The Solution of a Singular Integral Equation Arising From a Lifting Surface Theory for Rotating Blades

A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied to the propeller blade model lead to a radical reduction in complexity of the solution methodology. This research is motivated by the need to obtain accurate, cost efficient propeller blade surface pressure information to be used as input to Advanced Technology Propeller Noise Prediction methods. Currently, these data are supplied by state of the art computational fluid dynamics (CFD) methods which require the calculation of the entire flow field. Though these methods yield highly accurate solutions, they are considered by the aeroacoustician to be time consuming and expensive from a computational point of view. The above integral equation method, on the other hand, involves only surface calculations, requiring much less computational expense relative to CFD methods. Results are presented that demonstrate the validity of the integral equation model and the solution procedure. Propeller noise predictions using results from the method presented here are in excellent agreement with those obtained from CFD methods

The Fast Scattering Code (FSC): Validation Studies and Program Guidelines

The Fast Scattering Code (FSC) is a frequency domain noise prediction program developed at the NASA Langley Research Center (LaRC) to simulate the acoustic field produced by the interaction of known, time harmonic incident sound with bodies of arbitrary shape and surface impedance immersed in a potential flow. The code uses the equivalent source method (ESM) to solve an exterior 3-D Helmholtz boundary value problem (BVP) by expanding the scattered acoustic pressure field into a series of point sources distributed on a fictitious surface placed inside the actual scatterer. This work provides additional code validation studies and illustrates the range of code parameters that produce accurate results with minimal computational costs. Systematic noise prediction studies are presented in which monopole generated incident sound is scattered by simple geometric shapes - spheres (acoustically hard and soft surfaces), oblate spheroids, flat disk, and flat plates with various edge topologies. Comparisons between FSC simulations and analytical results and experimental data are presented

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

Experiments on a scale model of an advanced unconventional subsonic transport concept, the Blended Wing Body (BWB), have demonstrated significant shielding of inlet-radiated noise. A computational model of the shielding mechanism has been developed using a combination of boundary integral equation method (BIEM) and equivalent source method (ESM). The computation models the incident sound from a point source in a nacelle and determines the scattered sound field. In this way the sound fields with and without the airfoil can be estimated for comparison to experiment. An experimental test bed using a simplified wedge-shape airfoil and a broadband point noise source in a simulated nacelle has been developed for the purposes of verifying the analytical model and also to study the effect of engine nacelle placement on shielding. The experimental study is conducted in the Anechoic Noise Research Facility at NASA Langley Research Center. The analytic and experimental results are compared at 6300 and 8000 Hz. These frequencies correspond to approximately 150 Hz on the full scale aircraft. Comparison between the experimental and analytic results is quite good, not only for the noise scattering by the airframe, but also for the total sound pressure in the far field. Many of the details of the sound field that the analytic model predicts are seen or indicated in the experiment, within the spatial resolution limitations of the experiment. Changing nacelle location produces comparable changes in noise shielding contours evaluated analytically and experimentally. Future work in the project will be enhancement of the analytic model to extend the analysis to higher frequencies corresponding to the blade passage frequency of the high bypass ratio ducted fan engines that are expected to power the BWB

Open Rotor Noise Prediction Methods at NASA Langley- A Technology Review

Open rotors are once again under consideration for propulsion of the future airliners because of their high efficiency. The noise generated by these propulsion systems must meet the stringent noise standards of today to reduce community impact. In this paper we review the open rotor noise prediction methods available at NASA Langley. We discuss three codes called ASSPIN (Advanced Subsonic-Supersonic Propeller Induced Noise), FW - Hpds (Ffowcs Williams-Hawkings with penetrable data surface) and the FSC (Fast Scattering Code). The first two codes are in the time domain and the third code is a frequency domain code. The capabilities of these codes and the input data requirements as well as the output data are presented. Plans for further improvements of these codes are discussed. In particular, a method based on equivalent sources is outlined to get rid of spurious signals in the FW - Hpds code

Superspreading on hydrophobic substrates:effect of glycerol additive

The spreading of solutions of three trisiloxane surfactants on two hydrophobic substrates, polyethylene and polyvinylidenefluoride, was studied with the addition of 0–40 mass % of glycerol. It was found that all the surfactant solutions spread faster than silicone oil of the same viscosity, confirming the existence of a mechanism which accelerates the spreading of the surfactant solutions. For the non-superspreading surfactant, BT-233, addition of glycerol improved the spreading performance on polyvinylidenefluoride and resulted in a transition from partial to complete wetting on polyethylene. The fastest spreading was observed for BT-233 at a concentration of 2.5 g/L, independent of glycerol content. For the superspreading surfactants, BT-240 and BT-278, the concentration at which the fastest spreading occurs systematically increased with concentration of glycerol on both substrates from 1.25 g/L for solutions in water to 10 g/L for solutions in 40% glycerol/water mixture. Thus, the surfactant equilibration rate (and therefore formation of surface tension gradients) and Marangoni flow are important components of a superspreading mechanism. De-wetting of the solutions containing glycerol, once spread on the substrates, resulted in the formation of circular drop patterns. This is in contrast to the solely aqueous solutions where the spread film shrank due to evaporation, without any visible traces being left behind

The precision of today's satellite laser ranging systems

Recent improvements in the accuracy of modern satellite laser ranging (SLR) systems are strengthened by the new capability of many instruments to track an increasing number of geodetic satellite targets without significant scheduling conflict. This will allow the refinement of some geophysical parameters, such as solid Earth tidal effects and GM, and the improved temporal resolution of others, such as Earth orientation and station position. Better time resolution for the locations of fixed observatories will allow us to monitor more subtle motions at the stations, and transportable systems will be able to provide indicators of long term trends with shorter occupations. If we are to take advantage of these improvements, care must be taken to preserve the essential accuracy of an increasing volume of range observations at each stage of the data reduction process

Children's spontaneous correction of false beliefs in a conversation partner.

Preschool children were tested for their ability to vary the verbal information they offered regarding an object's location depending on whether the person searching for that object was likely to infer or misinfer its location. Older children (mean age: 5 years 3 months) offered information in a selective fashion: If the location of the hidden object could be readily inferred by their conversation partner, they indicated its location only when explicitly asked but if its location was likely to be misinferred, they often indicated that location prior to being explicitly asked. The response pattern of younger children (mean age: 3 years 6 months) was less conclusive. A relatively large number of younger children took matters "into their own hands" and immediately grasped for the concealed object, irrespective of whether its location could be readily inferred. However, the reactions of the remaining 3-year-olds suggest that even at this age children may be sensitive to the likely beliefs of their conversation partner. © 1999 The International Society for the Study of Behavioural Development

Exploring views on satisfaction with life in young children with chronic illness: an innovative approach to the collection of self-report data from children under 11

The objective of this study was to explore young children’s views on the impact of chronic illness on their life in order to inform future development of a patient-based self-report health outcome measure. We describe an approach to facilitating self-report views from young children with chronic illness. A board game was designed in order to obtain qualitative data from 39 children with a range of chronic illness conditions and 38 healthy controls ranging in age from 3 to 11 years. The format was effective in engaging young children in a self-report process of determining satisfaction with life and identified nine domains. The board game enabled children aged 5–11 years with chronic illness to describe the effects of living with illness on home, family, friends, school and life in general. It generated direct, non-interpreted material from children who, because of their age, may have been considered unable or limited their ability to discuss and describe how they feel. Obtaining this information for children aged 4 and under continues to be a challenge