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An edge based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions. Remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer.
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
This document describes progress in the development of finite element codes for the prediction of near and far field acoustic radiation from the inlet and aft fan ducts of turbofan engines. The report consists of nine papers which have appeared in archival journals and conference proceedings, or are presently in review for publication. Topics included are: 1. Aft Fan Duct Acoustic Radiation; 2. Mapped Infinite Wave Envelope Elements for Acoustic Radiation in a Uniformly Moving Medium; 3. A Reflection Free Boundary Condition for Propagation in Uniform Flow Using Mapped Infinite Wave Envelope Elements; 4. A Numerical Comparison Between Multiple-Scales and FEM Solution for Sound Propagation in Lined Flow Ducts; 5. Acoustic Propagation at High Frequencies in Ducts; 6. The Boundary Condition at an Impedance Wall in a Nonuniform Duct with Potential Flow; 7. A Reverse Flow Theorem and Acoustic Reciprocity in Compressible Potential Flows; 8. Reciprocity and Acoustics Power in One Dimensional Compressible Potential Flows; and 9. Numerical Experiments on Acoustic Reciprocity in Compressible Potential Flows.
The time-dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard-wall duct without flow and with spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the steady solutions of the acoustic field. The transient method did not converge to the steady-state solution for cutoff acoustic duct modes. This has implications as to its use in a variable-area duct, where modes may become cutoff in the smal-area portion of the duct. For single cutoff mode propagation the steady-state impedance boundary condition produced acoustic reflections during the initial transient that caused finite instabilities in the numerical calculations. The stability problem is resolved by reformulating the exit boundary condition. Example calculations show good agreement with exact analytical and numerical results for forcing frequencies above, below, and nearly at the cutoff frequency.
An intensive investigation into the cause of anomalous behavior commonly observed in impedance eduction techniques is performed. The investigation consists of grid refinement studies, detailed evaluation of results at and near anti-resonance frequencies, comparisons of different model results with synthesized and measured data, assessment or optimization techniques, and evaluation or boundary condition effects. Results show that the root cause of the anomalous behavior is the sensitivity of the educed impedance to small errors in the measured termination resistance at frequencies near anti-resonance or cut-on of a higher-order mode. Evidence is presented to show that the common usage of an anechoic, plane wave termination boundary condition in ducts where the "true" termination is reflective may act as a trigger for these anomalies. Replacing the exit impedance boundary condition by an exit pressure condition is shown to reduce the anomalous results.
This paper describes predictions of model problems in computational aeroacoustics. Two problem classes are considered: The first (Workshop Category 3, Problem 1 and 2) considers two-dimensional wave propagation and non-reflecting boundary conditions in the presence of a mean flow. The second (Workshop Category 4, Problem 1) examines wall boundary conditions. For the last problem we introduce the Impedance Mismatch Method (IMM) to treat the solid wall boundaries. In this method the solid wall is simulated using a wall region in which the characteristic impedance is set to a different value to that in the fluid region. This method has advantages over traditional solid wall boundary conditions including simplicity of coding, speed of computations, and the ability to treat curved boundaries efficiently. Several numerical examples are given in addition to the Workshop Problems. The discretization of the Euler equations is performed in all cases with a Dispersion-Relation-Preserving (DRP) algorithm. The numerical results are compared with either analytical solutions or solutions obtained using traditional solid wall boundary conditions.
An acoustic source/propagation model is used to interpret measured noise spectra from a long turbulent burner. The acoustic model is based on the perturbation solution of the equations describing the unsteady one-dimensional flow of an inviscid ideal gas with a distributed heat source. The model assumes that the measured noise spectra are due uniquely to the unsteady component of combustion heat release. The model was applied to a long cylindrical hydrogen burner operating over a range of power levels between 4.5 kW and 22.3 kW. Acoustic impedances at the inlet to the burner and at the exit of the tube downstream of the burner were measured and are used as boundary conditions for the model. These measured impedances are also presented.
Traditional Boussinesq or kinematic simulations of interflow (i.e., lateral subsurface flow) assume no leakage through the impeding layer and require a no-flow boundary condition at the ridge top. However, recent analyses of many interflow-producing landscapes indicate that leaky impeding layers are common, that most interflow percolates well before reaching the toe slope, and therefore, the downslope contributing length is shorter than the hillslope length. In watersheds characterised by perched interflow over a low conductivity layer through permeable topsoil, interflow with percolation may be modelled with a kinematic wave model using a mobile upslope boundary condition defining the hillslope portion contributing interflow to valleys. Here, we developed and applied a dynamic interflow model to simulate interflow using a downslope travel distance concept such that only the active contributing length is modelled at any time. The model defines a variable active area based on the depth of the perched layer, the topographic slope and the ratio of the hydraulic conductivity of topsoil to that of the impeding layer. It incorporates a two-layer soil moisture accounting water balance analysis, a pedo-transfer function, and percolation and evaporation routines to predict interflow rates in continuous and event-based scenarios. We tested the modelling concept on two sets of data (2-year dataset of rainfall observations for the continuous simulation and a multi-day irrigation experiment for the event simulation) from a 121-m-long open interflow collection trench on an experimental hillslope at the Savannah River Site, South Carolina. The continuous model simulation partially represented the observed interflow hydrograph and perched water depth in the experimental hillslope with correlation coefficients of 0.85 and 0.35, respectively. Model performance improved significantly at event-scale analysis. The modelling approach realistically represents interflow dynamics in hillslopes with leaky impeding layers and can be integrated into catchment-scale hydrology models for more detailed hillslope process modelling.
This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.
An analysis of the number and form of the required inflow-outflow boundary conditions for the full two-dimensional time-dependent nonlinear acoustic system in subsonic mean flow is performed. The explicit predictor-corrector method of MacCormack (1969) is used. The methodology is tested on both uniform and sheared mean flows with plane and nonplanar sources. Results show that the acoustic system requires three physical boundary conditions on the inflow and one on the outflow boundary. The most natural choice for the inflow boundary conditions is judged to be a specification of the vorticity, the normal acoustic impedance, and a pressure gradient-density gradient relationship normal to the boundary. Specification of the acoustic pressure at the outflow boundary along with these inflow boundary conditions is found to give consistent reliable results. A set of boundary conditions developed earlier, which were intended to be nonreflecting is tested using the current method and is shown to yield unstable results for nonplanar acoustic waves.
A 2-D impedance eduction methodology is extended to quasi-3-D sound fields in uniform or shearing mean flow. We introduce a nonlocal, nonreflecting boundary condition to terminate the duct and then educe the impedance by minimizing an objective function. The introduction of a parallel, sparse, equation solver significantly reduces the wall clock time for educing the impedance when compared to that of the sequential band solver used in the 2-D methodology. The accuracy, efficiency, and robustness of the methodology is demonstrated using two examples. In the first example, we show that the method reproduces the known impedance of a ceramic tubular test liner. In the second example, we illustrate that the approach educes the impedance of a four-segment liner where the first, second, and fourth segments consist of a perforated face sheet bonded to honeycomb, and the third segment is a cut from the ceramic tubular test liner. The ability of the method to educe the impedances of multisegmented liners has the potential to significantly reduce the amount of time and cost required to determine the impedance of several uniform liners by allowing them to be placed in series in the test section and to educe the impedance of each segment using a single numerical experiment. Finally, we probe the objective function in great detail and show that it contains a single minimum. Thus, our objective function is ideal for use with local, inexpensive, gradient-based optimizers.
The solution to the equation governing the propagation of sound in a uniform shear layer is expressed in terms of parabolic cylinder functions. This result is used to develop a closed-form solution for acoustic wall impedance which accounts for both the duct liner and the presence of a boundary layer in the duct. The effective wall impedance can then be used as the boundary condition for the much simpler problem of sound propagation in uniform flow.
A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.
The acoustical properties of locally and nonlocally reacting acoustical liners in grazing flow are described. The effect of mean flow and shear flow are considered as well as the application to rigid and limp bulk reacting materials. The axial wavenumber of the least attenuated mode in a flow duct is measured. The acoustical properties of duct liners is then deduced from the measured axial wavenumber and known flow profile and boundary conditions. This method is a natural extension of impedance-like measurements.
MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.
Test article vibration test responses will vary from one test laboratory to another due to differences in shaker and fixture dynamic characteristics. This is also seen between the field and laboratory due to the differing dynamic characteristics between field assembly loading and boundary conditions compared to the laboratory configuration. This work introduces a technique called Impedance Fixture Neutralization which customizes input forces to cause consistent responses for the Device Under Test across different vibration testing conditions. The customized force neutralizes the dynamic variations between configurations for the Device Under Test. The device responses can be replicated in several situations: when using a different fixture with the same attachment points, when the test article mounting location on the fixture changes, when the force location changes, or any combination of these situations. Impedance Fixture Neutralization uses the uncoupled dynamic characteristics of the test article and excitation fixtures to customize the input thereby causing the same test article responses between two mounting configurations (either field to laboratory or two different laboratory configurations). The application of the technique is shown using an analytical model of a two-beam system and analytically using experimental FRFs from plate and frame component hardware characterization tests. In both cases a device under test is attached to two test fixtures wherein the dynamic differences in the configurations are neutralized.
The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The nonlinear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.
Despite recent advancements in the development of human thermal physiology models, clothing is often considered in only a rudimentary manner, that is, as a boundary condition at the skin characterized by its bulk thermal and evaporative impedances. While such an approach may be sufficient for thermoregulation modeling of humans operating in relatively low thermal burden scenarios, e.g., within an office environment, a clothing thermal model that does not explicitly consider the layer-to-layer transport of vapor can yield incorrect results, especially under conditions corresponding to high thermal stress or extreme environments. For example, vapor diffusing through layers of clothing can reach its dew point, in which case a phase change will occur that can fundamentally affect the transport of moisture and heat within the clothing ensemble. Specifically, the evaporation and condensation of moisture within the fabric layers can affect liquid content and temperature and, ultimately, affect thermo-physiological response and thermal comfort perception. Development of an advanced clothing model that considers heat and moisture transport within the fabric layers can improve the accuracy of human thermal predictions in scenarios where clothing-based condensation and evaporation occur. This paper describes how a general heat transfer software modeling tool was modified to consider the transport of vapor, the storage of liquid, and the thermal effects of phase change within a clothing ensemble. The advanced clothing moisture model was tested by comparing its predictions to measurements derived from sweating hot plate experiments and human physiological experiments. The model was able to reproduce the thermal and moisture results from tests performed under conditions in which condensation within the clothing layers was known to occur. This study demonstrates the importance of considering layer-to-layer vapor transport in clothing models and its impact on human thermal modeling predictions.