Thermodynamic vapor quality

Their database covered the following experimental conditions tube diameters from 0.25 to 15 mm, tube length and diameter ratios from 2 to 200, mass velocities from 300 to 30000 kg rrT s, equilibrium thermodynamic vapor qualities at the test section inlet from —2 to 0 and equilibrium thermodynamic vapor qualities at the test section outlet from — 1 to 0 (that is, always subcooled at the exit). Based on the broad database used by these authors, which was also compared by Hall and Mudawar [96] against other methods from the literature, revealing this as the best predictive method, Equation (3.10) is suggested here as the most accurate method for predicting water flow CHF in tubes having a uniform axial heat flux and diameters down to 0.25 mm under subcooled conditions. 

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. 

If a liqnid is released while its temperatnre is above the atmospheric-pressnre boiling point, some of the liqnid will adiabatically and instantaneously flash to vapor that is, the energy that is released as the liqnid temperatnre drops to the boiling point is ntihzed in vaporizing some of the liqnid. The fraction of liqnid that is flash-vaporized often can be obtained from a thermodynamic diagram (snch as a pressnre-enthalpy plot [8, 13]) for the material of interest, where values of x (if shown) indicate the weight-fractions of vapor ( quality ) in the two-phase mixture. 

With flashes carried out along the appropriate thermodynamic paths, the formalism of Eqs. (6-139) through (6-143) applies to all homogeneous equilibrium compressible flows, including, for example, flashing flow, ideal gas flow, and nonideal gas flow. Equation (6-118), for example, is a special case of Eq. (6-141) where the quality x = 1 and the vapor phase is a perfect gas. 

In this equation the properties V, V1, and V may be either molar or unit-mass values. The mass or molar fraction of the system that is vapor xv is called the quality. Analogous equations can be written for the other extensive thermodynamic properties. All of these relations may be summarized by the equation... 

Data Quality Normally, it is not possible to evaluate LLE data for thermodynamic consistency [Sorenson and Arlt, Liquid-Liquid Equilibrium Data Collection, Binary Systems, vol. V, pt. 1 (DECHEMA, 1979), p. 12]. The thermodynamic consistency test for VLE data involves calculating an independently measured variable from the others (usually the vapor composition from the temperature, pressure, and liquid composition) and comparing the measurement with the calculated value. Since LLE data are only very weakly affected by change in pressure, this method is not feasible for LLE. However, if the data were produced by equilibration and analysis of both phases, then at least the data can be checked to determine how well the material balance closes. This can be done by plotting the total... 

If we further assume that the vapour and liquid are in thermal equilibrium in the cross section at point z, then their specific enthalpies in the saturated state have to be calculated at pressure p(z). This gives hG = h" and hL = h as well as h" — h1 = Ahv the enthalpy of vaporization at pressure p in the cross section being considered. As we have assumed thermodynamic equilibrium, the quality is indicated by x h and is called the thermodynamic quality. This yields... 

D)mamic properties of water determine several important kinetic processes that determine key deteriorative quality changes and hence commercial food shelf-lives. Foods are mostly in a state of thermodynamic instability and kinetic barriers do exist as water molecules are transferred from phase to phase and state to state. Molecular mobility of water in different domains can be measured by methods such as NMR which, as with a, involves the ability to become vapor and requires a thermodynamic equilibrium. In a non-equilibrium situation, the use of relative vapor pressure (RVP) has been proposed (Slade and Levine, 1988). 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

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