最大叶片式桨流体动力学性能的数值模拟

运用CFD方法研究了最大叶片式桨在层流区域内的流体动力学性能,模拟体系为高粘度牛顿流体和非牛顿流体,主要考察桨叶的功耗特性、Metzner常数、剪切性能和排液性能. 结果表明,功耗计算值与文献实验值基本一致;桨叶的Metzner常数ks=10与流变行为指数n无关;搅拌形成双循环流型,釜中部桨叶所在区剪切速率大、排液量大,产生的漩涡流也大,导致剪切效率低于0.5;随雷诺数增加(Ren=1.4, 5.0, 7.6),全釜平均剪切速率(3.40, 9.91, 15.05 s-1)和全釜平均排液量(0.0014, 0.0033, 0.0052 m3/s)逐渐增加,尤其是桨叶下端两翼区平均剪切速率(4.36, 11.48, 16.35 s-1)和平均排液量(0.0026, 0.0064, 0.0095 m3/s)增加相对较大. 说明Ren增加,搅拌混合作用加强,剪切速率大产生的界面积大,排液量大使高低剪切区内流体快速循环,有利于流体高效混合.     

Mixing of newtonian and non-newtonian liquids: Screw agitator and draft coil system

Mixing efficiency and power consumption have been investigated for several Newtonian and non-Newtonian liquids in a novel system consisting of a screw agitator rotating in a draft coil. For Reynolds numbers larger than 50, the inertial forces increase the pumping capacity of the screw impeller and hence its mixing efficiency. Shear-thinning effects can be accounted for by taking the effective rate of deformation to be proportional to the impeller rotational speed. Elasticity effects could be satisfactorily correlated with the Weissenberg number. The ratio of the mixing time to the average circulation time is constant. The power number could not be correlated with the Reynolds number; however, the ratio of the power number to the circulation number is inversely proportional to the Reynolds number for Newtonian as well as for shear-thinning inelastic fluids. The power consumption for elastic fluids is much larger.     

流体流变性对错位六弯叶桨流场特性的影响

利用计算流体力学(CFD)的方法,以高黏牛顿流体和假塑性非牛顿流体为研究对象,对错位六弯叶桨在层流域的搅拌流场特性进行了研究。结果表明:数值计算得到的功率值与实验测量值吻合较好,搅拌雷诺数对假塑性流体搅拌流场的量纲一速度和切应变速率影响较大,因此提高转速对改变流场的速度及切应变速率分布是一个有效的办法;而流体的流变性只对假塑性流体的量纲一速度有明显影响,对切应变速率影响较小,当流变指数n<0.3时与n基本无关。当流动由层流向过渡流转变时,搅拌桨的流量准数及泵送效率有显著提高;假塑性流体的流变指数降低时,其泵送效率显著下降。研究进一步认识了错位桨在不同流体中的搅拌流场特点,为高黏假塑性流体搅拌桨的设计、应用以及开发新型搅拌桨提供了参考。     

新型同心双轴搅拌器功率与混合特性的数值模拟

基于同心双轴搅拌器的结构与运行特点,建立了兼顾其流动、混合过程的三维数学模型,并以过程工业应用较多的两种不同尺寸双层组合桨作为内桨、框式桨作为外桨构成的同心双轴搅拌器为研究对象,数值模拟了其在中高黏牛顿流体中同向及反向转动模式的功率特性、流场特性及混合特性。模拟结果表明,同向转动模式下,整个系统的搅拌功耗更小、混合效率更高;外桨功耗受内桨影响较大,一般随内桨转速的增大,恒速外桨的功耗同向转动时会减小、反向转动时会增大;对由桨式搅拌器构成的组合式内桨而言,当内桨直径与釜体直径之比为0.35左右时,相同Reynolds数下的单位体积混合能更小;中高黏牛顿流体中,同心双轴搅拌器的内桨采用上层六斜叶桨+下层六直叶桨的组合形式时更高效节能,仅在体系Reynolds数小于36时,上层二斜叶桨+下层二直叶桨的内桨组合形式才具有相对优势。     

Effect of impeller type on continuous‐flow mixing of non‐Newtonian fluids in stirred vessels through dynamic tests

Mixing of non‐Newtonian fluids with axial and radial flow impellers is prone to a significant extent of nonideal flows (e.g., dead zones and channelling) within the stirred reactors. To enhance the performance of the continuous‐flow mixing of pseudoplastic fluids with yield stress, close‐clearance impellers were utilised in this study. We explored the effects of various parameters such as the type of close‐clearance impeller (i.e., the double helical ribbon (DHR) and anchor impellers), impeller speed (25–500 rpm), impeller pumping direction, fluid rheology (0.5–1.5% xanthan gum solution), fluid flow rate (3.20–14.17 L min^?1) and the locations of outlet (configurations: top inlet–top outlet, top inlet–bottom outlet) on the dynamic performance of the mixing vessel. The performance of the DHR impeller was then compared to the performance of various types of impellers such as axial‐flow (Lightnin A320) and radial‐flow (Scaba 6SRGT) impellers. The dynamic tests showed that the DHR impeller was the most efficient impeller for reducing the extent of nonideal flows in the continuous‐flow mixer among the impellers employed in this study. In addition, the mixing quality was further improved by optimising the power input, increasing the mean residence time, decreasing the fluid yield stress, using the up‐pumping impeller mode and using the top inlet–bottom outlet configuration. © 2011 Canadian Society for Chemical Engineering     

螺带桨搅拌槽内给热系数和所需功率的研究

本文详细研讨了螺带桨搅拌槽内给热系数及其与所需功率的关系.研究中使用了4个不同几何尺寸的螺带装以及8种不同稠度的假塑性非牛顿流体和高粘度牛顿流体.结果表明:在雷诺数小于0.1时,试验流体在槽内的给热系数与浆叶几何尺寸有关.通过回归分析法得到了4个对应于各螺带桨的给热系数关联式;雷诺数大于10时,给热系数和搅拌浆几何尺寸无关,从而得出一个适用于不同螺带浆的共同关联式.实验还研究了给热系数和所需搅拌功率的关系,并用多项式回归法得到了整个实验雷诺数范围的传热-搅拌功率关联式.     

锚式搅拌槽中高粘弹性流体的流速分布及其功率消耗

用照相法测定了锚式搅拌槽中高粘弹性流体的流型和流速分布,另测定了搅拌功率消耗,结果发现:1.与牛顿流体相比,在低Re数下,粘弹性流体的切向速度较大,而径向速度则较小.2.转速相同时,在高剪切率区域,粘弹性流体的剪切率大于牛顿流体.由CEF方程导出功率计算式N_pRe_af_s~(1-n)=k_pf_vf_s~2[1+F_1avf_s~(m-n-3)Wi/K_s~2]用实验数据确定f_(?)和F_(1av),得到可适用于牛顿流体、假塑性流体和粘弹性流体的普适功率计算式,计算结果与实验值比较接近.     

Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime

A computational fluid dynamics (CFD) model of flow in a mixing tank with a single axial-flow impeller was developed with the Fluent^TM software. The model consists of an unstructured hexagonal mesh (158,000 total cells), dense in the region from the surface of the impeller. The flow was modeled as laminar and a multiple reference frame approach was used to solve the discretized equations of motion in one-quarter of a baffled tank. A solution of 0.1% Carbopol in water, a shear-thinning fluid, was found to be clear enough to measure impeller discharge angles using laser Doppler velocimetry. This is the first time that impeller discharge angles have been reported in the literature for a shear-thinning fluid with a hydrofoil impeller. Rheological measurements indicated that the Carbopol solution can be characterized by the power law (K=9,n=0.2) under the range of shear conditions (0.1- expected near the impeller in the mixing tank. The CFD model accurately predicted the dependence of power number and discharge angle on Reynolds number (as predicted by Metzner and Otto), for an A200 (pitched blade turbine or PBT) and an A315 (Hydrofoil) impeller operating in the transitional flow regime (Reynolds numbers: 25-400) with glycerin and 0.1% Carbopol solutions. Subsequently, the results of a systematic CFD study with power law fluids indicated that the power number and discharge angle of an axial-flow impeller in the transitional flow regime depends not only on the Reynolds number (as determined by Metzner and Otto's method) but also on the flow behavior index n. Consequently, an alternative to Metzner and Otto's method was pursued. The results of converged CFD simulations indicate that the near-impeller “average shear rate” increases not only with increasing RPM (as proposed by Metzner and Otto), but also with decreasing flow behavior index (n) and discharge angle in the transitional flow regime. Considering this result, an improved method of estimating the power number and discharge angle for power law fluids in the transitional flow regime is proposed.     

Reduced IMRs in a mixing tank via agitation improvement

Mixing of Newtonian fluids in a stirred tank at low Reynolds numbers was investigated experimentally by means of a visual decolourization technique and shaft power measurements. The research was focused on the Isolated Mixing Regions (IMRs), which are “doughnut-shaped” structures in a stirred tank exhibiting little mixing with bulk of the fluids. The effect of Reynolds number on the IMRs was determined. The critical Reynolds numbers beyond which IMRs are destroyed were presented. The study was focused on agitation design which consumes less power input to destroy the IMRs. A pitch-bladed impeller with an alternating pitch was found more energy efficient than other test impellers in eliminating IMRs in both baffled and unbaffled configurations. It was also found that dramatic reduction in the power consumption could be achieved with installation of baffles to eliminate IMRs at typically low Reynolds numbers. The improved energy efficiency was thought related to generation of more chaotic mixing from the disturbance generated by the baffles, or impeller blade asymmetry such as alternating pitch. An energy parameter was introduced to account for the mixing time scale and the power required in regimes above the critical Reynolds number, in order to evaluate the energy efficiency when IMRs are non-existent.     

Determination of Mixing Times with Helical Ribbon Impeller for Non‐Newtonian Viscous Fluids Using an Advanced Imaging Method

New results on mixing times for viscous Newtonian and non‐Newtonian fluids being homogenized with a helical ribbon impeller are presented. In particular, a recently developed technique to determine the macromixing kinetics of an impeller in a transparent vessel was applied to investigate the effects of rheological properties on mixing times. Significant differences were observed in the mixing times for viscous Newtonian and non‐Newtonian fluids. Based on the new data obtained in this work, a correlation incorporating the elastic effects is proposed in terms of a Weissenberg number for predicting the mixing time as a function of the Reynolds number and the system geometry.     

Mixing of a lignin‐based slurry fuel

Lignin‐based slurry fuels are a potential alternative to fossil fuels in kraft pulp mills. Lignogels — mixtures of lignin, fuel oil, water and surfactant — are non‐Newtonian fluids, with shear‐thinning and thixotropic behaviour. Their mixing was investigated in tanks with volumes of 3 and 30 L. An A310 hydrofoil impeller was used in all experiments. Results were compared with measurements in Newtonian fluids, used to characterize the impeller over a broad range of Reynolds numbers (1–500 000). An aqueous CMC solution was also used for characterization of the impeller and estimation of the Metzner‐Otto constant. Results in the transition region were corrected by introduction of two empirical parameters.     

Some Characteristics of Stirred Vessel Flows of Dilute Polymer Solutions Powered by a Hyperboloid Impeller

Measurements of the power consumption and mean and turbulent velocities in the wall jet of a stirred vessel flow, powered by a hyperboloid impeller, were carried out. The fluids were aqueous solutions of tylose, CMC and xanthan gum (XG), at weight concentrations ranging from 0.1% to 0.6%, which exhibited varying degrees of shear‐thinning and viscoelasticity. The hyperboloid impeller parameter k of Metzner and Otto (1957) was found to be equal to 27.2 ±4. In the Reynolds number range of 10³ to 3 × 10⁴ the mixing power was reduced for all non‐Newtonian fluids, but never by more than 13%. The flows of the 0.2% CMC and 0.2% XG solutions were found to be less turbulent than those of water, especially for the latter fluid where a reduction in axial rms in excess of 50% was found in the wall jet. This was attributed to elasticity effects and especially to the high zero shear viscosity of the latter fluid.     

Using Tomography to Characterize the Mixing of Non‐Newtonian Fluids with a Maxblend Impeller

The flow field inside a cylindrical mixing vessel was visualized by electrical resistance tomography (ERT), a non‐intrusive measurement technique. Six tomography planes, each containing 16 sensing electrodes, measured the mixing time in the agitation of pseudoplastic fluid exhibiting yield stress. The effects of various parameters such as impeller types, impeller speed, fluid rheology, power consumption, Reynolds number, and absence of baffles on the mixing time were investigated. The Maxblend impeller was able to improve the mixing performance of non‐Newtonian fluids in a batch reactor. The mixing quality could be further enhanced by decreasing the xanthan gum concentration and using baffles in the mixing vessel.     

Power and mean flow characteristics in mixing vessels agitated by hyperboloid stirrers

The mean flow and energy consumption in vessels powered by hyperboloid stirrers was investigated. The Newton number followed an inverse linear law for Reynolds numbers below approximately 200, which had values more than twice higher the corresponding Newton number for a standard Rushton turbine. At high Reynolds number flows the Power number varied between 0.5 for a D/T = 0.78 impeller to 0.95 for a D/T = 0.24 impeller, as compared to a value of 5 for the standard Rushton stirrer, and to values of 0.31 and 1.58 for the Chemineer and Prochern hydrofoils. The power consumption did not change with the fluid height and was double for the double-stack configuration. The shear ribs below the impeller were the main contributor to the increased energy loss relative to a non-shear ribbed impeller and the small clearance had no major effect upon the power consumption. For the D/T= 1/3 hyperboloid stirrer the flow in the whole tank was rather gentle, defining a circulation number of 0.57, thus leading to a circulation efficiency more than 7 times lower than that of the hydrofoils.     

Predictions of heat transfer and pressure drop for a modified power law fluid flow in a square duct

Numerical Solutions for the Nusselt Numbers (CHF and CWT) and the Friction Factor times Reynolds Number have been obtained for fully developed laminar flow of a MPL (Modified Power Law) fluid within a square duct. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian at low shear rates through a transition region to power law behavior at higher shear rates. A shear rate parameter is identified, which allows the prediction of the shear rate range for a specified set of operating conditions. Numerical results of the Nusselt numbers (CHF and CWT) and the Friction factors times Reynolds number for the Newtonian and power law regions are compared with previous published results, showing agreement with 0.02% in Newtonian region and 4.0% in power law region.     

错位六弯叶搅拌槽内假塑性流体的混合特性

在直径为0.21 m的搅拌槽内,使用FLUENT?软件对错位六弯叶桨的流动场及混合性能进行了数值模拟.工作介质分别选用牛顿流体(水)和假塑性流体1.0%(wt)黄原胶水溶液,计算采用标准κ-ε湍流模型,并将牛顿流体的速度场分布与粒子图像测速仪(PIV)实验结果进行了比较.通过与标准六弯叶桨进行对比分析,阐述了错位桨用于假塑性流体搅拌时在混合速率和混合效率方面的特性.结果表明:速度矢量的计算值与 PIV 实验数据吻合较好,湍流模型的计算结果可靠;混合过程与流场结构密切相关,监测点位置对浓度变化有较大影响.错位六弯叶桨的混合时间数明显小于标准六弯叶桨,混合速率更高,同时错位六弯叶桨的混合效率大大高于标准六弯叶桨,单位体积混合能只有标准六弯叶桨的52%,具有节能功效,体现出错位桨的优越性.     

Predictions of pressure drop for modified power law fluids in conduits of three different cross-sectional shapes

Numerical solutions are presented for fully developed laminar flow for a modified power law fluid (MPL) in conduits of arbitrary cross sections. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian behavior at low shear rates, through a transition region, to power law behavior at higher shear rates.The analysis identified a dimensionless shear rate parameter which, for a given set of operating conditions, specifies where in the shear rate range a particular system is operating, i.e. in the Newtonian, transition, or power law regions.The numerical results of the friction factor times Reynolds number for the Newtonian and power law region are compared with previously published results showing agreement within 0.05% in the Newtonian region, and 0.9% and 5.1% in the power law region.     

POWER CONSUMPTION AND SOLID SUSPENSION IN COMPLETELY FILLED VESSELS

Mixing in a completely filled vessel, designed as a pressure vessel, has been investigated. The power demand of two pitched blade turbines of different sizes, and one high flow impeller was studied. The influence of side-mounted and bottom-mounted baffles, as well as the clearance between the bottom and the impeller was investigated. The experiments were carried out in a plexiglass vessel with a diameter of 288 mm. The Power number was calculated from measured data on the power demand and the impeller speed. Furthermore, preliminary studies on the critical impeller speed and power demand at the off-bottom suspension point for one set of glass particles were carried out. The Power number was mainly influenced by the impeller type, while the power demand at the off-bottom suspension point was more dependent of the impeller size and clearance. For bottom-mounted baffles a minimum in the Power number was noticed with increased clearance. It was found the minimum was located at the transition point between two different How patterns. This study shows that the configuration with the lowest Power number is not necessary the most efficient for suspending solid particles.     

RAPID SPECTROSCOPIC ASSESSMENT OF REACTION RATES IN PHASE-TRANSFER-CATALYSIS

Power for agitation has been measured under aerated and unaerated conditions in a 0.29 m vessel of Rushton dimensions at specific powers up to 18 W/kg. The fluids studied were water. Newtonian solutions up to 19 m Pas and non-Newtonian shear thinning fluids some of which also exhibited a yield stress and some of which were viscoelastic. For the unaerated case, the power number-Reynolds number plot is in good agreement with the literature. For the aerated case, the result can conveniently be divided into three Reynolds number regions. At Re > ～900, the data obtained for the solutions is not markedly different to that for water except that a higher impeller speed is required to achieve complete gas dispersion. For ～ 10 < Re < ～900. the power drawn is independent of gassing rate and greater levels of elasticity and the presence of a yield stress leads to the lowest power numbers. For Re < ～10, the gassed and ungassed power numbers are equal.     

Investigations of heat transfer and pressure drop between parallel channels with pseudoplastic and dilatant fluids

Central to the problem of heat exchangers design is the prediction of pressure drop and heat transfer in the noncircular exchanger duct passages such as parallel channels. Numerical solutions for laminar fully developed flow are presented for the pressure drop (friction factor times Reynolds number) and heat transfer (Nusselt numbers) with thermal boundary conditions [constant heat flux (CHF) and constant wall temperature (CWT) ] for a pseudoplastic and dilatant non‐Newtonian fluid flowing between infinite parallel channels. A shear rate parameter could be used for the prediction of the shear rate range for a specified set of operating conditions that has Newtonian behavior at low shear rates, power law behavior at high shear rates, and a transition region in between. Numerical results of the Nusselt number [constant heat flux (CHF) and constant wall temperature (CWT) ] and the product of the friction factor and Reynolds number for the Newtonian region were compared with the literature values showing agreement within 0.36% in the Newtonian region. For pseudoplastic and dilatant non‐Newtonian fluids, the modified power law model is recommended to use because the fluid properties have big discrepancies between the power law model and the actual values in low and medium range of shear rates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3601–3608, 2003