Fairing-PIA: Progressive iterative approximation for fairing curve and surface generation

The fairing curves and surfaces are used extensively in geometric design, modeling, and industrial manufacturing. However, the majority of conventional fairing approaches, which lack sufficient parameters to improve fairness, are based on energy minimization problems. In this study, we develop a novel progressive-iterative approximation method for fairing curve and surface generation (fairing-PIA). Fairing-PIA is an iteration method that can generate a series of curves (surfaces) by adjusting the control points of B-spline curves (surfaces). In fairing-PIA, each control point is endowed with an individual weight. Thus, the fairing-PIA has many parameters to optimize the shapes of curves and surfaces. Not only a fairing curve (surface) can be generated globally through fairing-PIA, but also the curve (surface) can be improved locally. Moreover, we prove the convergence of the developed fairing-PIA and show that the conventional energy minimization fairing model is a special case of fairing-PIA. Finally, numerical examples indicate that the proposed method is effective and efficient.Comment: 21 pages, 10 figure

Polynomial-based non-uniform interpolatory subdivision with features control

Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that the most convenient parameter values may be chosen as well as the intervals for insertion. Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control

Analysis of flow and aerodynamic noise behaviour of a simplified high-speed train bogie inside the bogie cavity

Aerodynamic noise becomes significant for high-speed trains but its prediction in an industrial context is difficult. The flow and aerodynamic noise behaviour of a simplified high-speed train bogie at scale 1:10 are studied here through numerical simulations. The bogie is situated in the bogie cavity and cases without and with a fairing are considered, allowing the shielding effect of the bogie fairing on sound generation and radiation to be investigated. A two-stage hybrid method combining computational fluid dynamics and acoustic analogy is applied. The near-field unsteady flow is obtained by solving the unsteady three-dimensional Navier-Stokes equations numerically using delayed detached-eddy simulation and the data are utilized to predict far-field noise signals based on the Ffowcs Williams-Hawkings acoustic analogy. Results show that when the bogie is located inside the bogie cavity, the shear layer developed from the cavity leading edge interacts strongly with the flow separated from the bogie upstream components and the cavity wall. Therefore, a highly turbulent flow is generated within the bogie cavity due to flow impingement and recirculation within the cavity. It is found that, for noise calculated from the bogie surface sources of both cases, the directivity exhibits a lateral dipole pattern with dominant radiation in the axial direction. Compared with the no fairing case, the noise level is about 1 dB higher in the bogie symmetry plane along the axle mid-span for the fairing case where a stronger flow interaction is produced around the bogie central region. Moreover, the noise radiated to the trackside is predicted based on a permeable integration surface close to the bogie and parallel to the carbody side wall. The results show that the bogie fairing is effective in reducing the noise levels in most of the frequency range due to its shielding effect and a noise reduction around 3 dB is achieved for the current model case by mounting a fairing in the bogie area

Aerodynamic shape optimization of a low drag fairing for small livestock trailers

Small livestock trailers are commonly used to transport animals from farms to market within the United Kingdom. Due to the bluff nature of these vehicles there is great potential for reducing drag with a simple add-on fairing. This paper explores the feasibility of combining high-fidelity aerodynamic analysis, accurate metamodeling, and efficient optimization techniques to find an optimum fairing geometry which reduces drag, without significantly impairing internal ventilation. Airflow simulations were carried out using Computational Fluid Dynamics (CFD) to assess the performance of each fairing based on three design variables. A Moving Least Squares (MLS) metamodel was built on a fifty-point Optimal Latin Hypercube (OLH) Design of Experiments (DoE), where each point represented a different geometry configuration. Traditional optimization techniques were employed on the metamodel until an optimum geometrical configuration was found. This optimum design was tested using CFD and it matched closely to the metamodel prediction. Further, the drag reduction was measured at 14.4% on the trailer and 6.6% for the combined truck and trailer

Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.

Fast B-spline Curve Fitting by L-BFGS

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods

Aerodynamic analysis of hypersonic waverider aircraft

The purpose of this study is to validate two existing codes used by the Systems Analysis Branch at NASA ARC, and to modify the codes so they can be used to generate and analyze waverider aircraft at on-design and off-design conditions. To generate waverider configurations and perform the on-design analysis, the appropriately named Waverider code is used. The Waverider code is based on the Taylor-Maccoll equations. Validation is accomplished via a comparison with previously published results. The Waverider code is modified to incorporate a fairing to close off the base area of the waverider configuration. This creates a more realistic waverider. The Hypersonic Aircraft Vehicle Optimization Code (HAVOC) is used to perform the off-design analysis of waverider configurations generated by the Waverider code. Various approximate analysis methods are used by HAVOC to predict the aerodynamic characteristics, which are validated via a comparison with experimental results from a hypersonic test model