Laminar Length Research Articles

Theoretical study of the expansion of Roper's theory on the laminar jet diffusion flame length in 2D and 3D in natural gas and hydrogen mixtures

In this work, three mathematical models were developed to study the laminar jet diffusion flame in mixtures of natural gas, hydrogen, and CO2 by extending and applying Roper's theory. Model M1 consists of derivation of the Roper's original equation described in the two-dimensional steady state without convection, thus showing the theoretical equations for the length of the diffusion flame for burners with circular, square, and rectangular cross sections and for regimes in which the flames are dominated by the momentum effects, the buoyancy effect, and in the transition regime. Models M2 and M3 extend the Roper's original theory by deriving analytical solutions of the two- and three-dimensional diffusion flame equation with convection in steady and transient states, taking into account the spatially variable velocity and diffusion coefficients. The flame lengths obtained with models M1 and M2 were compared with model M3 by Relative Percentage Difference (RPD) considering 5 mixtures of NG-H2-CO2. For t = 0.1, the maximum RPD in the circular cross-section for M1 in Gas20:60%NG-25%H2–15%CO2 was 14.75%, while for M2 in Gas14:70%NG-15%H2–15%CO2 was 6.47% and the minimum RPD in Gas1:100%NG was 9.78% and 4.83% for M1 and M2, respectively. The same analysis was developed for the square and rectangular (Fr ≪ 1) cross-sections and showed good agreement. The model M3 was tested under transient conditions, studying the effects of time and velocity on the distribution of the profile in the radial direction, in order to better understand the flame phenomenon, which cannot be observed with the Roper's original model M1. Finally, the models M2 and M3 were validated with experimental results and other analytical solutions showing a good performance considering the characteristics of each mixture.

A review on free miscible buoyant jets

Buoyant jets have been a topic of interest due to their presence in various natural and industrial phenomena, as well as in our daily lives. Covering extensive literature, our focus in this review article is on free, miscible buoyant jets with small-density differences (under the Boussinesq approximation) within uniform and stagnant environments. We examine the latest research on Newtonian jet flows and expand our scope to their viscoplastic counterparts, reflecting a burgeoning trend in contemporary literature. Our analysis covers negatively buoyant, pure, and positively buoyant jets, via delving into their dynamics. This includes regime classifications and key jet characteristics, such as laminar length, penetration length, mixing behavior, velocity profiles, and turbulence parameters. In particular, the effects of the key governing dimensionless parameters, including the Reynolds number, the Froude number, the Bingham number, the viscosity ratio, and the injection angle, on these characteristics are explored.

Insights into the transition of separation bubble over a rough surface at varying angles of attack

The evolution of a separated boundary layer on the rough surface in the vicinity of a leading edge of a model airfoil is documented at varying angles of attack. Particle image velocimetry and hotwire data are analyzed to elucidate the flow feature, depicting the manifestation of the shear layer, its rollup, growth of perturbations, spectral response, and intermittency. For a hydrodynamically smooth surface, a laminar separation bubble often appears near the leading edge, where the shear layer becomes inviscidly unstable. Wall roughness amplifies the near-wall perturbations, resulting in earlier transition and reattachment. This leads to a reduction in bubble length and laminar shear layer length compared to the smooth surface at the corresponding angle of attack. Notably, despite the amplification of selective frequency, the inviscid instability is bypassed on the rough surface for varying angles of attack. Moreover, the linear stability analysis proves inadequate in predicting the most amplified frequency and the growth of disturbances. Furthermore, the universal intermittency curve formulated for the bypass transition is valid for the separation-induced transition, illustrating the significance of viscous effect.

Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems

The aim of the work is an analysis of characteristics of intermittent behavior taking place near the boundary of generalized synchronization in unidirectionally coupled time-delayed generators. The case of interaction of systems characterized by different numbers of positive Lyapunov exponents is considered. To determine the lengths of characteristic phases of the system behavior the auxiliary system method has been used. The result of the work is the determination of the type of intermittency taking place near the boundary of generalized synchronization. In this case by calculation the statistical characteristics of the laminar phase lengths (distributions of the laminar phase lengths and the dependencies of the mean lengths of the laminar phases on the criticality parameters) it has been found that near the boundary of the synchronous regime the on-off intermittency is observed. It has been shown that the intermittent generalized synchronization in time-delayed systems is characterized by multistability. For these purposes a time-averaged measure of multistability depending on the value of the coupling parameter between systems has been calculated and compared with the behavior of the spectrum of Lyapunov exponents. It has been found that the multistability measure can be used to detect the generalized synchronization in time-delayed systems.

Features of laminar separation bubble subjected to varying adverse pressure gradients

This article describes the spatial development of a laminar separation bubble (LSB), its transition, and eventual breakdown under the influence of adverse pressure gradients (APGs) similar to those experienced by low-pressure turbine blades. The investigation combines a comprehensive experimental approach with a well-resolved large eddy simulation (LES). The streamwise pressure gradients were varied by manipulating the upper wall within the test section. The Reynolds number (Re), based on the plate length and inlet velocity, was 0.2 × 106 with a freestream turbulence intensity of 1.02%. The particle image velocimetry (PIV) and hotwire data were used to illustrate the vortex dynamics, growth of perturbations, and intermittency. The onset and end of transition progressively shift upstream, resulting in a reduction of the laminar shear layer length and bubble length with increasing APG. Interestingly, the flow features exhibit self-similarity in velocity profiles and the growth rate of velocity fluctuations when normalized against the bubble length. The formation of two-dimensional Kelvin–Helmholtz (K–H) rolls is apparent in the beginning, resulting in the selective amplification of frequency and exponential growth of fluctuations. Linear stability theory explains the most amplified frequency and phase speed of convective vortices, apart from the growth of disturbances. Analysis of LES data reveals intricate inviscid–viscous interactions that trigger shear layer breakdown. In brief, evolving perturbations within the braid region of vortices in the latter half interact with the advecting K–H rolls, culminating in the breakdown and the onset of turbulent flow downstream.

Synchronization of multiple mobile reservoir computing oscillators in complex networks

We investigate collective behavior of multiply moving reservoir computing oscillators. Each moving oscillator is fitted to a same dynamical system and then wanders a network navigating by random walk strategy. Interestingly, we find that the moving oscillators gradually present a coherent rhythmic behavior when their number is large enough. In this situation, temporal and spatial characteristics of each moving oscillator are in excellent agreement with that of their learned dynamical system under consideration. Remarkably, we show that these reservoir computing oscillators can exhibit significantly distinct collective behaviors that resemble bifurcation phenomenon when changing a critical reservoir parameter. Furthermore, we find that when studying a continuous chaotic system, intermittent synchronization emerges among these reservoir computing oscillators. But there is no evidence of enhanced correlation in the associated laminar length sequence. Our work provides a feasible framework for studying synchronization phenomena of mobile agents in nature when merely observed information is available.

Analysis of intermittency near the boundary of the phase synchronization in systems with complex topology of attractor

Intermittent behavior near the boundary of phase synchronization in systems with a complex topology of attractor is studied. Using the calculation of statistical characteristics of the laminar phase lengths it is shown that in the case of a relatively small detuning of the control parameters of interacting systems near the phase synchronization boundary the eyelet intermittency takes place.

Predicting buoyant jet characteristics: a machine learning approach.

We study positively buoyant miscible jets through high-speed imaging and planar laser-induced fluorescence methods, and we rely on supervised machine learning techniques to predict jet characteristics. These include, in particular, predictions to the laminar length and spread angle, over a wide range of Reynolds and Archimedes numbers. To make these predictions, we use linear regression, support vector regression, random forests, K-nearest neighbour, and artificial neural network algorithms. We evaluate the performance of the aforementioned models using various standard metrics, finding that the random forest algorithm is the best for predicting our jet characteristics. We also discover that this algorithm outperforms a recent empirical correlation, resulting in a significant increase in accuracy, especially for predicting the laminar length.

The turbulence development of a vertical natural convection boundary layer

Results from direct numerical simulations of a vertical natural convection boundary layer (NCBL) with $Pr=0.71$ reveal that the turbulence development of such a thermally driven convective flow has two distinct stages: at relatively low Grashof number, the bulk flow is turbulent while the near-wall region is laminar-like or weakly turbulent; at sufficiently high Grashof number, the entire flow becomes turbulent in the sense of von Kármán (cf. Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56, for the ultimate turbulent regime). Investigations on the turbulence statistics show that the near-wall Reynolds shear stress is negligible in the weakly turbulent regime but will grow in magnitude as the flow transitions to the ultimate regime at higher Grashof number. Similar behaviour is also seen in the streamwise turbulence intensity, where it develops from a mono-peak profile into a dual-peak structure as the Grashof number increases. At higher Grashof number, the near-wall energetic site is shown to have an energy distribution similar to that of a canonical wall-bounded turbulence (e.g. Hutchins & Marusic, Phil. Trans. R. Soc.A, vol. 365, 2007, pp. 647–664), with a peak centred at fixed location and wavelength ( $y^+=18$ and $\lambda ^+_x=1000$ ) in viscous coordinates. Investigation on the spanwise spectra also suggests that the turbulent near-wall streaks emerge only at sufficiently high Grashof number, with constant spacing $\lambda _z^+\approx 130$ . The extent of the weakly turbulent regime is identified using the maximum velocity location $\delta_m$ and a laminar length scale $\delta_u$ . The development of near-wall turbulence is also investigated by examining the turbulence kinetic energy budget. In the weakly turbulent regime, the near-wall turbulence is sustained predominantly by the pressure transport in addition to the shear production. At higher Grashof number, the flow becomes fully turbulent, and both turbulent transport and shear production become stronger, while the pressure transport is decreased. These results also reveal that the production–dissipation ratio $P/\varepsilon$ of the NCBL would follow a fundamentally different trend to the canonical wall-bounded flows, which further supports that the near-wall turbulence generation is affected by the bulk flow.

Ensemble-averaged kinematics of harmonically oscillating turbulent premixed flames

Direct numerical simulation (DNS) was used to characterize the kinematics of ensemble-averaged flame position in harmonically oscillating turbulent premixed flames. The flames are stabilized on a harmonically oscillating flame holder, and the fuel consists of methane and hydrogen at a volume ratio of 10:3 and is mixed with air at the stoichiometric ratio. Turbulence intensities of 3.7, 8.6, and 13.3% are simulated, and each turbulent flame is simulated for 20 forcing periods for ensemble averaging. A laminar flame speed calculation method is derived based on the G-equation framework; the new method reproduces the reference laminar flame speed and the laminar Markstein length. The turbulent flame speed shows strong linear correlation with the ensemble-averaged flame curvature. The turbulent flame speed at zero flame curvature increases proportional to the turbulence intensity, while the turbulent Markstein length is independent of turbulence intensity. When the flame is far from the oscillating flame holder, the correlations between the turbulent flame speed and the flame curvature exhibit either piecewise linear or power-law dependencies. At these locations, the turbulent Markstein length at high curvature is similar to the laminar Markstein length. When a power law model is applied, the turbulent flame speed dependency asymptotes to 0.7 powers of the ensemble-average flame curvature at the turbulence conditions considered here.

Multiple moving agents on complex networks: From intermittent synchronization to complete synchronization

We investigate multiple moving agents on complex networks. Each of them takes a random walk strategy and carries a chaotic oscillator. Remarkably, we find that with increasing the number of agents, a significant transition occurs from intermittent synchronization to complete synchronization. In particular, we observe that the distribution of laminar length presents a clearly power-law behavior in the intermittent synchronization stage. While reaching a complete synchronization state, correlation dimension and recurrence time statistics of synchronous orbits are in excellent agreement with that of their carrying chaotic system under consideration. Our work reveals that the number of moving agents has a profound effect on shaping synchronization behaviors.

Characteristics and Comparisons of Morphometric Measurements and Computed Tomography Hounsfield Unit Values of C2 Laminae for Translaminar Screw Placement Between Patients With and Without Basilar Invagination.

Patients with basilar invagination (BI) had high incidences of vertebral variations and high-riding vertebral artery (HRVA) that might restrict the use of pedicle or pars screw and increase the use of translaminar screw on axis. Here, we conducted a radiographic study to investigate the feasibility of translaminar screws and the bone quality of C2 laminae in patients with BI, which were compared with those without BI as control to provide guidelines for safe placement. In this study, a total of 410 patients (205 consecutive patients with BI and 205 matched patients without BI) and 820 unilateral laminae of the axis were included at a 1:1 ratio. Comparisons with regard to insertion parameters (laminar length, thickness, angle, and height) for C2 translaminar screw placement and Hounsfield unit (HU) values for the assessment of the appropriate bone mineral density of C2 laminae between BI and control groups were performed. Besides, the subgroup analyses based on the Goel A and B classification of BI, HRVA, atlas occipitalization, and C2/3 assimilation were also carried out. Furthermore, the factors that might affect the insertion parameters and HU values were explored through multiple linear regression analyses. The BI group showed a significantly smaller laminar length, thickness, height, and HU value than the control group, whereas no significant difference was observed regarding the laminar angle. By contrast, the control group showed significantly higher rates of acceptability for unilateral and bilateral translaminar screw fixations than the BI group. Subgroup analyses showed that the classification of Goel A and B, HRVA, atlas occipitalization, and C2/3 assimilation affected the insertion parameters except the HU values. Multiple linear regression indicated that the laminar length was significantly associated with the male gender (B = 0.190, p < 0.001), diagnoses of HRVA (B = -0.109, p < 0.001), Goel A (B = -0.167, p < 0.001), and C2/3 assimilation (B = -0.079, p = 0.029); the laminar thickness was significantly associated with the male gender (B = 0.353, p < 0.001), diagnoses of HRVA (B = -0.430, p < 0.001), Goel B (B = -0.249, p = 0.026), and distance from the top of odontoid to the Chamberlain line (B = -0.025, p = 0.003); laminar HU values were significantly associated with age (B = -2.517, p < 0.001), Goel A (B = -44.205, p < 0.001), Goel B (B = -25.704, p = 0.014), and laminar thickness (B = -11.706, p = 0.001). Patients with BI had narrower and smaller laminae with lower HU values and lower unilateral and bilateral acceptability for translaminar screws than patients without BI. Preoperative 3-dimensional computed tomography (CT) and CT angiography were needed for BI patients.

Analysis of the Type V Intermittency Using the Perron-Frobenius Operator

A methodology to study the reinjection process in type V intermittency is introduced. The reinjection probability density function (RPD), and the probability density of the laminar lengths (RPDL) for type V intermittency are calculated. A family of maps with discontinuous and continuous RPD functions is analyzed. Several tests were performed, in which the proposed technique was compared with the classical theory of intermittency, the M function methodology, and numerical data. The analysis exposed that the new technique can accurately capture the numerical data. Therefore, the scheme presented herein is a useful tool to theoretically evaluate the statistical variables for type V intermittency.

Numerical study of type-I intermittency in an atmospheric-pressure dielectric barrier discharge

Atmospheric-pressure dielectric barrier discharge (AP-DBD) as a complex dissipative dynamical system exhibits rich temporal nonlinear and chaotic behavior. The intermittent chaos in AP-DBD, where the abrupt intensive currents break the regular periodic current oscillations during a discharge process, is studied by numerical simulation. By increasing the control parameter of applied voltage amplitude, random intensive currents occur more frequently, reducing the average laminar length (time interval of regular oscillations). It is found that the average laminar length depending on the control parameter follows the scaling law with an exponent of −0.5, implying a type-I intermittent discharge. This study further supplements and strengthens the nonlinear theory in plasma discharge.

Turbulent flame speed and morphology of pure ammonia flames and blends with methane or hydrogen

Ammonia appears a promising hydrogen-energy carrier as well as a carbon-free fuel. However, there remain limited studies for ammonia combustion especially under turbulent conditions. To that end, using the spherically expanding flame configuration, the turbulent flame speeds of stoichiometric ammonia/air, ammonia/methane and ammonia/hydrogen were examined. The composition of blends studied are currently being investigated for gas turbine application and are evaluated at various turbulent intensities, covering different kinds of turbulent combustion regimes. Mie-scattering tomography was employed facilitating flame structure analysis. Results show that the flame propagation speed of ammonia/air increases exponentially with increasing hydrogen amount. It is less pronounced with increasing methane addition, analogous to the behavior displayed in the laminar regime. The turbulent to laminar flame speed ratio increases with turbulence intensity. However, smallest gains were observed at highest hydrogen content, presumably due to differences in the combustion regime, with the mixture located within the corrugated flamelet zone, with all other mixtures positioned within the thin reaction zone. A good correlation of the turbulent velocity based on the Karlovitz and Damköhler numbers is observable with the present dataset, as well as previous experimental measurements available in literature, suggesting that ammonia-based fuels may potentially be described following the usual turbulent combustion models. Flame morphology and stretch sensitivity analysis were conducted, revealing that flame curvature remains relatively similar for pure ammonia and ammonia-based mixtures. The wrinkling ratio is found to increase with both increasing ammonia fraction and turbulent intensity, in good agreement with measured increases in turbulent flame speed. On the other hand, in most cases, the flame stretch effect does not change significantly with increasing turbulence, whilst following a similar trend to that of the laminar Markstein length.

Type-V intermittency from Markov binary block visibility graph perspective

In this work, type-V intermittency is studied from Markov binary block visibility graphs perspective. We considered a piecewise quadratic Poincare map that is a simple model to exhibit this type of intermittency. The mechanism of type-V intermittency is collision of a stable fixed point with a point of discontinuity of the Poincare map. We study the behavior of a dynamical system in the vicinity of the discontinuous or non-differentiable points (NDP) using networks language. Numerical results showed that there is a logarithmic scaling law logε for the average laminar length of the type-V intermittency. We also described their properties based on statistical tools such as the length between reinjection points and the average laminar length. For further investigation, we verified the degree distribution of the complex network generated by type-V intermittency time series and finally, predicted the behavior of type-V intermittency by the proposed theoretical degree distributions.

Experimental study of laminar-to-turbulent transition in pipe flow

This paper describes an experimental study of the unforced laminar-to-turbulent transition in pipe flow. Two pipes with different length-to-diameter ratios are investigated, and the transition phenomenon is studied using pressure measurements and visual observations. The entropy change and force balance are examined, and the peak powers are measured through fast Fourier transform analysis at various Reynolds numbers. Visual observations show that the flow structure changes at the Reynolds numbers corresponding to the peak powers. There is no clear dependency of the transition on the ratio of pipe length to diameter. The flow conditions are classified as laminar flow, transitions I, II, and III, and turbulent flow, separated by Reynolds numbers of approximately 1200, 2300, 7000, and 12 000, respectively. The transition at a Reynolds number of 1200 is caused by the force balance between the laminar and turbulent flows. The other transitions are related to the flow condition in the development region upstream of the pipe flow region. That is, the laminar-to-turbulent transition in the development region affects the transition condition in the downstream pipe flow. The laminar and turbulent development length ratios derived from the entropy changes are in reasonable agreement with the formulas for both laminar and turbulent flows. At large Reynolds numbers, the laminar flow condition will be established through the creation of a laminar-flow velocity profile at the entrance to the pipe.

Intermittency Reinjection in the Logistic Map

Just below a Period-3 window, the logistic map exhibits intermittency. Then, the third iterate of this map has been widely used to explain the chaotic intermittency concept. Much attention has been paid to describing the behavior around the vanished fixed points, the tangent bifurcation, and the formation of the characteristic channel between the map and the diagonal for type-I intermittency. However, the reinjection mechanism has not been deeply analyzed. In this paper, we studied the reinjection processes for the three fixed points around which intermittency is generated. We calculated the reinjection probability density function, the probability density of the laminar lengths, and the characteristic relation. We found that the reinjection mechanisms have broader behavior than the usually used uniform reinjection. Furthermore, the reinjection processes depend on the fixed point.

Leaf and fruit characteristics of Parkia biglobosa (Jacq.) Benth according to agro climatic zones and land use in Southern Mali

A study was conducted in southern Mali to characterized Parkia biglobosa populations in the aim to contribute to the domestication of the species. Fields and fallows in the north sudanian, south sudanian and north guinean zones were concerned. Adult trees were marked in plots of 0.25 ha each and leaves and fruits were harvested from each tree for characterization. Petiole and laminar length, number of pairs of pinnae and leaflets, pedicel and pod length, pod wide, pod and seed weight, number of seed per pod were measured. The north guinean zone showed the highest number of pairs of pinnae and leaflets, the longest pods (23.06±9.91 cm in the fields), the highest mean seed weight (3.74±0.96 g in the fields) and the highest mean number of seeds per pod (17 ± 3 seeds in the fields). The South Sudanian zone showed the longest pedicels (3.85±1.08 cm in the fallows), the highest mean laminar length (18.02 cm) and mean petiole length (6.45 cm) in the fields but the same mean number of seeds per pod as for the north Guinean. The north Sudanian zone showed the widest (17.88±7.98 cm in the fields and 18.24±2.11 cm in the fallows) and heaviest (14.87±3.95 g in the fallows) pods. Leaf variables like the number of pairs of pinnae and leaflets seem to be influenced by the climatic gradient. The others leaf, pod and seed variables seem not to be influenced by the climatic gradient. These findings suggest that many leaf and fruit variables are controlled by endogenous factor that could be genetic. However, the manifestation of the endogenous factor seems to be influenced by factors such as environment and management practices.

Comparison of Applied Anatomy at L4-L5 and L5-S1 in Context of Tubular Decompression for Lumbar Canal Stenosis.

Tubular over-the-top decompression is getting popular in the management of lumbar canal stenosis (LCS). While L4-L5 is the most common level affected and operated for LCS, it is not uncommon to encounter patients with stenosis at L5-S1. No previous study has described the technical challenges of tubular decompression at the L5-S1 level as compared to at the L4-L5 level. This observational study was done on 40 consecutive patients older than 45 years who underwent magnetic resonance imaging (MRI) for back-related issues. The following radiological parameters: interlaminar angle, tube angle, laminar thickness ratio at the isthmus, and the laminar length ratio were evaluated at the L4-L5 level (group A) and the L5-S1 level (group B). The hypothesis behind the study was that if these patients were subjected to tubular decompression, then there will be technical differences between doing the surgery at the L4-L5 and L5-S1 levels. The mean age of the patients was 56.8 years (46-72) and the male to female ratio was 3:2. The mean interlaminar angle in group A was 71° and in group B was 102°. The tube angle in group A and group B was 36.8° and 49.7°, respectively. The laminar thickness ratio (L4:L5) was 1.34:1 and the laminar length ratio (L4:L5) was 1:1.42 in group A and B, respectively. Tubular decompression at the L5-S1 level has its own challenges because of the different anatomy of the L5 lamina compared to that of the L4 lamina. The wide interlaminar angle of L5 as compared to L4 dictates more oblique tube docking (tube angle) and more extensive table tilting to reach the contralateral lateral recess, thus making it challenging. The authors recommend that surgeons be conscious of this fact while performing tubular decompression at the L5-S1 level. This article provides information regarding technical challenges of doing surgery at L5-S1 level as compared to L4-L5 level. 3.