Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematical physics methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

Solutions of some problems in applied mathematics using MACSYMA

Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

Punjabi, Alkesh↗

Gravito-Inertial Force Resolution in Perception of Synchronized Tilt and Translation

Natural movements in the sagittal plane involve pitch tilt relative to gravity combined with translation motion. The Gravito-Inertial Force (GIF) resolution hypothesis states that the resultant force on the body is perceptually resolved into tilt and translation consistently with the laws of physics. The purpose of this study was to test this hypothesis for human perception during combined tilt and translation motion. EXPERIMENTAL METHODS: Twelve subjects provided verbal reports during 0.3 Hz motion in the dark with 4 types of tilt and/or translation motion: 1) pitch tilt about an interaural axis at +/-10deg or +/-20deg, 2) fore-aft translation with acceleration equivalent to +/-10deg or +/-20deg, 3) combined "in phase" tilt and translation motion resulting in acceleration equivalent to +/-20deg, and 4) "out of phase" tilt and translation motion that maintained the resultant gravito-inertial force aligned with the longitudinal body axis. The amplitude of perceived pitch tilt and translation at the head were obtained during separate trials. MODELING METHODS: Three-dimensional mathematical modeling was performed to test the GIF-resolution hypothesis using a dynamical model. The model encoded GIF-resolution using the standard vector equation, and used an internal model of motion parameters, including gravity. Differential equations conveyed time-varying predictions. The six motion profiles were tested, resulting in predicted perceived amplitude of tilt and translation for each. RESULTS: The modeling results exhibited the same pattern as the experimental results. Most importantly, both modeling and experimental results showed greater perceived tilt during the "in phase" profile than the "out of phase" profile, and greater perceived tilt during combined "in phase" motion than during pure tilt of the same amplitude. However, the model did not predict as much perceived translation as reported by subjects during pure tilt. CONCLUSION: Human perception is consistent with the GIF-resolution hypothesis even when the gravito-inertial force vector remains aligned with the body during periodic motion. Perception is also consistent with GIF-resolution in the opposite condition, when the gravito-inertial force vector angle is enhanced by synchronized tilt and translation.

Wood, Scott J.↗

Thermal Pollution Mathematical Model: Verification of One-Dimensional Numerical Model at Lake Keowee - Volume 2

A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.

Lee, S. S.↗

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

Measurement of Residual Flexibility for Substructures Having Prominent Flexible Interfaces

Verification of a dynamic model of a constrained structure requires a modal survey test of the physical structure and subsequent modification of the model to obtain the best agreement possible with test data. Constrained-boundary or fixed-base testing has historically been the most common approach for verifying constrained mathematical models, since the boundary conditions of the test article are designed to match the actual constraints in service. However, there are difficulties involved with fixed-base testing, in some cases making the approach impractical. It is not possible to conduct a truly fixed-base test due to coupling between the test article and the fixture. In addition, it is often difficult to accurately simulate the actual boundary constraints, and the cost of designing and constructing the fixture may be prohibitive. For use when fixed-base testing proves impractical or undesirable, alternate free-boundary test methods have been investigated, including the residual flexibility technique. The residual flexibility approach has been treated analytically in considerable detail and has had limited frequency response measurements for the method. This concern is well-justified for a number of reasons. First, residual flexibilities are very small numbers, typically on the order of 1.0E-6 in/lb for translational diagonal terms, and orders of magnitude smaller for off-diagonal values. This poses difficulty in obtaining accurate and noise-free measurements, especially for points removed from the excitation source. A second difficulty encountered in residual measurements lies in obtaining a clean residual function in the process of subtracting synthesized modal data from a measured response function. Inaccuracies occur since modes are not subtracted exactly, but only to the accuracy of the curve fits for each mode; these errors are compounded with increasing distance from the excitation point. In this paper, the residual flexibility method is applied to a simple structure in both test and analysis. Measured and predicted residual functions are compared, and regions of poor data in the measured curves are described. It is found that for accurate residual measurements, frequency response functions having prominent stiffness lines in the acceleration/force format are needed. The lack of such stiffness lines increases measurement errors. Interface drive point frequency respose functions for shuttle orbiter payloads exhibit dominant stiffness lines, making the residual test approach a good candidate for payload modal tests when constrained tests are inappropriate. Difficulties in extracting a residual flexibility value from noisy test data are discussed. It is shown that use of a weighted second order least-squares curve fit of the measured residual function allows identification of residual flexibility that compares very well with predictions for the simple structure. This approach also provides an estimate of second order residual mass effects.

Tinker, Michael L.↗

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗

Improving Regional Air Quality Forecasting Through Chemical Data Assimilation and Dynamic Emissions Adjustment

Poor air quality (AQ) is one of the most important human-health and environmental problems facing the United States (US). In addition to the detrimental impacts on human- and environmental-health, poor AQ has an economic cost of ~5% of the US gross domestic product (~$790 billion). AQ managers use AQ analyses and modeling to better understand, anticipate, and avoid poor AQ events. Our research focuses on improving AQ analysis/forecast skill, predictability, and emission estimates through improved and more efficient: (i) modeling and data assimilation strategies; (ii) dynamic emissions adjustment strategies; and (iii) use of satellite remote-sensing Earth observations (e.g., MOPITT, IASI, MODIS, OMI, TROPOMI, TEMPO, etc.). This seminar will review: (i) regional chemical weather forecasting/data assimilation with dynamic emissions adjustment with WRF-Chem/DART; (ii) strategies for efficiently assimilating satellite retrieval profiles with ‘compact phase space retrievals’ (CPSRs); (iii) results from joint assimilation of multiple satellite retrievals at medium (12 km × 12 km) and high (4 km × 4 km) spatial resolutions; and (iv) results from observing system simulation experiments (OSSEs) to investigate whether we can recover COVID-period anthropogenic emissions by assimilating synthetic TEMPO NO2 tropospheric column retrievals with dynamic emissions adjustment. Biographical Sketch: Dr. Mizzi is a Senior Research Fellow working and Dr. Johnson at the NASA Ames Research Center. He holds BA and MS degrees in Environmental Science from the University of Virginia, MS and PhD degrees in Applied Mathematics from the University of Colorado at Boulder (CUB), and a JD degree (with an emphasis in Environmental Law) from the University of Colorado School of Law. He worked at the National Center for Atmospheric Research for nearly 25 years on global atmospheric modeling, dynamic and physical initialization, regional hybrid data assimilation, and most recently on regional chemical data assimilation. He also worked as an environmental attorney and consultant for nearly 15 years. He is an expert in numerical modeling and is recognized internationally as a leading expert in regional, chemical data assimilation with dynamic emissions adjustment. Dr. Mizzi became affiliated with NASA Ames in March 2020 to work on improving AQ analysis/forecast skill, predictability, and ‘top-down’ emissions adjustment though the assimilation of Earth observations. An emphasis of his current work is developing methods for assimilating synthetic TEMPO retrievals to quantify the expected benefits of TEMPO relative to existing AQ observations.

Arthur P. Mizzi↗

Data Assimilation and Uncertainties in Early Solar Cycle Predictions

Stochastic nature of solar activity variations together with our limited knowledge of the dynamo mechanism and subsurface dynamics causes uncertainty in predictions of the solar cycle. For improving the physics-­‐based predictions we can take advantage of the mathematical data assimilation approach that allows us to take into account both, observational errors and model uncertainties, and provide estimates of the next solar cycle along with prediction uncertainties. In this study we use the Parker's migratory dynamo model together with the equation of magnetic helicity balance, which reproduces main properties of the sunspot cycles and allow us to minimize discrepancies between the observed global activity variations and the model solution. The test simulation runs show that a reliable prediction can be obtained for two phases of preceding solar cycle: 1) if the polar field reversals shortly after the solar maxima (strong toroidal field and weak poloidal field), and 2) during the solar minima (strongest poloidal and weak toroidal fields). The early estimate of Cycle 25 obtained by this method shows that this cycle will start in 2019 – 2020, reach the maximum in 2023 – 2024, and that the mean sunspot number at the maximum will be about 90 (for the v2.0 sunspot number series).

Data Assimilation↗

A Green's function method for high charge and energy ion transport

A heavy-ion transport code using Green's function methods is developed. The low-order perturbation terms exhibiting the greatest energy variation are used as dominant energy-dependent terms, and the higher order collision terms are evaluated using nonperturbative methods. The recently revised NUCFRG database is used to evaluate the solution for comparison with experimental data for 625A MeV 20Ne and 517A MeV 40Ar ion beams. Improved agreements with the attenuation characteristics for neon ions are found, and reasonable agreement is obtained for the transport of argon ions in water.

Energy Transfer↗

An algorithm for a semiempirical nuclear fragmentation model

In the present paper, an algorithm for HZE (High Charge and Energy) fragmentation based upon a combination of a two step abrasion/ablation model and electromagnetic dissociation is presented. Development of the model and detailed comparison with available experimental data are given elsewhere. The abrasion process accounts for the removal of nuclear matter in the overlap region of the colliding ions. An average transmission factor is used for the projectile and target nuclei at a given impact parameter to account for the finite mean free path in nuclear matter. The ions are treated otherwise on a geometric basis assuming uniform spheres. The ablation process is treated as a single nucleon-evaporation for every 10 MeV of excitation energy as used by Bowman in the original form of the model. The charge distribution of final fragments are calculated according to the Rudstam formula, except for some correction in mass 5, 8 and 9 fragments which show strong structure effects and correspondingly significant deviation from Rudstam's values. The nuclear electromagnetic dissociation is based on the Weizsacker-Williams (WW) method of virtual quanta where due to its simplicity, the virtual photon spectrum for individual multipoles, and finite extent of the charge distribution are not included. Comparisons of the model are made with the available experimental data here and more extensively elsewhere.

NASA Program Space Medicine↗

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Nelson, Andrea↗

Toward an IMU-based Space Suit Motion Capture System

Spacesuits are complex engineering systems that sustain human health and enable performance outside of Earth-like environments. These systems must support human mobility and physical workload demands while minimizing injury risk during extravehicular activity (EVA). Future EVA on the lunar surface during the Artemis program is expected to be more frequent and require higher physical workloads than previous EVAs during the ISS, Shuttle, or Apollo programs. Hence it is important to optimize future as well as current spacesuits to be efficient and comfortable for the success of space and planetary missions. To enable this, an efficient method is needed to test these spacesuits on the ground.When testing spacesuits in ground environments, it is often necessary to understand the kinematics of the suit to validate the design against relevant requirements or characterize the physical workload necessary to operate the suit. This is a challenging task for traditional optical motion capture (OMC) approaches: suit-mounted OMC markers are easily occluded by the subject or environment and may become detached during testing. Controlling lighting and reflectivity of objects in the motion capture volume is also difficult. Fixed-position OMC cameras also constrain testing to a small and contrived laboratory environment, disallowing kinematics capture in field environments.One promising alternative is the use of suit-mounted inertial measurement units (IMUs). These sensors are small, unobtrusive, and portable, but come at the cost of increased sensor noise and complexity of the software and mathematics to analyze the collected data. To this end, engineers at NASA are developing the Augmented Suit Inverse Kinematics (ASIK) system, a complete motion capture methodand inverse kinematics solver which relies solely on a network of wireless IMUs attached to the major kinematic segments of the spacesuit. The ASIK modeling language allows for the simple inclusion of probabilistic priors such as suit size and shape or IMU positions and rotations. Furthermore, to increase accuracy and reduce operational overhead to use this motion capture approach, the developed inverse kinematics solver exploits so-called self-calibratingalgorithmic techniques, which reduce the need for precise alignment of the sensors on the segments or scripted functional calibration procedures. The ASIK system was tested in a 7-subject pilot study. Each subject donned NASA’s new prototype exploration spacesuit in the Active Response Gravity Offload System (ARGOS) facility at the NASA Johnson Space Center. The subjects were outfitted with a set of 14 APDM (Portland, OR, USA) Opal IMUs, 12 of which were used in the ASIK model to estimate lower body and trunk kinematics. The subjects were also outfitted with a set of reflective OMC markers and traditional OMC data was collected and processed. Presented results will include characterization of ASIK-derived suit joint angles accuracy against an optical motion capture datum. Discussion of these results, as well as discussion of system calibration and nuances of mathematical observability, will be included.If successful, IMU-based motion capture will enable testing and validation of spacesuits more frequently, with less overhead, in more extreme environments. Future work will apply these techniques to common spacesuit testing tasks, such as gait, mobility, and balance assessment, physical workload characterization, and ergonomics evaluations.

Timothy Mcgrath↗

Annual Research Briefs, 2004: Center for Turbulence Research

This report contains the 2004 annual progress reports of the Research Fellows and students of the Center for Turbulence Research in its eighteenth year of operation. Since its inception in 1987, the objective of the CTR has been to advance the physical understanding of turbulent flows and development of physics based predictive tools for engineering analysis and turbulence control. Turbulence is ubiquitous in nature and in engineering devices. The studies at CTR have been motivated by applications where turbulence effects are significant; these include a broad range of technical areas such as planetary boundary layers, formation of planets, solar convection, magnetohydrodynamics, environmental and eco systems, aerodynamic noise, propulsion systems and high speed transportation. Numerical simulation has been the predominant research tool at CTR which has required a critical mass of researchers in numerical analysis and computer science in addition to core disciplines such as applied mathematics, chemical kinetics and fluid mechanics. Maintaining and promoting this interdisciplinary culture has been a hallmark of CTR and has been responsible for the realization of the results of its basic research in applications. The first group of reports in this volume are directed towards development, analysis and application of novel numerical methods for ow simulations. Development of methods for large eddy simulation of complex flows has been a central theme in this group. The second group is concerned with turbulent combustion, scalar transport and multi-phase ows. The nal group is devoted to geophysical turbulence where the problem of solar convection has been a new focus of considerable attention recently at CTR.

Moin, Parviz↗

Higgs-boson production in nucleus-nucleus collisions

Cross-section calculations are presented for the production of intermediate-mass Higgs bosons produced in ultrarelativistic nucleus-nucleus collisions via two-photon fusion. The calculations are performed in position space using Baur's method for folding together the Weizsacker-Williams virtual-photon spectra of the two colliding nuclei. It is found that two-photon fusion in nucleus-nucleus collisions is a plausible way of finding intermediate-mass Higgs bosons at the Superconducting Super Collider or the CERN Large Hadron Collider.

NASA Discipline Radiation Health↗

Signal Analysis of Helicopter Blade-Vortex-Interaction Acoustic Noise Data

Blade-Vortex-Interaction (BVI) produces annoying high-intensity impulsive noise. NASA Ames collected several sets of BVI noise data during in-flight and wind tunnel tests. The goal of this work is to extract the essential features of the BVI signals from the in-flight data and examine the feasibility of extracting those features from BVI noise recorded inside a large wind tunnel. BVI noise generating mechanisms and BVI radiation patterns an are considered and a simple mathematical-physical model is presented. It allows the construction of simple synthetic BVI events that are comparable to free flight data. The boundary effects of the wind tunnel floor and ceiling are identified and more complex synthetic BVI events are constructed to account for features observed in the wind tunnel data. It is demonstrated that improved recording of BVI events can be attained by changing the geometry of the rotor hub, floor, ceiling and microphone. The Euclidean distance measure is used to align BVI events from each blade and improved BVI signals are obtained by time-domain averaging the aligned data. The differences between BVI events for individual blades are then apparent. Removal of wind tunnel background noise by optimal Wiener-filtering is shown to be effective provided representative noise-only data have been recorded. Elimination of wind tunnel reflections by cepstral and optimal filtering deconvolution is examined. It is seen that the cepstral method is not applicable but that a pragmatic optimal filtering approach gives encouraging results. Recommendations for further work include: altering measurement geometry, real-time data observation and evaluation, examining reflection signals (particularly those from the ceiling) and performing further analysis of expected BVI signals for flight conditions of interest so that microphone placement can be optimized for each condition.

Rogers, James C.↗

Numerical Simulation of Two Phase Flows

Two phase flows can be found in broad situations in nature, biology, and industry devices and can involve diverse and complex mechanisms. While the physical models may be specific for certain situations, the mathematical formulation and numerical treatment for solving the governing equations can be general. Hence, we will require information concerning each individual phase as needed in a single phase. but also the interactions between them. These interaction terms, however, pose additional numerical challenges because they are beyond the basis that we use to construct modern numerical schemes, namely the hyperbolicity of equations. Moreover, due to disparate differences in time scales, fluid compressibility and nonlinearity become acute, further complicating the numerical procedures. In this paper, we will show the ideas and procedure how the AUSM-family schemes are extended for solving two phase flows problems. Specifically, both phases are assumed in thermodynamic equilibrium, namely, the time scales involved in phase interactions are extremely short in comparison with those in fluid speeds and pressure fluctuations. Details of the numerical formulation and issues involved are discussed and the effectiveness of the method are demonstrated for several industrial examples.

Liou, Meng-Sing↗

Jet Noise Diagnostics Supporting Statistical Noise Prediction Methods

The primary focus of my presentation is the development of the jet noise prediction code JeNo with most examples coming from the experimental work that drove the theoretical development and validation. JeNo is a statistical jet noise prediction code, based upon the Lilley acoustic analogy. Our approach uses time-average 2-D or 3-D mean and turbulent statistics of the flow as input. The output is source distributions and spectral directivity. NASA has been investing in development of statistical jet noise prediction tools because these seem to fit the middle ground that allows enough flexibility and fidelity for jet noise source diagnostics while having reasonable computational requirements. These tools rely on Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solutions as input for computing far-field spectral directivity using an acoustic analogy. There are many ways acoustic analogies can be created, each with a series of assumptions and models, many often taken unknowingly. And the resulting prediction can be easily reverse-engineered by altering the models contained within. However, only an approach which is mathematically sound, with assumptions validated and modeled quantities checked against direct measurement will give consistently correct answers. Many quantities are modeled in acoustic analogies precisely because they have been impossible to measure or calculate, making this requirement a difficult task. The NASA team has spent considerable effort identifying all the assumptions and models used to take the Navier-Stokes equations to the point of a statistical calculation via an acoustic analogy very similar to that proposed by Lilley. Assumptions have been identified and experiments have been developed to test these assumptions. In some cases this has resulted in assumptions being changed. Beginning with the CFD used as input to the acoustic analogy, models for turbulence closure used in RANS CFD codes have been explored and compared against measurements of mean and rms velocity statistics over a range of jet speeds and temperatures. Models for flow parameters used in the acoustic analogy, most notably the space-time correlations of velocity, have been compared against direct measurements, and modified to better fit the observed data. These measurements have been extremely challenging for hot, high speed jets, and represent a sizeable investment in instrumentation development. As an intermediate check that the analysis is predicting the physics intended, phased arrays have been employed to measure source distributions for a wide range of jet cases. And finally, careful far-field spectral directivity measurements have been taken for final validation of the prediction code. Examples of each of these experimental efforts will be presented. The main result of these efforts is a noise prediction code, named JeNo, which is in middevelopment. JeNo is able to consistently predict spectral directivity, including aft angle directivity, for subsonic cold jets of most geometries. Current development on JeNo is focused on extending its capability to hot jets, requiring inclusion of a previously neglected second source associated with thermal fluctuations. A secondary result of the intensive experimentation is the archiving of various flow statistics applicable to other acoustic analogies and to development of time-resolved prediction methods. These will be of lasting value as we look ahead at future challenges to the aeroacoustic experimentalist.

Bridges, James E.↗

Compatibility of Segments of Thermoelectric Generators

A method of calculating (usually for the purpose of maximizing) the power-conversion efficiency of a segmented thermoelectric generator is based on equations derived from the fundamental equations of thermoelectricity. Because it is directly traceable to first principles, the method provides physical explanations in addition to predictions of phenomena involved in segmentation. In comparison with the finite-element method used heretofore to predict (without being able to explain) the behavior of a segmented thermoelectric generator, this method is much simpler to implement in practice: in particular, the efficiency of a segmented thermoelectric generator can be estimated by evaluating equations using only hand-held calculator with this method. In addition, the method provides for determination of cascading ratios. The concept of cascading is illustrated in the figure and the definition of the cascading ratio is defined in the figure caption. An important aspect of the method is its approach to the issue of compatibility among segments, in combination with introduction of the concept of compatibility within a segment. Prior approaches involved the use of only averaged material properties. Two materials in direct contact could be examined for compatibility with each other, but there was no general framework for analysis of compatibility. The present method establishes such a framework. The mathematical derivation of the method begins with the definition of reduced efficiency of a thermoelectric generator as the ratio between (1) its thermal-to-electric power-conversion efficiency and (2) its Carnot efficiency (the maximum efficiency theoretically attainable, given its hot- and cold-side temperatures). The derivation involves calculation of the reduced efficiency of a model thermoelectric generator for which the hot-side temperature is only infinitesimally greater than the cold-side temperature. The derivation includes consideration of the ratio (u) between the electric current and heat-conduction power and leads to the concept of compatibility factor (s) for a given thermoelectric material, defined as the value of u that maximizes the reduced efficiency of the aforementioned model thermoelectric generator.

Snyder, G. Jeffrey↗