Drag reduction by coupled systems: microbubble injection with homogeneous polymer and surfactant solutions

 The influence of homogeneous surfactant and homogeneous polymer solutions on the performance of microbubble skin friction reduction was investigated on an axisymmetric body. Carbon dioxide was injected into water, homogeneous surfactant (Aerosol OT) solutions, and homogeneous dilute polymer (Polyethylene oxide) solutions. Integrated skin friction measurements were obtained at two freestream velocities as a function of gas injection rate and polyethylene-oxide concentration. A moderate (50%) decrease in surface tension had little to no effect on the drag reducing characteristics of microbubble injection. At similar gas injection rates, microbubble injection exhibited more drag reduction in the polymer solutions than obtained with microbubble injection into water. However, the increased drag reduction obtained with polymer additives was no more than a multiplicative factor related to the baseline levels of drag reduction achieved by the individual methods, and suggests the mechanism for microbubble skin friction reduction acts independently of the polymer drag reduction. Received: 17 April 1998 / Accepted: 12 October 1998     

Drag reduction in aqueous cationic soap solutions

The pipe flow drag-reducing properties of mixtures of alkyltrimethylammonium halides with 1-naphthol in aqueous solution have been investigated. The effects of solution concentration, soap-naphthol ratio, soap molecular weight and solution temperature upon drag reduction and swirl decay time are reported. The critical wall shear stresses above which the drag-reducing properties cease correlate well with swirl decay time. At low soap concentrations greater than equimolar proportions of 1-naphthol with the soap are required for maximum drag reduction. The drag-reducing properties of these solutions are greatest at and around the Krafft point of the pure soap. A phenomenon similar to onset for polymer solution drag reduction is reported for these soap solutions.     

Drag reduction by polymer solutions in a riblet-lined pipe

The flow of 3 to 100 wppm aqueous solutions of a polyethyleneoxide polymer,M _w=6.2×;10⁶, was studied in a 10.2 mm i.d. pipe lined with 0.15 mm V-groove riblets, at diametral Reynolds numbers from 300 to 150000. Measurements in the riblet pipe were accompanied by simultaneous measurements in a smooth pipe of the same diameter placed in tandem. The chosen conditions provided turbulent drag reductions from zero to the asymptotic maximum possible. The onset of polymer-induced drag reduction in the riblet pipe occurred at the same wall shear stress, * _w =0.65 N/m², as that in the smooth pipe. After onset, the polymer solutions in the riblet pipe initially exhibited linear segments on Prandtl-Karman coordinates, akin to those seen in the smooth pipe, with specific slope increment . The maximum drag reduction observed in the riblet pipe was independent of polymer concentration and well below the asymptotic maximum drag reduction observed in the smooth pipe. Polymer solution flows in the riblet pipe exhibited three regimes: (i) Hydraulically smooth, in which riblets induced no drag reduction, amid varying, and considerable, polymer-induced drag reduction; this regime extended to non-dimensional riblet heightsh ⁺<5 in solvent andh ⁺<10 in polymer solutions. (ii) Riblet drag reduction, in which riblet-induced flow enhancementR>0; this regime extended from 5<h ⁺<22 in solvent and from 10<h ⁺<30 in the 3 wppm polymer solution, with respective maximaR=0.6 ath ⁺=14 andR=1.6 ath ⁺=21. Riblet drag reduction decreased with increasing polymer concentration and increasing polymer-induced flow enhancement S. (iii) Riblet drag enhancement, whereinR<0; this regime extended for 22<h ⁺<110 in solvent, withR;–2 forh ⁺>70, and was observed in all polymer solutions at highh ⁺, the more so as polymer-induced drag reduction increased, withR<0 for allS>8. The greatest drag enhancement in polymer solutions,R=–7±1 ath ⁺=55 whereS=20, considerably exceeded that in solvent. Three-dimensional representations of riblet- and polymer-induced drag reductions versus turbulent flow parameters revealed a hitherto unknown dome region, 8<h ⁺<31, 0<S<10, 0<R<1.5, containing a broad maximum at (h ⁺,S,R) = (18, 5, 1.5). The existence of a dome was physically interpreted to suggest that riblets and polymers reduce drag by separate mechanisms.     

Drag reduction change of polyethyleneoxide solutions in pipe flow

Change of drag reduction (DR) along a tube (D=2 mm, L=4 m) was experimentally investigated. To attain turbulent flow with Re=8 × 10⁴, a tank operated under high pressure up to 16 MPa. Solutions of different brands of polyethyleneoxide (PEO) with concentrations from 1 ppm to 100 ppm were tested. The results indicate that DR is not a constant value but depends on the time and intensity of interaction between the polymer and the turbulent flow. There are three regions with different behaviors of DR: growth, maximum, and slope down. Maximum DR coincides with the Virk ultimate DR and can be described by the suggested simple formula . A decrease in the DR maximum has not been found even for high shear stresses τ _p < 800 Pa. DR dynamics for four brands of PEO with different molecular weight was studied. Direct experimentally determined DR may be greater than the Virk ultimate value if the change in velocity profile is not taken into account. The corrected DR never exceeds the ultimate DR. Received: 10 April 2000/Accepted: 24 May 2001     

Secondary flows in turbulent surfactant solutions at maximum drag reduction

Secondary flows are always present when a turbulent Newtonian fluid flows through a square duct. We show that they are suppressed in surfactant solutions at maximum drag reduction. This result confirms the one-dimensional behaviour of such flows, which is caused by the alignment of the micelles.     

Flow patterns and heat transfer in vertical upward air–water flow with surfactant

Flow patterns, the pressure drag reduction and the heat transfer in a vertical upward air–water flow with the surfactant having negligible environmental impact were studied experimentally in a tube of 2.5 cm in diameter. Visual observations showed that gas bubbles in the air–water solution with surfactant are smaller in size but much larger in number than in pure air–water mixture, at the all flow regimes. The transition lines in the flow regime map for the solution of air–water mixture with surfactant of the 300 ppm concentration are mainly consistent with the experimental data obtained in clear air–water mixture. An additive of surfactant to two-phase flow reduces the total pressure drop and decrease heat transfer, especially in the churn flow regime.     

Time-dependent drag reduction and ageing in aqueous solutions of a cationic surfactant

The turbulent pipe flow of a highly dilute aqueous cationic surfactant solution is investigated by means of a pulsed ultrasound Doppler method with special emphasis on the wall boundary layer. The velocity profiles are recorded for several Reynolds numbers at varying ages of the solution. The wall shear stress velocities u _τ used for the normalization of the velocity profiles are determined by fitting the measured profiles to the universal linear velocity profile in the viscous sublayer. The theoretical pressure loss is then calculated from the numerical values of u _τ and compared to the experimental values. Two different scaling methods are discussed for the velocity fluctuations concerning the correlation of the root-mean square values with the effect and the amount of drag reduction. It is shown that outer scaling with the mean velocity is appropriate for the detection of drag reduction in surfactant solutions, rather than inner scaling with the wall shear stress velocity, which is common practice in investigations of 'usual' turbulent flows.     

Drag reduction in polymer mixtures

Summary Drag reduction was studied in dilute toluene solutions of a mixture of two polymers: polyisobutylene (of three different molecular weights) and 1,4-cis-isoprene rubber in the turbulent region at low (up to 5000) Reynolds numbers. Experiments were carried out with mixed solutions at a concentration equal to optimum concentration of polyisobutylene or higher than it. Drag reduction of the polymer mixtures depending on the ratio of the two polymers showed a positive deviation from the additive straight line at all concentrations investigated. To evaluate the degree of deviation from additivity, the excess drag reduction, was introduced which represents the difference between the actually measured drag reduction and that read from the additive straight line. The excess drag reduction showed almost no dependence on the molecular weight of polyisobutylene in the investigated range of this magnitude. Deviation from additivity depending on the ratio of the two polymers in the mixture growed higher with increasing the flow rate at a given molecular weight of polyisobutylene. The highest excess drag reduction was observed in solutions containing a larger amount of the lower molecular isoprene rubber polymer. The effect of polymer coils on drag reduction in binary polymer solutions was studied. An assumption was made that higher drag reduction in the polymer mixtures as compared to the additive was due to the change of polymer coil dimensions caused by the copresence of the macromolecules of both polymers in the solution. It was further supposed that low shear stresses at which the experiments were carried out caused sufficient orientation and deformation of isoprene rubber enlarged molecules and the contribution of the latter in increasing drag reduction of the mixture was higher.

---

Zusammenfassung Die Widerstandsverminderung in verdünnten toluolischen Lösungen einer Mischung von zwei verschiedenen Polymeren wird untersucht. Verwendet werden Polyisobutylene (mit drei verschiedenen Molekulargewichten) und 1,4-cis-Isopren-Kautschuk, und es wird im turbulenten Bereich bei Reynolds-Zahlen bis zu 5000 gemessen. Die Versuche werden bei Konzentrationen, die der Optimalkonzentration von Polyisobutylen entsprechen, oder höheren Konzentrationen durchgeführt. Die Widerstandsverminderung der Polymermischungen zeigt bei allen untersuchten Konzentrationen eine positive Abweichung von der additiven Geraden, deren Größe vom Mischungsverhältnis abhängt. Zur Beschreibung der Abweichung vom additiven Verhalten wird die überschüssige Widerstandsverminderung (excess drag reduction) eingeführt, welche die Differenz zwischen dem wirklich gemessenen Wert und dem zugeordneten Wert auf der additiven Geraden beschreibt. Diese Größe zeigt nur eine geringe Abhängigkeit vom Molekulargewicht der eingesetzten Polyisobutylene. Die Abweichung vom additiven Verhalten als Funktion des Mischungsverhältnisses beider Polymeren wächst mit zunehmendem Volumenstrom. Die größte überschüssige Widerstandsverminderung wird in Lösungen beobachtet, die einen größeren Anteil des weniger hochmolekularen Isopren-Kautschuks enthalten. Der Einfluß der Polymerverknäuelung auf die Widerstandsverminderung wird betrachtet. Es wird angenommen, daß die überschüssige Widerstandsverminderung auf eine Änderung der Knäuelgröße infolge der Anwesenheit des jeweils anderen Polymeren in der Lösung zurückzuführen ist. Weiter wird vermutet, daß die relativ niedrigen Schubspannungen, bei denen die Versuche ausgeführt wurden, doch schon eine hinreichend starke Orientierung und Deformation der aufgeweiteten Isopren-Kautschuk-Moleküle bewirken, so daß deren Beitrag zur Erhöhung der Widerstandsverminderung überwiegt.

---

Notations D diameter of capillary - DR drag reduction - DR _add additive drag reduction - DR excess drag reduction,DR = DR – DR _add - DR _mixture theoretical drag reduction of the mixture - DR _mixture ^* actually measured drag reduction of the mixture - DR _1R drag reduction of an IR molecule in a separate IR solution - DR _1R ^* drag reduction of an IR molecule in the presence of molecules of another polymer in the solution - DR _PIB drag reduction of a PIB molecule in a separate PIB solution - DR _PIB ^* drag reduction of a PIB molecule in the presence of molecules of another polymer in the solution - L length of the capillary - flow rate - c concentration - n number of IR molecules - p number of PIB molecules - _w wall shear stress - CMC carboxymethylcellulose - IR isoprene rubber - PAA polyacrylic acid - PAM polyacrylamide - PEI polyethyleneimine - PEO polyethylene oxide - PIB polyisobutylene - PS polystyrene     

Drag reduction in riblet-lined pipes

The possibilities of reducing the drag in pipes with a circular cross section by lining them with riblets have been investigated experimentally for developed turbulent air flow. The maximum drag reduction of 6–7% in the riblet-lined as compared with the smooth pipe was obtained for a dimensionless riblet pitch, expressed in law-of-the-wall parameters,s ⁺=14–18.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 57–61, January–February, 1995.     

Quasi-similar solutions for blast waves with internal heat transfer effects

The point explosion problem with internal heat transfer effects taken into account is analysed. The classical inviscid solutions to this problem yield a non-physical phenomenon of infinite temperature and zero density at the center of explosion for all times. With heat transfer fluxes considered, the solution near the center of symmetry is improved and finite values for temperature are obtained. The non-self-similar solution of the problem is based on the quasi-similar approximate technique which reduces the non-linear partial differential equations governing the problem to ordinary differential ones. However, this formulation yields a two-point boundary-value problem. To facilitate the integration, the flow field is first divided into two regions: an outer inviscid region and an inner region where dissipation effects are manifested. This results in two sets of ordinary differential equations expressing the conservation equations in the inner and outer regions which are then solved and matched together to yield the composite solution. Secondly, the problem is then transformed into an initial-value one. Using the results of the composite solution, the governing equations can be integrated directly from the center until the shock front. The structure of the non-self-similar flow fields with internal heat transfer effects is then fully determined for specified values of the heat transfer parameters.     

Nucleate boiling heat transfer in aqueous solutions with carbon nanotubes up to critical heat fluxes

In this study, pool boiling heat transfer coefficients (HTCs) and critical heat fluxes (CHFs) are measured on a smooth square flat copper heater in a pool of pure water with and without carbon nanotubes (CNTs) dispersed at 60 °C. Tested aqueous nanofluids are prepared using multi-walled CNTs whose volume concentrations are 0.0001%, 0.001%, 0.01%, and 0.05%. For the dispersion of CNTs, polyvinyl pyrrolidone polymer is used in distilled water. Pool boiling HTCs are taken from 10 kW/m² to critical heat flux for all tested fluids. Test results show that the pool boiling HTCs of the aqueous solutions with CNTs are lower than those of pure water in the entire nucleate boiling regime. On the other hand, critical heat flux of the aqueous solution is enhanced greatly showing up to 200% increase at the CNT concentration of 0.001% as compared to that of pure water. This is related to the change in surface characteristics by the deposition of CNTs. This deposition makes a thin CNT layer on the surface and the active nucleation sites of the surface are decreased due to this layer. The thin CNT layer acts as the thermal resistance and also decreases the bubble generation rate resulting in a decrease in pool boiling HTCs. The same layer, however, decreases the contact angle on the test surface and extends the nucleate boiling regime to very high heat fluxes and reduces the formation of large vapor canopy at near CHF. Thus, a significant increase in CHF results in.     

Functional solutions for problems of heat and mass transfer

Meccanica - We prove the existence and, in certain cases, the uniqueness of functional solutions for boundary value problems of systems of P.D.E. in divergence form with constant boundary...     

Friction and heat transfer in drag-reducing surfactant solution flow through curved pipes and elbows

A study of drag-reducing flow in curved pipes was conducted. In contrast to earlier studies we show that if we use a modified definition of drag reduction that includes only the turbulence effects, we observe indeed the same level of drag reduction in both coiled and straight pipes. More complex results showing reduced drag reduction compared to curved pipes were achieved with elbows. Two elbows of different size and type were tested in turbulent flow of both water and drag-reducing surfactant solution. A more elaborate analysis was conducted for a half-inch threaded elbow with a ratio of curvature radius to diameter of 1.2. The pressure drop and heat transfer were measured in a section downstream from the elbow over a distance of x/D = 130 in order to investigate the hydrodynamic and thermal developments of the flow. The pressure drop coefficient of the elbow was calculated for water and a surfactant solution, based on the total increase in pressure drop in the system due to the presence of the elbow. For a larger welded elbow of 6″ diameter some drag reduction was measured for the surfactant solution.     

Effect of variations in counterion to surfactant ratio on rheology and microstructures of drag reducing cationic surfactant systems

Rheology, drag reduction and cryo-TEM experiments were performed on Arquad 16–50/NaSal and Ethoquad O/12/NaSal surfactant systems at different counterion-to-surfactant ratios and at constant low surfactant concentrations, 5 mM, appropriate for drag reduction. The molar ratio of counterion-to-surface was varied from 0.6 to 2.5. All the surfactant systems described here are viscoelastic and drag reducing. The viscoelasticity and drag reducing effectiveness increase with increase in counterion/surfactant ratio. Network are present in the solutions with high ratio, and they are viscoelastic. However, shear is needed to induce network formation for solutions at low ratio. Cryo-TEM images confirm the existence of thread-like micelles which form entanglement networks, and show that the micellar network becomes denser with increasing counterion/surfactant ratio in one surfactant series. Both increase in the counterion/surfactant ratio and increase in the shear rate result in shorter relaxation times. For some of these systems, abrupt increase in viscosity is observed at certain shear rates which are time effects affecting microstructure rearrangements rather than formation of shear induced structures.     

Heat transfer characteristics of water and APG surfactant solution in a micro-channel heat sink

The steady increase in internal heat production of cost and high performance electronic components has lead researchers to seek improved ways to remove the heat generated. Single-phase liquid flow has been considered as a potential solution for solving this cooling problem. However, when considering that any solution needs to be of low cost and low mass fluxes and yet retain low temperature gradients across the electronic components, it seems that two-phase boiling flow is preferred. Surfactant solutions have been introduced in connection with enhancement of the boiling processes. We investigated the effects of surfactant solution flows through a micro-channel heat sink. The experimental setup included a high-speed IR radiometer and a CCD camera that were used to characterize the test module. The module consisted of inlet and outlet manifolds that distributed surfactant solutions through an array of 26 parallel micro-channels. The experimental results have shown that there exists an optimal solution concentration and mass flux for enhancing heat removal. Surfactant solution boiling flows were also found to stabilize the maximum and average surface temperatures for a wide range of applied heat fluxes. In addition, the use of surfactant solutions at low mass fluxes has led to CHF enhancement when compared to regular water flows. In the last part of this work, possible explanations for the observed non-ionic surfactant effects are presented.     

Topology optimization of conjugate heat transfer systems: A competition between heat transfer enhancement and pressure drop reduction

Topology optimization method is developed for a multi-objective function combining pressure drop reduction and thermal power maximization (incompressible flows at low to moderate Reynolds numbers). Innovative optimal designs are obtained, discussed and presented on a Pareto-frontier. The numerical developments (continuous adjoint technique) have been conducted inside an open source CFD platform via the finite volume method. Comparisons have been presented with an optimal design obtained by a Lattice Boltzmann Method from the literature. Finally, this contribution presents and discuss several detailed numerical vitrification steps which are essential to be conducted in topology optimization method when applied with multi-objective functions.     

Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.