Effect of drag force on backward-facing step gas-particle turbulent flows

An improved drag force coefficient of gas-particle interaction based on the traditional Wen’s 1966 model is proposed. In this model, a two-stage continuous function is used to correct the discontinuous switch when porosity less than 0.2. Using this proposed correlation and the Wen’s 1966 model, a gas-particle kinetic energy and particle temperature model is developed to predict the hydrodynamic characteristics in backward-facing step gas-particle two-phase turbulent flows. Numerically results showed that they are in good agreement with experiment measurements and presented model are better due to a improvement of momentum transport between gas and particle phases. Particle dispersions take on the distinctively anisotropic behaviors at every directions and gas phase fluctuation velocity are about twice larger than particle phases. Particle phase has a unique transportation mechanism and completely different from the gas phase due to different density. Furthermore, the correlation values of axial–axial gas-particle are always greater than the radial–radial values at fully flow regions. The gas-particle two-phase interactions will make influence on two-phase turbulent flow behaviors.     

Reconstruction of three-dimensional particle trajectories in flows through curved circular tubes

An automated technique is described for reconstructing three-dimensional trajectories of tracer particles in curved circular ducts. Individual particles are tracked in real time by a rotating camera under computer control. A digital imaging system enables the computer to locate the particle, adjust the speed of rotation, and store position and calibration data. By viewing the tube from approximately orthogonal directions, three-dimensional information on the position of the particle is obtained. Its precise location is calculated by tracing rays from the camera to the interior of the tube. This technique yields detailed three-dimensional position and velocity data along a trajectory.     

Pulsating flow of viscoelastic fluids in straight tubes of arbitrary cross-section—Part II: secondary flows

The secondary flow field in the pulsating flow of a constitutively non-linear fluid, whose structure is defined by a series of nested integrals over semi-infinite time domains, in straight tubes of arbitrary cross-sections is investigated. The transversal field arises at the second order of the perturbation of the non-linear constitutive structure, and is driven by first-order terms which define the linearly viscoelastic longitudinal flow in the hierarchy of superposed linear flows stemming from the perturbation of the constitutive structure. The unconventional conduit contours are obtained through a novel approach to the concept of domain perturbation. Time-averaged, mean secondary flow streamline patterns are presented for triangular, square and hexagonal pipes.     

Effect of drag reducing polymer on air–water annular flow in an inclined pipe

Drag reduction (DR) for air and water flowing in an inclined 0.0127 m diameter pipe was investigated experimentally. The fluids had an annular configuration and the pipe is inclined upward. The injection of drag reducing polymer (DRP) solution produced drag reductions as high as 71% with concentration of 100 ppm in the pipeline. A maximum drag reduction that is accompanied (in most cases) by a change to a stratified or annular-stratified pattern. The drag reduction is sensitive to the gas and liquid superficial velocities and the pipe inclination. Maximum drag reduction was achieved in the case of pipe inclination of 1.28° at the lowest superficial gas velocity and the highest superficial liquid velocity. For the first time in literature, the drag reduction variations with the square root of the superficial velocities ration for flows with the same final flow patterns have self-similar behaviors.     

A tentative approach to the direct simulation of drag reduction by polymers

An efficient technique for drag reduction uses dilute solutions of a few p.p.m. of polymers. A possible reduction in drag of up to 80% is achieved. Several experimental observations have been made which tend to indicate that the polymers modify the turbulence structures within the buffer layer. Flow visualisations have shown that the changes consist of a weakening of the strength of the streamwise vortices. Existing literature reveals no attempts of numerical simulation of this phenomenon. In this paper an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow. According to this model this viscosity is large in zones where the amount of strain rate is greater than the amount of vorticity, and is zero when the vorticity exceeds the strain rate. Simulations have been performed in a “minimal channel” to give good resolution with a limited number of grid points. The accuracy of the method is tested by comparison with the results of other techniques. For simulations with polymers, quantitative comparisons cannot be made, but the results reproduce the qualitative outputs of the experiments. The mean streamwise velocity is modified in the buffer layer; the peak of the streamwise turbulent intensity, in wall units, increases and its maximum moves far from the wall; and the vertical turbulent intensity is largely reduced in the wall region. An interesting outcome from both the simulation and the experiments is that the strength of the longitudinal vortices is reduced when the polymers are present.     

Experimental study of the possibility of reducing supersonic drag by employing plasma technology

The possibility of reducing the aerodynamic drag of a body by injecting plasma into the oncoming supersonic flow is confirmed experimentally.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–182, March–April, 1996.     

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.     

Degradation effects of dilute polymer solutions on turbulent drag reduction in pipe flows

An important practical problem in the application and study of drag reduction by polymer additives is the degradation of the polymer, for instance due to intense shearing, especially in recirculatory flow systems. Such degradation leads to a marked loss of the drag-reducing capability of the polymer.Three different polymer types were tested on degradation effects in a closed pipe flow system. The polymers used were Polyox WSR-301, Separan AP-273 and Superfloc A-110, dissolved in water in concentrations of 20 wppm each. The flow system consisted of a 16.3 mm pipe of 4.25 m length. Two different pumps were used: a centrifugal pump and a disc pump. Different solution-preparation procedures were tried and the experiments were performed at different flow rates.Superfloc A-110 proved to be both the most effective drag reducer and most resistant to degradation. Because of very fast degradation, Polyox WSR-301 was found to be unsuitable for being used as a drag reducer in re-circulatory systems. The disc pump proved to be much better suited for pumping the polymer solutions than the centrifugal pump. The degradation curve of the combination Superfloc/disc pump showed a plateau-like region with reasonable drag reduction, which makes it possible to perform (laser Doppler) measurements under nearly constant circumstances during a sufficient time.     

On the effects of dilute polymers on driven cavity turbulent flows

Effects of dilute polymer solutions on a lid-driven cubical cavity turbulent flow are studied via particle image velocimetry (PIV). This canonical flow is a combination of a bounded shear flow, driven at constant velocity and vortices that change their spatial distribution as a function of the lid velocity. From the two-dimensional PIV data we estimate the time averaged spatial fields of key turbulent quantities. We evaluate a component of the vorticity–velocity correlation, namely 〈ω₃v〉, which shows much weaker correlation, along with the reduced correlation of the fluctuating velocity components, u and v. There are two contributions to the reduced turbulent kinetic energy production −〈u v〉S_uv, namely the reduced Reynolds stresses, −〈u v〉, and strongly modified pointwise correlation of the Reynolds stress and the mean rate-of-strain field, S_uv. The Reynolds stresses are shown to be affected because of the derivatives of the Reynolds stresses, ∂〈u v〉/∂y that are strongly reduced in the same regions as the vorticity–velocity correlation. The results, combined with the existing evidence, support the phenomenological model of polymer effects propagating from the polymer scale to the velocity derivatives and through the mixed-type correlations and Reynolds stress derivatives up to the turbulent velocity fields. The effects are shown to be qualitatively similar in different flows regardless of forcing type, homogeneity or presence of liquid–solid boundaries.     

Effect of drag-reducing polymers on pseudo-slugs––interfacial drag and transition to slug flow

Drag-reducing polymers were added to air and water flowing in a stratified configuration in a horizontal 2.54 cm pipe. The interface was covered with large amplitude roll waves, that have been called pseudo-slugs, over a range of flow conditions. The damping of small wavelength waves causes a large decrease in the interfacial stress and, therefore, an increase in the liquid holdup. At superficial gas velocities greater than 4 m/s the transition to slug flow is delayed in that it occurs at larger liquid holdups. This observation is interpreted by assuming that turbulence in slugs is damped. This increases the shedding rate of a slug and, therefore, its stability. The pressure drop can increase or decrease when polymers are added. The increase in holdup is accompanied by an increase in gas velocity, which causes an increase in the pressure drop. The decrease in the interfacial stress has the opposite effect.     

分块法研究圆柱绕流升阻力

使用新的分块耦合方法，分别对单圆柱和串列双圆柱绕流进行了数值模拟．对于单圆柱绕流，低Re下计算所得到的定常涡尺寸与实验非常接近．对于串列双圆柱绕流，研究分析了改变双圆柱中心间距对上下游圆柱的升阻力系数和脉动频率所产生的影响，计算结果与实验非常吻合，为进一步研究涡致振动提供了依据．     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

Effects of buoyancy on heat transfer during turbulent flow of drag reducing fluids in vertical pipes

The effect of buoyancy on the heat transfer during upward turbulent flow of drag reducing fluids in vertical tubes has been theoretically analyzed. A criteria has been established for limiting the decrease in heat transfer to less than 5% for fluids of varying drag reducing ability. The final expression for quantitative evaluation of natural convection effect on forced convection could be applied to upward as well as downward turbulent flow of drag-reducing fluids merely by a change in sign of the controlling term.

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Einfluß des Auftriebes auf den Wärmeübergang bei turbulenter Strömung mit widerstandsreduzierenden Fluiden in vertikalen Rohren

Zusammenfassung Es wird der Einfluß des Auftriebes auf den Wärmeübergang bei turbulenter Aufwärtsströmung von widerstandsreduzierenden Fluiden in vertikalen Rohren theoretisch analysiert. Dabei wird ein Kriterium für die Begrenzung der Abnahme des Wärmeübergangs auf weniger als 5% für Fluide unterschiedlicher Widerstandsverringerung aufgestellt. Die endgültige mathematische Formulierung für die quantitative Beschreibung des Einflusses der natürlichen Konvektion auf die erzwungene Konvektion konnte sowohl auf Aufwärts-als auch auf Abwärtsströmung eines Fluids mit vermindertem Strömungswiderstand einfach dadurch angewandt werden, daß man ein Vorzeichen in dem die Strömung bestimmenden Term ändert.

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Nomenclature C _p specific heat at constant pressure (KJ/kg) - D pipe diameter (m) - De Deborah number - f friction factor - f reduced friction factor - g acceleration due to gravity (m/sec²) - Gr Grashof number - k thermal conductivity (KW/m °K) - Nu Nusselt number - Nu reduced Nusselt number - Pr Prandtl number - R pipe radius (m) - Re Reynolds number - Re reduced Reynolds number - T temperature (°C or °K) - T _b temperature of bulk of the fluid (°C or °K) - T _i initial temperature (°C or °K) - T _w wall temperature (°C or °K) - u ^* friction velocity (m/sec) - u ⁺ dimensionless axial velocity - V _m average velocity (m/sec) - y ⁺ dimensionless distance from the wall Greek symbols , functions ofDe (Table 1) - wall shear rate (sec^–1) - _fl fluid relaxation time (sec) - kinematic viscosity (m²/sec) - _B buoyant boundary layer thickness (m) - _m thickness of boundary sub-layer plus buffer layer (m) - _m ⁺ dimensionless thickness of boundary sub-layer plus buffer layer - _t thermal boundary layer (m) - density (kg/m³) - integrated density (kg/m³) - _b density of bulk of the fluid (kg/m³) - _w density of fluid at the wall (kg/m³) - _b viscosity of bulk of the fluid (Pa · sec) - _w viscosity of fluid at the wall (Pa · sec) - _w wall shear stress (N/m²) - _w reduced wall shear stress (N/m²) - change of shear stress across buoyant layer (N/m²)     

Experimental investigation on secondary currents in the turbulent flow through a straight conduit

In continuation to an earlier publication, experiments have been made in the turbulent flow through a conduit of rectangular cross-section with large aspect ratio. One of the long walls has been made rough, except for a strip, located centrally. As shown in the earlier paper, secondary currents will occur in the regions of transition from smooth to rough wall-condition. The main purpose of the investigation was to check the admissibility of the simplifying assumptions made to the mechanical-energy balance equation. The results of the measurements indeed justified the neglect of unimportant terms of this equation, leading to the following rule. When in a localized region the production is much greater (smaller) than the viscous dissipation, there must be a secondary current that transports turbulence-poor fluid into (outwards) this region and turbulence-rich fluid outwards (into) the region. Dedicated to Dr. Hans Reichardt on the occasion of his 70th birthday on the first of March, 1971.     

Calculating the flows of a viscoplastic medium in tubes using the local variation method

This article considers the problem of the motion of a visco-plastic medium in tubes and channels. The results of [1, 2] are used, which present the variational formulation and the qualitative analysis of this problem. The method of local variations suggested in [3] is used for the numerical solution of the variational problem. A more detailed presentation of the algorithm of this method in application to boundary-value and variational problems is given in [4]. Results of calculations of certain concrete problems on an electronic computer are presented.The author wishes to express his sincere gratitude to F. L. Chernous'ko for the problem formulation and helpful counsel, and G. I. Barenblatt and S. S. Grigoryan for useful discussions.