Friction factor correlations for gas–liquid/liquid–liquid flows with drag-reducing polymers in horizontal pipes

In the present paper, two correlations have been developed to predict the effect of DRP on friction factor of two-phase flow for any pipe diameter. The correlations have been verified using published experimental results of DRP added to air–liquid annular flow and for oil–water flows with any flow pattern at the asymptotic state (maximum drag reduction). Such correlations are not available in literature and considered to be very useful in predicting the drag reduction using DRP and in understanding the most significant parameters that affecting the mechanism of drag reduction by polymers in multiphase flow.     

An experimental investigation of heat transfer to pulsating pipe air flow with different amplitudes

Heat transfer characteristics to both laminar and turbulent pulsating pipe flows under different conditions of Reynolds number, pulsation frequency, pulsator location and tube diameter were experimentally investigated. The tube wall of uniform heat flux condition was considered for both cases. Reynolds number varied from 750 to 12,320 while the frequency of pulsation ranged from 1 to 10 Hz. With locating the pulsator upstream of the inlet of the test section tube, results showed an increase in heat transfer rate due to pulsation by as much as 30% with flow Reynolds number of 1,643 and pulsation frequency of 1 Hz, depending on the upstream location of the pulsator valve. Closer the valve to the tested section inlet, the better improvement in the heat transfer coefficient is achieved. Upon comparing the heat transfer results of the upstream and the downstream pulsation, at Reynolds number of 1,366 and 1,643, low values of the relative mean Nusselt number were obtained with the upstream pulsation. Comparing the heat transfer results of the two studied test sections tubes for Reynolds number range from 8,000 to 12,000 and pulsation frequency range from 1.0 to 10 Hz showed that more improvement in heat transfer rate was observed with a larger tube diameter. For Reynolds number ranging from 8,000 to 12,000 and pulsation frequency of 10 Hz, an improvement in the relative mean Nusselt number of about 50% was obtained at Reynolds number of 8,000 for the large test section diameter of 50 mm. While, for the small test section diameter of 15 mm, at same conditions of Reynolds number and frequency, a reduction in the relative mean Nusselt number of up to 10% was obtained.     

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.     

Heat transfer characteristics and Nusselt number correlation of turbulent pulsating pipe air flows

Heat transfer characteristics to turbulent pulsating pipe flows under a wide range of Reynolds number and pulsation frequency were experimentally investigated under uniform heat flux condition. Reynolds number was varied from 8462 to 48540 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by both pulsation frequency and Reynolds number. Enhancements in mean Nusselt number of up to 50% were obtained at medium pulsation frequency between 4.1 and 13.9 Hz for Reynolds number range of 8462 to 14581. An enhancement of up to 50% in mean Nusselt number was obtained at high pulsation frequency range between 13.9 and 29.5 Hz, specially as Reynolds number is close to 15000, while a reduction was observed at higher Reynolds number more than 21200. This reduction, at high Reynolds number, increased as pulsation frequency increased. Also, there was a reduction in mean Nusselt number of up to 20% that obtained at low pulsation frequency range between 1 and 4.1 Hz for Reynolds number range of 8462 to 48543. A significant reduction in mean Nusselt number of up to 40% was obtained at medium pulsation frequency between 4.1 and 13.9 Hz for Reynolds number range of 21208 to 48543. Empirical equations have been developed for the relative mean Nusselt number that related to Reynolds number and dimensionless frequency with about uncertainty of 10% rms.The support of both King Fahd University of Petroleum and Minerals and Cairo University for this research is acknowledged.     

超声速钝体逆向喷流减阻的数值模拟研究

为研究逆向喷流技术对超声速钝体减阻的影响,采用标准k-ε湍流模型,通过求解二维Navier-Stokes方程对超声速球头体逆向冷喷流流场进行了数值模拟,并着重分析了喷口总压、喷口尺寸对流场模态和减阻效果的影响。计算结果显示:随着喷流总压的变化,流场可出现两种流动模态,即长射流穿透模态和短射流穿透模态;喷流能使球头体受到的阻力明显减小;存在最大减阻临界喷流总压值(在所研究参数范围内最大减阻可达51.1%);在其它喷流物理参数不变时,随着喷口尺寸的增大,同一流动模态下的减阻效果下降。本文的研究对超声速钝体减阻技术在工程上的应用具有一定的参考价值。     

Pathline analysis of traveling wavy blowing and suction control in turbulent pipe flow for drag reduction

Skin friction drag is much greater in turbulent flows as compared with that in laminar flows. It is well known that traveling wave control can be used to achieve a large drag reduction. In the present study, a direct numerical simulation of a turbulent pipe flow was performed to clarify the mechanism of the drag reduction caused by the traveling wave control. The flow induced by the control was evaluated using pathline analysis. Near the wall, a “closed flow” was formed, wherein the injected particles return to the wall owing to the suction flow. The random component of Reynolds shear stress was perfectly suppressed in the closed flow, which suggests that there was no turbulence. The controlled flow was categorized into four patterns, and each flow characteristic and drag reduction effect was discussed. When the closing rate is high, the drag decreases, while when the closing rate is low, i.e., when the injected particles are released into the main flow, the turbulence is maintained. If the thickness of the layer suppressing turbulence is insufficient, a significant effect in terms of the drag reduction cannot be expected. The large drag reduction owing to the traveling wave control can be attributed to the elimination of turbulence in the region near the wall.     

Experimental study on the effect of pulsating inflow to an enclosure for improved mixing

Optimal control of inlet jet flows is of broad interest for enhanced mixing in ventilated rooms. The general approach in mechanical ventilation is forced convection by means of a constant flow rate supply. However, this type of ventilation may cause several problems such as draught and appearance of stagnation zones, which reduces the ventilation efficiency. A potential way to improve the ventilation quality is to apply a pulsating inflow, which has been hypothesised to reduce the stagnation zones due to enhanced mixing. The present study aims at testing this hypothesis, experimentally, in a small-scale two-dimensional water model using Particle Image Velocimetry with an in-house vortex detection program. We are able to show that for an increase in pulsation frequency or alternatively in the flow rate the stagnation zones are reduced in size and the distribution of vortices becomes more homogeneous over the considered domain. The number of vortices (all scales) increases by a factor of four and the swirl-strength by about 50% simply by turning on the inflow pulsation. Furthermore, the vortices are well balanced in terms of their rotational direction, which is validated by the symmetric Probability Density Functions of vortex circulation (Γ) around Γ = 0. There are two dominating vortex length scales in the flow, namely 0.6 and 0.8 inlet diameters and the spectrum of vortex diameters become broader by turning on the inflow pulsation. We conclude that the positive effect for enhanced mixing by increasing the flow rate can equally be accomplished by applying a pulsating inflow.     

垂直下降管中两相流的流型以及液相粘度对流型的影响

对空气－油在垂直下降管中的流型进行了实验研究，采用的管径为２９ｍｍ，油和空气的折算流速分别达到４ｍ／ｓ和２０ｍ／ｓ，并借助于压降脉动分析和目测观察相结合的方法来进行流型的识别。研究表明，油气两相流的流型不同于低粘液体的两相流流动，通过实验研究并结合前人的研究成果，给出了液相粘度对流型转变的影响趋势。     

Compressible gas-liquid mixture flow at abrupt pipe enlargements

A detailed investigation was made of the flow of compressible gas-liquid mixtures through sudden enlargements in diameter of circular pipes. One-dimensional analysis shows that the dimensionless pressure rise varies with mixture void fraction and mixture momentum, while the establishment of choking conditions at the enlargement is controlled by the length of pipe downstream in which frictional pipe flow occurs. The flows were found to exhibit two characteristic modes, jet flow and submerged flow, with intermediate flows displaying unsteady oscillation between these modes. The distance to the downstream position of maximum pressure increased steadily with mixture void fraction when the upstream pipe outlet was choked, varying from 5 to 50 times the downstream pipe diameter. If the flow was not choked, this distance was much smaller and showed discrete fixed values associated with the mode of flow.

One-dimensional analysis accurately predicted maximum pressure, but when flow was choked at the enlargement the calculation was sensitive to the pressure in the region of separated flow surrounding the central jet in the enlargement. Although analysis of maximum pressure in terms of flow expansion and normal shock gave a general indication of the maximum pressure (which was thus concluded to depend on the general flow processes expected in the enlargement), accurate prediction of maximum pressures will depend on empirical knowledge of the separated flow region pressures. The maximum pressure rise was found to be in the range extending down to 0.3 of the upstream pipe outlet pressure and reduced with void fraction; it was also influenced by the enlargement area ratio. Flows in the approach and outlet pipes were found to be compressible, frictional pipe flows of the Fanno type, with somewhat reduced friction factors occurring in the outlet pipe.     

Modeling fluid-particle interaction in dilute-phase turbulent liquid-particle flow simulation

The present work examines the predictive capability of a two-fluid CFD model that is based on the kinetic theory of granular flow in simulating dilute-phase turbulent liquid-particle pipe flows in which the inter-stitial fluid effect on the particle fluctuating motion is significant.The impacts of employing different drag correlations and turbulence closure models to describe the fluid-particle interactions(i.e.drag force and long-range interaction)are examined at both the mean and fluctuating velocity levels.The model pre-dictions are validated using experimental data of turbulent liquid-particle flows in a vertical pipe at different particle Reynolds numbers(ReP > 400 and ReP < 400),which characterize the importance of the vortex shedding phenomenon in the fluid-phase turbulence modulation.The results indicate that(1)the fluctuating velocity level predictions at different ReP are highly sensitive to the drag correlation selec-tion and(2)different turbulence closure models must be employed to accurately describe the long-range fluid-particle interaction in each phase.In general,good agreement is found between the model predic-tions and the experimental data at both the mean and fluctuating velocity levels provided that appropriate combinations of the drag correlation and the turbulence closure model are selected depending on Rep.     

Effect on the flow and heat transfer characteristics for sinusoidal pulsating laminar flow in a heated square cylinder

Two-dimensional numerical simulation is performed to understand the effect of flow pulsation on the flow and heat transfer from a heated square cylinder at Re = 100. Numerical calculations are carried out by using a finite volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid. The effects of flow pulsation amplitude (0.2 ≤ A ≤ 0.8) and frequency (0 ≤ f _p  ≤ 20 Hz) on the detailed kinematics of flow (streamlines, vorticity patterns), the macroscopic parameters (drag coefficient, vortex shedding frequency) and heat transfer enhancement are presented in detail. The Strouhal number of vortices shedding, drag coefficient for non-pulsating flow are compared with the previously published data, and good agreement is found. The lock-on phenomenon is observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, time averaged drag coefficient and heat transfer from the square cylinder is substantially augmented, and when the pulsating frequency in about the natural vortex shedding frequency, the heat transfer is also substantially enhanced. In addition, the influence of the pulsating amplitude on the time averaged drag coefficient, heat transfer enhancement and lock-on occurrence is discussed in detail.     

Heat transfer in laminar pulsating flows of fluids with temperature dependent viscosities

The effect of time-dependent pressure pulsations on heat transfer in a pipe flow with constant temperature boundaries is analysed numerically when the viscosity of the pulsating fluid is an inverse linear function of the temperature. The coupled differential equations are solved using Crank-Nicholson semi-implicit finite difference formulation with some modifications.The results indicate local variations in heat transfer due to pulsations. They are useful in the design of heat exchangers working under pulsating flow conditions. The analytical results are presented for both heating and cooling. The conditions under which pulsating flows can augment the heat transfer are discussed. The results are applicable for heat exchangers with fluids of high Prandtl number.     

Drag reduction and improvement of material transport in creeping films

It is widely accepted that for bodies in turbulent flows a reduction of skin friction can be reached if the surface of the body is provided with small ridges aligned in the local flow direction. This surprising and counterintuitive phenomenon is called the shark-skin effect, motivated from the dermal surface morphology of sharks. In the present article we examine the possibility of resistance reduction due to a rippled surface topography in Stokes flow. We especially analyse the influence of wall riblets perpendicular to the flow direction on the mean transport velocity in gravity-driven creeping film flows following the idea that eddies generated in the valleys of the riblets act like fluid roller bearings and hence may reduce drag. Using a theoretical treatment of the Stokes equations with complex function theory, parameter studies with varying flow rate, bottom amplitude and bottom shape are presented. For the given bottom shapes the maximum enhancement of transport velocity is found by optimising the film thickness.     

Analysis of polymer drag reduction mechanisms from energy budgets

The transfer of energy in drag reducing viscoelastic flows is analyzed through a sequence of energetic budgets that include the mean and turbulent kinetic energy, and the mean polymeric energy and mean elastic potential energy. Within the context of single-point statistics, this provides a complete picture of the energy exchange between the mean, turbulent and polymeric fields. The analysis utilizes direct simulation data of a fully developed channel flow at a moderately high friction Reynolds number of 1000 and at medium (30%) and high (58%) drag reduction levels using a FENE-P polymeric model.Results show that the primary effect of the interaction between the turbulent and polymeric fields is to transfer energy from the turbulence to the polymer, and that the magnitude of this transfer does not change between the low and high drag reduction flows. This one-way transfer, with an amplitude independent of the drag reduction regime, comes in contradiction with the purely elastic coupling which is implicit within the elastic theory of the polymer drag reduction phenomenon by Tabor and De Gennes (Europhys. Lett. 2, pp. 519–522, 1986).     

Drag reduction and heat transfer in surfactant solutions with excess counterion

We present the results of a study of turbulent drag reduction in a small circulating loop using surfactant solutions with excess counterion. In addition, these solutions were used in measurements of heat transfer, both in pipe flow and in an impinging jet. Both frictional drag and heat transfer were reduced in the pipe flow experiments. Measurements of heat transfer in the impinging jet revealed a dependence on the molar concentration ratio of the counterion. When the counterion was added at a molar concentration 30 times higher than that of the surfactant, the resulting surfactant solution did not reduce the rate of heat transfer in the impinging jet. By using this surfactant system in an impinging jet, we show both a reduction in pipe friction and normal heat transfer potential in a circulating heat exchange system. In order to investigate this difference in heat transfer between pipe flows and impinging jet flows, a comparison was made of the wall shear stress between these two flow regimes. The estimated wall shear stress was of the same order in both flows, and thus was not considered to be the primary cause of the difference in heat transfer. It is instead suggested that the micellar structure of the surfactant is influenced by a compressive deformation of the impinging flow in a manner that is different from the shear deformation observed in pipe flow.     

Influence of drag laws on pressure and bed material recirculation rate in a cold flow model of an 8 MW dual fluidized bed system by means of CPFD

A cold flow model of an 8 MW dual fluidized bed (DFB) system is simulated using the commercial computational particle fluid dynamics (CPFD) software package Barracuda. The DFB system comprises a bubbling bed connected to a fast fluidized bed with the bed material circulating between them. As the hydrodynamics in hot DFB plants are complex because of high temperatures and many chemical reaction processes, cold flow models are used. Performing numerical simulations of cold flows enables a focus on the hydrodynamics as the chemistry and heat and mass transfer processes can be put aside. The drag law has a major influence on the hydrodynamics, and therefore its influence on pressure, particle distribution, and bed material recirculation rate is calculated using Barracuda and its results are compared with experimental results. The drag laws used were energy-minimization multiscale (EMMS), Ganser, Turton–Levenspiel, and a combination of Wen–Yu/Ergun. Eleven operating points were chosen for that study and each was calculated with the aforementioned drag laws. The EMMS drag law best predicted the pressure and distribution of the bed material in the different parts of the DFB system. For predicting the bed material recirculation rate, the Ganser drag law showed the best results. However, the drag laws often were not able to predict the experimentally found trends of the bed material recirculation rate. Indeed, the drag law significantly influences the hydrodynamic outcomes in a DFB system and must be chosen carefully to obtain meaningful simulation results. More research may enable recommendations as to which drag law is useful in simulations of a DFB system with CPFD.     

Robust design and numerical simulation on drag reduction by a mixture film for liquid turbulence in a channel

An important way of increasing the speed and lowering the fuel consumption of ships is by decreasing the frictional drag. One of the most promising techniques for reducing drag is the use of air bubbles. The goal of this investigation is to establish a set of optimum robust parametric levels for drag reduction by a mixture (air–water) film in turbulent channel flow. Based on the conditions laid out by the Taguchi orthogonal array method, turbulent flows, with air bubbles injected into a channel, are simulated using commercial computational fluid dynamics software. The local shear stress on the upper wall is computed to evaluate the efficiency of drag reduction. Many factors can affect drag reduction. The factors investigated in this study are the rate of air injection, bubble size, area of air injection, flow speed, and measured position of the shear stress. These factors have been investigated through the analysis of variance, which has revealed that the rate of air injection and water flow speed dominate the efficiency of drag reduction by a mixture film. According to the results, the drag can be reduced by an average of 83.4%; and when the configuration of the parametric levels is optimum the maximum drag reduction of 88.5% is achieved. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow and mixing characteristics of pulsed confined opposed jets in turbulent flow regime

A numerical study is performed on a two-dimensional confined opposed-jet configuration to gain basic understanding of the flow and mixing characteristics of pulsed turbulent opposed-jet streams. The sinusoidal pulsating flows with different temperature are imposed at opposed-jet inlets, which are mixed with each other in a confined flow channel. The current mathematical model taking the effect of temperature-dependent thermo-physical properties of fluid into account can present a good prediction for opposed-jet streams compared with experimental data. The numerical results indicate that introduction of temperature difference between opposed jet flows can lead to an asymmetric flow field immediately after jet impact, and the sinusoidal flow pulsations can effectively enhance mixing rate of opposed jets. Parameter studies are conducted for optimization of pulsed opposed jets. The effect of Reynolds number and flow pulsation as well as the configuration geometry on the mixing performance are discussed in detail. Examination of the flow and thermal field shows that the mixing rate is highly dependent on the vortex-induced mixing and residence time of jet fluid in the exit channel.     

On pipe diameter effects in surfactant drag-reducing pipe flows

Remarkable power saving in a fluid transport system is possible if the surfactant drag reduction technology is used. Application of surfactant drag reduction to district heating and cooling systems has been investigated in the past. The establishment of the scale-up law in drag-reducing pipe flows is one of the most important problems in this application. Main purpose of this study is aimed to develop a reliable scale-up law in surfactant drag-reducing flows. As the basic data of surfactant solutions, both non-Newtonian viscosity and viscoelasticity were experimentally determined. A turbulent eddy diffusivity model based on the Maxwell model was employed to estimate the drag reduction of surfactant solutions. The predictions by the turbulence model developed in this study with proper rheological characteristics of surfactant solutions has resulted in a reliable estimation of the pipe diameter effect in surfactant drag-reducing flows over the pipe diameter range from 11 to 150mm. Received: 30 June 1997 Accepted: 29 December 1997     

Experimental investigations of flow field and heat transfer characteristics due to periodically pulsating impinging air jets

The paper concentrates on increasing convective heat transfer due to periodically pulsating impinging air jets. A maximum enhancement rate of cooling effectiveness up to 20% could be detected at an excitation Strouhal number of Sr = 0.82 when using a high pulsation magnitude. Reductions up to 5% occured at low Strouhal numbers with coincident high pulsation magnitudes as well. The thermal results were completed with phase-locked flow field investigations by means of PIV and surface visualizations using the oil film method.