Section Curves Research Articles

CFD Optimisation of the Longitudinal Volume Distribution of a Ship’s Hull by Constrained Transformation of the Sectional Area Curve

Abstract The paper presents a proposal for a formalised approach to hull shape optimisation with respect to total resistance, by fine-tuning longitudinal volume distribution. An algorithm for automated modification of the hull is presented, allowing for varying the sectional area distribution with a negligible influence on the resulting displacement. Computational fluid dynamics (CFD) solver STAR-CCM+ and computer computer-aided design (CAD) software NX were used to search the optimal volume distribution of selected parent shapes, with respect to total resistance. The bow part and the aft part were optimised separately. The resulting resistances of the selected optimal shapes were then verified by means of scale model tests, realised in the towing tank at the Maritime Advanced Research Centre (CTO) S.A. A noticeable gain in total resistance was achieved and confirmed by experimental tests. The proposed approach seems to be a promising method for relatively quick parametric optimisation of the designed hull shapes; it is also applicable for generic CFD optimisation studies.

An unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulations

The thoracic diaphragm is the muscle that drives the respiratory cycle of a human being. Using a system of partial differential equations (PDEs) that models linear elasticity we compute displacements and stresses in a two-dimensional cross section of the diaphragm in its contracted state. The boundary data consists of a mix of displacement and traction conditions. If these are imposed as they are, and the conditions are not compatible, this leads to reduced smoothness of the solution. Therefore, the boundary data is first smoothed using the least-squares radial basis function generated finite difference (RBF-FD) framework. Then the boundary conditions are reformulated as a Robin boundary condition with smooth coefficients. The same framework is also used to approximate the boundary curve of the diaphragm cross section based on data obtained from a slice of a computed tomography (CT) scan. To solve the PDE we employ the unfitted least-squares RBF-FD method. This makes it easier to handle the geometry of the diaphragm, which is thin and non-convex. We show numerically that our solution converges with high-order towards a finite element solution evaluated on a fine grid. Through this simplified numerical model we also gain an insight into the challenges associated with the diaphragm geometry and the boundary conditions before approaching a more complex three-dimensional model.

Analysis of probability matrix model for seismic damage vulnerability of highway bridges

The present study was aimed at assessing more accurately the seismic vulnerability and performance of highway bridges in an earthquake-damaged area. Based on mathematical statistics (data collection) and a probability model, (i) survey data for 2134 bridges in 22 highway sections (47 sub-sections) affected by the Wenchuan earthquake on May 12, 2008 were obtained and analysed, (ii) Gaussian and exponential regression models were developed, (iii) the empirical seismic-damage vulnerability function, plane, surface and curve model of the 22 highway sections with sample number and failure ratio were established, and (iv) a regression parameter matrix was constructed considering the empirical seismic-damage data. Using the method of probability exceedance, the bridge vulnerability curve models considering the seismic-damage exceedance probability of each section were analysed, and a parameter matrix model (mean seismic-damage index) was proposed to evaluate and predict the seismic vulnerability of regional bridges. Based on creating the actual seismic-damage sample database, vulnerability point-cloud models of the 22 highway bridges were constructed, and the vulnerability probability matrix, function, curve and point-cloud model of each highway section can be used to evaluate and estimate the vulnerability of regional bridges in the future.

Micro Aspheric Convex Lenses Fabricated by Precise Scraping.

An easy, fast, inexpensive, and simple method utilizing a microshaper with a very small knife nose is used to fabricate microconvex aspherical lenses. The microshaper is mounted on a computer numerical control (CNC) machine. To achieve an accurately designed profile of the lens surface, a cutter-path planning algorithm with compensation for knife interference is developed. Exerting this algorithm in CNC machining, the microconvex aspheric surface is precisely scraped. To verify the precise machining of the cutter path planning algorithm, three aspheric surfaces of conic sections (ellipsoid, paraboloid, and hyperboloid) are successfully fabricated. The profiles scraped by the microshaper agree well and precisely with the designed theoretical conic section curve. Using a simple polishing method to make the machined surface smoother, the roughness is reduced from 143 and 346 nm to 52 and 44 nm for the path line direction and its transverse direction, respectively. The micro-aspherical lenses have moderate machining properties using a simple polishing method. The results show that the designed profiles of micro-aspheric convex lenses can be machined precisely and efficiently by the microshaper with the cutter-path planning algorithm developed in this work. From the image comparison formed by the aspherical and spherical microlenses, the aspherical lenses provide a better image. It is feasible that the designed profile of the micro-aspherical lenses with specific functions could be machined using the cutter-path planning algorithm developed in this work.

Relevant integrals of NURBS and its application in hull line element design

NURBS are a powerful mathematical tool for representing free-form curves and surfaces and have been the international industrial standards for the representation, design, data exchange of geometric information. In this paper, starting from the NURBS matrix form, a piecewise-integration is used to derive the formula of relevant integrals of NURBS curve based on the properties of NURBS. A benefit of matrix representation for NURBS is that the explicit mathematical expression of each curve segment is obtained. The area and perimeter of a circle and an ellipse are evaluated from the matrix representation for NURBS. The integrand function from the matrix is solved by composite Newton-Cotes formula and composite Gauss-Legendre formula respectively and the relative error is evaluated with the analytical solution. Results show that three-point composite Gauss-Legendre rule has fast convergence, high accuracy and low evaluation cost. Subsequently, the formula of relevant integrals of NURBS curve is applied to the hull line elements. Taking the hull sectional area curve (SAC) as an example, the evaluation of prismatic coefficient (CP) and longitudinal center of buoyancy (LCB) is carried out; taking the design waterline (DWL) as an example, the evaluation of waterplane coefficient (CW) and transverse center of floation (Xf) is carried out; taking the middle cross section as an example, the evaluation of midship section area coefficient (CM) is carried out. Finally, taking the revolution as an example, the surface area and volume are evaluated. Through these real ship examples, the effectiveness and universality of the engineering application in hull line element design are verified.

An accurate calculation method of side mill profile from the coordinates of discrete points of helicoid section curve

An accurate calculation method of side mill profile from the coordinates of discrete points of helicoid section curve

An SRAM SEU Cross Section Curve Physics Model

Static random access memories (SRAMs) are prone to a single-event upset (SEU), also known as soft errors, due to transient noise caused by a single strike of radiation. Beam testing has been extensively used to measure the SEU cross section of SRAMs as a function of the linear energy transfer (LET) of charged particle radiation. The evolution of the cross section as a function of LET is called the cross section curve, which plays a vital role in upset rate analysis for hardness assurance. Various analytical models have been developed to describe SRAM SEU cross-section curves, and they have proven to be useful in reducing the cost of beam testing as well as revealing the physics behind test results. However, they involve arbitrary parameters, which make it challenging to predict cross-section curves without any beam results. Moreover, the current method of analyzing cross-section curves or the LET dependence of cross sections relies on a model different from that is used in the analysis of power-supply-voltage dependence, which is becoming increasingly important because of the demand for low-power operation. To overcome these problems, this paper proposes a unified equation that describes both LET and the power-supply-voltage dependence of SRAM SEU cross sections. It comprises only parameters that are physically clear and familiar to SEU researchers. As well as giving possible constraints, comparisons with data from the literature suggest it can be applied to SRAMs fabricated in bulk and silicon-on-insulator (SOI) processes across generations from the early 1000-nm-scale to the current 10-nm-scale technology nodes.

Hull Form Optimization Study Based on Multiple Parametric Modification Curves and Free Surface Reynolds-Averaged Navier–Stokes (RANS) Solver

In this study, the hull form optimization process to minimize resistance of KCS (KRISO containership) at Fn=0.26 is described. The bow hull form of KCS was modified by varying such design parameters as sectional area curve (SAC), section shape, bulb breadth, and bulb height using multiple parametric modification curves devised by the authors. The resistance performances of modified hull forms were analysed by the viscous flow Reynolds-Averaged Navier–Stokes (RANS) solver of WAVIS ver.2.2. With a view to saving computational time during iterative analyses in the optimization process, the sinkage and trim were set to the fixed values which had been obtained for the original hull form with free condition. The validity of such constant sinkage/trim was then verified by conducting analysis for the optimal hull form with free condition. Optimization to minimize the cost function of the total resistance coefficient of model CTM was performed by sequential quadratic programming (SQP), which is one of the gradient-based local optimization methods. Utilization of parallel computing led to the simultaneous calculation of the gradient, thereby speeding up the whole optimization process. At the design speed of 24 knots, the optimal hull yielded CTM reduction by 1.8%, which is extrapolated to 3.1% reduction of effective power PE in full scale.

3D Modelling with C2 Continuous PDE Surface Patches

In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly.

A novel model reconstruction strategy for polishing turbine blade based on position optimization of sectional curve

A novel model reconstruction strategy for polishing turbine blade based on position optimization of sectional curve

Method for shield tunnel cross-section curve reconstruction based on FBG sensors and neural network

To improve the accuracy of reconstructing morphology in shield tunnel monitoring by fiber-optic Bragg grating (FBG) sensors, a Transformer network-based optimized tunnel cross-sectional curve reconstruction method is proposed to solve the problem of low reconstruction accuracy due to the cumulative error of discrete curvature points. In this research, the optimization method uses all interpolation points as initial points to minimize the cumulative error in fitting the curve with discrete curvature points. Simulation model experiments of the shield tunnel were carried out to verify the accuracy of the optimization method in reconstructing the tunnel section curve. The results show that the shield tunnel simulation model experiments, more accurate tunnel section reconstruction curves were obtained using this optimization method, increasing reconstruction accuracy by 27.3424%.

Evaluation of Pavement Runoff and Driving Safety on Highway Curve Segment

Runoff depth distribution on the concave and circular curve sections is obtained from a two-dimensional numerical simulating model in order to analyze the temporal and spatial variation of the pavement runoff on the curve section. The two-dimensional model verified by the field data can depict the alignment of pavement more accurately as compared to the empirical equation and a one-dimensional model. The runoff on the concave section and circular curve section is compared for the free water drainage and centerline drainage. Results show that a two-dimensional model is essential for the analysis of the centerline drainage. The runoff depth can be controlled by a reasonable curb height and location interval. The drainage type affects the variation of the runoff depth on the nearside lane, and the maximum water depth can be up to more than 80 mm on the concave section and nearly 60 mm on the circular curve section under centerline drainage. Besides the existing hydroplaning results, the runoff depth difference of the wheel trace should be considered to evaluate driving safety. Sideslip will occur when the depth difference becomes more than 6 mm under condition that the runoff depth is less than the tread depth (7 mm). When the runoff depth is more than the tread depth, sideslip will occur once the depth difference exceeds 4 mm.

Simulation and Optimization of the Nozzle Section Geometry for a Suspension Abrasive Water Jet

In order to improve the life cycle and cutting ability of a suspension abrasive water jet nozzle at the same time, hydrodynamics technology, an enumeration method and multiparameter orthogonal optimization are used to optimize the nozzle section geometry, taking the inlet diameter coefficient of the nozzle, the axial length coefficient of the contraction section and the contraction section curve as optimization variables, and selecting the peak velocity and the unit flow erosion rate as the indicators, it is concluded that the optimal contraction section curve is a Widosinski curve, the optimal inlet diameter coefficient of the nozzle is 0.333 and the optimal axial length coefficient of the contraction section is 2.857. Compared with the commercial product single cone nozzle, the performance of the optimal section nozzle improves by 5.64% and the life cycle increases by 43.2%. On this basis, the effects of operating parameters, including inlet pressure, abrasive particle flow rate and abrasive particle size, are further studied. It is determined that the optimal section nozzle has the best performance under the above operating parameters. It is demonstrated that by optimizing the nozzle section geometry, the cutting capacity and life cycle of the nozzle are improved, the performance of the nozzle can be significantly improved and the optimization of the performance of the nozzle is realized.

Impacts of structural parameters of baffle plate on jetting pigging robot in the underwater oil and gas pipeline

During the operation of oil and gas transportation pipeline, condensate forms on the inner wall of the pipeline can lead to reduced transportation efficiency and potential safety hazards. Pigging is a widely used technology to remove deposition in pipelines. From the studies, it is found that the effect of pigging largely depends on the structure of the pig. The jetting pig is a new type of pigging device designed to prevent the blocking in the pigging process, and its baffles play an important role in guiding the jet fluid. In this paper, the impact of the structure of the baffle plate on the downstream flow field of the jetting pig is simulated and analyzed. The surface of the baffle plate is changed by using the curve of the contraction section of the water tunnel. It is found that the baffle plate structure has a great influence on the flow field at the outlet of the jet pig: (1) The increase of buffle area leads to the increase of turbulent kinetic energy and the decrease of velocity; (2) The rise of edge angle lead to the regular change of turbulent kinetic energy; (3) Different curved surfaces make the change of turbulent kinetic energy and velocity. The results in this study are helpful for a better understanding of mechanism of jetting pig and improved design of mechanical structure for improved pigging performance.

Impacts of point cloud density reductions on extracting road geometric features from mobile LiDAR data

The variation in point cloud density is driven by many different factors. This variation is expected to affect the quality of the information extracted from the point clouds, however, the extent to which these variations impact the ability to accurately extract and assess geometric features of highways from point cloud data are unknown. This paper investigates the impacts of point density reduction on the extraction and assessment of four critical geometric features. The density of light detection and ranging (LiDAR) data was first reduced and the different features were extracted at varying levels of point density and on a selection of different highway segments in Alberta, Canada. The information obtained at lower point density was then compared to what was obtained at 100% point density. It was found that clearance assessments and sight distance assessments had low sensitivity to reductions in point density (i.e., reducing the point density to as low as 10% of the original data (30 ppm2 on the pavement surface) yielded results comparable to what was obtained at 100% density (300 ppm2) In contrast, for cross section slope estimation and curve attribute estimation higher sensitivity to point density was observed. These findings are critical for transportation agencies considering the adoption of LiDAR technology to manage elements of their infrastructure and for researchers developing data processing tools and algorithms for the semantic segmentation of transportation features from remotely sensed point clouds.

Fully relativistic study on electron impact elastic scattering from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), and Xeq+ (q = 2–6, 8)

AbstractA study is presented on the elastic scattering of electrons from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), Xeq+ (q = 2–6, 8) to understand the available experimental differential cross section results. A model potential approach has been utilized to describe the scattering process. The model potential includes the static, exchange, polarization and absorption potentials. The static potentialis obtained through the charge density calculated by obtaining ionic wave functions using multi‐configuration Dirac‐Fock (MCDF) approximation. Thereafter, the static potential is added to the suitable exchange, polarisation and absorption potentials to construct the spherically averaged complex optical potential. Using the obtained potential in the Dirac equations,these are solved with the partial wave phase shift analysis method and the differential cross sections are calculated. Results for different ions exhibit prominent interference structures in the energy versus cross section curves and show good agreement on comparison with the experimental results available in the selected energy ranges.

Surface modification by superimposing piecewise shape function satisfying hull variation given by arbitrary characteristic curve on surface

Abstract The ship hull form is directly related to each design phase of a ship. This form is thus frequently designed based on a variation of a well-made parent ship to avoid new design risks. However, in hull form variation, satisfactory geometric preservation and good performance continuity of the parent ship are considered competing requirements. To effectively facilitate the variation, an appropriate compromise between these requirements should be achieved. Instead of altering hull form parameters, we propose a flexible and intuitive approach to interactively vary the hull surfaces with arbitrary curve constraints and to focus on preserving the properties of the original hull surface. The advantage of the superposition of the curve or surface is leveraged to modify the hull shape. An intermediate surface that satisfies an intermediate curve constraint and has a smooth shape is constructed and superimposed on the top of the original surface to yield the desired surface. A shape control mechanism using a shape function simplifies the control of the surface modification with a curve constraint. The developed method was applied to modify the characteristic curves and section curves situated on the stern part of a container vessel. The changes in the geometric shape and hydrodynamic performance due to the curve-constraint variation were assessed to demonstrate the practicality and efficiency of the proposed method. The results show that the proposed method produces a smooth shape and almost unchanging hydrodynamic patterns. The proposed variation provides an effective tool for varying the hull in a linear fashion.

An approximation method combined with conformal transformation for the fast measurement of blade section curves

To realize high-precision machining of free-form blade surfaces, it is necessary to measure and reconstruct the blade morphology several times. Sampling measurements and data compression through free-curve approximation technology are of great benefit in shortening the processing time. A novel B-spline approximation method is proposed in this paper, which can determine a few dominant points based on curvature characteristics to approximate dense and noisy measured points with high precision. We adopt a unique adaptive knot placement strategy combined with a curvature dependent evaluation parameter and a conformal transformation method. This strategy is error-bounded in the initial knot placement, which greatly reduces the time consumed by subsequent iterative insertions. The proposed method shows advantages in approximation accuracy, compression rate, and especially in computational efficiency, in comparison with four traditional knot placement methods. Experiments were carried out and the results show that the dominant point selected by this method can replace the fine measurement results, and the compression rate of the measurement points can reach more than 90%. This method is suitable for the sampling measurement and compression of the data of blades, aircraft wings, and other similar free-form surfaces, and is especially suitable for solving the inefficiency problem caused by repeated measurements made in the process of iterative machining of aero-engine blades.

Photoionization Cross Section of the NH2 Free Radical in the 11.1-15.7 eV Energy Range.

The NH2 radical is a key component in many astrophysical environments, both in its neutral and cationic forms, being involved in the formation of complex N-bearing species. To gain insight into the photochemical processes into which it operates and to model accurately the ensuing chemical networks, the knowledge of its photoionization efficiency is required, but no quantitative determination has been carried out so far. Combining a flow-tube H-abstraction radical source, a double imaging photoelectron-photoion spectrometer, and a vacuum-ultraviolet synchrotron excitation, the absolute photoionization cross section of the amino radical has been measured in the present work for the first time at two photon energies: σionNH2(12.7 eV) = 7.8 ± 2.2 Mb and σionNH2(13.2 eV) = 7.8 ± 2.0 Mb. These values have been employed to scale the total ion yield previously recorded by Gibson et al. ( J. Chem. Phys. 1985, 83, 4319-4328). The resulting cross section curve spanning the 11.1-15.7 eV energy range will help in refining the current astrophysical models.

Offset approximation of polygons on an ellipsoid

We present an approximation method for offset curves of polygons on an oblate ellipsoid using implicit algebraic surfaces. The polygon on the ellipsoid is given by a set of vertices, i.e. points on the ellipsoid. The edges are the shortest geodesic paths connecting two consecutive points. The offset curve of the polygon consists of two parts. The offset curve of an edge is the set of points that are at the same distance from each point on the edge, in the normal direction of the edge. The offset curve of a vertex is the set of points that are at the same geodesic distance from the vertex. Our offset approximation method uses plane section curves for offset curves of edges and prolate ellipsoids for offset curves of vertices. Since our offset approximation curve is constructed from implicit algebraic surfaces, it is easy to check whether a given point on the oblate ellipsoid has intruded into the inside of the offset curve. Moreover our method achieves extremely small approximation errors. We apply our method to numerical examples on the Earth.