On the ignition and extinction problems in forced convection systems

In this paper the problem of ignition and extinction has been formulated for the flow of a compressible fluid with Prandtl and Schmidt numbers taken as unity. In particular, the problems of (i) a jet impinging on a wall of combustible material and (ii) the opposed jet diffusion flame have been studied. In the wall jet case, three approximations in the momentum equation namely, (i) potential flow, (ii) viscous flow, (ii) viscous incompressible with k = 1 and (iii) Lees' approximation (taking pressure gradient terms zero) are studied. It is shown that the predictions of the mass flow rates at extinction are not very sensitive to the approximations made in the momentum equation. The effects of varying the wall temperature in the case (i) and the jet temperature in the case (ii) on the extinction speeds have been studied. The effects of varying the activation energy and the free stream oxidant concentration in case (ii), have also been investigated.

Comparative study of some constitutive equations characterising non-Newtonian fluids

This paper compares, in a general way, the predictions of the constitutive equations given by Rivlin and Ericksen, Oldroyd, and Walters. Whether we consider the rotational problems in cylindrical co-ordinates or in spherical polar co-ordinates, the effect of the non-Newtonicity on the secondary flows is collected in a single parameterα which can be explicitly expressed in terms of the non-Newtonian parameters that occur in each of the above-mentioned constitutive equations. Thus, for a given value ofα, all the three fluids will have identical secondary flows. It is only through the study of appropriate normal stresses that a Rivlin-Ericksen fluid can be distinguished from the other two fluids which are indistinguishable as long as this non-Newtonian parameter has the same value.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Critical phenomena in the coexistence curve of the binary liquid system

The coexistence curve of the carbondisulphide-acetic anhydride system has been measured. The shape of the curve in the critical region (Xc ≈ 70.89 mole % mole % CS2 and Tc ≈ 30.56° C) is determined by the equation |X′ - X″| = Bx (1 - T/Tc)β with the critical indices β = 0.34 ± 0.01 and Bx = 1.7 ± 0.1 over a range 10-6 < (Tc - T)/Tc < 10-2. The values of β and Bx agree with those of other systems and the theoretical predictions of the Ising model.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

Stabilizing hadron resonance gas models

We examine the stability of hadron resonance gas models by extending them to include undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that observables such as hydrodynamics and hadron yield ratios change little upon extending the model. As a result, heavy-ion collisions at the RHIC and LHC are insensitive to a possible exponential rise in the hadronic density of states, thus increasing the stability of the predictions of hadron resonance gas models in this context. Hadron resonance gases are internally consistent up to a temperature higher than the crossover temperature in QCD, but by examining quark number susceptibilities we find that their region of applicability ends below the QCD crossover.

Charge-order driven multiferroic and magneto-dielectric properties of rare earth manganates

Charge-order driven magnetic ferroelectricity is shown to occur in several rare earth manganates of the general formula, Ln(1-x)A(x)MnO(3) (In = rare earth, A = alkaline earth). Charge-ordered manganates exhibit dielectric constant anomalies around the charge-ordering or the antiferromagnetic transition temperature. Magnetic fields have a marked effect on the dielectric properties of these compounds, indicating the presence of coupling between the magnetic and electrical order parameters. Magneto-dielectric properties are retained in small particles of the manganates. The observation of magneto-ferroelectricity in these manganates is in accordance with theoretical predictions.

Charge-order driven multiferroic and magneto-dielectric properties of rare earth manganates

Charge-order driven magnetic ferroelectricity is shown to occur in several rare earth manganates of the general formula, Ln(1-x)A(x)MnO(3) (In = rare earth, A = alkaline earth). Charge-ordered manganates exhibit dielectric constant anomalies around the charge-ordering or the antiferromagnetic transition temperature. Magnetic fields have a marked effect on the dielectric properties of these compounds, indicating the presence of coupling between the magnetic and electrical order parameters. Magneto-dielectric properties are retained in small particles of the manganates. The observation of magneto-ferroelectricity in these manganates is in accordance with theoretical predictions.

Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Flow Generated By Pitched Blade Turbines Ii: Simulation Using Κ-Ε Model

Experimental data on average velocity and turbulence intensity generated by pitched blade downflow turbines (PTD) were presented in Part I of this paper. Part II presents the results of the simulation of flow generated by PTD The standard κ-ε model along with the boundary conditions developed in the Part 1 have been employed to predict the flow generated by PTD in cylindrical baffled vessel. This part describes the new software FIAT (Flow In Agitated Tanks) for the prediction of three dimensional flow in stirred tanks. The basis of this software has been described adequately. The influence of grid size, impeller boundary conditions and values of model parameters on the predicted flow have been analysed. The model predictions successfully reproduce the three dimensionality and the other essential characteristics of the flow. The model can be used to improve the overall understanding about the relative distribution of turbulence by PTD in the agitated tank

An elastic-viscoplastic constitutive model for the hot-forming of aluminum alloys

Under hot-forming conditions characterized by high homologous temperatures and strain-rates, metals usually exhibit rate-dependent inelastic behavior. An elastic-viscoplastic constitutive model is presented here to describe metal behavior during hot-forming. The model uses an isotropic internal variable to represent the resistance offered to plastic deformation by the microstructure. Evolution equations are developed for the inelastic strain and the deformation resistance based on experimental results. A methodology is presented for extracting model parameters from constant true strain-rate compression tests performed at different temperatures. Model parameters are determined for an Al-1Mn alloy and an Al-Mg-Si alloy, and the predictions of the model are shown to be in good agreement with the experimental data. (C) 2000 Kluwer Academic Publishers.

Helicopter blade flapping with and without small angle assumption in the presence of dynamic stall

The flapping equation for a rotating rigid helicopter blade is typically derived by considering (1)small flap angle, (2) small induced angle of attack and (3) linear aerodynamics. However, the use of nonlinear aerodynamics such as dynamic stall can make the assumptions of small angles suspect as shown in this paper. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived. A semi-empirical dynamic stall aerodynamics model (ONERA model) is used. Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are examined. It is shown that the small flapping assumption, and to a lesser extent, the small induced angle ofattack assumption, can lead to inaccurate predictions of the blade flap response in certain flight conditions for some rotors when nonlinear aerodynamics is considered. (C) 2010 Elsevier Inc. All rights reserved.

Constraining uncertainty in regional hydrologic impacts of climate change: Nonstationarity in downscaling

Regional impacts of climate change remain subject to large uncertainties accumulating from various sources, including those due to choice of general circulation models (GCMs), scenarios, and downscaling methods. Objective constraints to reduce the uncertainty in regional predictions have proven elusive. In most studies to date the nature of the downscaling relationship (DSR) used for such regional predictions has been assumed to remain unchanged in a future climate. However,studies have shown that climate change may manifest in terms of changes in frequencies of occurrence of the leading modes of variability, and hence, stationarity of DSRs is not really a valid assumption in regional climate impact assessment. This work presents an uncertainty modeling framework where, in addition to GCM and scenario uncertainty, uncertainty in the nature of the DSR is explored by linking downscaling with changes in frequencies of such modes of natural variability. Future projections of the regional hydrologic variable obtained by training a conditional random field (CRF) model on each natural cluster are combined using the weighted Dempster-Shafer (D-S) theory of evidence combination. Each projection is weighted with the future projected frequency of occurrence of that cluster (''cluster linking'') and scaled by the GCM performance with respect to the associated cluster for the present period (''frequency scaling''). The D-S theory was chosen for its ability to express beliefs in some hypotheses, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The methodology is tested for predicting monsoon streamflow of the Mahanadi River at Hirakud Reservoir in Orissa, India. The results show an increasing probability of extreme, severe, and moderate droughts due to limate change. Significantly improved agreement between GCM predictions owing to cluster linking and frequency scaling is seen, suggesting that by linking regional impacts to natural regime frequencies, uncertainty in regional predictions can be realistically quantified. Additionally, by using a measure of GCM performance in simulating natural regimes, this uncertainty can be effectively constrained.

The stress in a slowly sheared granular column

We report measurements of the wall stress in a granular material sheared in a cylindrical Couette cell, as a function of the distance from the free surface. Our results shows that when the material is static, all components of the stress saturate to constant values within a short distance from the free surface, in conformity with earlier experiments and theoretical predictions. When the material is sheared by rotating the inner cylinder at a constant rate, the stresses are remarkably altered. The radial normal stress does not saturate, and increases even more rapidly with depth than the linear hydrostatic pressure profile. The axial shear stress changes sign on shearing, and its magnitude increases with depth. These results are discussed in the context of the predictions of the classical and Cosserat plasticity theories.