M. Najafi

Publications

3 Rotor Dynamic Analysis for a Shaft Train by Using Finite Element Method

Authors: M. Najafi

Abstract:

In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.

Keywords: Finite Element Method, campbell diagram, rotor dynamic analysis, shaft train

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2 Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

Authors: F. Rahimi Dehgolan, M. Najafi

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Stability, bifurcation, non-linear vibration, axially moving beam, multiple scales method

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1 Super Harmonic Nonlinear Lateral Vibration of an Axially Moving Beam with Rotating Prismatic Joint

Authors: F. Rahimi Dehgolan, S. Bab, M. Najafi

Abstract:

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Galerkin Method, super harmonic resonances, non-linear vibration, axially moving beam

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Abstracts

6 Rotor Dynamic Analysis for a Shaft Train by Using Finite Element Method

Authors: M. Najafi

Abstract:

In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.

Keywords: Finite Element Method, campbell diagram, rotor dynamic analysis, shaft train

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5 Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

Authors: F. Rahimi Dehgolan, M. Najafi

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Stability, bifurcation, non-linear vibration, axially moving beam, multiple scales method

Procedia PDF Downloads 189
4 Super Harmonic Nonlinear Lateral Vibration of an Axially Moving Beam with Rotating Prismatic Joint

Authors: F. Rahimi Dehgolan, S. Bab, M. Najafi

Abstract:

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Galerkin Method, super harmonic resonances, non-linear vibration, axially moving beam

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3 2D CFD-PBM Coupled Model of Particle Growth in an Industrial Gas Phase Fluidized Bed Polymerization Reactor

Authors: M. Najafi, H. Kazemi Esfeh, V. Akbari, M. Ehdaei, T. N. G. Borhani, A. Shamiri

Abstract:

In an industrial fluidized bed polymerization reactor, particle size distribution (PSD) plays a significant role in the reactor efficiency evaluation. The computational fluid dynamic (CFD) models coupled with population balance equation (CFD-PBM) have been extensively employed to investigate the flow behavior in the poly-disperse multiphase fluidized bed reactors (FBRs) utilizing ANSYS Fluent code. In this study, an existing CFD-PBM/ DQMOM coupled modeling framework has been used to highlight its potential to analyze the industrial-scale gas phase polymerization reactor. The predicted results reveal an acceptable agreement with the observed industrial data in terms of pressure drop and bed height. The simulated results also indicate that the higher particle growth rate can be achieved for bigger particles. Hence, the 2D CFD-PBM/DQMOM coupled model can be used as a reliable tool for analyzing and improving the design and operation of the gas phase polymerization FBRs.

Keywords: Computational Fluid Dynamics, population balance equation, fluidized bed polymerization reactor, direct quadrature method of moments

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2 Experimental Investigation on the Effect of Adding CuO Nanoparticles to R-600a Refrigerant on Heat Transfer Enhancement of a Horizontal Flattened Tube

Authors: A. Abbasi, M. Najafi, M. A. Akhavan-Behabadi

Abstract:

An empirical investigation was performed in order to study the heat transfer characteristics of R600a flow boiling inside horizontal flattened tubes and the simultaneous effect of nanoparticles on boiling heat transfer in flattened channel. Round copper tubes of 8.7 mm I.D. were deformed into flattened shapes with different inside heights of 6.9, 5.5, and 3.4 mm as test areas. The effect of different parameters such as mass flux, vapor quality and inside height on heat transfer coefficient was studied. Flattening the tube caused significant enhancement in heat transfer performance so that the maximum augmentation ratio of 163% was obtained in flattened channel with lowest internal height. A new correlation was developed based on the present experimental data to predict the heat transfer coefficient in flattened tubes. This correlation estimated 90% of the entire database within ±20%.

Keywords: flattend tube, nano particles, R600a, CuO

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1 The Effect of Adding CuO Nanoparticles on Boiling Heat Transfer Enhancement in Horizontal Flattened Tubes

Authors: A. Abbasi, M. Najafi, M. A. Akhavan-Behabadi

Abstract:

An empirical investigation was performed in order to study the heat transfer characteristics of R600a flow boiling inside horizontal flattened tubes and the simultaneous effect of nanoparticles on boiling heat transfer in flattened channel. Round copper tubes of 8.7 mm I.D. were deformed into flattened shapes with different inside heights of 6.9, 5.5, and 3.4 mm as test areas. The effect of different parameters such as mass flux, vapor quality and inside height on heat transfer coefficient was studied. Flattening the tube caused a significant enhancement in heat transfer performance, so that the maximum augmentation ratio of 163% was obtained in flattened channel with lowest internal height. A new correlation was developed based on the present experimental data to predict the heat transfer coefficient in flattened tubes. This correlation estimated 90% of the entire database within ±20%. The best flat channel with the point of view of heat transfer performance was selected to study the effect of nanoparticle on heat transfer enhancement. Four homogenized mixtures containing 1% weight fraction of R600a/oil with different CuO nanoparticles concentration including 0.5%, 1% and 1.5% mass fraction of R600a/oil/CuO were studied. Observations show that heat transfer was improved by adding nanoparticles, which lead to maximum enhancement of 79% compare to the pure refrigerant at the same test condition.

Keywords: Heat Transfer, Transport Phenomena, nano fluids, flattend tube

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