Convex Cylindrical Surfaces Research Articles

A modified dynamic contact angle model applied to double droplet impact curved surface

The microscopic processes involving droplet impact and interaction on spatially curved surfaces remain unclear. In this study, we implement a dynamic contact angle model with adjusted upper and lower limits into a simulation of droplet motion, constructing a three-dimensional numerical model to depict the dynamics and heat transfer characteristics of symmetric double droplets impacting plane, concave, and convex cylindrical, and concave and convex spherical surfaces. The processes of droplet spreading, retraction, rebound, splitting, and heat transfer are elaborated, revealing the role of surface curvature during impact. Our results show that different curvatures significantly affect the flow morphology of the flow dividing line. For the two main curvatures of the surface, the curvature in the direction of droplet arrangement predominates. Positive curvature promotes spreading and repels the liquid phase, while negative curvature promotes agglomeration and attracts the liquid phase. Extreme situations arise when both positive and negative curvatures occur simultaneously. Regarding heat transfer, the overall heat transfer rate is mainly determined by the spread area, and the heat transfer performance of convex surfaces is better than that of plane or concave surfaces. Residual bubbles increase heat transfer inhomogeneity, but different surfaces do not show significant variability. Additionally, the heat flow intensity in the central interaction region has the following relationship with its rebound height and is independent of the overall heat transfer intensity.

Experimental study on flow and turbulence characteristics of jet impinging on cylinder using three-dimensional Lagrangian particle tracking velocimetry

When a round jet impinges on a convex cylindrical surface, complex three-dimensional (3D) flow structures occur, accompanied by the Coanda effect. To characterize the flow and turbulence properties of the general system, ensemble averages of 3D Lagrangian particle tracking velocimetry measurements were taken. The radial bin-averaging method was used in post-processing the tracked particles and corresponding instantaneous velocity vectors to generate appropriate ensemble-averaged statistics. Two impinging angles were selected, and at a fixed Reynolds number, the ensemble-averaged volumetric velocity field and turbulent stress tensor components were measured. The flow and turbulence characteristics of the impinging jet on the cylinder were notably different based on the impinging angle, especially in the downstream region. Surprisingly, the attached wall jet with a half-elliptic shape was abruptly thickened in the wall-normal direction, similar to the axis switching phenomenon observed in elliptic jets in the case of oblique impingement. In the jet-impinging region, the flow spread in all directions with high mean vorticity values. With the development of a 3D curved wall jet, both the Coanda effect and centrifugal force played a significant role in the flow behavior. A notable feature of the self-preserving region was the similarity of mean velocity profiles with scaling by the maximum velocity and the jet half-width for both impinging angle cases. Local isotropy of turbulent normal stresses was observed in this region, supporting the existence of self-preservation in the 3D curved wall jet. The volumetric ensemble-averaged Reynolds stress tensor revealed strong inhomogeneous turbulence in the boundary layer region and the curvature effect on the Reynolds shear stress in the free shear layer.

Self-Debonding of Adhesive Thin Films on Convex Cylindrical Surfaces and Spherical Surfaces

Abstract The emerging skin-integrated devices have been embedded with various functions, whose ideal implementation typically relies on intact bonding to curved substrates. However, the predeformation, which originates from the attachment of a thin film to a curved substrate, attempts to peel the film (i.e., self-debonding). It calls for strong enough interfacial adhesion in applications. On the other hand, too strong adhesion can destroy the surfaces of devices and substrates when the devices are peeled off after service. Therefore, seeking critical conditions becomes essential. Herein, we study the self-debonding of an adhesive thin film on a convex cylindrical surface. Taking Dugdale’s constant-stress law to describe the interfacial traction–separation relationship, we analytically unveil that the self-debonding behaviors are not solely determined by the interfacial energy. Instead, both the interfacial strength and critical interfacial separation are decisive. We thus obtain a phase diagram consisting of two critical conditions correspondingly. Similar results appear in the finite element analysis with the trapezoidal cohesive law, quantitatively showing the evolution of deflection and interfacial detachment force. Furthermore, we find that the circular film, symmetrically adhering to a spherical surface with small deflection, can still share similar self-debonding behavior. Our results provide guidance on how to stick a thin film on a convex cylindrical or spherical surface well with proper interfacial adhesion.

Axisymmetric lattice Boltzmann model for liquid flows with super-hydrophobic cylindrical surfaces

The lattice Boltzmann (LB) method has been extensively applied to the simulation of various fluid flows. Nonetheless, the standard LB model in rectangular coordinates faces some challenges when attempts are made to use it to simulate single-phase liquid flows involving super-hydrophobic cylindrical surfaces with a large slip length. Therefore, in this paper, boundary conditions for an axisymmetric LB model are proposed for the simulation of liquid slip at both convex and concave cylindrical surfaces. Based on the Navier slip boundary conditions, an equilibrium–nonequilibrium boundary scheme is developed to obtain the liquid slip in the azimuthal direction, with a combined bounce-back and specular-reflection boundary condition being developed to obtain the liquid slip in the axial direction. These boundary schemes are verified by simulating several established cases, namely, cylindrical Couette flow, harmonic oscillatory cylindrical Couette flow, Hagen–Poiseuille flow, and annular Poiseuille flow. The results are in excellent agreement with analytical results. Furthermore, some more complex flows involving super-hydrophobic cylindrical surfaces, such as stepwise oscillatory cylindrical Couette flow, are also simulated and studied using the proposed LB model. The axisymmetric LB model presented here overcomes the inability of standard LB models to accurately and efficiently simulate single-phase liquid flows involving super-hydrophobic cylindrical surfaces with a large slip length.

Interferometric stitching method for testing cylindrical surfaces with large apertures.

Cylindrical surfaces widely used in high-energy laser systems can have nearly semi-meter-scale dimensions, and aperture angles can exceed R/3. State-of-the-art interferometric stitching test methods involve stitching only along the arc direction, and the reported dimensions of ∼50 × 50 mm2 are far smaller than those required in high-energy laser systems. To rectify this limitation, an interferometric stitching method for cylindrical surfaces with large apertures is proposed. Moreover, a subaperture stitching algorithm that can stitch along both the linear and arc directions is developed. An interferometric stitching workstation equipped with a six-axis motion stage and a series of computer-generated holograms is established, where cylindrical surfaces with R/# values as large as R/0.5 and apertures up to 700 mm can be tested based on the theoretical analysis. A convex cylindrical surface with a 350 × 380 mm2 aperture is tested to validate the proposed method's feasibility in enlarging the testable aperture of cylindrical surfaces significantly from Ф50 mm to Ф700 mm, thereby promoting the application of large cylindrical surfaces in high-energy laser systems.

Surface conductivity effects during shock wave reflection off curved surfaces

Previous work has shown that heat transfer into a plane conducting surface affects shock wave reflection properties. In the more complex reflection case of a curved surface the situation would be different because of the increased number of reflection patterns, with a rapid change in reflection geometry as the wave propagates up the surface. Test pieces of different thermal conductivities (0.19 W/mK and 401 W/mK) and hydraulically smooth surfaces are used on both convex and concave cylindrical surfaces. The test pieces are placed in identical positions on either side of a plane of symmetry and at the same incident angles in a shock tube. Tests are performed at incident shock Mach numbers of 1.22< M <1.5 and imaged using high-speed shadowgraph photography. The images are analyzed both quantitatively through reflection angle measurements and qualitatively by searching for asymmetry. Both the qualitative and quantitative measurements clearly indicate that the thermal conductivity of the surface affects the reflection patterns due to the complex transient thermal environment. Asymmetry in the reflection patterns is found at all Mach numbers. In contrast to the plane wall case the lack of theory limits comparison, where in that case it was shown that the lower the thermal conductivity the closer the experimental results approached the ideal adiabatic case. Similar comparisons in the relationship of reflection types between different materials are found in the current case. The findings could be refined by using higher imaging frame rates and spatial resolution, and sophisticated numerical modeling.

The Effect of the Feed Direction on the Micro- and Macro Accuracy of 3D Ball-end Milling of Chromium-Molybdenum Alloy Steel.

The machining of free form surfaces is one of the most challenging problems in the field of metal cutting technology. The produced part and machining process should satisfy the working, accuracy, and financial requirements. The accuracy can describe dimensional, geometrical, and surface roughness parameters. In the current article, three of them are investigated in the case of the ball-end milling of a convex and concave cylindrical surface form 42CrMo4 steel alloy. The effect of the tool path direction is investigated and the other cutting parameters are constant. The surface roughness and the geometric error are measured by contact methods. Based on the results, the surface roughness, dimensional error, and the geometrical error mean different aspects of the accuracy, but they are not independent from each other. The investigated input parameters have a similar effect on them. The regression analyses result a very good liner regression for geometric errors and shows the importance of surface roughness.

Reconfigurable RCS Reduction from Curved Structures Using Plasma Based FSS

The radar cross section (RCS) reduction from curved surfaces using plasma based frequency selective surfaces (FSS) is investigated. A frequency reconfigurable plasma based FSS unit-cell element with target-shaped structure is proposed. The operating frequency of the FSS is governed by the plasma ionization degree (i.e. plasma frequency). zero crossing frequency of the FSS unit-cell has a tuning range extending from 9.6 GHz to 11.3 GHz with an average bandwidth of 1.1 GHz. Planar and curved metallic surfaces are investigated. The curves structures include cylindrical (convex and concave), and spherical (convex and concave) surfaces. Single ionization source is applied at the rare end of the plasma FSS array design is optimized to maintain uniform plasma flow over the metallic surfaces by applying a single ionization source at the rare end of the array. The plasma FSS arrangement with ωp = 9 × 1011 rad/Sec loading a planar sheet reduces the RCS by 23 dB at 10.2 GHz and the (− 5 dB) frequency band of 14.7% for planar plate compared with the unloaded plate case. Different hybrid arrangements are investigated for wideband RCS reduction of 36.4% by superimposing reduction bands of three different plasma frequencies. A 21.5 dB reduction is achieved at 9.8 GHz for FSS arrangements (III). The effect of changing the radii of curvature for convex and concave cylindrical and spherical metallic surfaces is studied at different plasma frequencies. A full-wave analysis of the loaded metallic plates with plasma FSS is used to calculate the backscattered and bistatic RCS for different surfaces.

Calculating Acoustic Channel for a Crack-Like Corrosion–Mechanical Defect

For the previously proposed model of the corner reflector with a convex cylindrical surface at the base, intended for simulating crack-like corrosion–mechanical defects, formulas for high-resolution acoustic in-line inspection tool (ILI) have been derived in the geometrical acoustics approximation. Based on simulation results, it is demonstrated that the geometrical characteristics of the proposed model of the corner reflector affect the amplitude of angled incident transverse waves reflected from its surface in comparison with the model of a corner reflector coming to a flat surface prescribed by technical regulations.

Heat transfer distribution on a cylindrical convex surface due to obliquely impinging row of circular jets

Heat transfer characteristics on a cylindrical convex surface impinged by a row of circular jets are presented in this study. Two different jet-jet spacing values equal to 4d and 8d were studied with the curvature ratio (ratio of diameters of jet and impinging surface, d/D) keeping constant at 0.05. Results for a single jet impinging onto the convex surface are also reported. The impinging angle ‘θ’, dimensionless jet-target distance ‘L/d’, and Reynolds number ‘Re’ were varied in the range 0°−45°, 2–10 and 5000–40,000 respectively. The Nusselt number variations from impinging point till midpoint between adjacent jets for jet-jet spacing of 8d were similar in nature with those for single jet with a maximum difference approximately equal to 5% at the secondary peak region. The Nusselt number distribution for the multiple jets with spacing equal to 4d was different as the interaction of adjacent walljets restricted the spread of inner jets, especially for inclined impingement, with nearly 10% increase in the secondary peak value compared to single jet. The peak Nusselt number occurs at the impinging point for perpendicular impingement and moves to the uphill side with inclination of jet. Secondary peaks are observed for all jet configurations at Re > 10,000 and L/d ≤ 4 for perpendicular impingement, but for large jet inclinations, no secondary peaks were observed on the uphill side. The magnitude of secondary peak in the downhill side reduces with increase in inclination and the position shifts further downstream in the downhill side. A correlation for peak Nusselt number is proposed as a function of Re, L/d and θ.

Post-collision hydrodynamics of droplets on cylindrical bodies of variant convexity and wettability

Droplet impact, dynamics, wetting, and spreading behavior on surfaces impose rich and interesting physics, in addition to extensive understanding of processed employing droplets and sprays. The physics and mechanisms become more interesting and insightful when the geometry and wettability of the surface provide additional constraints to the fluid dynamics. Post-impingement morphology and dynamics of water droplets on convex cylindrical surfaces, having diameters similar to that of the droplet, have been explored experimentally. Droplet impact and post-impact feature studies have been conducted on hydrophilic and superhydrophobic (SH) cylindrical surfaces. Effects of the impact Weber number (We) and target-to-drop diameter ratio on the wetting and spreading hydrodynamics have been studied and discussed. The post-impact hydrodynamics have been quantified employing dedicated non-dimensional variables, such as the wetting fraction, the spreading factor, and the non-dimensional film thickness at the north pole of the target. The observations reveal that the wetting fraction and spread factor increase with an increase in the impact We and a decrease in the target-to-drop diameter ratio. An opposite trend is noted for the non-dimensional film thickness at the target’s north pole. It is also deduced that the spread factor is independent of the target wettability, whereas the wetting fraction is remarkably low for SH targets. The lamella dynamics post spreading has also been observed to be a strong function of the wettability, the impact We, and the diameter ratio, and the same has been explained based on wetting and inertial principles. An analytical expression for temporal evolution of film thickness at the north pole of the cylindrical target is derived from first principles. The article also proposes a theoretical model based on energy conservation for predicting the maximum wetting fraction for variant cylindrical targets in terms of the governing We and Capillary number. It is observed that the experimental measurements are in good agreement with the theoretical predictions.

Experimental and numerical studies on detonation reflections over cylindrical convex surfaces

The detonation reflection over a cylindrical convex surface was investigated experimentally and numerically by focusing on the length-scale effect on the reflection process, such as the triple-point trajectory and the critical wedge angle at which a transition occurs from regular reflection to Mach reflection. The results show that the critical wall angle plots exhibit significant scatter because of the cellular properties of the detonation front. If the transverse spacing is large as compared to the radius of curvature, the scatter range extends. If the transverse spacing is small as compared to the radius of curvature, the scattering is dramatically reduced. The critical wall angle is found to mainly depend on the scaled length i.e., the radius of curvature (R) over the cell size λ (or the reaction zone thickness Δ). Moreover, the critical wall angle increases with the decrease in the detonation thickness or with the increase in the radius. As R/λ increases to approximately ten, the critical wall angle approaches a value calculated using the non-reactive two-shock theory for pseudo-steady flows. The numerical results reveal that the transition to Mach reflection occurs earlier in the case of a ZND detonation than in the case of an inert shock wave because of the higher sound speed due to the release of chemical heat.

Effectiveness distribution measurements for a row of heated circular jets impinging on a cylindrical convex surface at different inclinations

The spatially resolved effectiveness distributions for a single jet and row of circular jets impinging on a convex surface are reported in the present study. The impinging surface was inclined at 0°, 15°, 30° and 45° to the jet axis. Studies were conducted for a single curvature ratio equal to 0.05 at a constant Reynolds number equal to 40,000 for non-dimensional jet-to-target distances, L/d equal to 2, 4, 6, 8 and 10. Two non-dimensional jet-to-jet spacings, S/d, equal to 4 and 8 were studied. The effectiveness distribution for multiple jet impingement was noticed to be different from that for a single jet impingement. The entrainment from the surrounding was mitigated for the inner jets by the outer jets. The interaction of adjacent walljets forms a ‘barrier’ against the percolation of entrained ambient from the outer jet region towards the inner region. The zone of walljet interaction and region near to the inner jets were therefore observed to result in high effectiveness values. The inclined impingement of the jet reduces the strength of interaction of the walljets on up and downhill sides and thereby reduces the ‘barrier effect’ against the entrainment of ambient, which causes similar variation of effectiveness for all the jets in a row at high inclinations.

Local effectiveness and Nusselt number distributions for a rectangular jet impinging on a cylindrical convex surface at different angles

Local effectiveness and Nusselt number distribution measurements for heated rectangular jets impinging perpendicularly and obliquely on a cylindrical convex surface are reported here. The jets exit from a rectangular nozzle of height ‘H’ and width ‘W’ with aspect ratios, H/W, equal to 10 and 5 and the corresponding the curvature ratios (ratio of hydraulic diameter of nozzle to diameter of the impinging convex surface), b/D, were equal to 0.083 and 0.076. Studies were conducted for non dimensional jet-to-target distances, L/b, equal to 2, 3, 4 and 5, and for inclination of jet axis with the convex target surface, θ, equal to 0°, 30° and 45°. The Reynolds numbers, Re (based on average exit velocity of jet and hydraulic diameter of nozzle) was kept constant at 17000.The entrainment of the fluid from the surroundings into the walljet from the top surface and edge regions, which is symmetric on the either side of the impingement zone for perpendicular impingement, gives a ‘rhombus like’ shape for the effectiveness contours. However, the entrainment is asymmetric for oblique impingement, with the drop in effectiveness rapid in the uphill side and gradual in the downhill side, giving the effectiveness contours a ‘kite like’ shape. The fluid entrainment from the top surface and edge regions influence the Nusselt number distribution also. The relatively higher mixing of the jet fluid with the ambient at the edge regions increases the turbulence and thereby increases the Nusselt number at these locations, resulting in contour shapes different from those observed for the effectiveness.

Shock formation and nonlinear saturation effects in the ultrasound field of a diagnostic curvilinear probe.

Newer imaging and therapeutic ultrasound technologies may benefit from in situ pressure levels higher than conventional diagnostic ultrasound. One example is the recently developed use of ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe has been used to deliver the acoustic pushing pulses. The probe is a curvilinear array comprising 128 elements equally spaced along a convex cylindrical surface. The effectiveness of the treatment can be increased by using higher transducer output to provide a stronger pushing force; however nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the three-dimensional Westervelt equation with the boundary condition set to match low power measurements of the acoustic pressure field. Nonlinear focal waveforms simulated for different numbers of operating elements of the array at several output power levels were compared to fiber-optic hydrophone measurements and were found to be in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of a diagnostic imaging probe.

Dendron and Hyperbranched Polymer Brushes in Good and Poor Solvents.

We present a theory of conformational transition triggered by inferior solvent strength in brushes formed by dendritically branched macromolecules tethered to planar, concave, or convex cylindrical and spherical surfaces. In the regime of linear elasticity for brush-forming dendrons, an analytical strong stretching self-consistent field (SS-SCF) approach provides brush conformational properties as a function of solvent strength. A boxlike model is applied to describe the collapse transition in brushes formed by macromolecules with arbitrary treelike topology, including hyperbranched polymers. We demonstrate that an increase in the degree of branching, that is, an increase in the number of generations or/and functionality of branching points in tethered macromolecules, makes the swelling-to-collapse transition less sharp. A decrease in surface curvature has a similar effect. The numerical Scheutjens-Fleer self-consistent field approach is used to analyze the collapse transition in dendron brushes in the nonlinear stretching regime. It is demonstrated that inferior solvent strength suppresses stratification that is exhibited under good solvent conditions by densely grafted dendron brushes.

English

Based on the foot structure of the climbing biology and multivariate coupling bionic technology, the bionic flexible convex surface was designed and a 3D model was created using the digital modeling software. Finite Element Analysis software was used for contacting analysis to the bionic flexible convex foot structure in the state of dry friction and wet adhesion, and then studied frictional contact performance. The results of Finite Element Analysis shows that the contact stress of the convex is much larger than the stress of the area around it in the dry friction state and the deformation is mainly concentrated in the convex’s top. The friction between the hemispherical convex surface and the contact surface is the maximum and the cylindrical convex surface is the minimum. The friction between the bionic flexible convex structure and the solid contact surface in wet adhesion state is larger than dry state. Key words: Bionic, flexible, contact, finite element, wet adhesion.

Analysis of Conformal Reflectarray on Cylindrical Surface

As the important case of conformal arrays, conformal arrays on cylindrical surfaces have been widely used in radar and communication systems. This paper explores the chances of designing conformal reflectarray on cylindrical platform. An extended array theory method is proposed in this paper for analyzing the radiation patterns of cylindrical conformal reflectarray. The radiation characteristics of conformal reflectarray on convex and concave cylindrical surfaces are studied, and the performances of the two cases are compared with planar cases. It is shown that the cylindrical conformal reflectarray can be a good candidate of high gain antennas for applications where a slightly curved conformal platform is available.

Simulation Analysis on the Profiles of Droplets Wetting on the Substrates

To study the structural characteristics and physical properties of droplets sitting on the inclined substrates and cylindrical surfaces, wetting experiments are conducted in different cases. The profile curves of the droplets are recorded and extracted by a CCD camera and image processing, respectively. Contact angles are figured out by fitting the profile curves and taking the derivative at the front and rear triple points. Based on the experimental results, a Surface Evolver is employed to simulate the morphological changes by minimizing the total energy of the system. Furthermore, theoretical shapes and feature parameters, including the heights and the spreading distances of the droplets, which are hard to obtain by normal experimental measurements are provided. The contact-angle hysteresis when the heavy droplet sitting on the inclined substrate is discussed. Meanwhile, the evolutions of the contour of the three-phase contact line are predicted when heavy droplets spread on the convex and concave cylindrical surfaces, respectively. This study provides a finite-element analysis method to describe the surface properties of molten droplets on different substrates, and the simulation results agree well with the experimental results.

Nonlinear Effects in Ultrasound Fields of Diagnostic-type Transducers Used for Kidney Stone Propulsion: Characterization in Water.

Newer imaging and therapeutic ultrasound technologies require higher in situ pressure levels compared to conventional diagnostic values. One example is the recently developed use of focused ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe is used to deliver the acoustic pushing pulses. The probe comprises 128 elements equally spaced at the 55 mm long convex cylindrical surface with 38 mm radius of curvature. The efficacy of the treatment can be increased by using higher transducer output to provide stronger pushing force; however, nonlinear acoustic saturation effect can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the 3D Westervelt equation; the boundary condition was set to match low power pressure beam scans. Focal waveforms simulated for increased output power levels were compared with the fiber-optic hydrophone measurements and were found in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of the transducer. This work has application to standard diagnostic probes and imaging.