Numerical evaluation of laminar heat transfer enhancement in nanofluid flow in coiled square tubes

Convective heat transfer can be enhanced by changing flow geometry and/or by enhancing thermal conductivity of the fluid. This study proposes simultaneous passive heat transfer enhancement by combining the geometry effect utilizing nanofluids inflow in coils. The two nanofluid suspensions examined in this study are: water-Al2O3 and water-CuO. The flow behavior and heat transfer performance of these nanofluid suspensions in various configurations of coiled square tubes, e.g., conical spiral, in-plane spiral, and helical spiral, are investigated and compared with those for water flowing in a straight tube. Laminar flow of a Newtonian nanofluid in coils made of square cross section tubes is simulated using computational fluid dynamics (CFD)approach, where the nanofluid properties are treated as functions of particle volumetric concentration and temperature. The results indicate that addition of small amounts of nanoparticles up to 1% improves significantly the heat transfer performance; however, further addition tends to deteriorate heat transfer performance.     

水平管外水膜流型判据与特征长度

建立了蒸发式冷凝器水平管外水膜流动测试装置。观测发现水膜流动指示剂扩张角小于30°时,水膜湍流明显;扩张角大于50°时,水膜层流明显。研究了水平管外水膜流型随管径及喷淋量的变化,归纳出管外水膜层流临界Reynolds数阈值为15,湍流临界Reynolds数阈值为25。喷淋量增加的过程中,粗管比细管更容易达到湍流。管外水膜流动Reynolds数中的特征长度与水膜厚度一个量级。水膜越厚,特征长度越大;且管径越大,特征长度越大。     

The residence time distribution for laminar flow in helically coiled tubes

Sizable errors exist in previously published studies on the residence time distribution for ideal laminar flow in a helically coiled tubes. The numerical methods used to give corrected results are generally useful for flow situations where the projections of the streamlines on the channel cross-section are closed curves.An asymptotic solution, valid at long residence times, has been obtained. This solution confirms the numerical observation that the tail of the distribution is similar to that for laminar flow in a straight tube. If molecular diffusion is ignored, this form of asymptotic behavior is shown to be a general characteristic of all flow systems involving a fixed wall. When diffusion is considered, the asymptotic residence time distribution will be a decaying exponential in time. This confirms the widespread experimental observation that residence time distributions have exponential tails.     

组织工程多孔支架微管内流场数值模拟

骨支架内部微管结构对营养液和细胞在其内部的流动有着非常重要的影响。利用流体计算软件Fluent对不同尺寸的人工骨微管结构内部营养液和细胞的流动状况进行了数值模拟,得到了不同几何结构骨支架内部流场的速度和压力分布图。结果表明,从进口到出口,主管道内流体流速随管道的深入不断减小。上端浮克曼管中流体流速比下端浮克曼管中流体流速高,但是比同一高度主管道内流体流速低。哈佛氏管与第一行浮克曼管交叉处下端的哈佛氏管内存在流动缓慢区,第三行浮克曼管与哈佛氏管交叉处开始,流体速度不断增大。随浮克曼管长度的增加,上端哈佛氏管中流体流动的缓慢区减小;随浮克曼管直径的增加,浮克曼管中的流速有所增加,并且各微管中流体的流速更为均匀;随浮克曼管与主管道夹角的增加,骨支架各微管内流体流速更加均匀,利于细胞和营养液在各管道的输运。本数值模拟范围内,最佳骨支架结构参数为浮克曼管长度3mm,直径0.6mm,浮克曼管与主管道夹角90°。     

Augmentation of heat transfer performance in coiled flow inverter vis-à-vis conventional heat exchanger

In the present work, primarily two studies were carried out to ascertain the performance of coiled flow inverter (CFI) as heat exchanger at pilot plant scale. In the first study, performance of CFI heat exchanger has been compared with conventional heat exchangers, i.e. shell and tube heat exchanger (SHE) and plate type heat exchanger (PHE) under identical heat transfer area and process conditions. Experiments were conducted with water flowing under laminar flow regime within the flow range of 30–300 kg/h in the tube side of SHE and PHE. Friction factor and Nusselt number calculated from present experimental study in SHE and PHE were compared with the experimental data previously reported for CFI heat exchanger (Kumar et al., 2007). The Number of Transfer units (NTU) calculated in the present study for CFI was nearly 3.7–7.5 times higher as compared to SHE and 2–2.5 times higher as compared to PHE. In the second part of the study, experiments were performed first time to investigate the pressure drop and heat transfer of compressed air flowing under turbulent flow condition in CFI heat exchanger at pilot plant scale. Hot air at elevated pressures (10–30 kg/cm²) in the tube side of CFI heat exchanger with flow range 3×10⁴<N_Re<1.4×10⁵ was cooled by either cooling water or ambient air. The friction factor and Nusselt number values for compressed air flowing in the CFI were also compared with the experimental data reported in the literature for coiled tube at ambient conditions. On the basis of experimental results, new correlations for friction factor and Nusselt number of compressed air flowing under turbulent flow condition in CFI heat exchanger have been developed.     

Coiled flow inverter as a heat exchanger

In the present work attempts are made to investigate the hydrodynamics and heat-transfer characteristics of a coiled flow inverter (CFI) as heat exchanger at the pilot plant scale. The experiments are carried out in counter-current mode operation with hot fluid in the tube side and cold fluid in the shell side. Experimental study is made over a range of Reynolds numbers from 1000 to 16,000 using water in the tube side of the heat exchanger. The shell side fluids used are either cooling water or ambient air. The coiled flow inverter is made up of coils and 90^° bends and inserted in a closed shell. The shell side is fitted with three types of baffles to provide high turbulence and avoid channeling in the shell side. The bulk mean temperatures at various downstream positions are reported for different flow rate on tube side, as well as the heat transfer efficiency of the heat exchanger is also reported. Pressure drop and overall heat-transfer coefficient is calculated at various tube and shell side process conditions. The outer and inner heat-transfer coefficients are determined using Wilson plot technique. The results show that at low Reynolds numbers, heat-transfer is 25% higher as compared to coiled tubes. At high Reynolds numbers, the configuration has less influence on heat transfer. New empirical correlations are developed for hydrodynamic and heat-transfer predictions in the coiled flow inverter.     

PREDICTION OF VELOCITY PROFILES OF SHEAR THINNING FLUIDS FLOWING IN ELASTIC TUBES

Non-Newtonian fluid flow characteristics in inflatable and collapsible elastic tubes are relevant to bio-fluid mechanics and other applications. The radial velocity profiles in an elastic tube during steady laminar flow of a shear thinning aqueous solution of 1.5% carboxy methyl cellulose (CMC) were investigated using ultrasound Doppler velocimetry. The shear rate–dependent viscosities obtained using a rheometer were well represented by the Carreau model. Measured storage and loss moduli indicated the CMC solution to be inelastic up to 2% concentration. The velocity profiles were predicted by integrating the theoretical equation derived by equating the shear stress along the tube radius involving pressure drop to that of the Carreau model using its parameters. The agreement between predicted and measured velocity profiles was good. The predicted pressure drop is about the same as the experimental value at lower flow rates. In contrast, the measured pressure drop is lower than that predicted at higher flow rates due to inflation of the tube. Good agreement between estimation (Hagen-Poiseuille's law) and measurement (tube shape image analysis) for the detection of elastic tube expansion while increasing flow rates is found.     

Mechanical degradation of semi-dilute polymer solutions in laminar flows

Mechanical degradation of a semi-dilute solution of non-hydrolyzed polyacrylamide was studied under laminar flow conditions through fine capillary systems. Using a multi-pass device and capillary tubes of the same diameter and of various lengths we have shown that mechanical degradation (i) occurs at a critical value of the wall shear rate, chosen as a reference deformation rate, which is slightly higher than that of the appearance of high pressure losses in the entrance region of the capillary tube; (ii) is independent of the capillary tube length; (iii) increases with the number of passes N up to a maximum value for a limiting number of passes N_lim which is a decreasing function of deformation rates but does not depend on capillary length. The amount of degradation is expressed in terms of loss of viscous dissipation in shear and transient elongational flow. This last point is determined by studying the total end pressure loss through the capillary tube as a function of the pass number. The high pressure loss is related to viscous dissipation on macromolecules stretched by rapid converging flow. A comparison between a fresh and a fully degraded solution indicates that the degradation affects shear viscosity much less than viscous dissipation in rapid converging flow which is related to the properties of extended macromolecules. Both experimental results and theoretical interpretation suggest that, in our capillary system, the mechanical degradation occurs in the entrance region of the capillary where macromolecules are stretched and consequently submitted to extensional forces which can overcome the C–C bonds strength.     

Heat transfer to molten polymers flowing through tubes

A theoretical and experimental study of heat transfer to polymer melts flowing through circular tubes is presented. The mathematical model provides for shear heating and expansion cooling effects, and also heat of reaction during flow for various wall boundary conditions. Experimental results, obtained using low density polyethylene, show reproducible temperature and velocity profiles. The measured inlet melt temperature profile and the axial wall temperature profile provide the boundary conditions for the calculations. The experimental data confirm the predictions of the magnitude of the shear heating and expansion cooling effects during tube flow.     

3种管内强化管沸腾换热性能对比

对3种不同螺纹结构的强化管的管内沸腾换热性能进行对比实验研究, 采用R22为实验工质。3种强化管的内径和外径相同, 分别为6.9 mm和7.92 mm;管外均为光滑表面, 管内的强化结构参数则不同:螺纹的螺旋角变化范围为14°~18°, 螺纹高为0.15~0.22 mm, 螺纹槽宽度为0.1~0.2 mm。在给定进口和出口制冷剂的状态下, 通过改变管内工质的质量流速, 测试3根强化管的换热特性与质量流速的关系, 并进行性能对比。实验结果表明:3种螺纹管管内沸腾传热系数分别比光管高出60%~80%, 80%~120%和80%。分析认为, 当流动处于层状流或者层状流与环状流的过渡区时, 较大的螺旋角有利于换热;当流体处于环状流时, 较多的螺纹头数有利于换热。     

Prediction of lower/upper limiting viscosities

An analysis based on steady uniform laminar flow of a non-Newtonian fluid in a tube is presented which predicts Newtonian flow behaviour in the limits of zero and infinite shear, respectively. It is shown that an upper limiting viscosity occurs in the limit of infinite shear for a fluid with or without a yield stress, whereas a lower limiting viscosity is obtained for a fluid without a yield stress in the limit of zero shear. For a fluid with a yield stress, an infinite viscosity is found in the limit as the shear stress approaches the yield stress.     

螺旋管丙烷流动沸腾换热特性

丙烷作为自然工质具有良好的换热性能并且对环境影响较小,是替代传统制冷剂的选择。目前对于丙烷在螺旋管中沸腾传热的研究较少。实验测量了丙烷在管内径8 mm、螺旋半径42 mm、螺距21.5 mm的螺旋管中的流动沸腾传热系数。实验采用套管的形式,在螺旋管外用恒温水对丙烷进行加热,调整水入口温度与水流量得到不同的热通量。实验表明,螺旋管对流动沸腾换热具有一定的强化作用。实验数据与已有的螺旋管流动沸腾换热关联式进行了比较,在6 kW·m⁻²以下的低热通量时,Guo（1998）换热关联式比Ji（2015）预测准确度更高,推荐使用Guo（1998）关联式。     

Caractéristiques rhéologiques des suspensions de tourbe

The flow of peat suspensions in water has been studied in the concentration range of 0.75 to 2.25% by weight on a dry basis; the fibre size was below 3 mesh. The pressure drop has been measured, for an extensive range of flow rates (the Reynolds numbers varying from 10³ to 10⁵), in 3 horizontal tubes, the internal diameter of which was 50.8, 38.1 and 25.4 millimeters, respectively. The results have shown that the deviation from the new-tonian behaviour increased with the concentration and the tube diameter. A comparison with dilute pulp slurries has indicated that the behaviour of both suspension had the same characteristics. The fibre suspensions are non-homogeneous fluids and the conventional rheological models cannot describe their behaviour. The annular ring model, which implies the presence, in a laminar flow, of an entangled-fibre network, explains the experimental results obtained. A size analysis of the particles has shown that the type of pump used had an effect on the fibre degradation.     

Modelling laminar pulsed flow in rectangular microchannels

Fully developed laminar pulsed flow of an incompressible Newtonian fluid through rectangular ducts has been modelled and analyzed using Green functions. Based on the solutions for the velocity profile presented previously [Fan, C., Chao, B.-T., 1965. Unsteady, laminar, incompressible flow through rectangular ducts. Zeitschrift für Angewandte Mathematik und Physik 16, 351-369], exact analytical solutions in series form for wall shear stress and volumetric flow rate have been obtained. Various flow effects in periodic pulsed flow through rectangular microchannels, including flow reversal, phase shift and wall shear stress enhancement were calculated indicating that a substantial increase in local wall shear stress can be achieved with a modest increase of average flow rate over a cycle. The analytical solutions and the calculated results will help optimize parameters in cleaning of microfluidic devices by pulsed flow.     

CONVECTIVE TRANSPORT IN A ROTATING COILED TUBE

Regular perturbation techniques are used to study fully developed mass transfer in fluids flowing through rotating coiled tubes. A double series solution of the governing mass balance equation is developed for a constant wall flux boundary condition. The local, asymptotic mass transfer Nusselt number is computed from these results. Within the estimated region of validity of this solution the convective mass transfer coefficient is found to depend on essentially three independent dimensionless parameters. Mass transfer relative to the stationary coiled tube solution will either increase or decrease with rotation depending on the relative orientation of the fluid and rotational velocities.     

Compartmental modelling of stirred tank for flocculation requiring a minimum critical shear rate

In uniform shear flow, a minimum critical shear rate is known to be present during flocculation of a partially destabilized suspension so that at shear rates below the critical value, the flocculation rate is zero. In a stirred tank with distributed shear rates, it is possible for the shear rates in some parts of the tank to be below the critical value. In this paper the flocculation kinetics are described by a compartmental model in which zones of low shear rate are treated as a separate compartment. The theoretical flocculation rate for a monosized suspension is obtained by numerical integration from the mean shear rate for the whole tank, or from the stirring speed in a given geometry.     

不同倾角放置螺旋管汽波两相摩擦阻力特性

在宽广的参数范围内试验研究了螺旋管在不同倾角放置时的单相及汽液两相摩擦阻力特性,获得了螺旋管放置方向及各主要系统参数对汽液两相摩擦阻力特性的影响规律。在对试验结果及前人研究结果进行详细分析的基础上,获得了第一个能适用于不同倾角放置螺旋管的单相及汽液两相摩擦阻力计算式,从而为汽液两相摩擦阻力及螺旋管的进一步研究和应用提供了依据。     

Studies on cocurrent gas-liquid flow in helically coiled tubes. I. Flow patterns,pressure drop and holdup

The effects of tube diameter, coil diameter, helix angle and liquid viscosity on flow patterns, pressure drop and holdup for cocurrent gas-liquid flow in helically coiled tubes have been investigated. Nine coils of varying coil diameter and helix angle have been used with liquids of three different viscosities and air at varying pressures. The effect of tube diameter on pressure drop and holdup was determined by using tubes of diameters up to 2-in. Flow patterns were adequately predicted for all the systems by Baker's plot. Small helix angles were found to have no effect on pressure drop or holdup in coiled tubes. Both pressure drop and holdup could be adequately correlated using the Lockhart-Martinelli approach with modified correlating parameters.     

Modeling of flow dynamics in laminar aerosol flow tubes

Flow behaviour in laminar aerosol flow tubes was investigated using a Computational Fluid Dynamics (CFD) model. Since these flow tubes are typically operated at low gas velocity, even small temperature gradients produce convection currents strong enough to interfere with laminar flow. This results in recirculation, causing the residence times of aerosol particles to be poorly defined. The situation is exacerbated when temperature inversions are present, or when the flow direction and temperature are changed simultaneously. We analyzed several characteristic flow tube configurations to define the range of experimental conditions that will ensure a laminar flow profile with minimal recirculation. For a laminar flow situation, we evaluated the extent of diffusion-controlled exchange between aerosol and the flow tube wall.     

一种新型变截面换热管强化传热性能

针对工程中广泛存在的管内层流换热传热系数低的问题进行了强化传热研究,并在传热强化理论的指导下,开发了一种新型变截面换热管。分别建立不同参数下的新型变截面换热管和普通圆管模型,采用大型CFD分析软件FLUENT借助数值模拟的方法,研究新型变截面换热管结构对管内层流换热的影响。研究结果表明,该新型变截面换热管在层流情况下可较大程度地强化管内换热,而其流阻增加较小,具有良好的综合强化传热性能。在本文研究的范围内,变截面换热管的Nu和η均随L₁/d_i或L₂/d_i的减小而增大,且η>2.22。计算结果为强化管内层流换热提供了一定的指导和理论依据。