The energy balance in the Ramdas layer

On calm clear nights, air at a height of a few decimetres above bare soil can be cooler than the surface by several degrees in what we shall call the Ramdas layer (Ramdas and Atmanathan, 1932). The authors have recently offered a logical explanation for such a lifted temperature minimum, together with a detailed numerical model. In this paper, we provide physical insight into the phenomenon by a detailed discussion of the energy budget in four typical cases, including one with a lifted minimum. It is shown that the net cooling rate near ground is the small difference between two dominant terms, representing respectively radiative upflux from the ground and from the air layers just above ground. The delicate energy balance that leads to the lifted minimum is upset by turbulent transport, by surface emissivity approaching unity, or by high ground cooling rates. The rapid variation of the flux emissivity of humid air is shown to dominate radiative transport near the ground.

Triply-periodic balance surfaces

The list of possible G-H symmetries for triply-periodic balance surfaces, given by Koch and Fischer, is studied with a view to finding new types. It is found that balance surfaces exist for all the cases that were labelled as undecided in the work of Koch and Fischer. For some of these, new minimal surfaces have been found, with the aid of Brakke's 'Surface Evolver'. (C) 1997 Elsevier Science B.V.

Lubricity of an oil in water emulsion in metal cutting: The effect of hydrophilic/lypophilic balance of emulsifiers

A steel disc is cut using a single point tool. The coefficient of friction of the nascent cut surface is measured by a spherical steel pin situated in close proximity of the point of cutting. The tool, disc and the friction pin are immersed in an oil in water emulsion bath during the experiment. The purpose of the experiments conducted here is to record the effect of hydrophilic/lypophilic balance (HLB) of the emulsifier on the lubricity experienced in the cutting operation. The more lypophilic emulsifiers were found to give greater lubricity than what is recorded when the emulsifier is more hydrophilic. XPS and FTIR spectroscopy are used to explore the tribofilm generated on the nascent cut surface to indicate a possible rationale for the effect. (C) 2011 Elsevier B.V. All rights reserved.

Aerodynamic Load Measurements at Hypersonic Speeds Using Internally Mounted Fiber-Optic Balance System

This paper describes the measurement of aerodynamic loads using fiber-optic strain gauge sensors and associated signal processors at hypersonic speeds in the 300mm hypersonic wind tunnel. at the Department of Aerospace Engineering, Indian Institute of Science. Fiber-optic sensors have been developed in USA since 1990, for variety of applications in experimental stress analysis, skin friction measurement in fluid flows, smart structures, smart materials, sensing of acoustic emission and more recently in the development of compact devices for measurement of displacement, stress/strain, pressure, temperature, acceleration etc. Our group at llSc has been playing a lead role in the use of these fiber - optic sensors for successful measurement of aerodynamic loads in wind tunnels and the first ever six-component wind tunnel strain gauge balance in the world based on fiber optic sensors was built at the Indian Institute of Science in the year 1999. We report here the results of our efforts in the development of an internal strain gauge balance for high-speed wind tunnel applications.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

A new 6-component accelerometer force balance for short duration ground testing facilities

A new six-component accelerometer force balance is developed and used in the HST2 shock tunnel of Indian Institute of Science. Aerodynamic forces and moments for a hypersonic slender body measured using this balance system at a free stream Mach number of 5.75 and Reynolds number of 1.5 million and stagnation enthalpy of 1.5 and 2 MJ/kg are presented. These measured values compare well with the theoretical values estimated using modified Newtonian theory.

A novel free floating accelerometer force balance system for shock tunnel applications

In order to overcome the interference of the model mounting system with the external aerodynamics of the body during shock tunnel testing, a new free floating internally mountable balance system that ensures unrestrained model motion during testing has been designed, fabricated and tested. Minimal friction ball bearings are used for ensuring the free floating condition of the model during tunnel testing. The drag force acting on a blunt leading edge flat plate at hypersonic Mach number has been measured using the new balance system. Finite element model (FEM) and CFD are exhaustively used in the design as well as for calibrating the new balance system. The experimentally measured drag force on the blunt leading edge flat plate at stagnation enthalpy of 0.7 and 1.2 MJ/kg and nominal Mach number of 5.75 matches well with FEM results. The concept can also be extended for measuring all the three fundamental aerodynamic forces in short duration test facilities like free piston driven shock tunnels.

On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.