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At least 397 records · Page 22

Metallized Gelled Propellants: Oxygen/RP-1/Aluminum Rocket Engine Calorimeter Heat Transfer Measurements and Analysis

A set of analyses was conducted to determine the heat transfer characteristics of metallized gelled liquid propellants in a rocket engine. The analyses used the data from experiments conducted with a small 30- to 40-lbf thrust engine composed of a modular injector, igniter, chamber and nozzle. The fuels used were traditional liquid RP-1 and gelled RP-1 with 0-wt %, 5-wt%, and 55-wt% loadings of aluminum with silicon dioxide gellant, and gaseous oxygen as the oxidizer. Heat transfer was computed based on measurements using calorimeter rocket chamber and nozzle hardware with a total of 31 cooling channels. A gelled fuel coating formed in the 0-, 5- and 55-wt% engines, and the coating was composed of unburned gelled fuel and partially combusted RP-1. The coating caused a large decrease in calorimeter engine heat flux in the last half of the chamber for the 0- and 5-wt% RP-1/Al. This heat flux reduction effect was analyzed by comparing engine runs and the changes in the heat flux during a run as well as from run to run. Heat transfer and time-dependent heat flux analyses and interpretations are provided. The 5- and 55-wt% RP-1/Al fueled engines had the highest chamber heat fluxes, with the 5-wt% fuel having the highest throat flux. This result is counter to the predicted result, where the 55 wt% fuel has the highest combustion and throat temperature, and therefore implies that it would deliver the highest throat heat flux. The 5-wt% RP-1/Al produced the most influence on the engine heat transfer and the heat flux reduction was caused by the formation of a gelled propellant layer in the chamber and nozzle.

Palaszewski, Bryan↗

Planetary Astronomy

This 1-year project was an augmentation grant to my NASA Planetary Astronomy grant. With the awarded funding, we accomplished the following tasks: (1) Conducted two NVK imaging runs in conjunction with the ILAW (International Lunar Atmosphere Week) Observing Campaigns in 1995 and 1997. In the first run, we obtained repeated imaging sequences of lunar Na D-line emission to better quantify the temporal variations detected in earlier runs. In the second run we obtained extremely high resolution (R=960.000) Na line profiles using the 4m AAT in Australia. These data are being analyzed under our new 3-year Planetary Astronomy grant. (2) Reduced, analyzed, and published our March 1995 spectroscopic dataset to detect (or set stringent upper limits on) Rb. Cs, Mg. Al. Fe, Ba, Ba. OH, and several other species. These results were reported in a talk at the LPSC and in two papers: (1) A Spectroscopic Survey of Metallic Abundances in the Lunar Atmosphere. and (2) A Search for Magnesium in the Lunar Atmosphere. Both reprints are attached. Wrote up an extensive, invited Reviews of Geophysics review article on advances in the study of the lunar atmosphere. This 70-page article, which is expected to appear in print in 1999, is also attached.

Stern, S. Alan↗

Parallel 3D Multi-Stage Simulation of a Turbofan Engine

A 3D multistage simulation of each component of a modern GE Turbofan engine has been made. An axisymmetric view of this engine is presented in the document. This includes a fan, booster rig, high pressure compressor rig, high pressure turbine rig and a low pressure turbine rig. In the near future, all components will be run in a single calculation for a solution of 49 blade rows. The simulation exploits the use of parallel computations by using two levels of parallelism. Each blade row is run in parallel and each blade row grid is decomposed into several domains and run in parallel. 20 processors are used for the 4 blade row analysis. The average passage approach developed by John Adamczyk at NASA Lewis Research Center has been further developed and parallelized. This is APNASA Version A. It is a Navier-Stokes solver using a 4-stage explicit Runge-Kutta time marching scheme with variable time steps and residual smoothing for convergence acceleration. It has an implicit K-E turbulence model which uses an ADI solver to factor the matrix. Between 50 and 100 explicit time steps are solved before a blade row body force is calculated and exchanged with the other blade rows. This outer iteration has been coined a "flip." Efforts have been made to make the solver linearly scaleable with the number of blade rows. Enough flips are run (between 50 and 200) so the solution in the entire machine is not changing. The K-E equations are generally solved every other explicit time step. One of the key requirements in the development of the parallel code was to make the parallel solution exactly (bit for bit) match the serial solution. This has helped isolate many small parallel bugs and guarantee the parallelization was done correctly. The domain decomposition is done only in the axial direction since the number of points axially is much larger than the other two directions. This code uses MPI for message passing. The parallel speed up of the solver portion (no 1/0 or body force calculation) for a grid which has 227 points axially.

Turner, Mark G.↗

A PTC Optimization and Control Surface Interference Study HSR Airframe Technical Review

This report considers the effect of canard and horizontal tail vertical position on the aerodynamic characteristics of the PTC configuration without nacelles and diverters. This analysis is followed by three optimization studies using canard and tail incidence as design variables in the first problem followed by an optimization run with canard and tail incidence and wing camber design variables and finally an optimization run with canard incidence and wing camber. The first problem was run at fixed lift while the other two problems were run at fixed angle of attack. The final investigation reported here will show data from a component buildup study using the PTC configuration. This final study will show the aerodynamic interference between the canard, wing and horizontal tail.

Hicks, Raymond↗

Computer Modeling of Electrostatic Aggregation of Granular Materials in Planetary and Astrophysical Settings

Electrostatic forces strongly influence the behavior of granular materials in both dispersed (cloud) systems and semi-packed systems. These forces can cause aggregation or dispersion of particles and are important in a variety of astrophysical and planetary settings. There are also many industrial and commercial settings where granular matter and electrostatics become partners for both good and bad. This partnership is important for human exploration on Mars where dust adheres to suits, machines, and habitats. Long-range Coulombic (electrostatic) forces, as opposed to contact-induced dipoles and van der Waals attractions, are generally regarded as resulting from net charge. We have proposed that in addition to net charge interactions, randomly distributed charge carriers on grains will result in a dipole moment regardless of any net charge. If grains are unconfined, or fluidized, they will rotate so that the dipole always induces attraction between grains. Aggregates are readily formed, and Coulombic polarity resulting from the dipole produces end-to-end stacking of grains to form filamentary aggregates. This has been demonstrated in USML experiments on Space Shuttle where microgravity facilitated the unmasking of static forces. It has also been demonstrated in a computer model using grains with charge carriers of both sign. Model results very closely resembled micro-g results with actual sand grains. Further computer modeling of the aggregation process has been conducted to improve our understanding of the aggregation process, and to provide a predictive tool for microgravity experiments slated for Space Station. These experiments will attempt to prove the dipole concept as outlined above. We have considerably enhanced the original computer model: refinements to the algorithm have improved the fidelity of grain behavior during grain contact, special attention has been paid to simulation time steps to enable establishment of a meaningful, quantitative time axis, and calibration of rounding accuracies have been conducted to test cumulative numerical influences in the model. The model has been run for larger grain populations, variable initial cloud densities, and we have introduced random net charging to individual grains, as well as a net charge to the cloud as a whole. The model uses 3 positive and 3 negative charges randomly distributed on each grain, with up to 160 grains contained within various size "boxes" that define the initial number densities in the clouds. Each charge represents localized charged region on a grain, but does not necessarily imply single quantized charge carriers. The Coulomb equations are then allowed to interact for each monopole: dipoles and any higher order charge coupling is a natural product of these "free" interactions over which the modeler exerts no influence. The charges are placed on surfaces of grains at random locations. A series of runs was conducted for neutral grains that had a perfect balance of negative and positive char carriers. Runs were also conducted with grains having additional fractional charges ranging between 0 and 1. By adding fractional charges of one sign, the model created grain populations in which all grains had excess charges the same sign, giving the cloud an overall net charge. This simulates clouds subjected to ionizing radiation (e. protoplanetary debris disk around a protosun), or any other process of charge biasing in a grain population (e.g., volcanic plumes). In another run series, random fractional charges of either sign were added to the grains so th some grains had a slight net positive charge while others had a slight net negative charge. This simulates triboelectrically-charged grain populations in which acquisition of an electron by one surface is at the expense creating a hole elsewhere. This dual sign charging was applied in two ways: in one case the cloud remained neutral by ensuring that all grain excess charges added to zero; in the other case, the cloud was permitted slight net char by not imposing a charge-balance condition. Additional information is contained in the original.

Marshall, J.↗

Cirrus Parcel Model Comparison Project

The Cirrus Parcel Model Comparison (CPMC) is a project of the GEWEX Cloud System Study Working Group on Cirrus Cloud Systems (GCSS WG2). The primary goal of this project is to identify cirrus model sensitivities to the state of our knowledge of nucleation and microphysics. Furthermore, the common ground of the findings may provide guidelines for models with simpler cirrus microphysics modules. We focus on the nucleation regimes of the warm (parcel starting at -40 C and 340 hPa) and cold (-60 C and 170 hPa) cases studied in the GCSS WG2 Idealized Cirrus Model Comparison Project. Nucleation and ice crystal growth were forced through an externally imposed rate of lift and consequent adiabatic cooling. The background haze particles are assumed to be lognormally-distributed H2SO4 particles. Only the homogeneous nucleation mode is allowed to form ice crystals in the HN-ONLY runs; all nucleation modes are switched on in the ALL-MODE runs. Participants were asked to run the HN-lambda-fixed runs by setting lambda = 2 (lambda is further discussed in section 2) or tailoring the nucleation rate calculation in agreement with lambda = 2 (exp 1). The depth of parcel lift (800 m) was set to assure that parcels underwent complete transition through the nucleation regime to a stage of approximate equilibrium between ice mass growth and vapor supplied by the specified updrafts.

Lin, Ruei-Fong↗

Are Fibre Channel SANs a Commodity?

The goal of this work is to evaluate the feasibility of putting together a Fibre Channel Storage Area Network with heterogeneous hardware running both open-source and commercial operating systems. Adherence to the Fibre Channel Specification is supposed to guarantee interoperability in such an environment. We also want to evaluate how difficult it might be to put together a SAN using open-source components. While all the commercial vendors provide Fibre Channel support, this comes at a cost, e.g., not only O/S and drivers, but usually an expensive support contract. The open-source model could lower the cost of building and maintaining a SAN. Of course, for this to be the case, the open-source platforms would have to provide the functionality to construct a SAN. We are assembling a Fibre Channel SAN from heterogeneous hardware (i386, alpha, sparc) running *BSD, Linux, Tru64, NT and Solaris operating systems. We are running several tests to investigate the level of Fibre Channel support provided by each OS. Our current testbed is specified in the table below. Currently, it only contains open-source platforms. We plan to add a PC running OpenBSD, as well as the following commercial systems: Sun Ultra 1/Solaris, DEC AlphaServer 4000/Tru64 Unix, Pentium Pro PC/Windows NT.

Becker, Jeff↗

Soil Moisture and Snow Cover: Active or Passive Elements of Climate?

A key question in the study of the hydrologic cycle is the extent to which surface effects such as soil moisture and snow cover are simply passive elements or whether they can affect the evolution of climate on seasonal and longer time scales. We have constructed ensembles of predictability studies using the NCAR CCM3 in which we compared the relative roles of initial surface and atmospheric conditions over the central and western U.S. GAPP region in determining the subsequent evolution of soil moisture and of snow cover. We have also made sensitivity studies with exaggerated soil moisture and snow cover anomalies in order to determine the physical processes that may be important. Results from simulations with realistic soil moisture anomalies indicate that internal climate variability may be the strongest factor, with some indication that the initial atmospheric state is also important. The initial state of soil moisture does not appear important, a result that held whether simulations were started in late winter or late spring. Model runs with exaggerated soil moisture reductions (near-desert conditions) showed a much larger effect, with warmer surface temperatures, reduced precipitation, and lower surface pressures; the latter indicating a response of the atmospheric circulation. These results suggest the possibility of a threshold effect in soil moisture, whereby an anomaly must be of a sufficient size before it can have a significant impact on the atmospheric circulation and hence climate. Results from simulations with realistic snow cover anomalies indicate that the time of year can be crucial. When introduced in late winter, these anomalies strongly affected the subsequent evolution of snow cover. When introduced in early winter, however, little or no effect is seen on the subsequent snow cover. Runs with greatly exaggerated initial snow cover indicate that the high reflectivity of snow is the most important process by which snow cover can impact climate, through lower surface temperatures and increased surface pressures. In early winter, the amount of solar radiation is very small and so this albedo, effect is inconsequential while in late winter, with the sun higher in the sky and period of daylight longer, the effect is much stronger. The results to date were obtained for model runs with present-day conditions. We are currently analyzing runs made with projected forcings for the 21st century to see if these results are modified in any way under likely scenarios of future climate change.

Oglesby, Robert J.↗

Creating Web-Based Scientific Applications Using Java Servlets

There are many advantages to developing web-based scientific applications. Any number of people can access the application concurrently. The application can be accessed from a remote location. The application becomes essentially platform-independent because it can be run from any machine that has internet access and can run a web browser. Maintenance and upgrades to the application are simplified since only one copy of the application exists in a centralized location. This paper details the creation of web-based applications using Java servlets. Java is a powerful, versatile programming language that is well suited to developing web-based programs. A Java servlet provides the interface between the central server and the remote client machines. The servlet accepts input data from the client, runs the application on the server, and sends the output back to the client machine. The type of servlet that supports the HTTP protocol will be discussed in depth. Among the topics the paper will discuss are how to write an http servlet, how the servlet can run applications written in Java and other languages, and how to set up a Java web server. The entire process will be demonstrated by building a web-based application to compute stagnation point heat transfer.

Palmer, Grant↗

Using Modules with MPICH-G2 (and "Loose Ends")

A new approach to running complex, distributed MPI jobs using the MPICH-G2 library is described. This approach allows the user to switch between different versions of compilers, system libraries, MPI libraries, etc. via the "module" command. The key idea is a departure from the prescribed "(jobtype=mpi)" approach to running distributed MPI jobs. The new method requires the user to provide a script that will be run as the "executable" with the "(jobtype=single)" RSL attribute. The major advantage of the proposed method is to enable users to decide in their own script what modules, environment, etc. they would like to have in running their job.

Chang, Johnny↗

Impact of Mineral Aerosol on TOVS Temperature and Moisture Retrievals

Mineral aerosols can absorb significant radiation in the infrared spectrum. Consequently, there may be errors in TIROS Operational Vertical Sounder (TOVS) retrieved temperature and moisture profiles in regions of heavy dust loading. We first investigate the potential error in the temperature retrievals and secondly attempt to account for radiative effects of the dust in retrievals. Information on the dust concentrations and size distribution is from the Goddard Chemistry Aerosol Transport model (GOCART). Aerosol optical parameters are calculated from mie scattering theory assuming a composition of pure illite. We used the cloud-clearing DAO TOVS retrieval system of Joiner and Rokke (2000). It is incorporated into the Data Assimilation Office (DAO) Finite Volume Data Assimilation System (NDAS). The advantage of this approach is that the first guess temperature profile used in the TOVS retrieval are forecasted temperatures from the previous assimilated time period. The operational DAO fvDAS was run for 10 days during June 2001 during a period of dust outbreaks off the coast of Africa over the Atlantic. The observed minus the forecast (O-F) brightness temperature at each TOVS channel is a measure of the accuracy of the retrieval. Since there was no account of dust during this operational run, a dependence of O-F on the estimated atmospheric dust concentrations from GOCART indicates that the dust is contaminating the TOVS retrievals. Channels that measure the surface temperature, lower tropospheric temperature and moisture show this dependence. There are errors in the retrieved brightness temperature of a half a degree or more during heavy dust loading conditions. The forecasted brightness temperature is always greater than the observed value. The radiative transfer module used in the DAO TOVS retrieval system was modified to account for dust. We calculate the sensitivity of the brightness temperature of the TOVS channels to the dust concentrations in GOCART assuming pure illite. For most channels the observed relationship between O-F and dust concentrations in GOCART is consistent with these calculated sensitivities. The fvDAS run was repeated using the modified DAO TOVS retrieval system that accounts for dust. Preliminary results from this run show that there are significant effects on the retrieved surface temperature and tropospheric moisture.

Weaver, Clark↗

Soil Moisture and Snow Cover: Active or Passive Elements of Climate

A key question is the extent to which surface effects such as soil moisture and snow cover are simply passive elements or whether they can affect the evolution of climate on seasonal and longer time scales. We have constructed ensembles of predictability studies using the NCAR CCM3 in which we compared the relative roles of initial surface and atmospheric conditions over the central and western U.S. in determining the subsequent evolution of soil moisture and of snow cover. Results from simulations with realistic soil moisture anomalies indicate that internal climate variability may be the strongest factor, with some indication that the initial atmospheric state is also important. Model runs with exaggerated soil moisture reductions (near-desert conditions) showed a much larger effect, with warmer surface temperatures, reduced precipitation, and lower surface pressures; the latter indicating a response of the atmospheric circulation. These results suggest the possibility of a threshold effect in soil moisture, whereby an anomaly must be of a sufficient size before it can have a significant impact on the atmospheric circulation and climate. Results from simulations with realistic snow cover anomalies indicate that the time of year can be crucial. When introduced in late winter, these anomalies strongly affected the subsequent evolution of snow cover. When introduced in early winter, however, little or no effect is seen on the subsequent snow cover. Runs with greatly exaggerated initial snow cover indicate that the high reflectivity of snow is the most important process by which snow cover can impact climate, through lower surface temperatures and increased surface pressures. The results to date were obtained for model runs with present-day conditions. We are currently analyzing runs made with projected forcings for the 21st century to see if these results are modified in any way under likely scenarios of future climate change. An intriguing new statistical technique involving 'clustering' is developed to assist in this analysis.

Oglesby, Robert J.↗

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental building block in numerous image processing applications. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute the coordinates of a set of cluster centers in d-space, such that those centers minimize the mean squared distance from each data point to its nearest center. This clustering algorithm is similar to another well-known clustering method, called k-means. One significant feature of ISOCLUS over k-means is that the actual number of clusters reported might be fewer or more than the number supplied as part of the input. The algorithm uses different heuristics to determine whether to merge lor split clusters. As ISOCLUS can run very slowly, particularly on large data sets, there has been a growing .interest in the remote sensing community in computing it efficiently. We have developed a faster implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm of Kanungo, et al. They showed that, by using a kd-tree data structure for storing the data, it is possible to reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm, and we show that it is possible to achieve essentially the same results as ISOCLUS on large data sets, but with significantly lower running times. This adaptation involves computing a number of cluster statistics that are needed for ISOCLUS but not for k-means. Both the k-means and ISOCLUS algorithms are based on iterative schemes, in which nearest neighbors are calculated until some convergence criterion is satisfied. Each iteration requires that the nearest center for each data point be computed. Naively, this requires O(kn) time, where k denotes the current number of centers. Traditional techniques for accelerating nearest neighbor searching involve storing the k centers in a data structure. However, because of the iterative nature of the algorithm, this data structure would need to be rebuilt with each new iteration. Our approach is to store the data points in a kd-tree data structure. The assignment of points to nearest neighbors is carried out by a filtering process, which successively eliminates centers that can not possibly be the nearest neighbor for a given region of space. This algorithm is significantly faster, because large groups of data points can be assigned to their nearest center in a single operation. Preliminary results on a number of real Landsat datasets show that our revised ISOCLUS-like scheme runs about twice as fast.

Memarsadeghi, Nargess↗

Spiral Bevel Pinion Crack Detection in a Helicopter Gearbox

The vibration resulting from a cracked spiral bevel pinion was recorded and analyzed using existing Health and Usage Monitoring System (HUMS) techniques. A tooth on the input pinion to a Bell OH-58 main rotor gearbox was notched and run for an extended period at severe over-torque condition to facilitate a tooth fracture. Thirteen vibration-based diagnostic metrics were calculated throughout the run. After 101.41 hours of run time, some of the metrics indicated damage. At that point a visual inspection did not reveal any damage. The pinion was then run for another 12 minutes until a proximity probe indicated that a tooth had fractured. This paper discusses the damage detection effectiveness of the different metrics and a comparison of effects of the different accelerometer locations.

Decker, Harry J.↗

What Went Wrong: Explaining Counterexamples

Model checking, initially successful in the field of hardware design, has recently been applied to software. One of the chief advantages of model checking is the production of counterexamples demonstrating that a system does not satisfy a speci cation. However, it may require a great deal of human effort to extract the essence of an error from even a detailed source-level trace of a failing run. We use an automated method for nding multiple versions of an error (and similar executions that do not produce an error), and analyze these executions to produce a more succinct description of the key elements of the error. The description produced includes identi cation of portions of the source code crucial to distinguishing failing and succeeding runs, di erences in invariants between failing and non-failing runs, and information on the necessary changes in scheduling and environmental actions needed to cause suc- cessful runs to fail. In addition, this analysis allows a classi cation of errors by features such as whether they are purely concurrent (i.e. can be induced by changing only thread scheduling).

Groce, Alex↗

Migration of Dust Particles from Comet 2P Encke

We investigated the migration of dust particles under the gravitational influence of all planets (except for Pluto), radiation pressure, Poynting-Robertson drag and solar wind drag for Beta equal to 0.002, 0.004, 0.01, 0.05, 0.1, 0.2, and 0.4. For silicate particles such values of Beta correspond to diameters equal to about 200, 100, 40, 9, 4, 2, and 1 microns, respectively. We used the Bulirsh-Stoer method of integration, and the relative error per integration step was taken to be less than lo-'. Initial orbits of the particles were close to the orbit of Comet 2P Encke. We considered initial particles near perihelion (runs denoted as Delta tsub o, = 0), near aphelion (Delta tsub o, = 0.5), and also studied their initial positions when the comet moved for Pa/4 after perihelion passage (such runs are denoted as Delta tsub o, =i 0.25), where Pa is the period of the comet. Variations in time T when perihelion was passed was varied with a step 0.1 day for series 'S' and with a step 1 day for series 'L'. For each Beta we considered N = 101 particles for "S" runs and 150 particles for "L" runs.

Ipatov, S. I.↗

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental tool in numerous image processing and remote sensing applications. For example, unsupervised clustering is often used to obtain vegetation maps of an area of interest. This approach is useful when reliable training data are either scarce or expensive, and when relatively little a priori information about the data is available. Unsupervised clustering methods play a significant role in the pursuit of unsupervised classification. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points (or samples) in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute a set of cluster centers in d-space. Although there is no specific optimization criterion, the algorithm is similar in spirit to the well known k-means clustering method in which the objective is to minimize the average squared distance of each point to its nearest center, called the average distortion. One significant feature of ISOCLUS over k-means is that clusters may be merged or split, and so the final number of clusters may be different from the number k supplied as part of the input. This algorithm will be described in later in this paper. The ISOCLUS algorithm can run very slowly, particularly on large data sets. Given its wide use in remote sensing, its efficient computation is an important goal. We have developed a fast implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm, the filtering algorithm, by Kanungo et al.. They showed that, by storing the data in a kd-tree, it was possible to significantly reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm. For technical reasons, which are explained later, it is necessary to make a minor modification to the ISOCLUS specification. We provide empirical evidence, on both synthetic and Landsat image data sets, that our algorithm's performance is essentially the same as that of ISOCLUS, but with significantly lower running times. We show that our algorithm runs from 3 to 30 times faster than a straightforward implementation of ISOCLUS. Our adaptation of the filtering algorithm involves the efficient computation of a number of cluster statistics that are needed for ISOCLUS, but not for k-means.

Memarsadeghi, Nargess↗

Self-Scheduling Parallel Methods for Multiple Serial Codes with Application to WOPWOP

This paper presents a scheme for efficiently running a large number of serial jobs on parallel computers. Two examples are given of computer programs that run relatively quickly, but often they must be run numerous times to obtain all the results needed. It is very common in science and engineering to have codes that are not massive computing challenges in themselves, but due to the number of instances that must be run, they do become large-scale computing problems. The two examples given here represent common problems in aerospace engineering: aerodynamic panel methods and aeroacoustic integral methods. The first example simply solves many systems of linear equations. This is representative of an aerodynamic panel code where someone would like to solve for numerous angles of attack. The complete code for this first example is included in the appendix so that it can be readily used by others as a template. The second example is an aeroacoustics code (WOPWOP) that solves the Ffowcs Williams Hawkings equation to predict the far-field sound due to rotating blades. In this example, one quite often needs to compute the sound at numerous observer locations, hence parallelization is utilized to automate the noise computation for a large number of observers.

Long, Lyle N.↗