Concave Corners Research Articles

In-plane dynamics crushing of a combined auxetic honeycomb with negative Poisson's ratio and enhanced energy absorption

In order to improve the energy absorption capacity of the honeycomb, a combined auxetic honeycomb is designed in this paper. By using the double-inclined walls replacing the horizontal walls of the star-shaped honeycomb (SSH), and introducing a thin-walled circle contacting with the four concave corners of the SSH, the star-circle honeycomb (SCH) is designed. The in-plane dynamic crushing behaviors was explored based on finite element method (FEM). There are three types of deformation modes observed with different impact velocity, including low-, medium- and high-velocity loading modes and the stress-strain curve exhibits two plateau stress stages. Based on the deformation characteristics of the representative unit, theoretical calculation models were established to estimate the plateau stress of the SCH under low- and high-velocity loading according the conservation of energy and the theoretical calculation was in keep well with the numerical simulation. A deformation modes map was summarized to investigate the effects of the impact velocity and the relative density on the deformation modes and the energy absorption capability and the dynamic Poisson's ratio were studied. The result shows that the SCH presents better energy absorption compared with SSH as well as retaining the negative Poisson's ratio property. The deformation mechanism was revealed form the structural design and plastic hinge dissipation. This work presents a different design strategy for the auxetic honeycomb, expected to guide the design of more novel auxetic with better energy absorption and mechanical property.

Effects of Processing Parameters for Vacuum-Bagging-Only Method on Shape Conformation of Laminated Composites

Complex composite structures manufactured using a low-pressure vacuum bag-only (VBO) method are more susceptible to defects than flat laminates because of the presence of complex compaction conditions at corners. This study investigates the contribution of multivariate processing parameters such as bagging techniques, curing profiles, and laminate structures on laminates’ shape conformation. Nine sets of laminates were produced with a concave corner and another nine sets with a convex corner, both with a 45° inclined structure. Three-way analysis of variance (ANOVA) was performed to quantify thickness variation and spring effect of laminated composites. The analysis for concave and convex corners showed that the bagging techniques is the main factor in controlling the laminate thickness for complex shape applications. The modified (single) vacuum-bag-only (MSVB) technique appeared to be superior when compared to other bagging techniques, exhibiting the least coefficients of variation of 0.015 and 0.016 in composites with concave and convex corners, respectively. Curing profiles and their interaction with bagging techniques showed no statistical significance in the contribution toward laminate thickness variation. The spring effect of laminated composites was investigated by calculating the coefficient of determination (R2) relative to that of the mold. The specimens exhibited a good agreement with R2 values ranging from 0.9824 to 0.9946, with no major data offset. This study provides guidelines to reduce thickness variations and spring effect in laminated composites with complex shapes by the optimum selection of processing parameters for prepreg processing.

How does boiling occur in lattice Boltzmann simulations?

The lattice Boltzmann (LB) method has been employed to simulate boiling phenomena in recent years. However, a very important issue still remains open, i.e., how does boiling occur in the LB simulations? For instance, the existing LB studies showed that the boiling on a hydrophobic surface begins at a lower wall superheat than that on a hydrophilic surface, which qualitatively agrees well with experimental studies, but no one has yet explained how this phenomenon appears in the LB simulations and what happened in the simulations after changing the wettability of the heating surface. In this paper, the LB boiling mechanism is revealed by analyzing boiling on a flat surface with mixed wettability and boiling on a structured surface with homogeneous wettability. Through a theoretical analysis, we demonstrate that, when the same wall superheat is applied, in the LB boiling simulations, the fluid density near the heating surface decreases faster on a hydrophobic surface than that on a hydrophilic surface. Accordingly, a lower wall superheat can induce the phase transition from liquid to vapor on a hydrophobic surface than that on a hydrophilic surface. Furthermore, a similar theoretical analysis shows that the fluid density decreases fastest at concave corners in the case of a structured surface with homogeneous wettability, which explains why vapor bubbles are nucleated at concave corners in boiling on structured surfaces.

Rarefied flow separation in microchannel with bends

Abstract

Shock wave boundary layer interactions in hypersonic flows over a double wedge geometry by using conjugate heat transfer

AbstractShock wave boundary layer interaction phenomena play a critical role in the design of supersonic and hypersonic vehicles. Consequently, this paper mainly focuses on hypersonic flow over a double wedge model, flow fields around concave corners are relatively complicated, and produce several classical viscous flow features depending on the combination of the first and second wedge, and the important characteristic phenomena are mainly the shock‐boundary layer and shock‐shock interaction. For these interactions, aerodynamic heating and pressure loads increase greatly when interactions are present. The conjugate heat transfer (CHT) technique is expected to exactly predict the separation bubble length, heat flux, skin friction coefficient, and pressure distributions in double wedge studies in hypersonic applications. In the present CHT studies, the different wall materials used are thermal insulation, Macor, and SiC, it is clearly shown that while using Macor and thermal insulctation wall material in CHT studies, the interface temperature, skin friction coefficient, heat flux distribution along the length change significantly with increase in simulation time. In comparing the CHT results with the fluid flow solver with the wall, considering isothermal and adiabatic boundary results, it is clearly indicated that the fluid flow solver results are either underpredicting or overpredicting the interface properties, but CHT studies give an accurate prediction of the separation length and interface properties.

Hybrid grid generation for viscous flow simulations in complex geometries

In this paper, we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions. Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. With respect to marching directions, three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness. A novel weighted strategy is used in the normal smoothing scheme, which evidently reduces the possibility of early stop of front generation at complex corners. With respect to marching distances, the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first; a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries. These efforts, plus other special treatments such as multi-normal generation and fast detection of local/global intersection, as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities.

Curvature Regularized Surface Reconstruction from Point Clouds

We propose a variational functional with a curvature constraint to reconstruct implicit surfaces from point cloud data. In the point cloud data, only locations are assumed to be given, without any normal direction or any curvature estimation. The minimizing functional balances two terms: the distance function from the point cloud to the surface and the mean curvature of the surface itself. We explore both the $L_1$ and $L_2$ norms for the curvature constraint. With the added curvature constraint, the computation becomes particularly challenging. We propose two efficient algorithms. The first algorithm is a novel operator splitting method. It replaces the original high-order PDEs by a decoupled PDE system, which is solved by a semi-implicit method. We also discuss an approach based on an augmented Lagrangian method. The proposed model shows robustness against noise and recovers concave features and corners better compared to models without curvature constraint. Numerical experiments on two- and three-dimensional data sets, noisy data and sparse data, are presented to validate the model. Experiments show that the operator splitting semi-implicit method is flexible and robust.

The interaction of inner and outer surface corners during spontaneous wetting

Real world surfaces can often be modeled as a collection of edges, corners, dents or spikes of varying roundness. These features exhibit individual spontaneous wetting behaviors comprising pinned contact lines, rivulets or cusps. If occurring in proximity to one another, as is often the case in applications, these wetting properties interact, resulting in an overall changed wetting pattern on the surface. Hence, there is considerable interest in understanding when, and to what extent, interactions occur, and how wetting then deviates from the wetting of isolated surface features.The present study addresses these questions by experimentally and theoretically studying the capillary interaction of sharp-edged 90° (outer) and 270° (inner) corners in proximity to one another. It is shown that the spontaneous wetting at the convex outer corner is influenced by the concave inner corner even when they are separated by a distance of several times the capillary length, while the wetting of the inner corner takes place unaffected by the outer corner, except when the separating distance is much smaller than the capillary length. The final contact line shape at the inner corner is measured and theoretically modeled for contact angles up to 90°.

Direct numerical simulation and in-depth analysis of thermal turbulence in square annular duct

The thermal turbulence in an infinitely-long square annular duct (SAD) was studied by the direct numerical simulation with the Reynolds (Re) number Reb≈6400 based on the bulk velocity. The isothermal boundary condition was applied to the side walls in SAD with the higher and lower temperatures on the outer and inner walls, respectively. As one of the most fascinating features for the corner turbulence, the turbulent-driven secondary flow (TDSF) presented the twin counter-rotating vortex pairs symmetrically located at the outer concave and inner convex corners. The TDSF was found significantly increase the spatially-averaged Nusselt (Nu) number comparing to the laminar flow. The instantaneous vortex structures were visualized by the third-generation vortex-identification method based on Liutex. The budget analyses of the governing-equation for the turbulent boundary layer (TBL) in SAD distinguished the balancing mechanisms from the one in the traditional flat-plate TBL, which justified the necessity to classify the generic TBLs into their sub-categories of Type-A, B and C TBLs. Moreover, the current study focused on a number of issues in the thermal TBL, such as the TDSF structures with their thermal effects and the TBL law formulations. For the present TBL in SAD, it was found that the buffer layer located in between the inner and the semi-log layers tended to be wider than that in a flat-plate TBL, and an outer linear conduction layer was, for the first time, found for the Type-B temperature TBL. Based on the indicator function, the quantitative sublayer partitions were first conducted for both the velocity and temperature TBLs and then the applicable ranges for the linear and semi-log sublayers were rigorously determined. Further, the profound damping mechanism was first introduced and applied to the traditional linear and semi-log laws to derive more accurate analytical law formulations for the entire velocity and temperature TBL sublayers.

Boundary Conditions for Planar Stokes Equations Inducing Vortices Around Concave Corners

Fluid flows around an obstacle generate vortices which are difficult to locate and to describe. A variational formulation for a class of mixed and nonstandard boundary conditions on a smooth obstacle is discussed for the Stokes equations. Possible boundary data are then derived through separation of variables of biharmonic equations in a planar region having an internal concave corner. Explicit singular solutions show that, at least qualitatively, these conditions are able to reproduce vortices over the leeward wall of the obstacle.

Toeplitz operators on concave corners and topologically protected corner states

We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz operator of index one. By using this, a relation between Fredholm indices of quarter-plane and concave corner Toeplitz operators is clarified. As an application, topological invariants and corner states for some bulk-edges gapped Hamiltonians on two-dimensional (2-D) class AIII and 3-D class A systems with concave corners are studied. Explicit examples clarify that these topological invariants depend on the shape of the system. We discuss the Benalcazar--Bernevig--Hughes' 2-D Hamiltonian and see that there still exists topologically protected corner states even if we break some symmetries as long as the chiral symmetry is preserved.

Second harmonic generation from complementary triangular Au metamaterials

Sub-wavelength square array of a triangular Au platelet and its complementary structure (i.e. that of a triangular hole in a square film of Au) are compared in terms of second harmonic generation efficiency for fundamental light in the near infrared and visible region of spectrum for normal incidence. Electric field strength around the convex corners of a triangular particle is at least 10 times larger than the one around the concave corners of triangular hole in the complementary structure. Nevertheless the SHG intensity at the respective resonant frequency is found to be comparable, which are numerically estimated by an overlap integral of nonlinear polarization and electric field at the SHG frequency in the nonlinear optical scattering theory originally proposed by Roke et al. (Phys. Rev. B 70, 115106 (2004)). The reason is due to the large electric field strength at the sides of the triangular hole at the resonance frequency, which compensates the suppressed electric field at the concave corners in the overlap integral.

Mechanical modeling of five-axis single root clean-up machining of complex surface

Root clean-up machining is an important process for five-axis machining of complex curved surface parts. Subjected to harsh cutting conditions and lack of analysis of cutting force, single root clean-up machining cannot be used widely though it is a machining method with high efficiency and no residue. Whereupon, this paper establishes a single root clean-up machining mechanical model for five-axis ball-end milling of complex surface creatively. According to the characteristic of the ball-end mill, expression of differential element cutting force is optimized. Concave corner of a complex surface is discretized into a series of concave crescent cylinders (CCCs) along tool path. Aiming at five-axis single root clean-up machining of CCC, cutter axis and feed direction are defined parametrically. The analytical expressions of complex surface to-be-clean-up and allowance section plane are derived in cutter coordinate system to limit spatial conditions of cutter edge participating in cutting. In-cut cutting edge (ICCE) is defined by searching and judging the cutter edge elements one by one, and a one-dimensional binary search method is used to further improve the precision of boundary. Cutter run-out parameters are defined, and its effect on undeformed chip thickness is deduced. In conclusion, the mechanical model for single root clean-up machining of five-axis ball-end milling of CCC can be established which is applicable to complex surface. A series of experiments and simulations were arranged. The ICCE analytical algorithm based on the CCC has the same precision and higher efficiency compared with solid modeling method. Due to the influence of curvature of the two flank surfaces and the tool path, there will be a slight deviation when the ICCE applies to the complex surface. The predicted force of single root clean-up machining of complex surface agrees well with measured force, which validates the mechanical model.

Molecular dynamics research on geometric effect of nanostructured diamond-like carbon substrates on potassium stearate adsorption

Molecular dynamics (MD) simulations were performed to investigate the geometric effect of nanostructured substrates on adsorptive behavior of potassium stearate monolayers. A typical protective coating, diamond-like carbon (DLC), was employed as adsorptive substrates. For the substrates with square grooves, complete penetration of molecules can only occur under large width and small depth. The occurrence of partial penetration would make monolayer atoms away from substrate surfaces and therefore induce weak substrate-molecules interactions. Compared with the square groove bottoms, monolayers are much more strongly adsorbed to the groove concave corners. For substrates with triangle and semi-circle grooves, complete penetrations are achieved in both cases and thus monolayer atoms can interact with the whole groove surface. The effect of substrate morphology on monolayer adsorption would be sufficiently weakened by the decrease of geometric size, and the surface adsorptivity of semi-circle grooves with large radius is similar to that of the smooth surface. The results indicate that the substrates with triangle grooves have better adsorptivity than other morphologies.

Second-harmonic generation from complementary Au metasurfaces with triangular resonators

We demonstrate the contribution of local electric near-field enhancement around convex and concave corners at resonant fundamental excitation to the second-harmonic (SH) emission intensity using complementary Au metasurfaces with triangular resonators (i.e., a square array of triangular particles and a square array of a thin film of Au with a triangular hole). It is demonstrated that for an electric near-field enhancement at normal incidence, the fundamental excitation around convex corners of a triangular particle is many times stronger than the one around concave corners of a complementary triangular hole. Notwithstanding, the SH emission intensity of the complementary structure is found to be comparable at their respective optimal resonant fundamental excitations. SH emission intensity is numerically estimated using mode overlap between the fundamental and SH waves. The comparable SH emission intensity is found to originate from the strong electric near-field enhancement on the sides of a triangular hole with zero curvature, which compensates for the field suppression around the concave corners of the triangular hole. In addition, the strong electric near-field enhancement around convex corners of a triangular particle (accompanied with suppression around the sides of the triangular particle) and field suppression around concave corners of a triangular hole (accompanied with strong field enhancement around the side of the triangular hole) are demonstrated using Babinet’s principle.

Toward Information Transfer Around a Concave Corner by a Surface-Plasmon-Polariton Wave

As optical interconnects employing surface-plasmon-polariton (SPP) waves are expected to enable faster communication in integrated circuits, the time-domain Maxwell equations were solved using the finite-difference time-domain method to investigate the transfer of information via a pulse-modulated carrier SPP wave around a concave corner formed by two planar metal/air interfaces. The signal is launched along the first metal/air interface and received along the second metal/air interface. The corner angle affects the intensity and the duration of the received signal, but its shape is largely independent of the corner angle of the corner. Accordingly, the signal received around the concave corner is strongly and positively correlated with the transmitted signal, a promising result for SPP-wave-based optical interconnects. The energy of the received signal varies with the frequency of the carrier SPP wave. The received signal is better correlated with the transmitted signal when the carrier frequency is higher for a fixed value of the corner angle.

Introduction of Multiscaled Longitudinal Vortices by Fractal-Patterned Surface Roughness

To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested: geometric patterns, fractal patterns, reptile-skin patterns, and patterns of circular cylinders arranged in a lattice and in a zigzag manner. A suitable pattern for adaptive control of flow is one that generates longitudinal vortices with nonconstant distances. The preferred instability mode of a laminar boundary layer is expected to be selected automatically from fluctuations involving many frequencies and caused by fractal patterns. Snake- and reptile-skin patterns may have a similar ability as fractal patterns because they consist of multiscale patterns. The longitudinal vortices generated from peculiar positions and concave corners in patterns were observed. The distance between these vortices is not constant because the onset of vortices is at concave corners in fractal patterns. These vortices have differing strengths and easily cause nonlinear interactions, so they can disturb a laminar boundary layer with several higher-harmonic frequencies. The velocity profiles of the laminar boundary-layer flow over the fractal patterns were measured by using hydrogen bubbles. The results show the down-wash flow between the longitudinal vortices, which means that the vortices may effectively suppress the boundary layer separation in an adverse pressure gradient.

Dokładność geometryczna naroży po obróbce frezowaniem stopów aluminium

The study comparing a geometry of the inner corners after milling operation of aluminum alloy 7075 elements was conducted. The influence of changes of technological parameters and types of treatment on the geometric accuracy of the samples was investigated. The correct process of corner milling involves the need to select the right feed speed as well as the correct engagement angle of the milling tool. Corner milling is problematic due to the increase of engagement angle in their area. This makes it much more difficult to perform stable machining and adversely affects the surface accuracy and geometry of the concave corners. The tests using various strategies and technological parameters for milling corners with variable opening angles were carried out. When analyzing the obtained results, conclusions were formulated indicating the relationship between the change of selected technological parameters of milling in the corners and the geometric accuracy of the samples tested.

Entropy solution at concave corners and ridges, and volume boundary layer tangential adaptivity

Two particular aspects of volume boundary layer mesh generation applied to non smooth geometries are considered in this work. First, the treatment of concave ridges and corners is tackled from a generic viewpoint. Entropy satisfying elements are generated where shocks form in the volume. This proves useful to avoid premature halt of the boundary layer, and therefore potential jumps in the normal size. The connection with the Voronoi diagram is commented. Second, boundary layer adaptivity in the tangential plane is considered to honor arbitrary sizing prescription, and avoid size mismatch between the boundary layer and the isotropic sizing.It is shown that a strict semi-structured framework has to be abandoned in general to accommodate changes in the mesh topology. Size transition between boundary layer and fully unstructured anisotropic mesh is automatically taken into account. Both the concavity problem and the tangential adaptivity are presented together, since they require similar mesh operators. Various numerical examples illustrate the method.

Two Inoculation Methods for Refining As-Cast Grain Structure in Austenitic 316L Steel

Two inoculation methods were utilized to introduce titanium nitride (TiN) particles into an AISI 316L steel melt to refine the as-cast grain structure during solidification. The design of the experimental melt treatments and grain refining additions was performed using thermodynamic simulations. The first inoculation method is based on in situ formation of heterogeneous nuclei by TiN co-precipitation on preexisting Mg–Al spinel inclusions. This method included a two-stage melt treatment using spinel forming additions followed by an addition of titanium in the ladle just prior to pouring. The second inoculation method used a newly developed master alloy that contains TiN precipitates which was added in the ladle during furnace tapping. In this method, protective conditions to prevent full dissolution of the TiN nuclei before the onset of solidification were determined by thermodynamic simulations. Grain refinement of the cast macrostructure was observed with both methods. The in situ method provided finer equiaxed grains than the master alloy method, while a thicker zone with columnar grains next to the chill was observed. A scanning electron microscope (SEM) with automated feature analysis was used to quantify the resulting inclusions. The master alloy method eliminated the need for spinel, gave better control of the amount and size of heterogeneous nuclei, and reduced clustering tendency in comparison with the in situ method. However, the in situ formed nuclei method is more effective to refine grain size. The effects of contact angle and nuclei surface geometry on the activity of heterogeneous nucleation were discussed. It is proposed that clustering TiN particles provides numerous sharp, concave corners which favors the heterogeneous nucleation of austenite grains. This is illustrated by SEM images of extracted TiN particles and electron backscatter diffraction analysis of grain orientation.