Maximum critical power ratio

The maximum critical heat flux ratio (MCHFR) is expected to be sufficiently high due to the low power density and low operating temperature detailed analysis is yet to be performed. 

The steady-state solution for fiber spinning (Newtonian and isothermal case) was presented in Section 9.1.1, and it consists of Eqs. 9.26 and 9.28. Linearized (small disturbances) stability analysis involves (Fisher and Denn, 1976) the study of finite amplitude disturbances, and we do not present it. Rather, we present the results of such an analysis. The value of Dr = 20.21 is considered to be the critical draw ratio beyond which the flow becomes unstable. Figure 9.13 (Donnelly and Weinberger, 1975) shows experimental data that confirm the theory. More specifically, silicone oil (of viscosity equal to 100 Pa-s), which seems to be Newtonian, was extruded and the ratio of maximum to minimum filament diameters was plotted against the draw ratio. An instability appears at a draw ratio of about 17, or about 22 if we take into consideration about 14% die swell. The value of the critical draw ratio of 22 compares well with the theoretical value of 20.21. Pearson and Shah (1974) extended the analysis to a power-law fluid and included surface tension, gravitational. 

Experimentally, the critical draw ratio for various polymers is measured as the draw ratio at which the ratio of maximum to minimum filament diameters increases above 1. Figure 9.15 shows experimental data for PP, HDPE, and PS. The corresponding critical draw ratios are 2.7, 3.8, and 4.6. The power-law index of PP and PS is about 0.5, and thus the agreement between experimental data and theory is generally good. 

The expression for the maximum permissible detector dispersion, given by equation (21), also shows it s strong dependance on the product of the solute diffusivity and the viscosity of the mobile phase together with the inverse of the fourth power of (or1) A graph relating (op) to the separation ratio of the critical pair is shown in figure (6)... 

More detailed information can be obtained from noise data analyzed in the frequency domain. Both -> Fourier transformation (FFT) and the Maximum Entropy Method (MEM) have been used to obtain the power spectral density (PSD) of the current and potential noise data [iv]. An advantage of the MEM is that it gives smooth curves, rather than the noisy spectra obtained with the Fourier transform. Taking the square root of the ratio of the PSD of the potential noise to that of the current noise generates the noise impedance spectrum, ZN(f), equivalent to the impedance spectrum obtained by conventional - electrochemical impedance spectroscopy (EIS) for the same frequency bandwidth. The noise impedance can be interpreted using methods common to EIS. A critical comparison of the FFT and MEM methods has been published [iv]. 

In addition to the limitation on the maximum diameter of the pressure vessel, there will also be a limitation, for a given total power output, on the minimum diameter of the core vessel. This minimum diameter is determined by the pow er density at the core wall, since high powder densities at the wall will lead to intolerable corrosion of the w all material (Zircaloy-2). In order to take this factor into consideration, the power densities, as well as critical concentrations and breeding ratios, w-ere calculated for the various reactors. 

For moderate inlet velocities, which can reach up to 2.5 m/s for the conditions of Fig. 5.4, a linear increase in power output is observed with rising inlet velocity. The combustion efficiency remains high since almost complete fuel conversion is achieved ( 99.99%), while the power output is directly proportional to the equivalence ratio. As long as fuel conversion is nearly complete, no difference is observed between reactors of different solid thermal conductivities. The linearity in reactor response ceases as the inlet velocity approaches a critical value. With increasing inlet velocity, every power curve reaches a maximum. These maxima lie at combustion efficiencies (i.e. fuel conversions) of 71-83% for all cases considered. 

---