Sharif Digital Repository

A fully analytical solution of the classic coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads is presented. Axisymmetric thermal and mechanical boundary conditions are considered in general forms of arbitrary heat transfer and traction, respectively, at the inner and outer radii of the disk. To solve the governing system of equations, an analytical procedure based on the Fourier-Bessel transform is employed. Closed form formulations are presented for temperature and displacement fields. The results of the present formulations are in good agreement with the numerical results available in the literature. The radial distribution and time history... 

Numerical investigation of fluid flow structure and convective heat transfer due to a circular jet impinging on a rotating disk is performed. Temperature and convection heat transfer coefficient are calculated. Flow is considered to be steady, incompressible and turbulent. k-ε RNG model is used to model the turbulent flow. Results are compared with experimental data showing good agreement. Two new criteria are introduced and used to evaluate the performance of cooling process, the first is maximum temperature difference on the disk, and the second is the average temperature of the disk. The first parameter shows the uniformity of temperature distribution in the disk and the second shows the... 

A variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange... 

In this article, a new double spinning disks reactor (DSDR) has been proposed and tested successfully for the synthesis of barium sulfate nanoparticles by means of the reactive precipitation. The proposed DSDR consists of two coaxial rotating disks placed horizontally in a cylindrical chamber. Continuous precipitation of barium sulfate nanoparticles as a chemical test system was carried out using this new contacting device and the effects of operating and design parameters such as the disk rotational speed, distance between the disks, feed concentration, feed flow rate, free ion ratio, feed location, and feed distribution pattern on the mean size, size distribution, and morphology of the... 

In this paper, a refined finite element method (FEM) based on the Carrera unified formulation (CUF) is extended for stress analysis of rotors and rotating disks with variable thickness. The variational form of the 3D equilibrium equations is obtained using the principle of minimum potential energy and solved by this method. Employing the 1D CUF, a rotor is assumed to be a beam along its axis. In this case, the geometry of the rotor can be discretized into a finite number of 1D beam elements along its axis, while the Lagrange polynomial expansions may be employed to approximate the displacement field over the cross section of the beam. Therefore, the FEM matrices and vectors can be written in... 

Understanding the time water takes as it moves from rain or snowmelt through the terrestrial system to arrive as stream discharge, or evapotranspiration (ET) is an important hydrologic quantity. We develop a Lagrangian particle tracking method to capture transient residence times from source to either ET or outflow in an integrated hydrologic model. This method is parallel and efficiently captures time evolution of parcels of water in the model and tracks the source of water for hydrograph or ET separation. We demonstrate this model using hypothetical hillslope simulations driven by snow or rain dominated forcing and two different land cover types. We show that land cover and forcing both... 

The small-scale effects on the mechanical responses of micro-rotating disks with angular acceleration are investigated based on the strain gradient theory, as one of the powerful non-classical continuum theories which have been developed to justify the empirical observations of mechanical behavior in small-scale structures and components. The differential equations governing motion of the micro-disk elements in radial and circumferential direction together with the corresponding boundary conditions are derived. Then, an analytical solution is presented for the components of the displacement field which can be used as a base for determination of the components of the stress field. In a... 

In this paper, the in-plane free vibration analysis of the functionally graded rotating disks with variable thickness is presented utilizing DQM. It is assumed that the rotational velocity of the disk is constant and the thickness and material properties including modulus of elasticity and density vary along the radial coordinate. The distribution of the forward and backward traveling waves versus the angular velocity is demonstrated for several modal circles and nodal diameters with respect to the fixed and rotating coordinate systems. After presenting the accuracy and convergence of the numerical method, the derived formulation and the solution method are validated by comparing the results... 

High mixing efficiency that is of great importance in various industrial processes is a significant feature of spinning disk reactors. This work was focused on the characterization of mixing in a new reactor called Double Spinning Disk Reactor (DSDR) by adopting a competitive parallel reaction system known as iodide–iodate test reaction. The proposed DSDR consists of two coaxial rotating disks that the feeds are introduced into the gap between them. The mixing improves with an increase in the rotational speed of the disk, the radial distance of the feed introduced through the lower disk, and its number of feed points, while an increase in each of the feed flow rate and the distance between... 

In this research a computer model based on elasto hydrodynamic fluid film lubrication is developed in order to calculate the torque transmission efficiency of a half-toroidal CVT variator. Validation of this model is verified by comparing the experimental and the model results. Sensitivity of torque transmission efficiency to eleven parameters is investigated. These parameters are: dimensionless roller curvature, aspect ratio, half cone angle, fluid viscosity index, pressure constant for Roelands model, input rotational velocity, absolute viscosity at atmospheric pressure, Young modulus of disks and power rollers, Poisson ratio of disks and power rollers, number of power rollers and variator... 

During the varying angular speed timespans of the start or shutdown of rotating machinery, the machinery components may be subjected to intense mechanical loadings which should be taken into account by its fabricator in the designing processes. In the microscale rotating systems, where the angular velocity is typically very high, the importance of this issue is much higher. In this paper, a comprehensive strain-gradient elasticity formulation is presented for functionally graded rotating micro-disks under the effects of varying angular velocity. The gradation of the constituent material along the radial direction can be a helpful option to mitigate the stresses in rotating micro-disks under... 

The elasticity formulation for equations of motion of micro-rotating disks in the presence of angular acceleration as well as the corresponding boundary conditions are developed based on the non-classical continuum theory of couple stress. The system of the boundary value problem is derived on the basis of the variational method. Analytical elasticity solutions to the system of equations are then provided. Based on the elasticity solution, the mechanical responses, including the displacement and stress fields, for varying-speed micro-rotating disks are studied. In a numerical case study, the effect of the couple stresses on the distribution of stress and displacement components are... 

A semi-analytical method is developed for the analysis of deformation and three-dimensional stress field in rotating annular disks made of cylindrically orthotropic nested rings. The method is based on a layerwise theory and the Hamilton principle. The proposed method is applied to calculate in-plane and out-of-plane stresses in a rotating disk made up of two nested rings that is rigidly fixed (or free) at the inner boundary and is free at the outer boundary. The computed results are compared with those obtained from the finite element method. It is found that because of discontinuity of material properties, the stress field is three-dimensional at the interface of two rings. © 2004 Elsevier... 

The present study investigates the dynamic filtration of concentrated slurry fluids containing colloidal clay particles under different salinity, shear flow, and flux rate conditions. The dynamic filtration study was carried out by the filtration cell equipped with a rotating disk to apply shear stress over the membrane surface. A 3D CFD simulation has been implemented to model the hydrodynamic flows inside the filtration cell to obtain the wall shear stress (WSS) on the membrane surface at different disk rotation speeds. The thickness and surface patterns of fouling were captured utilizing a surface profilometer. First, the cake-filtration model was used to predict the flux rate and fouling... 

In this survey, the reactive mass transfer data are determined for extraction technique in the modified rotating disc column. Mathematical models are investigated to compute the mass transfer coefficients of the dispersed phase. An increase in the dispersed phase holdup from 0.85 to 0.12 and a decrease in droplet diameter from 2.24 to 0.74 mm are observed with increasing rotation speed from 170 to 410 rpm in the optimized system. The experiments showed that the optimum transport efficiency in rotor speed of 410 rpm in this column is equal to 98.85% and 99.45% for extraction and stripping stages, respectively. The model's achievement is compared with the solvent extraction data and a... 

In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elasto-plastic loading are obtained by semi-exact method of Liao's homotopy analysis method (HAM) and finite element method (FEM). The materials are assumed to be elastic-linear strain hardening and isotropic. The analysis of rotating disk is based on Von Mises' yield criterion. A two dimensional plane stress analysis is used. The distribution of temperature is assumed to have power forms with the hotter point located at the outer surface of the disk. A mathematical technique of transformation has been proposed to solve the homotopy equations... 

In the present paper, radial and hoop thermal and mechanical stress analysis of a rotating disk made of functionally graded material (FGM) with variable thickness is carried out by using finite element method (FEM). To model the disk by FEM, one-dimensional two-degree elements with three nodes are used. It is assumed that the material properties, such as elastic modulus, Poisson's ratio and thermal expansion coefficient, are considered to vary using a power law function in the radial direction. The geometrical and boundary conditions are in the shape of two models including thermal stress (model-A) and mechanical stress (model-B). In model-A there exists no pressure in both external and... 

Titanium nitride-carbon nanocomposites are synthesized by the reaction of TiCl4 and NaN3 in supercritical benzene medium that also serves as a carbon source. The as-prepared precursors (SI, SII) are subjected to several heat treatments (SIII-SV). The synthesized nanoparticles are characterized by X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), and transmission electron microscopy (TEM). The samples are tested as electrocatalyst for oxygen reduction reaction in an alkaline electrolyte. It is shown that the electrocatalytic properties of the synthesized nanoparticles are... 

In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elastic loading under different boundary conditions are obtained by semi-exact methods of Liao's homotopy analysis method (HAM), Adomian's decomposition method and He's variational iteration method (VIM). The materials are assumed to be perfectly elastic and isotropic. A two dimensional plane stress analysis is used. The distribution of temperature over the disk radius is assumed to have power forms with the higher temperature at the outer surface. The results of the three methods are compared with those obtained by Runge-Kutta's numerical...