Viscous flow computations using a meshless solver, LSFD-U

The Upwind-Least Squares Finite Difference (LSFD-U) scheme has been successfully applied for inviscid flow computations. In the present work, we extend the procedure for computing viscous flows. Different ways of discretizing the viscous fluxes are analysed for the positivity, which determines the robustness of the solution procedure. The scheme which is found to be more positive is employed for viscous flux computation. The numerical results for validating the procedure are presented.

Vertical profile of aerosol single scattering albedo over west coast of India during W_ICARB

Altitude profile of aerosol Single Scattering Albedo (SSA), derived from simultaneous in-situ airborne measurements of the coefficients of aerosol absorption and scattering off the west coast of India over the Arabian Sea (AS), during January 2009 is presented. While both the absorption and scattering coefficients decreased with altitude, their vertical structure differed significantly. Consequently, the derived SSA, with a surface value of 0.94, decreased with altitude, illustrating increasing relative dominance of aerosol absorption at higher altitudes. Altitude profile of SSA, when examined in conjunction with that of hemispheric backscatter fraction, revealed that the continental influence on the aerosol properties was higher at higher altitude, rather than the effect of marine environment. During an east-west transect across the peninsular India at an altitude of similar to 2500 m (free troposphere), it was found that the aerosol scattering coefficients remained nearly the same over both east and west coasts. (C) 2010 Elsevier Ltd. All rights reserved.

PROMIDS: A PROtotype multi-rIng data flow system for functional programming languages

This paper presents a detailed description of the hardware design and implementation of PROMIDS: a PROtotype Multi-rIng Data flow System for functional programming languages. The hardware constraints and the design trade-offs are discussed. The design of the functional units is described in detail. Finally, we report our experience with PROMIDS.

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

A Note on Diffraction of Water Waves by a Nearly Vertical Barrier

A simplified perturbational analysis is employed, together with the application of Green's theorem, to determine the first-order corrections to the reflection and transmission coefficients in the problem of diffraction of surface water waves by a nearly vertical barrier in two basically important cases: (i) when the barrier is partially immersed and (ii) when the barrier is completely submerged. The present analysis produces the desired results fairly easily and relatively quickly as compared with the known integral equation approach to this class of diffraction problems.

Exact solution for the unsteady flow and heat transfer between eccentrically rotating disks

The unsteady heat transfer associated with flow due to eccentrically rotating disks considered by Ramachandra Rao and Kasiviswanathan (1987) is studied via reformulation in terms of cylindrical polar coordinates. The corresponding exact solution of the energy equation is presented when the upper and lower disks are subjected to steady and unsteady temperatures. For an unsteady flow with nonzero mean, the energy equation can be solved by prescribing the temperature on the disk as a sum of steady and oscillatory parts

Unsteady MHD forced flow due to a point sink

An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.

A numerical study of the role of the vertical structure of vorticity during tropical cyclone genesis

An eight-level axisymmetric model with simple parameterizations for clouds and the atmospheric boundary layer was developed to examine the evolution of vortices that are precursors to tropical cyclones. The effect of vertical distributions of vorticity, especially that arising from a merger of mid-level vortices, was studied by us to provide support for a new vortex-merger theory of tropical cyclone genesis. The basic model was validated with the analytical results available for the spin-down of axisymmetric vortices. With the inclusion of the cloud and boundary layer parameterizations, the evolution of deep vortices into hurricanes and the subsequent decay are simulated quite well. The effects of several parameters such as the initial vortex strength, radius of maximum winds, sea-surface temperature and latitude (Coriolis parameter) on the evolution were examined. A new finding is the manner in which mid-level vortices of the same strength decay and how, on simulated merger of these mid-level vortices, the resulting vortex amplifies to hurricane strength in a realistic time frame. The importance of sea-surface temperature on the evolution of full vortices was studied and explained. Also it was found that the strength of the surface vortex determines the time taken by the deep vortex to amplify to hurricane strength.

The hard-particle model for a dense granular flow down an inclined plane

Perfectly hard particles are those which experience an infinite repulsive force when they overlap, and no force when they do not overlap. In the hard-particle model, the only static state is the isostatic state where the forces between particles are statically determinate. In the flowing state, the interactions between particles are instantaneous because the time of contact approaches zero in the limit of infinite particle stiffness. Here, we discuss the development of a hard particle model for a realistic granular flow down an inclined plane, and examine its utility for predicting the salient features both qualitatively and quantitatively. We first discuss Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.58 are in the rapid flow regime, due to the very high particle stiffness. An important length scale in the shear flow of inelastic particles is the `conduction length' delta = (d/(1 - e(2))(1/2)), where d is the particle diameter and e is the coefficient of restitution. When the macroscopic scale h (height of the flowing layer) is larger than the conduction length, the rates of shear production and inelastic dissipation are nearly equal in the bulk of the flow, while the rate of conduction of energy is O((delta/h)(2)) smaller than the rate of dissipation of energy. Energy conduction is important in boundary layers of thickness delta at the top and bottom. The flow in the boundary layer at the top and bottom is examined using asymptotic analysis. We derive an exact relationship showing that the a boundary layer solution exists only if the volume fraction in the bulk decreases as the angle of inclination is increased. In the opposite case, where the volume fraction increases as the angle of inclination is increased, there is no boundary layer solution. The boundary layer theory also provides us with a way of understanding the cessation of flow when at a given angle of inclination when the height of the layer is decreased below a value h(stop), which is a function of the angle of inclination. There is dissipation of energy due to particle collisions in the flow as well as due to particle collisions with the base, and the fraction of energy dissipation in the base increases as the thickness decreases. When the shear production in the flow cannot compensate for the additional energy drawn out of the flow due to the wall collisions, the temperature decreases to zero and the flow stops. Scaling relations can be derived for h(stop) as a function of angle of inclination.

Semi-similar solutions of the unsteady compressible second-order boundary layer flow at the stagnation point

Semi-similar solutions of the unsteady compressible laminar boundary layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer are studied for all the second-order boundary layer effects when the free stream velocity varies arbitrarily with time. The set of partial differential equations governing the unsteady compressible second-order boundary layers representing all the effects are derived for the first time. These partial differential equations are solved numerically using an implicit finite-difference scheme. The results are obtained for two particular unsteady free stream velocity distributions: (a) an accelerating stream and (b) a fluctuating stream. It is observed that the total skin friction and heat transfer are strongly affected by the surface mass transfer and wall temperature. However, their variation with time is significant only for large times. The second-order boundary layer effects are found to be more pronounced in the case of no mass transfer or injection as compared to that for suction. Résumé Des solutions semi-similaires d'écoulement variable compressible de couche limite sur des corps bi-dimensionnels thermique, sont étudiées pour tous les effets de couche limite du second ordre, lorsque la vitesse de l'écoulement libre varie arbitrairement avec le temps. Le systéme d'équations aux dérivées partielles représentant tous les effets est écrit pour la premiére fois. On le résout numériquement á l'aide d'un schéma implicite aux différences finies. Les résultats sont obtenus pour deux cas de vitesse variable d'écoulement libre: (a) un écoulement accéléré et (b) un écoulement fluctuant. On observe que le frottement pariétal total et le transfert de chaleur sont fortement affectés par le transfert de masse et la température pariétaux. Néanmoins, leur variation avec le temps est sensible seulement pour des grandes durées. Les effets sont trouvés plus prononcés dans le cas de l'absence du transfert de masse ou de l'injection par rapport au cas de l'aspiration.

Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Kinetic theory for the density plateau in the granular flow down an inclined plane

The striking lack of observable variation of the volume fraction with height in the center of a granular flow down an inclined plane is analysed using constitutive relations obtained from kinetic theory. It is shown that the rate of conduction in the granular energy balance equation is O(delta(2)) smaller than the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions, where the small parameter delta = (d/(1 - e(n))H-1/2), d is the particle diameter, en is the normal coefficient of restitution and H is the thickness of the flowing layer. This implies that the volume fraction is a constant in the leading approximation in an asymptotic analysis in small delta. Numerical estimates of both the parameter delta and its pre-factor are obtained to show that the lack of observable variation of the volume fraction with height can be explained by constitutive relations obtained from kinetic theory.

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

Diagnosis of dominant forcing factors for large-scale vertical velocities during active and break phases of the monsoon

An attempt to diagnose the dominant forcings which drive the large-scale vertical velocities over the monsoon region has been made by computing the forcings like diabatic heating fields,etc. and the large-scale vertical velocities driven by these forcings for the contrasting periods of active and break monsoon situations; in order to understand the rainfall variability associated with them. Computation of diabatic heating fields show us that among different components of diabatic heating it is the convective heating that dominates at mid-tropospheric levels during an active monsoon period; whereas it is the sensible heating at the surface that is important during a break period. From vertical velocity calculations we infer that the prime differences in the large-scale vertical velocities seen throughout the depth of the atmosphere are due to the differences in the orders of convective heating; the maximum rate of latent heating being more than 10 degrees Kelvin per day during an active monsoon period; whereas during a break monsoon period it is of the order of 2 degrees Kelvin per day at mid-tropospheric levels. At low levels of the atmosphere, computations show that there is large-scale ascent occurring over a large spatial region, driven only by the dynamic forcing associated with vorticity and temperature advection during an active monsoon period. However, during a break monsoon period such large-scale spatial organization in rising motion is not seen. It is speculated that these differences in the low-level large-scale ascent might be causing differences in convective heating because the weaker the low level ascent, the lesser the convective instability which produces deep cumulus clouds and hence lesser the associated latent heat release. The forcings due to other components of diabatic heating, namely, the sensible heating and long wave radiative cooling do not influence the large-scale vertical velocities significantly.