The effect of polymer additives on transition in pipe flow

Summary Small amounts of long chain water soluble polymers have a marked effect on turbulent flow resulting in an appreciable reduction of turbulent friction. The maximum reduction in pipe flow resistance is obtained at such low concentrations that the density and viscosity are not altered appreciably. The minimum friction curve varies as Re ^–2/3 and appears to be the same for all effective additives tested. The transition process is affected by these additives. Quantitative results are presented showing a reduction in the intensity of the turbulent flashes and the fraction of the time the flow is turbulent at a given Reynolds number.     

The energy balance in turbulent motion in a plane curvilinear channel

We determine the component energy equations for mean and pulsating motion in a plane curvilinear channel. We discuss the characteristics of the turbulence in curvilinear channels by comparison with those of rectilinear flows.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5,pp. 150–153, September–October, 1970.     

The effect of the expansion ratio on a turbulent non-Newtonian recirculating flow

 Measurements of the mean and turbulent flow characteristics of shear-thinning moderately elastic 0.1% and 0.2% xanthan gum aqueous solutions were carried out in a sudden expansion having a diameter ratio of 2. The inlet flow was turbulent and fully developed, and the results were compared with data for water in the same geometry and with previous published Newtonian and non-Newtonian data in a smaller expansion of diameter ratio equal to 1.538. An increase in expansion ratio led to an increase in the recirculation length and in the axial normal Reynolds stress at identical normalised locations, but the difference between Newtonian and non-Newtonian characteristics was less intense than in the smaller expansion. An extensive comparison of mean and turbulent flow characteristics was carried out in order to understand the variation of flow features. Received: 31 July 2000 / Accepted: 27 August 2001     

The effect of polymer additives which lower the friction resistance on flow in smoothly contracting and expanding channels

Vortical formations near the wall and their subsequent disintegration are sources of turbulization of the flow [1, 2]. Their intensity at smooth walls depends on the magnitude and the sign of the longitudinal pressure gradient [1]. With considerable values of a negative pressure gradient, vortices do not develop. In a number of publications, for example [3], note is taken of the special importance of vortices of the transition layer in the phenomenon of the lowering of the friction resistance by polymer additives. In this work, experimental investigations were made of flows with negative and positive pressure gradients. Data are obtained which attest to the fact that the flow of weak solutions of polymers with negative pressure gradients does not differ from the flow of Newtonian liquids, while, with positive gradients, the effect of polymer additives manifests itself fully.     

Turbulence energy balance in reacting turbulent flows

The turbulence accompanying combustion and the propagation of detonation waves in gases has been studied theoretically and experimentally in many papers [1–8]. The attention of researchers has been concentrated on essential questions like how the turbulent flow field interacts with the kinetics of the chemical reaction and to what extent the process of chemical change is intensified, and how the turbulence itself is deformed by the heat released and the accompanying expansion of the gases. The various mechanisms proposed for these phenomena are based on various hypotheses concerning the structure of the combusion zone and the determinative stage of the interaction of the turbulence with the chemical-reaction kinetics. The mechanism of turbulence generation by combustion proposed in a number of papers [3–6] is based on the observation in turbulent flow of a weakly curved flickering laminar flame. This gives rise to a nonuniform flow field of the gas, part of the energy of which goes over into the energy of turbulent fluctuations. Other authors [7, 8] considered the turbulence field to interact with the chemical-reaction kinetics via a volume mechanism and suggested a criterion of turbulence intensification based on certain physical considerations, e.g., the condition for the intensification of thermogaskinetic oscillations proposed by Rayleigh [9]. In the present paper the problem is analyzed by introducing Kolmogorov's general equation for the turbulence energy balance in reacting turbulent flows [10]. In accordance with, this equation the turbulence energy can vary due to energy exchange between the turbulent motion and the mean gas flow as a result of the work on turbulent mass transport in the acceleration field of the mean flow, and due to the effect of pressure fluctuations on the rate of thermal expansion from the chemical reaction. Each of these effects is considered and analyzed.     

Investigation of the effect of polymeric additives on turbulent friction at sharp changes of section in pipe flow

The effect of polymeric additives on the turbulent flow of water through pipes has been experimentally investigated in the presence of local resistances in the form of orifices and sudden expansions and contractions of the flow at several values of the area ratio and at various concentrations of different polymers. At the experimental values of the Reynolds number Re10⁴ the motion is self-similar. It is these regimes that are characteristic of the turbulent flows of most practical interest.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–156, March–April, 1972.     

The concentration field in a turbulent channel flow with polymer injection at the wall

Instantaneous concentration profiles have been measured in turbulent water channel flows at 5 axial locations immediately downstream of a line, wall injection of a dyed 700 ppm polymer solution and for comparison, dyed water. Concentration was deduced from a line of fluoresced radiation that was stimulated by a laser beam directed through the dyed injectant and normal to the channel wall. Both statistical and time-resolved results show how the turbulent mixing is modified and damped when the injectant is a polymer solution. A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Influence of polymer additives in a flow on the hydrodynamic characteristics of two-dimensional profiles

The problem of separationless flow of homogeneous dilute polymer solutions over two-dimensional profiles is considered. The complete flow is divided by the outer edge of the boundary layer and the wake into two regions: a region of irrotational flow and a region of viscous flow — the boundary layer and wake. The characteristics of the two regions are matched at their boundary. The problem is solved by successive approximation with allowance for the mutual influence of the two regions on each other. The influence of the irrotational region on the viscous region is taken into account through the distribution of the pressure on the boundary of the wake and the boundary layer. The influence of the viscous part of the flow is taken into account by the introduction of an associated vortex whose intensity is equal to the integral of the vorticity in the complete viscous region, and also by the introduction of additional velocities on the boundary of the wake and the boundary layer. These deform the streamlines in the irrotational part of the flow and ensure that they match the flow pattern in the real fluid. The results of the calculations of the hydrodynamic characteristics of a Zhukovskii profile are compared with experimental data. The influence of the introduction into the flow of polymer additives on the distributed and total characteristics of the flow at a number of Reynolds numbers is analyzed for the example of the modified profile NACA66.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–41, October–December, 1981.     

Use of turbulent energy balance equation in the theory of turbulent flows along walls

The turbulent flow of an incompressible fluid is considered in a plane channel, a circular tube, and the boundary layer on a flat plate. The system of equations describing the motion of the fluid consists of the Reynolds equations and the mean kinetic energy balance equation for turbulent fluctuations. On the basis of an analysis of experimental data, hypotheses are formulated with respect to the eddy kinematic viscosity and lengthl entering into the expression for specific dissipation of turbulent energy into heat. It is assumed that in the central (outer) region of the flow in a channel, andl are constants, and expressions are taken for them which are used for a free boundary layer; near the walll varies linearly and almost linearly. Results of calculations of the turbulent energy distribution, the mean velocity, and the drag coefficient are in good agreement with the existing experimental data. The values of two empirical coefficients, which enter into the system of equations as the result of the hypotheses, are close to those obtained for a free boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–33, May–June, 1973.     

Turbulent kinetic energy balance in a LEBU modified turbulent boundary layer

An experimental study of the turbulent kinetic energy balance is performed in a LEBU manipulated turbulent boundary layer. The estimation of almost all the terms of the k-equation is obtained by hot wire anemometry. Near the manipulating device, strong alterations are observed, when compared with the natural conditions. The wake of the manipulator imposes two distinct zones. The lower part is characterized by negligible production compensated by diffusion, while, in the outer part, a large excess of production is balanced by diffusion and dissipation. The excess of dissipation rapidly vanishes downstream. The relaxation process is slower for production and diffusion.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Numerical and experimental investigation of turbulent characteristics in a drag-reducing flow with surfactant additives

Cetyltrimethyl ammonium chloride (CTAC) surfactant additives, because of their long-life characteristics, can be used as promising drag-reducers in district heating and cooling systems. In the present study we performed both numerical and experimental tests for a 75 ppm CTAC surfactant drag-reducing channel flow. A two-component PIV system was used to measure the instantaneous streamwise and wall-normal velocity components. A Giesekus constitutive equation was adopted to model the extra stress due to the surfactant additives, with the constitutive parameters being determined by well-fitting apparent shear viscosities, as measured by an Advanced Rheometric Expansion System (ARES) rheometer. In the numerical study, we connected the realistic rheological properties with the drag-reduction rate. This is different from previous numerical studies in which the model parameters were set artificially. By performing consistent comparisons between numerical and experimental results, we have obtained an insight into the mechanism of the additive-induced drag-reduction phenomena.

Our simulation showed that the addition of surfactant additives introduces several changes in turbulent flow characteristics: (1) In the viscous sublayer, the mean velocity gradient becomes gentler due to the viscoelastic forces introduced by the additives. The buffer layer becomes expanded and the slope of the velocity profile in the logarithmic layer increases. (2) The locations where the streamwise velocity fluctuation and Reynolds shear stress attain their maximum value shifted from the wall region to the bulk flow region. (3) The root-mean-square velocity fluctuations in the wall-normal direction decrease for the drag-reducing flow. (4) The Reynolds shear stress decreases dramatically and the deficit of the Reynolds shear stress is mainly compensated by the viscoelastic shear stress. (5) The turbulent production becomes much smaller and its peak-value position moves toward the bulk flow region. All of these findings agree qualitatively with experimental measurements.

Regarding flow visualization, the violent streamwise vortices in the near wall region become dramatically suppressed, indicating that the additives weaken the ejection and sweeping motion, and thereby inhibit the generation of turbulence. The reduction in turbulence is accomplished by additive-introduced viscoelastic stress. Surfactant additives have dual effects on frictional drag: (1) introduce viscoelastic shear stress, which increases frictional drag; and (2) dampen the turbulent vortical structures, decrease the turbulent shear stress, and then decrease the frictional drag. Since the second effect is greater than the first one, drag-reduction occurs.     

An experimental investigation of the effect of a constriction on turbulent pipe flow

Measurements have been made of the distributions of the mean-velocity and the axial turbulence velocity component in a cross-section of a circular tube at various distances downstream from a number of different constrictions. Also spectral distributions of the turbulence velocity have been measured in the axis of the tube and in a point very close to the wall. The constrictions had a contraction ratio of 0.25 except one which had a ratio of 0.5. One of the constrictions was made of a thin rubber hose. When for this constriction the contraction ratio was reduced to a value smaller than 0.25, self-excited vibrations of the hose took place, producing an oscillating flow of the air in the tube. The Reynoldsnumber was kept at roughly 5,000. As could be expected, after 40 tube diameter distance downstream from the constrictions an almost complete recovery of the disturbed turbulent flow, as far as the distributions of the mean velocity and relative turbulence intensity are concerned, was obtained. Depending on the shape of the constriction even a shorter distance appeared to be sufficient. The flexible constriction then was in the non-vibrating condition. However, the spectral distributions showed in some cases still a difference with the undisturbed case, in particular in the low frequency range. If the flexible constriction was vibrating, the induced oscillations of the flow which showed up as discrete peaks in the spectral distributions, persisted over the entire length of the tube, again as expected.     

Fictitious domain methods for two‐phase flow energy balance computations in nuclear components

This paper is dedicated to the numerical simulation of nuclear components (cores and steam generators) by fictitious domain methods. The fictitious domain approach consists in immersing the physical domain under study in a Cartesian domain, called the fictitious domain, and in performing the numerical resolution on this fictitious domain. The calculation times are then efficiently reduced by the use of fast solvers. In counterpart, one has to handle with an immersed boundary, generally non‐aligned with the Cartesian mesh, which can be non‐trivial. The two fictitious domain methods compared here on industrial simulations and developed by Ramière et al. deal with an approximate immersed interface directly derived from the uniform Cartesian mesh. All the usual immersed boundary conditions (Dirichlet, Robin, Neumann), possibly mixed, are handled through a unique formulation of the fictitious problem. This kind of approximation leads to first‐order methods in space that exhibit a good ratio of the precision of the approximate solution over the CPU time, which is very important for industrial simulations. After a brief recall of the fictitious domain method with spread interface (Ramière et al., CMAME 2007) and the fictitious domain method with immersed jumps (Ramière et al., JCP 2008), we will focus on the numerical results provided by these methods applied to the energy balance equation in a steam generator. The advantages and drawbacks of each method will be pointed out. Generally speaking, the two methods confirm their very good efficiency in terms of precision, convergence, and calculation time in an industrial context. Copyright © 2011 John Wiley & Sons, Ltd.     

Turbulence structure of polymer turbulent channel flow with and without macromolecular polymer structures

The presence of macromolecular polymer structures in a fully developed turbulent channel flow has been shown to substantially increase the drag reduction compared to non-structured polymer flows. This study presents a detailed analysis of experimental data obtained using laser Doppler velocimetry (LDV) to develop insights into the effects of the presence of macromolecular polymer structures on the turbulence characteristics of a channel flow. It is argued that polymer structures could contribute to minimizing the interaction between the inner and outer regions of the flow, which, in turn, can contribute to the modification of the coherent structure of the turbulence.     

The inverse energy cascade and self-organization in homogeneous turbulent shear flow

Stability of a homogeneous turbulent shear flow upon large-scale perturbations is being considered. The mean flow equations demonstrate a superexponential growth of 3-D perturbations prolonged along the basic flow in the presence of non-zero mean helicity.     

Friction drag and energy loss in a turbulent pulsating flow in a tube

The results of an experimental investigation of the kinematic structure and tangential wall stresses are used for an analysis of the time-dependent friction drag and loss of mechanical energy in a turbulent pulsating flow in a round tube. The question of the applicability of the quasistationary approach to calculation of the friction and the dissipative loss in unsteady flow is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 160–162, January–February, 1977.We thank O. F. Vasil'ev, on whose initiative and with whose support this work was carried out, and also E. M. Romanov, V. V. Zykov, and P. A. Drozhzhin for their great contribution to the. design of the experimental apparatus and provision of apparatus for the investigations.     

Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.An erratum to this article can be found at