Chaotic Flow Research Articles

High-Precision Numerical Investigation of a VAWT Starting Process

For both conventional and renewable energy conversion processes, computational fluid dynamics (CFD) has been used to address more energy-related challenges in recent decades. Using CFD to investigate vertical-axis wind turbines has become more common in recent years. The main goals of this application have been to more accurately predict the turbine’s performance and to comprehend the complicated nature of the complex turbulent flow. The vertical-axis wind turbine (VAWT) simulation for energy-generating applications has several intricate components. One of them is the study of the chaotic flow that occurs during the first stages of the starting process, and which greatly influences overall effectiveness. In this article, the performance of the wind turbine was increased using a passive flow control approach. The numerical research was carried out using Large Eddy Simulation for four alternative tip speed ratios in both cases, the classic and the optimized case, equipped with a vortex trap on the extrados of the blades. The power and torque coefficient variations, as well as the velocity magnitude contours, show that the starting process may begin with a significant improvement in efficiency when flow control is used.

Investigation into the Energy Loss Mechanism of Pump Turbine During the Runaway Process Based on Entropy Production Theory

Abstract The power-trip of the pump under certain conditions leads to the runaway of the unit, causing dangerous transitional process in pumped storage power stations. This process is characterized by transient hydraulic features like flow separation and vortex structures, which increase hydraulic losses significantly and severely impact unit efficiency and stability. This paper aims to elucidate the mechanism of energy loss due to unstable flow during pump turbine runaway. It focuses on a high-head model pump turbine, examining the transient flow process from pump conditions to runaway conditions. It conducts quantitative analysis of energy loss using entropy production theory, besides, further clarifies the location and causes of hydraulic losses by integrating with internal flow analysis. The results show that a significant high-entropy production zone is captured in the pump braking condition, indicating extremely chaotic internal flow in this area during the runaway transition process. Additionally, throughout the transition process, turbulent entropy production initially increases, then decreases. Turbulent entropy production accounts for more than 80% of total entropy production, indicating that turbulent entropy production dominates throughout the entire transition process. The energy of the water is primarily dissipated within the runner during the runaway process. The maximum proportion is 87%, which is in the pump braking condition. Correlation analysis between flow and hydraulic losses reveals that vortex structure induced by flow separation under off-design conditions is the primary contributor to increased hydraulic losses.

Surface roughness effects in a transonic axial flow compressor operating at near-stall conditions

Surface roughness is a major contributor to performance degradation in gas turbine engines. The fan and the compressor, as the first components in the engine's air path, are especially vulnerable to the effects of surface roughness. Debris ingestion, accumulation of grime, dust, or insect remnants, typically at low atmospheric conditions, over several cycles of operation are some major causes of surface roughness over the blade surfaces. The flow in compressor rotors is inherently highly complex. From the perspective of the component designers, it is, thus, important to study the effect of surface roughness on the performance and flow physics, especially at near-stall conditions. In this study, we examine the effect of surface roughness on flow physics such as shock-boundary layer interactions, tip and hub flow separations, the formation and changes in the critical points, and tip leakage vortices among other phenomena. Steady and unsteady Reynolds Averaged Navier Stokes calculations are conducted at near-stall conditions for smooth and rough National Aeronautics and Space Administration rotor 67 blades. Surface streamlines, Q-criterion, and entropy contours aid in analyzing the flow physics qualitatively and quantitatively. It is observed that from the onset of stall, to fully stalled conditions, the blockage varies from 21.7% to 59.6% from 90% span to the tip in the smooth case, and from 40.5% to 75.2% in the rough case. This significant blockage, caused by vortex breakdown and chaotic flow structures, leads to the onset of full rotor stall.

Chaotic mixing coupled electromagnetic heating in a tubular reactor

To address the need for enhanced biochemical reactions and overcome the shortcomings associated with passive and active mixer fabrication, reactor designs must utilize the coupled mixing concept to address the lack of insufficient heat and mass transfer through notable alterations of the physical properties. This study introduces a tubular microwave reactor based on chaotic flow dynamics, attempting to combine the concept of active and passive mixing to stimulate the development of eddy and secondary flows through electromagnetic fields and geometric disturbance enhance heat and mass transfer. Experiments and simulation analysis validate the validity of the prediction model, and reveal the fluid flow, mixing, electromagnetic and thermal characteristics and their synergistic mechanism, and shows the potential to enhance the mass and heat transfer performance at low Reynolds number, which provides a new idea for the design of chemical reactors and biological analysis.

Influence of the channel inclination on the exchange flow and vorticity transport characteristics in a regenerative flow pump

To enhance the overall performance of regenerative flow pump (RFP) to achieve efficient and stable operation over a broad range, this paper employs numerical simulation to study the internal flow conditions of RFP models with three different inclination coefficients (Ic = −0.25, Ic = 0, Ic = 0.25). The analysis focuses on the pressure distribution, energy exchange, velocity variation, and vorticity distribution characteristics within the impeller and channel. The comparison indicates that at Ic = −0.25 with an outward channel, the flow within the pump is stabilized, and the rate of pressure growth and exchange intensity are increased. When Ic = 0 with a semi-circular channel and Ic = 0.25 with an inward channel, there are narrower flow space at the channel's outer diameter, impeding effective fluid motion along the channel and inducing chaotic flow. This condition escalates flow losses and adversely affects the hydraulic performance of the RFP. Additionally, the analysis based on the vorticity transport equation reveals that the Coriolis force term significantly contributes to the generation and transport of vortex in the impeller, while the vortex stretching term dominates the transport of vortex in the channel.

Combining Computational Fluid Dynamics and Experimental Data to Understand Fish Schooling Behavior.

Understanding the flow physics behind fish schooling poses significant challenges due to the difficulties in directly measuring hydrodynamic performance and the three-dimensional, chaotic, and complex flow structures generated by collective moving organisms. Numerous previous simulations and experiments have utilized computational, mechanical, or robotic models to represent live fish. And existing studies of live fish schools have contributed significantly to dissecting the complexities of fish schooling. But the scarcity of combined approaches that include both computational and experimental studies, ideally of the same fish schools, has limited our ability to understand the physical factors that are involved in fish collective behavior. This underscores the necessity of developing new approaches to working directly with live fish schools. An integrated method that combines experiments on live fish schools with computational fluid dynamics (CFD) simulations represents an innovative method of studying the hydrodynamics of fish schooling. CFD techniques can deliver accurate performance measurements and high-fidelity flow characteristics for comprehensive analysis. Concurrently, experimental approaches can capture the precise locomotor kinematics of fish and offer additional flow information through particle image velocimetry (PIV) measurements, potentially enhancing the accuracy and efficiency of CFD studies via advanced data assimilation techniques. The flow patterns observed in PIV experiments with fish schools and the complex hydrodynamic interactions revealed by integrated analyses highlight the complexity of fish schooling, prompting a reevaluation of the classic Weihs model of school dynamics. The synergy between CFD models and experimental data grants us comprehensive insights into the flow dynamics of fish schools, facilitating the evaluation of their functional significance and enabling comparative studies of schooling behavior. In addition, we consider the challenges in developing integrated analytical methods and suggest promising directions for future research.

Equivariant Divergence Formula for Hyperbolic Chaotic Flows

We prove the equivariant divergence formula for axiom A flow attractors. It is a pointwisely-defined and recursive formula for perturbation of SRB measures along center-unstable manifolds. It depends on only the zeroth and first order derivatives of the map, the observable, and the perturbation. Hence, the linear response acquires an ‘ergodic theorem’, which means that it can be sampled by recursively computing a few vectors on one orbit.

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%.

CFD Simulation of Chaotic Flow Characteristics in an Oscillating Feedback Microreactor and Its Application for Preparing Zeolitic Imidazolate Framework-8 Nanoparticles

CFD Simulation of Chaotic Flow Characteristics in an Oscillating Feedback Microreactor and Its Application for Preparing Zeolitic Imidazolate Framework-8 Nanoparticles

Leidenfrost Effect-Induced Chaotic Vortex Flow for Efficient Mixing of Highly Viscous Droplets.

Efficiently mixing highly viscous liquids in microfluidic systems is appealing for green chemistry such as chemical synthesis and catalysis, but it is a long-standing challenge owing to the unfavorable diffusion kinetics. In this work, a new strategy is explored for mixing viscous droplets by harnessing a peculiar Leidenfrost state, where the substrate temperature is above the boiling point of the liquid without apparent liquid evaporation. Compared to the control experiment where the droplet stays at a similar temperature but in the contact boiling regime, the mixing time can be reduced significantly. Moreover, it is demonstrated that the liquid mixing originates from the chaotic convection flow in the Leidenfrost droplet, characterized by the internal vortex motion evidenced by the microscale visualization. A correlation between mixing time and droplet volume is also proposed, showing a good agreement with experimental results. It is further shown that Leidenfrost droplets can be used to synthesize nanoparticles of the desired morphology, and it is anticipated that this simple and scalable fabrication approach will find applications in the biological, pharmaceutical, and chemical industries.

Transition to chaotic flow, bifurcation, and entropy generation analysis inside a stratified trapezoidal enclosure for varying aspect ratio

In this numerical study, we investigate the effect of aspect ratio (AR) on the natural convection (NC) flow and entropy generation (Sgen) in a stratified fluid confined inside a trapezoidal enclosure with thermally stratified side walls. The bottom of the enclosure is heated, and top of the enclosure is cooled. We use the Finite Volume Method (FVM) for simulating unsteady flows. We consider a Prandtl number (Pr = 0.71 for air) and explore AR of 0.2, 0.5, and 1.0, covering a wide range of Grashof numbers (Gr) from 10 to 108. The outcomes are presented for Grashof numbers and the effect of the AR on fluid flow, rates of heat transfer (HT), and Sgen inside the enclosure. Critical Grashof numbers are identified, marking the shift in flow behavior from being influenced by baroclinic to Rayleigh–Bénard instability, and from a steady to an unsteady state for various AR. In the context of this transition to chaotic flow, several supercritical bifurcations are observed, including a Pitchfork bifurcation from symmetric to asymmetric states and a Hopf bifurcation from a steady state to an unsteady state. Additionally, we analyze the discrepancies in average entropy generation (Savg) and average Bejan number (Beavg) across the entire enclosure, considering various AR and Gr values. It is observed that for enclosures with Gr ≥ 105, Savg increases as AR decreases, indicating an enhancement in HT rate with decreasing AR. Furthermore, a quantitative relationship between Savg, HT, AR, and Gr is presented. The study concludes that, as AR increases, the ecological coefficient of performance (ECOP) decreases, signifying a reduction in thermodynamics efficiency.

Nested travelling wave structures in elastoinertial turbulence

Elastoinertial turbulence (EIT) is a chaotic flow resulting from the interplay between inertia and viscoelasticity in wall-bounded shear flows. Understanding EIT is important because it is thought to set a limit on the effectiveness of turbulent drag reduction in polymer solutions. Here, we analyse simulations of two-dimensional EIT in channel flow using spectral proper orthogonal decomposition (SPOD), discovering a family of travelling wave structures that capture the sheetlike stress fluctuations that characterise EIT. The frequency-dependence of the leading SPOD mode contains distinct peaks and the mode structures corresponding to these peaks exhibit well-defined travelling structures. The structure of the dominant travelling mode exhibits shift–reflect symmetry similar to the viscoelasticity-modified Tollmien–Schlichting (TS) wave, where the velocity fluctuation in the travelling mode is characterised by large-scale regular structures spanning the channel and the polymer stress field is characterised by thin, inclined sheets of high polymer stress localised at the critical layers near the channel walls. The travelling structures corresponding to the higher-frequency modes have a very similar structure, but are nested in a region roughly bounded by the critical layer positions of the next-lower-frequency mode. A simple theory based on the idea that the critical layers of mode $\kappa$ form the ‘walls’ for the structure of mode $\kappa +1$ yields quantitative agreement with the observed wave speeds and critical layer positions, indicating self-similarity between the structures. The physical idea behind this theory is that the sheetlike localised stress fluctuations in the critical layer prevent velocity fluctuations from penetrating them.

Mixing as a correlated aggregation process

Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae that coalesce due to molecular diffusion. Owing to the linearity of the advection–diffusion equation, coalescence can be envisioned as an aggregation process. Here, we demonstrate that in smooth two-dimensional chaotic flows, mixing obeys a correlated aggregation process, where the spatial distribution of the number of lamellae in aggregates is highly correlated with their elongation, and is set by the fractal properties of the advected material lines. We show that the presence of correlations makes mixing less efficient than a completely random aggregation process because lamellae with similar elongations and scalar levels tend to remain isolated from each other. We show that correlated aggregation is uniquely determined by a single exponent that quantifies the effective number of random aggregation events. These findings expand aggregation theories to a larger class of systems, which have relevance to various fundamental and applied mixing problems.

EFFECTS OF CONTINUOUS AND FRACTURED RIBS PLACED AT THE ENDWALL SURFACE UPSTREAM OF THE TURBINE-VANE LEADING-EDGE

Total pressure loss, chaotic and heavy flow downstream of the turbine passage exit area are a few effects of the desired increase in inlet temperature input at the upstream part of the turbine vane passage. Huge amount of energy from the cross-flows near the middle of the vane actual chord are transported downstream by this chaotic flow which often results in aerodynamic loss and differential heat penalties. To compare the different arrangement, comparisons of the two geometries, the impact of adding various rib configurations upstream are studied for heat augmentation efficacies. The leading-edge rib(s) effects at the mid-stream of the vane passage are quantitatively examined in this work using computational fluid dynamics (CFD) technique. With the employment of Reynolds Averaged Navier-Stoke energy equations, the geometries are modelled choosing the appropriate boundary conditions. Polyhedral mesh is used with fifteen prism layer mesh at the endwall and vane surfaces to capture the flow physics close to the endwall area. Although the two configurations employed showed relative reduction in the total pressure loss coefficient, however, the fractured ribs produced superior outcomes of Nusselt number reduction of over 10% along the passage exit region. The data demonstrate a considerable difference in the overall pressure loss between the two configurations.

A 4D conservative chaotic system: dynamics and realization

This paper proposes a novel four-dimensional conservative chaotic system (4D CCS) with a simple algebraic representation, comprising only two quadratic nonlinear terms. The dynamic characteristics of the 4D CCS are investigated by Poincaré mappings, Lyapunov exponents (LE), bifurcation diagrams, equilibrium points and spectral entropy (SE) complexity algorithm. Variations in parameters, initial values, and Hamiltonian energy lead to alternations between quasi-periodic and chaotic flows in the 4D CCS. The maximum Lyapunov exponent of the 4D CCS can reach a high value of 366300 under adjusting appropriate parameters and initial values. The pseudorandom sequences generated by the 4D CCS successfully pass the NIST test. Additionally, both the electronic circuit and FPGA implementation of the 4D CCS are carried out, with the experimental results aligning closely with the simulation results.

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number.

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

Natural Convection Fluid Flow and Heat Transfer in a Valley-Shaped Cavity

The phenomenon of natural convection is the subject of significant research interest due to its widespread occurrence in both natural and industrial contexts. This study focuses on investigating natural convection phenomena within triangular enclosures, specifically emphasizing a valley-shaped configuration. Our research comprehensively analyses unsteady, non-dimensional time-varying convection resulting from natural fluid flow within a valley-shaped cavity, where the inclined walls serve as hot surfaces and the top wall functions as a cold surface. We explore unsteady natural convection flows in this cavity, utilizing air as the operating fluid, considering a range of Rayleigh numbers from Ra = 100 to 108. Additionally, various non-dimensional times τ, spanning from 0 to 5000, are examined, with a fixed Prandtl number (Pr = 0.71) and aspect ratio (A = 0.5). Employing a two-dimensional framework for numerical analysis, our study focuses on identifying unstable flow mechanisms characterized by different non-dimensional times, including symmetric, asymmetric, and unsteady flow patterns. The numerical results reveal that natural convection flows remain steady in the symmetric state for Rayleigh values ranging from 100 to 7 × 103. Asymmetric flow occurs when the Ra surpasses 7 × 103. Under the asymmetric condition, flow arrives in an unsteady stage before stabilizing at the fully formed stage for 7 × 103 < Ra < 107. This study demonstrates that periodic unsteady flows shift into chaotic situations during the transitional stage before transferring to periodic behavior in the developed stage, but the chaotic flow remains predominant in the unsteady regime with larger Rayleigh numbers. Furthermore, we present an analysis of heat transfer within the cavity, discussing and quantifying its dependence on the Rayleigh number.

Harnessing elastic instabilities for enhanced mixing and reaction kinetics in porous media

Turbulent flows have been used for millennia to mix solutes; a familiar example is stirring cream into coffee. However, many energy, environmental, and industrial processes rely on the mixing of solutes in porous media where confinement suppresses inertial turbulence. As a result, mixing is drastically hindered, requiring fluid to permeate long distances for appreciable mixing and introducing additional steps to drive mixing that can be expensive and environmentally harmful. Here, we demonstrate that this limitation can be overcome just by adding dilute amounts of flexible polymers to the fluid. Flow-driven stretching of the polymers generates an elastic instability, driving turbulent-like chaotic flow fluctuations, despite the pore-scale confinement that prohibits typical inertial turbulence. Using in situ imaging, we show that these fluctuations stretch and fold the fluid within the pores along thin layers ("lamellae") characterized by sharp solute concentration gradients, driving mixing by diffusion in the pores. This process results in a [Formula: see text] reduction in the required mixing length, a [Formula: see text] increase in solute transverse dispersivity, and can be harnessed to increase the rate at which chemical compounds react by [Formula: see text]-enhancements that we rationalize using turbulence-inspired modeling of the underlying transport processes. Our work thereby establishes a simple, robust, versatile, and predictive way to mix solutes in porous media, with potential applications ranging from large-scale chemical production to environmental remediation.

Analysis of Multistability of Financial Risk Chaos Systems and Its Application to Voice Cryptography

In the chaos literature, the application of modeling and control of dynamic systems in chaos theory arising in several fields is investigated. In this article we analyze complex financial chaos systems with countries as interest rates, investment demand, and price indices. The proposed chaotic flow's dynamic behavior is examined using phase portraits, eigenvalues, bifurcation diagrams, and Lyapunov exponent spectra. A significant quantity of research on secure communication systems has been published in recent years as a result of the major advancements in communications equipment and encryption techniques. A new voice encryption algorithm design is given using a financial chaos model. An application for voice encryption is conducted using the suggested algorithm, and the outcomes are described.

Thermal and Hydrodynamic Measurements of a Novel Chaotic Micromixer to Enhance Mixing Performance

In this study, three-dimensional simulations were conducted on a new passive micromixer to assess the thermal and hydrodynamic behaviors of Newtonian and non-Newtonian fluids subjected to low generalized Reynolds numbers (0.1 to 50) and shear-thinning properties. To acquire a more profound comprehension of the qualitative and quantitative fluctuations in fluid fraction using the CFD Fluent Code, the mass mixing index, rheological behavior, performance index, mixing energy cost, mass fraction distributions, temperature contours, and pressure drop were compared to illustrate the importance of the mixer geometry in the context of two miscible fluids with varying inlet temperatures. The selected geometry is characterized by a robust chaotic flow that substantially enhances thermal and hydrodynamic performance across all Reynolds numbers. A mass mixing exceeding 72.5% is obtained when Re = 5, reaching 93.5% when Re = 50. Furthermore, the evolution of thermal mixing for all behavior indexes reaches a step of 98% with minimal pressure losses. This work enabled the demonstration of a chaotic geometry in a highly efficient mixing system, leading to enhanced thermal performance for both Newtonian and non-Newtonian fluids. The results of the hydrodynamic and thermal characterization of the mixing of shear-thinning fluids within the micromixers under investigation are conclusive.