Critical Fluid Velocity Research Articles

Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation

In this study, nonlinear vibration and stability of a polymeric pipe reinforced by single-walled carbon naotubes (SWCNTs) conveying fluid-nanoparticles mixture flow is investigated. The Characteristics of the equivalent composite are determined using Mori-Tanaka model considering agglomeration effects. The surrounding elastic medium is simulated by orthotropic visco-Pasternak medium. Employing nonlinear strains-displacements, stress-strain energy method the governing equations were derived using Hamilton\'s principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The influence of volume percent of SWCNTs, agglomeration, geometrical parameters of pipe, viscoelastic foundation and fluid velocity are shown on the frequency and critical fluid velocity of pipe. Results showed the increasing volume percent of SWCNTs leads to higher frequency and critical fluid velocity.

THERMO-FLUIDIC PARAMETERS EFFECTS ON NONLINEAR VIBRATION OF FLUID-CONVEYING NANOTUBE RESTING ON ELASTIC FOUNDATIONS USING HOMOTOPY PERTURBATION METHOD

In this paper, effects of thermo-fluidic parameters on the nonlinear dynamic behaviours of single-walled carbon nanotube conveying fluid with slip boundary conditions and resting on linear and nonlinear elastic foundations under external applied tension and global pressure is studied using homotopy perturbation method.  From the result, it is observed that increase in the Knudsen number, the slip parameter,  leads to decrease in the frequency of vibration and the critical velocity while natural frequency and the critical fluid velocity increase as the in stretching effect increases.  Also, as the Knudsen number increases, the bending stiffness of the nanotube decreases and in consequent, the critical continuum flow velocity decreases as the curves shift to the lowest frequency zone. As the change in temperature increases, the natural frequencies and the critical flow velocity of the structure increase for the low or room temperature while at high temperature, increase in temperature change, decreases the natural frequencies and the critical flow velocity of the structure. Further, it is established that the alteration of nonlinear flow-induced frequency from linear frequency is significant as the amplitude, flow velocity and axial tension increase. The developed analytical solutions can be used as starting points for better understanding of the relationship between the physical quantities of the problem.

Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects

Fluid velocity analysis on the instability of pipes reinforced by silica nanoparticles (SiO2) is presented in this paper. Mori-Tanaka model is used for obtaining the effective materials properties of the nanocomposite structure considering agglomeration effects. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on the Reddy higher-order shear deformation theory, the motion equations are derived based on energy method and Hamilton\'s principal. The frequency and critical fluid velocity of structure are calculated using differential quadrature method (DQM) so that the effects of different parameters such as volume fractions of SiO2 nanoparticles, SiO2 nanoparticles agglomeration, boundary conditions and geometrical parameters of pipes are considered on the nonlinear vibration and instability of the pipe. Results indicate that increasing the volume fractions of SiO2 nanoparticles, the frequency and critical fluid velocity of the structure are increased. Furthermore, considering SiO2 nanoparticles agglomeration, decreases the frequency and critical fluid velocity of the pipe.

Nonlinear dynamics analysis of pipe conveying fluid by Riccati absolute nodal coordinate transfer matrix method

Based on the absolute nodal coordinate (ANC) formulation and transfer matrix method (TMM), a novel efficient Riccati ANC–TMM is applied to nonlinear dynamics analysis of pipe conveying fluid with large deformations. By deducing the new transfer equations of pipe elements in the ANC frame and introducing Riccati transform technology into the dynamics solution algorithm, the nonlinear dynamics of pipe conveying fluid can be calculated highly efficient and stable. An illustrative comparison simulation of a cantilever pipe conveying fluid by using this method and ordinary ANC method is presented, and its critical fluid velocity and other nonlinear dynamics behavior are analyzed. Compared with ordinary ANC method, this method avoids the higher-order global differential or differential-algebra equations of the system, therefore, its computational efficiency could be improved essentially. It may be further extended to study nonlinear dynamic characteristics of a pipe conveying fluid under the condition of arbitrarily large overall motions and commonly elastic supports easily.

Численное исследование влияния дефектов поверхности на устойчивость цилиндрической трубы с жидкостью

Работа посвящена исследованию динамического поведения упругих цилиндрических труб, имеющих поверхностный дефект и взаимодействующих с внутренним потоком сжимаемой жидкости. Дефект в виде кольца прямоугольного сечения располагается на внутренней или внешней поверхности упругого тела и характеризуется собственным набором физико-механических параметров. Поведение идеальной сжимаемой жидкости описывается согласно потенциальной теории, а труба рассматривается в рамках линейной теории упругости. Для определения гидродинамического давления, действующего со стороны жидкости на внутреннюю поверхность трубы (дефекта), используется уравнение Бернулли. Математическая постановка задачи динамики упругого тела выполнена с помощью вариационного принципа возможных перемещений, а система уравнений для жидкой среды формируется с использованием метода Бубнова - Галeркина. Численная реализация алгоритма осуществляется на основе полуаналитического варианта метода конечных элементов. Оценка устойчивости базируется на вычислении и анализе комплексных собственных значений связанной системы уравнений. Верификация модели произведена для случая идеальной трубы путeм сопоставления результатов с известными экспериментальными и численными данными. Для цилиндрической трубы, жeстко защемлeнной с обоих краeв, изучено влияние геометрических и физико-механических параметров дефекта на критическую скорость потока жидкости, при которой система теряет устойчивость. Показано, что наличие дефекта снижает границу гидроупругой устойчивости. Установлено, что размещение дефекта на внешней поверхности трубы оказывает большее влияние, чем его расположение на смоченной поверхности.

Parametric excitation analysis of a piezoelectric-nanotube conveying fluid under multi-physics field

In this study, nonlinear vibration of a carbon nanotube conveying fluid is investigated. The nanotube is covered by a piezoelectric layer and is subjected to a magnetic field. It is assumed that the structure is rested on Winkler---Pasternak foundation and, the Euler---Bernoulli beam theory is employed to establish the governing equations of motion for the vibration behavior of the system. The slip boundary condition of CNT conveying fluid is considered based on Knudsen number and the mathematical modeling of the structure is developed by means of Hamilton's principle. Then, the Galerkin method is employed to discretize the equations of motion and the frequency response of the system is extracted by applying the multiple scale method for piezoelectric-based parametric excitation. It is shown that nonlocal-affected terms and Knudson number have major unpredictable effects on natural frequency, critical fluid velocity and frequency response of the system and one should precisely consider their effects. Also it is shown that approaching to the resonance frequency of the system from lower or greater values highly affects the response of the system which is recommended to be considered.

A brief compendium of correlations and analytical formulae for the thermal field generated by a heat source embedded in porous and purely-conductive media

This work reviews and compares suitable models for the thermal analysis of forced convection over a heat source in a porous medium. The set of available models refers to an infinite medium in which a fluid moves over different three heat source geometries: i.e. the moving infinite line source, the moving finite line source, and the moving infinite cylindrical source. In this perspective, the present work presents a plain and handy compendium of the above-mentioned models for forced external convection in porous media; besides, we propose a dimensionless analysis to figure out the reciprocal deviation among available models, helping the selection of the most suitable one in the specific case of interest. Under specific conditions, the advection term becomes ineffective in terms of heat transfer performances, allowing the use of purely-conductive models. For that reason, available analytical and numerical solutions for purely-conductive media are also reviewed and compared, again, by dimensionless criteria. Therefore, one can choose the simplest solution, with significant benefits in terms of computational effort and interpretation of the results. The main outcomes presented in the paper are: the conditions under which the system can be considered subject to a Darcy flow, the minimal distance beyond which the finite dimension of the heat source does not affect the thermal field, and the critical fluid velocity needed to have a significant contribution of the advection term in the overall heat transfer process.

Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid

In this paper, divergence and flutter instabilities of supported piezoelectric nanotubes containing flowing fluid are investigated. To take the size effects into account, the nonlocal elasticity theory is implemented in conjunction with the Euler-Bernoulli beam theory incorporating surface stress effects. The Knudsen number is applied to investigate the slip boundary conditions between the flow and wall of nanotube. The nonlocal governing equations of nanotube are obtained using Newtonian method, including the influence of piezoelectric voltage, surface effects, Knudsen number and nonlocal parameter. Applying Galerkin approach to transform resulting equations into a set of eigenvalue equations under the simple-simple (S-S) and clamped-clamped (C-C) boundary conditions. The effects of the piezoelectric voltage, surface effects, Knudsen number, nonlocal parameter and boundary conditions on the divergence and flutter boundaries of nanotubes are discussed. It is observed that the fluid-conveying nanotubes with both ends supported lose their stability by divergence first and then by flutter with increase in fluid velocity. Results indicate the importance of using piezoelectric voltage, nonlocal parameter and Knudsen number in decrease of critical flow velocities of system. Moreover, the surface effects have a significant role on the eigenfrequencies and critical fluid velocity.

Vibration and stability of embedded cylindrical shell conveying fluid mixed by nanoparticles subjected to harmonic temperature distribution

Nonlinear vibration and instability of cylindrical shell conveying fluid-nanoparticles mixture flow are studied in this article. The surrounding elastic medium is modeled by Pasternak foundation. Mixture rule is used for obtaining the effective viscosity and density of the fluid-nanoparticles mixture flow. The material properties of the elastic medium and cylindrical shell are assumed temperature-dependent. Employing first order shear deformation theory (FSDT), the motion equations are derived using energy method and Hamilton\'s principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The effects of different parameters such as volume percent of nanoparticles, boundary conditions, geometrical parameters of cylindrical shell, temperature change, elastic foundation and fluid velocity are shown on the frequency and critical fluid velocity of the structure. Results show that with increasing volume percent of nanoparticles in the fluid, the frequency and critical fluid velocity will be increases.

Investigation on Vibration Characteristics of Fluid Conveying Single Walled Carbon Nanotube Via DTM

In this work differential transform method (DTM) is used to study the vibration behavior of fluid conveying single-walled carbon nanotube (SWCNT). Based on the theories of elasticity mechanics and nonlocal elasticity, an elastic Bernoulli-Euler beam model is developed for thermal-mechanical vibration and instability of a single-walled carbon nanotube (SWCNT) conveying fluid and resting on an elastic medium. The critical fluid velocity is being found out with different boundary conditions, i.e. Fixed-Fixed and simply supported at ends. Effects of different temperature change, nonlocal parameters on natural frequency and critical fluid velocity are being discussed.

Investigation on vibration characteristics of fluid conveying single walled carbon nanotube via DTM

In this work the vibration response of fluid conveying single-walled carbon nanotube embedded in an elastic medium is studied. Based on the theories of elasticity mechanics and nonlocal elasticity, an elastic Euler–Bernoulli–Euler beam model is developed .The critical fluid velocity is found out with different boundary conditions, i.e. fixed-fixed and simply supported at ends. Effects of different temperature change, nonlocal parameters on natural frequency and critical fluid velocity are discussed. The differential transform method is implemented for the nonlocal single-walled carbon nanotube analysis and this yields results with high degree of accuracy. MATLAB was used to solve the governing differential equations.

Dynamic stability of viscoelastic plates under axial flow by differential quadrature method

PurposeCantilever plates subject to axial flow can lose stability by flutter and properties such as viscoelasticity and laminar friction affect dynamic stability. The purpose of the present study is to investigate the dynamic stability of viscoelastic cantilever plates subject to axial flow by using the differential quadrature method.Design/methodology/approachEquation of motion of the viscoelastic plate is derived by implementing Kelvin-Voigt model of viscoelasticity and applying inverse Laplace transformation. The differential quadrature method is employed to discretize the equation of motion and the boundary conditions leading to a generalized eigenvalue problem. The solution is verified using the existing results in the literature and numerical results are given for critical flow velocitiesFindingsIt is observed that higher aspect ratios lead to imaginary part of third frequency becoming negative and causing single-mode flutter instability. It was found that flutter instability does not occur at low aspect ratios. Moreover the friction coefficient is found to affect the magnitude of critical flow velocity, however, its effect on the stability behaviour is minor.Originality/valueThe effects of various problem parameters on the dynamic stability of a viscoelastic plate subject to axial flow were established. It was shown that laminar friction coefficient of the flowing fluid increases the critical fluid velocity and higher aspect ratios lead to single-mode flutter instability. The effect of increasing damping of viscoelastic material on the flutter instability was quantified and it was found that increasing viscoelasticity can lead to divergence instability.

Hot fluid induced temperature-dependent vibration and instability of embedded FG-CNTRC Reddy pipes

ABSTRACTIn this paper, nonlinear vibration and instability of embedded nano-composite temperature-dependent polymeric pipes conveying hot viscous fluid are investigated. The pipe is reinforced by Single-Walled Carbon NanoTubes (SWCNTs) with Uniform Distribution (UD) and three types of Functionally Graded (FG) distribution patterns. The FG-carbon nanotube reinforced composite (FG-CNTRC) pipe is located in an orthotropic temperature-dependent visco-elastomeric medium. Reddy higher-order shear deformation theory is employed to establish the governing equations. The frequency and critical fluid velocity of the structure are calculated using Differential Quadrature Method (DQM). The effects of different parameters on the nonlinear vibration and instability of the pipe are investigated.

Differential transform method and Adomian decomposition method for free vibration analysis of fluid conveying Timoshenko pipeline

The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs.

Mathematical modeling of concrete pipes reinforced with CNTs conveying fluid for vibration and stability analyses

In this study, vibration and stability of concrete pipes reinforced with carbon nanotubes (CNTs) conveying fluid are presented. Due to the existence of CNTs, the structure is subjected to magnetic field. The radial fore induced with fluid is calculated using Navier-Stokes equations. Characteristics of the equivalent composite are determined using Mori-Tanaka model. The concrete pipe is simulated with classical cylindrical shell model. Employing energy method and Hamilton's principal, the motion equations are derived. Frequency and critical fluid velocity of structure are obtained analytically based on Navier method for simply supported boundary conditions at both ends of the pipe. The effects of fluid, volume percent of CNTs, magnetic field and geometrical parameters are shown on the frequency and critical fluid velocity of system. Results show that with increasing volume percent of CNTs, the frequency and critical fluid velocity of concrete pipe are increased.

Frequency and critical fluid velocity analysis of pipes reinforced with FG-CNTs conveying internal flows

This paper addresses vibration and instability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced pipes conveying viscous fluid. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Flugge shell model is applied for mathematical modeling of structure. Based on energy method and Hamilton

Comparison of different cylindrical shell theories for stability of nanocomposite piezoelectric separators containing rotating fluid considering structural damping

Rotating fluid induced vibration and instability of embedded piezoelectric nano-composite separators subjected to magnetic and electric fields is the main contribution of present work. The separator is modeled with cylindrical shell element and the structural damping effects are considered by Kelvin–Voigt model. Single-walled carbon nanotubes (SWCNTs) are used as reinforcement and effective material properties are obtained by mixture rule. The perturbation velocity potential in conjunction with the linearized Bernoulli formula is used for describing the rotating fluid motion. The orthotropic surrounding elastic medium is considered by spring, damper and shear constants. The governing equations are derived on the bases of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT). The nonlinear frequency and critical angular fluid velocity are calculated by differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the stability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that with increasing volume fraction of SWCNTs, the frequency and critical angular fluid velocity are increased.

Nonlinear Vibration Analysis of Single-Walled Carbon Nanotube Conveying Fluid in Slip Boundary Conditions Using Variational Iterative Method

In this paper, nonlinear dynamic behaviour of the carbon nanotube conveying fluid in slip boundary conditions is studied using the variation iteration method. The developed solutions are used to investigate the effects of various parameters on the nonlinear vibration of the nanotube. The results indicate that an increase in the slip parameter leads to a decrease in the frequency of vibration and the critical velocity, while the natural frequency and the critical fluid velocity increase as the stretching effect increases. Also, as the nonlocal parameter increases, the natural frequency and the critical velocity decreases. The analytical solutions help to have better insights and understand the relationship between the physical quantities of the problem.

Nonlinear higher order Reddy theory for temperature-dependent vibration and instability of embedded functionally graded pipes conveying fluid-nanoparticle mixture

This paper addresses temperature-dependent nonlinear vibration and instability of embedded functionally graded (FG) pipes conveying viscous fluid-nanoparticle mixture. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Reddy third-order shear deformation theory (RSDT) of cylindrical shells are developed using the strain-displacement relations of Donnell theory. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on energy method and Hamilton\'s principal, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as mode numbers, nonlinearity, fluid velocity, volume percent of nanoparticle in fluid, gradient index, elastic medium, boundary condition and temperature gradient are discussed. Numerical results indicate that with increasing the stiffness of elastic medium and decreasing volume percent of nanoparticle in fluid, the frequency and critical fluid velocity increase. The presented results indicate that the material in-homogeneity has a significant influence on the vibration and instability behaviors of the FG pipes and should therefore be considered in its optimum design. In addition, fluid velocity leads to divergence and flutter instabilities.

Size-dependent Vibration and Instability of Magneto-electro-elastic Nano-scale Pipes Containing an Internal Flow with Slip Boundary Condition

Size-dependent vibrational and instability behavior of fluid-conveying magneto-electro-elastic (MEE) tubular nano-beam subjected to magneto-electric potential and thermal field has been analyzed in this study. Considering the fluid-conveying nanotube as an Euler-Bernoulli beam, fluid-structure interaction (FSI) equations are derived by using non-classical constitutive relations for MEE materials, Maxwell’s equation, and Hamilton’s principle. Thereafter, with consideration of the non-uniformity of the flow velocity profile and slip boundary conditions, modified FSI equation is obtained. By utilizing Galerkin weighted-residual solution method, the obtained FSI equation is approximately solved to investigate eigen-frequencies and consequently instability (critical fluid velocity) of the system. In numerical results, a detailed investigation is conducted to elucidate the influences of nano-flow and nano-structure small scale effect, non-uniformity, temperature change, and external magneto-electric potential on the vibrational characteristics and stability of the system. This work and the obtained results may be useful to smart control of nano structures and improve their efficiency.