969 research outputs found
Direct numerical simulation of fluid flow accompanied by coupled mass and heat transfer in dense fluid-particle systems
No full textIn this paper we report the extension of an earlier reported DNS method (Deen et al., 2012 and Deen and Kuipers, 2013) based on a novel Immersed Boundary Method (IBM) which incorporates the fluid–solid coupling at the level of the discrete field equations. The extended method is used to study coupled mass and heat transport in dense fluid–particle systems where the coupling arises as a consequence of an exothermal chemical reaction proceeding at the exterior surface of the particles. Following a detailed verification (using an independent numerical technique) and validation (using established empirical correlations) we apply our DNS technique to study coupled mass and heat transfer in a dense fluid–particle system. In addition a comparison is made with results obtained from a simple one-dimensional (1D) heterogeneous reactor model which uses empirical closures for the fluid–particle mass and heat transfer coefficients. The main features of the complex transient temperature profiles obtained from our DNS agree quite well with the corresponding profiles obtained from the 1D heterogeneous reactor model
Pore-scale level numerical simulation of flow in a solid foam: an Immersed Boundary Method (IBM) based approach
No full textThere has been an increasing trend on the use of novel materials to improve the process efficiency in a cost effective way and to minimize the total weight/volume of equipment. Open cell solid foams, consisting of cellular structures made of metal or ceramics is one such material which is extensively used over the past few decades to form porous media. Due to its large surface area to volume ratio with minimal pressure drop, it is widely applied in heat transfer devices like heat exchangers, thermal energy absorbers, vaporizers, heat shielding devices etc.. Moreover, it is also gaining popularity in several other applications like high temperature filters, pneumatic silencers, catalytic reactors etc. In chemical process industries solid foams are popular as catalyst support which improves gas-liquid contacting to enhance heat and/or mass transfer rates with minimal pressure drop as compared to other packing material. Also high velocity difference between the flowing phase and stationary support increase the transport rate, which can be achieved by using solid foam. To design and optimize such processes it is necessary to understand the hydrodynamic behaviour of fluid flow through such material. Due to the random and complex geometrical shapes, most of the work on solid foams is experimental, and a limited number of numerical and analytical studies are available in literature. To study the flow at pore-scale level, we have developed an Immersed Boundary Method (IBM) based simulation technique. A second order accurate implicit Immersed Boundary Method (IBM) inspired by Deen et al. (2012, Chem. Eng. Sci. 81, pp. 329-344) is implemented to resolve such structure on a non-boundary fitted computational-grid. A single representative unit cell (RUC) of the solid foam in a periodic computational domain is considered and the geometry of the RUC is approximated based on structural packing of a tetrakaidecahedron (Kelvin?s unit cell) with cylindrical strut morphology [Fig. 1]. A total of twelve foam structures of different porosity varying from 0.638 to 0.962 are considered. The flow Reynolds number based on superficial velocity and equivalent spherical diameter is varied from creeping flow regime to as high as 500. The current simulation results can also be extended for foams of different pore densities. An empirical correlation for the friction factor is proposed as a function of porosity and Reynolds number
Cutting bubbles using direct numerical simulation
No full textDue to an increase in the oil price, Fischer-Tropsch synthesis, methanol synthesis and other gas-to-liquid processes become increasingly attractive. These gas-liquid-solid processes are mostly performed in bubble slurry columns [Wang et al., 2007, Yang et al., 2007]. However, the efficiency of these columns is restricted due to limited heat removal rates or limited interfacial mass-transfer rates. To improve the efficiency of these reactors, a new reactor concept is developed: a micro-structured bubble column [Jain et al. 2013, Segers et al., 2013]. In a micro-structured bubble column, a static wire mesh is introduced. This wire mesh can be used as a catalyst carrier, eliminating a filtration unit to remove the catalyst particles from the product stream. Furthermore, the wire mesh also ensures cutting of the bubbles. This will reduce the bubble size and enable a higher surface per volume ratio [Jain et al. 2013, Segers et al., 2013]. To determine the efficiency gain due to the introduction of the wire mesh, a multi-scale modelling approach is used. In this approach there are three types of models. The largest scale models, the Euler-Euler and the Euler-Lagrangian models, need closures to accurately model the interactions between the bubbles, the liquid and the mesh. These interactions can be determined using the smallest scale model: the Direct Numerical Simulations (DNS). While these DNS models are able to simulate these interactions without any a priori assumptions, they are only capable of simulating a small part of the micro-structured bubble column [Segers et al., 2013, Roghair et al., 2011]. In this work, a DNS model was developed to study the effect of a wire mesh in a micro-structured bubble column. The DNS model is a combination of the Volume Of Fluid (VOF) model of Baltussen et al. (2014) and the second order implicit Immersed Boundary (IB) method of Deen et al. (2012). The advantage of the use of the VOF model is the relatively easy treatment of break-up of bubbles and the inherent mass conservation. The used IB method enables an implicit fluid-solid coupling, Using this VOF-IB method, the effect of the simplest wire mesh, a single wire, on a single bubble is determined. Several simulations have been performed to study the effect of the alignment of the bubble with the wire and the relative size of the bubble upon break-up. An example of such a simulation is shown in figure 1
Eulerian modeling of reactive gas-liquid flow in a bubble column
Full text linkDespite the widespread application of bubble columns and intensive research efforts devoted to understand their complex behavior, detailed knowledge on the fluid flow, mass transfer and chemical reactions as well as their interactions is currently very limited. Gas-liquid flow in bubble column reactors is characterized by a combination of inherently unsteady complex processes with widely varying spatial and temporal scales. The complicated interactions between the gas and the liquid phases comprising hydrodynamics, mass transfer and chemical reaction cause many challenging modeling problems to be solved. The Euler–Euler model is adopted throughout this thesis to investigate gas-liquid flow in bubble columns. In this study, efforts have been focused on the assessment of suitable closure laws for interfacial forces and for turbulence in the continuous phase. Furthermore, gas-liquid heterogeneous flow and reactive gas-liquid flows have been studied. All the numerical simulations were carried out with the commercial CFD package CFX-4.4 and all simulation results were compared with the available experimental PIV data of Deen (2001)
Application of coalescence and breakup models in a discrete bubble model for bubble columns
Full text linkIn this work, a discrete bubble model (DBM) is used to investigate the hydrodynamics, coalescence, and breakup occurring in a bubble column. The DBM, originally developed by Delnoij et al. (Chem. Eng. Sci. 1997, 52, 1429-1458; Chem. Eng. Sci. 1999, 54, 2217-2226),1,2 was extended to incorporate models describing the breakup and coalescence along with a subgrid scale closure model for the turbulence. To validate the turbulence model, simulation results of the DBM are compared to experimental PIV data of Deen et al. (Chem. Eng. Sci. 2001, 56, 6341-6350).3 It is shown that incorporation of the subgrid scale model results in a better prediction of the mean and fluctuating velocity components in the bubble column, which can be subscribed to an increase of the effective viscosity. Furthermore, it was found that the predicted hydrodynamics are hardly altered when the subgrid scale velocity is taken into account in the evaluation of the interface forces. Finally, the bubble size distributions predicted by the DBM including the coalescence models of Chesters (Trans. IchemE 1991, 69, 259-270)4 and Lee et al. (Chem. Eng. Commun. 1987, 59, 65-84)5 are compared with experimental data that were obtained through digital image analysis in a pseudo 2D bubble column. It is found that the number of collisions between two bubbles that result in coalescence is 43% with the model of Chesters4 and 85% with the model of Lee et al.5 Coalescence occurs mostly in the lower part of the column. The mean diameter obtained from the DBM is higher than those measured experimentally, which is probably due to the lack of breakup
Direct numerical simulation of effective drag in dense gas–liquid–solid three-phase flows
Full text linkGas–liquid–solid three phase flows are commonly found in (bio-)chemical processes, e.g. in bubble slurry columns in the Fischer–Tropsch process. In order to facilitate the rational scale-up and the design of such columns, a detailed understanding of the complex phase interactions is required. In this work, we focus on the effective drag acting on particles and bubbles, using Direct Numerical Simulations. We combined the Front Tracking method of Roghair et al. (2013b) and the second order implicit Immersed Boundary method of Deen et al. (2012). The resulting hybrid Front Tracking Immersed Boundary method is able to simulate dense three phase flows and is used to study swarm effects in terms of drag. A correlation has been obtained for the drag coefficient for a system consisting of 2 mm bubbles and 1 mm particles at several phase volume fractions. In future research, the developed methodology can be applied to study the effect of the bubble and particle size and their ratio
One Equation subgrid scale (SGS) modeling for Euler-Euler large Eddy simulation (EELES) of dispersed bubbly flow
No full textIn this work, we have presented a one-equation model for sub-grid scale (SGS) kinetic energy and applied it for an Euler-Euler large eddy simulation (EELES) of a bubble column reactor. The one-equation model for SGS kinetic energy shows improved predictions over the state-of-the-art dynamic procedure. With grid refinement, the amount of modelled SGS turbulent kinetic energy diminishes, as one would expect. Bubble induced turbulence (BIT) at the SGS level was modelled with two approaches. In the first approach an algebraic model was used, while in the other approach extra source terms were added in the transport equation for SGS kinetic energy. It was found that the latter approach improved the quantitative prediction of the turbulent kinetic energy. To the best of authors knowledge, this is the first use of a transport equation for SGS kinetic energy in bubbly flows
On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers
No full textAn accurate and fast simulation of large-scale gas/liquid contact apparatusses, such as bubble columns, is essential for the optimization and further development of many (bio)chemical and metallurgical processes. Since it is not feasible to simulate an entire industrial-scale bubble column in full detail from first principles (direct numerical simulations), higher-level models rely on algebraic closure relations to account for the most important physical phenomena prevailing at the smallest length and time scales, while keeping computational demands low. The most important closure for describing rising bubbles in a liquid is the closure for the drag force, since it dominates the terminal rise velocity of the bubbles.
Due to the very high gas loadings used in many industrial processes, bubble–bubble (or ‘swarm’) interactions need to be accounted for in the drag closure. An advanced front-tracking model was employed, which can simulate bubble swarms up to 50% gas hold-up without the problem of (numerical) coalescence. The influence of the gas hold-up for mono-disperse bubble swarms with different bubble diameters (i.e. Eötvös numbers) was quantified in a single drag correlation valid for the intermediate to high Reynolds numbers regime . Also the physical properties of the liquid phase were varied, but the simulation results revealed that the drag force coefficient was independent of the Morton number. The newly developed correlation has been implemented in a larger-scale model, and the effect of the new drag closure on the hydrodynamics in a bubble column is investigated in a separate paper (Lau et al., 2011 Lau, Y., Roghair, I., Deen, N.G., Van Sint Annaland, M., Kuipers, J.A.M. Numerical investigation of the drag closure for bubbles in bubble swarms. Chemical Engineering Science, this issue, doi:10.1016/j.ces.2011.01.053. Lau et al., this issue)
Direct numerical simulation of wall-to liquid heat transfer in dispersed gas-liquid two-phase flow using a volume of fluid approach
No full textIn this paper a simulation model is presented for the direct numerical simulation (DNS) of wall-to-liquid heat transfer in dispersed gas–liquid two-phase flow using a volume of fluid (VOF) approach. Our model extends the VOF model developed by van Sint Annaland et al. (2005) to non-isothermal conditions. Our VOF method involves an interface reconstruction technique based on piecewise linear interface representation. The surface tension is incorporated using a three-dimensional version of the continuous surface force (CSF) model of Brackbill et al. (1992). The model is applied to predict the heat exchange rate between the liquid and a hot wall kept at a fixed temperature. It is found that, due to bubble induced agitation in the liquid phase, the heat transfer rate between the wall and the liquid is considerably enhanced especially when bubble coalescence prevails in the vicinity of the hot wall. Although this finding is obvious from an intuitive point here we present quantitative results to describe this phenomenon
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