Water hammer prediction and control: the Green’s function method

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 method.The predicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and,by adjusting the eddy viscosity coefficient,experimentally measured turbulent flow data.Optimal WH control principle is thereby constructed and demonstrated.     

Study of pure transverse motion in free cylinders and plates in flexural vibration by Ritz’s method

In this work the flexural vibration of a free cylinder of any aspect ratio is analysed. A general solution by powers series of the coordinates is proposed here to represent the displacements, with restrictions on the powers of the radial coordinates which prevent potential energy and stress singularities at the axis of the cylinder. By means of an analytic method, it is concluded that certain points of the cylinder have no axial motion. As a result of the pure transverse movement and of the fact that the cylinder bends, it is inferred that the axis is extended. Furthermore, in the symmetric modes, the points situated at the centres of the bases are displaced in the same direction and sense, and hence the distance between them does not vary in time. Flexural natural frequencies are numerically calculated by Ritz’s method with the general solution series proposed. Since the series used are more adequate, convergence is better than with classic series. The results are verified by FEM. Some consequences are extended to a rectangular plate, whose points of the middle surface vibrate transversally in the double-symmetric mode. In order to verify the theoretical results, a set of experiments with a laser interferometer is carried out. The experimental frequencies agree with the theoretical values.     

Investigation of generalized Fick’s and Fourier’s laws in the second-grade fluid flow

The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Christov double diffusions. The thermal and solutal stratifications at the surface are also accounted. The relevant nonlinear ordinary differential systems after using appropriate transformations are solved for the solutions with the homotopy analysis method (HAM). The effects of various involved variables on the temperature, velocity, concentration, skin friction, mass transfer rate, and heat transfer rate are discussed through graphs. From the obtained results, decreasing tendencies for the radial, axial, and tangential velocities are observed. Temperature is a decreasing function of the Reynolds number, thermal relaxation parameter, and Prandtl number. Moreover, the mass diffusivity decreases with the Schmidt number.     

Chaos synchronization and transmission of information in coupled SC-CNN-based canonical Chua’s circuit

In this paper, an experimental implementation of State Controlled Cellular Neural Network (SC-CNN)-based canonical Chua’s circuit is presented. Two such electronic circuits are realized. One of the circuits is configured as driver or transmitter, and other circuit is configured as response or receiver system. Synchronization of chaos between the driver and the driven system is demonstrated. The conditions under which complete synchronization is ensured are derived by applying a strategy based on the Master Stability Function and Lyapunov function. We show that transmitter and receiver systems consisting of cascaded SC-CNN-based canonical Chua’s oscillator can synchronize when they are coupled using direct information from the transmitter into the receiver. The communication performances of different information signals such as sinusoidal, square, and speech signals are demonstrated by real-time hardware experiments. The experimentally observed results are in agreement with the numerically obtained results, and they closely match with each other.     

Chaos in a tethered satellite system induced by atmospheric drag and Earth’s oblateness

Nonlinear Dynamics - This paper describes the chaos behavior of an in-plane tethered satellite system induced by atmospheric drag and the Earth’s oblateness. A commonly used model, the...     

Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models

To get a clear picture of the pulsatile nature of blood flow and its role in the pathogenesis of atherosclerosis, a comparative study of blood flow in large arteries is carried out using the two widely used models, McDonald＇s and Burton＇s models, for the pressure gradient. For both models, the blood velocity in the lumen is obtained analytically. Elaborate investigations on the wall shear stress （WSS） and oscillatory shear index （OSI） are carried out. The results are in good agreement with the available data in the literature. The superiority of McDonald＇s model in capturing the pulsatile nature of blood flow, especially the OSI, is highlighted. The present investigation supports the hypothesis that not only WSS but also OSI are the essential features determining the pathogenesis of atherosclerosis. Finally, by reviewing the limitations of the present investigation, the possibility of improvement is explored.     

Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure

In this paper, an analytical solution is developed to determine deformations and stresses in circular disks made of functionally graded materials subjected to internal and/or external pressure. Taking mechanical properties of the materials of circular disks to be linear variations, the governing equation is derived from basic equations of axisymmetric, plane stress problems in elasticity. By transforming the governing equation into a hypergeometric equation, an accurate analytical solution of deformations and stresses in circular disks is obtained. The comparison with the numerical solution indicates that both approaches give very agreeable results, indicating correctness of the proposed analytical solution. The obtained analytical solution is employed to determine the radial displacement and stresses in circular disks subjected to external pressure, internal pressure, and internal and external pressure, respectively. How the radius ratio of circular disks affects deformations and stresses is also investigated.     

Image singularities of Green’s functions for isotropic elastic bimaterials subjected to concentrated forces and dislocations

Green’s functions for isotropic materials in the two-dimensional problem for elastic bimaterials with perfectly bonded interface are reexamined in the present study. Although the Green’s function for an isotropic elastic bimaterial subjected to a line force or a line dislocation has been discussed by many authors, the physical meaning and the structure of the solution are not clear. In this investigation, the Green’s function for an elastic bimaterial is shown to consist of eight Green’s functions for a homogeneous infinite plane. One of the novel features is that Green’s functions for bimaterials can be expressed directly by knowing Green’s functions for the infinite plane. If the applied load is located in material 1, the solution for the half-plane of material 1 is constructed with the help of five Green’s functions corresponding to the infinite plane. However, the solution for the half-plane of material 2 only consists of three Green’s functions for the infinite plane. One of the five Green’s functions of material 1 and all the three Green’s functions of material 2 have their singularities located in the half-plane where the load is applied, and the other four image singularities of material 1 are located outside the half-plane at the same distance from the interface as that of the applied load. The nature and magnitude of the image singularities for both materials are presented explicitly from the principle of superposition, and classified according to different loads. It is known that for the problem of anisotropic bimaterials subjected to concentrated forces and dislocations, the image singularities are simply concentrated forces and dislocations with the stress singularity of order O(1/r). However, higher orders (O(1/r²) and O(1/r³)) of stress singularities are found to exist in this study for isotropic bimaterials. The highest order of the stress singularity is O(1/r³) for the image singularities of material 1, and is O(1/r²) for material 2. Using the present solution, Green’s functions associated with the problems of elastic half-plane with free and rigidly fixed boundaries, for homogeneous isotropic elastic solid, are obtained as special cases.     

Two-phase co-current flow simulations using periodic boundary conditions in horizontal, 4, 10 and 90° inclined eccentric annulus,flow prediction using a modified interFoam solver and comparison with experimental results

Two-phase oil and gas flow were simulated in an entirely eccentric annulus and compared with experimental data at horizontal, 4, 10, and 90° inclination. The gas-phase was sulphur hexafluoride and the liquid phase a mixture of Exxsol D60 and Marcol 82 for the inclined cases (5–16), and pure Exxsol D60 for the horizontal cases (1–4). The diameter of the outer and inner cylinders was 0.1 and 0.04 m, respectively, for the inclined domains and 0.1 and 0.05 m for the horizontal domain. The cases studied consist of liquid phase fractions between 0.3 and 0.65 and mixture velocities from 1.2 to 4.25 m/s. The mean pressure gradient is within 33% of the expected experimental behavior for all inclined cases. In contrast, the low-velocity horizontal domains exhibit significant deviation, with a drastic over-prediction of the mean pressure gradient by as much as 200–335% for cases 1 and 2. The two remaining horizontal cases (3 and 4) are within 22% of the expected mean pressure gradient. Cases 13–16 are a replication of cases 5–8 at an increased inclination; the mean pressure gradient is within 6.5% of the expected increase due to the increase in hydrostatic pressure. By comparing cases 1–4 to previous published simulations at a lower eccentricity, we found a decrease of the mean pressure gradient by 30–40%, which is in line with existing literature, although for single-phase flows. The simulated and experimental liquid holdup profiles are in good agreement when comparing the fractional data; wave and slug frequencies match to within 0.5 Hz; however, at closer inspection, it is apparent that there is a decrease in the amount of phase-mixing of the simulations compared to the experiments. When increasing the mesh density from 115 k cells/m to 2 million cells/m, the simulations exhibit significantly more phase mixing, but are still unable to produce conventional slugs. In a simplified case, conventional slugs are observed at grid sizing of 1 × 1 × 1 mm, whereas the cells of the 2 million cells/m mesh are roughly 1.5 × 1.5 × 1.5 mm.