Laminar State Research Articles

Bump Attractors and Waves in Networks of Leaky Integrate-and-Fire Neurons

Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is characterised by a core in which neurons fire frequently, while those away from the core do not fire. We uncover a relationship between bump attractors and travelling waves in a classical network of excitable, leaky integrate-and-fire neurons. This relationship bears strong similarities to the one between complex spatiotemporal patterns and waves at the onset of pipe turbulence. Waves in the spiking network are determined by a firing set, that is, the collection of times at which neurons reach a threshold and fire as the wave propagates. We define and study analytical properties of the voltage mapping, an operator transforming a solution's firing set into its spatiotemporal profile. This operator allows us to construct localised travelling waves with an arbitrary number of spikes at the core, and to study their linear stability. A homogeneous "laminar" state exists in the network, and it is linearly stable for all values of the principal control parameter. Sufficiently wide disturbances to the homogeneous state elicit the bump attractor. We show that one can construct waves with a seemingly arbitrary number of spikes at the core; the higher the number of spikes, the slower the wave, and the more its profile resembles a stationary bump. As in the fluid-dynamical analogy, such waves coexist with the homogeneous state, are unstable, and the solution branches to which they belong are disconnected from the laminar state; we provide evidence that the dynamics of the bump attractor displays echoes of the unstable waves, which form its building blocks.

Generalized quasi-linear approximation and non-normality in Taylor-Couette spiral turbulence.

Taylor-Couette flow is well known to admit a spiral turbulence state in which laminar and turbulent patches coexist around the cylinder. This flow state is quite complex, with delicate internal structure, and it can be traced into certain regimes of linear stability. This behaviour is believed to be connected to the non-normality of the linear operator, which is itself a function of the control parameters. Using spiral turbulence in both linearly stable and unstable regimes, we investigate the effectiveness of the generalized quasi-linear approximation (GQL), an extension of quasi-linear theory designed to capture the essential aspects of turbulent flows. We find that GQL performs much better in the supercritical regime than the subcritical. By including only a small number of modes in the nonlinear interactions, GQL simulations maintain a turbulent-like state when in the supercritical regime. However, a much larger number is required to avoid returning to the laminar state when in the subcritical regime. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

A fundamental limit on energy savings in controlled channel flow, and how to beat it

We derive a limit on energy savings in controlled channel flow. For flow in a channel driven by pressure, shear or any combination of the two, and controlled via wall transpiration or spanwise wall motion, the uncontrolled laminar state requires the least net energy (accounting for the energetic cost of control). Thus, the optimal control solution is to laminarize the flow. Additionally, we raise the possibility of beating this limit. By simultaneously applying wall transpiration and spanwise wall motion, we show that it may be possible to attain sustained sub-laminar energy expenditure in a controlled flow. We provide a necessary design criterion for net energy savings.

Entropy generation analysis on thermo-hydraulic characteristics of microencapsulated phase change slurry in wavy microchannel with porous fins

• Combined design enables smaller temperature gradient and more uniform temperature. • Larger h m and lower ΔP can be concurrently gained in wavy MCHS with porous fins. • Thermal entropy is three orders of magnitude larger than the frictional entropy. • Thermal entropy increases with heat flux but the frictional entropy is opposite. • Lower irreversible losses can be achieved at the cost of higher power consumption. Recent advancement in micro/nano-scale electronic systems, the need for efficient heat dissipation has become more rigorous, and traditional thermal management solutions are facing enormous challenges. In this study, a novel combined design of wavy microchannel heat sink (MCHS) with porous fins and microencapsulated phase change material (MPCM) suspension is developed and numerically studied to achieve a balance between flow and heat transfer behaviors. The equivalent heat capacity method is adopted to deal with the phase change process of microcapsule particles in steady and laminar states, and the Brinkman–Darcy–Forchheimer model based on the volume-averaged method is employed to characterize the fluid flow in porous fins. A three-dimensional solid-fluid conjugate model is established based on the finite-volume method to investigate the effects of different coolant types (water and MPCM suspension), geometric parameters (wavy amplitude, wavelength, and channel width ratio), and working conditions (inlet flow velocity, heat flux, and slurry concentration) on the thermo-hydraulic properties and entropy generation of wavy MCHS. The results reveal that the combination of porous fins and MPCM suspension presents smaller temperature gradient and more uniform temperature distribution than conventional design. Larger heat transfer coefficient and lower pressure drop can be simultaneously obtained in wavy MCHS with porous fins than in solid fin configuration. The thermal entropy generation is three orders of magnitude larger than the frictional entropy generation, and the Bejan number is close to 1 for different microchannel configurations. Thermal entropy generation increases with increasing heat flux but the frictional entropy generation decreases. Lower irreversible losses can be achieved at the expense of greater pumping power consumption caused by increasing inlet velocity and suspension concentration. The superior effect of wavy MCHS with porous fins using MPCM suspension as coolant has been observed in all cases.

CFD model of acceleration of thermal-hydrodynamic processes in solar air collectors

Recent studies on increasing the thermal-hydrodynamic efficiency of solar air collectors have been carried out on the installation of barriers of various shapes on the surface of the absorber, and this method ensures a significant increase in the energy efficiency of the collector. The transfer of the air flow washing the surface of the absorber from a laminar flow state to an accelerated lumped air flow is carried out by installing obstacles. Installation of barriers is the main factor in increasing the heat transfer in solar air collectors and prolongs the time of air flow in the collector. The barrier solar air collector has a high local heat transfer coefficient, and the Nusselt number value is up to 3.5 times higher than that of the flat plate solar air collector. Also, this article presents the results of CFD modeling of the air flow in the solar air collector, the results of which can be used in the theoretical research of the solar air collector.

Effect of synthetic jet on circular cylinder radiated noise in laminar flow state

This article focuses on the effect of active control via synthetic jets (SJs) on sound generated by a two-dimensional circular cylinder by using the acoustic analogy method. The cylinder is immersed in a uniform upstream flow, where the corresponding Reynolds number is 100 and the Mach number is 0.1. A pair of SJs is placed near the cylinder’s separation point issuing periodically varying forcing, with different combinations of forcing frequency and phase difference. The lattice Boltzmann method (LBM) is coupled with the multi-direct forcing immersed boundary method to solve the near-field flow dynamics. The mechanism of the sound generation lies in the fact that pressure pluses are induced by the periodic vortex shedding from the cylinder’s surface, i.e. dipoles. In the case with active flow control, extra monopoles are generated by the unsteady flow rate resulting from the SJs' periodic blow/suction. The interaction between monopoles and dipoles is confirmed to have a big influence on the acoustic field. The acoustic analogy method is used in various cases with a wide range of control parameters, because it has a considerably lower computational cost than the direct simulation method. Taking into account the effect of the monopole, the acoustic analogy method is developed for solving two-dimensional sound field by substituting the Green’s function. Results indicate that the primary lock-on and the secondary lock-on occur in the case of specified control parameters. The frequency of vortex shedding is related to the SJs’ frequency, deviating from the unforced frequency. Owing to the noise induced by flow, the frequency and phase difference of the SJs also have significant influence on sound field. The far-field noise is enlarged although the SJs reduce drag, due to the induced extra monopole, as well as the strengthened hydrodynamic fluctuation. Further increasing SJs’ frequency or reducing the phase difference will enlarge the far-field noise and make the directivity transformed from dipole to monopole, since the SJs’ self-noise is stronger. Moreover, it is found that the acoustic power increases approximately 4–18 dB compared with the unforced circular cylinder and the drag dipole is strengthened in all combinations of control parameters. This study deepens the understanding of the effect of SJs on sound field, and provides a reference for future studying the control strategies of suppressing noise generated from bluff bodies.

On the competition of transverse and longitudinal modes of Marangoni convection in a three-dimensional layer of viscoelastic fluid

Within the vast array of applications encompassed by viscoelastic fluids, some lack of knowledge seems to affect the non-linear behavior of Marangoni convection when its typical initial unicellular and steady states are taken over by more complex flow configurations. These still hide a not-fully understood competition of complex and diverse physical mechanisms that determine the prevailing macroscopic behavior. In the present study, relevant insights are sought from consideration of the classical differentially heated rectangular layer of liquid with adiabatic bottom and top free surface. It is shown that, for increasing values of the Marangoni number and/or the elasticity parameter, this problem offers a multifaceted spectrum of different outcomes depending on the non-trivial interplay established between two distinct categories of disturbances (transverse and longitudinal). These are studied using a diversity of model types in which some processes are on or off to discern selectively their effect in the laminar state and their contribution to the evolution of the system toward chaos. The characteristic marks by which the ensuing elastic turbulence can be distinguished from the companion Kolmogorov counterpart are highlighted through analysis of the emerging scaling laws in the velocity spectrum and the sensitivity of these to the intensity of the driving force and the considered elasticity level. It is shown that these two forms of turbulence can coexist in the considered problem.

Effective aero-optical suppression by steady wall blowing and wall suction schemes for supersonic turbulent boundary layer

AbstractAs a basic flow model for engineering applications, wall-bounded turbulent flow has been widely studied in the field of aero-optics, but the flow control methods that could effectively suppress aero-optical effects are relatively rare. As an urgent requirement in engineering application, the concept of the steady wall blowing and suction is proposed by the author. Firstly, the author briefly described the flow model and physical method. Secondly, the choice of disturbance type is given. Then, the results of wall blowing-suction, suction and blowing ways based on steady and unsteady disturbance are compared. Finally, it is concluded that employing the high steady wall blowing disturbance (A = 0.2) could realise aero-optical suppression by around 20%. Besides, the steady wall suction scheme contributes to about 70%–80% reduction effect within a wide amplitude range (A = 0.2–1.0), which suppresses this effect by maintaining laminar state downstream contrasted by the baseline case.

Turbulence suppression by streamwise-varying wall rotation in pipe flow

Direct numerical simulations of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is able to achieve drag reduction and even relaminarize the flow under certain control parameters at friction Reynolds number $Re_\tau =180$ . Two control parameters, which are velocity amplitude and wavelength, are considered. It is found that increasing the wavelength rather than increasing the amplitude seems to be a better choice to improve the control efficiency. An annular boundary layer, called the spatial Stokes layer (SSL), is formed by the wall rotation. Based on the thickness of the SSL, two types of drag-reduction scenarios can be identified roughly. When the thickness is low, the SSL acts as a spacer layer, inhibiting the formation of streamwise vortices and thereby reducing the shear stress. The flow structures outside the SSL are stretched in the streamwise direction due to the increased velocity gradient. Within the SSL, the turbulence intensity diminishes dramatically. When the thickness is large, a streamwise wavy pattern of near-wall streaks is formed. The streak orientation is dominated by the mean shear-strain vector outside the viscous sublayer, and there is a phase difference between the streak orientation and local mean velocity vector. The streamwise scales of near-wall flow structures are reduced significantly, resulting in the disruption of downstream development of flow structures and hence leading to the drag reduction. Furthermore, it is found that it requires both large enough thickness of the SSL and velocity amplitude to relaminarize the turbulence. The relaminarization mechanism is that the annular SSL can absorb energy continuously from wall-normal stress due to the rotational effect, thereby the turbulence self-sustaining process cannot be maintained. For the relaminarization cases, the laminar state is stable to even extremely large perturbations, which possibly makes the laminar state the only fixed point for the whole system.

Impact of the Thermophysical Properties of a Cuo-H<sub>2</sub>O-Based Nanofluid on the Performance of a Cylindrical Solar Concentrator

Sustainability in energy production, energy security, and global warming are major concerns facing the globe today. Cylindrical Solar Concentrator is extensively utilized for technologically advanced processes, heat, and power plant applications by utilizing daylight sunshine at no running cost. Numerous inputs and characteristics impact the concentrator's performance, with the type of heat transfer fluid and its mass flow rate being two of the most important. This paper gives a numerical investigation of the influence of thermo-physical attribute of CuO water-based nanofluids on the effectiveness of the Parabolic Trough Solar Concentrator in Ogbomosho weather condition (lat. 8o011, long. 4o111).The governing equations of nanofluids with laminar flow and steady state, using iterative relaxation techniques, as well as the efficiency of the concentrator, were solved. A C++ simulation program was developed to investigate the impacts of thermo physical parameters on concentrator efficiency, with nanoparticle sizes ranging from 1 to 10 percent and mass flow rates of 0.1 kg/s, 0.15 kg/s, and 0.2 kg/s, at a constant incident solar insolation flux of 186 W/m2. The results demonstrated that increasing the mass flow rate of the nanofluids improves the heat transmission properties. The thermo physical properties of CuO-based nanofluids and its effects on the performance of the solar parabolic trough collector are being examined. The impact of thermophysical attributes on thermal effectiveness results in improved thermal efficacy, heat transfer characteristics of nanofluids, and factors influencing its features in solar collectors, which determines its usability. The Parabolic Trough Collector system based on nanofluids is a promising technology with applications in green surroundings.

A traveling wave bifurcation analysis of turbulent pipe flow

Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al 2015 Nature 526 550–3], which describes the rise of turbulent pipe flow via a PDE system of reduced complexity. The fast evolution of turbulence is governed by reaction-diffusion dynamics coupled to the centerline velocity, which evolves with advection of Burgers’ type and a slow relaminarization term. Applying to this model a spatial dynamics ansatz and geometric singular perturbation theory, we prove the existence of a heteroclinic loop between a turbulent and a laminar steady state and establish a cascade of bifurcations of various traveling waves mediating the transition to turbulence. The most complicated behaviour can be found in an intermediate Reynolds number regime, where the traveling waves exhibit arbitrarily long periodic-like dynamics indicating the onset of chaos. Our analysis provides a systematic mathematical approach to identifying the transition to spatio–temporal turbulent structures that may also be applicable to other models arising in fluid dynamics.

The nonlinearity properties of pulse signal of pregnancy in the three trimesters

The purpose of this work sought to investigate the underlying activity state and dynamics characteristic changes of pulse in the three trimesters from healthy pregnant subjects by using nonlinear methods. Firstly, 176 healthy young pregnant women of different gestational ages were allocated for the study. The subjects were divided into three trimesters, namely first trimester, second trimester and third trimester, according to gestational age (8–12 weeks; 24–28 weeks; 32–36 weeks). Secondly, methods of nonlinear time series analysis, including phase-space reconstruction, time delay embedding, recurrence plot (RP), recurrence quantification analysis (RQA), Poincaré section and largest Lyapunov exponent (LLE) were applied to pulse time series to identify the unique characteristics of the pulse as a dynamical system. Finally, the natural complexity of pulse dynamics has been analyzed and assessed. The results demonstrated that (a) the predictability and regularity (DET: 97.499 vs. 98.471 vs. 98.319, p<0.05), stability (LMAX: 5874.167 vs. 9311.667 vs. 5733.833, p<0.05) and laminar states (LAM: 97.216 vs. 98.224 vs. 97.967, p<0.05) of three trimesters are significantly; (b) the long-term changes of pregnancy pulse in second trimester is significantly higher compared with the first and third trimesters (SD2: 1.0697 vs. 1.0747 vs. 1.0075, p<0.05); (c) the ability of subjects to respond to external stimuli gradually increases (λ: 0.752 vs. 0.768 vs. 0.782, p<0.05). The result of these analyses validates nonlinear characteristics of pulse with different gestation periods, while presence of significant difference has also been noticed. Additionally, the nonlinear methods are used to characterize the pulse changes during pregnancy from both qualitative and quantitative perspectives, which reveal important characteristics of biological signals. This gives us a good theoretical basis for the analysis and applied studies in Traditional Chinese Medicine(TCM).

New Insights into Turbulent Spots

Transitional–turbulent spots bridge the deterministic laminar state with the stochastic turbulent state and affect the transition zone length in engineering flows. Turbulent spot research over the past four decades has expanded from incompressible flat-plate boundary layer and pipe flow to hypersonic boundary layer flow, turbomachinery flow, channel flow, plane Couette flow, and a range of more complex flows. Progress has been made on the origination, composition, demarcation, growth, mutual interaction, reproduction, sustainability, and self-organization of turbulent spots. The hypothesis that transitional–turbulent spots are a basic module of the fully turbulent boundary layer has been proven through the discovery of locally generated turbulent–turbulent spots dominating the wall layer. Splitting of transitional–turbulent spots in pipe flow has been linked to a life cycle localized in the spot frontal section. This review discusses these advances and outlines future research directions.

Entropy Generation of Graphene Nanoplatelets in Micro and Mini Channels: Nanofluid Flow in Automotive Cooling Applications

The present study examines the entropy generation of graphene nanoplatelet (GnP) suspended in different basefluids, theoretically. GnP in water (W), ethylene glycol (EG) and ethylene glycol- water (EGW, 1:1) was examined under laminar flow state in a unit length mini and micro-channel of 3mm and 0.05mm diameter. The coefficient of conductivity (Ck) and viscosity (Cμ) of the nanofluid were determined from experimental analysis and their order of magnitude were established for analysis of entropy generation in mini and micro-channels. Entropy generation by fluid friction (Ṡgen, ff) in the channels containing EG was higher than with W and EGW by 75.6% and 79.9%, respectively. Thermal irreversibility (Ṡgen, th) of W was lower by132.9% and 58.2% compared to EG and EGW. Sgen,th in all the fluids decreased with increased solid volume fraction in mini-channels, while, Ṡgen,ff increased with increase in volume fraction for micro-channels. Total entropy generation (Ṡgen, tot) of water was lower by 75.6% and higher by 64.8% compared to EG and EGW, respectively in a micro-channel, whereas Ṡgen, tot of water was lower by 123.7% and 38.4% compared to EG and EGW, respectively. As GnP volume fraction was increased in the basefluids, entropy generation ratio decreased, highlighting the positive influence of thermal properties of the nanofluid. A lower Bejan number for water (Bew), 36.8% and 358.9% were observed compared to EG and EGW in micro-channel, whereas Bew was lower by 3.8% and 13.8% when compared to EG and EGW nanofluids in the mini channel.

Subcritical transition of Taylor−Couette−Poiseuille flow at high radius ratio

We performed direct numerical simulations of Taylor–Couette–Poiseuille flows within an annular channel with a radius ratio of 0.883. A parametric study was conducted on subcritical transition processes of the wall-bounded combined shear flow with a torsional base-flow profile with three control parameters of F(P) representing the axial mean pressure gradient and two Reynolds numbers Rein and Reout, based on the inner cylinder and outer cylinder rotational velocities, respectively. In the set (Rein,Reout)=(400,−1000), the laminar flow becomes turbulent via finite-length and infinite-length turbulent bands, called one-way helical turbulence, as F(P) increases. Two-way helical turbulence appeared in the counterpart of the annular Poiseuille flow without cylindrical rotations, suggesting that the azimuthal Couette flow broke the symmetry of the helical turbulence of the axial Poiseuille flow. In the set of (Rein,Reout)=(800,−2000) and (1200,−3000), we found a ring-shaped localized turbulence at F(P) that provided an axial friction Reynolds number comparable to the azimuthal one. The flow states were mapped in parameter space spanned by the axial and azimuthal friction Reynolds numbers. Eight different flow regimes, including the laminar state, were identified based on turbulent statistics during these flow visualizations.

Dynamic Coefficients of Tilting Pad Bearing by Perturbing the Turbulence Model

Tilting pad bearings are appropriate for the trend of high efficiency and reliability design of rotating machinery due to their high stability. The laminar and turbulent flow states exist in the lubricating oil film of high-speed and heavy-load tilting pad bearings simultaneously. By perturbing the multiple flow state lubrication model with a partial derivative method, together with the pad-pivot structural perturbations, the frequency-dependent stiffness and damping coefficients of tilting pad bearings, embracing the effect of dynamical variations of both turbulence and pressure-viscous, were numerically solved in this research. The importance of each perturbed variable was studied, and the results indicate that the perturbed film thickness included in turbulence coefficients perturbations is significant enough to be taken into account otherwise the equivalent stiffness coefficients will be obviously overestimated. Unlike the perturbed film thickness, the consideration of the perturbed viscosity is optional, because it makes the stiffness and damping coefficients larger at both laminar and turbulent flow states. For a simplified simulation and conservative prediction results, the perturbed viscosity can be neglected.

Simulation Analysis of Concrete Pumping Based on Smooth Particle Hydrodynamics and Discrete Elements Method Coupling

With an increase of suction efficiency of fresh concrete pumping in confined spaces, the laminar flow state will be damaged by the return flow caused by distribution value direction changes and concrete gravity. This is a fact, but one which is rarely studied. In this work, the flow state, flow velocity, and suction efficiency of fresh concrete pumping are simulated using the coupled smooth particle hydrodynamics and Discrete Elements Method (SPH-DEM). The rheological parameters and Herschel-Bulkley-Papanastasiou (HBP) rheological model are adopted to simulate fresh concrete in the numerical simulation model. The study reveals that the error between the slump experimental result and that obtained by the HBP model is negligible. A model is therefore established for numerical simulations of the suction efficiency of fresh concrete pumping. An experimental concrete pumping platform is built, and the pressure and efficiency data during pumping are collected. A comparison of the numerical simulation with experimental results shows that the error is less than 10%.

Numerical investigation of the influence of a rotating vortex generator array on the performance of a thermal storage system

The thermal performance of an energy storage device was studied using computational models in both laminar and turbulent states of operations. To help explain the melting processes of phase change materials, numerical simulations in three dimensions were carried out by employing the enthalpy porosity method. Furthermore, to predict the separation flow in the turbulent regime, the k-ω SST turbulence model was employed. The numerical approach was shown to be exceptionally accurate when compared to existing experimental data in both laminar and turbulent regimes. It was also investigated how a turbulator made up of rotatonal vortex generators affects phase change material structure in numerical simulations. To this end, the series of vortex generators was placed at the center of the tube of the thermal storage system with five different rotational speeds, such as 0, 1, 1.5, 2, and 3. According to the findings, in comparison to a basic system, rotational vortex generators led to a quicker expansion of liquid area in the phase change unit and a 70% reduction in melting time. Also, it was found that the rotational vortex generator decreased the freezing time by up to 50%. This study can be a real application in thermal storage systems with vortex generators in the central of the tubes when heat transfer augmentation is under consideration.

Fiber Orientation Analysis of Overflow Water-Assisted Injection Molding with Short Glass Fiber Reinforced Polypropylene

The fiber orientation is playing an important performance indexed for glass fiber reinforced polypropylene for water-assisted injection molding. Based on the viscoelastic constitutive equation (White-Metzner) and the fiber orientation model (iARD-RPR), the effects of fiber mass content, water injection delay time, water injection pressure, and melt temperature, which are on the fiber orientation along the flow direction and shear rate distribution of the melt, were investigated. Studies found that the orientation degree of the fiber along the flow direction was reduced with the increase of the fiber mass content, the extension of the water injection delay time, and the improvement of the melt temperature and that the orientation degree of the fiber along the flow direction was raised with the increase of the water injection pressure flow in the laminar flow state, but it was reduced with the increase in the turbulent state. It can be further learned from the shear rate distribution that decreasing fiber mass content, reducing the water injection delay time, lower melt temperature, and increasing water injection pressure in laminar flow conditions will increase the shear rate in the channel layer and the shear rate gradient along the thickness direction of the melt, while the water injection pressure in the turbulent state is on the contrary.

Extreme events in transitional turbulence.

Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier-Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.