonisotropic supports ( K st Y / K st X =0.4, where K st X and K st Y stand for the structural stiffnesses), which exhibit interesting dynamics, show a quite good agreement between this type of approximate models and the corresponding analytical exact (but quite involved) model, developed in the past by the authors. With the proposed symbolic-numerical approach one can obtain accurate nonlinear dynamical formulations enabling the study, understanding and prediction of nonlinear orbital rotor dynamics.

TIME-DOMAIN MODELING OF THE RANDOM VIBRATIONS OF TUBES SUBJECTED TO TURBULENCE-CONVEYING FLOWS

The vibrations of multi-supported tubes subjected to flow excitation have been the subject of active research for many years, in particular connected with the critical design of heat exchangers and fuel bundles of nuclear power facilities. Because tubes are often loosely supported, their nonlinear dynamics are conveniently addressed through time-domain numerical simulations, for the predictive analysis with respect to wear and fatigue. Turbulence is one of the main excitation mechanisms which drive tube vibrations. We recently revisited the problem of random excitation generation in the time domain, for transverse flows. A new simplified an efficient technique was developed, which properly emulates the spectral and spatial features of the turbulence force field. Results were successfully compared with those from another generation method based on the classical work by Shinozuka and co-workers. In the present paper, we extend our previous work by modeling the time-domain random excitation from flows which display a significant axial velocity component, leading to the convection of turbulence fluctuations. This problem has been addressed by many authors in the past, mainly focusing on linear analysis in the frequency domain, for flow-excited plates, pipes and tubes. Here, for the purpose of nonlinear analysis, we focus on two techniques for generating time-domain turbulence excitations which properly account for the effects of the axial transport term in convective flows. We start by extending our original random force generation method, in order to emulate axial turbulent flows. For the purpose of physical discussion and computational efficiency evaluation, we also implemented an updated version of Shinozuka’s excitation generation technique. We discuss the use of random forces applied at fixed locations, but also investigate the use of axially convected travelling forces. The practical significance of the cross-spectral convection term is evaluated for pure axial and mixed flows. Finally, because time-domain dynamical simulations of practical interest are usually two-dimensional, we discuss the correlation of the orthogonal random forces generated along the motion directions, when simulating two-dimensional turbulence fields.Copyright

Experimental Validation of Theoretical Models for the Linear and Nonlinear Vibrations of Immersed Rotors

Vibration of rotating shafts has been studied for different gap geometries, ranging from bearing configurations to pump systems. This paper deals with the rotor-flow dynamics of immersed shafts under moderate confinement-clearance gap about S=#=O.l( h w ere H is the average gap and R is the rotor radius). Following simplified assumptions, analytical models for the linearized forces, for both centered and eccentric immersed rotors have been developed as well as a theoretical nonlinear model which fully describes the nonlinear flow terms. These models were supported by encouraging results from preliminary experiments. In the present paper, we discuss some recent and representative results of an extensive series of tests performed on a small-scale model, in order to assert the validity of our theoretical models. From the overall experimental programma, the following conclusions emerged: (1) The linearized bulk-flow model is adequate, provided the dissipative effects are duly accounted for using an empirical friction coefficient to empirically model the turbulent stresses. Such predictions are quite accurate if the system is working at low rotor eccentricities and far from the instability boundaries. (2) However, for large rotor eccentricities and for dynamic regimes near the linear instability, the fully nonlinear model ‘Visiting researcher at Institute of Nuclear Technology. leads to better predictions. Obviously, these effects are instrumental to obtaining reasonable predictions for all post-stable motion regimes. (3) When discrepancies arise, the nonlinear model was usually found to be conservative. INTRODUCTION The effects of co-rotating annular flows on rotor vibrations have been studied extensively by many researchers, mostly in connection with bearings and seals [see for instance (Chills, 1993)]. However, flow structure interaction can also lead to significant effects in less common devices. In this paper we will address the dynamical behavior of immersed rotors, such as found in fast-breeder nuclear reactor pumps (for circulating the liquid sodium), and other ap plications. In such components, the clearance ratio 6 = H/R (where H is the average gap and R is the rotor radius) is typically about 0.1 -one or two orders of magnitude higher than the clearances found in bearings and seals. As a consequence, the flow is quite turbulent, inertial effects are then of prime importance and cannot be neglected as assumed in the basic Reynolds equation approach. Also, the shaft length subject to fluid forces is quite significant, these combined effects leading to specific rotordynamic properties. Using simplified assumptions for the flow, we have developed analytical models for the linearized forces, for both centered and eccentric rotors [ (Axisa and Antunes, 1992), (Antunes et al., 1996) and (Moreira et al., 2OOO)]. Because the flow was modeled as being two-dimensional, it was possible to extend our analytical solutions to fully account for the nonlin-

Design of duct cross sectional areas in bass-trapping resonators for control rooms

Small rooms, such as the ones specifically designed for listening to amplified music, like control rooms in recording studios, face the problem of low-frequency over-enhancement by acoustic resonances. Several devices have been developed to tackle this problem, such as Helmoltz resonators. The number of controlled acoustic modes depends on several factors among which are the central frequency chosen, the modal density in that frequency range, and the coupling between the resonator and the room. In this paper we suggest that the efficiency of such resonators may be significantly improved if, instead of using basic Helmholtz or devices with uniform cross-section, more complex shape-optimized resonators are used, in order to cope with a larger number of undesirable acoustic modes. We apply optimization techniques to the uncoupled resonator, developed in our previous work, in order to obtain the optimal shapes for devices that resonate at a design set of acoustic eigenvalues, within imposed physical and/or geometrical constraints. One-dimensional and three-dimensional finite element models were implemented. The one-dimensional model was coupled to optimization techniques in order to achieve the design goal. We illustrate the proposed approach with two examples of resonator shapes and different design sets of absorption frequencies.

An improved linear model for rotors subject to dissipative annular flows

Abstract In a previous paper, Antunes, Axisa, and co-workers, developed a linearized model for the dynamic of rotors under moderate fluid confinement, based on classical perturbation analysis, covering two different cases: (i) dissipative motions of a centered rotor; (ii) motions of an eccentric rotor for frictionless flow. Following the same procedures and assumptions, we derive here an improved model for the more general case of dissipative linearized motions of an eccentric rotor . Besides the rotor motion variables, a new variable—which can be interpreted as the fluctuating term of the average tangential velocity—is introduced, yielding an additional eigenvalue in the linear analysis. The new variable introduced, which is coupled with the rotor motions, is very convenient when frictional effects are not neglected. Under dissipative flows, a richer modal behavior is highlighted, which can be related to delay effects of the flow responses to the rotor motions. Our approach can be applied as well to other flow-excited systems, for example, those subjected to axial or leakage flows. Because rotor-dynamics are strongly dependent on the mean rotor eccentricity, the adequacy of this (or any other) model rely on using the actual value for such parameter.