Comments on “A phenomenological interpretation and correlation of drag reduction”
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The correlation of drag reduction data proposed by Astarita et al. (1969) (AGN correlation) is rather appealing due to its simplicity. Patterson et al. (1970) compared the shape of the AGN correlation with that of a correlation based on a model with some phenomenological considerations. Peterson and Beckwith ( 1971) have examined the validity of AGN correlation for systems of polymers dissolved in polar and nonpolar solvents. In this work some interesting features of this type of correlation are examined with respect to drag reduction in certain external flow problems. Some limitations of this type of correlation are also pointed out.In particular, the problem of correlation of turbulent drag reduction data for flow around rotating discs, cones, and cylinders is considered. It is generally agreed that drag reduction arises out of some interaction of turbulence and elasticity, although the exact manner of such an interaction is not completely clear. The data could be usually correlated by assuming that the friction factor (or power number) is a function of the Reynolds number Re and a Deborah number De. The latter corresponds to a ratio of the natural time of the fluid T and a characteristic process time t.The choice of the characteristic time of the process is primarily based on the postulated mechanism of the phenomenon of drag reduction. Kelkar and Mashelkar (1972) have, however, shown recently that in spite of the apparent diversity of the postulated mechanisms of drag reduction, the characteristic process time has remarkably the same form. Thus, for instance in the case of pipe flow the mechanisms of drag reduction proposed by Hershey and Zakin (1967), Seyer and Metzner (1967), Meek and Baer (1970) and Gordon ( 1970) are fundamentally quite different but their arguments result approximately in the same form of characteristic process time. The simplest model for drag reduction under external flow conditions will be chosen in this work. This model is based on the ideas extended by Astarita (1965), which make use of the arguments of Levich (1962).Under turbulent flow conditions a rotating body continuously generates eddies determined by certain sizes and frequency distribution and also by certain geometric orientation. The large scale eddies are of the size of the characteristic dimension of the rotating body and have their periods equal to the reciprocal of the angular velocity of the body. These large scale eddies transfer the kinetic energy to smaller and smaller eddies and continuation of this process eventually leads to eddies so small that viscous dissipation is very rapid. These small scale high frequency dissipating eddies are in the universal equilibrium range, which is independent of the geometric details of the body and is only dependent upon the rate at which the energy is supplied and the tendency of these eddies to dissipate this energy viscously. In ,other words, the properties of the small scale eddies are determined by the transfer processes and not by the properties of the mechanism of tu...
The correlation of drag reduction data proposed by Astarita et al. (1969) (AGN correlation) is rather appealing due to its simplicity. Patterson et al. (1970) compared the shape of the AGN correlation with that of a correlation based on a model with some phenomenological considerations. Peterson and Beckwith ( 1971) have examined the validity of AGN correlation for systems of polymers dissolved in polar and nonpolar solvents. In this work some interesting features of this type of correlation are examined with respect to drag reduction in certain external flow problems. Some limitations of this type of correlation are also pointed out.In particular, the problem of correlation of turbulent drag reduction data for flow around rotating discs, cones, and cylinders is considered. It is generally agreed that drag reduction arises out of some interaction of turbulence and elasticity, although the exact manner of such an interaction is not completely clear. The data could be usually correlated by assuming that the friction factor (or power number) is a function of the Reynolds number Re and a Deborah number De. The latter corresponds to a ratio of the natural time of the fluid T and a characteristic process time t.The choice of the characteristic time of the process is primarily based on the postulated mechanism of the phenomenon of drag reduction. Kelkar and Mashelkar (1972) have, however, shown recently that in spite of the apparent diversity of the postulated mechanisms of drag reduction, the characteristic process time has remarkably the same form. Thus, for instance in the case of pipe flow the mechanisms of drag reduction proposed by Hershey and Zakin (1967), Seyer and Metzner (1967), Meek and Baer (1970) and Gordon ( 1970) are fundamentally quite different but their arguments result approximately in the same form of characteristic process time. The simplest model for drag reduction under external flow conditions will be chosen in this work. This model is based on the ideas extended by Astarita (1965), which make use of the arguments of Levich (1962).Under turbulent flow conditions a rotating body continuously generates eddies determined by certain sizes and frequency distribution and also by certain geometric orientation. The large scale eddies are of the size of the characteristic dimension of the rotating body and have their periods equal to the reciprocal of the angular velocity of the body. These large scale eddies transfer the kinetic energy to smaller and smaller eddies and continuation of this process eventually leads to eddies so small that viscous dissipation is very rapid. These small scale high frequency dissipating eddies are in the universal equilibrium range, which is independent of the geometric details of the body and is only dependent upon the rate at which the energy is supplied and the tendency of these eddies to dissipate this energy viscously. In ,other words, the properties of the small scale eddies are determined by the transfer processes and not by the properties of the mechanism of tu...
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