Sharif Digital Repository

In this paper, collision of two balls in three dimensions with regard to energy loss and friction is studied. This investigation intends to propose the procedure which can determine the condition of pure sliding, sliding with rolling or sticking, and rolling or sticking at the beginning of contact. Furthermore, the other aim of this research is to suggest the closed-form relation for post-collision angular and linear velocities in which the possibility of three regimes of impact, pure sliding, sliding with rolling, and pure rolling, are considered. In this investigation, viscous Hertz contact force describes the normal interaction force. Moreover, stick regime is not taken into account and... 

In this paper, using an analytical optimization method, optimum design of multi-layer compound cylinders with different materials in layers is investigated. For this purpose, considering Tresca criterion, maximum shear stress in each layer is minimized. At the optimum condition, the maximum shear stress at all layers occurs simultaneously. The general analytical relations for optimum dimension of layers, residual pressures and radial interferences are derived. The existence condition of the optimum solution is also investigated and the constraints for materials selection are derived too. It is shown that the allowable shear stress ratio of materials must be close to their geometric mean... 

Breakup of non-uniform droplets in an asymmetric T junction consisting of an inlet channel and two different-size outlet channels has been investigated numerically. Also, an analytical approach in the limit of the lubrication approximation has been extended to provide some analytical relations to study the system and verify the numerical results. Parameters that are important in the performance of the system have been determined and discussed. Our results indicate that smaller droplets can be produced by increasing the capillary number. As the geometry becomes symmetric the pressure drop decreases. Our results also reveal that the breakup time and the pressure drop for this system are... 

We develop accurate analytical relations for the droplet volume ratio, droplet length during breakup process, and pressure drop of asymmetric T junctions with a valve in each of the branches for producing unequal-sized droplets. An important advantage of this system is that after manufacturing the system, the size of the generated droplets can be changed simply by adjusting the valves. The results indicate that if the valve ratio is smaller than 0.65, the system enters a nonbreakup regime. Also the pressure drop does not depend on the time and decreases by increasing the valve ratio, namely, opening the degree of valve 1 to valve 2. In addition, the results reveal that by decreasing... 

In high-voltage applications, due to the use of high-ratio step-up transformers, the value of parasitic capacitance of these transformers is large compared to the low-voltage transformers. Moreover In these applications it is prefered to use single-capacitor filters instead of filters with inductors. In this paper a simple electrical model for two-winding high frequency transformer considering all of the parasitic elements is presented. This model is used in a full-bridge based dc-dc converter with capacitive output filter controlled by phase-shifted method. The operation of this converter in DCM is analysed and its analytical relations in different time intervals is derived and confirmed by... 

This paper introduces a shock-wave-detection technique based on the schlieren imaging for continuum and rarefied-gas flows. The scheme is applicable for any existing two-dimensional flowfields obtained by experimental or numerical approaches. A Gaussian distribution for a schlieren function within the shock-wave region is considered. This enables the authors to access any desired locations through the shock (e.g., shock center, or leading- and trailing-edge locations). The bow shock-wave profile is described via a rational function, which could be employed for the estimation of shock angle. The relation between pre- and postshock flow properties along the shock wave with a high resolution... 

A CFD code has been developed to describe the salt solution density current, which propagates three-dimensionally in deep ambient water. The height and width of the dense layer are two dominated length scales in a 3-D structure of the density current. In experimental efforts, it is common to measure the height and width of this current via its brightness. Although there are analytical relations to calculate the current height in a two-dimensional flow, these relations cannot be used to identify the width and height of a 3-D density current, due to the existence of two unknown parameters. In the present model, the height and width of the dense layer are obtained by using the boundary layer... 

Based on Lagrangian mechanics, use of velocity constraints as a special set of quasi-velocities helps derive explicit equations of motion. The equations are applicable to holonomic and nonholonomic constrained multibody systems. It is proved that in proposed quasi-spaces, the Lagrange multipliers are eliminated from equations of motion; however, it is possible to compute these multipliers once the equations of motion have been solved. The novelty of this research is employing block matrix inversion to find the analytical relations between the parameters of quasi-velocities and equations of motion. In other words, this research identifies arbitrary submatrices and their effects on equations... 

Well-known polars in classical shock wave theory, that is, flow deflection angle-shock angle (θ-β), hodograph (u*,v*), and pressure deflection (θ-P*) diagrams, are investigated for the rarefied gas flows using a recently proposed shock wave detection technique by Akhlaghi and coworkers. The agreement between the obtained polars with the analytical relations in classical shock wave theory has been shown in the continuum limit for the cases of supersonic flow over the wedge and cylinder geometries. Investigations are performed using the RGS2D direct simulation Monte Carlo solver for supersonic gas flows over a circular cylinder at continuum limit and Kn = 10-4, 10-3, 0.01, 0.03, 0.07, and... 

Well-known polars in classical shock wave theory, that is, flow deflection angle-shock angle (θ-β), hodograph (u*,v*), and pressure deflection (θ-P*) diagrams, are investigated for the rarefied gas flows using a recently proposed shock wave detection technique by Akhlaghi and coworkers. The agreement between the obtained polars with the analytical relations in classical shock wave theory has been shown in the continuum limit for the cases of supersonic flow over the wedge and cylinder geometries. Investigations are performed using the RGS2D direct simulation Monte Carlo solver for supersonic gas flows over a circular cylinder at continuum limit and Kn = 10-4, 10-3, 0.01, 0.03, 0.07, and... 

This paper presents an analytical model to predict the residual stress distribution induced by Shot peening. The analytical approach is based on the work of Shen and Atluri (2006) [18] with some modifications. The modifications are related to the elasto-plastic unloading of shot impingements, friction coefficient effect and the fraction of kinetic energy transmitted to the treated material. In order to predict more realistic residual stresses, the elasto-plastic unloading phase of shot impacts is modeled using two nonlinear kinematic hardening models considering the Bauschinger effect. Moreover, the effect of the Coulomb friction between target surface and shots is evaluated. For this... 

In this paper we report experimental results for the performance and rate of heat transfer in copper tubes in solar water heaters with thermosyphonic flow in continuation of experimental data reported in previous publications (Solar Energy, 2003, vol. 74, pp. 441-445, and Energy Sources, 1997, vol. 19, pp. 147-152). We also show a comparison between performances of three kinds of tubes: copper, polypropylene and steel under similar conditions. An analytical relation for calculation of rate of heat transfer in copper tubes is also presented in terms of Nusselt versus Reynolds and Prantdl numbers. A comparison of experimental data showed that performance of copper tubes is slightly better than... 

Appealing advantages of high-temperature superconducting (HTS) transformers are very promising for the contemporary and future power delivery systems. Cryogenic insulation technology is one of the key technologies for their commercialization. In this paper insulation design of the end part of cryogenic high voltage (H. V.) bushing of a 230/20 kV HTS transformer is developed. Analytical relations and finite element method (FEM) modelling, through application of COMSOL Multiphysics software, are employed for determination of electric field distribution in this design process. Weibull 0.1% dielectric breakdown strength has been considered as criterion for insulation design. Different shape and... 

Finite impulse response (FIR) and infinite impulse response (IIR) digital filters are proposed to allow for time-domain simulation of optical pulse propagation by using the operator-splitting technique. These filters simulate polarization mode dispersion and chromatic dispersion effects with acceptable accuracy in time-domain. An analytical relation between the coefficients of these filters and the simulation step-size is established to accommodate the possibility of carrying out the time-domain split-step method with variable split-step length at virtually no computational burden. The superiority of the proposed method over the conventional frequency-domain technique is particularly... 

Purpose - The purpose of this paper is to investigate the aeroelastic behavior of a supersonic flight vehicle flying at moderate angles of attack using global analytic nonlinear aerodynamic model. Design/methodology/approach - Aeroelastic behavior of a supersonic flight vehicle flying at moderate angles of attack is considered, using nonlinear aerodynamics and linear elastodynamics and structural models. Normal force distribution coefficient over the length of the vehicle and pitching moment coefficient are the main aerodynamic parameters used in the aeroelastic modeling. It is very important to have closed form analytical relations for these coefficients in the model. They are generated...