Dipankar Chatterjee

Bio: Dipankar Chatterjee is an academic researcher from Central Mechanical Engineering Research Institute. The author has contributed to research in topics: Reynolds number & Richardson number. The author has an hindex of 25, co-authored 99 publications receiving 1715 citations. Previous affiliations of Dipankar Chatterjee include Academy of Scientific and Innovative Research & Indian Institute of Technology Kharagpur.

An enthalpy-based lattice Boltzmann model for diffusion dominated solid liquid phase transformation

Abstract: An extended lattice Boltzmann (LB) formulation is developed for simulation of three-dimensional heat diffusion, coupled with solid–liquid phase transition aspects. Thermodynamic variables are obtained through the evolution equation of a single particle distribution function. Phase change aspects are tackled by an enthalpy-based approach. The proposed model is subsequently utilized to simulate a generic laser surface melting process and compared with the continuum model results obtained by solving the governing equation for energy transport. The comparison shows a potentiality of the developed LB method to solve phase change problems in a computationally effective and convenient manner.

An enthalpy-based hybrid lattice-Boltzmann method for modelling solid-liquid phase transition in the presence of convective transport

Abstract: An extended lattice Boltzmann model is developed for simulating the convection–diffusion phenomena associated with solid–liquid phase transition processes. Macroscopic hydrodynamic variables are obtained through the solution of an evolution equation of a single-particle density distribution function, whereas, the macroscopic temperature field is obtained by solving auxiliary scalar transport equations. The novelty of the present methodology lies in the formulation of an enthalpy-based approach for phase-change modelling within a lattice-Boltzmann framework, in a thermodynamically consistent manner. Thermofluidic aspects of phase transition are handled by means of a modified enthalpy–porosity formulation, in conjunction with an appropriate enthalpy-updating closure scheme. Lattice-Boltzmann simulations of melting of pure gallium in a rectangular enclosure, Rayleigh–Benard convection in the presence of directional solidification in a top-cooled cavity, and crystal growth during solidification of an undercooled melt agree well with the numerical and experimental results available in the literature, and provide substantial evidence regarding the upscaled computational economy provided by the present methodology.

A hybrid lattice Boltzmann model for solid–liquid phase transition in presence of fluid flow

Abstract: In the present Letter, a hybrid lattice Boltzmann methodology is developed for simulating convection–diffusion transport processes pertinent to melting/solidification problems. The model is derived by coupling a modified thermal lattice Boltzmann model with an adapted enthalpy-porosity technique. The hydrodynamic variables are simulated using a single particle density distribution function, whereas the thermodynamic variables are obtained from an enthalpy density distribution function. An exhaustive comparison with other standard methods reveals that the proposed technique is computationally more convenient to be implemented for solving topologically-complicated phase boundary evolution problems during solidification of pure materials, such as the growth of an equiaxed dendrite in an undercooled melt.

Effect of thermal buoyancy on vortex shedding behind a square cylinder in cross flow at low Reynolds numbers

Abstract: Two-dimensional numerical simulation is performed to understand the influence of cross buoyancy on the vortex shedding process behind a stationary heated square cylinder at low Reynolds numbers. The flow is considered in an unbounded medium, however, fictitious confining boundaries are chosen to make the problem computationally feasible. Numerical calculations are carried out by using a finite volume method based on the PISO algorithm in a collocated grid system. The range of Reynolds number is chosen to be 5–40. In this range the flow and thermal fields are found to be steady and separated without the superimposed thermal buoyancy (i.e. for pure forced convection). However, as the buoyancy parameter (Richardson number) increases flow becomes unstable and subsequently, at some critical value of Richardson number, periodic vortex shedding is observed to characterize the flow and thermal fields. The global flow and heat transfer quantities such as the recirculation length, overall drag coefficient and surface average Nusselt number are computed for the steady separated flow (without buoyancy effect) and are found in good agreement with the available results in the literature. The effect of superimposed thermal buoyancy for the range of Reynolds number is studied for various Richardson numbers. The frequency of vortex shedding (Strouhal number) is calculated for the unsteady periodic flow. The critical Richardson number for the onset of vortex shedding decreases and the corresponding critical Strouhal number increases with increasing Reynolds number in the chosen range.

Numerical simulation of flow past row of square cylinders for various separation ratios

Abstract: A systematic study for the flow around a row of five square cylinders placed in a side-by-side arrangement and normal to the oncoming flow at a Reynolds number of 150 is carried out through the numerical solution of the two-dimensional unsteady incompressible Navier-Stokes equations. Special attention is paid to investigate the effect of the spacing between the five cylinders on the wake structure and vortex shedding mechanism. The simulations are performed for the separation ratios (spacing to size ratio) of 1.2, 2, 3 and 4. Depending on the separation ratio the following flow patterns are observed: a flip-flopping pattern, in-phase and anti-phase synchronized pattern and non-synchronized pattern. These flow patterns are supposed to be a consequence of the interaction between two types of frequencies viz. the vortex shedding (primary) and the cylinder interaction (secondary) frequencies. At small separation ratio the flow is predominantly characterized by the jet in the gaps between successive cylinders and the secondary frequencies play a role in the resulting chaotic flow. On the contrary, at higher separation ratio the secondary frequencies almost disappear and the resulting flow becomes more synchronized dominated by the primary frequency.

Boundary Layer Theory

Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

A User’s Guide

Abstract: OUTPU T 29 OUTPU T 30 OUTPU T 31 OUTPU T 32 OUTPU T 25 OUTPU T 26 OUTPU T 27 OUTPU T 28 OUTPU T 21 OUTPU T 22 OUTPU T 23 OUTPU T 24 OUTPU T 17 OUTPU T 18 OUTPU T 19 OUTPU T 20 OUTPU T 13 OUTPU T 14 OUTPU T 15 OUTPU T 16 OUTPU T 9 OUTPU T 10 OUTPU T 11 OUTPU T 12 OUTPU T 5 OUTPU T 6 OUTPU T 7 OUTPU T 8 OUTPU T 1 OUTPU T 2 OUTPU T 3 OUTPU T 4 29 30 31 32 25 26 27 28 21 22 23 24 17 18 19 20 13 14 15 16 9

Numerical Heat Transfer And Fluid Flow

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An overview of Direct Laser Deposition for additive manufacturing; Part I: Transport phenomena, modeling and diagnostics

Abstract: Laser-based additive manufacturing (LBAM) processes can be utilized to generate functional parts (or prototypes) from the ground-up via layer-wise cladding – providing an opportunity to generate complex-shaped, functionally graded or custom-tailored parts that can be utilized for a variety of engineering applications. Directed Energy Deposition (DED), utilizes a concentrated heat source, which may be a laser or electron beam, with in situ delivery of powder- or wire-shaped material for subsequent melting to accomplish layer-by-layer part fabrication or single-to-multi layer cladding/repair. Direct Laser Deposition (DLD), a form of DED, has been investigated heavily in the last several years as it provides the potential to (i) rapidly prototype metallic parts, (ii) produce complex and customized parts, (iii) clad/repair precious metallic components and (iv) manufacture/repair in remote or logistically weak locations. DLD and Powder Bed Fusion-Laser (PBF-L) are two common LBAM processes for additive metal part fabrication and are currently demonstrating their ability to revolutionize the manufacturing industry; breaking barriers imposed via traditional, ‘subtractive’ metalworking processes. This article provides an overview of the major advancements, challenges and physical attributes related to DLD, and is one of two Parts focused specifically on DLD. Part I (this article) focuses on describing the thermal/fluidic phenomena during the powder-fed DLD process, while Part II focuses on the mechanical properties and microstructure of parts manufactured via DLD. In this current article, a selection of recent research efforts – including methodology, models and experimental results – will be provided in order to educate the reader of the thermal/fluidic processes that occur during DLD, as well as providing important background information relevant to DLD as a whole. The thermal/fluid phenomena inherent to DLD directly influence the solidification heat transfer which thus impacts the part's microstructure and associated thermo-mechanical properties. A thorough understanding of the thermal/fluid aspects inherent to DLD is vital for optimizing the DLD process and ensuring consistent, high-quality parts.

Two circular cylinders in cross-flow: A review

Abstract: Pairs of circular cylinders immersed in a steady cross-flow are encountered in many engineering applications. The cylinders may be arranged in tandem, side-by-side, or staggered configurations. Wake and proximity interference effects, which are determined primarily by the longitudinal and transverse spacing between the cylinders, and also by the Reynolds number, have a strong influence on the flow patterns, aerodynamic forces, vortex shedding, and other parameters. This paper reviews the current understanding of the flow around two “infinite” circular cylinders of equal diameter immersed in a steady cross-flow, with a focus on the near-wake flow patterns, Reynolds number effects, intermediate wake structure and behaviour, and the general trends in the measurements of the aerodynamic force coefficients and Strouhal numbers. A primary focus is on the key experimental and numerical studies that have appeared since the last major review of this subject more than 20 years ago.