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NASA NTRS1998

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗
NASA NTRS2002

"We Freeze to Please": A History of NASA's Icing Research Tunnel and the Quest for Flight Safety

The formation of ice on wings and other control surfaces of airplanes is one of the oldest and most vexing problems that aircraft engineers and scientists continue to face. While no easy, comprehensive answers exist, the staff at NASAs Icing Research Tunnel (IRT) at the Glenn Research Center in Cleveland has done pioneering work to make flight safer for experimental, commercial, and military customers. The National Advisory Committee for Aeronautics (NACA) initiated government research on aircraft icing in the 1930s at its Langley facility in Virginia. Icing research shifted to the NACA's Cleveland facility in the 1940s. Initially there was little focus on icing at either location, as these facilities were more concerned with aerodynamics and engine development. With several high-profile fatal crashes of air mail carriers, however, the NACA soon realized the need for a leading research facility devoted to icing prevention and removal. The IRT began operation in 1944 and, despite renovations and periodic attempts to shut it down, has continued to function productively for almost 60 years. In part because icing has proved so problematic over time, IRT researchers have been unusually open-minded in experimenting with a wide variety of substances, devices, and techniques. Early icing prevention experiments involved grease, pumping hot engine exhaust onto the wings, glycerin soap, mechanical and inflatable "boots," and even corn syrup. The IRT staff also looked abroad for ideas and later tried a German and Soviet technique of electromagnetism, to no avail. More recently, European polymer fluids have been more promising. The IRT even periodically had "amateur nights" in which a dentist's coating for children's teeth proved unequal to the demands of super-cooled water droplets blown at 100 miles per hour. Despite many research dead-ends, IRT researchers have achieved great success over the years. They have developed important computer models, such as the LEWICE software, and made significant contributions to prevent ice buildup on turbine-powered commercial aircraft, helicopters, and military planes.

Leary, William M.↗
NASA NTRS2002

Program Instrumentation and Trace Analysis

Several attempts have been made recently to apply techniques such as model checking and theorem proving to the analysis of programs. This shall be seen as a current trend to analyze real software systems instead of just their designs. This includes our own effort to develop a model checker for Java, the Java PathFinder 1, one of the very first of its kind in 1998. However, model checking cannot handle very large programs without some kind of abstraction of the program. This paper describes a complementary scalable technique to handle such large programs. Our interest is turned on the observation part of the equation: How much information can be extracted about a program from observing a single execution trace? It is our intention to develop a technology that can be applied automatically and to large full-size applications, with minimal modification to the code. We present a tool, Java PathExplorer (JPaX), for exploring execution traces of Java programs. The tool prioritizes scalability for completeness, and is directed towards detecting errors in programs, not to prove correctness. One core element in JPaX is an instrumentation package that allows to instrument Java byte code files to log various events when executed. The instrumentation is driven by a user provided script that specifies what information to log. Examples of instructions that such a script can contain are: 'report name and arguments of all called methods defined in class C, together with a timestamp'; 'report all updates to all variables'; and 'report all acquisitions and releases of locks'. In more complex instructions one can specify that certain expressions should be evaluated and even that certain code should be executed under various conditions. The instrumentation package can hence be seen as implementing Aspect Oriented Programming for Java in the sense that one can add functionality to a Java program without explicitly changing the code of the original program, but one rather writes an aspect and compiles it into the original program using the instrumentation. Another core element of JPaX is an observation package that supports the analysis of the generated event stream. Two kinds of analysis are currently supported. In temporal analysis the execution trace is evaluated against formulae written in temporal logic. We have implemented a temporal logic evaluator on finite traces using the Maude rewriting system from SRI International, USA. Temporal logic is defined in Maude by giving its syntax as a signature and its semantics as rewrite equations. The resulting semantics is extremely efficient and can handle event streams of hundreds of millions events in few minutes. Furthermore, the implementation is very succinct. The second form of even stream analysis supported is error pattern analysis where an execution trace is analyzed using various error detection algorithms that can identify error-prone programming practices that may potentially lead to errors in some different executions. Two such algorithms focusing on concurrency errors have been implemented in JPaX, one for deadlocks and the other for data races. It is important to note, that a deadlock or data race potential does not need to occur in order for its potential to be detected with these algorithms. This is what makes them very scalable in practice. The data race algorithm implemented is the Eraser algorithm from Compaq, however adopted to Java. The tool is currently being applied to a code base for controlling a spacecraft by the developers of that software in order to evaluate its applicability.

Havelund, Klaus↗
NASA NTRS2003

Hiproofs

We introduce a hierarchical notion of formal proof, useful in the implementation of theorem provers, which we call highproofs. Two alternative definitions are given, motivated by existing notations used in theorem proving research. We define transformations between these two forms of hiproof, develop notions of underlying proof, and give a suitable definition of refinement in order to model incremental proof development. We show that our transformations preserve both underlying proofs and refinement. The relationship of our theory to existing theorem proving systems is discussed, as is its future extension.

Denney, Ewen↗
NASA NTRS2003

Performance Expectations of Closed-Brayton-Cycle Heat Exchangers in 100-kWe Nuclear Space Power Systems

Performance expectations of closed-Brayton-cycle heat exchangers to be used in 100-kWe nuclear space power systems were forecast. Proposed cycle state points for a system supporting a mission to three of Jupiter s moons required effectiveness values for the heat-source exchanger, recuperator and rejection exchanger (gas cooler) of 0.98,0.95 and 0.97, respectively. Performance parameters such as number of thermal units (Nm), equivalent thermal conductance (UA), and entropy generation numbers (Ns) varied from 11 to 19,23 to 39 kWK, and 0.019 to 0.023 for some standard heat exchanger configurations. Pressure-loss contributions to entropy generation were significant; the largest frictional contribution was 114% of the heat-transfer irreversibility. Using conventional recuperator designs, the 0.95 effectiveness proved difficult to achieve without exceeding other performance targets; a metallic, plate-fin counterflow solution called for 15% more mass and 33% higher pressure-loss than the target values. Two types of gas-coolers showed promise. Single-pass counterflow and multipass cross-counterflow arrangements both met the 0.97 effectiveness requirement. Potential reliability-related advantages of the cross-countefflow design were noted. Cycle modifications, enhanced heat transfer techniques and incorporation of advanced materials were suggested options to reduce system development risk. Carbon-carbon sheeting or foam proved an attractive option to improve overall performance.

Barrett, Michael J.↗
NASA NTRS2003

Computer Simulation of a Digital Global Velocimeter

The objective is to continue the development of a Monte-Carlo simulation of a Doppler Global Velocimetry (DGV) optical system starting with the Mie scattering from the particles in the fluid to the collection optics, through the beamsplitter, Iodine absorption cell and finally to the CCD sensor. The simulation program will read in a configuration file that completely describes the attributes of a DGV system (optical, physical layout, location of detectors, laser properties, CCD sensor noise characteristics...). The simulation program will output a set of images that simulate the data collected from a DGV system. NASA GRC has the DGV software developed at NASA Langley and this simulation program will prove invaluable for determining the accuracy of the DGV technique and provide insight into optimizing the data reduction techniques. The DGV simulation software will also prove valuable in a DDF funded projected entitled Planar Particle Imaging Doppler Velocimetry (PPIDV), which was recently awarded in March 2002.

Cheung, H. Mike↗
NASA NTRS2004

Product-oriented Software Certification Process for Software Synthesis

The purpose of this document is to propose a product-oriented software certification process to facilitate use of software synthesis and formal methods. Why is such a process needed? Currently, software is tested until deemed bug-free rather than proving that certain software properties exist. This approach has worked well in most cases, but unfortunately, deaths still occur due to software failure. Using formal methods (techniques from logic and discrete mathematics like set theory, automata theory and formal logic as opposed to continuous mathematics like calculus) and software synthesis, it is possible to reduce this risk by proving certain software properties. Additionally, software synthesis makes it possible to automate some phases of the traditional software development life cycle resulting in a more streamlined and accurate development process.

Nelson, Stacy↗
NASA NTRS2003

Understanding the Wind/Ejecta of ETA Carinae with the STIS

The mysterious Luminous Blue Variable, Eta Carinae, and its ejecta, the Homunculus, are yielding much new and exciting information to the Space Telescope Imaging Spectrograph (STIS). With 0.05 in. pixels and R=5000, we have followed changes in the Central Source and the surrounding ejecta over the past 5.5 year period in the spectral region 1650-10300A. Neutral, partially-ionized and highly-excited nebular regions have been resolved. With 0.025 in., R=30000 and R=120000 between 1180 and 3160A, we are following the changes in the Central Source, the wind structure and at least 20 absorption components, thought to be within the wall of the Humunculus. The Central Source proves to be slightly extended at HST angular resolutions. Theoretical models of the nebular line fluxes are providing new insight to the sources of excitation. Photo-excitation, line and continuum pumping, plus shocks, all play a role. Laboratory measurements of Fe-like elements and improved atomic data bases prove necessary for proper interpretation. Increased angular resolution by larger-aperture space telescopes and improved optics and detectors will lead to new understanding of massive stars, their wind structures and history of ejecta.

Gull, Theodore R.↗
NASA NTRS2002

The Strengths and Weaknesses of Logic Formalisms to Support Mishap Analysis

The increasing complexity of many safety critical systems poses new problems for mishap analysis. Techniques developed in the sixties and seventies cannot easily scale-up to analyze incidents involving tightly integrated software and hardware components. Similarly, the realization that many failures have systemic causes has widened the scope of many mishap investigations. Organizations, including NASA and the NTSB, have responded by starting research and training initiatives to ensure that their personnel are well equipped to meet these challenges. One strand of research has identified a range of mathematically based techniques that can be used to reason about the causes of complex, adverse events. The proponents of these techniques have argued that they can be used to formally prove that certain events created the necessary and sufficient causes for a mishap to occur. Mathematical proofs can reduce the bias that is often perceived to effect the interpretation of adverse events. Others have opposed the introduction of these techniques by identifying social and political aspects to incident investigation that cannot easily be reconciled with a logic-based approach. Traditional theorem proving mechanisms cannot accurately capture the wealth of inductive, deductive and statistical forms of inference that investigators routinely use in their analysis of adverse events. This paper summarizes some of the benefits that logics provide, describes their weaknesses, and proposes a number of directions for future research.

Johnson, C. W.↗
NASA NTRS2004

Inducer Hydrodynamic Forces in a Cavitating Environment

Marshall Space Flight Center has developed and demonstrated a measurement device for sensing and resolving the hydrodynamic loads on fluid machinery. The device - a derivative of the six-component wind tunnel balance - senses the forces and moments on the rotating device through a weakened shaft section instrumented with a series of strain gauges. This rotating balance was designed to directly measure the steady and unsteady hydrodynamic loads on an inducer, thereby defining the amplitude and frequency content associated with operating in various cavitation modes. The rotating balance was calibrated statically using a dead-weight load system in order to generate the 6 x 12 calibration matrix later used to convert measured voltages to engineering units. Structural modeling suggested that the rotating assembly first bending mode would be significantly reduced with the balance s inclusion. This reduction in structural stiffness was later confirmed experimentally with a hammer-impact test. This effect, coupled with the relatively large damping associated with the rotating balance waterproofing material, limited the device s bandwidth to approximately 50 Hertz Other pre-test validations included sensing the test article rotating assembly built-in imbalance for two configurations and directly measuring the assembly mass and buoyancy while submerged under water. Both tests matched predictions and confirmed the device s sensitivity while stationary and rotating. The rotating balance was then demonstrated in a water test of a full-scale Space Shuttle Main Engine high-pressure liquid oxygen pump inducer. Experimental data was collected a scaled operating conditions at three flow coefficients across a range of cavitation numbers for the single inducer geometry and radial clearance. Two distinct cavitation modes were observed symmetric tip vortex cavitation and alternate-blade cavitation. Although previous experimental tests on the same inducer demonstrated two additional cavitation modes at lower inlet pressures, these conditions proved unreachable with the rotating balance installed due to the intense dynamic environment. The sensed radial load was less influenced by flow coefficient than by cavitation number or cavitation mode although the flow coefficient range was relatively narrow. Transition from symmetric tip vortex to alternate-blade cavitation corresponded to changes in both radial load magnitude and radial load orientation relative to the inducer. Sensed moments indicated that the effective load center moved downstream during this change in cavitation mode. An occurrence of "higher+rdex cavitation" was also detected in both the stationary pressures and the rotating balance data although the frequency of the phenomena was well above the reliable bandwidth of the rotating balance. In summary the experimental tests proved both the concept and device s capability despite the limitations and confirmed that hydrodynamically-induced forces and moments develop in response to the unbalanced pressure field, which is, in turn, a product of the cavitation environment.

Skelley, Stephen E.↗
NASA NTRS2002

Effect of 6 degrees head-down tilt on cardiopulmonary function: comparison with microgravity

BACKGROUND: Head-down tilt (HDT) of 6 degrees is a commonly used model of weightlessness, but there are few comparisons with actual microgravity. HYPOTHESIS: Our study was designed to prove that the changes in cardiopulmonary function seen in HDT would be similar to those seen in microgravity. METHODS: We compared measurements of cardiovascular and pulmonary function from three separate spaceflights of 14 to 17 d duration, with data collected during a 17-d period of HDT. RESULTS: HDT proved a good model of the cardiovascular response to microgravity, resulting in increases in cardiac output and stroke volume of a similar magnitude to those seen in microgravity, with a concomitant reduction in heart rate. By contrast, HDT was a poor model of the effects of microgravity on pulmonary ventilation and gas exchange. CONCLUSION: Pulmonary function in HDT approximated the changes seen in the 1-G supine posture, while in microgravity this was much closer to that seen in the 1-G upright position. The differences probably reflect the fact that changes in cardiovascular function result primarily from fluid shifts within the entire body, whereas changes in pulmonary ventilation are primarily a result of mechanical influences on the lung and chest and abdominal wall.

NASA Discipline Cardiopulmonary↗
NASA NTRS1998

Ground-based studies with Super-Dwarf wheat in preparation for space flight

Several experiments were carried out to test responses of a Super-Dwarf cultivar of wheat (Triticum aestivum L.) to various environmental parameters that were anticipated to be present in our attempts to grow the wheat in a small growth chamber on the Russian Space Station, Mir, or that proved to be present in a 1995 trial space experiment. Under low photosynthetic photon flux (40-400 micromoles m-2 s-1 PPF), development (e.g. anthesis) was retarded, but heads (often sterile) always formed, even if light was so low that plants died before the heads could mature. Longer photoperiods promoted flowering, but night interruptions combined with short days did not provoke a long-day response as occurs with true long-day plants. The long-day effect could prove to be a summation of photosynthetic products. Heat stress (40 degrees C for 1-24 h) did not influence flowering but killed plants that were 13-16-day-old (no effect on younger plants). Concentrations of iodine or silver-fluoride disinfectants present in the water used for plants on Mir (1.0-4.0 mg L-1) did not affect plant growth although higher concentrations (8.0-1.6 mg L-1) were inhibitory. GA3 or indoleacetic acid applied every other day at concentrations from 1.0 x 10(-6) mg L-1 to 3.162 x 10(-4) mg L-1 did not change the height of Super-Dwarf wheat, suggesting that this cultivar is not a gibberellin mutant.

Flight Experiment↗
NASA NTRS2003

Performance Expectations of Closed-Brayton-Cycle Heat Exchangers in 100-kWe Nuclear Space Power Systems

Performance expectations of closed-Brayton-cycle heat exchangers to be used in 100-k We nuclear space power systems were forecast. Proposed cycle state points for a system supporting a mission to three of Jupiter's moons required effectiveness values for the heat-source exchanger, recuperator and rejection exchanger (gas cooler) of 0.98, 0.95, and 0.97, respectively. Performance parameters such as number of thermal units (Ntu), equivalent thermal conductance (UA), and entropy generation numbers (Ns) varied from 11 to 19, 23 to 39 kW/K, and 0.019 to 0.023 for some standard heat exchanger configurations. Pressure-loss contributions to entropy generation were significant; the largest frictional contribution was 114% of the heat transfer irreversibility. Using conventional recuperator designs, the 0.95 effectiveness proved difficult to achieve without exceeding other performance targets; a metallic, plate-fin counterflow solution called for 15% more mass and 33% higher pressure-loss than the target values. Two types of gas-coolers showed promise. Single-pass counterflow and multipass cross-counterflow arrangements both met the 0.97 effectiveness requirement. Potential reliability-related advantages of the cross-counterflow design were noted. Cycle modifications, enhanced heat transfer techniques and incorporation of advanced materials were suggested options to reduce system development risk. Carbon-carbon sheeting or foam proved an attractive option to improve overall performance.

Barrett, Michael J.↗
NASA NTRS2004

A Unified Fault-Tolerance Protocol

Davies and Wakerly show that Byzantine fault tolerance can be achieved by a cascade of broadcasts and middle value select functions. We present an extension of the Davies and Wakerly protocol, the unified protocol, and its proof of correctness. We prove that it satisfies validity and agreement properties for communication of exact values. We then introduce bounded communication error into the model. Inexact communication is inherent for clock synchronization protocols. We prove that validity and agreement properties hold for inexact communication, and that exact communication is a special case. As a running example, we illustrate the unified protocol using the SPIDER family of fault-tolerant architectures. In particular we demonstrate that the SPIDER interactive consistency, distributed diagnosis, and clock synchronization protocols are instances of the unified protocol.

Miner, Paul↗
NASA NTRS2002

The D3 Middleware Architecture

DARWIN is a NASA developed, Internet-based system for enabling aerospace researchers to securely and remotely access and collaborate on the analysis of aerospace vehicle design data, primarily the results of wind-tunnel testing and numeric (e.g., computational fluid-dynamics) model executions. DARWIN captures, stores and indexes data; manages derived knowledge (such as visualizations across multiple datasets); and provides an environment for designers to collaborate in the analysis of test results. DARWIN is an interesting application because it supports high-volumes of data. integrates multiple modalities of data display (e.g., images and data visualizations), and provides non-trivial access control mechanisms. DARWIN enables collaboration by allowing not only sharing visualizations of data, but also commentary about and views of data. Here we provide an overview of the architecture of D3, the third generation of DARWIN. Earlier versions of DARWIN were characterized by browser-based interfaces and a hodge-podge of server technologies: CGI scripts, applets, PERL, and so forth. But browsers proved difficult to control, and a proliferation of computational mechanisms proved inefficient and difficult to maintain. D3 substitutes a pure-Java approach for that medley: A Java client communicates (though RMI over HTTPS) with a Java-based application server. Code on the server accesses information from JDBC databases, distributed LDAP security services, and a collaborative information system. D3 is a three tier-architecture, but unlike 'E-commerce' applications, the data usage pattern suggests different strategies than traditional Enterprise Java Beans - we need to move volumes of related data together, considerable processing happens on the client, and the 'business logic' on the server-side is primarily data integration and collaboration. With D3, we are extending DARWIN to handle other data domains and to be a distributed system, where a single login allows a user transparent access to test results from multiple servers and authority domains.

Walton, Joan↗
NASA NTRS2005

Doppler Global Velocimetry Measurements for Supersonic Flow Fields

The application of Doppler Global Velocimetry (DGV) to high-speed flows has its origins in the original development of the technology by Komine et al (1991). Komine used a small shop-air driven nozzle to generate a 200 m/s flow. This flow velocity was chosen since it produced a fairly large Doppler shift in the scattered light, resulting in a significant transmission loss as the light passed through the Iodine vapor. This proof-of-concept investigation showed that the technology was capable of measuring flow velocity within a measurement plane defined by a single-frequency laser light sheet. The effort also proved that velocity measurements could be made without resolving individual seed particles as required by other techniques such as Fringe- Type Laser Velocimetry and Particle Image Velocimetry. The promise of making planar velocity measurements with the possibility of using 0.1-micron condensation particles for seeding, Dibble et al (1989), resulted in the investigation of supersonic jet flow fields, Elliott et al (1993) and Smith and Northam (1995) - Mach 2.0 and 1.9 respectively. Meyers (1993) conducted a wind tunnel investigation above an inclined flat plate at Mach 2.5 and above a delta wing at Mach 2.8 and 4.6. Although these measurements were crude from an accuracy viewpoint, they did prove that the technology could be used to study supersonic flows using condensation as the scattering medium. Since then several research groups have studied the technology and developed solutions and methodologies to overcome most of the measurement accuracy limitations:

Meyers, James F.↗
NASA NTRS2002

Command and Control of Space Assets Through Internet-Based Technologies Demonstrated

The NASA Glenn Research Center successfully demonstrated a transmission-control-protocol/ Internet-protocol- (TCP/IP) based approach to the command and control of onorbit assets over a secure network. This is a significant accomplishment because future NASA missions will benefit by using Internet-standards-based protocols. Benefits of this Internet-based space command and control system architecture include reduced mission costs and increased mission efficiency. The demonstration proved that this communications architecture is viable for future NASA missions. This demonstration was a significant feat involving multiple NASA organizations and industry. Phillip Paulsen, from Glenn's Project Development and Integration Office, served as the overall project lead, and David Foltz, from Glenn's Satellite Networks and Architectures Branch, provided the hybrid networking support for the required Internet connections. The goal was to build a network that would emulate a connection between a space experiment on the International Space Station and a researcher accessing the experiment from anywhere on the Internet, as shown. The experiment was interfaced to a wireless 802.11 network inside the demonstration area. The wireless link provided connectivity to the Tracking and Data Relay Satellite System (TDRSS) Internet Link Terminal (TILT) satellite uplink terminal located 300 ft away in a parking lot on top of a panel van. TILT provided a crucial link in this demonstration. Leslie Ambrose, NASA Goddard Space Flight Center, provided the TILT/TDRSS support. The TILT unit transmitted the signal to TDRS 6 and was received at the White Sands Second TDRSS Ground Station. This station provided the gateway to the Internet. Coordination also took place at the White Sands station to install a Veridian Firewall and automated security incident measurement (ASIM) system to the Second TDRSS Ground Station Internet gateway. The firewall provides a trusted network for the simulated space experiment. A second Internet connection at the demonstration area was implemented to provide Internet connectivity to a group of workstations to serve as platforms for controlling the simulated space experiment. Installation of this Internet connection was coordinated with an Internet service provider (ISP) and local NASA Johnson Space Center personnel. Not only did this TCP/IP-based architecture prove that a principal investigator on the Internet can securely command and control on-orbit assets, it also demonstrated that valuable virtual testing of planned on-orbit activities can be conducted over the Internet prior to actual deployment in space.

Foltz, David A.↗
NASA NTRS2005

Studies of Operating Frequency Effects On Ejector-based Thrust Augmentation in a Pulse Detonation Engine

Studies were performed in order to characterize the thrust augmentation potential of an ejector in a Pulse Detonation Engine application. A 49-mm diameter tube of 0.914-m length was constructed with one open end and one closed end. Ethylene, oxygen, and nitrogen were introduced into the tube at the closed end through the implementation of a fast mixing injector. The tube was completely filled with a stoichiometric mixture containing a one to one molar ratio of nitrogen to oxygen. Ethylene was selected as the fuel due to its detonation sensitivity and the molar ratio of the oxidizer was chosen for heat transfer purposes. Detonations were initiated in the tube through the use of a spark ignition system. The PDE was operated in a multi-cycle mode at frequencies ranging from 20-Hz to 50-Hz. Baseline thrust measurements with no ejector present were performed while operating the engine at various frequencies and compared to theoretical estimates. The baseline values were observed to agree with the theoretical model at low operating frequencies and proved to be increasingly lower than the predicted values as the operating frequency was increased. The baseline thrust measurements were observed to agree within 15 percent of the model for all operating frequencies. A straight 152-mm diameter ejector was installed and thrust augmentation percentages were measured. The length of the ejector was varied while the overlap percentage (percent of the ejector length which overlapped the tube) was maintained at 25 percent for all tests. In addition, the effect of ejector inlet geometry was investigated by comparing results with a straight inlet to those of a 38-mm inlet diameter. The thrust augmentation of the straight inlet ejector proved to be independent of engine operating frequency, augmenting thrust by 40 percent for the 0.914-m length ejector. In contrast, the rounded lip ejector of the same length seemed to be highly dependent on the engine operating frequency. An optimum operating frequency observed with the rounded inlet occurred at an operating frequency of 30-Hz, resulting in thrust augmentation percentages greater than 100 percent. The effect that the engine operating frequency had on thrust augmentation levels attained with an ejector was characterized and optimum performance parameters were established. Insight into the frequency dependent nature of the ejector performance was pursued. Suggestions for future experiments which are needed to fully understand the means in which thrust augmentation is achieved in a PDE-ejector configuration were noted.

Landry, K.↗