Soft Turbulence Research Articles

Shape-Morphing Dynamics of Soft Compliant Membranes for Drag and Turbulence Modulation.

We study the kinematics and dynamics of a highly compliant membrane disk placed head-on in a uniform flow. With increasing flow velocity, the membrane deforms nonlinearly into increasingly parachutelike shapes. These aerodynamically elongated materials exhibit a modified drag law, which is linked to the elastohydrodynamic interactions. We predict the unsteady structural response of the membranes using a nonlinear, aeroelastic model-in excellent agreement with experimental measurements of deformations and force fluctuations. With simultaneous membrane interface tracking, force measurements and flow tracing, we reveal that a peculiar skewness in the membrane's oscillations triggers turbulence production in the wake, thereby modulating the drag. The present work provides a demonstration of the complex interplay between soft materials and fluid turbulence, leading to new, emergent system properties.

Turbulent Rayleigh-Bénard convection of cold water near its maximum density in a vertical cylindrical container

In order to understand the effects of density inversion parameter and Rayleigh number on the fluid motion and heat transfer characteristics of penetrative Rayleigh-Bénard convection in a cylindrical container, a series of large eddy simulations were performed. The working fluid is cold water and Prandtl number is 11.57. Rayleigh number up to 1011 is considered and the density inversion parameter ranges from 0 to 0.7. The results indicate that the effect of cold plumes on the larger scale circulation gradually diminishes and finally disappears with the increase of density inversion parameter. Furthermore, an increase of the temperature within the bulk region and a decrease of the penetration depth are also certified with the increase of density inversion parameter. With the increase of Rayleigh number, soft and hard turbulent states are successively observed. In the soft turbulence state, the evolution of Nusselt number shows a weak fluctuation, the corresponding histogram has a Gaussian distribution, and the penetration depth increases sharply with the increase of Rayleigh number. In the hard turbulence state, the evolution of Nusselt number presents a much stronger fluctuation than that in the soft turbulence state, the corresponding histogram fits more exponential distribution, and the variation of the penetration depth with Rayleigh number is small. A single power law between the heat transfer efficiency (Nusselt number) and Rayleigh number that covers soft and hard turbulence states is developed for each density inversion parameter. It is found that the average Nusselt number decreases linearly with the increase of density inversion parameter.

Analysis of coherent structures in Rayleigh–Bénard convection

Using direct numerical simulation, we investigate characteristics of coherent structures in Rayleigh–Bénard convection in a soft turbulence regime. The role of thermal plumes, essential structures in Rayleigh–Bénard convection, is studied by splitting flow regimes into thermal plume and background by investigating joint probability density function (PDF) of invariants of velocity gradient tensor. The contribution to thermal dissipation rate by these two regions is analysed separately. Through the joint PDF of invariants, we also examine the thermal effect on velocity structures.

Heat transport regimes in an inclined channel

In this paper we report measurements of the heat flux in a slightly tilted channel (angle less than 45°), filled with water, that connects two chambers: the hot in the lower part and the cold on the top. We show that different regimes develop depending on the angle and the applied power. We put in evidence a hard turbulent regime, a soft turbulent regime, a laminar regime, and an intermittent one. In the last regime, the flow oscillates between laminar and turbulent, which locks the temperature gradient to a constant value. We characterize those regimes thanks to the measurement of the axial gradient of temperature and to the measurement of the power. We model them giving descriptions in term of Nusselt and Rayleigh numbers. The soft turbulence to hard turbulence transition is interpreted as the birth of the inertial range of developed turbulence. This transition, which appears in several systems, is particularly clear here, thanks to its consequences on heat transport properties.

Numerical Study of Effect of Polymer Additives on Heat Transport in Turbulent Rayleigh- Bénard Convection

In this study, the Reynolds-Averaged-Navier-Stokes (RANS) model combined with the Cross Viscosity Equation is used, applied to the soft turbulence regime (Ra =5×105~4×107) and hard turbulence regime (Ra>4×107) of Rayleigh-Bénard convection (RBC). The relation curves between heat transport (Nusselt number) and other parameters, as well as flow pattern changes of RBC are obtained for the cases with different Rayleigh number and concentration of the polymer additive. The simulations show that the presence of polymer additive can lead to an enhancement of the heat transfer with larger effect in the hard turbulence regime than those in the soft turbulence regime. It is also shown that in the soft turbulence regime the reversal cycles are shorter than in hard turbulence regime. The symmetric vortices in the diagonal corner of enclosed space shrink and the velocities of large-scale circulation (LSC) increase accordingly.

Removal of Natural Organic Matter from Wastewater by Electrocoagulation Using Aluminum Electrodes

Electrocoagulation is a promising alternative to the conventional chemical coagulation in water treatment systems. In electrocoagulation, coagulants are generated in situ by anodic dissolution of sacrificial electrodes, usually aluminum or iron electrodes. Anodic dissolution of the sacrificial anodes leads to the formation of hydrolysis products (hydroxo-metal species) that involve the destabilization of suspended, emulsified or dissolved pollutants and/or the formation of insoluble particles that adsorb and enmesh the pollutants. Furthermore, the formation of hydrogen bubbles as a result of water reduction at the cathode surface promotes the flocculation process by the soft turbulence in the system and produces a soft mix. The electrogenerated gaseous bubbles help the destabilized particles to colloid and generate larger particles which facilitate separation of the flocculated pollutants by carrying the particles to the top of the solution where they can be more easily removed by electroflotation. Electrochemical coagulation was successfully applied for turbidity, heavy metals, dyes and phenols removals from synthetic and real wastewaters and for breaking oil/water emulsions at both laboratory scale and pilot plant scale. In this work, effects of some experimental parameters (supporting electrolyte, current density, and initial pH) on anodic dissolution of aluminum and on electrocoagulation of tannic acid aqueous solutions as well as real industrial wastewaters containing tannic acid were investigated. Experimental results indicated that both chemical and electrochemical dissolution play an important role in the formation of hydroxo-aluminum species. The chemical dissolution of aluminum is strongly influenced by the solution pH. Electrocoagulation using aluminum electrodes achieved high removal efficiency of chemical oxygen demand from aqueous solutions containing tannic acid. The primary mechanism for removing tannic acid from water by electrocoagulation using Al electrodes involves the adsorption of tannic acid molecules on the aluminum hydroxide surface. Also, results of the treatment of real wastewater obtained from pulp and paper industry with initial COD concentration of 1450 mg/L have shown that more than 60 % of COD can be removed by electrocoagulation using Al electrodes under optimized experimental conditions. The specific energy required for the electrochemical process with Al electrodes was estimated to range from 1 to 2 kWh m-3.

Large-eddy simulation of melt turbulence in a 300-mm Cz–Si crystal growth

We built a curvilinear dynamic Smagorinsky subgrid-scale (SGS) model based on filtering the covariant physical velocity components in the computational space. We implemented our proposed SGS model in large-eddy simulations (LES) of turbulent flows in complex configurations. Our model was validated when compared with direct numerical simulation (DNS) data of the melt turbulent flow in an idealized cylindrical crucible in a Cz–Si crystal growth. Then, we carried out LES computations for the melt turbulence in a real ellipsoidal crucible in a 300 mm Cz–Si crystal growth. We studied instantaneous behaviors and statistical features of the melt turbulence. Spectral analyses of the temperature fluctuations show that the melt flow is in a soft turbulence state of Rayleigh–Bénard convection under the rotating crystal. A cluster of big vortices is formed in the time-averaged bulk flow due to the complex interaction among the thermal buoyancy, surface tension and crucible/crystal rotations. Heat transport in the melt flow is turbulence-dominated with notable fluctuations. The maximal temperature fluctuation in the crystallization zone is close to the crystal edge with a value of 1.8 K. The flow instability mainly attributes to the thermal buoyancy in the melt.

Large-eddy simulation and deduced scaling analysis of Rayleigh–Bénard convection up to Ra = 109**

Large-eddy simulation of turbulent Rayleigh–Bénard (RB) convection has been performed for a 6:1:6 open-ended domain for Rayleigh numbers ranging from 6.3 × 105 to 109 at Prandtl number of Pr = 0.71. The scaling analysis based on the LES data shows that the heat transfer follows a single relation of Nu = 0.162 Ra 0.286, which is consistent with the scaling law for the hard turbulence regime reported in several earlier experimental and DNS studies. The present LES also supports some earlier experimental and DNS findings that most of characteristic parameters can be scaled reasonably well with Ra number in the considered Ra number range using a single relation. Nonetheless, it is found that the scaling of several quantities shows a sensible offset from a single relation, and could be fitted better with the separate scaling relations for the soft and hard convective turbulence transitioned at about Ra = 4 × 107. It has been argued that the transition, reflected in the scaling relation, may be attributed to the increasing ‘containing effect’ of the plume leaving the horizontal wall on the plume approaching the wall at large Ra numbers in the near-wall region. **This paper is a modified version from the paper presented at the Forth International Symposium of Turbulence and Shear Flow Phenomena (Williamsburg, Virginia, 27–29 June 2005).

Pattern formation in Rayleigh-Bénard convection: numerical simulation with a coupled-map-lattice model

The various patterns formed in Rayleigh-Benard convection under different conditions are numerically simulated with a coupled-map-lattice model. In the case of a lower aspect ratio (L/d=5), the simulations vividly depicted the main features of the transition process from a laminar state to a soft turbulence and then to a hard turbulence. In this case, the cellular structure in a horizontal section is also reproduced. In the case of a larger aspect ratio (L/d=30), the simulations successfully reproduced the spiral-defect chaos and target chaos in the initial stage of the pattern evolution which were recently found in experiments. In this case, for a fluid ofPr=1, it is verified in simulations that both the ideal straight rolls and spiral-defect chaos are stable attractors in the same parameter regime, and that the initial condition is a decisive factor for which one of the two is formed. In the same case, for a fluid ofPr=4, the target patterns are dominant instead of the spirals, the sizes and distributions of the target are also notably dependent on the initial condition.

Heat flux in Rayleigh–Bénard convection

Abstract We calculate the heat conductivity of the turbulence induced in the Rayleigh–Benard convection. We show that the heat conductivity becomes large as we increase the temperature difference between the top and the bottom plates, i.e., the strength of the turbulence. We can easily see that the heat conductivity diverges in the transition regime from soft turbulence to hard turbulence as we can see in the viscosity coefficient in the same system.

Momentum flux in Rayleigh–Bénard convection II

We showed that the turbulent viscosity coefficient defined as the molecular viscosity coefficient diverges in the transition region from soft turbulence to hard turbulence in the Rayleigh–Bénard convection in the last paper (Physica A 333(2004)71). In the present paper, we measure the strength of the divergence in the viscosity coefficient. The strongest point of the divergence is in the middle of the transition region. In addition, we show how the strength of the divergence depends on the temperature difference between two plates.

Momentum flux in Rayleigh–Bénard convection II

We showed that the turbulent viscosity coefficient defined as the molecular viscosity coefficient diverges in the transition region from soft turbulence to hard turbulence in the Rayleigh–Bénard convection in the last paper (Physica A 333(2004)71). In the present paper, we measure the strength of the divergence in the viscosity coefficient. The strongest point of the divergence is in the middle of the transition region. In addition, we show how the strength of the divergence depends on the temperature difference between two plates.

Momentum flux in Rayleigh–Benard convection

The statistical quantities concerning the momentum flux in the Rayleigh–Benard convection are investigated in detail. The transition from soft turbulence to hard turbulence is captured through the momentum flux. The time series of the momentum flux is studied and its power spectrum shows the sign of the transition. The two-time correlation function does not saturate its value in the range of the transition. Except for the transition regime the two-time correlation function for the momentum flux converges to 0 and we estimate the viscosity by the turbulence. We confirm that the viscosity coefficient increases as we increase the temperature difference between the top and bottom plates.

Investigation of natural convection heat transfer to the cooled top boundary of a heated pool

Experiments have been performed in the framework of the BALI program for the investigation of turbulent heat transport to the upper cooled top boundary of a volumetrically heated pool. A specific LIF (laser induced fluorescence) technique has been used to visualise the plumes detaching from the top boundary. Results concerning flow configurations, detachment time intervals, size of plumes and characteristic distances between plumes will be presented as a function of Rayleigh and Prandtl numbers. A model has been developed for the description of these plumes and the resulting heat transfer. A physical understanding of the effect of Rayleigh and Prandtl numbers on heat transfer has been gained. The so-called soft turbulence regime is associated with negligible interaction between plumes detaching from the boundary and the main flow. In this regime, the Nusselt number is proportional to Ra 1/3. The so-called hard turbulence regime is associated with an interaction between the plumes and the main flow. The plumes are locally and intermittently destroyed by a laminar boundary layer developing from large eddies issued from the main flow and impacting the boundary. The development of these laminar layers explains the dependency of the Nusselt number as approximately Ra 2/7 in this regime. For elevated Rayleigh numbers, the increase of the Reynolds number in the main flow explains the development of fully turbulent boundary layers. In the so-called asymptotic regime, experiments by Chavanne (1997) have shown that Nusselt is approximately proportional to Ra 0.4. Effects of the aspect ratio have been reported.

Analysis of turbulent flow in silicon melts by optical temperature measurement

Turbulent convection in silicon melts plays a decisive role for the transport of heat and oxygen during the silicon Czochralski crystal growth. Information on the state of turbulence is usually derived from the frequency behaviour of temperature fluctuations. Until now, temperature fluctuations were mostly detected by thermocouples, which are protected from the chemically aggressive melt by silica quartz tubes. The major disadvantage of this technique is the damping effect on amplitudes of temperature fluctuations at frequencies higher than 0.5 Hz. This drew back significantly the information available on the state of turbulence. A method to overcome this disadvantage is an optical technique of measuring temperatures that provides sampling rates up to 100 Hz. In this contribution, we present optical temperature measurements using silica rods as waveguides in large-diameter Czochralski silicon melts. The detected temperature fluctuations give slopes of power spectra that are approximately proportional to f −4 for higher frequencies, in the case of the smaller crucible of 14 inch diameter. This indicates a soft turbulence state where melt flow is stabilised by rotational forces. On the other hand, a hard turbulence state of melt flow, indicated by an f −5/3 behaviour of the power spectra, was found for the large crucible with 32 inch diameter. In contrast to the smaller crucible, we found no changes of the state of turbulence by increasing the crucible rotation rate. The results are discussed with respect to its consequences on the properties of silicon crystals grown by the Czochralski method from large-scale melts.

Quasi-periodic state and transition to turbulence in a rotating Couette system

An experimental study of flow transition in a rotating Taylor–Couette system was made by investigating the spatio–temporal velocity field (axial velocity component) by the ultrasonic Doppler method. The flow fields for the range of Reynolds numbers 9<R*<40 (where R*=R/Rc; Rc is the critical Reynolds number for Taylor vortex flow) were decomposed by two-dimensional Fourier transform and the orthogonal decomposition technique, and intensities of coherent structural modes were quantitatively obtained. The variation of the intensities of various modes with respect to Reynolds number clearly shows a transition behaviour of the quasi-periodic state resulting from the wavy vortex mode and the modulating waves, which is found to disappear suddenly at about R*=21. A new mode was found after the disappearance of the quasi-periodic state, which in turn disappears at R*=36. Beyond this regime, there was no coherent structure found except for the stationary Taylor vortices and so-called broad-band component, which is attributed to chaos. The total energy occupation (the number of modes which occupy 90% of the total energy) and the global entropy support such transition behaviour quantitatively. After the disappearance of the newly found mode, the number of modes needed to compose the velocity field is still finite and small – about 40–50. We call this flow state ‘soft turbulence’.

Density anomaly effect upon silicon melt flow during Czochralski crystal growth I. Under the growth interface

Temperature fluctuations under the growth interface region were measured to evaluate the flow structure during the Czochralski silicon growth process. The impurities which influence the density anomaly of the silicon melt are doped as experimental parameters. The flow structure of this region was found to be basically a random one that is supposed to represent the “soft turbulence” induced by Rayleigh-Bénard convection. The addition of gallium to the melt changes the flow structure to a laminar-like one when the melt depth is shallow while the flow structure is still similar to a soft turbulence in the cases of boron-doped and undoped at the same melt depth. These results suggest that the density anomaly of the silicon melt influences the melt flow structure of this region.

Density anomaly effect upon silicon melt flow during Czochralski crystal growth II. Time-topical flow structure under the growth interface

The purpose of this work is to investigate the effect of density anomaly upon the time-topical structure of the melt flow under the crystal growth interface by applying a wavelet transform to the temperature fluctuation in this region. The fluctuation components that have a period of about 44 seconds appear irregularly on the time axis and are considered to be caused by detachment of the boundary layer near the bottom of the crucible in the case of a relatively deep melt. This is the characteristic phenomenon of “soft turbulence”, as described in a previous paper [Togawa et al., J. Crystal Growth 160 (1996) 41]. These fluctuation components disappear when gallium is added to the shallow melt, whereas the flow structure remains turbulence-like in the cases of undoped and B-doped shallow melts. A detailed statistical analysis of this time-topical flow structure showed that this flow regime stays unsteady and the flow situation changes from moment to moment. When gallium is added, the flow structure becomes laminar-like and differs clearly from the other two cases. We can thus confirm the existence of a silicon melt density anomaly in the crystal growth system and its influence upon the flow structure.

Pattern Forming Instability in Homeotropically Aligned Liquid Crystals

The electrohydrodynamic pattern forming instability (EHC) driven by an ac voltage applied to a homeotropically aligned nematic liquid crystal layer is experimentally studied near onset. By controlling an external magnetic field, many different scenarios become accessible. For finite fields various regular convective structures are observed, which we call, for example, wavy, chain, and bamboo-chevron patterns. The various types are documented with the help of a phase diagram governed by the frequency and the strength of the applied ac voltage. In addition the stability regimes in the voltage−wavenumber plane (the “Busse balloon”) are mapped out. One finds significant differences from the conventional planar case, for which a theoretical analysis is lacking so far. For zero magnetic field, on the other hand, no regular structure is observed, even immediately above the onset of EHC. A new spatiotemporally chaotic pattern called the soft mode turbulence directly appears via a supercritical bifurcation from the nonconvective state. This is due to the presence of the Goldstone mode related to the spontaneously broken rotational symmetry associated with the director component in the plane of the layer.

Measured local-velocity fluctuations in turbulent convection.

Turbulent Rayleigh-B\'enard convection in water has been studied using a newly developed technique of incoherent cross-correlation spectroscopy. At high Rayleigh number Ra (hard turbulence), local velocity fluctuations are isotropic, and their probability density functions in the center region have an invariant Gaussian form, with the rms velocity ${\ensuremath{\upsilon}}_{0}\ensuremath{\sim}{\mathrm{Ra}}^{0.44}$. At low Ra in the soft turbulence regime, the probability density functions for the vertical velocity fluctuations do not have a universal form and appear to depend on the coherence of thermal plumes emitted from the boundary layers.