Surface Curvature Distribution Research Articles

Investigation of surface curvature distribution characteristic on the mechanical properties of 3D printed lattice structures

Investigation of surface curvature distribution characteristic on the mechanical properties of 3D printed lattice structures

Influence of curvature distribution smoothing on the reduction of aerofoil self-noise

PurposeThis paper aims to investigate the influence of smooth curvature distributions on the self-noise of a low Reynolds number aerofoil and to unveil the flow mechanisms in the phenomenon.Design/methodology/approachIn this paper, large Eddy simulation (LES) approach was performed to investigate the unsteady aerodynamic performance of both the original aerofoil E387 and the redesigned aerofoil A7 in a time-dependent study of boundary layer characteristics at Reynolds number 100,000 and angle of attack (AoA) 4-degree. The aerofoil A7 is redesigned from E387 by removing the irregularities in the surface curvature distributions and keeping a nearly identical geometry. Flow vorticity magnitude of both aerofoils, along with the spectra of the vertical fluctuating velocity component and noise level, are analysed to demonstrate the bubble flapping process near the trailing edge (TE) and the vortex shedding phenomenon.FindingsThis paper provides quantitative insights about how the flapping process of the laminar separation bubble (LSB) within the boundary layer near the TE affects the aerofoil self-noise. It is found that the aerofoil A7 with smooth curvature distributions presents a 10% smaller LSB compared to the aerofoil E387 at Reynolds number 100,000 and AoA 4-degree. The LES results also suggest that curvature distribution smoothing leads to a 6.5% reduction in overall broadband noise level.Originality/valueThis paper fulfils an identified need to reveal the unknown flow structure and the boundary layer characteristics that resulted in the self-noise reduction phenomenon yielded by curvature distribution smoothing.

Experimental and Numerical Study on the Performance of Double Membrane Wing for Long-Endurance Low-Speed Aircraft

Flexible membrane structure is generally used as wing skin for long-endurance low-speed aircraft, such as solar aircraft, to control the structure weight within the allowable range. Predictably, the elastic deformation of the membrane under complex loads will cause uncertain impacts on the aerodynamic performance. The existing research indicates that the deformation of the membrane wing is helpful to improve the aerodynamic characteristics. However, most of the research objects are non-thickness membrane wings. In this paper, wind tunnel experiments are performed on double membrane wings. The experiment results indicate that the membrane deformation behavior is related to the surface curvature distribution and will change the camber and thickness of the airfoil. The deformation has little effect on lift but has a significant effect on drag and pitching moment. On this basis, a high-precision fluid structure coupling analysis method for the wider range of research is introduced. The numerical analysis indicates that the deformation can delay the stall angle by 1°. Furthermore, based on the numerical results, suggestions on prestress setting during membrane skin laying are provided, and the numerical simulation results of two flexible skin wings are compared. The research results of this paper provide a scientific basis for the aerodynamic design and analysis of long-endurance low-speed aircraft.

An attempt to predict spray characteristics at early stage of the atomization process by using surface density and curvature distribution

Nowadays, numerical simulations of atomization has reached a mature state through interface capturing approaches. With these approaches, the liquid–gas flow with its complex interface morphology can be precisely described but at the price of high mesh resolution, that makes these simulations very intensive in terms of computational cost. Practically, for most of the injection system, it is not possible to achieve a simulation up to a point where the spray formation is completed. Thus, there are several attempts based on the transformation of liquid elements such as ligaments, liquid sheet or other non-spherical to equivalent droplets. Overall, these approaches assumed that before the complete finalization of the atomization process the spray under formation carries enough information to be representative of the final spray. In this work, we have pushed this idea a step further by using global variables such as the liquid volume fraction and the surface density available in ELSA models to ensure the transports and the conservation of the main features of the spray. Then, the surface curvature distribution is analysed assuming that a part of the interface carries already curvatures that are relevant with respect to the final spray. A well-known academic test case representative of an aeronautical injection system and based on a planar prefilmer atomizer with a gas co-flow has been selected to evaluate our proposal. This configuration was studied both experimentally and numerically thanks to high-fidelity simulations. Our purpose has been to follow the already validated numerical approaches but with less computationally intensive simulations. Then, new analysis based on surface density and surface curvature distribution have been tested to recover spray characteristics and even the spray diameter distribution. It appears that these variables are meaningful even when there is no droplet yet formed, and thus they allow the description of the full atomization process from the early stage even on the liquid film. Finally, a procedure has been proposed where the spray is sufficiently atomized to reconstruct the diameter distribution from the curvature distribution. At our best knowledge, this last step is a first attempt on practical injection system. We have proposed a very simple method to detect which part of the interface carries the relevant curvature, thus obtaining a reconstructed diameter distribution that fit well with available experimental data. Although the proposed approach cannot be still considered universally applicable to any case, this preliminary assessment clearly shows its potential.

A Comparative Study on Asperity Peak Modeling Methods

The peak identification scheme based method (three-point definition) and the spectral moments based method (spectral moment approach) are both widely used for asperity peak modeling in tribology. To discover the differences between the two methods, a great number of rough surface profile samples with various statistical distributions are first randomly generated using FFT. Then the distribution parameters of asperity peaks are calculated for the generated samples with both methods. The obtained results are compared and verified by experiment. The variation rules of the differences between the two methods with statistical characteristics of rough surfaces are investigated. To explain for the discovered differences, the assumptions by spectral moment approach that the joint distribution of surface height, slope and curvature is normal and that the height distribution of asperities is Gaussian, are examined. The results show that it is unreasonable to assume a joint normal distribution without inspecting the correlation pattern of [z], [z′] and [z′′], and that the height distribution of asperities is not exactly Gaussian before correlation length of rough surface increases to a certain extent, 20 for instance.

Prompt Estimation of Die and Mold Machining Time by AI Without NC Program

Machining time estimation is essential for the due-date estimation of products as well as for production planning. Conventionally, machining time has been estimated by a computer aided manufacturing (CAM) system, which requires time and effort to create its numerical control (NC) program and requires machining expertise to operate it. In addition, among the problems with conventional methods, an error in the estimated machining time arises owing to the machine tool’s control characteristics. In this study, an artificial intelligence (AI)-based system capable of estimating machining time promptly and simply based on shape data without requiring any NC program is developed. The input data to the AI system are color information regarding the machined depths, which are used to estimate the rough-machining time, and color information regarding the machined surface curvature distributions to estimate the finish-machining time. Color information on the machined depths and machined surface curvature distributions is created using three-dimensional computer aided design (3D CAD) data. To build the AI system, the shape data and machining time data accumulated at the machining site are used, so that the machining time estimated reflects the machining method, machining expertise, and the machine tool characteristics employed.

Gaussian Surface Curvature Mapping Indicating High Risk Type B Thoracic Aortic Dissections

Identifying fragile aortas that are more likely to lead to adverse clinical outcomes would provide surgeons with a better sense of how to balance the risks of surgical versus medical management in patients with type B dissections. We examine the progression of a type B dissection into a type A dissection in a patient and analyze changes in the Gaussian surface curvature distribution, as well as the response of the stress distribution at the lesser curve in response to pressurization. We hypothesize that examining the Gaussian curvature will provide us with a link between aortic surface geometry and the stress distribution, which is crucial to understanding the process driving aortic dissection. Computed tomography scans of a patient before and after the type A dissection are obtained. These are segmented in Simpleware ScanIP. Centerline curvatures are calculated on segmented models in ScanIP. Models are then pressurized in the finite element analysis software Abaqus. The Gaussian curvature is calculated by exporting segmentations into the computational program Matlab and applying a modified previously published algorithm. The centerlines generated in ScanIP fail to capture the change in the acuity of the lesser curve before and after the type A dissection. Instead, Gaussian curvature analysis shows that the curvature distribution before the type A dissection is much wider compared with the distribution after the type A dissection. In addition, analyzing the stress distribution in response to pressurization reveals that before the type A dissection there is a large divergence in the principal stress vectors at the lesser curve but this transitions to a more uniform hoop stress after the type A dissection. Our analysis demonstrates that Gaussian surface curvature analysis captures changes in aortic geometry that are otherwise silent in centerline curvature analysis. Here, we show that as the aorta develops a type A dissection it is able to more smoothly handle the hoop stress at the lesser curve compared with the stress focusing seen in the before type A geometry. We propose that the geometric focusing before type A creates a higher energy stress state, which is relaxed on retrograde dissection. Thus, Gaussian curvature analysis may provide a window to capture underlying geometric instability in type B dissections.

A Method for Parametrically Representing the Aerodynamic Profiles of Axial Turbine Machinery Blades

A parametric method for designing the cross sections of axial turbine machinery blade airfoils is described. Analytical Bezier curves are used for representing the profile generatrices and the skeleton line. Their shapes are uniquely determined by a set of 13 parameters that are related to the turbine cascade’s aerodynamic and strength characteristics. These parameters determine the main points through which the profile generatrices must pass at the specified tangent line angles. In general terms, the blade shape’s design calculation involves the following sequential stages: calculating the geometrical constraints based on 13 parameters, determining the skeleton line shape, and calculating the profile suction and pressure sides. By using the proposed method, it is possible to control the blade shape taking into account the imposed geometrical conditions, including the surface curvature distributions. A distinguishing feature of the proposed method is its adaptability: the degree of Bezier curves is determined during calculation by means of multidimensional minimization. This feature imparts flexibility to the method in terms of the possibility to specify the parameters in wide ranges of their values, thus making the method versatile in nature. An algorithm for iteratively determining the curve shape through calculating the skeleton line is presented. The proposed approach is supplemented by a procedure for automatically parameterizing the profiles specified as unevenly distributed point-wise coordinates of their generatrices. This opens up the possibility to represent the already existing blade shapes in the form of 13 parameters and to optimize them.

Biological and mechanical property analysis for designed heterogeneous porous scaffolds based on the refined TPMS

For tissue engineering (TE), triply periodic minimal surfaces (TPMSs) have received widespread application, as they produce smooth surfaces and pore interconnectivity, which can satisfy the biological/mechanical requirements and efficiently construct many complex bone scaffolds. To control the microstructure of the scaffold and mimic the anisotropy of native tissue, a design approach for heterogeneous porous scaffolds is proposed in this paper. It is carried out by discretizing the original model using the conformal refinement of an all-hexahedral mesh and mapping the TPMS units to the mesh elements with the help of a shape function. Another aim of this work is to assess the impact on the biologic/mechanical properties of the model, as it is discretized with different mesh patterns. It is found that the mesh pattern has a non-obvious effect on the surface curvature distribution that is a crucial factor to osteoblast proliferation in the TPMS scaffold. Nevertheless, the comparison presents that the mechanical properties of the refined scaffolds model exhibited anisotropy and improvements in elasticity, strengths, and especially energy absorption. With the help of conformal remeshing, the local density of architecture can be conveniently controlled and the elastic modulus of scaffold can be designed to the appropriate range in a specified area in order to mimic the actual cancellous bone.

Analysis of pressure distribution during movement for the top part of female socks

Female sports socks were studied to achieve the correlation between the ankle surface curvature and pressure distribution of the top part of socks. The transverse tension performance of the socks’ top part was obtained using an Instron universal strength tester, and the leg size was measured with a [TC]2 contactless 3D body scanner. The pressure was monitored by a Pliance-X-32 pressure test system. Gray correlation, variance, and regression analysis were applied to study the correlation between movement velocity, fabric performance, leg circumference, and ankle pressure distribution. The dynamic pressure prediction models of multiple regression and back propagation (BP) neural network on the top part of socks were also established. The results show that the transverse tension performance and sock density have a significant effect on the ankle static pressure. Movement velocity, sock density, and leg circumference are positively correlated with dynamic pressure, while the elastic recovery rate of the fabric is negatively correlated with the pressure. Both of the multiple regression and BP neural network models can predict the dynamic pressure, and the BP neural network model is better than multiple regression at prediction error, which was kept to less than 0.5%. Therefore, the BP neural network model can be effectively used in female ribbed sock top design.

Breast-Shape Classification and Implant Construction Method for Unilateral Breast Reconstruction

Unilateral breast reconstruction is different from bilateral breast reconstruction and breast augmentation, as it requires more consideration of the symmetry between the reconstructed breast and the contralateral breast. However, there are currently no implants specifically targeted to unilateral breast reconstruction, nor is there is objective classification criteria for breast appearance type. A total of 212 breasts from 153 patients were measured. Breast measurements, breast surface curvature distributions, and elliptic Fourier coefficients were used to describe breast features. We objectively classified the appearance of breasts using machine learning and used the resulting cluster centers to construct the most adaptive implants for each type of breast. All of the breasts clustered into 4 types. The implants corresponding to each type of breast were constructed using cluster centers. The resulting cluster centers were then used to choose a suitable implant for patients requiring unilateral breast reconstruction. Contour coefficients were used to evaluate the clustering results, with an average score of 0.53. The two breasts that develop normally in the same person were treated as the same class. The score obtained after statistical classification was 0.47. These results demonstrate that our proposed method can improve the classification of breasts of different shapes. This method provides a foundation for improving the symmetry of unilateral breast reconstruction and the construction and selection of implants.

Where does the droplet size distribution come from?

This study employs DNS of two-phase flows to enhance primary atomization understanding and modeling to be used in numerical simulation in RANS or LES framework. In particular, the work has been aimed at improving the information on the liquid-gas interface evolution for modeling approaches, such as the Eulerian–Lagrangian Spray Atomization (ELSA) framework. Even though this approach has been already successfully employed to describe the complete liquid atomization process from the primary region to the dilute spray, improvements are still expected on the derivation of the drop size distribution (DSD). The main aim of the present work is the introduction of a new framework to achieve a continuous description of the DSD formation during the atomization process. The attention is here focused on the extraction from DNS data of the behavior of geometrical variable of the liquid-gas interface, such as the mean (H) and Gauss (G) surface curvatures. The use of a Surface Curvature Distribution is also proposed and studied.A Rayleigh–Plateau instability along a column of liquid and a droplet collision case are first of all considered to analyze and to verify the capabilities of the code to correctly predicting the curvature distributions. A statistical analysis based on the curvatures data, in terms of probability density function, is presented in order to determine the physical parameters that control the curvatures on this test case. Then, the same formulation is applied in the analysis of the two phase Homogeneous Isotropic Turbulence (HIT) configuration to study how the curvatures evolve all along the atomization process. Joint PDFs are used to illustrate the topological changes of the interface when increasing the liquid volume fraction.

Morphological similarity and structure-dependent scaling laws of nanoporous gold from different synthesis methods

Application of the foam scaling laws to the mechanical properties of nanoporous gold (np-Au) implicitly assumes geometrical similarity of structures of different relative density and synthesis methods. While the very few studies addressing the issue of geometric similarity during thermal coarsening show contradicting results, there are no studies covering np-Au from different synthesis routes. This paper performs quantitative morphological and topological comparison of np-Au of ca. 30% relative density synthesized by free and electrochemical corrosion methods, and thermally coarsened samples. Nanoindentation tests were performed to obtain elastic modulus and hardness. Uniaxial compression simulations of three-dimensional structures from FIB-nanotomography have been conducted using finite element analysis, and the results are compared with experiments. The three-dimensional np-Au structure has been quantified in terms of the ligament diameter and length distributions, ligament tortuosity, surface curvature distributions, structural anisotropy, nodal connectivity, and genus. Our results suggest that neither the synthesis route nor the thermal coarsening, to change length scale by up to a factor of 3, significantly altered the morphology and topology. The modulus and strength from both experiment and simulations exhibit a linear dependency on the scaled genus density, modifying the geometry-dependent prefactors in the Gibson and Ashby scaling relations.

Surface curvature effects on the tonal noise performance of a low Reynolds number aerofoil

This paper presents wind tunnel experiments to illustrate the effects of surface curvature on the aeroacoustic performance of airfoil E387. For the first time, surface curvature effects are considered in an investigation of the airfoil’s self-noise. To distinguish the effects of surface curvature, the CIRCLE method is applied to the airfoil E387 to remove slope-of-curvature discontinuities and the redesigned airfoil is denoted A7. Anechoic wind tunnel tests were performed with E387 and A7 at three low Reynolds numbers to investigate aeroacoustic performance by measuring airfoil self-noise at different angles of attack (AoA) and spatial positions. At 2° and 4° AoA, A7 presents a tone with a reduced amplitude compared with E387 due to its improved slope-of-curvature distribution. It is concluded that improving surface curvature distribution improves airfoil aeroacoustic performance.

Surface curvature in triply-periodic minimal surface architectures as a distinct design parameter in preparing advanced tissue engineering scaffolds

Reproduction of the anatomical structures and functions of tissues using cells and designed 3D scaffolds is an ongoing challenge. For this, scaffolds with appropriate biomorphic surfaces promoting cell attachment, proliferation and differentiation are needed. In this study, eight triply-periodic minimal surface (TPMS)-based scaffolds were designed using specific trigonometric equations, providing the same porosity and the same number of unit cells, while presenting different surface curvatures. The scaffolds were fabricated by stereolithography using a photocurable resin based on the biocompatible, biodegradable and rubber-like material, poly(trimethylene carbonate) (PTMC). A numerical approach was developed to calculate the surface curvature distributions of the TPMS architectures. Moreover, the scaffolds were characterized by scanning electron microscopy, micro-computed tomography and water permeability measurements. These original scaffold architectures will be helpful to decipher the biofunctional role of the surface curvature of scaffolds intended for tissue engineering applications.

Computational methods for investigation of surface curvature effects on airfoil boundary layer behavior

This article presents computational algorithms for the design, analysis, and optimization of airfoil aerodynamic performance. The prescribed surface curvature distribution blade design (CIRCLE) method is applied to a symmetrical airfoil NACA0012 and a non-symmetrical airfoil E387 to remove their surface curvature and slope-of-curvature discontinuities. Computational fluid dynamics analysis is used to investigate the effects of curvature distribution on aerodynamic performance of the original and modified airfoils. An inviscid–viscid interaction scheme is introduced to predict the positions of laminar separation bubbles. The results are compared with experimental data obtained from tests on the original airfoil geometry. The computed aerodynamic advantages of the modified airfoils are analyzed in different operating conditions. The leading edge singularity of NACA0012 is removed and it is shown that the surface curvature discontinuity affects aerodynamic performance near the stalling angle of attack. The discontinuous slope-of-curvature distribution of E387 results in a larger laminar separation bubble at lower angles of attack and lower Reynolds numbers. It also affects the inherent performance of the airfoil at higher Reynolds numbers. It is shown that at relatively high angles of attack, a continuous slope-of-curvature distribution reduces the skin friction by suppressing both laminar and turbulent separation, and by delaying laminar-turbulent transition. It is concluded that the surface curvature distribution has significant effects on the boundary layer behavior and consequently an improved curvature distribution will lead to higher aerodynamic efficiency.

Experimental study of surface curvature effects on aerodynamic performance of a low Reynolds number airfoil for use in small wind turbines

This paper presents the wind tunnel experimental results to investigate the effects of surface gradient-of-curvature on aerodynamic performance of a low Reynolds number airfoil Eppler 387 for use in small-scale wind turbines. The prescribed surface curvature distribution blade design method is applied to the airfoil E387 to remove the gradient-of-curvature discontinuities and the redesigned airfoil is denoted as A7. Both airfoils are manufactured with high precision to reflect the design. Low-speed wind tunnel experiments are conducted to both airfoils at chord based Reynolds numbers 100 000, 200 000, and 300 000. Surface pressure measurements are used to calculate the lift and pitching-moment data, and the wake survey method is applied to obtain the drag data. The experimental results of E387 are compared with NASA Low Turbulence Pressure Tunnel (LTPT) results for validation. The gradient-of-curvature discontinuities of E387 result in a larger laminar separation bubble which causes higher drag at lower angles of attack. As the angle of attack increases the separation bubble of the airfoil E387 moves faster towards the leading edge than that of A7, resulting in a premature bubble bursting and earlier stall on E387. The impact of the gradient-of-curvature distribution on the airfoil performance is more profound at higher angles of attack and lower Reynolds number. The aerodynamic improvements are integrated over the 3D geometry of a 3 kW small wind turbine, resulting in up to 10% increase in instantaneous power and 1.6% increase in annual energy production. It is experimentally concluded that an improved curvature distribution results in a better airfoil performance, leading to higher energy output efficiency.

Numerical Investigation of Surface Curvature Effects on Aerofoil Aerodynamic Performance

The prescribed surface curvature distribution blade design (CIRCLE) method optimises aerofoils and blades by controlling curvature continuity and slope of curvature distribution along their surfaces. The symmetrical NACA0012 exhibits a surface curvature discontinuity at the leading edge point, and the non-symmetrical E387 exhibits slope-of-curvature discontinuities in the surface. The CIRCLE method is applied to both aerofoils to remove both surface curvature and slope-of-curvature discontinuities. Computational fluid dynamics analyses are used to investigate the curvature effects on aerodynamic performance of the original and modified aerofoils. These results are compared with experimental data obtained from tests on the original aerofoil geometry. The computed aerodynamic advantages of the modified aerofoil are analysed in different operating conditions. The leading edge singularity of NACA0012 is removed and it is shown that the surface curvature discontinuity affects the aerodynamic performance near the stalling angle of attack. The discontinuous slope-of-curvature distribution of E387 influences the size of the laminar separation bubble at lower Reynolds numbers, and it affects the inherent profile of the aerofoil at higher Reynolds numbers. It is concluded that the surface curvature distribution of aerofoils has a significant effect on aerofoil aerodynamic performance, which can be improved by redesigning the surface curvature distribution of the original aerofoil geometry.

Axis estimation and grouping of rotationally symmetric object segments

This paper proposes a new method for estimating the symmetric axis of a pottery from its small fragment using surface geometry. Also, it provides a scheme for grouping such fragments into shape categories using distribution of surface curvature. For automatic assembly of pot from broken sherds, axis estimation is an important task and when a fragment is small, it is difficult to estimate axis orientation since it looks like a patch of a sphere and conventional methods mostly fail. But the proposed method provides fast and robust axis estimation by using multiple constraints. The computational cost is also too lowered. To estimate the symmetric axis, the proposed algorithm uses three constraints: (1) The curvature is constant on a circumference CH. (2) The curvature is invariant in any scale. (3) Also the principal curvatures does not vary on CH. CH is a planar circle which is one of all the possible circumferences of a pottery or sherd. A hypothesis test for axis is performed using maximum likelihood. The variance of curvature, multi-scale curvature and principal curvatures is computed in the likelihood function. We also show that the principal curvatures can be used for grouping of sherds. The grouping of sherds will reduce the computation significantly by omitting impossible configurations in broken pottery assembly process.

Two- and Three-Dimensional Prescribed Surface Curvature Distribution Blade Design (CIRCLE) Method for the Design of High Efficiency Turbines, Compressors, and Isolated Airfoils

The prescribed surface curvature distribution blade design (CIRCLE) method is presented for the design of two-dimensional (2D) and three-dimensional (3D) blades for axial compressors and turbines, and isolated blades or airfoils. The original axial turbine blade design method is improved, allowing it to use any leading-edge (LE) and trailing-edge (TE) shapes, such as circles and ellipses. The method to connect these LE and TE shapes to the remaining blade surfaces with curvature and slope of curvature continuity everywhere along the streamwise blade length, while concurrently overcoming the “wiggle” problems of higher-order polynomials is presented. This allows smooth surface pressure distributions, and easy integration of the CIRCLE method in heuristic blade-optimization methods. The method is further extended to 2D and 3D compressor blades and isolated airfoil geometries providing smooth variation of key blade parameters such as inlet and outlet flow angles, stagger angle, throat diameter, LE and TE radii, etc. from hub to tip. One sample 3D turbine blade geometry is presented. The efficacy of the method is examined by redesigning select blade geometries and numerically evaluating pressure-loss reduction at design and off-design conditions from the original blades: two typical 2D turbine blades; two typical 2D compressor blades; and one typical 2D isolated airfoil blade geometries are redesigned and evaluated with this method. Further extension of the method for centrifugal or mixed-flow impeller geometries is a coordinate transformation. It is concluded that the CIRCLE method is a robust tool for the design of high-efficiency turbomachinery blades.