Stability of spatially developing boundary layers in pressure gradients

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of order R(-1) in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to O(R(-1)) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal order R(-1) except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.

Theoretical Analysis of the Electromotive Force of a Cell Incorporating a Composition Gradient Solid Electrolyte

New composition gradient solid electrolytes have been designed for application in high temperature solid-state galvanic sensors and in thermodynamic measurements. The functionally gradient electrolyte consists of a solid solution between two or more ionic conductors with a common ion and gradual variation in composition of the other ionic species. Unequal rates of migration of the ions, caused by the presence of the concentration gradient, may result in the development of space charge, manifesting as diffusion potential. Presented is a theoretical analysis of the EMF of cells incorporating gradient solid electrolytes. An analytical expression is derived for diffusion potential, using the thermodynamics of irreversible processes, for different types of concentration gradients and boundary conditions at the electrode/electrolyte interfaces. The diffusion potential of an isothermal cell incorporating these gradient electrolytes becomes negligible if there is only one mobile ion and the transport numbers of the relatively immobile polyionic species and electrons approach zero. The analysis of the EMF of a nonisothermal cell incorporating a composition gradient solid electrolyte indicates that the cell EMF can be expressed in terms of the thermodynamic parameters at the electrodes and the Seebeck coefficient of the gradient electrolyte under standard conditions when the transport number of one of the ions approaches unity.

Genesis of the monsoon trough boundary layer experiment (MONTBLEX)

This paper sets out the motivation for carrying out an observational experiment on the atmospheric boundary layer along the monsoon trough, in the light of earlier studies of the atmospheric boundary layer in India and elsewhere, and the significant role that the trough has been shown to play as a key semi-permanent feature of the southwest monsoon. The scientific objectives of the experiment are set out, and its planning and execution are touched upon. Some of the gains resulting from the experiment are mentioned, and lessons for the future about the conduct of such programmes are drawn.

Nature of the Oxygen Species at Ni(110) and Ni(100) Surfaces Revealed by Exposure to Oxygen and Oxygen-Ammonia Mixtures: Evidence for the Surface Reactivity of O- Type Species

Adsorption of dioxygen at clean Ni(110) and Ni(100) surfaces gives rise to two prominent features in the O(1s) spectra at 530 and 531 eV due to O2- and O- type species, respectively. Interaction of ammonia with a Ni(100)-O surface where theta(oxygen) < 0.1 ML favors the dissociation of NH3 giving NHn, (n = 1, 2) and N(a) species. This is accompanied by a decrease in the intensity of the 531 eV feature. On the other hand. a Ni(100)-O surface where the oxygen species are mainly of the O2- type is unreactive, Coadsorption studies of NH3-O-2 mixtures show that at Ni(110) surfaces the uptake of both oxygen and ammonia increase with the proportion of oxygen in the NH3-O-2 mixture. The surface concentrations of the O- species and the NHn species also increase with the increase in the O-2/NH3 ratio while the slope of the plot of sigma(N) versus sigma(O-) is around unity. The results demonstrate the high surface reactivity of the O- species and its role in the dissociation of ammonia. Based on these observations, the possibility of the formation of a surface complex between ammonia and oxygen (specifically O-) is suggested. Results from vibrational spectroscopic studies of the coadsorption of NH3-O-2 mixtures are consistent with those from core-level spectroscopic studies.

Oxidation of methanol on the surfaces of model Cu/ZnO catalysts containing Cu1+ and Cu-0 species

Interaction of CH3OH with Cu clusters deposited on ZnO films grown on a Zn foil as well as on a ZnO(0001)Zn crystal, has been examined by X-ray photoelectron spectroscopy. On clean Cu clusters, reversible molecular adsorption or formation of CH3O is observed. However if the Cu clusters are pretreated with oxygen, both CH3O and HCOO- species are produced. Model Cu/ZnO catalyst surfaces, containing both Cu1+ and Cu-0 species, show interesting oxidation properties. On a Cu-0-rich catalyst surface, only CH3O species is formed on interaction with CH3OH. On a Cu1+-rich surface, however, HCOO- ion is the predominant species.

Similarity solution of unsteady boundary layer equations with a magnetic field

The unsteady laminar incompressible boundary layer flow of an electrically conducting fluid in the stagnation region of two-dimensional and axisymmetric bodies with an applied magnetic field has been studied. The boundary layer equations which are parabolic partial differential equations with three independent variables have been reduced to a system of ordinary differential equations by using suitable transformations and then solved numerically using a shooting method. Here, we have obtained new solutions which are solutions of both the boundary layer and Navier-Stokes equations.

The two-step positive temperature coefficient in resistance characteristics of n-(Ba,Pb)TiO3 ceramics created through inclusion of grain boundary modifier additives

Donor-doped n-(Ba,Pb)TiO3 polycrystalline ceramics exhibit distinctly two-step positive temperature coefficient of resistance (PTCR) characteristics when formulated with suitable combinations of B2O3 and Al2O3 as grain boundary modifiers by heterogeneous addition. B2O3 or Al2O3 when added singularly resulted in either steep or broad PTCR jumps respectively across the phase transition. The two-step PTCR is attributed to the activation of the acceptor states, created through B2O3 and Al2O3, for various temperature regimes above the Curie point (T-c). The changing pattern of trap states is evident from the presence of Ti4+-O--Al3+ type hole centres in the grain boundary layer regions, identified in the electron paramagnetic resonance (EPR) spectra. That charge redistribution occurs among the inter-band gap defect states on crossing the Curie temperature is substantiated by the temperature coefficient in the EPR results. Capacitance-voltage results clearly show that there is an increase in the density of trap states with the addition of B2O3 and Al2O3. The spread in energy values of these trap states is evident from the large change in barrier height (phi similar or equal to 0.25-0.6 eV) between 500 and 650 K.

Transformation of a laterally diverging boundary layer flow to a two-dimensional boundary layer flow

Laterally diverging boundary layer flow over a plate is shown to be reducible to a two-dimensional flow by modelling the diverging streamlines by a source flow.

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

Abstract: An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal, to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time.

Latitude variation of boundary layer height over Indian Ocean during pre- and First Field Phase (FFP-98) of INDOEX

This paper describes the results of the measurement of the Marine Boundary Layer (MBL) height from spectral analysis of the u and v components of the wind and from CLASS/radiosonde temperature profiles. The data were collected on ORV Sagar Kanya during the pre-INDOEX (27 December 1996 through 31 January 1997) and FFP-98 (18 February to 31 March 1998) over the latitude range 15 degrees N to 14 degrees S and 15 degrees N to 20 degrees S respectively. During the pre-INDOEX, the MBL heights gradually decrease from 2.5 km at 13 degrees N to around 500 to 600 m at 10 degrees S, Similar results are observed in the return track. The MBL heights (0.5 to 1 km) obtained during FFP-98 are less compared to those obtained during pre-INDOEX. The MBL heights during FFP-98 are less compared to the pre-INDOEX and are believed to be due to the presence of stratus, stratocumulus and cumulus clouds during the cruise period, compared to a relatively cloud free pre-INDOEX cruise.

Synthesis based on cyclohexadienes: Part 26 - Total synthesis of some naturally occurring phthalides from Alternaria species

Total synthesis of the naturally occurring phytotoxic phthalides, silvaticol 7, zinniol 5 and the phthalides 1 and 2, is reported from the substrate 16 derived from the Alder-Rickert reaction of 1-methoxy-2-methyl-3-trimethylslyloxycyclohexa-1,3-diene 15 with dimethyl acetylenedicarboxylate.

Growth mechanism of phases, Kirkendall voids, marker plane position, and indication of the relative mobilities of the species in the interdiffusion zone

Often, wrong conclusions about the mobilities of species are drawn from the position of the Kirkendall marker plane or voids in the interdiffusion zone. To clarify, I have discussed the growth mechanism of the phases and the position of the marker plane depending on the relative mobilities of the species. The formation of different kinds of voids in the interdiffusion zone is discussed. Further, the microstructure that could be found because of the Kirkendall effect is also explained.

The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

A current error space vector based hysteresis controller with constant switching frequency and simple online boundary computation for VSI fed IM drive

This paper proposes a simple current error space vector based hysteresis controller for two-level inverter fed Induction Motor (IM) drives. This proposed hysteresis controller retains all advantages of conventional current error space vector based hysteresis controllers like fast dynamic response, simple to implement, adjacent voltage vector switching etc. The additional advantage of this proposed hysteresis controller is that it gives a phase voltage frequency spectrum exactly similar to that of a constant switching frequency space vector pulse width modulated (SVPWM) inverter. In this proposed hysteresis controller the boundary is computed online using estimated stator voltages along alpha and beta axes thus completely eliminating look up tables used for obtaining parabolic hysteresis boundary proposed in. The estimation of stator voltage is carried out using current errors along alpha and beta axes and steady state model of induction motor. The proposed scheme is simple and capable of taking inverter upto six step mode operation, if demanded by drive system. The proposed hysteresis controller based inverter fed drive scheme is simulated extensively using SIMULINK toolbox of MATLAB for steady state and transient performance. The experimental verification for steady state performance of the proposed scheme is carried out on a 3.7kW IM.

Boundary conditions at a rigid wall for rough granular gases

We derive boundary conditions at a rigid wall for a granular material comprising rough, inelastic particles. Our analysis is confined to the rapid flow, or granular gas, regime in which grains interact by impulsive collisions. We use the Chapman-Enskog expansion in the kinetic theory of dense gases, extended for inelastic and rough particles, to determine the relevant fluxes to the wall. As in previous studies, we assume that the particles are spheres, and that the wall is corrugated by hemispheres rigidly attached to it. Collisions between the particles and the wall hemispheres are characterized by coefficients of restitution and roughness. We derive boundary conditions for the two limiting cases of nearly smooth and nearly perfectly rough spheres, as a hydrodynamic description of granular gases comprising rough spheres is appropriate only in these limits. The results are illustrated by applying the equations of motion and boundary conditions to the problem of plane Couette flow.