Micro-scale modelling

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. 

Usually, CBRN-protective suits consist of air-permeable garments with protective properties based on the incorporation of activated carbon. The most popular 

1 Micro-scale simulation of the flow through woven textiles 

The micro-scale study focuses on the flow around the textile fibres. For this, one needs a computational representation of the fabric microstructure (sometimes referred to as a virtual textile). An example is schematically presented in Fig. 11.3 (left). Here, the shape, diameter and distribution of the textile fibres is based on the average values observed in a microscopic image of an actual CBRN protective textile. The inflow boundary conditions (velocity magnitude and direction) can be obtained from experimental data or from meso-scale RANS and DNS simulations. 

This relatively simple study is conducted to determine the air permeability of a woven textile as a function of air velocity (fibre diameter-based Reynolds number), fibre diameter and solid volume fraction. At a given fibre diameter and solid volume fraction, many fibre structures are possible. Therefore, we also need to study the influence of the precise geometry of the textile fibres on the permeability. Of particular interest is the influence of irregularities in the fibre-to-fibre distance. 

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Micro-scale Model for Urban Environment (M2UE)... 

The M2UE (Micro-scale Model for Urban Environment Nuterman 2008) is Computational Fluid Dynamics (CFD) microscale model for analysis of atmospheric processes and pollution prediction in the urban environment, which takes into account a complex character of aerodynamics in non-uniform urban relief with penetrable (vegetation) and impenetrable (buildings) obstacles and traffic induced... 

Lenz C-J, Muller F, Schliinzen KH (2000) The sensitivity of mesoscale chemistry transport model results to boundary values. Environ Monit Assess 65 287-298 L6pez SD, Liipkes C, Schliinzen KH (2005) The effects of different k-e-closures on the results of a micro-scale model for the flow in the obstacle layer. Meteorol Z 14 839-848 Muller F, Schliinzen KH, Schatzmann M (2000) Test of numerical solvers for chemical reaction mechanisms in 3D air quality models. Environ Model Softw 15 639-646 Schliinzen KH (1990) Numerical studies on the inland penetration of sea breeze fronts at a coastline with tidally flooded mudflats. Beitr Phys Atmos 63 243-256 Schliinzen KH, Katzfey JJ (2003) Relevance of subgrid-scale land-use effects for mesoscale models. Tellus 55A 232-246... 

MICRO SCALE MODELING (ABSORPTION-REACTION MODELS)... 

Hydraulic permeability f as a function of fibre volume fraction. Results of micro-scale model at two values of disorder measure (a) are verified against the literature and present numerical data. 

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 ... 

Research efforts in li-ion batteries have thus been widely distributed over the multiple intrinsic length scales, as illustrated in Figure 26.3. Although new materials syntheses and battery performance tests have been successively employed over the last three decades, recent important findings have come from particle-/micro-scale modeling and experimental studies, which investigate how the mechanics of battery cells and materials affect cell performance during the cycle Hfe, as described in Section 26.2.2. 

Multi-scale modeling makes no such assumptions about the underlying constitutive model. Rather, essential features of the micro-scale model are directly linked to the macroscale model via a homogenization process. The constitutive relationship at the macro-scale is thus allowed to develop from the microscopic behavior. This necessitates the solution of a separate micro-scale model at selected points such as quadrature points, in the macroscopic body. 

The size of the micro-scale model is determined via the concept of a representative volume element (RVE). The RVE should represent the smallest sample at the micro-scale capable of capturing the behavior accurately. If the RVE is too small then a biased and unrepresentative view of the micro-structure is obtained. If the RVE is too large then computational effort is wasted. The procedure to determine the optimal RVE size is based upon physical measurement and numerical tests. Methodologies to determine the optimal RVE size have been presented by various authors (see, for example, Kouznetsova [14] and Zohdi and Wriggers [15]) and will be elaborated on further in this work. 

Fig. 11.13 Illustration of how mobile CA (here used to model elementary combat ) can be used to explore the relationship between primitive rules governing behavior on the micro-scale and emergent behavior on the macro-scale see text.

Fig. 2. Properties of model and biological particle systems Micro scale related particle diameter dp/riL versus maximum energy dissipation e , in stirred reactors explanations see Table 3 and Table 4...

It is emphasized by several authors that an all-round mathematical model describing the thermochemical conversion process in the conversion zone needs to take both the micro- and the macro-perspective into account [25,26]. The micro-scale perspective in this context will refer to the single particle scale, whereas the macro-scale corresponds to an overall fuel-bed perspective. 

Here follows a section outlining the heat and mass transport phenomena of the thermochemical conversion on both the micro- and the macro-scale of the fuel bed. Knowledge about the heat and mass transport phenomena on micro-scale is very important to be able to understand and model, for example, the mass flow of conversion gas. 

The multiplicity of solutions at the continuum level can be viewed as arising from a constitutive deficiency in the theory, reflecting the need to specify additional pieces of constitutive information through some kind of phenomenological modeling (see, for instance, Truskinovsky, 1987 Abeyaratne and Knowles, 1991). Here we take a different point of view and interpret the nonuniqueness as an indicator of essential interaction between macro and micro scales. 

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. 

In summary, we may expect that the correlative type of multi-scale CFD can be used for the problems with clear scale separations between the micro-scale and the meso-scale, while the variational type, provided with appropriate stability condition, seems free of such limitation. In what follows we will detail some examples of the variational approach by introducing its basis of the EMMS model. 

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