Micro-scale modelling simulation

Drying and liquid penetration are also important for the process already discussed in Section 7.3.3, namely spray fluidized bed agglomeration. The reason for this is that agglomeration takes place with the help of droplets sprayed on the particles, so that it slows down when such droplets are lost either by evaporation (drying) or by liquid penetration into the porous substrate. Influences of this kind can be captured very well with the help of respective micro-scale models integrated into discrete simulations, as we will see in Section 7.7. 

Based on the derived critical penetration conditions from the micro-scale modelling and simulation, the accumulative collisions derived from the mesoscale modelling and simulation (Fig. 18.57) can be thus divided into two groups as sketched in Fig. 18.64 ... 

To meet the industrial demand for both large-scale computation and good predictability, the reasonable way out is not to simulate from the beginning of the micro-scale, but to use coarse-grid simulation with meso-scale modeling for the effects of structure. This kind of approach can be termed the "multi-scale CFD." It is entitled "multi-scale," not because the problem it solves is multi-scale, but because its meso-scale model contains multi-scale structure parameters. 

S //Asa mediator between CFD calculations and macro-scale process simulations, the reactor geometry is represented by a relatively small number of cells which are assumed to be ideally mixed. The basic equations for mass, impulse and energy balance are calculated for these cells. Mass transport between the cells is considered in a network-of-cells model by coupling equations which account for convection and dispersion. The software is capable of optimizing a process in iterative simulation cycles in a short time on a standard PC, but it also requires experimentally-based data to calibrate the software modules to a specific micro reactor. 

As a more critical example concerning the transfer of macroscopic modeling to micro-scale applications, the following example of a simulation of a homogeneous catalytic reaction is described [133], This example also represents a typical approach in process simulation if a new reactor model or a model for a new unit operation... 

Pardhanani, A.L. and Carey, G.F. (2000) Multidimensional Semiconductor Device and Micro-scale Thermal Modeling Using the PROPHET Simulator with Dial-an-Operator Framework. Comput. Model. Eng. Sci., 1, 141-150. 

More precisely, climate modeling consists in the simulation of large-scale atmospheric processes by applying the basic physical principles and the correct initial conditions in a consistent way (Smagorinsky, 1974). An important part of climate modeling is the consideration of the interaction of macro-processes with phenomena taking place on the micro-scale (radiative transfer, turbulence, and processes of cloud physics and air chemistry). In the equations, the horizontal scale of variations is at least 100 km, while the vertical scale lies between 10 m and 100 km. The volume of air taken into account is a measure of the resolution of the calculation. Phenomena of smaller scale can be included in the model by appropriate statistical methods. This procedure is termed the parameterization. 

From the micro-scale simulations, information will be obtained about the permeability as a function of fibre stmcmre and flow velocity, which can be fed into the porous medium model used in all the meso-scale simulations. The range of velocities of interest for the micro-scale simulations is obtained from the meso-scale DNS and RANS simulations. Thus, there is a two-way information exchange... 

Our main goal is to perform (iii) macro-scale simulations at the full body scale of a moving marmeqitin. This aspect has remained outside the scope of this article. However, based on smaller-scale simulations, conclusions will also be drawn as to which type of modelling can be applied successfully at the macro-scale, taking into account feasibility and accuracy as well as the many practical demands mentioned in the previous section. In the following sections, the micro-scale DNS, meso-scale DNS and (T-)RANS studies will be described in more detail. 

Timing tests indicate that the atomistic level simulation took twice as long to complete 2 ns than the meso-scale did to complete 2 ps (150 vs 69 CPU hours). This is remarkable, and represents a 2,000 x speedup for the meso-scale model. This opens the door for studying DNA system in the micro-second timescale. 

Other model considerations are necessary for simulating bench-scale, laboratory reactors and micro-scale reactors with integrated catalyst and reactor. Flow regimes are at different gas velocities and catalyst particle sizes are smaller than in an industrial reactor or the catalyst is integrated... 

The model species, total mass, momentum, and energy continuity equations are similar to those presented in Section 13.7 on fluidized bed reactors. Constant values of the gas and liquid phase densities, viscosities, and diffusivities were assumed, as well as constant values of the interphase mass transfer coefficient and the reaction rate coefficient. The interphase momentum transfer was modelled in terms of the Eotvos number as in Clift et al. [1978]. The Reynolds-Averaged Navier-Stokes approach was taken and a standard Computational Fluid Dynamics solver was used. In the continuous liquid phase, turbulence, that is, fluctuations in the flow field at the micro-scale, was accounted for using a standard single phase k-e model (see Chapter 12). Its applicability has been considered in detail by Sokolichin and Eigenberger [1999]. No turbulence model was used for the dispersed gas phase. Meso-scale fluctuations around the statistically stationary state occur and were explicitly calculated. This requires a transient simulation and sufficiently fine spatial and temporal grids. 

The direct use of micromechanical models for nanocomposites is however doubtfid due to the significant scale difference between nanoparticles and macro-partides. As such, two methods have recently been proposed for modeling the mechanical behavior of polymer nanocomposites equivalent continuum approach and self-similar approach. In equivalent continuum approach, molecular dynamics (MD) simulation is first used to model the molecular interaction between nanopartide and polymer. Then, a homogeneous equivalent continuum reinforcing element (i.e., an effective nanopartide) is constmcted. Finally, micro-mechanical models are used to determine the effective bulk properties of a... 

A key application of the multi-scale modeling formulation discussed previously is to determine munerically the appropriate macro-scale material parameters for use in a macroscale model, see for example Zohdi and Wriggers [15]. The solution of the macro-scale model can then be performed using mature finite element software in a fraction of the time that it would take to do a full multi-scale simulation. The motivation for adopting this strategy would be to capture as closely as possible the micro-scale material parameters, for use at the macro-scale. 

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