Viscous Forces Research Articles

Non-negligible buoyancy effect on bubbles travelling in horizontal microchannels of comparable size at small Bond numbers

When a gas bubble is transported by a liquid flow confined within a horizontal channel of comparable size, buoyancy effects are usually assumed to be negligible if the Bond number of the flow is less than unity. However, recent experimental studies showed that buoyancy may still significantly impact the bubble dynamics even when Bo≪1, provided that the flow speed is sufficiently small, such that the viscous and inertial forces are weak. To derive a new criterion to assess the significance of buoyancy on the flow of small bubbles in horizontal microchannels, we have performed systematic numerical simulations using the free software Basilisk, covering a wide range of Bond, capillary and Reynolds numbers, Bo=0.004−0.4, Ca=10−4−0.5 and Re=0−100, and exploring the bubble-to-channel diameter ratios db/D=0.2−0.9. We demonstrate that the nondimensional group Bo(db/D)2/Ca is effective in assessing the importance of buoyancy in flows with negligible inertial effects. When Bo(db/D)2/Ca<0.1, buoyancy effects are negligible and the bubble travels along the channel axis. When Bo(db/D)2/Ca>10, buoyancy effects dominate and the bubble travels in the vicinity of the upper wall. For intermediate values, bubbles take equilibrium positions between the channel centre and the wall, and the threshold Bo(db/D)2/Ca=1 is effective in predicting whether bubbles will travel closer to the channel centre or to the wall. The capillary number at the denominator describes the lift force generated by the deformation of the bubble due to viscous shear, which acts towards the channel centre thus opposing buoyancy. Inertial forces significantly alter the shape and equilibrium position of the bubble when the Weber number of the flow exceeds unity and Bo/We<1. Under the action of inertia, bubbles of size comparable to the channel diameter become elongated but remain centred. Smaller bubbles migrate towards the channel wall and do not exhibit a preferential near-wall circumferential position.

Numerical simulation of particles distribution of environmental tobacco smoke (ETS) and its concentration in a closed environment

Humans are frequently exposed to various chemical hazards, with smoking being a significant source of indoor air pollution. This pollution is particularly pronounced in environments such as smoking rooms, conference halls, cafes, and coffee houses. This study focuses on analyzing the concentration, distribution, and behavior of emitted particles from both mainstream and sidestream smoke in a controlled smoking room environment. A critical aspect of the research is the consideration of the thermal plume generated by the smoker's body, particularly around the breathing zone, which plays a crucial role in the dispersion and inhalation of pollutants. To conduct this analysis, a computational fluid dynamics approach was employed, incorporating a displacement ventilation (DV) system integrated with a detailed surface mesh model of a standing manikin. A Lagrangian approach was utilized to track the particle paths, considering factors such as particle size, density, and initial velocity. This approach was complemented by an Eulerian method to simulate the complex airflow patterns within the smoking room, accounting for turbulent flow and temperature variations. The integration of these methods provides a comprehensive understanding of both the macroscopic and microscopic behaviors of smoke particles. The motion equations governing the particles incorporated several forces, including inertial drag force, viscous drag force, buoyancy force, and gravitational force. Additionally, the study examined the interaction between thermal plumes and smoke particles, particularly how temperature gradients around the body affect particle dispersion and concentration. The study meticulously evaluated the distribution and volume average of respirable suspended particles (RSPs) and nicotine by analyzing a plane opposite to the breathing zone of both heated and unheated manikins. It was observed that the thermal plume generated by the temperature gradient around the body could significantly alter the flow field of both sidestream and mainstream smoke between puff periods. The simulation results demonstrated that the thermal plume increased the concentration of RSPs in the breathing zone, highlighting a critical exposure pathway for smokers and nonsmokers alike. A significant increase of approximately 70% in the nicotine concentration is due to the thermal plume. The concentration of nicotine peaks at approximately 0.003 mg/m3 by the third second in smoker#1's (6 smokers' position) breathing zone. Specific configurations of the DV system showed varying efficiencies in reducing pollutant concentrations, emphasizing the need for targeted ventilation strategies. In a chamber with six smokers, researchers found that the time required for suspended particles to reach a cleaning ratio, considering the dynamics of particle movement due to smoking activity, was approximately 184 s per puff.

Immiscible non-Newtonian displacement flows in stationary and axially rotating pipes

We examine immiscible displacement flows in stationary and rotating pipes, at a fixed inclination angle in a density-unstable configuration, using a viscoplastic fluid to displace a less viscous Newtonian fluid. We employ non-intrusive experimental methods, such as camera imaging, planar laser-induced fluorescence (PLIF), and ultrasound Doppler velocimetry (UDV). We analyze the impact of key dimensionless numbers, including the imposed Reynolds numbers (Re, Re*), rotational Reynolds number (Rer), capillary number (Ca), and viscosity ratio (M), on flow patterns, regime classifications, regime transition boundaries, interfacial instabilities, and displacement efficiency. Our experiments demonstrate distinct immiscible displacement flow patterns in stationary and rotating pipes. In stationary pipes, heavier fluids slump underneath lighter ones, resulting in lift-head and wavy interface stratified flows, driven by gravity. Decreasing M slows the interface evolution and reduces its front velocity, while increasing Re* shortens the thin layer of the interface tail. In rotating pipes, the interplay between viscous, rotational, and capillary forces generates swirling slug flows with stable, elongated, and chaotic sub-regimes. Progressively, decreasing M leads to swirling dispersed droplet flow, swirling fragmented flow, and, eventually, swirling bulk flow. The interface dynamics, such as wave formations and velocity profiles, is influenced by rotational forces and inertial effects, with Fourier analysis showing the dependence of the interfacial front velocity's dominant frequency on Re and Rer. Finally, UDV measurements reveal the existence/absence of countercurrent flows in stationary/rotating pipes, while PLIF results provide further insight into droplet formation and concentration field behavior at the pipe center plane.

Nonlinear parametric models of viscoelastic fluid flows.

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate , we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows.

Topology optimization of regenerative cooling structures under high Reynolds number flow with variable thermo-physical properties

In the design of thermal protection system for hypersonic vehicles, the efficient convective heat transfer within regenerative cooling channels plays a critical role in maintaining their thermal performance. This study focuses on the topology optimization (TO) of the cooling channels that operate at high Reynolds number and have variable thermo-physical properties. A novel approach is introduced to enhance the density-based method by incorporating an effective artificial force correction and tabulating the temperature-dependent thermal properties. Several topology-optimized cooling layouts were generated to minimize the maximum temperature within the design domain while considering different power dissipation constraints. This confirms the validity of the proposed lumped correction term in momentum equation accounting both viscous and convective body forces. Regarding the thermal performance of the optimized layouts, the staggered arrangement of cellular ribs in the TO channel was found to induce multiple flow separations and promote turbulent mixing, thereby improving heat transfer efficiency and mitigating the thermal acceleration effect. Conjugate heat transfer calculations revealed that the optimal topology-optimized channel achieved a 24.3% improvement in overall thermal performance while being 15.3% lighter than the straight channel design. Furthermore, the optimal topology optimized layout consistently outperformed the straight channel design by 6.6% to 24.3% in terms of the overall thermal performance across a wide range of heat flux distribution and mass flow rate conditions. This investigation highlights the effectiveness of topology optimization in designing regenerative cooling structures featuring high Reynolds number hydrocarbon thermal fluid flow.

Biophysics of protist behaviour

Protists, an umbrella term first coined by Ernst Haeckel in 1866, are a vast collection of (primarily unicellular) eukaryotes that are "neither animals nor plants". This basic definition by exclusion has been exercised for centuries, even though recent advances have led to more rigorous taxonomic assignment of various protist groups. Pioneering comparative phylogenetic approaches have been applied to these organisms to reconstruct the deep branches of the eukaryotic tree, revealing essential clues about early eukaryotic evolution. Protists, including amoebae, flagellates, ciliates, and algae, are also vital constituents of global ecosystems, where they appear at the base of food chains, control the relative abundance of other microbes, and participate in global biogeochemical recycling. Due to their typically small size and lack of nervous systems, protists are often associated with the unfortunate label 'primitive'. Yet they exhibit remarkable behavioural sophistication and are able to feed, predate, navigate and interact with their surroundings. Unlike macroscopic animals, many protists reside in a non-intuitive physical regime where viscous forces dominate over inertia, and where they use diverse propulsion and navigation strategies. Interdisciplinary research into these cell-scale phenomena, characterised by a complex interplay of physical forces and mechanical constraints, has significantly advanced the emerging fields of active matter, microhydrodynamics, and non-equilibrium statistical physics. This primer discusses the biophysics of protist behaviour, with a focus on locomotion and feeding. I will highlight the most extensively studied principles and describe some more esoteric behaviours that have not yet been systematically explored.

On the transport of a millimeter-sized compound droplet in a Poiseuille flow

The compound droplet consists of the inner and outer droplets. The outer droplet's ability to isolate the inner contents from its surroundings makes applications such as drug delivery, cell encapsulation, and cell sorting possible. Here, we experimentally explore the transport of the compound droplet at different Reynolds numbers, viscosity ratios, and volume ratios. Compound droplets have a longer dimensionless transport distance along the X-axis than single-phase droplets at Reynolds numbers from 44 to 366. When the Reynolds number is increased from 81.2 to 243.7, the dimensionless maximum transport distance of the compound droplet along the X-axis becomes 2.04 times. As the Re increases, the compound droplet deflection rate decreases continuously. For a constant initial velocity of the compound droplet, an increase in the viscosity ratio leads to an increase in the dimensionless velocity along the x axis with the compound droplet during transport. The maximum transport distance along the x-axis increases, and the deflection rate decreases as the inertial and viscous forces increase with increasing viscosity and dimension ratios. The chemical droplets become more stable as a result.

Competitive effects of anion mobility and viscous forces on the interactions of hyaluronic acid and alginic acid with hofmeister salts

The specific ion effect takes into account the hydration, mobility, and kosmotropic/chaotropic effects. However, another important aspect to consider is the solution viscosity, which influences ion mobility. A limited number of publications have considered the impact of specific ion effects on polyelectrolytes. However, none of the studies have considered the viscous effect of polyelectrolytes. This study aims to investigate the impact of kosmotropic and chaotropic anions on negatively charged alginic acid and hyaluronic acid using dynamic light scattering, rheology, and molecular dynamic simulations. Different concentration regimes and the change in the chain conformations in these regimes, along with the viscosity scaling and impact of the salts on the polyelectrolytes, have been discussed. An interesting finding regarding the solution viscosity was reported. The solution viscosity leads to the reversal of the diffusivity and viscosity trend of the polymer with kosmotropes and chaotropes. A threshold is also identified above which viscous forces dominate. Specific ion effects dominate below the threshold. It was concluded that the specific ion effect shows a competitive nature with the viscous forces in the case of a high-viscosity polyelectrolyte solution, which becomes an important aspect to consider for unveiling such interactions. Prior knowledge of the conformations of polymers can be used for designing drug delivery/nutrient delivery systems and for understanding phase separation behavior. Considering the viscosity of polymer solution becomes an important factor which, in turn, impacts the anion's mobility and ultimately influences the polymer conformations.

Electronically actuated artificial hinged cilia for efficient bidirectional pumping.

Cilial pumping is a potent mechanism used to control and manipulate fluids on microscales. Recently, we introduced an electronically driven μ-cilial platform that can create arbitrary flow patterns in liquids near a surface with the potential for various engineering applications. This μ-cilial platform, however, utilized the coupling between elasticity and viscous drag to obtain pumping and had several limitations. For example, each cilium could only pump in one direction. Thus, to create bidirectional flows, it was necessary to fabricate and separately actuate two oppositely facing cilia. As another example, the generation of non-reciprocal cilial motions, a necessary condition for pumping at these scales, could only be achieved by matching the elastic stresses inherent in actuating the cilia with the viscous drag forces generated by the flows. This criterion severely restricted the frequency range over which the cilia could be operated and resulted in a small swept area, both of which restricted the volume of fluid being pumped in each cycle. These limitations contrast with the capabilities of natural cilia, which can achieve omnidirectional transport and operation over a broad range of frequencies. In natural cilia, these capabilities arise from their complex internal structure. Inspired by this strategy we designed hinged cilia and show they can achieve bidirectional pumping of larger fluid volumes over a broad range of frequencies. Finally, we demonstrate that even regular arrays of individually controlled hinged cilia can generate a variety of flow patterns using fewer cilia than in previous cilia metasurface designs.

Settling of two rigidly connected spheres

Laboratory experiments and particle-resolved simulations are employed to investigate the settling dynamics of a pair of rigidly connected spherical particles of unequal size. They yield a detailed picture of the transient evolution and the terminal values of the aggregate's orientation angle and its settling and drift velocities as functions of the aspect ratio and the Galileo number $Ga$ , which denotes the ratio of buoyancy and viscous forces acting on the aggregate. At low to moderate values of $Ga$ , the aggregate's orientation and velocity converge to their terminal values monotonically, whereas for higher $Ga$ -values the aggregate tends to undergo a more complex motion. If the aggregate assumes an asymmetric terminal orientation, it displays a non-zero terminal drift velocity. For diameter ratios much larger than one and small $Ga$ , the terminal orientation of the aggregate becomes approximately vertical, whereas when $Ga$ is sufficiently large for flow separation to occur, the aggregate orients itself such that the smaller sphere is located at the separation line. Empirical scaling laws are obtained for the terminal settling velocity and orientation angle as functions of the aspect ratio and $Ga$ for diameter ratios from 1 to 4 and particle-to-fluid density ratios from 1.3 to 5. An analysis of the accompanying flow field shows the formation of vortical structures exhibiting complex topologies in the aggregate's wake, and indicates the formation of a horizontal pressure gradient across the larger sphere, which represents the main reason for the emergence of the drift velocity.

Revised Friction Groups for Evaluating Hydraulic Parameters: Pressure Drop, Flow, and Diameter Estimation

Suitable friction groups are provided for solving three typical hydraulic problems. While the friction group based on viscous forces is used for calculating the pressure drop or head loss in pipes and open channels, commonly referred to as the Type 1 problem in hydraulic engineering, additional friction groups with similar behaviors are introduced for calculating steady flow discharge as the Type 2 problem and, for estimating hydraulic diameter as the Type 3 problem. Contrary to the viscous friction group, the traditional Darcy–Weisbach friction factor demonstrates a negative correlation with the Reynolds number. This results in curves that slope downward from small to large Reynolds numbers on the well-known Moody chart. In contrast, the friction group used here, based on viscous forces, establishes a more appropriate relationship. In this case, the friction and Reynolds number are positively correlated, meaning that both increase or decrease simultaneously. Here, rearranged diagrams for all three mentioned problems show similar behaviors. This paper compares the Moody diagram with the diagram for the viscous force friction group. The turbulent parts of both diagrams are based on the Colebrook equation, with the newly reformulated version using the viscous force friction group. As the Colebrook equation is implicit with respect to friction, requiring an iterative solution, an explicit solution using the Lambert W-function for the reformulated version is offered. Examples are provided for both pipes and open channel flow.

Multicellularity and increasing Reynolds number impact on the evolutionary shift in flash-induced ciliary response in Volvocales

BackgroundVolvocales in green algae have evolved by multicellularity of Chlamydomonas-like unicellular ancestor. Those with various cell numbers exist, such as unicellular Chlamydomonas, four-celled Tetrabaena, and Volvox species with different cell numbers (~1,000, ~5,000, and ~10,000). Each cell of these organisms shares two cilia and an eyespot, which are used for swimming and photosensing. They are all freshwater microalgae but inhabit different fluid environments: unicellular species live in low Reynolds-number (Re) environments where viscous forces dominate, whereas multicellular species live in relatively higher Re where inertial forces become non-negligible. Despite significant changes in the physical environment, during the evolution of multicellularity, they maintained photobehaviors (i.e., photoshock and phototactic responses), which allows them to survive under changing light conditions.ResultsIn this study, we utilized high-speed imaging to observe flash-induced changes in the ciliary beating manner of 27 Volvocales strains. We classified flash-induced ciliary responses in Volvocales into four patterns: “1: temporal waveform conversion”, “2: no obvious response”, “3: pause in ciliary beating”, and “4: temporal changes in ciliary beating directions”. We found that which species exhibit which pattern depends on Re, which is associated with the individual size of each species rather than phylogenetic relationships.ConclusionsThese results suggest that only organisms that acquired different patterns of ciliary responses survived the evolutionary transition to multicellularity with a greater number of cells while maintaining photobehaviors. This study highlights the significance of the Re as a selection pressure in evolution and offers insights for designing propulsion systems in biomimetic micromachines.

A numerical investigation to assess changes to displacement front and by-passed zones employing kinetic interface-sensitive tracer

An important aspect in groundwater remediation is to understand changes of multiphase fluid front morphology and stagnant regions on macro scale. However, the prediction of those changes during two-phase flow remains a challenging task due to the interplay of various physical factors. Recent laboratory experiments have demonstrated tracers' ability to predict deformation in the front of a two-phase flow system by utilizing a new reactive tracer known as, the kinetic interface sensitive tracer (KIS). This research employs a reactive transport model coupled with a macro-scale two-phase flow model to numerically analyse how viscosity ratio, capillary number, and heterogeneities on the tracer's signal and its impact the frontal deformation. One homogeneous and two heterogeneous types of porous media are considered. The background porous medium is a fine-grained, low-permeability medium, with a coarser, high-permeability lenses, generating heterogeneous material properties. The high-permeability lenses account for 25 % of the total model area and are arranged in either periodic or random patterns. The findings are evaluated using four parameters (effective front length, swept area, front roughness, and transition zone length). The flow patterns dominating the shape of the front are characterized by the viscous and capillary forces i.e. capillary number and the viscosity ratio between the two fluids. The results show that changes in flow regimes can be quantified using effective front length, thus employing the effective front length the viscous fingering regions can be quantified. Furthermore, front roughness and transition zone length are extracted and their relevance to the by-passed zones is presented. The slope of the reactive KIS tracer breakthrough curve, plotted on a phase diagram, can also be used to predict the existence of the by-passed zones for a low viscosity ratio. Finally, changes in front roughness and transition zone length induced by the inclusions are correlated to the slope of the KIS tracer BTC. The findings of this study can contribute to a better understanding of the impact of different flow regimes on the KIS tracer breakthrough signals and the linkages between the tracer signals and the front sizes.

Force-Field based assisted control for upper-limb rehabilitation robots

Robot-assisted training with an assist-as-needed (AAN) control strategy has been used in clinical investigations to effectively enhance the subject’s active effort and promote the rehabilitation of individuals with upper-limb motor impairment. In this paper, a force field-based AAN control scheme is proposed for robot-assisted upper limb rehabilitation training and then implemented in a robot-assisted rehabilitation training system (RaRTS). A spatial varying assistance force field is constructed around the predetermined trajectory in this scheme, and then a varying force field coefficient based on the subject’s motor performance is adopted to deliver the AAN features with temporal freedom. The normal force field, tangential force field, and viscous force field are the three components of the constructed spatial varying assistance force field. Furthermore, the proposed scheme contains three training modes that are switched according to the subject’s trajectory tracking error. Finally, task-oriented continuous training experiments with different force field factors are conducted on able-bodied subjects to evaluate and validate the performance and feasibility of the proposed scheme. Preliminary experimental results and statistics analysis suggest that the subjects were able to keep much closer to the predetermined trajectory through an appropriate selection of force-field assistance factors. Furthermore, the robot would apply an assistance force as needed as the motor performance deteriorate, which could prevent the subject from losing confidence due to poor performance.

Numerical and experimental investigation of the effect of interstitial liquid viscosity on the collapse of wet granular columns

The collapse of wet granular columns with high- and low-viscosity interstitial liquid is investigated through experiments and numerical simulations. By incorporating both capillary and viscous force models of interstitial liquid in the Discrete Element Method (DEM), simulations have been conducted and reproduced consistent collapse processes with the experiment. The influence of water content, contact angle, particle diameter, liquid surface tension, and viscosity is explored over a large parameter space using DEM. For wet granular columns with low-viscosity interstitial liquid of water, the final profile of the collapsed column can be predicted by Bond number (Bo), a ratio of particle gravity to capillary force. For wet granular columns where the inertial effect dominates and both capillary and viscous forces are significant, dimensional analysis is employed to characterize the collapse, indicating that the collapsed profile can be predicted by Bo and Galileo number (Ga). Using water and silicone oils with different viscosities as interstitial liquids, simulations show that the collapsed profile depends on Bo with a low capillary number (Ca ∼ 10−3), Bo and Ga when Ca is intermediate (Ca ∼ 10−1). When Ca is high (Ca > 100), the final profile is solely controlled by Bo and a rolling-collapsed regime is observed.

Effect of SDS Solutions on the Jamin Effect in a Capillary Tube with a Contracted Throat.

With the continuous exploitation of petroleum resources, the distribution and displacement of residual oils have become key issues in enhancing oil recovery. In a reservoir, there are various forms of residual oils caused by the capillary force, viscous force, and some other hydrodynamic effects, which lead to the Jamin effect, and they restrict the oil displacement process. In this study, the morphologies of oil droplets in a capillary tube laden with water and sodium dodecyl sulfate (SDS) solutions are experimentally investigated. The pinning behavior of the oil droplet is observed in the waterflood with a lower velocity, while depinning and rupturing behaviors occur at a higher velocity. Hereto, we build a mechanics model to analyze the evolution of the Jamin effect in a capillary tube with varying cross sections. Using this theoretical model, we obtain the two critical velocities for the depinning and rupture of the oil droplet, which agree with the experimental results. Moreover, we find that oil droplets can more easily pass through the entire capillary tube in SDS solutions compared with water. The time required for oil droplets to pass through the pore throat becomes shorter with the increase of SDS concentration. Therefore, a theoretical model is established to determine the total pressure difference and the minimum applied pressure difference. These findings are beneficial to obtain a deep insight into the detailed oil displacement and achieve a higher oil recovery rate.

Pinch-off of a regular bubble during the impact of droplets on a liquid pool

A droplet impacting a liquid pool can result in the pinch-off of a regular bubble. In this study, the cavity deformation and regular bubble pinch-off after droplets impacting a liquid pool were experimentally investigated. The results indicate that the phenomenon of regular bubble pinch-off results from the combined effects of cavity expansion and capillary wave propagation. The inertial force, viscous force, and droplet diameter are all crucial to the cavity evolution and the process of regular bubble pinch-off. The cavity depth increases with the droplet's inertial force but does not change with the droplet's viscous force. As the droplet's inertial force increases, the diameter of the regular bubble first increases and then decreases. The diameter of the regular bubble at We = 165 is almost four times that at We = 193. In addition, the peak size of the regular bubble decreases as the liquid viscosity increases, but increases as the droplet diameter increases. These variations in the regular bubble size are explained using a theoretical analysis. Finally, the effects of the inertial and viscous forces on the thresholds between no-bubble and regular-bubble pinch-off regimes are studied. As the Ohnesorge number increases from 1.37 × 10−2 to 2.03 × 10−2, the upper and lower critical Weber numbers for the occurrence of the regular bubble pinch-off can increase by 30 and 25, respectively. The theoretical boundaries of regular bubble pinch-off agree well with the boundaries observed in the experiments.

Irreversibility and response functions in the turbulent energy cascade

Abstract The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a scenario dubbed “direct energy cascade”. Here, we aim at characterizing the non-equilibrium properties of turbulent cascades in a shell model of turbulence by studying an asymmetric time-correlation function and the relaxation behavior of an energy perturbation, measured at scales smaller or larger than the perturbed one. We shall contrast the behavior of these two observables in both non-equilibrium (forced and dissipated) and equilibrium (inviscid and unforced) cases. Finally, we shall show that equilibrium and non-equilibrium physics coexist in the same system, namely at scales larger and smaller, respectively, of the forcing scale.

Aerodynamic Characterization of a Hypersonic Projectile Using Acceleration-Based Measurements and Numerical Methods

Armor-piercing fin-stabilized projectiles stand out by their exceptionally high slenderness ratios and ground-level flight at super- and hypersonic speeds. As space constraints limit the integration of measurement equipment into such slender test models, nonintrusive measurement techniques become favorable. The present analysis demonstrates a renewed approach to the free-flight technique, which sets models into unconstrained flight through the test section. It enabled the evaluation of the quasi-steady drag, lift, and pitching moment characteristics, and, to some extent, also the dynamic pitch damping characteristics. An alternative to the free-flight technique is the free-oscillation technique, which limits the motion to a rotation around the center of gravity. The free-oscillation technique allowed a higher-fidelity analysis of the static and dynamic pitching moments. Both methods were based on the analysis of the accelerations derived from trajectory tracking. This acceleration-based approach enabled the evaluation of the highly nonlinear characteristics. The high slenderness of the investigated projectile leads to a significant contribution of the viscous forces to the overall drag. These viscous forces are sensitive to the laminar-turbulent boundary-layer state, as well as the thermal boundary conditions. The application of a high-resolution schlieren system enabled the assessment of the local laminar-turbulent boundary-layer state, while the use of low- and high-enthalpy testing facilities enabled the assessment of the aerothermal influence. Steady-state Reynolds-averaged Navier–Stokes simulations, which included laminar-turbulent transition modeling, were employed to replicate the results of the experimental efforts.

Translations of multiple interacting bubbles in one-dimensional system

Abstract The pulsations and translations of N cavitation bubbles obey combined ordinary differential equations on one-dimensional chain by analyzing the pressures near the cavitation bubbles, and the translations of the cavitation bubbles are discussed. The results indicate that the cavitation bubbles with the same ambient radii at both ends move symmetrically towards or away from the middle cavitation bubble, and the secondary Bjerknes forces on the cavitation bubbles at both ends are equal in magnitude and opposite in direction and the secondary Bjerknes force on the middle cavitation bubble is zero. In addition, dynamic balance can be maintained between bubbles due to the viscous drag force, and the secondary Bjerknes forces on the cavitation bubbles at both ends are equal in magnitude and opposite in direction, and the secondary Bjerknes force on the middle cavitation bubble is almost zero. This is of immediate consequence for understanding cavitation structure formation processes in an acoustic field.