Turbulent Flow Of Polymer Solutions Research Articles

Study Rheological Behavior of Polymer Solution in Different-Medium-Injection-Tools.

Previous studies showed the difficulty during polymer flooding and the low producing degree for the low permeability layer. To solve the problem, Daqing, the first oil company, puts forward the polymer-separate-layer-injection-technology which separates mass and pressure in a single pipe. This technology mainly increases the control range of injection pressure of fluid by using the annular de-pressure tool, and reasonably distributes the molecular weight of the polymer injected into the thin and poor layers through the shearing of the different-medium-injection-tools. This occurs, in order to take advantage of the shearing thinning property of polymer solution and avoid the energy loss caused by the turbulent flow of polymer solution due to excessive injection rate in different injection tools. Combining rheological property of polymer and local perturbation theory, a rheological model of polymer solution in different-medium-injection-tools is derived and the maximum injection velocity is determined. The ranges of polymer viscosity in different injection tools are mainly determined by the structures of the different injection tools. However, the value of polymer viscosity is mainly determined by the concentration of polymer solution. So, the relation between the molecular weight of polymer and the permeability of layers should be firstly determined, and then the structural parameter combination of the different-medium-injection-tool should be optimized. The results of the study are important for regulating polymer injection parameters in the oilfield which enhances the oil recovery with reduced the cost.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions.

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

Application of Different Low-Reynolds k-ɛ Turbulence Models to Model the Flow of Concentrated Pulp Suspensions in Pipes

In the pulp and paper industry, the design of industrial equipment based on empirical correlations can be avoided using Computational Fluid Dynamics (CFD) tools. The present study aims at investigation of the turbulent pipe flow of concentrated Eucalyptus pulp suspension using the ANSYS FLUENT® CFD software package. The modelling strategy was a pseudo-homogeneous approach. The non-Newtonian behavior of the pulp suspension was introduced into the CFD code considering its viscosity as a function of a shear rate. Additionally, the existence of a water annulus at the pipe wall surrounding the core flow was taken into account. Four low-Reynolds k-ɛ turbulence models were selected in the present study aiming at describing the presence of a drag reduction effect. All the models used were able to reproduce the drag reduction effect. Additionally the Lam-Bremhorst model was modified taking into account alterations applied successfully by other authors for the turbulent flow of polymer solutions. A good correspondence between the peculiar S-shaped profile near the wall, for the dimensionless velocity, reported in literature for these systems and those obtained numerically was achieved. The approach followed was validated by comparing the numerical results of pressure drop with those from literature.

A mechanistic model of turbulent drag reduction by additives

The phenomenon of drag reduction in walled turbulent flows of polymer solutions is theoretically modeled. A new mechanistic model of a polymer molecule in a turbulent flow field is suggested. It is argued that the dominant forces on a polymer fiber in the turbulent flow field are elastic and centrifugal. According to this model, an additional route of dissipation exists, in which eddy kinetic energy is converted to polymer elastic energy by the centrifugal elongation of the rotated polymer, which in turn is viscously damped by the surroundings, when the polymer relaxes. A novel approach is then illustrated, where it is shown that this mechanistic model can be accounted for as a turbulent scale alteration, instead of addition, which enables the classical dimensional analysis of a turbulent boundary layer to apply. Using this dimensional analysis with the equivalent altered scale yields remarkable results. Correct-form velocity profiles are obtained, and Virk's asymptote and slope are predicted with no empirical constants. Drag–flow rate curves are also calculated, and compared favorably with Virk's experiments. The onset of drag reduction phenomenon is also explained by this model, and calculations of it are also compared with Virk's data. The parametric dependencies of the onset point agree well with Virk's conclusions.

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. The present work examines the effect of polymer additives on these “exact coherent states” (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e., Wi∕Re=const). In this situation, we study the effects of viscoelasticity on velocity field and polymer stress field along some experimental paths, which represent different flow behaviors as Re (and Wi) increases. The changes to the velocity field for the viscoelastic nonlinear traveling waves qualitatively capture many of those experimentally observed in fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase, and wall-normal and spanwise velocity fluctuations decrease. The mechanism underlying these observations is the suppression of streamwise vortices by the polymer forces exerted on the fluid. Specifically, at sufficiently high wall shear rates, viscoelasticity completely suppresses these streamwise vortices in the near-wall region, as is found in experiments in the maximum drag reduction regime. The mean shear stress balance for the nonlinear traveling waves shows that Reynolds shear stress decreases and polymer stress increases monotonically with the increase of viscoelasticity, as is found in full turbulence. The study of the influence of the viscoelasticity on the turbulent kinetic energy and Reynolds stress budgets shows that as Re (and Wi) increases, there is a consistent decrease in the production, diffusion, and dissipation of turbulent kinetic energy. The decrease in the velocity pressure gradient term leads to a redistribution of the turbulent kinetic energy among the streamwise, wall-normal and spanwise directions. The influence of the rheological parameters on the viscoelastic ECS is analyzed. It is found that the degree of drag reduction is determined primarily by the extensional viscosity and Weissenberg number. The optimum wavelength conditions under which the viscoelastic ECS first come into existence are also investigated. The wavelengths in streamwise and spanwise directions and the wall-normal extent of the ECS all increase monotonically with the increase of viscoelasticity, as is found in experiments.

Polymer drag reduction in exact coherent structures of plane shear flow

Recently discovered traveling-wave solutions to the Navier–Stokes equations in plane shear geometries provide model flows for the study of turbulent drag reduction by polymer additives. These solutions, or “exact coherent states” (ECS), qualitatively capture the dominant structure of the near-wall buffer region of shear turbulence, i.e., counter-rotating pairs of streamwise-aligned vortices flanking a low-speed streak in the streamwise velocity. The optimum length scales for the ECS match well the length scales of the turbulent coherent structures and evidence suggests that the ECS underlie the dynamics of these structures. We study here the effect of viscoelasticity on these states. The changes to the velocity field for the viscoelastic ECS, where the FENE-P model calculates the polymer stress, mirror the modifications seen in experiments of fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase while wall-normal fluctuations decrease, and smaller wavelength structures are suppressed. These modifications to the ECS are due to the suppression of the streamwise vortices. The polymer molecules become highly stretched in the wavy, streamwise streaks, where the flow is predominately elongational, then relax as they move from the streaks into and around the streamwise vortices, where the flow is predominately rotational. This relaxation of the polymer molecules produces a force that directly opposes the fluid motion in the vortices, weakening them. Since the pressure fluctuations have their greatest magnitude (i.e., they are most negative) in the cores of the vortices, a reduction in vortex strength leads to a decrease in the magnitude of the pressure fluctuations. The pressure fluctuations redistribute energy from the streamwise velocity fluctuations to the Reynolds shear stress, so a decrease in their magnitude leads to a reduction in turbulent drag. For the viscoelastic ECS, we also find that after the onset of drag reduction (at Weissenberg number, We≈7) there is a dramatic increase in the critical wall-normal length scale at which the ECS can exist. This sharp increase in length scale mirrors experimental observations and is also consistent with the observed shift to higher Reynolds numbers of the transition to turbulence in polymer solutions.

Computation of the turbulent friction resistance of polymer solutions in pipes

We construct a nonlayer and a three-layer model for the effect of lowering of hydrodynamic resistance by polymer additives. When the nonlayer model is used for various pipe diameters, the results of the theory and experiments show satisfactory agreement and describe well the scale effect of the turbulent flows of polymer solutions. The three-layer model can be used to compute the resistance of turbulent flows with polymer additives, including the case of limiting reduction of hydrodynamic resistance.Two figures. Bibliography: 5 titles.

Heat transfer, drag reduction, and fluid characterization for turbulent flow of polymer solutions: recent results and research needs

Some results of investigations on the heat transfer and friction reduction for viscoelastic polymer solutions flowing in circular tubes are presented. The effects of concentration and mechanical degradation on the drag and heat transfer are discussed. Measurements of heat transfer in the thermal entrance region are also reported and indicate a very long entrance region for asymptotic conditions and a shorter one for the non-asymptotic regime. Both these and fully-developed results suggest a departure from the friction/heat transfer analogies, both at the macroscopic coefficient level and at the turbulent diffusivity level. In particular, our computations showed that the turbulent Prandtl number may reach values of up to 15 for asymptotic drag-reducing solutions. In addition to the presentation of these results, the current understanding in this research area is discussed, with a review of some of the most important recent results and of the current research needs in terms of modeling, correlations, experiments, and fluid characterization.

Use of laser doppler anemometer for the investigation of turbulent flow of polymer solutions

The results of measurements of the mean velocity, the intensity of the longitudinal and the transverse components of the fluctuation velocity, and Reynolds stresses in the wake of a disk with polyoxyethylene solution injected in the aft zone are presented. The measurements were made by a laser anemometer.

Connection between average and pulsation characteristics in turbulent flow of polymer solutions in a round tube

Results are given for measurements of the average and pulsation characteristics of dynamically stable turbulent flows of polymer solutions in a round tube. Experimental dependences are presented which indicate the presence of a close and unique connection between the turbulent pressures and shear stresses at the wall of the tube.

Friction reduction in turbulent flow of polymer solution

Recent theoretical results for the turbulent flow of polymer solutions in round tubes have been extended to deduce the similarity laws for the boundary-layer flow of drag-reducing polymer solutions. The analysis shows directly how the drag reduction depends on the elastic properties of the fluid and thereby defines the levels of elasticity necessary to achieve significant reductions in drag.Calculations employing available physical property measurements of highly elastic (0·1%) and moderately elastic (0·01%) polymer solutions indicate that, for boundary layers on large objects, drag reduction may not occur at polymer concentrations that are economically attractive. For example, at a Reynolds number of 109 the reduction in drag is predicted to be 60% and 10% for the concentrated and dilute polymer solutions respectively. Some savings in polymer however, may be realized by special injection techniques or fluid systems with specially tailored properties.

A molecular approach to predicting the onset of drag reduction in the turbulent flow of dilute polymer solutions

The significant variables in drag reduction have been separated into two classifications, flow variables and solution variables. A theory has been offered which permits prediction of the critical Reynolds number in the turbulent flow of polymer solutions. The theory states that the relaxation time of the polymer molecule in solution equals a characteristic flow time for the tube in question at the point of incipient turbulent suppression. This is equivalent to a Deborah number near unity. Reasonable agreement has been shown between the experimental results of this investigation and predictions of flow rates based on this theory for the presence or absence of drag reduction and for the onset of turbulence suppression. No adjustable parameters were used in the analysis. The theory seems to be applicable at values of C[η] greater than 0·10. The theory leads to the prediction that the wall shear rate at the point of incipient turbulence suppression decreases as the product of reduced viscosity, molecular weight and solvent viscosity increases. Thus for large effects this product should be made as large as possible. Friction factor measurements in both good and poor (Theta) solvents showed that the maximum drag reduction in the poor solvent was only about 40% of that in the good solvent at similar flow rates in the same tube. Thus the effect of an expanded configuration of the polymer molecule in solution is to increase drag reduction.