Taylor Transformation Research Articles

Investigation of Rotor Noise Shielding Effects by the Helicopter Fuselage in Forward Flight

This paper presents a numerical study on the rotor noise shielding effects by the helicopter fuselage. The method used to assess acoustic shielding is based on a fast multipole boundary element method, which includes the forward flight effect. A free-wake unsteady panel method, in combination with a Ffowcs Williams–Hawkings (FW-H) integral formulation, is used to compute the rotor noise sources for the blade vortex interaction flight condition. The prediction methodologies are described. Validation of boundary element method and the forward flight effect by means of Taylor’s transformation are conducted by using analytic solutions. The error estimation for the case without mean flow indicates that for sufficient grid resolution the maximum error occurring in the shadow region is less than 0.06 dB. The error estimation for the Taylor transformation shows that the error can be up to 6% for . In addition, a Kirchhoff source surface model used to treat the real rotor noise is described. Finally, the method is applied to a BO105 wind tunnel model to understand the noise shielding features of the main and tail rotors.

Installation: numerical investigation

Acoustic installation effects are considered as scattering problem. Two methods to investigate them are presented. First, a fast multipole method boundary element method (FMM-BEM) which can solve the Helmholtz wave equation for full scale aircraft configurations at frequencies of some kHz. There, low Mach number potential mean flow fields can be taken into account by a so-called Taylor transformation. Second, a discontinuous Galerkin method (DGM) which solves acoustic perturbation equations (APE) for realistic mean flow fields is presented. DGM calculations are very expensive and can be performed for full scale aircrafts only at low frequencies. Its main purpose so far is to assess the accuracy of the FMM for selected cases. The Taylor-transformed Helmholtz equation is derived and the fundamentals of the FMM are introduced. Some details of the DLR FMM code FMCAS are given. The basic DGM equations are derived for the APE and some implementation details of the DLR DGM code DISCO++ are discussed. For generic geometries results of the FMM and DGM are compared and the limits of the Taylor transformation are shown. Finally, scattering results for a 1 kHz Monopole at a full scale aircraft geometry will be presented.

Convective correction of metafluid devices based on Taylor transformation

The paper presents a method to modify the mechanical properties of a statically–designed metamaterial device in order to preserve its performance when operating in a non–uniform aerodynamic flow. The objective of the research is to contribute to the disclosure of the acoustic metamaterial potential in aeroacoustic applications, where acoustic propagation and scattering are deeply affected by aerodynamic convection. The emphasis is on aeronautical applications aiming at the development of methods for the design of breakthrough solutions for aircraft noise mitigation. The present approach is based on the application of the inverse Taylor transformation to the static design space in order to obtain the properties of an equivalent metamaterial in the convected space. The metamaterial so–obtained is capable to guarantee the target acoustic response in presence of a non–uniform background flow at low Mach number and with negligible vorticity. Numerical results obtained through finite–element simulations are presented for a free stream Mach number ≤0.35, which is compatible with the take–off and landing operation of a commercial airplane. The benchmark used is the widely assessed problem of the scattering cancellation (cloaking) of a circular obstacle. The acoustic disturbance is here assumed to be generated by an isotropic point source located in the vicinity of the scatterer and co–moving with it. The numerical results reveal that the effect of the proposed correction strongly depends on the relative position of the source and the metamaterial device, with the worst performance obtained when they are aligned with the free stream. The reason of this dependence is analytically explained and verified numerically. When the alignment of the source and the treated object is orthogonal to the flow, the Taylor–corrected metamaterial recovers almost completely its expected behaviour. This result makes the approach appealing for all those engineering applications where the relative position of sources and moving boundaries is fixed and compatible with the most favourable conditions.

On the Solution of Bi-level Large Scale Quadratic Programming Problem with Stochastic Parameters in the Constraints

In this paper, the bi-level large scale quadratic programming problem with stochastic parameters in the constraints (SBLLSQPP) is solved. Randomness is assumed only on the right-hand side of the constraints and the random variables are assumed to be normally distributed. The main features of the proposed solution procedure are based on convert the probabilistic nature of this problem into an equivalent deterministic, Taylor transformation and decomposition algorithms. An illustrative numerical example is given to clarify the main results developed in the paper.

Study on NURBS Surface Tool Trajectory Planning of 6R Engraving Robot

A NURBS surface tool trajectory planning method of engraving robot is proposed. The calculation algorithm including NURBS surface tool trajectory, cutting point and effective cutting radius of end milling cutter and inverse kinematics transform is discussed in detail using Taylor and coordinate transformation method. It is the foundation to further applied to the engraving robot tool trajectory planning or off-line programming.

Computational Scheme of Ordinary Differential Equations Integration on the Basis of Differential Taylor Transformation with Automatic Step and Order Selection

Computational Scheme of Ordinary Differential Equations Integration on the Basis of Differential Taylor Transformation with Automatic Step and Order Selection

Approximation and reconstruction of continuous signals using differential Chebyshev transformation

A method for physical process approximation using the differential Taylor transformation is substantiated. The power basis is transformed to bases of orthogonal Chebyshev polynomials. It is shown that the convergence of series is substantially increased by transition to expansion in Chebyshev polynomials of first kind and shifted Chebyshev polynomials. An algorithm for calculating differential spectrum discretes is formulated. It is observed that in the Chebyshev bases, the value of spectrum discretes decreases constantly as their number grows. In this case, it is possible to stop computing the discretes as they achieve the required small value, but this cannot be done in the power basis. Numerical examples illustrate the advantage of the proposed approach.

Optimization of convective–radiative fins by using differential quadrature element method

Abstract A first endeavor to exploit the differential quadrature element method (DQEM) as a simple, accurate and computationally efficient numerical tool for the shape optimization of convective–radiating extended surfaces or fins is made. The formulations are general so that the spatial and spatial-temperature dependent geometrical and thermal parameters can easily be implemented. The thermal conductivity of the fin is assumed to vary as a linear function of the temperature. The effects of a convective–radiative condition at the fin tip and effective convective condition at the fin base are considered. The optimization of fins with uniform and step cross-sections is investigated. The accuracy of the method is demonstrated by comparing its results with those generated by Adomian’s decomposition technique, Taylor transformation technique and finite difference method. It is shown that, using few grid points, highly accurate results are obtained. Less computational effort of the method with respect to the finite difference method is shown.

Coupled effects of temperature gradient and oxidation on thermal stress in thermal barrier coating system

The thermal stress fields in thermal barrier coating (TBC) system are studied in the present paper. The thermal stress fields are induced by the non-linear coupled effect of temperature gradient, oxidation, thermal fatigue, creep, morphology of TBC system as well as cooling rate. TBC system is assumed to be partially stabilized ZrO 2 by 8 wt.% Y 2O 3 (PSZ) or mullite over a NiCrAlY bond coat sprayed on nickel superalloy or steel substrate. The TBC system is a composite medium with four layers in cylindrical coordinate system. The temperature fields for the non-homogeneous problem with energy generation in medium are analytical solved by using Taylor transformation and Green’s function approach. The analytical solutions for thermal stress fields in composite medium are obtained when eigenstrain rate is taken into consideration. The constitutive equations, such as the creep of ceramic coating (PSZ and mullite) and substrate (Ni-superalloy), plasticity of bond coat are given by a general formula. Thermal growth oxidation (TGO) and the temperature dependence of thermal–mechanical parameters are taken into consideration. The calculated results of temperature fields and thermal stresses fields are given and the related results are discussed. TGO does not affect the temperature fields in PSZ coating systems. But it has influence on temperature fields in mullite coating systems. The residual stress with TGO considered is larger than that with TGO non-considered. It is very interesting to have the conclusion that TGO may make the residual tangent stress from tensile to compressive. The characterization of thermal stresses in PSZ coating system is very different from that in mullite coating system. It may be due to the difference of mechanical behavior such as creep, thermal mismatch as well as mechanical mismatch which is reflected by Dundurs' parameters α and β . The geometrical radius not only affects the quantum of thermal stress but also affects the characterization of thermal stress. The effect of cooling rate on residual stress is due to the high creep rate of ceramic coating operating at high temperature. The effect of cooling rate on residual stress is not large for system operating at relative low temperature.

Sampling Rhyparida nitida Clark (Coleoptera: Chrysomelidae) and symptoms of their damage on sugarcane

Sampling statistics were determined for larvae, pupae and adults of the chrysomelid Rhyparida nitida associated with sugarcane in Australia and for symptoms of their damage. Iwao’s patchiness regression was inappropriate for modelling the mean–variance relationships of the insect counts. Taylor’s power law was used to model these data and relationships were developed for counts of small, medium and large larvae, all larvae combined, pupae and adults. The mean–variance relationships of counts of live shoots and shoots killed by larvae of R. nitida were modelled using Iwao’s patchiness regression; Taylor’s power law was not appropriate to either data set. Relationships to determine sample sizes for fixed levels of precision and fixed‐precision‐level stop lines for sequential sampling of the different stages and live and dead shoots were also developed. Neither the ln(x + 1) transformation nor the Healy and Taylor transformation consistently standardised the mean–variance relationships of insect counts and the appropriate transformation should be selected on a case‐by‐case basis. Counts of both live and dead shoots were adequately transformed by the Iwao and Kuno transformation.

Application of the Hybrid Method to the Transient Thermal Stresses Response in Isotropic Annular Fins

This paper presents the transient stress distribution in a perfectly elastic isotropic annular fin. The nonlinear transient conduction-convection-radiation heat transfer annular fin equation is solved by the hybrid method of the Taylor transformation and the finite difference approximation. The temperature distribution curve is employed by the natural cubic spline fitting. The stress distribution is directly integrated to obtain the transient thermal stress distribution.

Application of the Taylor Transformation to the Transient Temperature Response of an Annular Fin

This article presents the transient temperature response of a convective-radiative rectangular profile annular fin under a step temperature change occurring in its base. A convection-radiation fin tip is considered. The nonlinear transient heat transfer and boundary conditions are solved by using the hybrid method of Taylor transformation and finite-difference approximation. Also, time domain is controlled by Taylor transformation, and the spatial coordinates are handled by finite-difference approximation. Temperature distribution is implemented by employing natural cubic spline fitting.

APPLICATION OF TAYLOR TRANSFORMATION TO THE THERMAL STRESSES IN ISOTROPIC ANNULAR FINS

This article presents the stresses distribution in a perfectly elastic isotropic annular fin. The Taylor transformation method is used to solve the nonlinear temperature field equation. The stresses distribution are integrated obtain the results. The thickness of the fins is assumed to be sufficiently small so as to have a state of plane stress and one-dimensional heat conduction.

Application of Taylor transformation to optimize rectangular fins with variable thermal parameters

This research investigates the optimal fin length of a convective–radiative rectangular profile longitudinal fin (maximum heat dissipation for a fixed profile area at a given volume) under convective boundary conditions and variable thermal conductivity. Convective–radiative fin tips are considered. The nonlinear heat transfer and boundary condition equations are solved using the Taylor transformation. This method is well suited for nonlinear equations. The temperature of the fluid, T f, on the other side of the primary surface is considered as an important optimization parameter in this analysis.

Application of Taylor transformation to nonlinear predictive control problem

A Taylor transformation technique for nonlinear process predictive control is presented. In this approach, a prediction model for nonlinear predictive control (NPC) is introduced, using the Taylor transformation technique, to make the NPC design problem similar to the linear predictive control problem. It is then applied to the continuous stirred tank reactor (CSTR) control problem. The stability of the proposed nonlinear predictive control scheme to the CSTR problem is also studied. The model mismatch can also be made to cope with the proposed scheme. The results are compared with those obtained using nonlinear model predictive control and a fuzzy adaptive controller. The comparison shows that the proposed method leads to feasible results for NPC research.

Sampling Adults of Eoscarta carnifex (Hemiptera: Cercopidae) and Their Associated Symptoms on Sugarcane

Sampling statistics were determined for adults of the froghopper Eoscarta carnifex (F.) and associated symptoms on sugarcane crops in northern Queensland, Australia. Samples using 10 consecutive stems per sampling unit minimized the variance: mean ratios for all sample sizes used to sample adults. The Taylor power law described the relationship between mean and variance of samples based on 10-stem sampling units better than did the lwao regression model or the negative binomial model. All 3 models indicated that adults were aggregated in distribution. Relationships to determine sample sizes for fixed levels of precision and fixed-precision-level stop lines for sequential sampling of adults were developed. There was a functional relationship between the variance and mean of untransformed froghopper counts, but this was eliminated by the Healy and Taylor transformation. Samples using 5 consecutive stems per sampling unit minimized the variance: mean ratios for all sample sizes used to sample symptoms. The Iwao patchiness regression was the only appropriate model for symptom data, and the slope indicated that damage is distributed uniformly between samples. Relationships to determine fixed-precision-level stop lines for sampling of symptom data were developed.

Derivation and efficient implementation of the fast multipole method

The fast multipole method (FMM) of Greengard evaluates Coulomb interactions of point charges with computational requirements that increase linearly with the number of particles. In this work, the central transformations of the FMM are obtained in a very compact manner from simple algebraic manipulations of two addition theorems. The intermediate multipole and Taylor expansions are defined differently from previous work to yield simplified and more efficient transformations. Error estimates are obtained due to the effect of multipole truncation and the use of the multipole to Taylor transformation operator. Efficient implementation of the FMM for potential and forces is discussed, and calculations are presented that probe the accuracy and performance of the method.

The Taylor transformation of analytic functionals with non-bounded carrier

The Taylor transformation of analytic functionals with non-bounded carrier

Sample Sizes and Distributions of Japanese Beetles (Coleoptera: Scarabaeidae) Captured in Lure Traps

Sampling statistics were determined for Japanese beetles, Popillia japonica Newman, caught in traps baited with a 3:7:3 mixture of phenethyl propionate/eugenol/geraniol, or with ( R, Z )-5-(1-decenyl)dihydro-2(3 H )-furanone (Japonilure), or with a combination of both lures. Iwao’s patchiness regression and a quadratic model were inappropriate for modeling the mean-variance relationships. Taylor’s power law was used to model these data, and relationships were developed for beetle numbers captured by traps baited with phenethyl propionate-eugenol-geraniol alone or in combination with Japonilure and for males and females captured by traps baited with Japonilure alone. Relationships to determine sample sizes for fixed levels of precision were also developed. The I n ( X + 1) transformation did not standardize the mean-variance relationship for any data set, but the Healy & Taylor transformation was effective on all data sets.

Sampling Distributions and Sequential Sampling Plans for Perkinsiella saccharicida Kirkaldy (Hemiptera: Delphacidae) and Tytthus spp. (Hemiptera: Miridae) on Sugarcane

Sampling statistics of eggs, nymphs, and adults of Perkinsiella saccharicida Kirkaldy and its predators, Tytthus spp., were determined on six varieties of sugarcane ( Saccharum spp.) in southern Queensland, Australia. Iwao’s patchiness regression and Taylor’s power law were used to model the relationship between mean and variance of counts. Taylor’s power law gave better fits to all data except for counts of eggs per egg mass. Sample sizes for fixed levels of precision and fixed-precision-level stop lines for sequential sampling were developed for all stages of P. saccharicida and nymphs and adults of Tytthus spp. The In(x + 1) transformation standardized the mean-variance relationship for P. saccharicida nymphs, adults, and eggs per egg mass and Tytthus spp. adults, but not for P. saccharlctda egg masses or Tytthus spp. nymphs. The Healy and Taylor transformation was not effective on P. saccharicida data but standardized Tytthus spp. nymph and adult counts.