穿流式刚-柔组合搅拌桨强化混合澄清槽内油-水两相混沌混合

运用LabView和Matlab软件分别采集和处理穿流式刚-柔组合搅拌桨扰动澄清槽中油-水两相流体内部的压力脉动信号,得出的最大Lyapunov指数（LLE）和多尺度熵（MSE）,反映流体内部的混沌程度;同时采用流场可视化技术观测流体混合状态。结果表明,相比于刚性组合桨,穿流式刚-柔组合搅拌桨通过穿流孔与柔性部分的共同作用改变流场的结构和能量耗散方式,使流体的混沌程度和混合状态都优于刚性组合桨。当转速为88 r·min^-1时,流体的混沌混合都达到最佳状态,各实验条件下的LLE均大于零,表明流场混合体系已进入混沌状态,且穿流式刚-柔组合搅拌桨体系的MSE明显高于刚性组合桨体系,说明穿流式刚-柔组合搅拌桨的混合效果优于刚性组合桨。另外,柔性片上穿流孔的数目和柔性桨叶的厚度对流场的混沌特性也有明显的影响。     

Chaotic mixing performance enhanced by rigid-flexible impeller with long-short blades in stirred tank

The presence of a mixing isolation regions in a stirred reactor is a major obstacle to enhancing fluid mixing. Breaking the symmetrical flow field structure in the stirred tank and destroying the mixing isolation area can improve the fluid mixing efficiency. The Matlab software was used to calculate the maximum Lyapunov exponent (LLE) and multi-scale entropy (MSE). The effects of different blade types, flexible blade length, flexible blade number, blade height from bottom and rotation speed on fluid mixing were compared. The results show that the rigid-flexible impeller with long-short blades (RF-LSB) can enhance the flow field structure more unstable and asymmetric with deformation and random vibration of flexible pieces, destroy the symmetry flow in the process of fluid mixing, induce the asymmetric flow field, and make more fluid into the chaotic state. When at 90 r/min and three pieces of flexible, the LLE of the RF-LSB is larger than that of rigid impeller and rigid-flexible impeller RF-LSB with increase of 20.22% and 7.98% respectively. The mixing time (θ_m) of the three systems [RF-LSB (three pieces), rigid impeller, rigid-flexible impeller] has an exponential relationship with the power consumption per unit volume (P_v). When P_v is constant, θ_m of the RF-LSB system is the smallest. Results showed that the RF-LSB (three pieces) is superior to rigid impeller and rigid-flexible impeller, which is more conducive to fluid chaotic mixing.     

长短叶片复合型刚柔桨强化搅拌槽内流体混沌混合行为

搅拌反应器中混合隔离区的存在是强化流体混合的主要障碍。打破搅拌槽中的对称性流场结构，破坏混合隔离区，可以提高流体混合效率。采用Matlab软件编程计算最大Lyapunov指数（LLE）和多尺度熵（MSE），比较了不同桨叶类型、柔性片长度、柔性片数量和桨叶离底高度以及转速对流体混合的影响。结果表明，长短叶片复合型刚柔桨（RF-LSB）桨叶通过刚柔耦合错位连接，柔性片的形变与随机振动对流体的非稳态扰动，使流场结构不稳定性和不对称性增强，强化了流体混合效果。当柔性片数量为3，搅拌转速为90 r/min时，RF-LSB体系比刚性桨和刚柔桨体系的LLE值分别提高了20.22%和7.98%；三种体系[RF-LSB（柔性片数量为3）、刚性桨和刚柔桨体系]的混合时间（θ_m）与单位体积功耗（P_v）呈指数型关系，当P_v相同时，RF-LSB（柔性片数量为3）的θ_m最小，表明RF-LSB（柔性片数量为3）更有利于流体混沌混合。     

错位刚柔桨强化搅拌槽内流体混合实验及数值模拟

为消除搅拌反应器中混合隔离区，对标准刚性桨（R-RT）、错位刚性桨（PR-RT）和错位刚柔桨（PRF-RT）三种桨叶体系的流体混沌特性参数、流场结构以及流体运动速度进行了探讨。采用Matlab软件编程计算最大Lyapunov指数（LLE）和多尺度熵（MSE），通过计算流体力学研究了三种桨叶体系流场结构和流体运动速度的差异。实验及计算结果表明，错位刚柔桨通过柔性桨叶的随机扰动破坏了隔离区介稳态流场边界，较大程度地消除了混合隔离区。PRF-RT的LLE相比于R-RT和PR-RT分别提高了13.29%和7.25%，MSE也较PR-RT和R-RT大；PRF-RT增强了流场不稳定性，形成了不对称性流场结构，减少了隔离区分布范围；PRF-RT强化桨叶能量耗散，提高了搅拌槽底部、顶部液面以及搅拌槽壁区域流体运动速度，减小了流体混合时间。     

Experiment and numerical simulation of chaotic mixing performance enhanced by perturbed rigid-flexible impeller in stirred tank

To eliminate the isolated mixing regions in the stirred tank, factors associated with chaotic mixing performance were studied, including flow field structure and fluid velocity of rigid RT impeller (R-RT), perturbed rigid RT impeller (PR-RT) and perturbed rigid-flexible RT impeller (PRF-RT). The maximum Lyapunov exponent (LLE) and multi-scale entropy (MSE) were calculated by using Matlab software programming, and the differences in flow field structure and fluid velocity of the three blade systems were studied through computational fluid mechanics. The experimental and computational results showed that perturbed rigid-flexible RT impeller could destroy the boundary of the mesostatic flow field in the isolated mixing regions and the symmetry flow in the process of fluid mixing through the random disturbance of the flexible blade, eliminating the isolated mixing regions. At 90 r/min, the LLE of the perturbed rigid-flexible RT impeller is larger than that of rigid RT impeller and perturbed rigid RT impeller. The LLE of the rigid-flexible RT impeller compared with the rigid RT impeller and perturbed rigid RT impeller increases 13.29% and 7.25% respectively and the MSE of the perturbed rigid-flexible RT impeller is also larger than that of rigid RT impeller and perturbed rigid RT impeller. The perturbed rigid-flexible RT impeller enhances the flow field instability, forms an asymmetric flow field structure, and reduces the distribution range of isolated mixing regions. The perturbed rigid-flexible RT impeller enhances the energy dissipation of the blade, improves the fluid velocity at the bottom and top of the tank and the wall of the tank, and reduces the mixing time.     

Chaotic mixing and droplet dispersion characteristics of liquid - liquid with elastic combined impeller

Traditional mixing and clarification tanks generally use rigid stirring blades to achieve liquid-liquid two-phase mixed extraction, which generally suffers from low efficiency and high energy consumption. A kind of elastic combined impeller was used in the mixing clarifier in this work to enhance the liquid-liquid biphase mixing behavior. Lyapunov exponent (LLE) and multiscale entropy (MSE) were used to characterize the chaotic state of the system, the particle size distribution and D₃₂ were used to characterize the dispersion effect. The influence of impeller type (elastic combined impeller, rigid-flexible combined impeller and rigid impeller), spring length, wire diameter and outer diameter on mixing effect was studied. The results indicated that compared with the rigid impeller and the rigid-flexible combined impeller, the elastic combined impeller strengthens the energy dissipation mode of the flow field through the deformation and energy storage of the spring, improves the dispersion effect of the dispersed phase, and was conducive to the chaotic mixing of the liquid-liquid biphase. When stirring speed N = 200 r/min, the spring wire diameter was 0.6 mm, the relative length of the spring was 1.2, and the external diameter of the spring was 7 mm, the LLE value and the amplitude of MSE were the largest and the MSE values fluctuate most strongly. At the same time, there was a log-linear relationship between the D₃₂ of dispersed phase and the stirring speed in each stirring system, and the droplet size of dispersed phase in the elastic combined impeller system was smaller and more.     

弹性搅拌桨强化液-液两相混沌混合及液滴分散特性的研究

传统的混合澄清槽一般采用刚性搅拌桨来实现液-液两相的混合萃取，普遍存在效率低、能耗高等问题。将一种弹性搅拌桨应用在混合澄清槽中，以强化液-液两相混沌混合及分散特性。以最大Lyapunov指数（LLE）和多尺度熵（MSE）表征体系混沌状态，以分散相液滴粒径分布、Sauter平均粒径（D₃₂）等表征分散效果，分别研究了桨叶类型（弹性搅拌桨、刚柔组合桨及刚性桨）、弹簧长度、线径、外径等因素对混沌混合效果和分散特性的影响。结果表明，相比较刚性搅拌桨和刚柔组合搅拌桨，弹性搅拌桨通过弹簧的形变和储能作用，强化了搅拌能量的传递方式，提高了分散相的分散效果，有利于液液两相的混沌混合，在搅拌转速N=200 r/min、弹簧线径为0.6 mm、弹簧相对长度为1.2、弹簧外径为7 mm时，弹性搅拌桨体系的LLE和MSE更大，且MSE值波动最强；同时，各搅拌体系内分散相平均粒径D₃₂与转速呈对数线性关系，弹性搅拌桨体系内分散相液滴尺寸更小且数量更多。     

Enhancement of liquid–liquid mixing in a mixer-settler by a double rigid-flexible combination impeller

Mixing is crucial in the dispersion of two immiscible fluids. The rational design of an impeller is necessary to form suitable flow conditions and improve fluid mixing efficiency. A double rigid-flexible combination impeller was designed by connecting the upper and lower rigid impeller blades with flexible pieces. Experimental measurements were performed in a laboratory-scale mixer-settler under different impeller types. The largest Lyapunov exponent (LLE) and multi-scale entropy (MSE) were investigated using Matlab. Results showed that the double rigid-flexible combination impeller enhanced liquid–liquid mixing in the mixer-settler through the multiple-body motion behavior triggered by the swings of flexible pieces. At the optimum mixing point of each impeller, the LLEs of the double impeller, double rigid combination impeller, and double rigid-flexible combination impeller were 0.018, 0.055, and 0.057, respectively. At 75 rpm, the MSE of the combination impellers was obviously greater than that of the double impeller, and the rigid-flexible combination impeller had larger MSE than the double rigid combination impeller. The mixing efficiency of the rigid-flexible combination impeller increased with increasing width and quantity of the flexible piece. The quantity of rigid blade slice also influenced the enhancement of mixing ability. The double rigid-flexible combination impeller intensified the chaotic mixing of the two-phase fluid by changing the flow field structure and energy dissipation mode, ultimately achieving an efficient-mixing operation.     

偏心射流-刚柔组合桨搅拌器内混沌混合行为研究

搅拌反应器内普遍存在混合隔离区,是实现高效混合的一大障碍。流场耦合诱发流体的混沌现象,可减少混合隔离区,提高流体混合效率。结合Matlab软件,探究偏心空气射流-单层刚柔组合桨体系的混合行为演变规律,对比分析了不同偏心率下桨叶类型、桨叶离底高度、空气射流量以及转速对流体混沌混合的影响。结果表明,刚柔组合桨通过其自身刚-柔-流的多体运动与偏心空气射流的流场耦合,破坏了流体混合过程中出现的对称性流场,使更多的流体进入混沌状态。刚-柔组合桨（RF-RDT、RF-IRDT）比刚性桨（RDT、IRDT）的LLE值大,其中RF-RDT相比于其他3种类型的搅拌桨（IRDT、RDT、RF-IRDT）,其LLE值分别提高了约42.8%,27.0%、6.9%;空气射流的偏心率等于0.6时,其最大LLE值相比于其他偏心率（0.8、0.4、0.2、0）,依次提高了6.5%、2.4%、17.6%、25.1%。该研究结果可为刚柔组合桨的优化设计提供理论依据。     

穿流-柔性组合桨强化搅拌槽中流体混沌混合特性

刚性搅拌桨在搅拌混合过程中得到广泛的应用,在搅拌容器内容易形成两种不同的混合区域:混沌混合区和混合隔离区。强化流体混合的有效途径是合理设计搅拌桨,从而调控流体混沌混合行为。实验运用Labview和Matlab软件采集和处理流体内部压力脉动信号,并获取流体混沌特性参数Kolmogorov熵,对穿流-柔性组合桨体系的Kolmogorov熵随转速的变化规律进行了研究。结果表明,相比传统刚性桨,穿流桨对Kolmogorov熵影响不大。穿流-柔性组合桨通过穿流孔与柔性部分的共同作用调控流场结构,使流体混沌混合的效果最好,在转速为180 r·min^-1时流体的混沌混合达到最佳状态,穿流-柔性组合桨体系的Kolmogorov熵为0.285,而传统刚性桨体系的Kolmogorov熵只为0.125;穿流-柔性组合桨体系的混合时间明显低于传统刚性桨体系,当转速为120 r·min^-1时穿流-柔性组合桨体系的混合时间比传统刚性桨体系缩短了17%。     

刚柔组合桨强化粉煤灰酸浸搅拌槽内固液混沌混合

传统粉煤灰提铝工艺中酸浸搅拌槽均采用刚性搅拌桨。因刚性桨卷吸能力有限，导致固体颗粒易沉槽、流体混沌混合效率低。提出刚柔组合桨强化酸浸搅拌槽中固液混沌混合行为。实验基于固含率为30%的粉煤灰-自来水体系，研究了刚柔组合酸浸搅拌槽内混沌混合特性及能量耗散规律。采用扭矩传感器采集扭矩时间序列信号，借助Matlab软件编译计算混合过程中最大Lyapunov指数和多尺度熵等混沌特性参数，以单位体积功耗表征搅拌反应器的功率特性。实验考察了搅拌桨安装离底高度、柔性片长度、柔性片宽度等因素对酸浸槽内粉煤灰混沌混合的影响，对比了刚性桨与刚柔组合桨体系的能耗差异。研究结果表明：刚柔组合桨通过柔性片的作用，能增大搅拌桨的卷吸力，进而减少固体颗粒沉槽现象，促进全槽混沌混合；在最优化条件（120 r/min，搅拌桨安装离底高度为T/4，柔性片长度为1.2H ₁、柔性片宽度为D/8）下，体系最大Lyapunov指数达到最大值0.0645，各尺度下的MSE均比其他条件更大，表明刚柔组合桨能够通过柔性片的多体运动，强化体系混沌混合，均化体系能量分布；刚性桨与刚柔组合桨的单位体积功耗随着转速的增加呈现指数规律增长。     

湿法磷酸固-液体系混沌混合与浸出强化行为

湿法磷酸浸出过程中，传统刚性搅拌桨的作用方式主要是剪切作用，容易形成对称性流场结构，降低搅拌效率。实验考察了桨叶类型、离底高度、搅拌速度、柔性钢丝绳长度、柔性钢丝直径对磷矿浸出率及最大Lyapunov指数(LLE)的影响。实验结果表明：刚柔组合桨通过刚-柔-流的耦合作用，改善流场的结构，提高了流体混沌混合效果。当搅拌转速225 r/min，浸出时间120 min，离底高度h=T/4，柔性钢丝绳直径d= 0.42r，柔性钢丝绳长度L=1.3T时，刚柔组合桨的最大Lyapunov指数达到0.09071，磷矿浸出率提高了10.8%。另外，在相同的功耗(P _v=9890 W/m³)条件下，刚柔组合桨使反应器内的悬浮均匀度和渣中磷含量分别降低了40.8%和17.67%，有效地改善了晶体的形貌，提高了磷石膏的过滤性能，强化了颗粒的混合与浸出。     

逆流桨强化搅拌槽内流体混沌混合及流场结构失稳研究

在传统三斜叶桨的基础上,结合逆流桨结构,提出三斜叶逆流桨,以破坏或者消除搅拌槽内稳定的对称性流场结构,提高流体传递效率及混沌混合程度。结合实验和模拟两种方法,主要研究了上推式三斜叶桨(PBTU)、外推内压式三斜叶逆流桨(PBTC-U)、外压内推式三斜叶逆流桨(PBTC-D)三种桨叶体系以及不同外层桨叶长度的PBTC-U桨体系内搅拌功耗、混合时间、混沌特性参数、流场结构以及流体速度分布。实验结果表明,N=130 r/min时,PBTC-U桨相对于PBTU桨和PBTC-D桨,体系混合时间分别从22.0、37.5 s缩短到16.5 s,功耗分别降低了5.6%和12.8%,LLE值分别提高了13.69%和37.01%。在确定PBTC-U桨适宜外层桨叶长度的研究中发现当外层桨叶长度D₂=0.375D时,搅拌功耗最低且混合时间最短。PBTC-U型逆流桨通过内外层桨叶的逆流作用,强化体系内流体的随机运动,使得流场的不稳定性得到增强,对称性被破坏,进而流场结构失稳,流体混合效率得到提高。另外,PBTC-U桨可以增强流体轴、径向速度分布的波动性,有利于提高体系的混合效率。     

刚柔组合搅拌桨强化搅拌槽中流体混沌混合

搅拌槽内普遍存在着两种不同类型的混合区域：混沌混合区和规则区。增大混沌混合区,是提高流体混合效率、降低搅拌过程能耗的重要途径。而合理设计搅拌桨有助于流体形成适宜的流动状态,实现混沌混合。柔性体与刚性体组合,可设计出具有多体运动行为的刚柔组合搅拌桨,可强化流体混沌混合行为。结合Matlab 软件,实验研究了双层桨搅拌槽内自来水体系的最大Lyapunov指数（LLE）和多尺度熵（MSE）的变化规律,对比分析了刚性桨和刚柔组合桨两种桨叶对流体混沌混合的影响。结果表明,刚柔组合桨强化流体的运动特性,使更多流体进入混沌混合状态。在转速为210 r·min^-1时,流体的混沌混合达到最佳状态,刚性桨体系的LLE为0.041,而刚柔组合桨体系的LLE为0.048;刚柔组合桨可有效耗散能量,使整个槽体的能量分布均匀,刚柔组合桨在150 r·min^-1时的多尺度熵率与刚性桨在210 r·min^-1时基本相近;刚柔组合桨体系的混合时间均低于刚性桨体系,在转速为120 r·min^-1时,刚柔组合桨使流体的混合时间缩短了26%左右。刚柔组合桨可改变流场结构和能量耗散方式,强化流体混沌混合,实现高效节能操作。     

双组分层撞击流反应器浓度场混沌分析

采用平面激光诱导荧光技术测量双组分层式撞击流反应器撞击区浓度分布,利用混沌理论分析不同喷嘴间距、喷嘴直径和射流雷诺数下撞击流反应器浓度场混沌特征参数(关联维、Kolmogorov熵和最大Lyapunov指数)的变化规律。结果表明,撞击流反应器内浓度场混沌特征参数随喷嘴间距的增大呈上下波动的变化趋势,Kolmogorov熵在L=2d时达到最大。浓度场混沌特征参数随喷嘴直径增大呈上下波动的变化趋势,Kolmogorov熵在d=8 mm时整体上最大;射流雷诺数为Re=22 000时整体上混沌特征参数最佳。受二次撞击区的影响,撞击面上靠近二次撞击区各点的混沌特征参数有明显提高。     

多层刚柔组合桨诱发流场界面失稳强化非牛顿流体混沌混合行为

传统多层刚性桨用于假塑性非牛顿流体混合搅拌死区较大，流场界面稳定，混合效率低。提出多层刚柔组合桨诱发流场界面失稳强化非牛顿流体混沌混合的方法。实验以羧甲基纤维素钠为非牛顿流体体系，通过扭矩传感器测量功率特性，酸碱中和脱色法测定混合时间，并利用Matlab 软件编程计算最大Lyapunov 指数，分析了非牛顿流体混合过程中的混沌特性及其混合性能。结果表明，组合方式为RF-（PBTD+PBTD+DT）、桨叶排列方式θ=60°、柔性片长度安装比例r=0.8、1.2时，混沌程度较高，混合性能较好。多层刚柔组合桨可以产生多股螺旋流，并在层间柔性片扰动频率差下实现流场界面失稳，搅拌死区减小，在较低转速下使体系进入混沌状态（多层刚柔组合桨体系N>88 r/min时LLE>0，多层刚性桨体系N>125 r/min时LLE>0）；在相同转速下，多层刚柔组合桨混合速率、单位体积功率高于多层刚性桨，而单位体积混合能大致相同。     

Chaotic mixing behavior of non-Newtonian fluid intensified by multilayer rigid-flexible impeller induced flow field interface instability

The traditional multilayer rigid impeller has large dead zone for the mixing of pseudoplastic non-Newtonian fluid, stable flow field interface and low mixing efficiency. A method for enhancing the chaotic mixing of non-Newtonian fluid by multilayer rigid-flexible impeller induced flow field interface instability was proposed. In the experiment, sodium carboxymethylcellulose was used as the non-Newtonian fluid system. The power characteristics were measured by the torque sensor. The mixing time was determined by the acid-base neutralization and decolorization method. The largest Lyapunov exponents were calculated by using Matlab software programming. The chaotic characteristics and mixing performance in the mixing process are analyzed. The results show that when the combination mode was RF-(PBTD+PBTD+DT), the impeller arrangement mode θ=60°, and the flexible sheet length installation ratio r=0.8, 1.2, the degree of chaos was higher and the mixing performance was better. Multilayer rigid-flexible impeller can generate multiple spiral flows, and realize the flow field interface instability under the disturbance frequency difference of the flexible sheet between the layers, the stirring dead zone was reduced, and the system enters a chaotic state at a lower speed (when the multilayer rigid-flexible impeller system N>88 r/min, LLE>0; when the multilayer rigid impeller system N>125 r/min, LLE>0). At the same speed, the mixing rate and power per unit volume of the multilayer rigid-flexible combined impeller are higher than that of the multilayer rigid impeller, but the mixing energy per unit volume is approximately the same.     

脉冲射流-刚柔组合桨强化流体混沌混合及传质性能研究

传统搅拌反应器普遍使用刚性桨进行机械搅拌，导致反应器内容易产生混合隔离区而降低流体混合效率。采用多流场耦合诱发混沌现象，促使更多流体进入混沌状态，是提高流体混合效率的有效途径之一。结合Matlab软件编译PJ-RF-RT体系中的压力脉动信号得到最大Lyapunov指数（LLE）与多尺度熵（MSE），探究不同脉冲周期下占空比、桨型、柔性桨叶厚度、桨离底高度及脉冲空气射流量对搅拌反应器内流体混沌混合的影响，同时，对比分析了桨型、射流类型、气流量对体积氧传质系数K_La的影响。研究结果表明，在脉冲周期T=0.4 s，占空比D=80%时，RF-RT桨体系较R-RT桨体系的LLE增大了11.58%，且RF-RT体系的MSE显著高于R-RT桨体系，表明脉冲射流刚柔组合桨体系能更好地诱发流体混沌，增大流体混合效率，均化体系能量分布。此外，脉冲射流耦合RF-RT桨体系增强了流体的湍流特性，促使液膜厚度减小，强化了传质，在单位体积功耗P_v=360 W/m³时，PJ-RF-RT体系的K_La较PJ-R-RT提高了13.46%，PJ-R-RT体系的K_La较SJ-R-RT提高了11.86%。     

Chaotic mixing performance and mass transfer enhanced by rigid-flexible impeller with pulse jet

Conventional stirred reactors generally use rigid impeller for mechanical stirring, which leads to the easy creation of isolation mixing regions in the reactor and reduces the efficiency of fluid mixing. The use of multi-flow field coupling to induce chaos and promote more fluids into a chaotic state is one of the effective ways to improve fluid mixing efficiency. In this work, the largest Lyapunov exponent(LLE) and multi-scale entropy(MSE) are investigated with the Matlab compile pressure pulsation signals. The effects of duty ratio, paddle type, flexible paddle thickness, paddle height from the bottom and pulsed air jet flow rate on the chaotic mixing of fluids in a stirred reactor under different pulse periods are explored. In addition, the effects of different impeller types, jet types and air jet flow rate on the volume oxygen mass transfer coefficient K_La are compared and analyzed. When T=0.4 s and D=80%, the results show that the LLE of the rigid-flexible RT impeller compared with the rigid RT impeller increases 11.58% and the MSE of the rigid-flexible RT impeller is also larger than that of rigid RT impeller. It was showed that the pulsed jet rigid-flexible impeller system can better enhance fluid chaos, increase the fluid mixing efficiency and homogenize the system energy distribution. In addition, pulse jet coupling RF-RT impeller system enhances the turbulent characteristics of the fluid, promotes the reduction of the thickness of the liquid film, strengthens the mass transfer and increases the K_La value of the system. When power consumption per unit volume is 360 W/m³, the K_La of the PJ-RF-RT system compared with the PT-R-RT system increases 13.46%, and the K_La of the PJ-R-RT system compared with the SJ-R-RT system increases 11.86%.     

单层钢丝柔性桨强化搅拌槽中流体混沌混合行为

实验运用扭矩传感器测量搅拌功率特性,Matlab软件编程计算最大Lyapunov指数（LE_max）,流场可视化技术观测流体混合状态。研究了桨叶类型、桨叶离底距离、柔性钢丝长度、柔性钢丝直径对混合效率数（C_e）、LE_max的影响。结果表明：单层钢丝柔性桨通过刚-柔-流耦合作用,改变流场结构和能量耗散方式,提高了流体混沌混合程度,实现了流体的高效节能混合;当转速为120 r·min⁻¹时,与传统刚性桨相比,单层钢丝柔性桨使流体C_e减小了87.4%,LE_max增大了53.2%,与单层钢丝刚性桨相比,单层钢丝柔性桨使流体C_e减小了43.8%,LE_max增大了10.8%。另外,当搅拌转速相同时,柔性钢丝越长,越有利于流体混沌混合,但其功耗也会随之明显增加;当柔性钢丝直径为0.8 mm,桨叶离底距离为0.25T（T为搅拌槽内径）时,各个转速对应的C_e小于其他情况、LE_max大于其他情况,流体达到相对最佳混沌混合状态。