Dynamics of axially functionally graded conical pipes conveying fluid

In this paper, the dynamics of axially functionally graded (AFG) conical pipes conveying fluid are analyzed. The materials are distributed along the conical pipe axis as a volume fraction function. Either the elastic modulus or the density of the AFG conical pipe is assumed to vary from the inlet to the outlet. The governing equation of the AFG conical pipe is derived using the Hamiltonian principle and solved by the differential quadrature method. The effects of the volume fraction index, volume fraction function type and reduction factor on the natural frequency and critical velocity are analyzed. It is found that for a power function volume fraction type, the natural frequency and critical velocity increase with increasing volume fraction index and clearly increase when the volume fraction index is within the range (0, 10). For an exponential function volume fraction type, the natural frequency and critical velocity change rapidly within the range (−10, 10), besides the above range the relationship between the natural frequency, critical velocity and volume fraction index is approximate of little change. The natural frequency and critical velocity decrease linearly with increasing reduction factor.

Wave propagation analysis of thermoelastic functionally graded nanotube conveying nanoflow

As a hollow cylindrical structure, a nanotube has potential to convey nanoflow, which has opened up a field of research. Functionally graded nanotube as a designable structure with continuous variation of material properties can perform better than uniform nanotube, especially in physical field without introducing large stress concentration. In this article, we take the thermal effect into account and investigated the wave propagation characteristics of functionally graded material nanotube conveying nanoflow. In particular, we compared the effects of different kinds of volume fraction function and also the cases of uniform and nonuniform temperature variation. According to the numerical results, we can conclude that as we decrease the exponent n of the volume fraction function, the system is enhanced and larger enhancement can be observed in the case of the power volume fraction function. In addition, there is a positive correlation between the stability and both the temperature variation and the nonuniformity of temperature variation.

Multi-Objective Optimization of Functionally Graded Hollow Cylinders

In this study, two physical properties of simply supported hollow cylinders made of functionally graded materials are investigated. These two properties are mass and first natural frequency which is desirable to be minimized and maximized respectively in mechanical applications. The functionally graded material properties are assumed to vary continuously through the thickness of the cylinder. In this multi-objective optimization problem the first natural frequency of the FGM cylinders as well as its mass are formulated in terms of the volume fraction of the constituents, then by using Genetic algorithm optimization method the continuous volume fraction function of the constituents has been derived to minimize the mass and maximize the first natural frequency simultaneously.

Field-induced motion of ferrofluid droplets through immiscible viscous media

The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. The governing equations are the Maxwell equations for a non-conducting flow, momentum equation and incompressibility. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. A continuum-surface-force formulation is used to model the interfacial tension force as a body force, and the placement of the liquids is tracked by a volume fraction function. Three cases are studied. First, where inertia is dominant, the magnetic Laplace number is varied while the Laplace number is fixed. Secondly, where inertial effects are negligible, the Laplace number is varied while the magnetic Laplace number is fixed. In the third case, the magnetic Bond number and inertial effects are both small, and the magnetic force is of the order of the viscous drag force. The time taken by the droplet to travel through the medium and the deformations in the drop are investigated and compared with a previous experimental study and accompanying simpler model. The transit times are found to compare more favourably than with the simpler model.

New Physically Based Approach of Mass Conservation Correction in Level Set Formulation for Incompressible Two-Phase Flows

A novel physically based mass conservation model is developed in the framework of a level set method, as an alternative to the Heaviside function based formulation classically employed in the literature. In the proposed “volume fraction based level set approach,” expressions for volume fraction function for each interfacial computational cell are developed, and are subsequently correlated with the corresponding level set functions. The volume fraction function, derived from a physical basis, is found to be mathematically analogous to the Heaviside function, except for a one-dimensional case. The results obtained are compared with the benchmark experimental and numerical results reported in the literature. Finally, transient evolution of a circular bubble in a developing shear flow and rising bubbles in a static fluid, are critically examined. The Cox angle and the deformation parameter characterizing the bubble evolution are critically examined. An excellent satisfaction of the mass conservation requirements is observed in all case studies undertaken.