Thermodynamic similitude

Sauter mean, as in dSM, Sauter mean diameter subcooled condition superheated condition transition boiling, or Taylor bubble crossflow due to droplet deposition a group of thermodynamic similitude... 

A dynamic similitude embodies both hydrodynamic and thermodynamic similitudes. A hydrodynamic similitude requires a similar flow pattern and similar veloc-... 

The present considerations extend previous studies of peak quantities P]. Presuming thermodynamic similitude, we compare superheat data of liquefied gases with an empirical nitrogen correlation. 

The second kind of description, on the other hand, disregards the details of the transport mechanism and relies primarily on equilibrium relations of macroscopic thermodynamics instead. A fairly satisfactory correlation of this kind P] was previously compared with simple thermodynamic estimates p]. The comparison suggested a simplification which avoids extended property evaluation and makes use of thermodynamic similitude. This approach is near at hand since AT does not vary appreciably with q in fully established nucleate boiling. Further, in many applications it is sufficient to know only one pair of coordinates at peak conditions (g , ATp). The function (AT) then may be obtained by making use of the derivative dqfdAT from a similar known configuration. 

In view of the uncertainties involved, we base our comparison on the average data of (1), and account for the real superheat by specifying the multiple ATp/ATp. Excess pressure corrections will be neglected. Reduced superheat values of various liquefied gases are expected to agree closely provided thermodynamic similitude really exists. However, complete agreement should not be anticipated since differences in molecular structure are reflected in the different T/Tc values at the triple point of various substances. Thus, an extrapolation of (1) beyond its triple point value, or about TjTc 0.6, is not recommended without experimental support. 

Liquid helium can be regarded as an ordinary liquid however, its physical properties are modified somewhat compared to other liquids. The superheat data of Karagounis P ] correspond to reduced values larger than 1.5 ATp/Tc, whereas results from a vertical heater [- ] obtained at a very low power level, are small, as to be expected. In spite of the low temperature, there are no drastic deviations from thermodynamic similitude in the range 0.6 < T/Tc < 1, where equation (1) permits reasonable superheat estimates. 

Frequently, complete dimensional similitude cannot be reached between two reactors with widely different scales as a result, this method is usually limited in practice to relatively simple chemical reaction systems. For a cleaning vessel in which the reaction rate is very fast and the process is governed by the physical rates of the process, e.g., mass transfer, heat transfer, etc., the dimensionless groups describing the process consist of fluid mechanic and thermodynamic quantities. The cleaning process can usually be a relatively simple mechanism to describe, making dimensional similitude more easily achievable. 

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