Turbulence phenomena in drag reducing systems

Abstract

An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically.Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements o f the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction a t all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.A growing number of studies have been undertaken cesses there. A recent detailed study of the Newtonian which aim to characterize or elucidate the physical asflow wit,hin this wall region (3) has shown that the large pects of drag reduction. Several of these (7, 14, 20, 24, eddies exist as counter-rotating pairs with their axes 35, 39, 46) include sufficient ranges of the primary varialong the mean flow direction. In the lateral direction a ables such as tube size, the polymeric additive used and diffuse influx of material occurs which is concentrated its concentration to illustrate the varied nature and extent between the two eddies and rapidly ejected from the of drag reduction and t,he difficulty of obtaining a genboundary layer region owing to the counter-rotation of era1 and quantitative understanding of the phenomenon. the eddy pair. The eddy pattern remains defined to the Although in several instances (10, 22, 24, 28, 39) drag outer edge of the sublayer and as these patterns may be reduction data have been correlated empirically and associated with about 50% of the total turbulent energy several theoretical analysis have been presented (11, 16, they must control to a large extent the radial momentum 41, 42) little consistent information, pertinent to the transport rates which exist in the wall region. From the processes involved in drag reduction, has evolved. Comstreamline patterns presented by Bakewell a graphical pounding this problem is the utility of measurements using analysis has shown (38) that the streamlines are adethe usual tools of research in turbulence, impact, and hotquately described by: wire probes, which has been severely questioned ( 2 , 15, 23, 25, 36) and remains in doubt for viscoelastic fluids. Thus the several experimental investigations in which such tools were employed ( 2 , 12, 13, 28, 44, 4 6 ) , though clea...

Modeling of viscoelastic turbulent flow in channel and pipe

“…28,29 The equations of mean velocity distribution has been applied to the viscoelastic flows; it is found that the equations derived are in good agreement with experimental data measured by Virk, [30][31][32] Seyer and Metzner, 33 James and Acosta, 34 Reischman and Tiederman, 14 Rudd,13 etc.…”

Laser-Doppler Anemometer Measurements of Turbulence in Drag Reducing Flows

“…This contradicts the findings of Chung and Graebel (1972) and Seyer and Metzner (1969). The reason This is in direct contradiction with the work of Chung and Graebel (1972) and Rudd (1972) who show lunter velocity profiles for polymer solutions than for water.…”

“…Much of the data shows a large degree of scatter. Seyer and Metzner (1969) have observed significant differences in the axial turbulence intensities of the polymer solution as compared to a water flow. However, these differences are of the same order of magnitude as their confidence band.…”

Passive scalar transport in polymer drag‐reduced turbulent channel flow

“…The first mechanism is based on the fact that polymer molecules undergo a coil-to-stretch transition, causing an increase in the elongational viscosity of the solution leading to the suppression of Reynolds stress-producing events. 6,11 The second mechanism assumes that coil-to-stretch transition is not possible in channel or pipe flows with constant cross section; rather, drag reduction is associated with the storage of elastic energy in the polymer molecules and the resulting disruption of the energy cascade. 12 Direct numerical simulations of viscoelastic turbulent channel flow using kinetic theory-based models have identified that the enhancement in extensional viscosity caused by flow-induced chain stretching is a key characteristic of drag-reducing fluids.…”