Velocity Variations Research Articles

Closed-Form Solutions of Injection-Driven Flow and Heat Transfer Inside an Inclined Horizontal Filter Chamber

Abstract The closed-form solutions of models provide operators and designers with a better understanding of how the systems perform practically, thus improving critical industrial production operations. Due to this importance, the case study at hand seeks to find closed-form solutions of the internal momentum and temperature variation during the filtration process to advance fluid purification. Lie group analysis is used to transform a system of equations representing the flow and heat transfer into a solvable system without changing the dynamics of the case study. The transformed solvable system is then integrated to find closed-form solutions of the internal velocity (momentum) and temperature variation. The obtained closed-form solutions are then used to analyze the effects of physical parameters arising from the process dynamics to find combinations of parameters that yield maximum permeates outflow. The analysis conveys that the internal fluid velocity increases when enhancing the permeation parameter and minimizing Reynolds number, wave speed parameter, and chamber height.

Non-linear elasticity, earthquake triggering and seasonal hydrological forcing along the Irpinia fault, Southern Italy.

Pump-probe experiments investigate the strain sensitivity of crustal elastic properties, showing nonlinear variations during the strain cycle. In the laboratory, pre-seismic reductions in seismic velocity indicate that asperity contacts within the fault zone begin to fail before the macroscopic frictional sliding. The recognition of such effects in natural seismic-cycles has been challenging. Here we exploit seasonal hydrological strains, performing a natural analogue to a quasi-static laboratory pump-probe experiment to investigate the nonlinear strain sensitivity of crustal rocks and its role in seismic failure along the tectonically-active Irpinia Fault System (Southern Italy). By comparing 14-years-long series of spring discharge, strain, seismic velocity variations and earthquakes rate, we find that seismicity peaks during maximum hydrological forcing and minimum seismic velocity. Seasonal strains of ~10-6 are required for both earthquake triggering and significant nonlinearity effects arising from modulus reduction. We suggest that, for faults in a critical state, cyclical softening may lead to failure and seasonal seismicity.

Temperature-dependent density effects on oscillatory mixed convective flow across a non-conducting horizontal circular cylinder embedded in a porous medium

Temperature-dependent density and aligned magnetic field influence on mixed thermal convection heat and current density aspects over a non-conducting porous circular horizontal cylinder is the novelty of this investigation. The magnetic effects over the surface are minimal but maximum away from the surface. The density of the fluid is assumed as an exponential variable of temperature to record the heat and current density rates. The pertinent form of partial differential equations is designed using suitable dimensionless quantities. The computational outputs of fluid velocity, magnetic fields and temperature variations are drafted using fluctuating-stokes quantities. The primitive quantities are utilised to make similar and asymptotic programs in FORTRAN for geometrical and numerical outcomes. The transient and oscillating behaviour of gradient values is sketched by using steady results in the oscillating formula. The finite difference methodology is applied to examine the physical properties with the Gaussian elimination matrix scheme. Effects of buoyant force ( λ ), Prandtl (Pr), magnetic force ( ξ ), density factor ( m ) and MHD Prandtl factor ( γ ) on the thermal behaviour of magneto-hydrodynamic analysis are applied. Results are explored around three angles π / 6 , π / 3 , π of the cylinder. Increasing magnitude in fluid velocity is deduced with high amplitude as porosity, buoyant and density parameters are enhanced.

Performa Termal Kondensor Udara pada Wind Tunnel: Evaluasi Perpindahan Panas

Heat transfer in air condenser systems is a critical aspect in various industrial applications, especially refrigeration and air conditioning systems. The thermal efficiency of condensers is greatly influenced by airflow characteristics, but airflow velocity optimization remains a challenge due to the trade-off between improved heat transfer and energy consumption. Although previous research has examined various aspects of condenser design, there is still a need to explore the optimal limit of airflow velocity that can maximize thermal efficiency without excessively increasing system workload. This study aims to evaluate the thermal performance of an air condenser in a wind tunnel, focusing on the effects of airflow velocity variations on heat transfer rate and thermal efficiency. The experimental method uses a wind tunnel with dimensions of 280x28x28 cm, equipped with a precise temperature and flow velocity measurement system. The flow velocity was varied from 0.8 to 1.8 m/s. The results showed a significant increase in the heat transfer coefficient (h) and heat transfer rate (Q) as the flow velocity increased. Analysis of Reynolds and Nusselt numbers revealed the transition of the flow from laminar to turbulent, which contributed to the increase in heat transfer efficiency. Comparison of experimental results with simulations showed good agreement in the middle velocity range, but there were deviations at extreme velocities. In conclusion, increasing the airflow velocity proved effective in improving the thermal performance of the condenser, but further optimization is required to balance the thermal efficiency with the energy consumption of the system.

Curing monitoring of adhesive layers between metal adherends by ultrasonic resonance technique

Abstract Layer resonance induced by ultrasonic wave incidence is applied to monitor the viscoelastic properties of a curing adhesive layer between metal plates. The theoretical analysis shows that when the adhesive layer is modeled as a linear viscoelastic material, the ultrasonic reflection spectrum takes local minima at the layer resonance frequencies depending on the wave velocity of the adhesive. On the other hand, the local minima of the reflection spectrum can be expressed as a function of the loss factor of the adhesive. Based on these results, a characterization technique for the wave velocity and the loss factor of a curing adhesive layer is proposed. This technique enables the evaluation of the viscoelastic properties even if the reflected waves from both faces of a bond layer cannot be separated. The proposed method is employed to investigate the curing behavior of bi-component epoxy adhesives. As a result, it is shown that the bonding condition affects the variation of the wave velocity and loss factor. The estimated wave velocity increases as the curing proceeds, while the loss factor sometimes takes a local maximum depending on the bonding condition and the frequency range. When the mixing ratio of the main and curing agents is imbalanced, the variation of the wave velocity becomes gradual. Furthermore, the increase in the curing temperature leads to fast changes in the wave velocity and loss factor. The proposed technique has the potential to provide insight into the curing behavior of the adhesive layer by incorporating it into other measurement methods and theories.

Fluid responsiveness in pediatrics: an unsolved challenge

Predicting fluid responsiveness is a major challenge in the pediatric population as vascular and pulmonary compliance differ from the adults. However it is a crucial thing to avoid the harmful fluid overload. We count on different variables to identify responders being the dynamic parameters the ones with more evidence, specially the Respiratory Variation In Aortic Blood Flow Velocity based on echocardiography. Other variables rely on the arterial waveform, like Pulse Pressure Variation or Stroke Volume Variation seem to have limitations but new tests like VTC are arriving to overcome their drawbacks. We review the actual evidence regarding fluid responsiveness prediction in children and the anatomic and physiologic peculiarities of children that explain why they do not respond like adults and why we should study them in particular.

Imaging Complex Structures of the Los Angeles Basin via Adjoint-State Travel-Time Tomography

ABSTRACT In this study, we present high-resolution seismic velocity models for the Los Angeles basin (LAB) and its adjacent area using adjoint-state travel-time tomography, fitting an extensive database of P- and S-wave travel times accumulated from 1980 to 2021. We select 151,193 first P-wave travel times and 149,997 first S-wave travel times from local earthquakes archived in the Southern California Earthquake Data Center to determine the velocity models, with earthquake locations updated at each iteration. With seismic stations spaced more than 3.5 km apart, our dataset has limited resolution in the uppermost 1–2 km. However, starting from three different initial models, our VP models, which are optimally imaged between 3 and 15 km, show similar velocity heterogeneity and provide a better fit to the observed first travel-time data compared to the Community Velocity Model-Harvard 15.1.0 and Community Velocity Model-Southern California Earthquake Center 4.26. Our models provide a detailed delineation of the subsurface structure beneath the LAB, revealing significant velocity variations across active faults, a 10-km-thick sequence of sedimentary rocks within the basin, and a distinct basin margin marked by transitions from low to high-velocities. In addition, these models highlight basement structures with elevated VP and VS located at depths of 9 to 12 km and beyond. Specifically, beneath the northeastern part of the basin, the models demonstrate improved accuracy and reliability in reflecting the linear relationship between VP and VS in mafic rocks. The accurate delineation of the basin’s structure provided by our models could also offer robust constraints for seismic response modeling and seismic hazard assessment in the region.

A numerical investigation on rheological turbulent flow through a 90° mixing elbow

Mixing elbows are widely used in various industrial processes to mix two different Newtonian or non-Newtonian fluids under turbulent flow conditions. This study numerically investigates the fluid flow and mixing characteristics in 90-degree elbows with different bend curvatures (curvature ratios of 3, 6, and 9) and Reynolds numbers ranging from 1 × 104 to 5 × 105 for both fluid types. The Reynolds-Averaged Navier–Stokes equations are solved using the turbulent k-epsilon model in ANSYS Fluent. Results show that the bend curvature creates an adverse pressure gradient that drives secondary flows, which become more pronounced with higher Reynolds numbers and lower curvature ratios. Higher Reynolds numbers improve mixing quality, as indicated by velocity and temperature variations quantified using standard deviations. For Reynolds numbers in the range of 104, velocity fluctuations initially increase, but at higher values (~ 105), they decrease, even by up to 64% as the Reynolds number rises from 1 × 105 to 5 × 105. Similarly, increasing the curvature ratio enhances mixing efficiency, with a 32% reduction in velocity fluctuations when the curvature ratio increases from 6 to 9. Furthermore, shear-thinning fluids (n=0.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n = 0.6$$\\end{document}) exhibit superior mixing performance, with a standard deviation of velocity fluctuations at the outlet of 0.32, compared to 0.54 for shear-thickening fluids (n=1.4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n = 1.4$$\\end{document}). In terms of temperature fluctuations also, a similar trend is observed. These findings are valuable for optimizing mixing and fluid transport in industries such as chemical processing and food production, where effective mixing of complex fluids is critical. This study provides insights for improving the design of mixing systems that handle fluids with various rheological characteristics.

A High-Fidelity Computational Model for Predicting Blood Cell Trafficking and 3D Capillary Hemodynamics in Retinal Microvascular Networks.

To present a first principle-based, high-fidelity computational model for predicting full three-dimensional (3D) and time-resolved retinal microvascular hemodynamics taking into consideration the flow and deformation of individual blood cells. The computational model is a 3D fluid-structure interaction model based on combined finite volume/finite element/immersed-boundary methods. Three in silico microvascular networks are built from high-resolution in vivo motion contrast images of the superficial capillary plexus in the parafoveal region of the human retina. The maximum tissue area represented in the model is approximately 500 × 500 µm2, and vessel lumen diameters ranged from 5.5 to 25 µm covering capillaries, arterioles, and venules. Blood is modeled as a suspension of individual blood cells, namely, erythrocytes (RBC), leukocytes (WBC), and platelets in plasma. An accurate and detailed biophysical modeling of each blood cell and their flow-induced deformation is considered. A physiological, pulsatile boundary condition corresponding to an average cardiac cycle of 0.9 second is used. Detailed quantitative data and analysis of 3D retinal microvascular hemodynamics are presented, and their relationship to RBC flow dynamics is illustrated. Blood velocity is shown to have temporal oscillations superimposed on the background pulsatile variation, which arise because of the way RBCs partition at vascular junctions, causing repeated clogging and unclogging of vessels. Temporal variations in RBC velocity and hematocrit are anti-correlated in a given vessel, but their time-averaged distributions are positively correlated across the network. Whole blood velocity is 65% to 85% of RBC velocity, with the discrepancy related to the formation of an RBC-free region, adjacent to the vascular endothelium and typically 0.8 to 1.8 µm thick. The 3D velocity and RBC concentration profiles are shown to be oppositely skewed with respect to each other, because of the way that RBCs "hug" the apex of each bifurcation. RBC deformation is predicted to have biphasic behavior with respect to vessel diameter, with minimal cell length for vessels approximately 7 µm in diameter. The wall shear stress (WSS) exhibits a strongly 3D distribution with local regions of high value and gradient spanning a range of 10 to 80 dyn/cm2. WSS is highest where there is faster flow, greater curvature of the vessel wall, capillary bifurcations, and at locations of RBC crowding and associated thinning of the cell-free layer. This study highlights the usefulness of high-fidelity cell-resolved modeling to obtain accurate and detailed 3D, time-resolved retinal hemodynamic parameters that are not readily available through noninvasive imaging approaches. The results presented are expected to complement and enhance the interpretation of in vivo data, as well as open new avenues to study retinal hemodynamics in health and disease.

Single-Shot Time-Lapse Target-Oriented Velocity Inversion Using Machine Learning

In this study, we used machine learning (ML) to estimate time-lapse velocity variations in a reservoir region using seismic data. To accomplish this task, we needed an adequate training set that could map seismic data to velocity perturbation. We generated a synthetic seismic database by simulating reservoirs of varying velocities using a 2D velocity model typical of the Brazilian pre-salt ocean bottom node (OBN) acquisition, located in the Santos basin, Brazil. The largest velocity change in the injector well was around 3% of the empirical velocity model, which mimicked a realistic scenario. The acquisition geometry was formed by the geometry of 1 shot and 49 receivers. For each synthetic reservoir, the corresponding seismic data were obtained by estimating a one-shot forward-wave propagation using acoustic approximation. We studied the reservoir illumination to optimize the input data of the ML inversion. We split the set of synthetic reservoirs into two subsets: training (80%) and testing (20%) sets. We point out that the ML inversion was restricted to the reservoir zone, which means that it was inversion-oriented to a target. We obtained a good similarity between true and ML-inverted reservoir anomalies. The similarity diminished for a situation with non-repeatability noise.

A multi-task learning framework for aerodynamic computation of two-dimensional airfoils

Accurate and efficient prediction of airfoil aerodynamic coefficients is essential for improving aircraft performance. However, current research often encounters significant challenges in balancing accuracy with computational efficiency when predicting complex aerodynamic coefficients. In this paper, a Multi-Task Learning framework for Aerodynamic parameters Computation (MTL4AC) of two-dimensional (2D) airfoils is proposed. The MTL4AC processes two key subtasks: flow field prediction and pressure coefficient prediction. These two subtasks complement each other to reveal both global and local aerodynamic changes around the airfoil. The flow field prediction provides a coarse-grained global perspective, which focuses on the pressure and velocity variations on and around the airfoil surface. The pressure coefficient prediction offers a fine-grained local perspective, which concentrates on the pressure distribution on the airfoil surface to accurately calculate lift and drag coefficients. The MTL4AC demonstrated substantial improvements in the experiments conducted on the public dataset, achieving significant enhancements in accuracy and stability. This research contributes an accurate and efficient framework for aerodynamic computation, integrating geometric features and advanced multi-task learning techniques to achieve superior performance in predicting aerodynamic coefficients.

Dynamic Formulation of the Double Multiple Stream Tube Model of Offshore Vertical Axis Wind Turbines

Abstract The paper proposes a novel algorithm to simulate Vertical Axis Wind Turbines in floating motion based on a low-fidelity approach. The conventional Double Multiple Stream Tube Model is formulated as a steady state model to deal with the inherent unsteady aerodynamics of VAWTs. The Double Multiple Stream Tube Model makes use of an average contribution of the blade passages over a revolution to solve the Blade Element Momentum equation. The model reduces the dependence of the solution (the induction field) to a space variable. Floating Vertical Axis Wind Turbines undergoes a variation of aerodynamic quantities according to wave periods, also different from the rotor period. This paper provides a new formulation of the Double Multiple Stream Tube Model to solve the turbine rotation in time and space, introducing the variation of the platform velocity and a revised approach to the downstream actuator disc. The most impactful parameter is found to be the wave frequency: wave periods at full-scale are lower than the ones of the turbine rotor, featuring optimal operating points at low tip speed ratios. The increase of the wave frequency highlights the differences of the average torque prediction for a single blade up to 10% between the unsteady and the standard formulation. In this context, the development of fast low-fidelity computational tools play a key role in the assessment of the preliminary designs of Floating Offshore Vertical Axis Wind Turbines and it will be used to optimise the aerodynamic design of the laboratory scaled model under surge motion.

Implementation of actin polymerization and depolymerization in a two-dimensional cell migration model and its implications on mammalian cell morphology and velocity

Cell migration, a pivotal process in wound healing, immune response, and even cancer metastasis, manifests through intricate interplay between morphology, speed, and cytoskeletal dynamics. Mathematical modeling emerges as a powerful tool to dissect these complex interactions. This work presents a two-dimensional immersed boundary model for mammalian cell migration, incorporating both filamentous actin (F-actin) and monomeric actin (G-actin) to explicitly capture polymerization and depolymerization. This model builds upon our previous one-dimensional efforts, now enabling us to explore the impact of G-actin on not just cell velocity but also morphology. We compare predictions from both models, revealing that while the one-dimensional model captures core dynamics along the cell’s axis, the two-dimensional model excels in portraying cell shape evolution and transverse variations in actin concentration and velocity. Our findings highlight the crucial role of including G-actin in shaping cell morphology. Actin velocity aligned with migration direction elongates the cell, while velocity normal to the membrane promotes spreading. Importantly, the model establishes a link between these microscopic aspects and macroscopic observables like cell shape, offering a deeper understanding of cell migration dynamics. This work not only provides a more comprehensive picture of cell migration but also paves the way for future studies exploring the interplay of actin dynamics, cell morphology, and biophysical parameters in diverse biological contexts.

Measurement of ocean currents by seafloor distributed optical-fiber acoustic sensing.

Ocean current measurements play a crucial role in aiding our understanding of ocean dynamics and circulation systems. Traditional methods, such as drifters and ocean buoys, are sparsely distributed and of limited effectiveness due to the nature of the marine environment and high operating expenses. Distributed acoustic sensing (DAS) is an emerging technology using submarine optical-fiber (OF) cables as dense seismo-acoustic arrays, offering a new perspective for ocean observations. Here, in situ observations of ocean surface gravity waves (OSGWs) and ocean currents by DAS were made along a pre-existing 33.6 km seafloor OF cable. The average current velocity and water depth along the cable were determined from observed OSGW-induced seafloor noise (0.05-0.2 Hz) using ambient-noise interferometry and frequency-domain beamforming. Variations in current velocity were derived at high spatiotemporal resolution using the frequency-domain waveform-stretching method. The inverted current velocity was verified by nearby ocean buoy observations and forecasting results. The observations demonstrate the effectiveness of DAS-instrumented OF cables in monitoring ocean currents.

Investigation of Cross‐Sectional Characteristics of Internal Meshing Screw Mixing Flow Field for Dough Paste

ABSTRACTThe internal meshing screw mixer, driven by extensional rheology, demonstrates excellent mixing efficiency for high‐viscosity materials while minimizing fiber damage. This study developed a computational model for the mixing process of high‐viscosity fluids based on the motion equations of the internal meshing screw. The model was validated through experiments involving the mixing of corn syrup, flour and water. The results reveal the flow field's cross‐sectional streamlines and confirm the presence of chaotic mixing states at the system interface through horseshoe mapping and the existence of hyperbolic points. By comparing the extensional and shear rates, as well as analyzing the distribution of mixing indices, this paper establishes that the primary mixing mechanism within the cross‐section is extensional force, highlighting the role of the internal meshing screw as a mixer dominated by extensional flow fields. We investigate the variations in fluid velocity, velocity uniformity index, extensional rate, shear rate, and mixing index over time under different conditions of eccentricity, rotor radius, and rotational speed. The findings indicate that while eccentricity has a limited impact on average velocity, it significantly enhances velocity disturbances and increases the ratio of extensional effects within the fluid domain. In contrast, rotor radius and speed lead to a linear increase in average velocity but have little effect on velocity disturbances and the extensional effects in the fluid domain. This study provides valuable insights into how various cross‐sectional parameters influence the flow field of the internal meshing screw mixing process, offering crucial support for its application in mixing high‐viscosity non‐Newtonian fluids within the food industry.

Investigation into particle flow patterns during powder spreading in SLM process

Particle flow patterns and their variation mechanism during powder spreading in selective laser melting (SLM) are comprehensively investigated based on discrete element method. Two typical particle flow patterns, circulation and discharge, are identified. The patterns are found to alternate during powder spreading, and the underlying dynamical mechanism are clarified. Variations in the particle flow state across the gap induce variations in vertical velocities of particles in front of the blade, affecting the particle flow pattern. Effect of process parameters on flow pattern is studied, and the dynamical mechanism of the effect is analyzed in depth by two newly proposed indexes. Decreasing gap height, and increasing spreading speed and blade inclination, reduce the proportion of particles moving downward in shear band and enhance inter-particle forces near the gap, thus weakening discharge and intensifying circulation. This study provides a beneficial insight into the powder flow during powder spreading in SLM process.

Breaststroke and butterfly intercycle kinematic variation according to different competitive levels with Statistical Parametric Mapping analysis

Breaststroke and butterfly are complex swimming techniques requiring refined motor skills to perform successfully, with coordinated and consistent interaction between propulsive and resistive forces being decisive when considering swimmers expertise. The current study analysed those techniques intercycle kinematic variation in two swimmers cohorts. Twenty elite and 15 national level swimmers performed one 25 m breaststroke and one 25 m butterfly sprints, with an underwater camera recording images at 120 Hz in the sagittal plane. Mean velocity, maximum and minimum velocities, stroke rate and length, intracycle velocity variation and phases relative duration were calculated for consecutive cycles (elite: five breaststroke/butterfly, national level: eight breaststroke/seven butterfly). The two highest peaks and the lower peak in between in breaststroke were also addressed. Intercycle and inter-groups analysis were performed using ANOVA, ANCOVA and Statistical Parametric Mapping. Elite and national level differed regarding breaststroke mean and maximum velocities, 1st and 2nd peaks and minimum between peaks (1.30 ± 0.02 vs 1.15 ± 0.02 m/s, 2.13 ± 0.05 vs 1.88 ± 0.06 m/s, 1.63 ± 0.05 vs 1.48 ± 0.05 m/s, 2.13 ± 0.05 vs 1.86 ± 0.05 m/s, 1.33 ± 0.04 vs 1.23 ± 0.04 m/s), and butterfly mean, maximum and minimum velocities, stroke rate and intracycle velocity variation, respectively (1.65 ± 0.01 vs 1.50 ± 0.01 m/s, 2.20 ± 0.04 vs 2.09 ± 0.04 m/s, 1.12 ± 0.04 vs 0.79 ± 0.04 m/s, (57.9 ± 0.9 vs 54.9 ± 1.0cycles/min, 18.4 ± 1.3 vs 23.7 ± 1.3 %). Elite and national level swimmers showed consistent breaststroke intercycle kinematic variation, but a butterfly mean velocity decay, with the upper limbs release and recovery, and the outsweep phases originating variability between butterfly cycles. Skill levels contrasted in technical and strategic features at sprint breaststroke and butterfly but showed similar velocity variability between consecutive swimming cycles.

A Chebyshev collocation method for directly solving two-dimensional ocean acoustic propagation in linearly varying seabed.

It is one of the most concerning problems in hydroacoustics to find a method that can calculate the acoustic propagation accurately and adapt to the variation of the seabed. Currently, the one-dimensional spectral method has been employed to address the simplified ocean acoustic propagation model successfully. However, due to the model's application limitations and approximation error, it poses challenges when attempting to solve real-world ocean acoustic fields. Hence, there is a crucial need to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation, without relying on a simplified model. In previous work, we achieved successful solutions for the two-dimensional Helmholtz equation within a rectangular domain, utilizing a collocation-type spectral method. Taking into account the fluctuations in the actual seabed, we introduce a Chebyshev collocation spectral method to directly tackle the two-dimensional ocean acoustic propagation problem, which could solve the case of a seabed with linear variation, sound velocity variation and inhomogeneous medium situation. After comparative verification, the calculation result of the two-dimensional spectral method is more accurate than traditional mature models such as Kraken and COUPLE. By eliminating model constraints and enlarging the solution range, this spectral method holds immense potential in real marine environments.

The propulsive effect of thermal waves

The use of thermal waves as a potential propulsion method has been investigated. The test flow system involves two horizontal parallel plates, one fixed and exposed to thermal waves and the other allowed to move. The propulsive effect is quantified using the velocity of this plate. It is shown that, in general, the plate moves opposite to the wave direction, but its characteristics depend on whether the waves have subcritical or supercritical amplitudes. In the case of subcritical amplitudes, the plate velocity varies proportionally to the square of the wave amplitude, and its most effective wavelength corresponds to the wave number α≈2. In the case of supercritical amplitudes, the system response is affected by nonlinear thermal streaming, which produces faster plate movement. The plate velocity variations as a function of the wave velocity exhibit hysteresis with respect to changing wave direction; multiple solutions are possible for nominally identical flow conditions, with some of the solution branches terminating at limit points.

Inner–outer interaction of unsteady turbulent flow inside duct with wall corrugations: Augmentation and saturation

This study investigates the inner–outer interaction of the unsteady turbulent flow inside a duct with wall corrugations, where “inner” refers to the trapped flow in a corrugation-induced cavity array and “outer” relates to the mainstream flow transporting through a circular duct. Configurations with different pitch–diameter ratios (P/D) are used to demonstrate the effect of the cavity flow pattern on the mainstream flow variations. An improved delayed detached-eddy simulation with dynamic blending function is performed to acquire high-fidelity turbulent flow data, in which dynamic evolution of multi-scale vortex structures containing hairpin vortices and vortex fragments is clearly resolved. The subsequent statistical analysis reveals a nonlinear variation tendency of the inner–outer interaction intensity, experiencing sudden augmentation first and then a gradual attenuation toward the final saturation. Comparatively, a larger pitch ratio results in a stronger interaction under the effect of bicentric recirculation zones within the cavity array. Moreover, a proper orthogonal decomposition analysis allows for the visualization of energetic flow structures, as consistent velocity variations throughout the duct volume are identified for a larger pitch ratio, while discontinuity at the duct termination is found for a smaller pitch ratio. Finally, an advanced elliptical model based on the spatiotemporal cross correlation analysis is proposed to examine the convection velocity and sweeping velocity of the interactive mainstream flow and cavity flow. The results highlighted the presence of first-augmented and then saturated dynamics and kinematics inside the duct with the cavity array.