Temperature fluctuation within cells

Even when the number of grid cells in a LB LES simulation of a stirred vessel 1.1 m3 in size amounts to some 36 x 106 grid cells, this implies a cell size, or grid spacing, of 5 mm only. Even a cell size of just a few millimeters makes clear that substantial parts of the transport of heat and species as well as all chemical reactions take place at scales smaller than those resolved by the flow simulation. In other words concentrations of species and temperature still vary and fluctuate within a cell size. The description of chemical reactions and the transport of heat and species therefore ask for subtle approaches to these SGS fluctuations. 

An alternative approach (e.g., Patterson, 1985 Ranade, 2002) is the Eulerian type of simulation that makes use of a CDR equation—see Eq. (13)—for each of the chemical species involved. While resolution of the turbulent flow down to the Kolmogorov length scale already is far beyond computational capabilities, one certainly has to revert to modeling the species transport in liquid systems in which the Batchelor length scale is smaller than the Kolmogorov length scale by at least one order of magnitude see Eq. (14). Hence, both in RANS simulations and in LES, species concentrations and temperature still fluctuate within a computational cell. Consequently, the description of chemical reactions and the transport of heat and species in a chemical reactor ask for subtle approaches as to the SGS fluctuations. 

The density of CO2 in the absorption cell, however, is a function of both concentration and bulk air density. In normal process analyzers, where temperature and pressure within the absorption cell are controlled, measurements can be easily referred to gas density by a simple calibration curve. In an open path system, changes in bulk air density must be measured. Indeed, one of the major problems faced in testing the sensor was the development of test facilities where we could control the temperature, pressure and CC>2 more accurately than the sensor could measure. Even the small changes in building pressure associated with ventilation system fluctuations resulted in output signal changes three to four times the sensor signal to noise level. In operation, pressure and temperature near the open cell are measured and used to calculate gas density. 

To prevent fluctuations in the load cell and extensometer readings, caused by changes in ambient temperature, it is advantageous to enclose these transducers completely within the test chamber. 

Samples were melt pressed in a vacuum laboratory hot press (Carver Press, Model C) at 160°C for 30 min. The molded films were then allowed to cool to room temperature under vacuum. A dual temperature chamber for the melt crystallization experiments consists of two large thermal chambers maintained at the melt temperature (Ti = 160°C) and the crystallization temperature (Ts = 81°C, 83°C, 86°C, 89°C, 92°C or 96°C). After 5-10 min at Ti, the copper sample cell was transferred rapidly ( 2 s) to the other chamber by means of a metal rod connected to a pneumatic device. A detailed description of the arrangement of the sample and of the two detectors used to measure WAXS and SAXS simultaneously has been provided previously [32]. Each polymer sample within the copper cell was 1.5 mm thick and 7 mm in diameter and was contained between two 25 im thick Kapton films. The actual sample temperature during crystallization (T2) and melting (Ti) was monitored by means of a thermocouple inserted into the sample cell. The crystallization temperature was usually reached 120 s after transfer without overshooting. Under isothermal conditions the fluctuations in the sample temperature are less than 0.5°C. Unless stated otherwise, all references to time are times elapsed after transferring the sample to the crystaUization chamber. 

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