Drag coefficient

About: Drag coefficient is a research topic. Over the lifetime, 14471 publications have been published within this topic receiving 303196 citations. The topic is also known as: drag factor.

The Ultimate Asymptote and Mean Flow Structure in Toms’ Phenomenon

Abstract: The maximum drag reduction in turbulent pipe flow of dilute polymer solutions is ultimately limited by a unique asymptote described by the experimental correlation: f−1/2=19.0 log10(NRef1/2)−32.4 The semilogarithmic mean velocity profile corresponding to and inferred from this ultimate asymptote has a mixing-length constant of 0.085 and shares a trisection (at y+ ∼ 12) with the Newtonian viscous sublayer and law of the wall. Experimental mean velocity profiles taken during drag reduction lie in the region bounded by the inferred ultimate profile and the Newtonian law of the wall. At low drag reductions the experimental profiles are well correlated by an “effective slip” model but this fails progressively with increasing drag reduction. Based on the foregoing a three-zone scheme is proposed to model the mean flow structure during drag reduction. In this the mean velocity profile segments are (a) a viscous sublayer, akin to Newtonian, (b) an interactive zone, characteristic of drag reduction, in which the ultimate profile is followed, and (c) a turbulent core in which the Newtonian mixing-length constant applies. The proposed model is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile, respectively, at the limits of zero and maximum drag reductions.

The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow

Abstract: This work determines the pressure–velocity relation of bubble flow in polygonal capillaries. The liquid pressure drop needed to drive a long bubble at a given velocity U is solved by an integral method. In this method, the pressure drop is shown to balance the drag of the bubble, which is determined by the films at the two ends of the bubble. Using the liquid-film results of Part 1 (Wong, Radke & Morris 1995), we find that the drag scales as Ca2/3 in the limit Ca → 0 (Ca μU/σ, where μ is the liquid viscosity and σ the surface tension). Thus, the pressure drop also scales as Ca2/3. The proportionality constant for six different polygonal capillaries is roughly the same and is about a third that for the circular capillary.The liquid in a polygonal capillary flows by pushing the bubble (plug flow) and by bypassing the bubble through corner channels (corner flow). The resistance to the plug flow comes mainly from the drag of the bubble. Thus, the plug flow obeys the nonlinear pressure–velocity relation of the bubble. Corner flow, however, is chiefly unidirectional because the bubble is long. The ratio of plug to corner flow varies with liquid flow rate Q (made dimensionless by σa2/μ, where a is the radius of the largest inscribed sphere). The two flows are equal at a critical flow rate Qc, whose value depends strongly on capillary geometry and bubble length. For the six polygonal capillaries studied, Qc [Lt ] 10−6. For Qc [Lt ] Q [Lt ] 1, the plug flow dominates, and the gradient in liquid pressure varies with Q2/3. For Q [Lt ] Qc, the corner flow dominates, and the pressure gradient varies linearly with Q. A transition at such low flow rates is unexpected and partly explains the complex rheology of foam flow in porous media.

The effects of slightly soluble surfactants on the flow around a spherical bubble

Abstract: This paper reports the results of a numerical investigation of the transient evolution of the flow around a spherical bubble rising in a liquid contaminated by a weakly soluble surfactant. For that purpose the full Navier–Stokes equations are solved together with the bulk and interfacial surfactant concentration equations, using values of the physical-chemical constants of a typical surfactant characterized by a simple surface kinetics. The whole system is strongly coupled by nonlinear boundary conditions linking the diffusion flux and the interfacial shear stress to the interfacial surfactant concentration and its gradient. The influence of surfactant characteristics is studied by varying arbitrarily some physical-chemical parameters. In all cases, starting from the flow around a clean bubble, the results describe the temporal evolution of the relevant scalar and dynamic interfacial quantities as well as the changes in the flow structure and the increase of the drag coefficient. Since surface diffusion is extremely weak compared to advection, part of the bubble (and in certain cases all the interface) tends to become stagnant. This results in a dramatic increase of the drag which in several cases reaches the value corresponding to a rigid sphere. The present results confirm the validity of the well-known stagnant-cap model for describing the flow around a bubble contaminated by slightly soluble surfactants. They also show that a simple relation between the cap angle and the bulk concentration cannot generally be obtained because diffusion from the bulk plays a significant role.

A theory for local evaporation(or heat transfer)from rough and smooth surfaces at ground level.

Abstract: A model proposed earlier (Brutsaert, 1965) for evaporation as a molecular diffusion process into a turbulent atmosphere is extended by joining it with the similarity models for turbulent transfer in the surface sublayer. The assumed mechanisms were suggested by available flow visualization studies near smooth and rough walls; the theoretical result is in good agreement with available experimental evidence. The important dimensionless parameters governing the phenomenon near the surface are the Dalton (or Stanton) number (i.e., mass transfer coefficient), the drag coefficient (u*2/U2), the roughness Reynolds number (u*z0/v) (except for smooth surfaces), and the Schmidt (or Prandtl) number (v/k). The proposed formulation allows the evaluation of the effects of some parameters, such as surface roughness or molecular diffusivity, that were hitherto not well understood. An important practical result is that in contrast to the drag coefficient, the Dalton number is relatively insensitive to changes in roughness length Z0.