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225 records · Page 13

Clouds in ECMWF's 30 KM Resolution Global Atmospheric Forecast Model (TL639)

Global models of the general circulation of the atmosphere resolve a wide range of length scales, and in particular cloud structures extend from planetary scales to the smallest scales resolvable, now down to 30 km in state-of-the-art models. Even the highest resolution models do not resolve small-scale cloud phenomena seen, for example, in Landsat and other high-resolution satellite images of clouds. Unresolved small-scale disturbances often grow into larger ones through non-linear processes that transfer energy upscale. Understanding upscale cascades is of crucial importance in predicting current weather, and in parameterizing cloud-radiative processes that control long term climate. Several movie animations provide examples of the temporal and spatial variation of cloud fields produced in 4-day runs of the forecast model at the European Centre for Medium-Range Weather Forecasts (ECMWF) in Reading, England, at particular times and locations of simultaneous measurement field campaigns. model resolution is approximately 30 km horizontally (triangular truncation TL639) with 31 vertical levels from surface to stratosphere. Timestep of the model is about 10 minutes, but animation frames are 3 hours apart, at timesteps when the radiation is computed. The animations were prepared from an archive of several 4-day runs at the highest available model resolution, and archived at ECMWF. Cloud, wind and temperature fields in an approximately 1000 km X 1000 km box were retrieved from the archive, then approximately 60 Mb Vis5d files were prepared with the help of Graeme Kelly of ECMWF, and were compressed into MPEG files each less than 3 Mb. We discuss the interaction of clouds and radiation in the model, and compare the variability of cloud liquid as a function of scale to that seen in cloud observations made in intensive field campaigns. Comparison of high-resolution global runs to cloud-resolving models, and to lower resolution climate models is leading to better understanding of the upscale cascade and suggesting new cloud-radiation parameterizations for climate models.

Cahalan, R. F.↗

Computational and Experimental Study of Energetic Materials in a Counterflow Microgravity Environment

Counterflow diffusion flames are studied for various fuels flowing against decomposition products from solid ammonium perchlorate (AP) pellets in order to obtain fundamental understanding of composite propellant flame structure and chemistry. We illustrate this approach through a combined experimental and numerical study of a fuel mixture consisting of C2H4 CO + H2, and C2H2 + C2H4 flowing against solid AP. For these particular AP-fuel systems, the resulting flame zone simulates the various flame structures that are ex+ to exist between reaction products from Ap crystals and a hydrocarbon binder. As in all our experimental studies, quantitative species and temperature profiles have been measured between the fuel exit and AP surface. Species measured included CN, NH, NO, OH, N2, CO2, CO, H2, CO, HCl, and H2O. Temperature was measured using a thermocouple at the exit, spontaneous Raman scattering measurements throughout the flame, OH rotational population distributions, and NO vibrational population distributions. The burning rate of AP was also measured as a function of strain rate, given by the separation distance between the AP surface and the gaseous hydrocarbon fuel tube exit plane. This distance was nominally set at 5 mm, although studies have been performed for variations in separation distance. The measured 12 scalars are compared with predictions from a detailed gas-phase kinetics model consisting of 86 species and 531 reactions. Model predictions are found to be in good agreement with experiment and illustrate the type of kinetic features that may be expected to occur in propellants when AP particle size distributions are varied. Furthermore, the results constitute the continued development of a necessary database and validation of a comprehensive model for studying more complex AP-solid fuel systems in microgravity. Exploratory studies have also been performed with liquid and solid fuels at normal gravity. Because of melting (and hence dripping) and deep thermal wave penetration into the liquid, these experiments were found feasible, but not used for obtaining quantitative data. Microgravity experiments are needed to eliminate the dripping and boiling phenomena of these systems at normal gravity. Microgravity tests in the NASA Glenn 2.2 second drop tower were performed (1) to demonstrate the feasibility of performing propellant experiments using the NASA Glenn microgravity facilities, (2) to develop the operational procedures for safe handing of the energetic materials and disposal of their toxic combustion by-products and (3) to obtain initial measurements of the AP burning rate and flame structure under microgravity conditions. Experiments were conducted on the CH4/AP system previously studied at normal gravity using a modified design of the counterflow burner and a NASA Glenn Pig Rig, i.e., one of the existing drop rigs for general-purpose usage. In these experiments, the AP burning rate was measured directly with a linear variable differential transducer (LVDT) and video imaging of the flame structure was recorded ignition was achieved by hot wires stretched across the AP surfaces. Initial drop tower combustion data show that with the same burner separation distance and flow conditions of the normal gravity experiments, the AP burning rate is approximately a factor of two lower. This difference is likely a result of radiation effects, but further tests with longer test times need to be conducted to verify that steady state conditions were achieved under microgravity conditions.

Takahashi, Fumiaki↗

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

On the Contribution of Turbulent Boundary Layers to the Noise Inside a Fuselage

The following report deals in preliminary fashion with the transmission through a fuselage of random noise generated on the fuselage skin by a turbulent boundary layer. The concept of attenuation is abandoned and instead the problem is formulated as a sequence of two linear couplings: the turbulent boundary layer fluctuations excite the fuselage skin in lateral vibrations and the skin vibrations induce sound inside the fuselage. The techniques used are those required to determine the response of linear systems to random forcing functions of several variables. A certain degree of idealization has been resorted to. Thus the boundary layer is assumed locally homogeneous, the fuselage skin is assumed flat, unlined and free from axial loads and the 'cabin' air is bounded only by the vibrating plate so that only outgoing waves are considered. Some of the details of the statistical description have been simplified in order to reveal the basic features of the problem. The results, strictly applicable only to the limiting case of thin boundary layers, show that the sound pressure intensity is proportional to the square of the free stream density, the square of cabin air density and inversely proportional to the first power of the damping constant and to the second power of the plate density. The dependence on free stream velocity and boundary layer thickness cannot be given in general without a detailed knowledge of the characteristics of the pressure fluctuations in the boundary layer (in particular the frequency spectrum). For a flat spectrum the noise intensity depends on the fifth power of the velocity and the first power of the boundary layer thickness. This suggests that boundary layer removal is probably not an economical means for decreasing cabin noise. In general, the analysis presented here only reduces the determination of cabin noise intensity to the measurement of the effect of any one of our variables (free stream velocity, boundary layer thickness, plate thickness or the characteristic velocity of propagation in the plate). The plate generates noise by vibrating in resonance over a wide range of frequencies and increasing the damping constant is consequently an effective method of decreasing noise generation. One of the main features of the results is that the relevant quantities upon which noise intensity depends are non-dimensional numbers in which boundary layer and plate properties enter as ratios. This is taken as an indication that in testing models of structures for boundary layer noise it is not sufficient to duplicate in the model the structural characteristics of the fuselage. One must match properly the characteristics of the exicitng pressure fluctuations to that of the structure.

Corcos, G. M.↗

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.

Damon, M. R.↗

Let's Exploit Available Knowledge on Vegetation Fluorescence

The potential to measure vegetation fluorescence from space (1) and to derive from it direct information on the gross primary productivity (GPP) of terrestrial ecosystems is probably the most thrilling development in remote sensing and global ecology of recent years, as it moves Earth observation techniques from the detection of canopy biophysics (e.g., fraction of absorbed radiation) and biochemistry (chlorophyll and nitrogen content) to the realm of ecosystem function. The existence of a functional relationship between fluorescence and photosynthesis has been elucidated over the last decade by several laboratories, notably as part of the preliminary studies of the European Space Agency Fluorescence Explorer (FLEX) Earth Explorer Mission. The empirical observation presented by Guanter et al. (2) of a linear relationship between fluorescence radiance and GPP, however, provides the first experimental confirmation of the feasibility of the approach— already thoroughly tested at leaf level—at the desired scale, despite the confounding effects associated with the satellite detection of such a faint signal. A word of clarification is needed here. The use of fluorescence as a probe of leaf photochemistry has been a staple of plant ecophysiology for decades, rooted in a sound understanding of photosynthetic energy dissipation. However, most past studies had to rely for the interpretation of results on active (pulse-saturated) techniques, making them unsuitable for remote-sensing applications. Over recent years, however, novel process based models have been developed for the interpretation of steady-state, solar-induced fluorescence at the leaf to canopy scale (3). We are therefore in a position to move beyond the mere empirical observation of an association between GPP and fluorescence radiance. In particular, Guanter et al. (2) base their analysis on the assumption of a constant ratio between photosynthetic and fluorescence light use efficiencies (equation 3 in ref. 2).We know, however, that the ratio is not constant, but changes widely in response to light, CO2, stomatal limitations, and extreme stress (4, 5). What’s more, we can make sense of such changes, thus extracting valuable information from the very scatter that is apparent in their data. However, this process will require the availability of more tailored instruments, such as the one planned for the FLEX mission. As already stressed by Guanter et al. (2), the spatial resolution of the Global Ozone Monitoring Experiment-2 sensor (40 × 80 km) makes it difficult to compare meaningfully the fluorescence signal with ground measurements, when only 60–70% of the footprint consists of the desired land-cover type (table S1 in ref. 2), suggesting that this could be largely responsible for the low signals observed in European grasslands. Moreover, the overpass time of the MetOp-A satellite (9:30 AM) implies that fluorescence is generally measured under light-limiting conditions, when fluorescence is only marginally affected by stomatal closure even under stress conditions. This result could explain the seasonal mismatch with daily GPP observed in natural ecosystems in the absence of irrigation (figure 4 in ref. 2). We hope, therefore, that this welcome contribution to this fast-advancing field will help demonstrate the potential of the new technique, and pave the way for more refined studies under both a technological and scientific point of view.

Space↗

LOFTID Heat Flux Gauge Calibration: What is Truth?

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) is a demonstration of Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology, which may enable the delivery of heavy payloads to Mars, Venus, and Titan, as well as return to Earth. Unlike rigid aeroshells that are constrained by the size of the rocket’s shroud, inflatable aeroshells can be deployed to a much larger scale, thus allowing a spacecraft to begin its deceleration earlier and experience less heating. On LOFTID, there will be 4 total heat flux gauges (HFG) with a range of 70 W/cm2 and 1 radiometer with a range of 3 W/cm2, arranged as shown in Fig. 1. Both the radiometer and total HFGs are Schmidt-Boelter gauges purchased from an external vendor. Radiative calibrations were performed in-house at NASA Ames’ Sensors and TPS Advanced Research Laboratories (STAR Labs) before and after environmental testing to investigate how the testing affected the sensors' response. Additional rounds of radiative calibration at STAR Labs were also performed in order to investigate the large uncertainties associated with these tests. For example, a survey of multiple calibration facilities concluded that the uncertainty within a given facility was +/-3% [1]. An additional NIST study that calibrated heat flux gauges at 7 different facilities also found the variation in calibration coefficients to be up to ~3% within a given facility, but up to 15% between facilities, suggesting systematic differences between test setups [2]. Finally, the response of heat flux gauges to radiative versus convective heat flux has shown to differ by up to 20% [3],[4]. Because the heat flux gauges on LOFTID will predominantly experience convective heat flux during flight, a convective calibration study was performed at Boeing's Large-Core Arc Tunnel (LCAT) facility. Radiative Calibration Procedure The calibrations performed at STAR Labs utilize a quartz lamp bank (QLB) that provides a maximum heat flux of 50 W/cm2, which bounds the expected LOFTID flight environment. The calibration involves exposing a water-cooled Gardon gauge (reference) and then the unit-under-test (UUT) to 5 different heat fluxes multiple times for 10 seconds each, and then calculating a linear fit. The test setup is shown in Fig. 2. The total HFGs were calibrated at STAR Labs 3 times, denoted as STAR 1 (before environmental testing), STAR 2 (after protoflight vibration and thermal-vacuum testing), and STAR 3 (no change from previous test). All 8 flight-lot total HFGs showed a decrease in full-scale output from STAR 1 to STAR 2 by between 0.5% and 10. The first portion of this investigation was to determine whether the change could be due to differences in temperature between the two calibration runs. A typical linear fit to the calibration data was performed using Eq. 1 where q’ is the heat flux in W/cm2, c is the calibration coefficient, and mV is the sensor output. To account for temperature, the data were fit to a nonlinear function that included both the sensor output (mV) and the temperature from the thermocouple embedded inside the HFG near the surface (T): q'=mV/(c1* T + c0}. The residuals between the fits and the actual data points were calculated for every point, and proven to be much smaller for the temperature-compensated fits than for the linear fits for all sensors. An example is shown in Fig. 3. When the temperature-compensated fits from STAR 1 were applied to the STAR 2 data, the residuals did not improve, suggesting that the change in sensitivity between these two calibration runs was not due to temperature. A third round of calibration (STAR 3) was conducted to further address the temperature dependence of the total HFGs, and the resulting sensitivities matched closely to STAR 2 (within 2%). Temperature-compensated calibration curves were once again fit to the data. In this case, when the temperature-compensated fits from STAR 3 were applied to STAR 2 data, the residuals between the fits and STAR 2 data were much lower than the residuals due to the linear fits. This suggests that the changes seen between STAR 1 and STAR 2 were likely due to actual changes in the sensors caused by the environmental testing between the two calibrations. A modification of the original calibration process, in which the UUT was exposed to each heat flux for just 3 seconds (instead of 10) to reduce the temperature increase during the test, was additionally performed on several of the HFGs. In general, the sensitivities were 1-1.5% lower than from the 10-second tests, but the temperatures were also significantly lower. When the temperature-compensated fits from the 10-second tests were applied to the 3-second test data, the residuals were greatly improved than when just using the linear fits, further suggesting that the temperature-compensated fits may lead to better accuracy than the linear fits in flight. Convective Calibration The second portion of this study was to create a mapping between the radiative and convective calibration coefficients. The majority of the heating during flight will be convective, so it is important to understand how the HFG response differs under these conditions. However, there are no standardized methods for convective calibration [5]. Because the TPS aerothermal response models were validated at LCAT, the same facility was chosen for convective calibration of two of the total HFGs (Fig. 4). Preliminary results showed that the full-scale output was 3% and 8% higher in convective heat flux as compared to radiative heat flux. However, tunnel variation may have contributed to noise and uncertainty in the measurements, and more testing and analysis remains to be done. Scope of Presentation The presentation will include an overview of the changes seen in HFG calibration before and after environmental testing, differences between radiative and convective calibrations, the modeling work done to aid in understanding the sensor response to varying environments, and recommended future work.

H S Alpert↗

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗

Modeling and Prediction of the Noise from Non-Axisymmetric Jets

The new source model was combined with the original sound propagation model developed for rectangular jets to produce a new version of the rectangular jet noise prediction code. This code was validated using a set of rectangular nozzles whose geometries were specified by NASA. Nozzles of aspect ratios two, four and eight were studied at jet exit Mach numbers of 0.5, 0.7 and 0.9, for a total of nine cases. Reynolds-averaged Navier-Stokes solutions for these jets were provided to the contactor for use as input to the code. Quantitative comparisons of the predicted azimuthal and polar directivity of the acoustic spectrum were made with experimental data provided by NASA. The results of these comparisons, along with a documentation of the propagation and source models, were reported in a journal article publication (Ref. 4). The complete set of computer codes and computational modules that make up the prediction scheme, along with a user's guide describing their use and example test cases, was provided to NASA as a deliverable of this task. The use of conformal mapping, along with simplified modeling of the mean flow field, for noise propagation modeling was explored for other nozzle geometries, to support the task milestone of developing methods which are applicable to other geometries and flow conditions of interest to NASA. A model to represent twin round jets using this approach was formulated and implemented. A general approach to solving the equations governing sound propagation in a locally parallel nonaxisymmetric jet was developed and implemented, in aid of the tasks and milestones charged with selecting more exact numerical methods for modeling sound propagation, and developing methods that have application to other nozzle geometries. The method is based on expansion of both the mean-flowdependent coefficients in the governing equation and the Green's function in series of orthogonal functions. The method was coded and tested on two analytically prescribed mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant equations. Working with NASA Glenn Acoustics Branch personnel, numerical methods and boundary conditions appropriate for use in a high-resolution calculation of the full equations governing sound propagation in a steady base flow were identified. Computer codes were then written (by NASA) and tested (by OAI) for an increasingly complex set of flow conditions to validate the methods. The NASA-supplied codes were ported to the High-End Computing resources of the NASA Advanced Supercomputing facility for testing and validation against analytical (where possible) and independent numerical solutions. The cases which were completed during the course of this contract were solutions of the two-dimensional linearized Euler equations with no mean flow, a uniform mean flow and a nonuniform mean flow representative of a parallel flow jet.

Leib, Stewart J.↗