Secondary Motion Research Articles

Sensitivity analysis of an inertial calibration method: Influence of leg position on 3D knee kinematics

BackgroundInertial systems are increasingly used to analyze human motion, especially for gait analyses and in clinical settings. Calibration methods for these systems are designed for ease of implementation, and previous studies have shown that they can provide accurate knee kinematics in the sagittal plane. However, the reason of their lack of accuracy in the other planes (i.e., transverse and frontal) remain unknown. Research questionThis study aimed to evaluate the sensitivity of one posture of a double-pose calibration method to analyse 3D knee kinematics during gait with two magnetic inertial measurement units (MIMU). This method consists of a standing posture and a posture with the leg stretched forward in the sagittal plane, which together define the sagittal plane. Our hypothesis was that a change in the definition of the sagittal plane during the calibration process was likely to affect the assessment of knee kinematics in the frontal and transverse planes. MethodsTen healthy participants wearing the KneeKG system and two MIMU completed the calibration process in five different leg positions (0°, 3°, 5°, 10° or 15° from the sagittal plane) for the second calibration posture. After static calibration, the participants walked on an instrumented treadmill at a speed of 1.1 m/s and 3D knee kinematics were calculated using the five different calibration conditions. ResultsMean absolute difference (MAD) between the swing-phase peak value of the curve corresponding to the leg in the sagittal plane (0° shift from this plane) when performing the second calibration posture and each of the other curves was 0.20–0.46° for knee flexion, 1.67–2.90° for adduction, and 0.72–1.46° for external rotation. MAD of the swing-phase peak value in the frontal plane was correlated (R2=0.81) with the angulation of the femur in the sagittal plane during calibration. SignificanceAn angular shift from the sagittal plane when performing a double-pose calibration method induces a minimal influence on the knee flexion/extension but larger influences on secondary knee motions.

Anomalous Water Penetration in Al3+ Dissolution.

The physicochemical characterization of trivalent ions is limited due to a lack of accurate force fields. By leveraging the latest machine learning force field to model aqueous AlCl3, we discover that upon dissolution of Al3+, water molecules beyond the second hydration shell are involved in the hydration process. A combination of scissoring of coordinating water is followed by synchronized secondary motion of water in the second solvation shell due to hydrogen bonding. Consequently, the water beyond the second solvation penetrates through the second solvation shell and coordinates to the Al3+. Our study reveals a novel microscopic understanding of solvation dynamics for the trivalent ion.

Secondary predicates and motion events: the rise of complex predicates in Vedic Sanskrit

Secondary predicates and motion events: the rise of complex predicates in Vedic Sanskrit

Sensitized Reynolds stress modeling of a bubbly jet emerging into a water cross-flow

The present work is concerned with the computational study of an air–water mixture stream emanating from a nozzle submerged in a water cross-flow inside a rectangular open channel to form a curved, intensively dispersed, bubbly jet. The work focuses on evaluating the predictive performance of an eddy-resolving turbulence model applied to the described case of a multiphase gas-liquid flow system characterized by a variety of closely coupled phenomena, including: turbulence anisotropy-induced secondary motion, free surface flow, bubbly jet propagation, and the varying interaction dynamics of the carrier water flow with the air bubble dispersion. Correspondingly, an appropriately extended differential near-wall Reynolds stress model, which describes the dynamics of unresolved subscale structures within the Sensitized Reynolds-Averaged Navier–Stokes (RANS) computational framework, is currently used in conjunction with a two-way coupled Euler–Lagrange approach to simulate this gas-water bubbly flow, with the operating and boundary conditions following the experimental reference of Zhang and Zhu (2013). Accordingly, the conditions at the free surface are adequately derived for all components of the residual turbulence stress tensor and the corresponding length scale determining variable. It is shown that the statistics of the bubble phase can be accurately captured, and the proper-orthogonal-decomposition analysis of the dynamic properties of the flow reveals at least two large-scale transient effects associated with the bubbly jet. Furthermore, in the preliminary part of this work it is shown that the currently applied turbulence model can be successfully used to correctly capture the effects of Reynolds stress anisotropy in the single-phase open-channel configuration, representing the incoming flow field of the main two-phase flow configuration.

Study on secondary motions in supersonic boundary layers of a bent pipe

The present study employed direct numerical simulation to investigate the supersonic flow of Mach 3 in a bent pipe with a curvature of 0.0825, elucidating the dynamic mechanism of secondary motions within the turbulent boundary layer. The findings indicate that the compressible flow, affected by the wall curvature, is differentiated into several motion patterns as the bending angle increases: a portion of the outer fluid close to the wall, driven by the circumferential pressure gradient, moves inward through the lateral wall, causing an increase in the mass rate toward the lateral boundary layer and promoting the circumferential transport of energy and vorticity; other outer fluids at the start of the bent section, due to the centrifugal force, approach the wall to form a thinner boundary layer downstream; meanwhile, the fluid near the inner wall experiences the expansion, followed by the flow separation and reattachment at a bending angle of 14.6° and 22.0°, respectively, which induce a shear layer that develops from the inner end point toward the mainstream center, gradually reshaping the high-speed flow area within the pipe cross section into a U-shape, and enhancing the vorticity and temperature field of the inner region. Additionally, this study reveals a remarkable phenomenon that the separated flow in a localized inner region forms a rotating field, inducing vortices distinct from the mainstream Dean vortices in the low-speed flow region enclosed by the shear layer.

Study on the influence of labyrinth seal structure on the performance of shrouded stator cascades with inter-stage cavities

Numerical simulations of a shrouded stator cascade with an inter-stage cavity were conducted using validated numerical methods to investigate the impact of different labyrinth seal structures and positions on the aerodynamic performance of the stator cascade. The study discussed the development trends of secondary flow motion and corner separation within the cascade under different labyrinth seal structures, evaluated the stator performance using total pressure loss coefficient and entropy-based loss coefficient, and revealed the interaction between cavity leakage flow and mainstream flow. The results indicate that individually changing the labyrinth seal structure or position has a negligible impact on stator performance, but simultaneously altering both the structure and position of the labyrinth seal can effectively reduce stator losses. The structure case 1-position case 2 labyrinth seal structure can reduce total pressure loss by 6.25%, while structure case 4-position case 4 reduces entropy increase loss coefficient by 7.67%. Additionally, it was found that changing the labyrinth seal structure and position can increase the circumferential velocity and momentum of cavity leakage flow at the cavity outlet, enhance the resistance of cavity leakage flow to circumferential secondary flow within the stator passage, and reduce stator losses. Altering the structure and position of the labyrinth seal effectively reduces the cavity leakage vortex at the leading edge of the cascade during the mixing process of cavity leakage flow with the mainstream, causing the passage vortex to move rearward axially.

Stability Analysis of the Secondary Motion of a Textured Piston

Piston–cylinder pairs are very common in industrial mechanisms. While a piston is primarily designed for axial reciprocating motion, the occurrence of secondary motions—lateral and rotational—due to the small clearance between the piston and the cylinder may lead to frictional contact, energy loss, wear and an increase in unwanted leakage. This study focuses on mitigating the secondary motion of a ringless piston. The influence of a Rayleigh step bearing and partial surface texturing with numerous micro-dimples on the dynamic stability of the secondary motion is studied. A linear model was used to obtain the trajectory of the secondary motion and Floquet theory was applied to analyze the stability and draw stability maps. The influence of various texturing and step parameters, including the dimple area density and aspect ratio for partial texturing, as well as the length and depth of treatment for both partial texturing and step profiles, on the stability of the secondary motion was examined. The normalization method is presented, enabling the expansion of the results for various operating conditions and geometries. Conclusions and guidelines regarding the optimal parameters, in terms of a wider stability range and higher decay rate, are formulated.

Unveiling Turbulent Flow Dynamics in Blind-Tee Pipelines: Enhancing Fluid Mixing in Subsea Pipeline Systems

Blind tees, as important junctions, are widely used in offshore oil and gas transportation systems to improve mixing flow conditions and measurement accuracies in curved pipes. Despite the significance of blind tees, their unsteady flow characteristics and mixing mechanisms in turbulent flow regimes are not clearly established. Therefore, in this study, Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations, coupled with Explicit Algebraic Reynolds Stress Model (EARSM), are employed to explore the complex turbulent flow characteristics within blind-tee pipes. Firstly, the statistical flow features are investigated based on the time-averaged results, and the swirl dissipation analysis reveals an intense dissipative process occurring within blind tees, surpassing conventional elbows in swirling intensity. Then, the instantaneous flow characteristics are investigated through time and frequency domain analysis, uncovering the oscillatory patterns and elucidating the mechanisms behind unsteady secondary flow motions. In a 2D-length blind tee, a nondimensional dominant frequency of oscillation (Stbt = 0.0361) is identified, highlighting the significant correlation between dominant frequencies inside and downstream of the plugged section, which emphasizes the critical role of the plugged structure in these unsteady motions. Finally, a power spectra analysis is conducted to explore the influence of blind-tee structures, indicating that the blind-tee length of lbt = 2D enhances the flow-mixing conditions by amplifying the oscillation intensities of secondary flow motions.

Enhancing thermal-hydraulic performance in curved pipes through optimal radial fin placement: A numerical investigation

Increasing heat transfer in straight pipes, particularly in applications like heat exchangers, can be achieved by incorporating fins into the pipe wall. However, in curved pipes, the presence of more intricate flows resulting from centrifugal forces can alter this effect. The current study investigates how both the height and angular position of radial fins simultaneously influence the flow patterns within curved pipes. Adjusting the placement of radial fins is identified as a cost-effective and strategic approach to improve both the hydrodynamic and thermal efficiency in curved pipe systems. The numerical analysis focuses on studying laminar, incompressible flow in curved tubes with radial fins. The mass, momentum, and energy conservation equations in toroidal coordinates were discretized with the second-order finite difference method on a staggered grid, followed by their solution through the projection algorithm. The results indicate that adapting the angular position of the fins improves the thermal-hydraulic performance by 51.8%, 48.4%, 36.3%, and 20.6% for one to four fins, respectively. These changes are closely related to the behavior of the secondary flows. Furthermore, altering the height of the fins reveals that for three fins within the tube, the most optimal fin height is half of the tube radius. In other cases, a fin height equal to 0.7 multiplied by the tube radius provides the highest performance. From the numerical results, it is found that the primary factor affecting the heat transfer rate in curved pipes is the strength of secondary motions, while the generation of friction is influenced only by the axial velocity.

Anisotropic turbulence modeling for natural channel flow: A numerical approach with finite element method

In this study, we propose a numerical model aimed at improving the understanding and prediction of flow velocities in natural channels. This model specifically focuses on the challenges presented by anisotropic turbulence and bottom roughness. By incorporating the mixing length concept into an algebraic turbulence model and employing the finite element method with Streamline-Upwind/Petrov–Galerkin (SUPG) stabilization, our model seeks to refine the simulation of axial velocity distribution and secondary motions. Validation was achieved through Acoustic Doppler Current Profiler (ADCP) measurements in three sections of the Canal do Rodeador, showing our model’s predictions of discharge and average velocity to have a deviation of approximately 9.34% from experimental data. The results underline the significance of secondary currents and turbulence anisotropy in shaping channel flow behaviors, offering new insights into the interactions between flow characteristics and channel bed features. This model stands out as a robust tool for hydraulic structure design and hydrokinetic potential evaluation, providing a non-intrusive, cost-effective alternative to traditional methods.

Tribo-dynamic modeling method and application to three-dimensional flexible PRL system

Research on the tribo-dynamics of the piston-cylinder liner (PCL) and piston ring-cylinder liner (PRCL) is vital due to their role in generating over 50 % of total engine friction loss and the impact on carbon emissions. Traditional studies, hindered by the structural and functional differences between pistons and rings, required separate simulation models, often overlooking crucial coupling characteristics. A unified tribo-dynamics modeling method for the piston-ring-liner (PRL) system is proposed in this paper, integrating the ring pack and piston into one multi-body system. This article models with global coordinates, unifying the form of governing, film thickness, and load equations of discontinuous lubrication domains for more efficient dynamics-lubrication coupling. The described method is applied to a marine engine, and the new tribology characteristics discovered after calculations are exhibited. It shows how piston deformation impacts ring tribology, indicating that increased profile height reduces the squeezing effect by allowing more ring movement. Additionally, ring assembly position significantly affects tribology parameters' circumferential distribution. Installing the ring with the end gap facing the piston pin side should be avoided, as it maximizes the negative impact of elastic force and secondary motion, deteriorating lubrication.

Secondary motions in turbulent ribbed channel flows

Secondary motions in turbulent ribbed channel flows

Experimental study on the combustion and flame propagation characteristics of CH4/O2/N2 premixed turbulent jets

The combustion and flame propagation characteristics of CH4/O2/N2 premixed turbulent jets are investigated experimentally in a constant volume chamber (CVC) under different initial temperature (Tini, 300/400/500/600K) and oxygen fractions (γ, 0.4/0.6/0.8/1.0) conditions using High-speed camera and schlieren system. Four types of jet tip velocity were found: primary vortex motion at the jet top (M-type 1), secondary vortex motion (M-type 2), weaker positive and negative feedback between the flame and the flow field (M-type 3), and stronger positive and negative feedback (N-type 4). With the decrease of γ, the jet acceleration and deceleration mechanism is changed from the top vortex motion mechanism in M-type 1 and M-type 2 to the positive and negative feedback mechanism in M-type 3 and N-type 4. The interaction between the pulsating flow field and the heat release from the pre-chamber transitions to the flow field momentum dissipation. For M-type 1 and M-type 2, there is no significant difference in overpressure dynamics. The N-type 4 exhibits lower peak pressure and pressure rise rates. Moreover, the flame mode was predicted under higher Pini (10 bar ≤ Pini) and lower γ (γ ≤ 0.4) based on empirical equations established by the self-similar analytical model.

Multi‐scale edge aggregation mesh‐graph‐network for character secondary motion

AbstractAs an enhancement to skinning‐based animations, light‐weight secondary motion method for 3D characters are widely demanded in many application scenarios. To address the dependence of data‐driven methods on ground truth data, we propose a self‐supervised training strategy that is free of ground truth data for the first time in this domain. Specifically, we construct a self‐supervised training framework by modeling the implicit integration problem with steps as an optimization problem based on physical energy terms. Furthermore, we introduce a multi‐scale edge aggregation mesh‐graph block (MSEA‐MG Block), which significantly enhances the network performance. This enables our model to make vivid predictions of secondary motion for 3D characters with arbitrary structures. Empirical experiments indicate that our method, without requiring ground truth data for model training, achieves comparable or even superior performance quantitatively and qualitatively compared to state‐of‐the‐art data‐driven approaches in the field.

Magnetic field impact on ferronanofluid laminar flow

A comprehensive understanding of the magnetic field interaction with the flow of ferronanofluids is essential to determine the heat transfer effect and the potential for use in industrial applications. The purpose of this work is to determine the effects of magnetic field orientation and intensity, as well as inertia forces, on heat transfer in the laminar flow of a ferronanofluid. The experiment involved the use of five permanent magnets positioned both below and above the flowing magnetite-based ferronanofluid. The analysis of the effect on heat transfer is carried out using the similarity numbers, Reynolds number (ratio of inertia and viscous forces), magnetic number (ratio of magnetic and inertia forces) and product of the two (ratio of magnetic and viscous forces).The findings indicate that the orientation of the magnetic field relative to temperature gradient-induced secondary motions plays a crucial role in either enhancing or inhibiting heat transfer. The magnet positioned below the flow leads to improved heat transfer, while placement above hinders it. To determine the magnetic field effect on heat transfer, the ratio of magnetic to viscous force introduced as MnRe is used. Taking the 5 % Nusselt number change as the threshold, the critical value for the orientation of magnet above the tube is MnRe = 24,000, while for the configuration with the magnet below, MnRe = 32,000 for Re = 109 and MnRe = 88,000 for Re = 150 and 163. The magnetic field effect is local and diminishes as the fluid flows, ultimately causing the heat transfer parameters to revert to their reference state. However, an increase in the ratio of inertia and viscosity forces enables the magnetic field interaction effect to propagate over a longer distance.

Fundamental insights on turbulence characterization, vortex motion and ignition mechanism of sub/supersonic turbulent jet flames

This paper presents turbulence characterization and vortex behavior measurements of sub/supersonic jet flames subjected to extreme levels of turbulence. Specifically, sub/supersonic CH4/O2/N2 premixed jet flames were studied under calculated Reynolds (Re) number and measured jet tip velocity (Vtip) of around 20,000 and 100 m/s or greater, respectively. The vortex motion on the flame surface was measured by Schlieren image velocimetry (SIV), and ignition mechanisms of sub/supersonic jets are discussed by analyzing vortex motion and free radical reactions, respectively. Results show that the maximum vortex motion is maintained in the jet top edge region. In contrast, the velocity of vortex motion in the middle of the jet, i.e., near the side of the jet orifice, is reduced by a factor of 4–5, which visually shows a “mild” velocity gradient on the jet surface. The direction turning points of X/D = 7.25, X/D = 6.06, X/D = 6.06 and X/D = 3.40 were found in the flow direction (Y-direction) for four typical cases of supersonic jets with top primary swirling motion, supersonic jets with top secondary swirling motion, supersonic jets with weak top swirling motion and subsonic jets without top flame vortex motion. It is speculated that the ignition location is strongly correlated with the direction turning point of the vortex movement along the Y-direction. The vortex propagating along the flow direction disperses many small-scale vortices moving in the X-direction, the X-direction being perpendicular to the flow direction. Moreover, the ignition mechanisms of sub/supersonic jet were explored separately.

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate or the flow in a Taylor–Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg ( $Wi$ ) number. However, the combined effects of fluid elasticity, shear thinning and finite inertia (as quantified by the Reynolds number $Re$ ) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone–plate geometries, we experimentally explore the entire $Wi$ – $Re$ phase space for a series of nonlinear viscoelastic fluids (with the dependence on shear rate $\dot{\gamma}$ quantified using a shear-thinning parameter $\beta _P(\dot {\gamma })$ ). We tune $\beta _P(\dot {\gamma })$ by varying the dissolved polymer concentration in solution. This progressively reduces shear thinning but leads to finite inertial effects before the onset of elastic instability, and thus naturally results in elasto-inertial coupling. Time-resolved rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry, and document the combined effects of varying $Wi, Re$ and $\beta _P(\dot {\gamma })$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel & McKinley (Phys. Rev. Lett., vol. 77, no. 12, 1996, p. 2459) for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, and thus bridges the gap between purely elastic and elasto-inertial curved streamline instabilities.

Lateral Ankle Joint Injuries in Indoor and Court Sports: A Systematic Video Analysis of 445 Nonconsecutive Case Series

Background: Lateral ankle sprains are one of the most common injuries in indoor and court sports. Self-reports and case studies have indicated that these injuries occur via both contact and noncontact injury mechanisms typically because of excessive inversion in combination with plantarflexion and adduction of the foot. Video-based documentation of the injury mechanism exists, but the number of cases reported in the literature is limited. Purpose: To retrieve and systematically analyze a large number of video-recorded lateral ankle injuries from indoor and court sports, as well as describe the injury mechanism, injury motion, and injury pattern across different sports. Study Design: Cross-sectional study; Level of evidence, 3. Methods: A total of 445 unique video-recorded lateral ankle sprain injuries were retrieved from indoor and court sports of broadcasted levels of competition. The videos were independently analyzed by 2 different reviewers. Outcomes included classification of the injury mechanism according to the International Olympic Committee consensus guidelines, primary and secondary motions of ankle joint distortion, and documentation of the fixation point (fulcrum) around which the foot rotates. Results: Overall, 298 (67%) injuries were direct contact, 113 (25%) were noncontact, and 32 (7%) were indirect contact incidents. Direct contact injuries were especially prevalent in basketball (76%), handball (80%), and volleyball (85%), while noncontact injuries dominated in tennis and badminton (96% vs 95% across both). Inversion (65%) and internal rotation (33%) were the primary distortion motions, with the lateral forefoot (53%) and lateral midfoot (40%) serving as the main fulcrums. Landing on another player's foot was the leading cause of injury (n = 246; 55%), primarily characterized by inversion (79%) around a midfoot fulcrum (54%). The noncontact and indirect landings on floor (n = 144; 33%) were primarily characterized by a distortion around a forefoot fulcrum (69%). Conclusion: Two of 3 ankle sprains from online video platforms were direct contact injuries, with most involving landing on another player's foot. The distortion motion seems to be related to the injury mechanism and the fixation point between the foot and the floor. The injury mechanisms varied greatly between sports, and future studies should clearly differentiate and investigate the specific injury mechanisms.

Stability of penetrative convective currents in local thermal non-equilibrium

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

CFD-based investigation of turbulent flow behavior in 90-deg pipe bends

This work investigated the influence of bend curvature on the parameters of turbulent flow through a 90° pipe bend using the numerical CFD method, implemented in ANSYS Fluent. The numerical predictions were validated to be in good agreement with existing experimental measurements. The turbulence of the secondary motion was found to be generally stronger at the outer end of the pipe bend, with the most adverse effect recorded at about 45° along the bend. It was also observed that the RMS velocity is larger near the wall, especially at the outer wall region, and it is highest at 45° due to an increase in the circulation of dean vortices, indicating a turbulence generation. In addition, the RMS velocity increases downstream due to an additional mean strain resulting from the creation of secondary flow as the flow travels through the bend. Furthermore, larger static pressure and turbulent viscosity were observed at the outer wall due to the flow deceleration and swirling. Therefore, it can be established that the bend curvature affects the stability of the flow field inside a pipe bend.