Effects Of Wedge Angle Research Articles

Numerical investigation of forced convective MHD tangent hyperbolic nanofluid flow with heat source/sink across a permeable wedge

The combined effect of wedge angle and melting energy transfer on the tangent hyperbolic magnetohydrodynamics nanofluid flow across a permeable wedge is numerically evaluated. Electronic gadgets produce an excessive amount of heat while in operation, so tangent hyperbolic nanofluid (THNF) is frequently used to cool them. THNF has the potential to dissipate heat more efficiently, thereby lowering the possibility of excessive heat and malfunctioning components. The effects of thermal radiation and heat source/sink are also examined on the flow of THNF. The flow has been formulated in the form of PDEs, which are numerically computed through the MATLAB solver BVP4c. The numerical results of BVP4c are relatively compared to the published work for validity purposes. It has been detected that the results are accurate and reliable. Furthermore, from the graphical results, it has been perceived that the rising impact of the Weissenberg number accelerates the velocity and thermal profile. The effect of the power-law index parameter drops the fluid temperature, but enhances the velocity curve. The variation in the wedge angle boosts the shearing stress and energy propagation rate, whereas the increment of Wi declines both the energy transfer rate and skin friction.

Profile reconstruction and quantitative detection of planar defects with composite-mode total focusing method (CTFM)

The profile reconstruction of planar defects by ultrasonic imaging is helpful for obtaining the flaw type, size, orientation and other characteristics. In this paper, composite-mode total focusing method (CTFM) is proposed by selecting the strongest response from 21 views at every reconstructed point, realizing the profile reconstruction and quantitative detection of priori unknown planar defects except for the near-horizontal defects with a set of phased array (PA) probe and wedge. Subsequently, eight effective views corresponding to 45° longitudinal-wave wedge are determined considering Snell's law and beam directivity. The 64-element linear array probe with 5 MHz central frequency and 45° wedge were used to reconstruct a series of 5 mm length cracks with different orientations (0°, ±15°, ±30°, ±45°, ±60° and ±75°) by CTFM in simulation. The measurement errors of crack lengths, orientation angles and central depths with the 6 dB drop rule were within 0.42 mm, 1.87° and 0.58 mm, respectively. The experimental results showed that the characteristics of 5 mm length slots were presented with high accuracy, verifying the feasibility of CTFM. Meanwhile, the planar and volumetric defects can be distinguished qualitatively by CTFM. Finally, the reconstructed image by naive sum is compared with the CTFM image, and the effects of wedge angle and number of elements on profile reconstruction are discussed.

Experimental and DEM studies of velocity profiles and residence time distribution of non-spherical particles in silos

Residence time distribution (RTD) of barley grains with elliptical shape were investigated in wedge-shaped and flat-bottom silos using the discrete element method (DEM) and experiments. The velocity distribution of particles were captured using particle image velocimetry during silo discharge. Multi-sphere method (a combination of three spheres) was used to simulate the granular flow by DEM. The model was validated using the experimental results relative to distributions of lateral and axial components of particle velocity. The obtained RTDs were interpreted using the flow pattern of particles. In the flat-bottom silo, the regions on the top of the outlet showed the shortest residence times. The residence times of particles increased as the height increased above the outlet, in the center of the silos. In the regions close to the walls (outside of the outlet region) of the flat-bottom silo, residence time of particles decreased with increasing height. On the other hand, in the wedge-shaped silo, particles in the outlet zone showed the shortest residence times while the particles located on the inclined silo wall out of the outlet zone have the longest residence times. Effects of wedge angle and initial filled height were also studied and discussed on the residence time distribution.

Dependence of bonding strength and variations in residual stress on interface wedge angles and bonding temperature conditions

AbstractResidual stress can considerably weaken systems with ceramics-to-metal joints. Herein, we investigate the dependence of bonding strength and residual stress variation of a ceramics-to-metal joint system on the interface wedge angle and bonding temperature condition. First, disparity between large-scale displacement models with varying work-hardening parameters was confirmed using thermal elastoplastic Finite Element Method (FEM) analysis. Each interface wedge shape was set to a plane surface to compare FEM results to experimental results related to the effect of the interface wedge angle on the practical bonding strength. The experimental results were specifically for a system consisting of Si3N4-WC/TiC/TaC bonded to Ni plate. The effects of the wedge angle of the metal side on residual stress near the interface edge were numerically predicted using FEM models. The interface wedge angles for this model, φ1 and φ2, were defined using the configuration angle between the interface and free surfaces of both materials. The numerical results showed that the stress σr on the free surface of the ceramic side was concentrated near the interface edge at which discontinuity in the stress state is generated. Dependence of the residual stress variation on both the wedge angle and temperature conditions can be predicted. It was confirmed that the bonding strength improves with decreasing residual stress in geometrical conditions. Therefore, residual stress appears to be a predominant factor affecting bonding strength. The observed fracture pattern showed that the fracture originated near the interface edges, after which small cracks propagated on the ceramic side. The residual stress is presumed to dominate bonding strength as the fracture occurred near the interface edge of the ceramic side. Results showed that the maximum bonding strength appears at the geometrical condition where the fracture pattern changes to φ2 lower than 90° of joint bonded at 980 °C. Therefore, the optimum interface wedge angle depends on a combination of materials and bonding temperature conditions, because the weak point of the bonded joint system will affect the stiffness balance of both materials and the adhesion power of the bonded interface.

Exact Solutions for Interaction of Parallel Screw Dislocations with a Wedge Crack in One-Dimensional Hexagonal Quasicrystal with Piezoelectric Effects

The purpose of this paper is to consider the interaction between many parallel dislocations and a wedge-shaped crack and their collective response to the external applied generalized stress in one-dimensional hexagonal piezoelectric quasicrystal, employing the complex variable function theory and the conformal transformation method; the problem for the crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann–Hilbert boundary value problems. The analytical solutions of the generalized stress field are obtained. The dislocations are subjected to the phonon field line force, phason field line force, and line charge at the core. The positions of the dislocations are arbitrary, but the dislocation distribution is additive. The dislocation is not only subjected to the external stress and the internal stress generated by the crack, but also to the force exerted on it by other dislocations. The closed-form solutions are obtained for field intensity factors and the image force on a screw dislocation in the presence of a wedge-shaped crack and a collection of other dislocations. Numerical examples are provided to show the effects of wedge angle, dislocation position, dislocation distribution containing symmetric configurations and dislocation quantities on the field intensity factors, energy release rate, and image force acting on the dislocation. The principal new physical results obtained here are (1) the phonon stress, phason stress, and electric displacement singularity occur at the crack tip and dislocations cores, (2) the increasing number of dislocations always accelerates the crack propagation, (3) the effect of wedge angle on crack propagation is related to the distribution of dislocations, and (4) the results of the image force on the dislocation indicate that the dislocations can either be attracted or rejected and reach stable positions eventually.

An explicit matrix algorithm for solving three-dimensional elastic wedge under surface loads

Analytical solutions for three-dimensional wedge problems are difficult to obtain. It thus leads inevitably to the use of alternative methods such as the finite element method in practice. We here present an explicit matrix algorithm for solving 3D wedge problems under general surface loads: arbitrarily distributed normal and shear loads. The methodology is based on the concept of overlapping two half-spaces formed by the surfaces of a wedge and all calculations are based on half-space equivalent loads. We show that the equivalent loads on the two half-spaces are directly related to the product of the original loads on the wedge and transformation matrices. The transformation matrices are functions of wedge angle, mesh structure, and Poisson's ratio, but not the applied load. Hence, a 3D wedge problem can be solved using those classical solutions for half-spaces once the equivalent loads are obtained. Stress analyses of elastic wedge with different wedge angles are conducted. Results of three special cases: wedge angle of 170°, 90° and 60° are compared with half-space results, the published data of quarter-space and FEM, respectively. The new algorithm is validated by the good correlation shown in the comparison. The effect of wedge angle on internal stresses is also discussed.

Penumbral Dose Characteristics of Physical and Virtual Wedge Profiles

Purpose: Both physical and virtual wedges are used in radiotherapy to get uniform and desired dose distribution in clinical setting. All linear accelerators of different venders have computer controlled dynamic wedges called virtual wedge filters. Penumbra is one of the important photon beam characteristics needed to be understood in radiation therapy at the time of commissioning of Treatment Planning system (TPS) as well as applying various treatment planning algorithms in clinical applications. In this study we measured the dose profiles of open field, physical wedges (PW) and virtual wedges (VW) for energies (6 MV & 15 MV), various field sizes (10 × 10, 15 × 15 & 20 × 20 cm2), depths (dmax, 10 cm, 20 cm) and wedge angles (15°, 30°, 45° and 60°). From beam profile we calculated the penumbral width for open and wedged fields. The study was carried out on Siemens ONCOR IMRT Plus linear accelerator. The obtained penumbral width of PW and VW of all wedge angles was subtracted from the penumbral width of open field. The deviations in penumbral width were compared and statistically analyzed as a function of energy, depth, field size and wedge angles. Material and Method: The penumbral width was measured using IBA CC13 ion chamber in IBA Blue phantom (a 3D water phantom). The source to surface distance (SSD) during our study was kept 100cm and measurement was taken for 10 × 10, 15 × 15, 20 × 20 cm2 field sizes and for 15°, 30°, 45°, 60° wedges. These measurements were taken for both 6 MV and 15 MV photon energies. Virtual wedge profiles were acquired using LDA-99 linear detector array (IBA, Germany). The deviations in penumbral width for both PW and VW were calculated by subtracting the penumbral width from open field penumbral width in gun direction (in-plane) and deviation in VW penumbral width, and were obtained by subtracting the open field penumbral width in left-right direction (cross-plane) direction. The measured deviations were plotted for both PW and VW. Statistics on the measured deviations was performed by using SPSS Version 15. Results & Conclusion: The results of one way ANOVA (Analysis of Variance) show that the deviations are significant with energy and the deviations are higher in lower energy than higher energy. The deviations increase as depth increases, the deviations are also significant with depth. The deviations increase with field sizes; the deviations as a function of field size are highly significant. The deviations are higher in PW than VW but the deviations with wedge type are in-significant. As wedge angle increases, deviations also increase and the effect of wedge angle is highly significant on deviations.

On Discontinuous Dynamics of a Freight Train Suspension System

In this paper, a freight train suspension system is presented for all possible types of motion. The suspension system experiences impacts and friction between wedges and bolster. The impacts cause the chatter motions between wedges and bolster, and the friction will cause the stick and nonstick motions between wedges and bolster. Due to the wedge effect, the suspension system may become stuck and not move, which can cause the suspension to lose functions. To discuss such phenomena in the freight train suspension systems, the theory of discontinuous dynamical systems is used, and the motion mechanism of impacting chatter with stick and stuck is discussed. The analytical conditions for the onset and vanishing of stick motions between the wedges and bolster are presented, and the condition for maintaining stick motion was achieved as well. The analytical conditions are developed for the onset and vanishing conditions for stuck motion. An analytical prediction of periodic motions relative to impacting chatter with stick and stuck motions in the train suspension is performed through the mapping dynamics. The corresponding analyses of local stability and bifurcation are carried out, and the grazing and stick conditions are used to determine periodic motions. Numerical simulations illustrate periodic motions of stick and stuck motions. Finally, from field testing data, the effects of wedge angle on the motions of the suspension are presented to find a more desirable suspension response for design.

The Effect of Wedge Angle on the Evolution of a Stagnation Layer in a Colliding Plasma Experiment

Colliding plasmas are steadily gaining significance in hohlraum studies, pulsed laser deposition and laser-induced breakdown spectroscopy for a number of reasons, not least the levels of control they o.er over the properties of the slab of plasma that accumulates at the collision front, i.e. the stagnation layer. We present here some results of a time and space resolved optical-spectroscopic study of colliding plasmas formed at the front surfaces of flat and inclined Cu slab targets as a function of the wedge angle between them for angles ranging from 100° to 180° (i.e., laterally colliding plasmas). Presented here are the kinetics of atomic/ionic spatial distributions throughout the stagnation layers, both of which have been found to vary significantly with wedge angle.

Effect of wedge angle on surface roughness in finish turning: analytical and experimental study

Most of the theoretical models for surface roughness in finish turning assume that the work piece surface profile is formed by the rounded tip of the tool nose. The effect of the straight flank section in the tool nose region on the surface roughness is usually neglected. In this work, the straight flank section is taken into account in order to predict the arithmetic average roughness R a and root-mean-square roughness R q more accurately. The analytical models for R a and R q are developed as a function of three parameters, namely feed rate, nose radius, and wedge angle. These models were verified using digital simulation method. The surface roughness determined using the new three-parameter models were compared with the existing two-parameter models that consider only the feed rate and nose radius. Decreasing wedge angle was found to lower the surface roughness significantly. An experiment was conducted to test the validity of the three-parameter model at different feed rates in real machining operation. The experimental results agreed more closely with the proposed three-parameter models compared to the two-parameter models.

Numerical Study of the Effect of Wedge Angle of a Wedge-Shaped Body in a Channel using Lattice Boltzmann Method

The aim of this paper is to study the fluid flow behavior around a wedge shaped body with different wedge angles placed in a channel using Lattice-Boltzmann Method (LBM). The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The influence of the gap ratio G* = G/H, where H is the distance between two parallel walls, G is the gap between body and wall, on the flow field is illustrated. The gap ratio, G*, depends on the angle of wedge-shaped body (0° < < 180°). Streamlines, vorticity contours and pressure contours are provided to analyze the important characteristics of the flow field for a wide range of non dimensional parameters namely the Reynolds number (Re), Strouhal number (St) and the gap ratio(G*). However, it is seen that the flow can be characterized by three regions: (i) large gap ratio, 0.44 < G* < 0.50, with 0° < < 55°, (ii) intermediate gap ratio, 0.20 G* 0.44, with 55° 120° and (iii) small gap ratio, 0 < G* < 0.20, with 120° < < 180°. The simulation results are compared with experimental data and other numerical models and found to be very reasonable and satisfactory.

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

AbstractThis study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.

Three dimensional numerical investigation on the effect of wedge angle of a passage with pin-fin arrays

Heat transfer in passage with pin-fin arrays for cooling blade trailing edge was studied numerically. Three-dimensional numerical simulations were carried out for steady laminar flow in passages with different wedge angles between pressure surface and suction surface of cooling blade trailing edge to study the effect of different wedge angles (from 0° to 30°) on heat transfer and pressure losses. Research was carried out for both in-line array and staggered array. From this investigation, wedge angle 10° gives the best heat transfer performance.

Antiplane stress analysis of an isotropic wedge with multiple cracks

Stress analysis is accomplished for an infinite isotropic wedge weakened by a screw dislocation. Two different cases of boundary conditions, i.e., traction–displacement and traction–traction, is considered for the wedge. The Mellin transform is utilized to solve the governing differential equation. The dislocation solution is employed for the analysis of wedges containing multiple cracks under antiplane deformation. The resultant system of singular integral equations is solved numerically to determine dislocation density on the cracks surfaces. This allows the calculation of crack opening displacements and stress intensity factors. The effects of wedge angle and cracks location and orientation on the stress intensity factors of straight cracks are investigated.

FEM Simulation of Cutting Process of Sheet Metals with Wedge Shape Punches.

Cutting of a sheet metal by indentation of wedge shape punches is investigated as a process to achieve burr-free-cutting. Numerical simulations of the cutting process are done using a rigid plastic finite element code developed by the authors. Equivalent strain and hydrostatic stress distributions at the deformation region of the sheet are calculated, and the effects of wedge angle on the shape of the cut edge are discussed based on the calculated stress and strain states. To confirm the result of the finite element simulations, cutting experiments are carried out using a mild steel sheet of 3 mm in thickness, and the shape of the cut edge is observed using a scanning electron microscope. The experimental results show that the cutting mode depends very much on the wedge angle α and nose radius γ of punch; when the punch of γ=0.1mm and α=30 degree is used a sheet is separated by cutting, while when α=60 and 90 degrees ductile fracture is caused due to the secondary tensile force induced by the wedge indentation, and when α=120 degree brittle fracture is caused due to excessive work hardening during compression. When the nose radius of punch is increased from 0.1mm to 0.5mm, the deformation of sheet material between upper and lower punches becomes compression rather than cutting because of the suppression of the crack initiation and propagation from the punch nose portion. Therefore, when the punch of γ=0.5mm is used, the separated surface has a very thin flash. These experimental results are qualitatively in good agreement with the simulation results.

A simple chart for the estimation of the attenuation by a wedge diffraction

A simple method of estimating the effect of wedge angle on the sound attenuation achieved by diffraction with a wedge is described. The effect is defined as the difference between the attenuation brought about by the wedge and that due to a virtual thin barrier with the same Fresnel number, related to the source-receiver geometry. A single, reasonably accurate chart is derived from the exact solution by means of parametric studies, carried out with the aid of a computer under restricted conditions.