W. Q. Wang

Dynamical mode transitions of simply supported double-walled carbon nanotubes based on an elastic shell model

The nonlinear vibration behaviors of double-walled carbon nanotubes (DWCNTs) are investigated based on Donnell’s cylindrical shell model with van der Waals (vdW) forces between the inner and outer tubes. The harmonic balance method is used to analyze the relationship between the amplitudes and the frequencies of natural vibrations of the tubes. Numerical analyses are carried out to understand the effects of vdW forces and nonlinearity on the carbon nanotubes (CNTs). The results show that the radial vibrational modes of the inner and outer tubes of simply supported DWCNTs have twice dynamical mode transitions as the frequency increases. The transitions correspond to twice the noncoaxial vibrations, which play a critical role in the electronic and transport properties of CNTs.

LARGE-EDDY SIMULATION OF TURBULENT FLOW CONSIDERING INFLOW WAKES IN A FRANCIS TURBINE BLADE PASSAGE

Turbulent flow in a 3-D blade passage of a Francis hydro turbine was simulated with the Large Eddy Simulation (LES) to investigate the spatial and temporal distributions of the turbulence when strongly distorted wakes in the inflow sweep over the passage. In a suitable consideration of the energy exchanging mechanism between the large and small scales in the complicated passage with a strong 3-D curvature, one-coefficient dynamic Sub-Grid-Scale (SGS) stress model was used in this article. The simulations show that the strong wakes in the inflow lead to a flow separation at the leading zone of the passage, and to form a primary vortex in the span-wise direction. The primary span-wise vortex evolves and splits into smaller vortex pairs due to the constraint of no-slip wall condition, which triggers losing stability of the flow in the passage. The computed pressures on the pressure and suction sides agree with the measured data for a working test turbine model.

INTRINSIC FEATURES OF TURBULENT FLOW IN STRONGLY 3-D SKEW BLADE PASSAGE OF A FRANCIS TURBINE

The turbulent flow, with the Reynolds number of 5.9 × 105, in the strongly 3-D skew blade passage of a true Francis hydro turbine was simulated by the Large Eddy Simulation (LES) approach to investigate the spatial and temporal distributions of the fully developed turbulence in the passage with strongly 3-D complex geometry. The simulations show that the strong three-dimensionality of the passage has a great amplification effect on the turbulence in the passage, and the distributions of the turbulence are diversely nonuniform, for instance, the rise of turbulent kinetic energy in the lower 1/3 region of the passage is more than 45%, whereas its rise in the upper 1/3 region is less than 1%. With the LES approach, the details of the flow structures at the near-wall surfaces of the blades could be obtained. Several turbulent spots were captured.

Dynamical properties of multi-walled carbon nanotubes based on a nonlocal elasticity model

This paper investigates the free vibration of multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on the nonlocal elasticity theory which allows the effects of small length scale and the more refined van der Waals (vdW) interaction formulas, the equation of motion is first derived and then solved analytically. The results reveal that the effects of the small length scale are significant for small aspect ratios and high radial vibration modes, and are instead insensitive to the number of layers of MWCNTs and weakly dependent on the wall thickness of MWNTs. This finding means that the effects of small length scale on complicated MWCNTs may be simplified to double-walled carbon nanotubes (DWCNTs) or even single-walled carbon nanotubes (SWCNTs).

DYNAMICAL BEHAVIORS OF FLUID- CONVEYED MULTI-WALLED CARBON NANOTUBES

This paper is concerned with the free vibration of the fluid-filled multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on Donnells cylindrical shell model and potential flow theory, the effects of internal fluid and the different radii on the coupling vibration of the MWCNT-fluid system are discussed in detail. The results show that the fluid has only a little influence on the natural resonant frequency (frequency of the innermost tube) and the associated amplitude ratio in MWCNTs, while it plays a significant role in the intertube resonant frequency and the associated amplitude ratio. For the natural resonant frequency, the vibrational mode is almost coaxial, i.e., the MWCNTs vibrate like a single-layer shell, however, for the intertube resonant frequency, the system shows complex noncoaxial vibration, which plays a critical role in electronic and transport properties of carbon nanotubes (CNTs). Simultaneously, the effect of the innermost radius on the frequencies of MWCNTs is also examined and the conclusions accord well with those of another paper.

NUMERICAL SIMULATION OF FLOW FEATURES AND ENERGY EXCHANGE PHYSICS IN NEAR-WALL REGION WITH FLUID-STRUCTURE INTERACTION

Large eddy simulation is used to explore flow features and energy exchange physics between turbulent flow and structure vibration in the near-wall region with fluid–structure interaction (FSI). The statistical turbulence characteristics in the near-wall region of a vibrating wall, such as the skin frictional coefficient, velocity, pressure, vortices, and the coherent structures have been studied for an aerofoil blade passage of a true three-dimensional hydroturbine. The results show that (i) FSI greatly strengthens the turbulence in the inner region of y+ < 25; and (ii) the energy exchange mechanism between the flow and the vibration depends strongly on the vibration-induced vorticity in the inner region. The structural vibration provokes a frequent action between the low- and high-speed streaks to balance the energy deficit caused by the vibration. The velocity profile in the inner layer near the vibrating wall has a significant distinctness, and the viscosity effect of the fluid in the inner region decreases due to the vibration. The flow features in the inner layer are altered by a suitable wall vibration.

STUDY ON TURBULENCE FEATURES NEAR AN OSCILLATING CURVED WALL

In pursuit of possibly true turbulent characters and for exploring a change in turbulence structures near an oscillating flexible wall-curved surface, a sinusoidal oscillation mode was forced to a curved wall, whose vibrations disturbed the flow with an interacting effort between the fluid and the structure. The methodology used was the Large Eddy Simulation (LES) with fluid-structure interaction. The oscillating configuration was on a Fourier sinusoidal mode from the measurements of a Francis hydro turbine blade vibration. The effects of the vibration on the skin friction coefficient, vortices, turbulent coherent structures, and other statistical quantities were studied. The results showed that the streamwise velocity gradient along the normal direction and the normal velocity gradient along the spanwise direction were considerably increased within the viscous sublayer because of the oscillating wall, which additionally caused the low speed streaks to stay away from the wall and the high-momentum flows to be toward the wall. As a result, the streamwise vortices were much more elongated along the downstream to get an energy balance, and the wall skin friction coefficient or the wall friction velocity rose up.

LARGE EDDY SIMULATION OF HYDROELASTIC VIBRATION USING THE FINITE ELEMENT METHOD

This work is concerned with modeling the interaction of fluid flow with flexible solid structures. An improving spring smooth analogy and an improved constant volume transfer (ICVT) are used to provide fluid mesh control and transfer the information on the interfaces between fluid and structure, respectively. The time integrating algorithm is based on the predictor multi-corrector algorithm (PMA). An important aspect of this work is that we present a directly coupled approach, in which a large eddy simulation (LES) fluid solver and a structure solver have been coupled together to solve a hydroelasticity problem using the finite element method. To demonstrate the performance of the proposed approach, two working examples were used. One is the vibration of a beam immersed in incompressible fluid, another is the hydroelastic behavior of an ideal guide vane in a hydro turbine passage. The numerical results show the validity of the proposed approach.

NUMERICAL SIMULATION OF FLOW WITH LARGE-AMPLITUDE OSCILLATION OF SOLID BOUNDARIES BY PENALTY FINITE ELEMENT FORMULATIONS

A penalty finite element method for the incompressible viscous Navier–Stokes equations is incorporated in an arbitrary Lagrangian–Eulerian formulation to model a flow in the fluid–structure interaction (FSI) with moving meshes. The formulation is derived based on the classical Ritz–Galerkin framework for forming a coupled formulation on the finite element method. In such a way, the pressure-constrained equation is incorporated in the momentum equations of the system with FSI. An improving spring smooth and remeshing technique is used to successively accommodate fluid meshes as the oscillation of a solid boundary in simulation. To demonstrate the performance of the proposed approach, the simulations of the flow with an elastic beam in water, that is oscillating in a large amplitude are presented. The simulations show that the methodology suggested in this paper has a good numerical stability and reliability, and the results are highly agreeable with the published reference.

Dynamic global Vreman model for large eddy simulation of inhomogeneous turbulent flow in a full passage of Francis turbine

In the present study, the subgrid-scale (SGS) eddy-viscosity model developed by Vreman [Phys. Fluids 16 (2004) 3670] and its dynamic version [Phys. Fluids 19 (2007) 065110] are tested in large-eddy simulations (LES) of the inhomogeneous turbulent flow in a full passage of Francis turbine. Distributions of pressure, velocity and vortices as well as some flow structure are gained, which is helpful to examine the performance of SGS model for complex turbulent flow and understand the flow characters in full passage of Francis turbine.