Geometrical scale

The 212-MW unit features a turbine inlet temperature of 1260°C and a pressure ratio of 13.5 1. The manufacturer has subsequently installed a number of larger, more powerful versions of this unit, which produce up to 226.5 MW. Turbine inlet temperature is 1288°C the pressure ratio is 15 1. Five of these high output machines anchor a 1675-MW facihty in the Netherlands. These machines were developed by geometric scaling from a 168-MW,... 

When using dimensional analysis in computing or predicting performance based on tests performed on smaller-scale units, it is not physically possible to keep all parameters constant. The variation of the final results will depend on the scale-up factor and the difference in the fluid medium. It is important in any type of dimensionless study to understand the limit of the parameters and that the geometrical scale-up of similar parameters must remain constant. 

Thus, during geometric scale-up, the characteristic velocity is held constant by holding NqND constant. Qp is determined from the Pumping number and Figure 7-15. is a linear function of the characteristic velocity and is determined by... 

Scale-up is non-geometric with length/diameter ratios varying from 2 1 to 30 1. The non-geometric scale-up helps to increase heat transfer area as reactor volume increases. 

This general method can be used for geometrically scaled reactors with Newtonian liquids or with Newtonian suspensions in the turbulent flow region (NRe > 1000). 

In the late 1990 s, Foil et al.40-43 proposed the current burst theory. The basic hypothesis is that the electrochemical reactions involved in the dissolution of the silicon surface operate in microscopic units. These reaction units have a temporal and a spatial distribution in number and in the state of activity. The formation of pores is due to the synchronization of these operation units at certain time and geometrical scales. 

The basis of the scale-of-agitation approach is a geometric scale-up with the power law exponent, = 1 (Table 1). This provides for equal fluid velocities in both large- and small-scale equipment. Furthermore, several dimensionless groups are used to relate the fluid properties to the physical properties of the equipment being considered. In particular, bulk-fluid velocity comparisons are made around the largest blade in the system. This method is best suited for turbulent flow agitation in which tanks are assumed to be vertical cylinders. 

Table 4 Geometric Scaling Ratios of Primary and Secondary Variables for Screw Extruder...

Fig. 10.10 Rejection mask used in Visual Empirical Region of Influence (VERI). The shape of the mask is mathematically derived from the visual cognitive factors (a) geometrical scaling relationships used in the derivation of the shape (b) final mask which defines the exclusion region, that is, objects that do not belong to the group (Osbourn and Martinez, 1995)...

Plants used in micro reaction technology span a wide range of geometrical scales and operational limits. Also a variety of application modes such as commercial, research or training purposes are found. Supplier-specific set-ups exist which intend... 

Before scale-up in micro structured reactor plants is discussed, a short introduction to problems which occur during scale-up from a miniplant to a production plant will be given. Experimental correlations found in a miniplant will have to be transferred to the geometric scale of a production plant. Some scale-up factors which have been tested successfully for a number of devices are given in Table 4.10 [16, 137-139],... 

Thus, in a bubble column which has been geometrically scaled-up by a factor of p = 10, the same mixing time as in the model will be only obtained when the superficial velocity is increased by a factor of 101 5 = 32. Hence, v is not a scale-up criterion here. 

Which mathematical models or designing procedures were used to build the Egyptian pyramids or the gothic cathedrals Since the ancient times, geometric scaling-up procedures have been used. These rules are based on similitude laws, which are still used today. 

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