Chaotic Advection Flow Research Articles

A comprehensive study on the characterization of chaotic advection flow and heat transfer in a twisted pipe with elliptical cross-section

Chaotic advection flow is one of the most useful methods to enhance mixing and heat transfer simultaneously in the laminar flow which is generated by spatially chaotic trajectories of the fluid particles. The present study aims to characterize the behavior of chaotic advection flow and heat transfer in a twisted pipe. The considered geometry consists of three 90° bends with an elliptical cross-section; the angle between curvature planes of consecutive bends is 90°. Numerical simulations are performed for both steady-state and pulsatile (unsteady) inlet velocity conditions with the Reynolds numbers in the range of 200 ≤ Re ≤ 450, wall temperatures 310 ≤ Tw(K) ≤ 340, velocity amplitude ratios (the ratio of peak oscillatory velocity component to the mean flow velocity) 1 ≤ β ≤ 3, and Womersley numbers 2.1118 ≤ α ≤ 7.9018. Mixing and heat transfer are analyzed both qualitatively and quantitatively for various considered conditions. The results revealed that the elliptical cross-section has a considerable impact besides the chaotic configuration on mixing and heat transfer enhancement. In the steady-state flow, the desirable system efficiency can be achieved either by increasing the wall temperature or decreasing the Reynolds number. Moreover, in the pulsatile flow, the Womersley numbers in the range of 2.1118 ≤ α ≤ 3.9509 provide a favorable condition to augment the mixing and heat transfer in the twisted pipe.

ONE-DIMENSIONAL CHAOTIC LAMINAR FLOW WITH COMPETITIVE EXOTHERMIC AND ENDOTHERMIC REACTIONS

AbstractWe consider the numerical solution of competitive exothermic and endothermic reactions in the presence of a chaotic advection flow. The resulting behaviour is characterized by a strong dependence on the competitive reaction history. The burnt temperature is not immediately connected to simple enthalpy calculations, so there is a subtlety in the interplay between the major parameters, notably the Damköhler number, the ratio of the heats of exothermic and endothermic reactions, as well as the ratio of their respective activation energies. This paper seeks to explore the way these parameters affect the steady states of these reaction fronts and their stability.

Experimental and numerical analysis of Y-shaped split and recombination micro-mixer with different mixing units

Three representative types of Y-shaped split and recombination three-dimensional passive micromixers are analyzed for mixing efficiency both experimentally and by numerical simulation. These designs are important because of simple fabrication and better mixing ability. The flow and mixing capability of these mixers are numerically investigated for Reynolds number, in the range of 0.5–100. Mixing index and pressure drop of each micro-mixer design are evaluated in COMSOL 5.2a. All Proposed designs mixing index line graph and images are clearly showing that mixing is much improved as compared to straight mixer YSSAR. It is due to chaotic advection and Dean Flow effect in YCSAR, YRCSAR, and YRSAR that transverse flow mechanism enhance the mixing index. The mixing index of YRCSAR, having both circular and rhombus mixing units is 99% at Reynolds number 100 superior in mixing performance as compared other proposed micro-mixers. Mixers chips are fabricated from borosilicate glass and liquid silicone elastomer material. Red and yellow dye was used for evaluating the mixing performance experimentally. Simulation and experimental images of analyzed micro-mixers as well as the line plots, both shows that with an increase in Reynolds number mixing index increases. As a result of the increase in Reynolds number, there is an increase in the chaotic advection and Dean Flow effect, which creates rotations and vortices and hence improve the mixing index. There is a little difference in experimental and simulation results values but the overall trends are consistent in both cases.

Using chaotic advection to enhance the continuous heat-hold-cool sterilisation process

Abstract In a conventional continuous sterilisation process, the food product flows steadily through a heat-hold-cool system, but viscous flow poses a serious challenge as heat transfer is controlled by thermal conduction which leads to a wide radial temperature distribution and slow heating of the core region of the flow. We use a validated Computational Fluid Dynamics (CFD) model to show that the superimposition of transverse mechanical oscillations on the heat-hold-cool sterilisation process of a viscous single-phase Newtonian fluid, creates a strong oscillatory-perturbed or chaotic advection flow which leads to significant improvements in thermal processing uniformity and product quality compared with a conventional process with or without an inline static mixer fitted. Chaotic advection flow produces processing conditions which are more in line with the high temperature for short time (HTST) assumption. Results show that the vibrated process leads to faster nearly-uniform heating and cooling, thus, achieving much higher levels of sterility and product quality in a much shorter process. Industrial Relevance Technological solutions are needed to help solve the long-standing problem of wide variation of product sterility and nutritional quality across the tube in continuous thermal processing of viscous fluids, where much of the product has to be over-processed to ensure sterility throughout, thus, often violating the high temperature for short time (HTST) processing assumption. Superimposing a secondary chaotic flow on the process leads to high levels of sterility, processing uniformity and product quality over relatively short process lengths. This represents an enhanced process which surpasses conventional steady flow sterilisation even when an usually undesirable static mixer is fitted.

Assessing the potential of using chaotic advection flow for thermal food processing in heating tubes

Most food materials tend to be viscous and in general flow in the laminar regime. In continuous food sterilisation, the non-uniform velocity profile which characterises viscous flow coupled with a non-uniform temperature distribution result in a wide variation of product sterility and nutritional quality across the tube. The challenge is to be able to sterilise the fastest parts in the core region of the tube without over-processing too much the slowest parts near the wall. Chaotic advection is an alternative to turbulence, and uses the stretching and folding property of chaotic flows to promote fluid mixing at low Reynolds numbers. The use of inline static mixers or vortex generators to promote radial mixing and, thus, heat transfer and temperature uniformity, generates large pressure drops but more importantly these devices are unhygienic. We use a validated Computational Fluid Dynamics (CFD) model to show that mechanical vibration is an effective source of chaotic advection. The superimposition of a transverse harmonic motion on the flow of a single-phase viscous fluid in a heating tube, leads to large improvements in thermal processing uniformity and efficiency compared with a conventional process with or without an inline static mixer fitted. Results show that high levels of sterility, processing uniformity and product quality can be achieved in relatively short heating tubes, thus, potentially obviating the need for a holding stage.

Heat transfer enhancement by combination of chaotic advection and nanofluids flow in helically coiled tube

In this study, two passive techniques are simultaneously investigated for heat transfer improvement (i.e. chaotic advection and nanofluids) in coiled heat exchangers. Performance of these two different coils (one with normal configuration and another with chaotic configuration) is numerically analyzed and compared for both water and nanofluid as fluid. Effects of different parameters such as geometry, types of nanofluids, nanoparticle volumetric concentration and Reynolds number on heat transfer and pressure drop are studied. The CuO and Al2O3 base water nanofluids with different nanoparticle concentrations 1–3% were simulated. Equations of conservation of mass, momentum and energy were discretized using a finite element based technique and were solved using ANSYS software. Numerical results showed that heat transfer in the chaotic coil with water as fluid was higher than that in the normal coil with nanofluids at various volumetric concentrations and addition small amount of nanofluid in the chaotic coil flow resulted in significant enhancement of heat transfer.

Chaotic mixing by longitudinal vorticity

In this paper, scalar mixing by several arrays of vortex generators mounted inside a circular pipe is investigated using numerical simulations. Two flow configurations are studied in which the arrays are in-line and rotated periodically by an angle of 90°. Each vortex generator creates a pair of streamwise vortices which enhances the mixing process in the flow cross-section. It is shown that the alternate configuration, in which the vortex generators are rotated periodically by an angle of 90°, enhances the mixing process relative to the in-line one due to the generation of chaotic advection flow, while in the in-line configuration the flow is regular and the mixing process is only caused by the convective motion of the longitudinal vortices. Both Eulerian and Lagrangian analyses are used to investigate the chaotic behavior. From the Poincaré sections, the alternate rotation of the vortex generators is found to better disperse the fluid particles in the flow cross-section, while in the in-line array the particles are trapped into the vortex core. The Lagrangian study shows that initially close fluid particle paths exhibit an exponential remoteness in the alternate configuration, a sign of chaotic advection flow. This chaotic advection enhances the stretching and folding of the fluid particles which are responsible for mixing in laminar flows. The proposed flow configuration can be used as a multifunctional heat exchanger/reactor for industrial applications such as in chemical reaction and food processing.

Smooth and filamental structures in chaotically advected chemical fields

This paper studies the spatial structure of decaying chemical fields generated by a chaotic-advection flow and maintained by a spatially smooth chemical source. Previous work showed that in a regime where diffusion can be neglected (large Péclet number), the structures are filamental or smooth depending on the relative strength of the chemical dynamics and the stirring induced by the flow. The scaling exponent, gamma(q), of the qth -order structure function depends, at leading order, linearly on the ratio of the rate of decay of the chemical processes, alpha , and the average rate of divergence of neighboring fluid parcel trajectories (Lyapunov exponent), h. Under a homogeneous stretching approximation, gamma(q)/q=max[alpha/h,1] which implies that a well-defined filamental-smooth transition occurs at alpha=h. This approximation has been improved by using the distribution of finite-time Lyapunov exponents to characterize the inhomogeneous stretching of the flow. However, previous work focused more on the behavior of the exponents as q varies and less on the effects of alpha and hence the implications for the filamental-smooth transition. Here we set out the precise relation between the stretching rate statistics and the scaling exponents and emphasize that the latter are determined by the distribution of the finite-size (rather than finite-time) Lyapunov exponents. We clarify the relation between the two distributions. We show that the corrected exponents, [symbol: see text] depend nonlinearly on alpha with [formula: see text]. The magnitude of the correction to the homogeneous stretching approximation, [formula: see text], grows as alpha increases, reaching a maximum when the leading-order transition is reached (alpha=h). The implication of these results is that there is no well-defined bulk filamental-smooth transition. Instead it is the case that the chemical field is unambiguously smooth for alpha>h(max), where h(max) denotes the maximum finite-time Lyapunov exponent and unambiguously filamental for alpha<h, with an intermediate character for alpha between these two values. Theoretical predictions are confirmed by numerical results obtained for a linearly decaying chemistry coupled to a renewing type of flow together with careful calculations of the Crámer function.

Influence of Viscosity Ratio on Droplets Formation in a Chaotic Advection Flow

The efficiency of liquid/liquid dispersion is an important sake in numerous sectors, such as the chemical, food, cosmetic and environmental industries. In the present study, dispersion is achieved in an open-loop reactor consisting of simple curved pipes, either helically coiled or chaotically twisted. In both configurations, we investigate the drop breakup process of two immiscible fluids (W/O) and especially investigate the effect of the continuous phase viscosity, which is varied by the addition of different fractions of butanol in the native sunflower oil. The global Reynolds numbers vary between 40 and 240, so that the flow remains laminar while the Dean roll-cells in the bends develop significantly. Different fractions of butanol are added to the oil in each case to examine the influence of the continuous phase viscosity on the drop size distribution of the dispersed phase (water). When the butanol fraction is decreased, the dispersion process is intensified and smaller drops are created. The Sauter mean diameters obtained in the chaotic twisted pipe are compared with those in a helically coiled pipe flow. The results show that chaotic advection intensifies the droplet breakup until there is a 25% reduction in droplet size.

The role of a delay time on the spatial structure of chaotically advected reactive scalars

The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large P\'eclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a H\"older exponent that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate. In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. Depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length scales. An expression for the transition length scale dividing small-scale and intermediate-scale regimes is obtained and the scaling behavior of the scalar field is explained. The theoretical results are illustrated by numerical calculations for two types of reaction models, both based on delay differential equations, coupled to a two-dimensional chaotic advection flow. The first corresponds to a single reactive scalar and the second to a nonlinear biological model that includes nutrients, phytoplankton and zooplankton. As in the no-delay case, the presence of asymmetrical couplings among the biological species results in a non-generic scaling behavior.

Liquid/liquid dispersion in a chaotic advection flow

Mixing by chaotic advection in a twisted-pipe flow is used here to investigate the efficiency of this flow in the liquid/liquid dispersion process. This study focuses on water/oil dispersions produced by continuous water injection into a main oil flow, for small Dean numbers. The drop sizes obtained with the chaotic-advection twisted-pipe flow are compared with those in a straight pipe and a helically coiled flow for the same conditions. It is found that the resulting dispersions are finer and more mono-dispersed in the chaotic advection flow. These results are compared with the theoretical maximum diameter d max determined by the Grace theory in which the viscous stress controls the breakup phenomena. For this purpose, the kinematic field is computed from the theoretical formulae for Dean flow. The strain rate fields in the pipe cross-section are then analytically computed and used to predict the maximum drop diameter. The theoretical values are identical for the three configurations (straight, helically coiled, and twisted pipe) up to a critical Dean number, where the secondary flow becomes significant. Beyond this value, the shear stress is enhanced in the twisted-pipe flow compared with the straight-pipe flow, and the predicted drop diameters are smaller. An interpretation of the higher dispersive performance of the chaotic flow is provided by the Lagrangian trajectories of the particles.

Effect of chaotic mixing on enhanced biological growth and implications for wastewater treatment: A test case with Saccharomyces cerevisiae

Mixing patterns and modes have a great influence on the efficiency of biological treatment systems. A series of laboratory experiments was conducted with a controlled, small-scale analog of a pilot wastewater aeration tank, consisting of two eccentrically placed cylinders. By controlling the rotation direction and speed of the two cylinders, it has been possible to develop chaotic flow fields in the space between the walls of the cylinders. Our experiments utilized Saccharomyces cerevisiae as the biological oxidation organism and air bubbles as the mixing agent supplied by a large fine pore diffuser to the cells in their exponential growth phase. The effect of various mixing patterns on cell growth was studied at different cylinder eccentricities, rotation directions and speeds. It was found that chaotic advection flow patterns: (a) enhanced growth, and (b) sped up the onset of maximal growth of the organism by 15–18% and 14–20%, respectively.

A chaotic heat-exchanger for PEMFC cooling applications

High-efficiency cooling systems are key points in PEMFC transport applications, as the volume constraints force the reduction of the stack size while increasing the power density. Moreover, to ensure an optimal electrochemical reaction over the whole polymer membrane surface and hence a maximum efficiency, the temperature field in the cell must be uniform and stay in a narrow range, around 80–90 °C. This study focuses on improving the thermal performance of heat-exchangers integrated in the bipolar plates of PEMFCs. The current design of the heat-exchangers in these applications is quite simple; cooling liquid (water) flows in straight channels or serpentines in the rear of the plates. The flow regime is laminar with a Reynolds number around 200. In order to enhance convective heat transfer, we propose here to promote three-dimensional flow inside cooling channels using a novel channel geometry that generates chaotic advection flow. However, to limit the size and the electric resistance of the bipolar plates, the thickness must be severely limited. This work concentrates on developing and characterizing heat-exchangers that can be easily reduced in size while preserving high thermal performance.

A mapping tool using anisotropic unstructured meshes to study mixing in periodic flows

The objective of the present work is to describe a new mapping tool using anisotropic unstructured meshes to study mixing within a spatially periodic pipe flow. Instead of tracking the boundaries of elementary cell flow domains as it was done in the original mapping method established by Kruijt et al. (A.I.Ch.E. J. 47 (5) (2001a) 1005; Int. Polym. Process. 16 (2) (2001b) 151) and Galaktionov et al. (Comput. Fluids 30 (3) (2001) 271), the deformation of elementary triangles (only three nodal points) between the inlet and exit pipe cross-sections is followed. It is however necessary to adapt the initial mesh according to criteria which takes into account the spatial stretching and folding of fluid elements. The method developed is applied to the twisted curved pipes (TCP) three-dimensional (3D) flow. We show the evolution of concentration distributions along the TCP mixer for chaotic advection flow regimes. This method allows the emphasis of isolated unmixed regions (KAM islands). The flexibility of the method allows also the possibility of studying multiple stirring protocols, thus contributing to a better comprehension of the physical phenomena involved in chaotic mixing. The method developed is also applicable to 2D temporally periodic flows.

Scalar variance decay in chaotic advection and Batchelor-regime turbulence.

The decay of the variance of a diffusive scalar in chaotic advection flow (or equivalently Batchelor-regime turbulence) is analyzed using a model in which the advection is represented by an inhomogeneous baker's map on the unit square. The variance decays exponentially at large times, with a rate that has a finite limit as the diffusivity kappa tends to zero and is determined by the action of the inhomogeneous map on the gravest Fourier modes in the scalar field. The decay rate predicted by recent theoretical work that follows scalar evolution in linear flow and then averages over all stretching histories is shown to be incorrect. The exponentially decaying scalar field is shown to have a spatial power spectrum of the form P(k) approximately k(-sigma) at wave numbers small enough for diffusion to be neglected, with sigma<1.

Chaotic heat transfer for heat exchanger design and comparison with a regular regime for a large range of Reynolds numbers

An experimental comparison is made over a large range of Reynolds numbers (from 30 to 30,000) between two shell-and-tube heat exchangers having the same heat-transfer area and same number of bends, but different configurations: one has a helical configuration (regular flow), the other has a chaotic one (chaotic advection flow). Both are composed of 33 bends with circular tube cross section (inside diameter 23 mm) and are immersed in a closed shell. The working fluids are Newtonian with different Prandtl numbers (820, 230, 75 and 6.5) in order to cover the large-Reynolds-number range. The comparison is made by using a criterion L that takes into account thermal performance and energy expenditure. The results show that at low Reynolds numbers, heat transfer is higher and heating more homogeneous for chaotic advection flow, with no increase in energy expenditure. At high Reynolds numbers, the configuration has no influence on heat transfer. When the Prandtl number increases, the heat transfer increases. The flows have also been visualized by laser-induced fluorescence to assess the improvement of mixing in the chaotic configuration.