Chaotic Flow Field Research Articles

Research on factors affecting bubble and particle behavior in a three-phase flotation system based on COMSOL

ABSTRACT To investigate the impact of various parameters on bubble and particle dynamics in a flotation system, COMSOL software was utilized. The “two-phase flow – Level Set” module coupled with the “fluid particle interaction” module was used to explore the behavior of single bubbles and particle groups. The bubbles were set as a discrete phase to represent a group of floating bubbles. By combining the “Single-phase flow” module with dual “fluid-particle interaction” modules, we examined the interactions between bubble populations and particles within the system. The research results show that as the bubble diameter increases, the carrying effect of the bubbles on the particles becomes stronger. When the bubble radii are 1, 1.25, 1.5, 1.75, and 2 mm respectively, the maximum movement speed of the particles in the area increases by 3.0%, 2.3%, 5.1%, and 2.7%. The average speed of the particles increases by 7.9%, 7.3%, 9.0%, and 10.0%. Increasing the mass flow rate can increase the collision probability between particles and bubbles, thus increasing the flotation rate. However, a too high mass flow rate will make the state of bubbles unstable. When the mass flow rate is less than 1.5 kg/s, the bubbles remain stable. When the mass flow rate exceeds 1.5 kg/s, the severity of bubble splitting increases. In the study area, the irregularity of the bubble clusters results in a more chaotic flow field, leading to greater speed and displacement of the particles. Increasing the number of bubbles entering at one time and their initial speed enhances the impact of the bubble clusters on the solid particles. When the number of bubbles entering at one time is 5, 10, 15, and 20 respectively, the maximum movement speed of the particles increases by 6.9%, 8.1%, and 9.0%. When the initial speed of the bubble entering is 0, 0.1, 0.2, and 0.3 m/s respectively, the maximum movement speed of the particles increases by 6.4%, 3.0%, and 8.8%.

Multiobjective hydraulic optimization of the diffuser vane in an axial flow pump

Separation flows tend to induce a chaotic flow field that eventually leads to energy losses and reduced efficiency. The present study performed a multiobjective optimization to improve the hydraulic performance of an axial flow pump at the best efficiency point (BEP) and critical stall point based on the diffuser vane (DV) geometry. Computational fluid dynamics were applied to predict the hydraulic performance of a series of DV models with design points generated through design of experiment. Six different surrogate models were evaluated based on the R-squared criteria. The nondominated sorting genetic algorithm II was also employed to search for optimum solutions for design variables. Hydraulic performance balance between low and high flow rate conditions was analyzed based on the velocity triangle. After optimization, the efficiency and total head at the BEP of the optimum model were increased by 2.341% and 2.779%, respectively, compared to the reference model. Despite the minimal changes to the hydraulic performance at the critical stall point, the optimal operating range was notably expanded in the high flow rate region. Thorough evaluation of losses attributed to horseshoe, corner, and trailing-edge vortices was conducted in meridional planes, multiple spans, and various cross sections in the DV domain. Additionally, the formation and development of turbulent flow were analyzed in detail by transient simulation. Vibration and noise caused by instabilities in the flow characteristics of the reference model were substantially reduced by 36.76% and 67.342% at the first higher-harmonic frequencies at the BEP and the critical stall point, respectively.

Aerothermal Performance Robustness and Reliability Analysis of Turbine Blade Squealer Tip With Film Cooling

Abstract The uncertainty quantification in the turbine components' aerodynamic and heat transfer performances is widely considered to be the most challenging topic due to its intricate and nonlinear characteristics. This paper first proposes an efficient uncertainty quantification method based on an original parallel framework combining Polynomial Chaos Expansions (PCE) with two forms (stochastic response surface-based and Galerkin projection-based) and the Universal Kriging method. The rigorous mathematical tests are performed to verify the reliability and computational efficiency of the proposed method, and the results support that this method can dramatically reduce computational samples compared to the conventional PCE method while maintaining computational accuracy. Then, the genetic algorithm was introduced to establish an efficient uncertainty quantification framework, and it is applied to the aerothermal performance robustness investigation of the GE-E3 rotor blade tip with and without film cooling. Based on the findings of uncertainty quantification, the injection of cooling air drastically enhances the unstable tendency of the flow and thermal fields, resulting in the actual aerothermal performance of the squealer tip being much lower than that predicted by deterministic calculations. The setting of the film cooling, although effective in reducing the heat flux around the cooling holes, also induces more chaotic flow and thermal fields, leading to sharp heat flux fluctuations around the cooling holes. Finally, our novel reliability analysis algorithm, rooted in the quantification of uncertainty, corroborates the assertion that the introduction of coolant gas, while extending the operational longevity of turbine blades, confers only marginal improvements in the mitigation of lifespan variability. The comprehensive lifespan assessment elucidates that the mean operational longevity of the conventional squealer tip design stands at an estimated 16,169.44 h, accompanied by a standard deviation of 2,750.31 h. In stark contrast, the mean operational longevity of the squealer tip integrated with film cooling measures a significantly enhanced 17,035.17 h, exhibiting a standard deviation of 2,492.73 h. Consequently, the operational lifespan of the conventional squealer tip experiences a decrement of 10.17% in comparison to the anticipated mean lifespan, whereas the reduction for the film-cooled squealer tip registers at 5.36%.

Applications of Differential Geometry Linking Topological Bifurcations to Chaotic Flow Fields

At every point p on a smooth n-manifold M there exist n+1 skew-symmetric tensor spaces spanning differential r-forms ω with r=0,1,⋯,n. Because d∘d is always zero where d is the exterior differential, it follows that every exact r-form (i.e., ω=dλ where λ is an r−1-form) is closed (i.e., dω=0) but not every closed r-form is exact. This implies the existence of a third type of differential r-form that is closed but not exact. Such forms are called harmonic forms. Every smooth n-manifold has an underlying topological structure. Many different possible topological structures exist. What distinguishes one topological structure from another is the number of holes of various dimensions it possesses. De Rham’s theory of differential forms relates the presence of r-dimensional holes in the underlying topology of a smooth n-manifold M to the presence of harmonic r-form fields on the smooth manifold. A large amount of theory is required to understand de Rham’s theorem. In this paper we summarize the differential geometry that links holes in the underlying topology of a smooth manifold with harmonic fields on the manifold. We explore the application of de Rham’s theory to (i) visual, (ii) mechanical, (iii) electrical and (iv) fluid flow systems. In particular, we consider harmonic flow fields in the intracellular aqueous solution of biological cells and we propose, on mathematical grounds, a possible role of harmonic flow fields in the folding of protein polypeptide chains.

Experimental study on transpiration cooling through additively manufactured porous structures

Film cooling and thermal barrier coating are the most common external cooling techniques used for gas turbine components. In film cooling, coolant air is brought to the external surface via rows of discrete holes. This study investigates an alternative geometry, referred to as transpiration cooling. Here, the coolant air is brought to the external surface through an additively manufactured porous structure. An experimental study was performed to characterize the downstream cooling performance by obtaining film cooling effectiveness and heat transfer coefficient using thermochromic liquid crystals. The experimental setup was first validated using a cylindrical film cooling sample and the results were compared to results obtained from previously published film cooling studies. After validation, transpiration cooling samples were investigated. A total of three porous structure samples with different thicknesses were subjected to testing. The thickness of the porous structure had insignificant effect on both the heat transfer coefficient and the film cooling effectiveness. The samples were tested at blowing ratios ranging from 0.5 to 2.0. Results showed an increase in laterally averaged heat transfer coefficient with increasing blowing ratio and compared to cylindrical film cooling, transpiration cooling yielded significantly higher distributions. The spanwise averaged film cooling effectiveness displayed a similar trend with higher values for transpiration cooling, mainly due to a more even mixing in the lateral direction. Values of the heat flux ratio showed that the high heat transfer coefficient penalizes the porous cooling method and only for low blowing ratios may transpiration cooling be the beneficial choice. From visualizations with water and carbon dioxide, it could be concluded that the inclination angle is close to 90° which yields a chaotic flow field and, in turn, high values of the heat transfer coefficient. By changing the additive manufacturing's build direction, a more favorable inclination angle should be achievable and, thereby, an opportunity to utilize the porous structure's excellent mixing in the spanwise direction.

Comparison of reduced order models based on dynamic mode decomposition and deep learning for predicting chaotic flow in a random arrangement of cylinders

Three reduced order models are evaluated in their capacity to predict the future state of an unsteady chaotic flow field. A spatially fully developed flow generated in a random packing of cylinders at a solid fraction of 0.1 and a nominal Reynolds number of 50 is investigated. For deep learning (DL), convolutional autoencoders are used to reduce the high-dimensional data to lower dimensional latent space representations of size 16, which were then used for training the temporal architectures. To predict the future states, two DL based methods, long short-term memory and temporal convolutional neural networks, are used and compared to the linear dynamic mode decomposition (DMD). The predictions are tested in their capability to predict the spatiotemporal variations of velocity and pressure, flow statistics such as root mean squared values, and the capability to predict fluid forces on the cylinders. Relative errors between 15% and 20% are evident in predicting instantaneous velocities, chiefly resulting from phase differences between predictions and ground truth. The spatial distribution of statistical second moments is predicted to be within a maximum of 5%–10% of the ground truth with mean error in the range of 1%–2%. Using the predicted fields, instantaneous fluid drag force predictions on individual particles exhibit a mean relative error within 20%, time-averaged drag force predictions to within 5%, and total drag force over all particles to within 1% of the ground truth values. It is found that overall, the non-linear DL models are more accurate than the linear DMD algorithm for the prediction of future states.

Fluid Mechanical Effects of Fetal Aortic Valvuloplasty for Cases of Critical Aortic Stenosis with Evolving Hypoplastic Left Heart Syndrome

Fetuses with critical aortic stenosis (FAS) are at high risk of progression to HLHS by the time of birth (and are thus termed “evolving HLHS”). An in-utero catheter-based intervention, fetal aortic valvuloplasty (FAV), has shown promise as an intervention strategy to circumvent the progression, but its impact on the heart’s biomechanics is not well understood. We performed patient-specific computational fluid dynamic (CFD) simulations based on 4D fetal echocardiography to assess the changes in the fluid mechanical environment in the FAS left ventricle (LV) directly before and 2 days after FAV. Echocardiograms of five FAS cases with technically successful FAV were retrospectively analysed. FAS compromised LV stroke volume and ejection fraction, but FAV rescued it significantly. Calculations to match simulations to clinical measurements showed that FAV approximately doubled aortic valve orifice area, but it remained much smaller than in healthy hearts. Diseased LVs had mildly stenotic mitral valves, which generated fast and narrow diastolic mitral inflow jet and vortex rings that remained unresolved directly after FAV. FAV further caused aortic valve damage and high-velocity regurgitation. The high-velocity aortic regurgitation jet and vortex ring caused a chaotic flow field upon impinging the apex, which drastically exacerbated the already high energy losses and poor flow energy efficiency of FAS LVs. Two days after the procedure, FAV did not alter wall shear stress (WSS) spatial patterns of diseased LV but elevated WSS magnitudes, and the poor blood turnover in pre-FAV LVs did not significantly improve directly after FAV. FAV improved FAS LV’s flow function, but it also led to highly chaotic flow patterns and excessively high energy losses due to the introduction of aortic regurgitation directly after the intervention. Further studies analysing the effects several weeks after FAV are needed to understand the effects of such biomechanics on morphological development.

Enhanced heat transfer and symmetry breaking in three-dimensional electro-thermo-hydrodynamic convection

In this work, the electro-thermo-hydrodynamic convection system induced by unipolar charge injection between two parallel electrodes is numerically investigated. A two-relaxation-time lattice Boltzmann method coupled with a fast Poisson solver is implemented to obtain the temporal and spatial distributions of the flow field, temperature field, electric field, and charge density of the system. Due to the electric force and destabilizing buoyancy force, the system exhibits electro-thermo-convective vortices and transitions to a chaotic flow field, where the flow fluctuates irregularly in time. The strong electric driving force is shown to double the heat transfer effects measured by the Nusselt number ( Nu). The size of the computational domain is found to influence the stability and flow analysis. Specifically, the system is chaotic in a large computational domain but the same set of parameters can lead to a steady-state condition in a small domain.

Fluid viscoelasticity suppresses chaotic convection and mixing due to electrokinetic instability

When two fluids of different electrical conductivities are transported side by side in a microfluidic device under the influence of an electric field, an electrokinetic instability (EKI) is often generated after some critical values of the applied electric field strength and conductivity ratio. Many prior experimental and numerical studies show that this phenomenon results in a chaotic flow field inside a microdevice, thereby facilitating the mixing of two fluids if they are Newtonian in behavior. However, the present numerical study shows that this chaotic convection arising due to the electrokinetic instability can be suppressed if the fluids are viscoelastic instead of Newtonian ones. In particular, we observe that as the Weissenberg number (ratio of the elastic to that of the viscous forces) gradually increases and the polymer viscosity ratio (ratio of the solvent viscosity to that of the zero-shear rate viscosity of the polymeric solution) gradually decreases, the chaotic fluctuation inside a T microfluidic junction decreases within the present range of conditions encompassed in this study. We demonstrate that this suppression of the chaotic motion occurs due to the formation of a strand of high elastic stresses at the interface of the two fluids. We further show that this suppression of the chaotic fluctuation (particularly, the span-wise one) inhibits the mixing of two viscoelastic fluids. Therefore, one needs to be cautious when the EKI phenomenon is planned to use for mixing such viscoelastic fluids. Our observations are in line with that seen in limited experimental studies conducted for these kinds of viscoelastic fluids.

Chaotic Mixing Intensification and Flow Field Evolution Mechanism in a Stirred Reactor Using a Dual-Shaft Eccentric Impeller

Chaotic Mixing Intensification and Flow Field Evolution Mechanism in a Stirred Reactor Using a Dual-Shaft Eccentric Impeller

The fluid dynamics of propagating fronts with solutal and thermal coupling

We numerically explore the propagation of reacting fronts in a shallow and horizontal layer of fluid. We focus on fronts that couple with the fluid due to density differences between the products and reactants and also due to heat release from the reaction. We explore fronts where this solutal and thermal coupling is cooperative or antagonistic. We quantify the fluid motion induced by the front and investigate the interactions of the front with the fluid as it propagates through quiescent, cellular and chaotic flow fields. The solutal coupling induces an extended convection roll that travels with the front, the thermal coupling due to heat release from the reaction generates a pair of convection rolls that travels with the front, and when both couplings are present there is a complex signature of these contributions. The details of the front dynamics depend significantly upon the interactions of the front-induced flow field with the fluid ahead of the front.

A simple yet efficient approach for electrokinetic mixing of viscoelastic fluids in a straight microchannel

Many complex fluids such as emulsions, suspensions, biofluids, etc., are routinely encountered in many micro and nanoscale systems. These fluids exhibit non-Newtonian viscoelastic behaviour instead of showing simple Newtonian one. It is often needed to mix such viscoelastic fluids in small-scale micro-systems for further processing and analysis which is often achieved by the application of an external electric field and/or using the electroosmotic flow phenomena. This study proposes a very simple yet efficient strategy to mix such viscoelastic fluids based on extensive numerical simulations. Our proposed setup consists of a straight microchannel with small patches of constant wall zeta potential, which are present on both the top and bottom walls of the microchannel. This heterogeneous zeta potential on the microchannel wall generates local electro-elastic instability and electro-elastic turbulence once the Weissenberg number exceeds a critical value. These instabilities and turbulence, driven by the interaction between the elastic stresses and the streamline curvature present in the system, ultimately lead to a chaotic and unstable flow field, thereby facilitating the mixing of such viscoelastic fluids. In particular, based on our proposed approach, we show how one can use the rheological properties of fluids and associated fluid-mechanical phenomena for their efficient mixing even in a straight microchannel.

Chaotic mixing in a free‐helix extruder using a new solution to the biharmonic equation

AbstractA recently published approach for modeling the cross flow in an extruder channel using a new solution to the biharmonic equation is utilized in a study of chaotic mixing in a free‐helix single‐screw extruder. This novel extruder was designed and constructed with the screw flight, also referred to as the helix, detached from the screw core. The flight‐helix had straight sides that more closely emulated rectangular channel theory than the nominal sloped sides of a conventional single screw channel. Each of the screw elements could be rotated independently to obtain chaotic motion in the screw channel. Using the new extruder, experimental evidence for the increased mixing of a dye, for both a Dirac and droplet input, with a chaotic flow field relative to the traditional residence time distribution is presented. These experimental results are compared using the new biharmonic equation‐based model. Comparing the experimental chaotic mixing with theoretical calculations was facilitated by a recently published technique for accurately placing the dye in the extruder channel. Because of the ability to periodically rotate only the flight/helix, the chaotic mixing results are minimally confounded by the existence of Moffatt eddies.

Evaporation of Binary-Mixture Liquid Droplets: The Formation of Picoliter Pancakelike Shapes.

Small multicomponent droplets are of increasing importance in a plethora of technological applications ranging from the fabrication of self-assembled hierarchical patterns to the design of autonomous fluidic systems. While often far away from equilibrium, involving complex and even chaotic flow fields, it is commonly assumed that in these systems with small drops surface tension keeps the shapes spherical. Here, studying picoliter volatile binary-mixture droplets of isopropanol and 2-butanol, we show that the dominance of surface tension forces at small scales can play a dual role: Minute variations in surface tension along the interface can create Marangoni flows that are strong enough to significantly deform the drop, forming micron-thick pancakelike shapes that are otherwise typical of large puddles. We identify the conditions under which these flattened shapes form and explain why, universally, they relax back to a spherical-cap shape toward the end of drop lifetime. We further show that the formation of pancakelike droplets suppresses the "coffee-ring" effect and leads to uniform deposition of suspended particles. The quantitative agreement between theory and experiment provides a predictive capability to modulate the shape of tiny droplets with implications in a range of technologies from fabrication of miniature optical lenses to coating, printing, and pattern deposition.

Quantification of Measurement and Model Effects in Monopile Foundation Scour Protection Experiments

The present work introduces an analysis of the measurement and model effects that exist in monopile scour protection experiments with repeated small scale tests. The damage erosion is calculated using the three dimensional global damage number S3D and subarea damage number S3D,i. Results show that the standard deviation of the global damage number σ(S3D)=0.257 and is approximately 20% of the mean S3D, and the standard deviation of the subarea damage number σ(S3D,i)=0.42 which can be up to 33% of the mean S3D. The irreproducible maximum wave height, chaotic flow field and non-repeatable armour layer construction are regarded as the main reasons for the occurrence of strong model effects. The measurement effects are limited to σ(S3D)=0.039 and σ(S3D,i)=0.083, which are minor compared to the model effects.

Self-propelled slender objects can measure flow signals net of self-motion

The perception of hydrodynamic signals by self-propelled objects is a problem of paramount importance ranging from the field of bio-medical engineering to bio-inspired intelligent navigation. By means of a state-of-the-art fully resolved immersed boundary method, we propose different models for fully coupled self-propelled objects (swimmers, in short), behaving either as “pusher” or as “puller.” The proposed models have been tested against known analytical results in the limit of Stokes flow, finding excellent agreement. Once tested, our more realistic model has been exploited in a chaotic flow field up to a flow Reynolds number of 10, a swimming number ranging between zero (i.e., the swimmer is freely moving under the action of the underlying flow in the absence of propulsion) and one (i.e., the swimmer has a relative velocity with respect to the underlying flow velocity of the same order of magnitude as the underlying flow), and different swimmer inertia measured in terms of a suitable definition of the swimmer Stokes number. Our results show the following: (i) pusher and puller reach different swimming velocities for the same, given, propulsive force: while for pusher swimmers, an effective slender body theory captures the relationship between swimming velocity and propulsive force, this is not for puller swimmers. (ii) While swimming, pusher and puller swimmers possess a different distribution of the vorticity within the wake. (iii) For a wide range of flow/swimmer Reynolds numbers, both pusher and puller swimmers are able to sense hydrodynamic signals with good accuracy.

A study of the influence of coflow on flame dynamics in impinging jet diffusion flames

Non-premixed impinging jet flames with different coflow conditions are performed using PIV technology combined with numerical simulation to investigate flame instability in the vicinity of wall. Results indicate that the increase of coflow velocity results in a more chaotic flow field and higher fuel efficiency, and the increase of coflow temperature leads to ignition advance and the increase of NO concentration. These can be attributed to the coupling effect of Kelvin-Helmholtz instability, convective instability and Rayleigh-Taylor instability. High coflow velocity is more likely to induce Kelvin-Helmholtz instability and convective instability, and the increase of coflow temperature enhances Rayleigh-Taylor instability and convective instability. Due to the impact effect in the vicinity of wall, the flame instability is more likely to be induced at high coflow velocity. Meanwhile, the increase of coflow temperature can inhibit flame wrinkles. The flame dynamics is affected by turbulent mixing, head-on collision, shear and convective behaviors in non-premixed flames.

Numerical and experimental analysis on the non-uniform inflow characteristics of a reactor coolant pump with a steam generator channel head

ABSTRACT Distorted inflow caused by the complex structure of the steam generator channel head (SGCH) occurs at the entrance to the reactor coolant pump (RCP) in the AP1000 system, which may generate impeller cracks and result in deterioration of performance and stability. In this paper, to analyze the influence of distorted inflow on flow properties of the RCP, the inflow distortion characteristics are studied by a full three-dimensional steady and unsteady numerical simulation. The simulation model was verified experimentally by testing the RCP with a straight pipe and a channel head at different flow rates. Using this model, the inlet distortion was quantified and the variation law of different distortion was obtained. The results showed that a non-uniform swirling flow under lateral pressure differences was formed when the pump was coupled with a channel head instead of a straight pipe, leading to the destruction of circular symmetry of the inflow field. Further increasing the tube length alone was not effective in improving the inflow field of the RCP, and the inlet swirl effect always existed. As the distorted flow entered the pump with a pair of vortices, the chaotic flow field imposed a non-uniform stress on each blade of the impeller, resulting in the unevenly distributed flow rate of each flow-path of the blade. Then, in the flow channels of the impeller, there were obvious asymmetrical vortex core regions, even in opposite directions, which originally formed in the inflow field of the RCP and raised the risk of blade fatigue failure. Owing to the significant effects of inflow distortion produced by the SGCH, understanding the mechanism of non-uniform inflow characteristic is of great value to the design and optimization of the RCP. Abbreviations: RCP: reactor coolant pump; SG: steam generator; SGCH: steam generator channel head

Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection.

We probe the effectiveness of using topological defects to characterize the leading Lyapunov vector for a high-dimensional chaotic convective flow field. This is accomplished using large-scale parallel numerical simulations of Rayleigh-Bénard convection for experimentally accessible conditions. We quantify the statistical correlations between the spatiotemporal dynamics of the leading Lyapunov vector and different measures of the flow field pattern's topology and dynamics. We use a range of pattern diagnostics to describe the flow field structures which includes many of the traditional diagnostics used to describe convection as well as some diagnostics tailored to capture the dynamics of the patterns. We use the ideas of precision and recall to build a statistical description of each pattern diagnostic's ability to describe the spatial variation of the leading Lyapunov vector. The precision of a diagnostic indicates the probability that it will locate a region where the Lyapunov vector is larger than a threshold value. The recall of a diagnostic indicates its ability to locate all of the possible spatial regions where the Lyapunov vector is above threshold. By varying the threshold used for the Lyapunov vector magnitude, we generate precision-recall curves which we use to quantify the complex relationship between the pattern diagnostics and the spatiotemporally varying magnitude of the leading Lyapunov vector. We find that pattern diagnostics which include information regarding the flow history outperform pattern diagnostics that do not. In particular, an emerging target defect has the highest precision of all of the pattern diagnostics we have explored.

Chaotic characteristics enhanced by impeller of perturbed six-bent-bladed turbine in stirred tank

The fundamental way of improving the mixing efficiency is to induce the chaotic flow in a stirred vessel. The impeller form plays an important role for changing the structure of flow field and realizing chaotic mixing. Based on the velocity time series acquired by the experiment of particle image velocimetry (PIV), with the software Matlab, the macro-instability (MI), largest Lyapunov exponent (LLE), and Kolmogorov entropy in the water stirred tank is investigated respectively with the impeller of perturbed six-bent-bladed turbine (6PBT). The results show that the MI characteristics are obvious and two peak values of MI frequency are observed at the speed N=60rpm. With the increasing speed (more than 100rpm), the peak characteristics of MI frequency disappear and a multi-scale wavelet structure of characterizing the chaotic flow field appears. Moreover, under the speed N=60rpm, the LLE is less than 0 and Kolmogorov entropy is 0, which means that the flow field is in the periodic moving state. As the speed is increased to more than 100rpm, the LLE and Kolmogorov entropy are all more than 0, which indicates that the flow field goes into the chaotic mixing. When the speed reaches up to about 210rpm, both of the LLE and Kolmogorov entropy achieve the optimum values, which will result in an excellent chaos with the highest mixing efficient. So it is feasible that the MI frequency, the LLE and the Kolmogorov entropy can be used to analyze the flow field characteristics in a stirred tank. The research results promote the understanding of the chaotic mixing mechanism and provide a theoretical reference for the development of new type impeller.