Equilibrium quality

In Table 6.7, C is the Martinelli-Chisholm constant, / is the friction factor, /f is the friction factor based on local liquid flow rate, / is the friction factor based on total flow rate as a liquid, G is the mass velocity in the micro-channel, L is the length of micro-channel, P is the pressure, AP is the pressure drop, Ptp,a is the acceleration component of two-phase pressure drop, APtp f is the frictional component of two-phase pressure drop, v is the specific volume, JCe is the thermodynamic equilibrium quality, Xvt is the Martinelli parameter based on laminar liquid-turbulent vapor flow, Xvv is the Martinelli parameter based on laminar liquid-laminar vapor flow, a is the void fraction, ji is the viscosity, p is the density, is the two-phase frictional... 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

The next step in the calculation is to determine the actual quality in the region beyond the bubble detachment. There have been a number of attempts to predict this from mechanistic models in which the rates of evaporation near the wall and condensation in the core of the flow are estimated and the quality is evaluated surveys of early versions of such models are given by Mayinger [240] and Lahey and Moody [241]. A more recent example of such an approach is that of Zeitoun and Shoukri [242], A simpler class of methods uses a profile fit these methods are exemplified by that of Levy [243], who relates the actual quality xa to the local equilibrium quality x (calculated from Eq. 15.208) and x(Zd) (calculated from Eq. 15.213 or 15.214) as follows ... 

FIGURE 15.136 Post-CHF heat transfer coefficient as a function of equilibrium quality (from Hammouda et al. [335], with permission from Elsevier Science). (Continued on p. 15.133.)... 

FIGURE 15.138 Limiting cases for postdryout heat transfer in the dispersed flow film-boiling region (from Hewitt et al. [13], with permission. Copyright CRC Press, Boca Raton, FL). (ze0 is the point at which dryout occurs and Zcq is the point at which the equilibrium quality reaches unity.)... 

The provision of internal baflles is often claimed to improve the rate and/or equilibrium quality of mixing in the tumbler mixer. An equilibrium mixture quality is usually reached in 10 to 15 minutes. 

Greathead and Simmonds confirmed that the point of addition of a minor component can influence the equilibrium quality of a mixture in a ribbon blender. Most of the woric they report should be treated with caution, as the results are based on only six samples taken from the surface of the mixture. 

A similar general conclusion was reached by Williams and Khan mixing fertilizer granules of varying size ratio in a V-mixer, a ribbon blender and a Nautamix. Their results are plotted in Figure 3.14 and indicate the variation of the equilibrium quality of the mixture, with the size ratio of the granules. For all size ratios the performances of the ribbon blender and the Nauta mixer are signiHcantly better than those of the V-mixer. 

The two-phase system has three distinct qualities, equilibrium, real, and static. Equilibrium quality comes from an energy balance and is defined in terms of the enthalpy as... 

The subcooled void model used is the Levy s one (Jackson Todreas 1981), which calculates the true quality in terms of the equilibrium quality and the quality started by bubble departure. It is also necessary to choose a turbulent crossflow model. The model used is shown in Eq. 3. The slip ratio between liquid and vapor was considered equal to 1.0. 

The CHFs are determined by using the 1995 lookup table for CHF in tubes which was developed by Groeneveld et al. [6-8]. The 1995 lookup table was chosen because of its wider range of application and better prediction accuracy, with a root-mean-square error of 7.82% and an average error of 0.69%, compared with other correlations. The CHF lookup table is based on the tube data normalized to a tube inside diameter of 8 mm and provides CHF values at discrete values of pressure, mass flux, and equilibrium quality. It covers the ranges 0.1-20.0 MPa,... 

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