Analytical studies of gain optimization in CO2-N2 gasdynamic lasers employing two-dimensional wedge nozzles

An analytical method has been proposed to optimise the small-signaloptical gain of CO2-N2 gasdynamic lasers (gdl) employing two-dimensional (2D) wedge nozzles. Following our earlier work the equations governing the steady, inviscid, quasi-one-dimensional flow in the wedge nozzle of thegdl are reduced to a universal form so that their solutions depend on a single unifying parameter. These equations are solved numerically to obtain similar solutions for the various flow quantities, which variables are subsequently used to optimize the small-signal-gain. The corresponding optimum values like reservoir pressure and temperature and 2D nozzle area ratio also have been predicted and graphed for a wide range of laser gas compositions, with either H2O or He as the catalyst. A large number of graphs are presented which may be used to obtain the optimum values of small signal gain for a wide range of laser compositions without further computations.

Flow of metal in a wedge-shaped cavity

The wedge shape is a fairly common cross-section found in many non-axisymmetric components used in machines, aircraft, ships and automobiles. If such components are forged between two mutually inclined dies the metal displaced by the dies flows into the converging as well as into the diverging channels created by the inclined dies. The extent of each type of flow (convergent/divergent) depends on the die—material interface friction and the included die angle. Given the initial cross-section, the length as well as the exact geometry of the forged cross-section are therefore uniquely determined by these parameters. In this paper a simple stress analysis is used to predict changes in the geometry of a wedge undergoing compression between inclined platens. The flow in directions normal to the cross-section is assumed to be negligible. Experiments carried out using wedge-shaped lead billets show that, knowing the interface friction and as long as the deformation is not too large, the dimensional changes in the wedge can be predicted with reasonable accuracy. The predicted flow behaviour of metal for a wide range of die angles and interface friction is presented: these characteristics can be used by the die designer to choose the die lubricant (only) if the die angle is specified and to choose both of these parameters if there is no restriction on the exact die angle. The present work shows that the length of a wedge undergoing compression is highly sensitive to die—material interface friction. Thus in a situation where the top and bottom dies are inclined to each other, a wedge made of the material to be forged could be put between the dies and then compressed, whereupon the length of the compressed wedge — given the degree of compression — affords an estimate of the die—material interface friction.

Theoretical gain optimization in CO2-N2-H2 gasdynamic lasers with two-dimensional wedge nozzles

Attention is given to the results of optimization studies with a 16-micron CO2-N2-H2 GDL employing two-dimensional wedge nozzles. The optimum value of the achievable gain reaches 12.7 percent/cm on the P(15) line for a 30:50:20 percent respective apportionment of the aforementioned gases. The corresponding optimum values for reservoir pressure and area ratio are computed as functions of reservoir temperature, and presented graphically.

Steady compressible flow of granular materials through a wedge-shaped hopper: The smooth wall, radial gravity problem

A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

Crystallographic identification of a ‘stepped-cubane’ structure for the Cu4O4 core in [Cu4L2(bipy)4(µ3-OH)2][ClO4]4(HL = 5-hydroxy-6-methylpyridine-,4-dimethanol, bipy = 2,2′-bipyridine)

The structure of [Cu4L2(bipy)4(µ3-OH)2][ClO4]4 containing a Vitamin B6 ligand, pyridoxine (5-hydroxy-6-methylpyridine-3,4-dimethanol, HL), and 2,2′-bipyridine (bipy) has been determined by single-crystal X-ray analysis. This is the first report on a copper(II) complex having a ‘stepped-cubane’ structure. The compound crystallizes in the triclinic space group P[1 with combining macron](Z= 1) with a= 11.015(3), b= 11.902(1), c= 13.142(2)Å, α= 105.07(1), β= 102.22(1) and γ= 99.12(1)°; R= 0.054). The co-ordination geometry around each copper is trigonally distorted square pyramidal. Two of the basal sites are occupied by bipyridyl nitrogens in a bidentate fashion. The remaining basal positions for Cu(1) are filled by a phenolic oxygen and a 4-hydroxymethyl oxygen of the L moiety, whereas for Cu(2) they are occupied by two µ3-OH oxygens. The axial sites are occupied by a µ3-OH oxygen and the 4-hydroxymethyl oxygen of the same pyridoxine for Cu(1) and Cu(2), respectively. Both the bridging nature of the 4-hydroxymethyl oxygen of the L moiety and the unsymmetrical bridging nature of the µ3-OH groups with axial–equatorial bridging are novel features. The structure is discussed in relation to stepped-cubane structures reported in the literature. A comparative study is also made with µ3-hydroxo-bridged copper(II) complexes. Both the plasticity effect of CuII and the stacking interactions between the various rings appear to be important in stabilizing this unusual structure.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Finite element simulation of wedge indentation

A finite element simulation of frictionless wedge indentation of a copper strip has been carried out under plane strain conditions. The problem was first modelled using an one-pass contact algorithm. The difficulties associated with using this method to model wedge indentation problems are explained. An alternative procedure which alleviates some of the problems associated with the one-pass contact algorithm is proposed for modelling frictionless wedge indentation. Also, a re-meshing procedure which has to be carried out when the distortion of the elements around the indenter becomes significant, is discussed. A sample problem involving indentation of a 4 mm copper strip by a rigid wedge indenter has been modelled and the results are compared with experimental and theoretical results.

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.

Steady compressible flow of cohesionless granular materials through a wedge-shaped bunker

A continuum model based on the critical-state theory of soil mechanics is used to generate stress, density, and velocity profiles, and to compute discharge rates for the flow of granular material in a mass flow bunker. The bin–hopper transition region is idealized as a shock across which all the variables change discontinuously. Comparison with the work of Michalowski (1987) shows that his experimentally determined rupture layer lies between his prediction and that of the present theory. However, it resembles the former more closely. The conventional condition involving a traction-free surface at the hopper exit is abandoned in favour of an exit shock below which the material falls vertically with zero frictional stress. The basic equations, which are not classifiable under any of the standard types, require excessive computational time. This problem is alleviated by the introduction of the Mohr–Coulomb approximation (MCA). The stress, density, and velocity profiles obtained by integration of the MCA converge to asymptotic fields on moving down the hopper. Expressions for these fields are derived by a perturbation method. Computational difficulties are encountered for bunkers with wall angles θw [gt-or-equal, slanted] 15° these are overcome by altering the initial conditions. Predicted discharge rates lie significantly below the measured values of Nguyen et al. (1980), ranging from 38% at θw = 15° to 59% at θw = 32°. The poor prediction appears to be largely due to the exit condition used here. Paradoxically, incompressible discharge rates lie closer to the measured values. An approximate semi-analytical expression for the discharge rate is obtained, which predicts values within 9% of the exact (numerical) ones in the compressible case, and 11% in the incompressible case. The approximate analysis also suggests that inclusion of density variation decreases the discharge rate. This is borne out by the exact (numerical) results – for the parameter values investigated, the compressible discharge rate is about 10% lower than the incompressible value. A preliminary comparison of the predicted density profiles with the measurements of Fickie et al. (1989) shows that the material within the hopper dilates more strongly than predicted. Surprisingly, just below the exit slot, there is good agreement between theory and experiment.

Multiple beam interference of light in an absorbing wedge

Multiple beam interference of light in a wedge is considered when the wedge is filled with an absorbing medium. The aim is to examine a method that may give values of both the real and the imaginary parts of the refractive index of the absorbing medium. We propose here a method to determine these quantities from simple techniques like fringe counting and interferometry, by using as the incident wave either a single Gaussian beam or two parallel Gaussian beams.

Design of compact low pass filter with wide stop band using tri-section stepped impedance resonator

This paper reports the design of a compact low pass filter (LPF) with wide stop band region using trisection stepped impedance resonators in microstrip medium. Experimental results of a low pass filter designed at 1 GHz have been compared against the analytical and EM simulation results for the validation of the design. Results are satisfactorily matching each other. The maximum insertion of the measured filter is 0.2 dB and minimum return loss is 13.5 dB over the pass band. The stop band rejection is better than 20 dB from 1.5 GHz to 4.2 GHz and hence wide stop band performance is achieved. Overall size of the filter is 30 mm x 20 mm x 0.78 mm which is 0.1 lambda x 0.066 lambda. x 0.0026 lambda at 1 GHz. (C) 2011 Elsevier GmbH. All rights reserved.

Rotation field in wedge indentation of metals

A study is made of the rotation field in wedge indentation of metals using copper as the model material system. Wedges with apical angles of 60 and 120 are used to indent annealed copper, and the deformation is mapped using image correlation. The indentation of annealed and strain-hardened copper is simulated using finite element analysis. The rotation field, derived from the deformation measurements, provides a clear way of distinguishing between cutting and compressive modes of deformation. Largely unidirectional rotation on one side of the symmetry line with small spatial rotation gradients is characteristic of compression. Bidirectional rotation with neighboring regions of opposing rotations and locally high rotation gradients characterizes cutting. In addition, the rotation demarcates such characteristic regions as the pile-up zone in indentation of a strain-hardened metal. The residual rotation field obtained after unloading is essentially the same as that at full load, indicating that it is a scalar proxy for plastic deformation as a whole.

The variation of N-gamma with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing-soil interface friction angle (delta) on the bearing capacity factor N-gamma was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B-t from the footing edge. For a given footing width (B), the value of B-t increases continuously with a decrease in delta. For delta = 0, no trapped wedge exists below the footing base, that is, B-t/B = 0.5. On the contrary, with delta = phi, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in phi. The magnitude of N-gamma increases substantially with an increase in delta/phi. The maximum depth of the plastic zone becomes higher for greater values of delta/phi. The results from the present analysis were found to compare well with those reported in the literature.