Chandramouli Padmanabhan

Computationally efficient model for refrigeration compressor gas dynamics

In this paper a computationally efficient steady state model for a typical refrigeration reciprocating compressor is proposed. The plenum cavity is modelled using the acoustic plane wave theory, while the compression process is modelled as a one-dimensional gas dynamics equation. Valve dynamic models, based on a single vibration mode approximation, are coupled with the gas dynamics equation and acoustic plenum models. The steady-state solution of the resultant coupled non-linear equations are posed as a boundary value problem and solved using Warners algorithm. The Warners algorithm applied to compressor simulation is shown to be computationally more efficient as compared to conventional techniques such as shooting methods. Comparisons are based on the number of iterations and time taken for convergence. Effect of operating conditions on the overall compressor performance is also investigated.

A semi-analytical coupled finite element formulation for shells conveying fluids

Abstract A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoullis equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid–structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed.

Active control of beam with magnetostrictive layer

Abstract The paper analyses the damping characteristics obtained using a distributed magnetostrictive layer bonded to an aluminum beam for different boundary conditions and coil configurations. The magnetostrictive layer produces the actuating force required to control the vibration in the beam, based on a negative velocity feedback control law. The control input is the current to the solenoid surrounding the beam. Prior formulations in the literature have assumed that the current through the coil is a function of axial distance. Even though this assumption is mathematically valid, a physical consideration of the problem limits such an assumption. In the present study, perhaps for the first time, a finite element formulation, physically consistent with the problem has been developed. Vibration reduction in the beam, by positioning the magnetostrictive layer and its current carrying actuating coil pair along the beam is investigated. Issues associated with control for different boundary condition are highlighted.

Active control of cylindrical shell with magnetostrictive layer

This paper analyses the damping characteristics of a titanium shell with a magnetostrictive layer bonded to it. The magnetostrictive layer produces an actuating force required to control vibration in the shell, based on a negative velocity feedback control law. The control input is the current to the solenoid surrounding the shell. In the present study, a finite element formulation, physically consistent with the problem has been developed. Vibration reduction in the shell by changing the position of the magnetostrictive layer and its current carrying actuating coil pair along the shell is investigated.

VIBRO-ACOUSTIC RESPONSE OF A CIRCULAR ISOTROPIC CYLINDRICAL SHELL UNDER A THERMAL ENVIRONMENT

This paper presents numerical simulation studies on the vibration and acoustic response-characteristics of an isotropic cylindrical shell under a thermal environment using commercial softwares ANSYS and SYSNOISE. First, the critical buckling temperature is obtained, followed by modal and harmonic response analyses considering pre-stress due to the thermal field in the cylindrical shell, with the critical buckling temperature as a parameter. The vibration response predicted is then used to compute the sound radiation. It is found that there is a significant change in the vibration mode shapes and ring frequency towards the lowest natural frequency with an increase in temperature. There is a sudden increase in overall sound power level near the critical buckling temperature and significant changes in mode shapes with temperature does not affect the overall sound power level.

Model reduction for parametric instability analysis in shells conveying fluid

Abstract Flexible pipes conveying fluid are often subjected to parametric excitation due to time-periodic flow fluctuations. Such systems are known to exhibit complex instability phenomena such as divergence and coupled-mode flutter. Investigators have typically used weighted residual techniques, to reduce the continuous system model into a discrete model, based on approximation functions with global support, for carrying out stability analysis. While this approach is useful for straight pipes, modelling based on FEM is needed for the study of complicated piping systems, where the approximation functions used are local in support. However, the size of the problem is now significantly larger and for computationally efficient stability analysis, model reduction is necessary. In this paper, model reduction techniques are developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure. It is shown that only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible. The numerical technique developed by Friedmann and Hammond (Int. J. Numer. Methods Eng. Efficient 11 (1997) 1117) is used for the stability analysis. One of the key research issues is to establish criteria for deciding the basis vectors essential for an accurate stability analysis. This paper examines this issue in detail and proposes new guidelines for their selection.

Active control of simply supported plates with a magnetostrictive layer

This paper deals with the damping characteristics obtained by using a distributed magnetostrictive layer, bonded to an aluminum plate for different boundary conditions and coil configurations. The magnetostrictive layer is used to induce the actuating force to control vibration in the plate, based on a negative velocity feedback control law. The control input is the current to the solenoid surrounding the plate. In several prior formulations in the literature, it has been assumed that the current through the coil is a function of axial distance. Even though this assumption is mathematically valid, a physical consideration of the problem does not allow such an assumption. In the present study, perhaps for the first time, a finite element formulation, physically consistent with the problem, has been developed. Vibration reduction in the plate by positioning the magnetostrictive layer and its current carrying actuating coil pair along the plate is investigated. Issues associated with control for different boundary condition are highlighted.

Static and free vibration studies on a pulley-belt system with ground stiffness

The static and free vibration behavior of a pulley-belt system with ground stiffness is investigated using a nonlinear model based on Hamilton’s principle. In the equilibrium analysis a computational method based on boundary value problem solvers is adapted to obtain the numerical solution, whereas for free vibration analysis spatial discretization is done using the Galerkin’s method to evaluate the natural frequencies and vibration modes. The study indicates that there is a considerable decrease in equilibrium deflection due to ground stiffness, especially when it is larger than the belt bending stiffness and this effect is more pronounced for higher values of belt bending stiffness. Equilibrium deflections change reasonably with static span tension variation, but are more sensitive to variations of speed and longitudinal stiffness. The natural frequencies of the pulley-belt system increase with ground stiffness, but this is primarily restricted to the lower modes; higher

Experimental and numerical investigations on rotor–stator rub:

The focus of the current study is on the dynamics of rubbing between the rotor and stator parts in a rotating machine. Rub is a malfunction associated with the physical contact of rotating and stationary parts, which are otherwise not in contact. Because of the nonlinear nature of the problem the simulation time is significant even for small size systems. The rubbing is localized in space, either at the seal locations or at the interface between the rotor blade and stator. Since the nonlinearity is localized, reduced models can be developed for efficient computation. The objective of the present study is to develop a computationally efficient methodology for analyzing the rotor stator rub, by applying model reduction techniques using component mode synthesis, solving the reduced problem using harmonic balance method and time variational method. A hypersphere-based continuation algorithm is used for tracing the unstable branches and a backward differentiation formula based predictor is used for the Newton–Raphson update. The numerical results are validated by performing experiments.

Design relation and end correction formula for multi-orifice Helmholtz resonators with intrusions

Helmholtz resonators are used to control low-frequency noise in cavities. One of the ways to reduce the resonance frequency of a resonator without changing its volume is to introduce an intrusion. Similarly, the introduction of multiple orifices can increase the resonance frequency without changing the resonator volume. These features provide an ability to accommodate slight changes in the cavity/enclosure frequencies during the design process. However, one has to rely on extensive three-dimensional finite element or boundary element simulations to predict the resonator characteristics with the introduction of these features. To reduce the computational burden, a design relation, between the first resonance frequency of a single orifice intruded resonator with that of a multi-orifice intruded resonator, is proposed in this paper. In developing this design relation, the total cross-sectional area of the resonator with multiple orifices is the same as that of the single orifice resonator. It is shown that this design relation is independent of the shape/size of the orifices and resonator cavity. Using this relation, a new end correction formula for the orifice lengths of multi-orifice intruded resonators has been proposed. The end correction formula can be used to calculate the reactance of multi-orifice intruded Helmholtz resonators analytically. These expressions are derived by carrying out extensive simulations of the resonators using the boundary element method. Limited experiments have been carried out to validate the proposed approach. The use of these expressions will reduce the computational cost of simulating cavities embedded with resonators as one can avoid modeling the resonators and use impedance boundary conditions instead.