Slip ratio

Void Fraction and Slip Ratio in Diabatic Flow 147... 

In the following sections, the flow patterns, void fraction and slip ratio, and local phase, velocity, and shear distributions in various flow patterns, along with measuring instruments and available flow models, will be discussed. They will be followed by the pressure drop of two-phase flow in tubes, in rod bundles, and in flow restrictions. The final section deals with the critical flow and unsteady two-phase flow that are essential in reactor loss-of-coolant accident analyses. 

VOID FRACTION AND SLIP RATIO IN DIABATIC FLOW... 

An example of a slip equation of state combination is for thermodynamic equilibrium with a slip ratio of... 

The maximization of the pressure gradient as stated by assumption 4 above is achieved by varying the slip ratio, keeping other quantities constant ... 

Hence, at critical flow, the slip ratio becomes... 

Fauske (1966) achieved reasonable agreement with low-pressure experimental data using Armand s slip ratio (Armand, 1959), where... 

Since a is function of quality X and the slip ratio S, the above equation can be expanded to read ... 

Annular flow, smooth interface (Henry et al., 1969) Since the interface is relatively small compared to dispersed flow and assumed to be smooth, there is no significant momentum transfer or mass transfer between phases. Under such conditions, the change of slip ratio with pressure is... 

Most research has been performed in a two-phase medium with no flow conditions very little has been done in two-phase-flow systems. Although the flow condition may bring in new variables, such as slip ratio, it is reasonable to assume that the basic phenomena observed in the nonflow condition also occur in the flow condition. 

W-3 CHF correlation. The insight into CHF mechanism obtained from visual observations and from macroscopic analyses of the individual effect of p, G, and X revealed that the local p-G-X effects are coupled in affecting the flow pattern and thence the CHF. The system pressure determines the saturation temperature and its associated thermal properties. Coupled with local enthalpy, it provides the local subcooling for bubble condensation or the latent heat (Hfg) for bubble formation. The saturation properties (viscosity and surface tension) affect the bubble size, bubble buoyancy, and the local void fraction distribution in a flow pattern. The local enthalpy couples with mass flux at a certain pressure determines the void slip ratio and coolant mixing. They, in turn, affect the bubble-layer thickness in a low-enthalpy bubbly flow or the liquid droplet entrainment in a high-enthalpy annular flow. 

Malnes, D., 1966, Slip Ratios and Friction Factors in the Bubble Flow Regime in Vertical Tubes, Norwegian Rep. KR-110, Inst, for Atomenergi, Oslo, Norway. (5)... 

This can be rearranged to give the less dense phase volume fraction in terms of the mass fraction and slip ratio ... 

Note that both the local mixture density and the holdup increase as the slip ratio (S) increases. The no slip (S = 1) density or volume fraction is identical to the equilibrium value entering (or leaving) the pipe. 

A major complication, especially for separated flows, arises from the effect of slip. Slip occurs because the less dense and less viscous phase exhibits a lower resistance to flow, as well as expansion and acceleration of the gas phase as the pressure drops. The result is an increase in the local holdup of the more dense phase within the pipe (phase density, pm), as given by Eq. (15-11). A large number of expressions and correlations for the holdup or (equivalent) slip ratio have appeared in the literature, and the one deduced by Lockhart and Martinelli is shown in Fig. 15-7. Many of these slip models can be summarized in terms of a general equation of the form... 

The pressure drop over a given length of pipe must be determined by a stepwise procedure, as described for homogeneous flow. The major additional complication in this case is evaluation of the holdup (ipm) or the equivalent slip ratio (S) using one of the above correlations. 

Jamerson SC, HG Fisher. Using constant slip ratios to model non-flashing (frozen) two-phase flow through nozzles. Process Safety Prog 18(2) 89-98, 1999. 

A similar equation to that of Eq. (43) was proposed by Bankoff (B6) on the basis of a bubble-flow model for vertical flow. His derivations are discussed in the following section (Section V, B). Finally, it should be mentioned that the momentum exchange model of Levy (L4), and the slip-ratio model of Lottes and Flinn (L7) are more readily applied for the determination of void fractions than for pressure drops. In general, these methods seem to give rather poorer accuracy than those already discussed. 

Babinsky and Sojka [23] used DPF to study non-Newtonian liquid drop size distributions. For a single fluctuation, their results showed that fluctuations in ALR and interphase velocity slip ratio have the largest effect on effervescent atomizer/q. For two simultaneously fluctuating quantities, the influence on/o is found by adding... 

Figure 6 displays the effect of tackifier on abrasive resistance of mbber compound as the tread mbber of tire. The mbber compound was vulcanized at 170°C for 12 min and then was then evaluated as tread mbber in tire under the conditions of loading of 2.5 kg, a slip ratio of 40%, a temperature of 20°C, and a measuring time for 2 min using a Lamboum abrasion tester manufactured by Iwamoto Sei-sakusho Co., Ltd. The abrasive wear of the tire tread of passenger cars and tracks... 

Apart from the abovementioned devices, there are also the following skid resistance measuring devices the Japanese Skid Tester (locked wheel type operating speed during measurements, 30-90 km/h), DBV of NASA (locked wheel type operating speed, usually 65 km/h), Komatsu Skid Tester (Japan) (fixed slip ratio type between 10% and 30% slip ratio, operating speed between 30 and 60 km/h) and SRT-3 (Japan) (locked wheel type operating speed between 30 and 90 km/h). More information is provided in NCHRP (2000). 

Other devices to be mentioned are the Mu-meter (United Kingdom) (fixed slip ratio type 13% or 7.5% operating speed between 20 and 80 km/h) and the Runway Friction Tester (United States) (fixed slip ratio type 15% operating speed between 30 and 91 km/h). These devices have initially been developed for runway skid resistance measurements. 

Apart from the braking system (locked wheel or partially locked [fixed slip ratio]), other factors influence the skid resistance measurements. These factors are (a) the speed of the device during measurements, (b) the tyre type of test wheel (the smooth type is the most common, or ribbed), (c) the load applied on the test wheel, (d) the amount of water applied on the surface (water film created) before the measurement and (e) the temperature of the air, tyre and pavement. 

Name of device/vehicle Tech. spec. CEN/TS Type Operating typical speed (km/h) AAethod (% of slip ratio) Load wheel (N) Length for the mean value (m) Country... 

The measurements are taken with a standardised - not entirely blocked (34% fixed slip ratio) - smooth wheel positioned at a 20° angle to the direction of travel, loaded with a 1962 N load. The speed at which the measurements are taken is either 80 or 50 km/h (test speed). The 80 km/h test speed is used in motorways or other roads where the speed limit is greater than 80 km/h, whereas the 50 km/h test speed is used in all other cases. 

Skid resistance measurements are taken by the independent test wheel moving parallel to the direction of travel and with a fixed slip ratio of 15%. 

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