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Programmable Logic Application Notes

This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will continue a series of notes concentrating on analysis techniques with this issue's section discussing: Digital Timing Analysis Tools and Techniques. Articles in this issue include: SX and SX-A Series Devices Power Sequencing; JTAG and SXISX-AISX-S Series Devices; Analysis Techniques (i.e., notes on digital timing analysis tools and techniques); Status of the Radiation Hard reconfigurable Field Programmable Gate Array Program, Input Transition Times; Apollo Guidance Computer Logic Study; RT54SX32S Prototype Data Sets; A54SX32A - 0.22 micron/UMC Test Results; Ramtron FM1608 FRAM; and Analysis of VHDL Code and Synthesizer Output.

Katz, Richard↗

Combustion Characteristics in a Non-Premixed Cool-Flame Regime of n-Heptane in Microgravity

A series of distinct phenomena have recently been observed in single-fuel-droplet combustion tests performed on the International Space Station (ISS). This study attempts to simulate the observed flame behavior numerically using a gaseous n-heptane fuel source in zero gravity and a time-dependent axisymmetric (2D) code, which includes a detailed reaction mechanism (127 species and 1130 reactions), diffusive transport, and a radiation model (for CH4, CO, CO2, H2O, and soot). The calculated combustion characteristics depend strongly on the air velocity around the fuel source. In a near-quiescent air environment (< or = 2 mm/s), with a sufficiently large fuel injection velocity (1 cm/s), a growing spherical diffusion flame extinguishes at ≈1200 K due to radiative heat losses. This is typically followed by a transition to the low-temperature (cool-flame) regime with a reaction zone (at ≈700 K) in close proximity to the fuel source. The 'cool flame' regime is formed due to the negative temperature coefficient in the low-temperature chemistry. After a relatively long period (≈18 s) of the cool flame regime, a flash re-ignition occurs, associated with flame-edge propagation and subsequent extinction of the re-ignited flame. In a low-speed (≈3 mm/s) airstream (which simulates the slight droplet movement), the diffusion flame is enhanced upstream and experiences a local extinction downstream at ≈1200 K, followed by steady flame pulsations (≈0.4 Hz). At higher air velocities (4-10 mm/s), the locally extinguished flame becomes steady state. The present axisymmetric computational approach helps in revealing the non-premixed 'cool flame' structure and 2D flame-flow interactions observed in recent microgravity droplet combustion experiments.

diffusion flame↗

Improvements to Lunar BRDF-Corrected Nighttime Satellite Imagery: Uses and Applications

Observations made by the VIIRS day/night band (DNB) provide daily, nighttime measurements to monitor Earth surface processes.However, these observations are impacted by variations in reflected solar radiation on the moon's surface. As the moon transitions from new to full phase, increasing radiance is reflected to the Earth's surface and contributes additional reflected moonlight from clouds and land surface, in addition to emissions from other light sources observed by the DNB. The introduction of a bi-directional reflectance distribution function (BRDF) algorithm serves to remove these lunar variations and normalize observed radiances. Provided by the Terrestrial Information Systems Laboratory at Goddard Space Flight Center, a 1 km gridded lunar BRDF-corrected DNB product and VIIRS cloud mask can be used for a multitude of nighttime applications without influence from the moon. Such applications include the detection of power outages following severe weather events using pre-and post-event DNB imagery, as well as the identification of boat features to curtail illegal fishing practices. This presentation will provide context on the importance of the lunar BRDF correction algorithm and explore the aforementioned uses of this improved DNB product for applied science applications.

NWS↗

Maintaining Human Health for Humans-Mars

The Human Health Research Program states that Radiation is the most challenging hazard to human spaceflight beyond LEO. The International Space Station provides an analog for evaluating techniques for dealing with Altered Gravity, the Radiation Environment of the ISS is only about 45% of the deep space values where radiation due to Galactic Cosmic Rays (GCR) dominate the spectrum. The Moon and cis-lunar space are being considered as a Mars Analog training ground for preparing crews for human mission to Mars. Spending more than 200 days in deep space is considered unsafe based on our current proxy for lifetime radiation dose. The paper outlines a way forward for spending days training near the Moon and for completing roundtrip missions to Mars while remaining below the current proxy. In the first case, a GCR overcoat shields crews from radiation during cis-lunar activities before making fast transits without in-space GCR overcoats to and from Mars. This case requires continued maturation of low TRL propulsion and power technologies currently around 4 to 5 while depending on repeatable reductions in launch costs by a factor of 6 expected of current reusable rockets. The second case requires no new technology development except for the expectation that the next near-term generation of reusable rockets will reduce launch costs by a factor of around 14. Five trajectories and GCR overcoat sizes for all mission legs are presented herein to illustrate the opportunities to maintain human health for Humans-Mars missions.

Robert W Moses↗

Influence of nonequilibrium radiation and shape change on aerothermal environment of Jovian entry body

Radiative transfer equations are derived under nonequilibrium conditions which include multilevel energy transitions. The nonequalibrium results, obtained with and without ablation injection in the shock layer, are found to be greatly influenced by the temperature distribution in the shock layer. In the absence of ablative products, the convective and radiative heating to the entry body are reduced significantly under nonequilibrium conditions. The influence of nonequilibrium is found to be greater at higher entry altitudes. With coupled ablation and carbon phenolic injection, 16 chemical species are used in the ablation layer for radiation absorption. Equilibrium and nonequilibrium results are compared under peak heating conditions. A 45 degree sphere cone, a 35 degree hyperboloid, and a 45 degree ellipsoid were used to study probe shape change. Results indicate that the shock layer flow field and heat transfer to the body are influenced significantly by the probe shape change. The effect of shape change on radiative heating of the afterbodies is found to be considerably larger for the sphere cone and ellipsoid than for the hyperboloid.

Tiwari, S. N.↗

Radiation and Plasma Environments for Lunar Missions

Space system design for lunar orbit and extended operations on the lunar surface requires analysis of potential system vulnerabilities to plasma and radiation environments to minimize anomalies and assure that environmental failures do not occur during the mission. Individual environments include the trapped particles in Earth s radiation belts, solar energetic particles and galactic cosmic rays, plasma environments encountered in transit to the moon and on the lunar surface (solar wind, terrestrial magnetosheath and magnetotail, and lunar photoelectrons), and solar ultraviolet and extreme ultraviolet photons. These are the plasma and radiation environments which contribute to a variety of effects on space systems including total ionizing dose and dose rate effects in electronics, degradation of materials in the space environment, and charging of spacecraft and lunar dust. This paper provides a survey of the relevant charged particle and photon environments of importance to lunar mission design ranging from the lowest (approx.few 10 s eV) photoelectron energies to the highest (approx.GeV) cosmic ray energies.

Minow, Joseph I.↗

Arctic Radiation-Cloud-Aerosol-Surface Interaction eXperiment (ARCSIX)

The Arctic climate system is amidst a transition. Over the last 40 years, the Arctic sea ice pack has transformed from a predominantly thick, multi-year sea ice to a predominantly thin, seasonal sea ice, termed the “New Arctic”. The observed rapid changes in the Arctic sea ice pack are an integral part of the Arctic Amplification phenomenon and represent a response to and a feedback on global climate change. As a result, the role of the Arctic within the global climate system is changing. Substantial uncertainty exists in our understanding of the atmosphere-surface interactions within the Arctic system, limiting our knowledge of the Arctic’s role in the future climate. Advancing our understanding of the Arctic climate system requires (1) measurements of the coupling between radiative processes and sea ice surface properties during summer sea ice melt; (2) measurements of the processes controlling the predominant Arctic cloud regimes and their properties (Fig. 1); and (3) improvements in the ability to monitor Arctic cloud, radiation, and sea ice processes from space. A key challenge is that thin, low clouds that are radiatively important to the Arctic surface energy budget can go undetected (Fig. 1). The Arctic Radiation-Cloud-Aerosol-Surface-Interaction eXperiment (ARCSIX) is an airborne campaign based at the Pituffik Space Base in Greenland from May-August 2024 sponsored by the National Aeronautics and Space Administration (NASA) to address these needs. ARCSIX consists of two airborne measurement campaigns taking place in two 3-week intervals during the early and late sea ice melt season: late May through early June and late July through early August, respectively. ARCSIX science is guided by three broad science questions that encapsulate the key influences of radiation-cloud-aerosol-sea ice coupling and a remote sensing and modeling objective: Science Question 1 (Radiation): What is the impact of the predominant summer Arctic cloud types on the radiative surface energy budget? Science Question 2 (Cloud Life Cycle): What processes control the evolution and maintenance of the predominant cloud regimes in the summertime Arctic? Science Question 3 (Sea Ice): How do the two-way interactions between surface properties and atmospheric forcings affect the sea ice evolution? Remote Sensing and Modeling Objective: Enhance our long-term space-based monitoring and predictive capabilities of Arctic sea ice, clouds, and aerosols.

Patrick Taylor↗

Dynamical criterion for a marginally unstable, quasi-linear behavior in a two-layer model

A two-layer quasi-geostrophic flow forced by meridional variations in heating can be in regimes ranging from radiative equilibrium to forced geostrophic turbulence. Between these extremes is a regime where the time-mean (zonal) flow is marginally unstable. Using scaling arguments, it is concluded that such a marginally unstable state should occur when a certain parameter, measuring the strength of wave-wave interactions relative to the beta effect and advection by the thermal wind, is small. Numerical simulations support this proposal. A transition from the marginally unstable regime to a more nonlinear regime is then examined through numerical simulations with different radiative forcings. It is found that transition is not caused by secondary instability of waves in the marginally unstable regime. Instead, the time-mean flow can support a number of marginally unstable normal modes. These normal modes interact with each other, and if they are of sufficient amplitude, the flow enters a more nonlinear regime.

Ebisuzaki, W.↗

Radiative lifetimes and dipole moments of the A 2Sigma/+/, B 2Sigma /+/, and C 2Sigma/+/ states of OH

After describing independent theoretical studies of the eigenfunctions of the X 2Pi and excited A 2Sigma(+), B 2Sigma(+), and C 2Sigma(+) states of OH, results are presented for the transition dipole moments connecting each excited state to the others and to the ground state. The radiative lifetimes derived from calculation of the bound-bound and bound-free vibrational band transition probabilities are compared with measured values, confirming recent measurements of the A 2Sigma(+) and C 2Sigma(+) states but not the lifetimes measured for the B 2Sigma(+) state.

Langhoff, S. R.↗

TPSAS-NF1676L-23246-DND

The Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) was conducted from Fairbanks, Alaska during the September transition in the Beaufort-Chukchi Seas. Fifteen missions were flown with a NASA C-130 to characterize clouds, sea-ice, and associated radiative properties over a wide range of conditions. The advanced instrumentation payload included broadband and spectral radiometers, in-situ cloud probes, a laser altimeter and digital camera system. The flight profiles were tightly coordinated with multiple intersecting satellite overpasses allowing for a thorough evaluation of the Clouds and the Earth's Radiant Energy System (CERES) satellite climate data products. Thus, a rich dataset was acquired to help better understand cloud radiative effects as sea-ice conditions are changing due to arctic warming. The mission also acquired measurements to supplement the ongoing Operation Icebridge campaign. An overview of the mission operations, preliminary results, and a description of the datasets now available to the scientific community, will be presented.

William L Smith, Jr↗

Emission measures and structure of the transition region of a sunspot from emission lines in the far ultraviolet

Absolute intensities of emission lines in the wavelength range from 1200 A to 1817 A from the large sunspot in McMath region 12510 near the disk center are presented. The intensities are averaged across the umbra and penumbra of the sunspot. The observations were made with the NRL slit spectrograph on Skylab. Emission measures are derived from the measured intensities. Assuming a balance between the divergence of the conductive energy flux and the radiative energy losses, a self-consistent model of the lower transition region in the sunspot is constructed. The model gives a constant pressure of about 0.19 dyn/sq cm and a conductive flux which decreases approximately one order of magnitude between 200,000 and 40,000 K. The temperature gradient is relatively constant, increasing slowly with decreasing temperature

Cheng, C.-C.↗

Hybrid Active/Passive Control of Sound Radiation from Panels with Constrained Layer Damping and Model Predictive Feedback Control

There has been considerable interest over the past several years in applying feedback control methods to problems of structural acoustics. One problem of particular interest is the control of sound radiation from aircraft panels excited on one side by a turbulent boundary layer (TBL). TBL excitation appears as many uncorrelated sources acting on the panel, which makes it difficult to find a single reference signal that is coherent with the excitation. Feedback methods have no need for a reference signal, and are thus suited to this problem. Some important considerations for the structural acoustics problem include the fact that the required controller bandwidth can easily extend to several hundred Hertz, so a digital controller would have to operate at a few kilohertz. In addition, aircraft panel structures have a reasonably high modal density over this frequency range. A model based controller must therefore handle the modally dense system, or have some way to reduce the bandwidth of the problem. Further complicating the problem is the fact that the stiffness and dynamic properties of an aircraft panel can vary considerably during flight due to altitude changes resulting in significant resonant frequency shifts. These considerations make the tradeoff between robustness to changes in the system being controlled and controller performance especially important. Recent papers concerning the design and implementation of robust controllers for structural acoustic problems highlight the need to consider both performance and robustness when designing the controller. While robust control methods such as H1 can be used to balance performance and robustness, their implementation is not easy and requires assumptions about the types of uncertainties in the plant being controlled. Achieving a useful controller design may require many tradeoff studies of different types of parametric uncertainties in the system. Another approach to achieving robustness to plant changes is to make the controller adaptive. For example, a mathematical model of the plant could be periodically updated as the plant changes, and the feedback gains recomputed from the updated model. To be practical, this approach requires a simple plant model that can be updated quickly with reasonable computational requirements. A recent paper by the authors discussed one way to simplify a feedback controller, by reducing the number of actuators and sensors needed for good performance. The work was done on a tensioned aircraft-style panel excited on one side by TBL flow in a low speed wind tunnel. Actuation was provided by a piezoelectric (PZT) actuator mounted on the center of the panel. For sensing, the responses of four accelerometers, positioned to approximate the response of the first radiation mode of the panel, were summed and fed back through the controller. This single input-single output topology was found to have nearly the same noise reduction performance as a controller with fifteen accelerometers and three PZT patches. This paper extends the previous results by looking at how constrained layer damping (CLD) on a panel can be used to enhance the performance of the feedback controller thus providing a more robust and efficient hybrid active/passive system. The eventual goal is to use the CLD to reduce sound radiation at high frequencies, then implement a very simple, reduced order, low sample rate adaptive controller to attenuate sound radiation at low frequencies. Additionally this added damping smoothes phase transitions over the bandwidth which promotes robustness to natural frequency shifts. Experiments were conducted in a transmission loss facility on a clamped-clamped aluminum panel driven on one side by a loudspeaker. A generalized predictive control (GPC) algorithm, which is suited to online adaptation of its parameters, was used in single input-single output and multiple input-single output configurations. Because this was a preliminary look at the potential constrained layer damping for adaptive control, static feedback control with no online adaptation was used. Two configurations of CLD in addition to a bare panel configuration were studied. For each CLD configuration, two sensor arrangements for the feedback controller were compared. The first arrangement used fifteen accelerometers on the panel to estimate the responses of the first six radiation modes of the panel. The second sensor arrangement was simpler, using the summed responses of only four accelerometers to approximate the response of the first radiation mode of the panel. In all cases a PZT patch was mounted at the center of the panel for control input. The performance of the controller was quantified using the responses of the fifteen accelerometers on the panel to estimate radiated sound power. The paper begins with a brief discussion of the GPC algorithm and the experimental setup. The experimental results are discussed next, comparing the CLD and sensor configurations, followed by discussion and conclusions.

Cabell, Randolph H.↗

High LET Radiation Can Enhance TGF(Beta) Induced EMT and Cross-Talk with ATM Pathways

The TGF(Beta) pathway has been shown to regulate or directly interact with the ATM pathway in the response to radiation in mammary epithelial cells. We investigated possible interactions between the TGF(Beta) and ATM pathways following simulated space radiation using hTERT immortalized human esophageal epithelial cells (EPC-hTERT), mink lung epithelial cells (Mv1lu), and several human fibroblast cell lines. TGF(Beta) is a key modulator of the Epithelial-Mesenchymal Transition (EMT), important in cancer progression and metastasis. The implication of EMT by radiation also has several lines of developing evidence, however is poorly understood. The identification of TGF(Beta) induced EMT can be shown in changes to morphology, related gene over expression or down regulation, which can be detected by RT-PCR, and immunostaining and western blotting. In this study, we have observed morphologic and molecular alternations consistent with EMT after Mv1lu cells were treated with TGF(Beta) High LET radiation enhanced TGF(Beta) mediated EMT with a dose as low as 0.1Gy. In order to consider the TGF(Beta) interaction with ATM we used a potent ATM inhibitor Ku55933 and investigated gene expression changes and Smad signaling kinetics. Ku559933 was observed to reverse TGF(Beta) induced EMT, while this was not observed in dual treated cells (radiation+TGF(Beta)). In EPC-hTERT cells, TGF(Beta) alone was not able to induce EMT after 3 days of application. A combined treatment with high LET, however, significantly caused the alteration of EMT markers. To study the function of p53 in the process of EMT, we knocked down P53 through RNA interference. Morphology changes associated with EMT were observed in epithelial cells with silenced p53. Our study indicates: high LET radiation can enhance TGF(Beta) induced EMT; while ATM is triggering the process of TGF(Beta)-induced EMT, p53 might be an essential repressor for EMT phenotypes.

Wang, Minli↗

Redistribution of radiation in the absence of collisions

Redistribution and depolarization of near-resonant radiation is studied for the He 2(1P)-3(1D) line (668 nm) and some data for H-alpha (656 nm) are also presented. A Nd:YAG pumped dye laser, with a bandwidth of 0.1/cm and a power density of 100 kW/sq cm, is used in the experiment. The transitions have lower levels with natural line widths that are large compared with their upper-level natural widths, and, under experimental conditions, their collisional widths are also small. The ratio of fluorescence to Rayleigh intensity is measured and the results indicate that while the Rayleigh emission has the same temporal development as the laser pulse (5 ns FWHM), the fluorescent intensity has a decay time determined by the radiative decay lifetime and by collisional quenching. The prediction that redistribution of radiation occurs in the absence of collisions for transitions having significant lower-level radiative widths is confirmed. Depolarization rates by collisions with helium are also inferred from the measurements.

Lombardi, G. G.↗

Separating Propulsive Mass and Energy for Space Applications

Initially and traditionally, space access and in-space propulsion utilized combustion and expulsion of chemical “fuels” carried on board, with performance governed by the rocket equation. These chemicals produced energy, and after combustion, constituted the propulsive mass/momentum. The best such chemicals in terms of Isp that are deemed safe engineering/mission wise are hydrogen and oxygen, producing some 450 seconds of Isp. There are more reactive chemicals, such as fluorine, which have higher Isp, but also have serious safety issues. Propulsion in atmospheres can ingest atmospheric constituents (aka “airbreathing propulsion”) which provide additional propulsive mass when heated and a component of the combustion/energy generation process. This utilization of non-stored/carried propulsive mass provides partial separation of propulsive mass and energy and produces higher Isp. The other approach to separating propulsive mass and energy is to, either on board or added from offboard, supply additional energy, such as from nuclear or solar sources. This is the approach for fission nuclear thermal and electric propulsion, which can provide an Isp in excess of 800 seconds of Isp. Other processes or in addition to thermal expansion, such as electro-magnetics, can be employed to increase exit velocity and Isp. Separating propulsive mass and energy for space faring is commonly referred to as a means to circumvent the rocket equation and is capable of producing major benefits for the development of commercial deep space and space faring in general including affordable fast transits to mitigate the human health impacts of galactic cosmic radiation (GCR) and microG. The key to higher than chemical Isp, beyond H2-O2, and beyond the radiated energy and systems limitations of solar for space faring, is a light weight, high energy density source, either on board or via utilization of energy beaming to the vehicle. Traditional energy sources include chemical, heat, electrics, mechanical, photons, and nuclear. Propulsive mass can be carried on board, sourced beyond the surface of Earth via in-situ resource utilization (ISRU), and includes harvesting from atmospheres. High Isp via electromagnetic related propulsive mass acceleration requires sufficient ionization and conductivity. The major metrics for space propulsion are costs, safety, Isp, weight, and thrust level, the latter dependent upon mission requirements. High thrust for human missions is needed to reduce time exposed to radiation and microG and high thrust is required for space access. Costs of space access are reducing via reusability, printing manufacture, and robotization of manufacturing and operation. Chemical rockets provide high thrust from the expansion of the heated mass constituents at high mass flow. The other high thrust propulsion approach is magnetohydrodynamics (MHD), which, in addition to high thrust, has a high Isp of over 2,000 seconds of Isp. The VASIMIR engine offers some 5,000 seconds of Isp at high thrust [ref. 3]. Electric propulsion cycles are capable of Isp much higher than that but at low thrust levels using available energy sources. With cost as a major metric, reusable rockets and improved manufacturing and operations are rapidly greatly lowering the costs of space access, which could provide/supply in space fuel depots and affordable chemical propulsion for the desired human fast transits (e.g., some 200-day round trips to Mars). The other option for fast transits is VASIMIR, given a nuclear on-board energy source that has the requisite many megawatts of power and an alpha, kgs of weight/kW of energy produced, on the order of one (i.e., a light weight, high energy density energy source). The purpose of this report is to examine the options beyond traditional rocket engines, where propulsive mass and energy are combined, specifically the separation of propulsive mass and energy. This report considers the spectrum of advanced energetics, sources of propulsive mass, conductivity enhancement approaches, energy beaming possibilities, and candidate propulsion cycles. Suggestions are made for various combinatorial, system level, beyond traditional combustion rocket, space propulsion approaches for human deep space missions given the changing conditions of increased knowledge of deep space resources for ISRU, revolutionary energetics, and technology advancements writ large.

Dennis M. Bushnell↗

Orion Flight Test-1 Thermal Protection System Instrumentation

The Orion Crew Exploration Vehicle (CEV) was originally under development to provide crew transport to the International Space Station after the retirement of the Space Shuttle, and to provide a means for the eventual return of astronauts to the Moon. With the current changes in the future direction of the United States human exploration programs, the focus of the Orion project has shifted to the project s first orbital flight test, designated Orion Flight Test 1 (OFT-1). The OFT-1 is currently planned for launch in July 2013 and will demonstrate the Orion vehicle s capability for performing missions in low Earth orbit (LEO), as well as extensibility beyond LEO for select, critical areas. Among the key flight test objectives are those related to validation of the re-entry aerodynamic and aerothermal environments, and the performance of the thermal protection system (TPS) when exposed to these environments. A specific flight test trajectory has been selected to provide a high energy entry beyond that which would be experienced during a typical low Earth orbit return, given the constraints imposed by the possible launch vehicles. This trajectory resulted from a trade study that considered the relative benefit of conflicting objectives from multiple subsystems, and sought to provide the maximum integrated benefit to the re-entry state-of-the-art. In particular, the trajectory was designed to provide: a significant, measureable radiative heat flux to the windward surface; data on boundary transition from laminar to turbulent flow; and data on catalytic heating overshoot on non-ablating TPS. In order to obtain the necessary flight test data during OFT-1, the vehicle will need to have an adequate quantity of instrumentation. A collection of instrumentation is being developed for integration in the OFT-1 TPS. In part, this instrumentation builds upon the work performed for the Mars Science Laboratory Entry, Descent and Landing Instrument (MEDLI) suite to instrument the OFT-1 ablative heat shield. The MEDLI integrated sensor plugs and pressure sensors will be adapted for compatibility with the Orion TPS design. The sensor plugs will provide in-depth temperature data to support aerothermal and TPS model correlation, and the pressure sensors will provide a flush air data system for validation of the entry and descent aerodynamic environments. In addition, a radiometer design will be matured to measure the radiative component of the reentry heating at two locations on the heat shield. For the back shell, surface thermocouple and pressure port designs will be developed and applied which build upon the heritage of the Space Shuttle Program for instrumentation of reusable surface insulation (RSI) tiles. The quantity and location of the sensors has been determined to balance the needs of the reentry disciplines with the demands of the hardware development, manufacturing and integration. Measurements which provided low relative value and presented significant engineering development effort were, unfortunately, eliminated. The final TPS instrumentation has been optimized to target priority test objectives. The data obtained will serve to provide a better understanding of reentry environments for the Orion capsule design, reduce margins, and potentially reduce TPS mass or provide TPS extensibility for alternative missions.

Kowal, T. John↗

A model for the noise radiated by turbulent boundary layers and its interaction with laminar layers in supersonic flow

Motivated by the noise-boundary layer transition problem in supersonic flow, the interaction between incoming aerodynamic noise and the laminar boundary layer was studied. The noise field was modeled as a Mach wave radiation field consisting of discrete waves emanating from coherent turbulent entities moving downstream within the supersonic turbulent boundary layer. The individual disturbances are likened to miniature sonic booms and the laminar boundary layer is strafed by the waves as the sources move downstream. The mean, autocorrelation, and power spectral density of the field are expressed in terms of the wave shapes and their average arrival rates. The emphasis in the interaction analysis is on the behavior of the shocklets in the noise field. The shocklets are shown to be focused by the laminar boundary layer in its outer region. Borrowing wave-propagation terminology, this region is termed the caustic region. Using scaling laws from sonic boom work, focus factors at the caustic are estimated to vary from 2 to 6 for incoming shocklet strengths of 1 to .01 percent of the free stream pressure level. The situation regarding experimental evidence of the caustic region is reviewed. It is not clear whether the focusing effectively promotes early transition. Additional observations concerning the interaction problem are presented.

Schopper, M. R.↗