Acta Mechanica Sinica
     Acta Mechanica Sinica
  Acta Mechanica Sinica--2012, 28 (2)   Published: 25 April 2012
Research papers
Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids
Zhen-Hua Jiang, Chao Yan, Jian Yu, Wu Yuan
Abstract
A novel class of weighted essentially non-oscillaory (WENO) schemes based on Hermite polynomials, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin (DG) method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO reconstruction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order sc...
Viscous falling film instability around a vertical moving cylinder
Kadry Zakaria, Yasser Gamiel
Abstract
The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velocity. After studying the linear conditions, a generalized nonlinear kinematic model is then derived to present the physical system. Applying the boundary conditions, analytical solutions are obtained using the long-wave perturbation method. In the first step, the normal mode method ...
Water hammer prediction and control: the Green's function method
Li-Jun Xuan, Feng Mao, Jie-Zhi Wu
Abstract
By Green's function method we show that the water hammer (WH) can be analytically predicted for both laminar and turbulent flows (for the latter, with an eddy viscosity depending solely on the space coordinates), and thus its hazardous effect can be rationally controlled and minimized. To this end, we generalize a laminar water hammer equation of Wang et al. (J. Hydrodynamics, B2, 51, 1995) to include arbitrary initial condition and variable viscosity, and obtain its solution by Green's function...
Unsteady flow of viscoelastic fluid between two cylinders usingfractional Maxwell model
Muhammad Jamil, Constantin Fetecau, Corina Fetecau
Abstract
The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms. The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions. They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids. Finally, the influence of p...
Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis
Yang-Wei Liu, Bao-Jie Liu, Li-Peng Lu
Abstract
The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D ...
Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction
Yang-Wei Liu, Bao-Jie Liu, Li-Peng Lu
Abstract
The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system. The primary purpose of this study was to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 2 of this two-part paper, the influenc...
An investigation of an Emden-Fowler equation from thin film flow
Ebrahim Momoniat
Abstract
A third-order ordinary differential equation (ODE) for thin film flow with both Neumann and Dirichlet boundary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solutions of the nonlinear second-order ODE are investigated using finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order nonlinear ODE is shown to converge faster than a finite difference formulation of the standard form of ...
A note on the unsteady flow of a fractional Maxwell fluid througha circular cylinder
M. Athar, A. U. Awan, Corina Fetecau
Abstract
In this note the velocity field and the adequate shear stress corresponding to the unsteady flow of a fractional Maxwell fluid due to a constantly accelerating circular cylinder have been determined by means of the Laplace and finite Hankel transforms. The obtained solutions satisfy all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of pertinent parameters on the fluid motion, as well...
Effect of induced magnetic field on natural convection in vertical concentric annuli
R. K. Singh, A. K. Singh
Abstract
In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field ...
A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes
Wei Gao, Ru-Xun Liu, Hong Li
Abstract
This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex. For the temporal integration of the momentum ...
A class of exact solutions for the incompressible viscousmagnetohydrodynamic flow over a porous rotating disk
M. Turkyilmazoglu
Abstract
The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angular speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the ...
Simulation of vortex shedding behind a bluff body flame stabilizer using a hybrid U-RANS/PDF method
Min-Ming Zhu, Ping-Hui Zhao, Hai-Wen Ge, Yi-Liang Chen
Abstract
The present study aims at the investigation of the effects of turbulence-chemistry interaction on combustion instabilities using a probability density function (PDF) method. The instantaneous quantities in the flow field were decomposed into the Favre-averaged variables and the stochastic fluctuations, which were calculated by unsteady Reynolds averaged Navier-Stokes (U-RANS) equations and the PDF model, respectively. A joint fluctuating velocity-frequency-composition PDF was used. The governing...
Asymptotic analysis of outwardly propagating spherical flames
Yun-Chao Wu, Zheng Chen
Abstract
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy. The spherical flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Analytical solutions are separately obtained in these three zones and then asymptotically matched. In the asymptotic analysis, we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius. This correlation is compared with previous result...
The wake of falling disks at low Reynolds numbers Hot!
Hong-Jie Zhong, Cun-Biao Lee
Abstract
We visualized the wake structure of circular disks falling vertically in quiescent water. The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk. The Reynolds number, Re=Ud/ν, is in the range of 40-200. With the ascension of Reynolds numbers, a regular bifurcation occurred at the first critical Reynolds number Rec1, leading to a transition from an axisymmetric wake structure to a plane symmetric one;...
Experimental study of the boundary layer over an airfoil in plunging motion
F. Rasi Marzabadi, M. R. Soltani
Abstract
This is an experimental study on the boundary layer over an airfoil under steady and unsteady conditions. It specifically deals with the effect of plunging oscillation on the laminar/turbulent characteristics of the boundary layer. The wind tunnel measurements involved surface-mounted hot-film sensors and boundary-layer rake. The experiments were conducted at Reynolds numbers of 0.42× 106 to 0.84× 106 and the reduced frequency was varied from 0.01 to 0.11. The r...
Nonlinear magneto-electric response of a giant magnetostrictive/piezoelectric composite cylinder
Yuan-Wen Gao, Juan-Juan Zhang
Abstract
In this study, we investigate the nonlinear coupling magneto-electric (ME) effect of a giant magnetostrictive/piezoelectric composite cylinder. The nonlinear constitutive relations of the ME material are taken into account, and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases, respectively. The influences of different constraint conditions on the ME effect are discussed. In the dynamic case considering nonlinear material prope...
A new three-dimensional Hoek-Brown strength criterion
Hua Jiang, Yong-Li Xie
Abstract
The Hoek-Brown (HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion's latest version. At the same time, several three-dimensional (3D) HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu s...
The SPH approach to the process of container filling based onnon-linear constitutive models
Tao Jiang, Jie Ouyang, Lin Zhang, Jin-Lian Ren
Abstract
In this work, the transient free surface of container filling with non-linear constitutive equation's fluids is numerically investigated by the smoothed particle hydrodynamics (SPH) method. Specifically, the filling process of a square container is considered for non-linear polymer fluids based on the Cross model. The validity of the presented SPH is first verified by solving the Newtonian fluid and Oldroyd-B fluid jet. Various phenomena in the filling process are shown, including the jet buckli...
Stresses due to an adhesion crack in T-shaped junction of two orthotropic plates
Dai-Heng Chen
Abstract
The general solution of stresses is derived for a T-shaped junction of two thin plates with an adhesion crack. The plates are orthotropic. A shear force is applied on the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by a plane stress condition. The results obtained are verified by numerical calculation of FEM.
Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials
Ze-Jian Xu, Yu-Long Li, Feng-Lei Huang
Abstract
A novel approach is proposed in determining dynamic fracture toughness (DFT) of high strength steel, using the split Hopkinson tension bar (SHTB) apparatus, combined with a hybrid experimental-numerical method. The center-cracked tension specimen is connected between the bars with a specially designed fixture device. The fracture initiation time is measured by the strain gage method, and dynamic stress intensity factors (DSIF) are obtained with the aid of 3D finite element analysis (FEA). In thi...
Experimental analysis of crack tip fields in rubber materials underlarge deformation
Xia Xiao, Hai-Peng Song, Yi-Lan Kang, Xiao-Lei Li, Xiao-Hua Tan, Hao-Yun Tan
Abstract
A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation. The model is inspired by the distribution of the measured in-plane and out-of-plane deformation. The in-plane displacement of crack-tip fields under both Mode I and mixed-mode (Mode I-II) fracture conditions is measured by using the digital Moiré method. The deformation characteristics and experimental sector division mode are investigated by comparing the measured di...
Experimental study on detonation parameters and cellular structures of fuel cloud
Li-Feng Xie, Bin Li, Yu-Lei Zhang
Abstract
In this paper, detonation parameters of fuel cloud, such as propylene oxide (PO), isopropyl nitrate (IPN), hexane, 90# oil and decane were measured in a self-designed and constructed vertical shock tube. Results show that the detonation pressure and velocity of PO increase to a peak value and then decrease smoothly with increasing equivalence ratio. Several nitrate sensitizers were added into PO to make fuel mixtures, and test results indicated that the additives can efficiently enhan...
A comparison of two formulations of the fin efficiency for straight fins
Ebrahim Momoniat
Abstract
A formulation of the fin efficiency based on Newton's law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the surrounding fluid to the heat conducted through the base. The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known, whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is k...
Research on the iterative method for model updating based onthe frequency response function
Wei-Ming Li, Jia-Zhen Hong
Abstract
Model reduction technique is usually employed in model updating process. In this paper, a new model updating method named as cross-model cross-frequency response function (CMCF) method is proposed and a new iterative method associating the model updating method with the model reduction technique is investigated. The new model updating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency...
An iterative algorithm for analysis of coupled structural–acoustic systems subject to random excitations
Guo-Zhong Zhao, Gang Chen, Zhan Kang
Abstract
This paper analyzes the random response of structural-acoustic coupled systems. Most existing works on coupled structural-acoustic analysis are limited to systems under deterministic excitations due to high computational cost required by a random response analysis. To reduce the computational burden involved in the coupled random analysis, an iterative procedure based on the Pseudo excitation method has been developed. It is found that this algorithm has an overwhelming advantage in computing ef...
Free vibrations of beam-mass-spring systems: analytical analysis with numerical confirmation
Mohammad A. Darabi, Siavash Kazemirad, Mergen H. Ghayesh
Abstract
Free vibrations of a beam-mass-spring system with different boundary conditions are analyzed both analytically and numerically. In the analytical analysis, the system is divided into three subsystems and the effects of the spring and the point mass are considered as internal boundary conditions between any two neighboring subsystems. The partial differential equations governing the motion of the subsystems and internal boundary conditions are then solved using the method of separation of variabl...
Coordinating control of multiple rigid bodies based on motion primitives
Fan Wu, Zhi-Yong Geng
Abstract
This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and maneuvers, are given as building blocks for generating coordinated motions. In a motion-primitive based planning framework, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturbations. The control method combines the relative equilibria stabilization with maneuver design, and resu...
Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space
Xiao-Ting Rui, Edwin Kreuzer, Bao Rong, Bin He
Abstract
In this paper, by defining new state vectors and developing new transfer matrices of various elements moving in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid-flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system m...
Stochastic resonance in coupled weakly-damped bistable oscillators subjected to additive and multiplicative noises
Yan-Mei Kang, Mei Wang, Yong Xie
Abstract
With coupled weakly-damped periodically driven bistable oscillators subjected to additive and multiplicative noises under concern, the objective of this paper is to check to what extent the resonant point predicted by the Gaussian distribution assumption can approximate the simulated one. The investigation based on the dynamical mean-field approximation and the direct simulation demonstrates that the predicted resonant point and the simulated one are basically coincident for the case of pure add...
The maximal Lyapunov exponent of a co-dimension two-bifurcation system excited by a bounded noise
Sheng-Hong Li, Xian-Bin Liu
Abstract
In the present paper, the maximal Lyapunov exponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invariant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the thr...
A wavelet approach for active-passive vibration control of laminated plates
Ji-Zeng Wang, Xiao-Min Wang, You-He Zhou
Abstract
As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors, this paper proposes a hybrid active-passive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers. Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory, this wavelet-based control method has the ability to...
Sensitivity analysis for a type of statically stable sailcrafts
Zheng-Xue Li, Jun-Feng Li, He-Xi Baoyin
Abstract
Two types of sensitivities are proposed for statically stable sailcrafts. One type is the sensitivities of solar-radiation-pressure force with respect to position of the center of mass, and the other type is the sensitivities of solar-radiation-pressure force with respect to attitude. The two types of sensitivities represent how the solar-radiation-pressure force changes with the position of mass center and the attitude. Sailcrafts with larger sensitivities undergo larger error of the solar-radi...
Attitude maneuver of liquid-filled spacecraft with a flexible appendage bymomentum wheel
Dan-Dan Yang, Bao-Zeng Yue, Wen-Jun Wu, Xiao-Juan Song, Le-Mei Zhu
Abstract
Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied. The dynamic equations are derived by conservation of angular momentum and force equilibrium principle. A feedback control strategy of the momentum wheel is applied for the attitude maneuver. The residual nutation of the spacecraft in maneuver process changes with some chosen parameters, such as steady state time, locations of the liquid container and the appendage, and appendage par...
Failure-tolerant control for small agile satellites using single-gimbalcontrol moment gyros and magnetic torquers
Tao Meng, Saburo Matunaga
Abstract
This paper focuses on the attitude control problem of small agile satellites using single-gimbal control moment gyros (CMG) and magnetic torquers (MTQ). CMGs are regarded as effective torque generators for agile satellites because of their torque amplification capability. However, they are vulnerable to failure due to their complex inner mechanism. In this paper, different failure cases of CMGs are analyzed. A flexible failure-tolerant control strategy is developed by automatically redistributin...
 
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