Cathy Castelain

The effects of chaotic advection on heat transfer

Abstract The objective of this study is to characterize a new heating process in fluids, chaotic advection. The main mechanism generating this flow is the production of spatially chaotic trajectories in an alternating Dean flow. The present work examines the effects of chaotic advection on heat transfer at low Reynolds numbers. In order to assess the enhancement of heat transfer by chaotic advection, a helical heat exchanger and a chaotic heat exchanger (both of shell-and-tube type) of the same heat-transfer surface area and the same tube length were tested. The coils were assembled from 90° bends, and the chaotic coil was produced merely by turning each bend at a ± 90° angle with respect to the previous one. Experiments were performed for Reynolds numbers ranging from 60 to 200. Temperature profiles measured in the cross-section of the coils show that chaotic advection substantially homogenizes and enhances heating. Moreover, it is shown that the homogeneity of heating in chaotic flow is almost independent of the Reynolds number. Parallel to the temperature profiles measurements, axial velocity profiles were measured by laser Doppler velocimetry at the exit from the coils and used to characterize the flow in the isothermal regime and compare the temperature profiles to the velocity profiles. Global heat-transfer measurements show that the chaotic heat exchanger is more efficient than the helical one, with an efficiency enhancement between 13 and 27%.

Heat exchanger design based on chaotic advection

Abstract Experiments on hydrodynamic and heat transfer behavior of the flow in a twisted curved channel were conducted in a water tunnel and also in two heat exchanger coils tested in a heat exchanger test facility. The flow regime, designated “chaotic advection,” is a subclass of laminar flow with high mixing properties. Preliminary results show that heat transfer is enhanced due to the chaotic trajectories generated in the flow.

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

Abstract 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.

Experimental study of chaotic advection regime in a twisted duct flow

The generation of Lagrangian chaos has been studied experimentally in a twisted duct flow, a configuration representing a three-dimensional steady open flow in which various signatures of Lagrangian chaos are documented. The twisted duct consists of four 90∘ bends of square cross-section; the plane of curvature of each bend is at 90∘ to that of its neighbors. Dean roll-cells, generated by centrifugal forces and the geometrical perturbation due to the change in curvature plane, are the source of the irregular trajectories of the fluid particles. The Eulerian nature of the flow was investigated using a laser Doppler velocimeter (LDV). From the Eulerian point of view, the flow is completely regular. We show by laser-induced fluorescence (LIF) visualization that many characteristics of a Lagrangian chaotic system are present in this flow: − strong stretching and folding of material lines and surfaces; − sensitivity to initial conditions; − exponential growth of stretching in some flow regions. It is also shown that in some regions of the flow stretchings grow linearly with space, indicating non-chaotic behavior. Due to the chaotic nature of the flow, an equalization of the fly-time of fluid particles was observed during their passage through the twisted duct.

Experimental and numerical characterisation of mixing in a steady spatially chaotic flow by means of residence time distribution measurements

Abstract This work describes an experimental study and a numerical simulation of residence time distributions (RTD) in a spatially chaotic three-dimensional flow. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean roll-cells. Fluid particle trajectories become chaotic through geometrical perturbation obtained by rotating the curvature plane of each bend ±90° with respect to the neighbouring ones. Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the chaotic mixer. The experimental RTD is modelled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for Reynolds numbers between 30 and 13,000. Peclet number based on the diameter of the pipe Pe D = W D D ax increases with Reynolds number, whatever the number of bends in the system. This reduction in axial dispersion is due to the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction increases with Reynolds number, whatever the number of bends, to reach a maximum value between 90 and 100%. For Reynolds numbers between 50 and 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube centre. In order to characterise more completely the efficiency of the device, a criterion is proposed that takes into account both the mixing characteristics and the pressure drop. The RTD for low Reynolds numbers has also been obtained numerically using a flow model based on Dean’s asymptotic perturbation solutions of the mean flow in a curved pipe. At the end of each bend, the velocity field is rotated by ±90° before entering the next bend. The RTD is calculated by following the trajectories of 250,000 ‘numerical’ particles along the device. Numerical results are in good agreement with experiments in the same Reynolds number range.

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the suspensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119–127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can be described by the Simha model (Simha, J Appl Phys 23:1020–1024, 1952). For the largest values of the volume fraction investigated, an apparent yield stress behaviour is observed. Increasing and decreasing stress ramps within this range of volume fractions indicate a thixotropic behaviour as well. The rheological behaviour observed within the high concentration regime bears similarities with the measurements performed by Heymann and Aksel (Phys Rev E 75:021505, 2007) on polymethyl methacrylate suspensions: irreversible flow behaviour (upon increasing/decreasing stresses) and dependence of the flow curve on the characteristic time of forcing (the averaging time per stress values). All these findings indicate a behaviour of the microalgae suspensions similar to that of suspensions of rigid particles. A deeper insight into the physical mechanisms underlying the shear thinning and the apparent yield stress regime is obtained by an in situ analysis of the microscopic flow of the suspension under shear. The shear thinning regime is associated to the formation of cell aggregates (flocs). Based on the Voronoi analysis of the correlation between the cell distribution and cell sizes, we suggest that the repulsive electrostatic interactions are responsible for this microscale organisation. The apparent yield stress regime originates in the formation of large-scale cell aggregates which behave as rigid plugs leading to a maximally random jammed state.

Investigation and modeling of the effects of light spectrum and incident angle on the growth of Chlorella vulgaris in photobioreactors

An in‐depth investigation of how various illumination conditions influence microalgal growth in photobioreactors (PBR) has been presented. Effects of both the light emission spectrum (white and red) and the light incident angle (0° and 60°) on the PBR surface were investigated. The experiments were conducted in two fully controlled lab‐scale PBRs, a torus PBR and a thin flat‐panel PBR for high cell density culture. The results obtained in the torus PBR were used to build the kinetic growth model of Chlorella vulgaris taken as a model species. The PBR model was then applied to the thin flat‐panel PBR, which was run with various illumination conditions. Its detailed representation of local rate of photon absorption under various conditions (spectral calculation of light attenuation, incident angle influence) enabled the model to take into account all the tested conditions with no further adjustment. This allowed a detailed investigation of the coupling between radiation field and photosynthetic growth. Effects of all the radiation conditions together with pigment acclimation, which was found to be relevant, were investigated in depth.

Characterisation of elastic turbulence in a serpentine micro-channel

A systematic experimental investigation of the onset, development, and statistical and scaling properties of elastic turbulence in a curvilinear micro-channel of a dilute solution of a high molecular weight polymer is presented. By measurements of time series of high spatial resolution flow fields performed over a time 320 times longer than the average relaxation, we show that the transition to elastic turbulence occurs via an imperfect bifurcation. Slightly above the onset of the primary elastic instability, rare events manifested through a local deceleration of the flow are observed. By measurements of the spatial distributions and statistics of the second invariant of the rate of strain tensor, we show that the main prediction of the theory regarding the saturation of root mean square of fluctuations of the velocity gradients is qualitatively verified though a quantitative agreement could not be found. A systematic analysis of the statistics of the fluctuations of flow fields in terms of spatial and te...

Secondary Flow Velocity Field in Laminar Pulsating Flow Through Curved Pipes: PIV Measurements

Effects of different parameters on the secondary flow pattern have been studied experimentally by particle image velocimetry (PIV) for a developing laminar pulsating flow through a circular curved pipe. The curvature ratio is η = rc /r0 = 11 and the curvature angle is 90°. As different secondary flow patterns formed by oscillation cause different transverse mixings, the enhancement of transverse mixing is investigated here. A T-shaped structure installed downstream of the curved pipe allowed PIV measurements obviating light diffraction effects. From knowledge of the velocity components of the secondary flow, the variation in axial vorticity (ξ) and transverse strain (e) were calculated. The experiments were carried out for the range of stationary Reynolds numbers 420≤Rest ≤1000 (corresponding to Dean numbers 126.6≤Dn≤301.51), velocity component ratios 1≤(β = Umax,osc /Um,st )≤4 and frequency parameters 8.37<(α = r0 (ω/v)0.5 )<24.5. To guarantee being in the laminar regime, the higher values of β (β = 3 and 4) were studied just for Rest = 420. The effects of each parameter ((Rest , β and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζP |/|ζS |) and dimensionless transverse strains (|eP |/|eS |) during a complete oscillation period.Copyright

Laminar Mixing, Heat Transfer and Pressure Losses in a Chaotic Mini-Channel: Application to the Fuel Cell Cooling

Currently, the heat exchangers allowing the cooling of the low temperature fuel cells (PEMFC) are integrated in the bipolar plates and constituted of a network of straight channels. The flow regime is laminar, and thus, unfavorable to an intense convective heat transfer. In order to increase the power density of the fuel cells, the use of chaotic geometries in the cooling system is envisaged to intensify high convective heat transfer. In this numerical study, several chaotic three-dimensional mini-channels of rectangular section (2 millimeters × 1 millimeter) are evaluated in terms of heat transfer efficiency, mixing properties and pressure losses. Their performances are compared to those of a straight channel geometry currently used in the cooling systems of the PEMFC, and a serpentine 2-D channel. Hydrodynamic and thermal performances of these geometries are computed using the commercial CFD code Fluent©. At the inlet section, the velocity profile is hydrodynamically established. The thermophysical properties of the fluid are constant and equal to those of water at 300 K. The Nusselt number is evaluated for a Reynolds number equal to 200 and with a uniform density flux imposed on the walls and equal to 10,000 W/m2 . For the calculation of the mixing rate, a condition of adiabatic wall is imposed. The inlet section is horizontally divided into two parts. Water in the higher part is at the temperature of 320K and in the lower part is at the temperature of 300K. The calculation of the mixing rate is made for Reynolds numbers equal to 100 and 200. The present study shows that a 3-D chaotic channel geometry significantly improves the convective heat transfer compared to regular straight or serpentine channels. Among all the studied geometries, one of them induces the higher heat transfer intensification (mean Nusselt number equal to 20) with a strong pressure loss. With an alternative geometry, we obtained a better compromise between high heat transfer and reduced pressure loss. However, all the chaotic geometries present similar mixing rate for the two studied Reynolds number. To confirm the performances of the selected geometries, an experimental study is currently undertaken. The final aim is to realize and test a prototype of chaotic heat exchanger in a bipolar plate of PEMFC.© 2006 ASME