Critical Angle Research Articles

Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media

We theoretically investigate the scaling behavior of the localization length for s-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro–Loginov formula of differentiation, we accurately compute the localization length ξ of s waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter σ2 and the disorder correlation length lc. Away from the critical angle, ξ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber k, kξ depends on the single parameter klcσ2, satisfying a universal equation kξ≈1.3717klcσ2−1/3 across the entire range of parameter values. Additionally, we find that ξ scales as λ4/3 for the entire range of the wavelength λ, regardless of the values of σ2 and lc. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence.

The Critical Shoulder Angle: A Significant Radiological Measure in Rotator Cuff vs. Glenohumeral Osteoarthritis in Chilean Patients-A Descriptive Cross-Sectional Study.

Background: Shoulder pain is one of the most important musculoskeletal conditions affecting the upper extremities. Glenohumeral osteoarthritis (GHOA) and rotator cuff injuries (RCIs) are notable for their high prevalence. The critical shoulder angle (CSA) is a significant radiological measure for determining the diagnosis and progression of patients with these conditions. Although there are reports in the international literature about this measure, in our country, guideline values considering these two pathologies are unknown. Objective: Our objective was to assess patients diagnosed with GHOA and RCI using an AP X-ray view and the CSA. Methods: To conduct this, we identified differences between sexes and age categories. Fifty-nine adult patients with GHOA and RCI were included. CSA grades varied depending on the age category and type of injury evaluated. Results: Significant differences between the age ranges of 40 and 54 (p = 0.05), 55-69 (p = 0.001), and 70-84 (p = 0.017) were observed. Conclusions: Patients with RCI tended to be younger and have a higher CSA compared to those with GHOA. It is important to have more normative values and to continue monitoring the critical shoulder angle in these patients.

Model-guided navigation of magnetic soft guidewire for safe endovascular surgery

The emergent magnetic soft guidewires (MSGs) that can be remotely navigated by magnetic fields hold great promise in minimally invasive endovascular surgery. However, existing models of MSGs have been limited in practical applications, largely due to insufficient consideration of contacts within actual endovascular settings. In this work, we present a theoretical model incorporating the magneto-mechanical behavior of MSGs with these critical contacts, allowing for a detailed evaluation of their navigation capability in various vascular configurations. Specifically, we categorize blood vessels into two main types: curved vessels and bifurcated vessels and identify a critical contact angle between the MSG tip and the vessel wall, beyond which the vascular damage may occur. By applying the principles of hard-magnetic elastica to account for the large deflection of MSGs, we develop a numerical framework that employs polynomial approximations and an energy minimization strategy. Through parametric analysis of different vessel types, we propose a method for adjusting magnetic fields for the safe navigation of MSGs through them. Our theoretical predictions have been substantiated by finite element modeling and experimental validation. The results of this paper offer a solid foundation for establishing practical guidelines for remote MSG navigation with minimal risk of vascular damage.

The influence of geometric boundary features on droplet wetting and directional motion

Structured surfaces with micro and nanostructures have shown great potential for a wide range of applications, such as self-cleaning, deicing, and drag reduction. Previous research has extensively explored the interactions between droplets and microstructures, particularly in terms of Cassie-Baxter and Wenzel states. However, there is still a notable gap in systematically studying the interactions between droplets and various types of geometrical boundary features. In this study, we employed molecular dynamics simulations to investigate how different geometric boundary features affect the wetting behavior and motion of water droplets. Our detailed analysis led to the derivation of a formula to calculate the critical contact angle for a droplet interacting with any geometric boundary feature from a mechanical perspective. Based on these findings, we successfully controlled motion direction of water droplets along a separation membrane. We observed that due to the influence of geometric boundary features at the holes, droplets exhibited unidirectional motion on the separation membrane. By considering the influence of geometric boundary features, our research provides valuable insights for preventing wetting transition, enhancing the storage of lubricating oil in grooves, facilitating efficient oil–water separation, and regulating fluid flow in microchannels.

Deformation of solid earth by surface pressure: equivalence between Ben-Menahem and Singh’s formula and Sorrells’ formula

SUMMARY Atmospheric pressure changes on Earth’s surface can deform the solid Earth. Sorrells derived analytical formulae for displacement in a homogeneous, elastic half-space, generated by a moving surface pressure source with speed $c$. Ben-Menahem and Singh derived formulae when an atmospheric P wave impinges on Earth’s surface. For a P wave with an incident angle close to the grazing angle, which essentially meant a slow apparent velocity $c_a$ in comparison to P- ($\alpha ^{\prime }$) and S-wave velocities ($\beta ^{\prime }$) in the Earth ($c_a \ll \beta ^{\prime } \lt \alpha ^{\prime }$), they showed that their formulae for solid-Earth deformations become identical with Sorrells’ formulae if $c_a$ is replaced by $c$. But this agreement was only for the asymptotic cases ($c_a \ll \beta ^{\prime }$). The first point of this paper is that the agreement of the two solutions extends to non-asymptotic cases, or when $c_a /\beta ^{\prime }$ is not small. The second point is that the angle of incidence in Ben-Menahem and Singh’s problem does not have to be the grazing angle. As long as the incident angle exceeds the critical angle of refraction from the P wave in the atmosphere to the S wave in the solid Earth, the formulae for Ben-Menahem and Singh’s solution become identical to Sorrell’s formulae. The third point is that this solution has two different domains depending on the speed $c$ (or $c_a$) on the surface. When $c/\beta ^{\prime }$ is small, deformations consist of the evanescent waves. When $c$ approaches Rayleigh-wave phase velocity, the driven oscillation in the solid Earth turns into a free oscillation due to resonance and dominates the wavefield. The non-asymptotic analytical solutions may be useful for the initial modelling of seismic deformations by fast-moving sources, such as those generated by shock waves from meteoroids and volcanic eruptions because the condition $c / \beta ^{\prime } \ll 1$ may be violated for such fast-moving sources.

Properties of classical evanescent waves obtained by using the linear independence concept

Normally, the properties of evanescent optical waves are obtained by developing the Fresnel equations that are expressed in the complex numbers field when the incident angle exceeds the critical angle. Instead of using complex numbers, here we use real functions and the mathematical concept of linear independence to obtain all the properties of the evanescent waves.

P‐219: Research on the Direction of Luminance Modulation at Small Angles Based on Micro Lens

The study investigated the variations in luminance of active‐matrix organic light‐emitting diodes (AMOLED) when viewed at small angles, employing different micro lens arrangements. By examining the micro lens array (MLA) structure, we analyzed how luminance behaves at various angles. Concurrently, we explored the alignment of red, green, and blue (R/G/B) pixel apertures with the micro lens placement, aiming to achieve precise luminance modulation for acute viewing angles.Initially, micro lens arrays are crafted by utilizing materials with varying refractive indices above the pixel aperture, ensuring total internal reflection of light at thejunction between materials of high and low refractive indices. This arrangement also alters the emission angle of light. Within this architecture, the critical angle — determined by the disparity in refractive indices — and the variance in the angle at the reflective interface are crucial in influencing light emission reflection.Furthermore, we explored how the spacing of graphic openings with low refractive indices influences the angle of light emission. This spacing affects the reflection angle, as it is not produced by a singular interface but rather by a composite of multiple angles. The size of the pixel apertures and the spacing of these openings cause the point of total internal reflection to vary, altering the deflection angle of light. Thus, the design of pixel openings and the external expansion is crucial to controlling the light emission angle.Lastly, we examined the influence of the reflective interface and the external expansion design on the light output angle. This analysis highlighted the enhancement of light output at narrow angles and provided strategies to minimize luminance fluctuations at such angles, contributing to the development of high‐precision luminance control in AMOLED displays.

Reflected acoustic energy from geological layers during seismic reflection surveys.

Acoustic propagation is significantly impacted by seabed characteristics, which play a large role in propagation modeling. Shallow seabed characteristics comprise a notable area of research due to their impacts on bottom loss, but deep seabed characteristics are often ignored. At low frequencies (several hundred Hertz, particularly below 100 Hz) and at ranges less than that corresponding to the seafloor critical angle, these deep layer characteristics have non-negligible effects. Those effects are explored here using a subset of data from a marine seismic reflection survey, MGL2104, in an environment with a nearly constant ∼2.6 km bathymetry. The source is a 5700 in.3 airgun array and reflections are measured by a 1200 channel, ∼15 km streamer, with both arrays at 12 m depth. The results show that in one-third-octave bands below 100 Hz, a significant fraction of the reflected energy (sometimes >50%) at certain ranges in the water column is attributable to sub-seabed layers, and the seafloor reflections only become the dominant source at ranges where the reflection path approaches a critical angle. The analysis also considers the effects of layer depths on reflected energy, demonstrating that increased depth does not necessarily correlate with decreased energy reflected in the water column.

Arthroscopic Subacromial Balloon Spacer for Massive Rotator Cuff Tears Demonstrates Improved Shoulder Functionality and High Revision-Free Survival Rates at a Minimum 5-Year Follow-Up

To investigate the efficacy of arthroscopic subacromial balloon placement for massive rotator cuff tear (MRCT), assessing patient satisfaction, outcomes, shoulder functionality, pain scores, and revision-free survivorship up to 8 years after the initial surgery. In this retrospective study with prospective data collection, patients with MRCTs undergoing balloon placement from 2014 to 2017 were prospectively enrolled. Their outcomes were analyzed retrospectively over a minimum 5-year follow-up. Demographics, patient satisfaction, reoperations, and complications were documented. Minimal clinically important differences were calculated for 12-Item Short Form Health Survey scores and Constant-Murley score subscores. Pre- and postsurgery measures statistically compared for anatomic and functional evaluations. In a study with 61 participants initially, 10 were lost to follow-up over 3 years. Of the remaining 51, 9 were lost at the latest follow-up. The cohort (42 participants, mean age 63.17 ± 7.66 years) was monitored for 83.98 ± 9.50 months. Seven participants required revisions within 2 years, resulting in an 83.33% revision-free survival rate. Significant improvements were observed from preoperative to latest follow-up: acromiohumeral interval decreased (7.83 to 6.56, P= .004), critical shoulder angle increased (36.10 to 38.24, P= .001), osteoarthritis grade increased (1.45 to 2.81, P= .001), 12-Item Short Form Health Survey physical score improved (27.40 to 37.69, P= .001), and Constant-Murley total scores increased (26.50 to 68.69, P= .001). Minimal clinically important difference for total Constant-Murley scores was 11.78 points. Among those without revisions, satisfaction rates were 11.43% excellent, 57.14% satisfied, and 31.43% dissatisfied. Employing a balloon spacer for MRCTs yielded moderate satisfaction at the 5-year follow-up, with stable revision rates within the first 2 years. Notably, low revision surgery rates, high revision-free survival, and significant shoulder functionality improvements were observed at a minimum 5-year follow-up with arthroscopic subacromial balloon placement in conjunction with biceps tenotomy and subacromial bursectomy for MRCT. Level IV, retrospective study.

Effect of the yaw angle on the riblet performance

Direct numerical simulations are performed to investigate the effect of the yaw angle (α) on the drag-reduction performance by riblets in a turbulent channel flow. The yaw angles of α=0° and 90° correspond to the riblets parallel and perpendicular to the free-stream direction, respectively. It is well known that maximum drag reduction occurs at α=0°, and the drag-reduction performance by riblets is degraded with increasing α. We obtain the critical yaw angle below which drag reduction can be achieved and investigate the corresponding mechanism. From a parametric study, drag reductions are achieved for α<20°. As α increases, the form drag increases more rapidly than the skin-friction drag decreases, resulting in the increase in the total drag. At drag reducing and increasing yaw angles, the mean velocity profiles in wall units shift upward and downward, respectively, and the latter profile suggests that the drag-increasing riblet is similar to a rough surface. With increasing α, the wall-normal and spanwise velocity fluctuations and Reynolds shear stress increase, and stronger near-wall vortices are generated. By applying a scaling analysis to the momentum equation in the riblet-perpendicular direction and the FIK (Fukagata–Iwamoto–Kasagi) identity [Fukagata et al., “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73–L76 (2002); Peet and Sagaut, “Theoretical prediction of turbulent skin friction on geometrically complex surfaces,” Phys. Fluids 21, 105105 (2009); Bannier et al., “Riblet flow model based on an extended FIK identity,” Flow Turbul. Combust. 95, 351–376 (2015)] to the riblet-parallel direction, the total drag is expressed as a linear function of sin2α.

Complications and revisions in metal-backed anatomic total shoulder arthroplasty: a comparative study of revision rates between stemless and stemmed humeral components

BackgroundThe primary objective of this study was to evaluate and compare the incidence of complications and revision surgeries between in two of convertible metal-back glenoid systems in total shoulder arthroplasty (aTSA) groups over a follow-up period of up to five years. MethodsA retrospective analysis included 69 shoulders from 65 patients with primary aTSA. Patients were divided into Group 1 (n=31), receiving convertible cementless stemmed aTSA (Lima SMR) and Group 2 (n=38), receiving humeral head replacement aTSA (Arthrex, Eclipse) both with metal-back glenoid components. Clinical and radiological assessments were conducted at 2, 5, and 10 years postoperatively. Assessments included the following: Constant Score, DASH, SPADI, SSV, Glenohumeral Distance, Critical Shoulder Angle and Lateral Acromion Index. In addition, we compared complications, revision rates and survival rates between groups using Kaplan-Maier curves and Log-Rank-test. ResultsBaseline demographics and preoperative outcome scores showed no significant differences between groups (p≥0.05). The overall revision rate did not significantly differ between groups (Group 1:32% vs. Group 2:24%, p=0.60), nor did the mean time to revision (p=0.27). The mean follow-up was 71±41 months (Group 1: 94±48 months, Group 2: 53±23 months, p<0.001). Kaplan-Meier analysis showed similar mid-term survival probabilities (p=0.94). Revision reasons included rotator cuff insufficiency (n=4 in Group 1, n=2 in Group 2) and glenoid wear/loosening (n=5 in Group 1, n=7 in Group 2). Interestingly, Group 1 demonstrated no occurrence of glenoid metal baseplate or humeral loosening, while complex revisions were more common in the Group 2. At 2 and 5 years, non-revised patients in both groups had similar outcome scores. ConclusionMetal-backed glenoid implants in combination with both stemless and stemmed humeral components in aTSA exhibit comparable revision rates and survival probabilities. Rotator cuff insufficiency and polyethylene wear are the two most common complications leading to revision. To facilitate ongoing monitoring and optimize patient safety, we implemented a modification in the follow-up protocol, transitioning to annual appointments or earlier when necessary. This study underscores the unsolved disadvantages in metal-back components and the importance of a mid- to long-term longitudinal assessment of those patients.

Phase Transition near the Filling Factor ν = 3

A phase transition accompanied by the appearance of a spike in the longitudinal resistance of a two-dimensional electron system has been studied using the electron spin resonance near the filling factor ν = 3 in the ZnO/MgZnO heterojunction. This transition occurs when the tilt angle θ of the magnetic field is increased to some critical value θc. An analysis of the spin resonance amplitude has made it possible to demonstrate the spin nature of this phenomenon. For example, the ground state of the system on both sides of the transition has a nonzero spin polarization, which changes by several times when the phase of the system is changed. Strong spin resonance is observed both at θ < θc and at θ > θc. Surprisingly, the spin resonance at the critical angle θc has been detected in only one phase, which lies in the region of magnetic fields below the critical field Bc corresponding to the spike position in the longitudinal resistance. An increase in the magnetic field to this value leads to a decrease in the resonance amplitude and an increase in the resonance width. In the field region above Bc, the spin resonance disappears completely. Such behavior of the spin resonance is most likely due to the formation of domains with different spin polarizations in the electron system.

The Curriculum in NDT Training Have to Include Basics Information Technology to Accomplish Reliability of Automated NDT Result's

Automation in Non-Destructive Testing (NDT) is a reality of modern manufacturing and quality assurance. Information technology applications are simultaneously developed and applied to different fields of NDT methods. The future of doing reliability checks using automated system is inevitable. The results are important to make a variety of decisions regarding the quality of a product and/or service, hence affecting safety and reliability. Depending on artificial intelligence and quantum device development, various NDT training schemes have to adopt a new curriculum to address the issue of the basic knowledge of information technology and automation in NDT. NDT operators are basically dependent on the end results of software, in which the software developer uses a set of algorithms. These are obtained in three categories; 1) Real time database; 2) Synthetic database and 3) Hybrid or combination of them. The developers should know how the NDT systems run and NDT operators in the other hand know the mechanism of the program, so that appropriate action can be taken, in case there is a missed detection, or a detected indication is not very much detrimental to the reliability of the part (Over sizing or wrongly evaluated). For example, a set of algorithms are used to create the focal laws in a phased array ultrasonic test software in space of 1˚ beam steering. Each has a limit of maximum up to 2nd Critical angle. Operators try to copy the same algorithm and set up to 89˚ refraction angle, which will just create creep wave with unreliable results to detect effective size the reflector. Programming knowledge of the operator can effectively eliminate this type of unreliability. In various Schemes of NDT Syllabus which are in common place to employ and train plus certify operators does not have it; actually, the operators do the scope of work which does includes application of Artificial Intelligence (AI) and Software. With the development of Q coupler (Quantum Computing) system, it is obvious to adopt the upcoming technology into the application of NDT industry. Training needs to update the curriculum accordingly. The current topic has intended to focus on the training gap and to address related kind of unreliability.

Resonant chains in triple-planet systems

The mean motion resonance is the most important mechanism that may dominate the dynamics of a planetary system. In a multi-planetary system consisting of $N planets, the planets may form a resonant chain when the ratios of orbital periods of planets can be expressed as the ratios of small integers $T_1: T_2: :T_N=k_1: k_2: k_N$. Due to the high degree of freedom, the motion in such systems could be complex and difficult to depict. In this paper, we investigate the dynamics and possible formation of the resonant chain in a triple-planet system. We defined the appropriate Hamiltonian for a three-planet resonant chain and numerically averaged it over the synodic period. The stable stationary solutions -- apsidal corotational resonances (ACRs) -- of this averaged system, corresponding to the local extrema of the Hamiltonian function, can be searched out numerically. The topology of the Hamiltonian around these ACRs reveals their stabilities. We further constructed the dynamical maps on different representative planes to study the dynamics around the stable ACRs, and we calculated the deviation ($ of the resonant angle in the evolution from the uniformly distributed values, by which we distinguished the behaviour of critical angles. Finally, the formation of the resonant chain via convergent planetary migration was simulated and the stable configurations associated with ACRs were verified. We find that the stable ACR families arising from circular orbits always exist for any resonant chain, and they may extend to a high eccentricity region. Around these ACR solutions, regular motion can be found, typically in two types of resonant configurations. One is characterised by libration of both the two-body resonant angles and the three-body Laplace resonant angle, and the other by libration of only two-body resonant angles. The three-body Laplace resonance does not seem to contribute to the stability of the resonant chain much. The resonant chain can be formed via convergent migration, and the resonant configuration evolves along the ACR families to eccentric orbits once the planets are captured into the chain. Ideally, our methods introduced in this paper can be applied to any resonant chain of any number of planets at any eccentricity.

Investigating the origin of the far-field reflection interference fringe (RIF) of microdroplets

We show that the reflection interference fringe (RIF) is formed on a screen far away from the microdroplets placed on a prism-based substrate, which have low contact angles and thin droplet heights, caused by the dual convex–concave profile of the droplet, not a pure convex profile. The geometric formulation shows that the interference fringes are caused by the optical path difference when the reflected rays from the upper convex profile at the droplet–air interface interfere with reflection from the lower concave profile at oblique angles lower than the critical angle. Analytic solutions are obtained for the droplet height and the contact angle out of the fringe number and the fringe radius in RIF from the geometric formulation. Furthermore, the ray tracing simulation is conducted using the custom-designed code. The geometric formulation and the ray tracing show excellent agreement with the experimental observation in the relation between the droplet height and the fringe number and the relation between the contact angle and the fringe radius. This study is remarkable as the droplet's dual profile cannot be easily observed with the existing techniques. However, the RIF technique can effectively verify the existence of a dual profile of the microdroplets in a simple setup. In this work, the RIF technique is successfully developed as a new optical diagnostic technique to determine the microdroplet features, such as the dual profile, the height, the contact angle, the inflection point, and the precursor film thickness, by simply measuring the RIF patterns on the far-field screen.

Can the presence of SLAP-5 lesions be predicted by using the critical shoulder angle in traumatic anterior shoulder instability?

Although SLAP-5 lesions are associated with recurrent dislocations, their causes and pathomechanisms have not been fully elucidated. This study aimed to investigate the association between SLAP-5 lesions and scapular morphology in traumatic anterior shoulder instability (ASI). We hypothesized that there may be a relationship between SLAP-5 lesions and scapular morphology in traumatic ASI patients. The study included 74 patients with isolated Bankart lesions and 69 with SLAP-5 lesions who underwent arthroscopic labral repair for ASI. Critical shoulder angle (CSA) was measured on the roentgenograms, while glenoid inclination (GI) and glenoid version (GV) were measured on magnetic resonance imaging (MRI) by two observers in two separate sessions blinded to each other. Both groups were compared in terms of CSA, GI, and GV. The mean ages of Bankart and SLAP-5 patients were 28.4±9.1 and 27.9±7.7 (P=0.89), respectively; their mean CSA values were 33.1°±2.6° and 28.2°±2.4°, respectively (P<0.001). The ROC analysis's cut-off value was 30.5°, with 75.0% sensitivity and 76.7% specificity (AUC = 0.830). SLAP-5 lesions were more common on the dominant side than isolated Bankart lesions (P=0.021), but no difference was found between the groups in terms of GI and GV (P=0.334, P=0.081, respectively). In ASI, low CSA values appeared to be related to SLAP-5 lesions, and the cut-off value of CSA for SLAP lesion formation was 30.5° with 75.0% sensitivity and 76.7% specificity. Scapula morphology may be related to the SLAP-5 lesions, and CSA can be used as an additional parameter in provocative diagnostic tests and medical imaging techniques for the detection of SLAP lesions accompanying Bankart lesions. III retrospective case-control study.

Effect of patient-specific scapular morphology on the glenohumeral joint force and shoulder muscle force equilibrium: a study of rotator cuff tear and osteoarthritis patients.

Introduction: Osteoarthritis (OA) and rotator cuff tear (RCT) pathologies have distinct scapular morphologies that impact disease progression. Previous studies examined the correlation between scapular morphology and glenohumeral joint biomechanics through critical shoulder angle (CSA) variations. In abduction, higher CSAs, common in RCT patients, increase vertical shear force and rotator cuff activation, while lower CSAs, common in OA patients, are associated with higher compressive force. However, the impact of the complete patient-specific scapular morphology remains unexplored due to challenges in establishing personalized models. Methods: CT data of 48 OA patients and 55 RCT patients were collected. An automated pipeline customized the AnyBody™ model with patient-specific scapular morphology and glenohumeral joint geometry. Biomechanical simulations calculated glenohumeral joint forces and instability ratios (shear-to-compressive forces). Moment arms and torques of rotator cuff and deltoid muscles were analyzed for each patient-specific geometry. Results and discussion: This study confirms the increased instability ratio on the glenohumeral joint in RCT patients during abduction (mean maximum is 32.80% higher than that in OA), while OA patients exhibit a higher vertical instability ratio in flexion (mean maximum is 24.53% higher than that in RCT) due to the increased inferior vertical shear force. This study further shows lower total joint force in OA patients than that in RCT patients (mean maximum total force for the RCT group is 11.86% greater than that for the OA group), attributed to mechanically advantageous muscle moment arms. The findings highlight the significant impact of the glenohumeral joint center positioning on muscle moment arms and the total force generated. We propose that the RCT pathomechanism is related to force magnitude, while the OA pathomechanism is associated with the shear-to-compressive loading ratio. Overall, this research contributes to the understanding of the impact of the complete 3D scapular morphology of the individual on shoulder biomechanics.

Numerical Study of Transonic Buffet on SC(2)-0518 and OAT15A with Vortex Generators

Predicting the transonic buffet and its onset is important for ascertaining the performance limits of an aircraft at its critical angle of attack. Additionally, a physical understanding of the buffet suppression technique is important for preventing shock wave oscillations. In this study, we conducted zonal detached-eddy simulations to numerically investigate the effects of vortex generators (VGs) on buffet suppression and to discuss the differing flow characteristics of the SC(2)-0518 and OAT15A supercritical airfoils when the chordwise position of the VGs is varied. The results for both airfoils equipped with VGs demonstrated significant suppression of large-scale lift oscillations across all calculation steps. VGs placed at 10% of the chord (10%c) from the leading edge produced higher time-averaged lift coefficients for both airfoils, with the OAT15A airfoil showing a particularly notable 2.5% improvement in lift coefficient, leading to a 0.82% increase in L/D ratio. The visualized results indicated that the interaction between the shock wave and VGs leads to variations in the separation point, depending on the VG chordwise position. This separation is affected by the aerodynamic characteristics of the airfoil shapes and the wake induced by the VGs, ultimately resulting in changes to the lift coefficient.

Effect of crack surface friction on stress intensity factor for double-edge cracked Brazilian disk specimens under parabolic distribution load

The weight function method was employed to derive the closed-form solutions of stress intensity factors (SIFs) for double-edge cracked Brazilian disk (DECBD) specimens subjected to parabolic distribution loads, taking into account the influence of crack surface friction. Additionally, the accuracy and validity of these solutions were discussed in comparison with previous numerical results. Furthermore, the impact of friction coefficient and load distribution angle on SIFs was further investigated. The results indicate that the effect degree of load distribution angle on SIFs is closely correlated with both the loading angle θ and crack length α. Both the mode I and mode II SIFs increase with increasing load distribution angle γ for θ = 15° and α < 0.4. However, when α ≥0.60, the impact of load distribution angle γ on SIFs becomes negligible. Furthermore, the friction between crack surfaces of DECBD specimens significantly affects the dimensionless mode II SIF YII, leading to a decrease in dimensionless mode II SIF YII as the friction coefficient μ increases. Moreover, it further demonstrates that both the relative crack length α and friction coefficient μ play important roles in determining the critical loading angle θIIc for crack sticking. The critical loading angle θIIc for crack sticking increases with an increasing relative crack length; however, an increase in the friction coefficient leads to a reduction of this critical loading angle θIIc.

Shear rate dependency on flowing granular biomass material

The commercialization of bioenergy has been significantly limited by various material handling issues due to the poor flowability of granular biomass materials. Addressing these issues demands a fundamental understanding of flow physics and robust models to predict the multi-regime flow behavior of biomass particles. In this study, we investigated the multi-regime flow behavior of loblolly pine chips, a widely used bioenergy feedstock, through combined experiments and simulations. A quasi-static hypoplastic model and a cross-regime Drucker–Prager (DP)-μ(I) model were utilized and validated against inclined plane flow experiments to understand the quasi-static and dense flow behavior of milled pine chips. The results show that along the inclined plane, loblolly pine chips mainly present in heap flow (varying thickness along the plane), and in plane flow (iso-thickness along the plane) only when the inclination closes to the material’s critical state internal friction angle. The results also show that the multi-regime DP-μ(I) model predicts a completely different velocity profile from the hypoplastic model. DP-μ(I) model can capture the flow behavior of pine chips in both flow regimes well but at the cost of extra parameter determination, and the shear-rate dependent rheology model can successfully capture the flow of elongated high-frictional particles. These findings advance the scientific understanding of the multi-regime flow behavior of granular biomass materials and shed light on formulating novel constitutive models to assist granular biomass handling in the bioenergy industry.