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At least 919 records · Page 51

Scattering Properties of Heterogeneous Mineral Particles with Absorbing Inclusions

We analyze the results of numerically exact computer modeling of scattering and absorption properties of randomly oriented poly-disperse heterogeneous particles obtained by placing microscopic absorbing grains randomly on the surfaces of much larger spherical mineral hosts or by imbedding them randomly inside the hosts. These computations are paralleled by those for heterogeneous particles obtained by fully encapsulating fractal-like absorbing clusters in the mineral hosts. All computations are performed using the superposition T-matrix method. In the case of randomly distributed inclusions, the results are compared with the outcome of Lorenz-Mie computations for an external mixture of the mineral hosts and absorbing grains. We conclude that internal aggregation can affect strongly both the integral radiometric and differential scattering characteristics of the heterogeneous particle mixtures.

minerals↗

Next Generation Flight Displays Using HTML5

The Human Integrated Vehicles and Environments (HIVE) lab at Johnson Space Center (JSC) is focused on bringing together inter-disciplinary talent to design and integrate innovative human interface technologies for next generation manned spacecraft. As part of this objective, my summer internship project centered on an ongoing investigation in to building flight displays using the HTML5 standard. Specifically, the goals of my project were to build and demo "flight-like" crew and wearable displays as well as create a webserver for live systems being developed by the Advanced Exploration Systems (AES) program. In parallel to my project, a LabVIEW application, called a display server, was created by the HIVE that uses an XTCE (XML (Extensible Markup Language) Telemetry and Command Exchange) parser and CCSDS (Consultative Committee for Space Data System) space packet decoder to translate telemetry items sent by the CFS (Core Flight Software) over User Datagram Protocol (UDP). It was the webserver's job to receive these UDP messages and send them to the displays. To accomplish this functionality, I utilized Node.js and the accompanying Express framework. On the display side, I was responsible for creating the power system (AMPS) displays. I did this by using HTML5, CSS and JavaScript to create web pages that could update and change dynamically based on the data they received from the webserver. At this point, I have not started on the commanding, being able to send back to the CFS, portion of the displays but hope to have this functionality working by the completion of my internship. I also created a way to test the webserver's functionality without the display server by making a JavaScript application that read in a comma-separate values (CSV) file and converted it to XML which was then sent over UDP. One of the major requirements of my project was to build everything using as little preexisting code as possible, which I accomplished by only using a handful of JavaScript libraries. As a side project, I created a model of the HIVE lab and Building 29 using SketchUp. I obtained the floorplans of the building from the JSC Geographic Information Systems (GIS), which were computer-aided design (CAD) files, and imported them into SketchUp. I then took those floorplans and created a 3D model of the building from them. Working in conjunction with the Hybrid Reality lab in Building 32, the SketchUp model was imported into Unreal Engine for use with the HTC Vive. Using the Vive, I was able to interact with the model I created in virtual reality (VR). The purpose of this side project was to be able to visualize potential lab layouts and mockup designs as they are in development in order to finalize design decisions. Pending approval, the model that I created will be used in the Build-As-You-Test: Can Hybrid Reality Improve the SE/HSI Design Process project in the fall. Getting the opportunity to work at NASA has been one of the most memorable experiences of my life. Over the course of my internship, I improved my programming and web development abilities substantially. I will take all the skills and experiences I have had while at NASA back to school with me in the fall and hope to pursue a career in the aerospace industry after graduating in the spring.

Greenwood, Brian↗

Touch and gravitropic set-point angle interact to modulate gravitropic growth in roots

Plant roots must sense and respond to a variety of environmental stimuli as they grow through the soil. Touch and gravity represent two of the mechanical signals that roots must integrate to elicit the appropriate root growth patterns and root system architecture. Obstacles such as rocks will impede the general downwardly directed gravitropic growth of the root system and so these soil features must be sensed and this information processed for an appropriate alteration in gravitropic growth to allow the root to avoid the obstruction. We show that primary and lateral roots of Arabidopsis do appear to sense and respond to mechanical barriers placed in their path of growth in a qualitatively similar fashion. Both types of roots exhibited a differential growth response upon contacting the obstacle that directed the main axis of elongation parallel to the barrier. This growth habit was maintained until the obstacle was circumvented, at which point normal gravitropic growth was resumed. Thus, the gravitational set-point angle of the primary and lateral roots prior to encountering the barrier were 95 degrees and 136 degrees respectively and after growing off the end of the obstacle identical set-point angles were reinstated. However, whilst tracking across the barrier, quantitative differences in response were observed between these two classes of roots. The root tip of the primary root maintained an angle of 136 degrees to the horizontal as it traversed the barrier whereas the lateral roots adopted an angle of 154 degrees. Thus, this root tip angle appeared dependent on the gravitropic set-point angle of the root type with the difference in tracking angle quantitatively reflecting differences in initial set-point angle. Concave and convex barriers were also used to analyze the response of the root to tracking along a continuously varying surface. The roots maintained the a fairly fixed angle to gravity on the curved surface implying a constant resetting of this tip angle/tracking response as the curve of the surface changed. We propose that the interaction of touch and gravity sensing/response systems combine to strictly control the tropic growth of the root. Such signal integration is likely a critical part of growth control in the stimulus-rich environment of the soil. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Discipline Plant Biology↗

Miniature Trailing Edge Effector for Aerodynamic Control

Improved miniature trailing edge effectors for aerodynamic control are provided. Three types of devices having aerodynamic housings integrated to the trailing edge of an aerodynamic shape are presented, which vary in details of how the control surface can move. A bucket type device has a control surface which is the back part of a C-shaped member having two arms connected by the back section. The C-shaped section is attached to a housing at the ends of the arms, and is rotatable about an axis parallel to the wing trailing edge to provide up, down and neutral states. A flip-up type device has a control surface which rotates about an axis parallel to the wing trailing edge to provide up, down, neutral and brake states. A rotating type device has a control surface which rotates about an axis parallel to the chord line to provide up, down and neutral states.

Lee, Hak-Tae↗

Thin Film Multilayer Conductor/Ferroelectric Tunable Microwave Components for Communication Applications

High Temperature Superconductor/Ferroelectric (HTS/FE ) thin film multilayered structures deposited onto dielectric substrates are currently being investigated for use in low loss, tunable microwave components for satellite and ground based communications. The main goal for this technology is to achieve maximum tunability while keeping the microwave losses as low as possible, so as to avoid performance degradation when replacing conventional technology (e.g., filters and oscillators) with HTS/FE components. Therefore, for HTS/FE components to be successfully integrated into current working systems, full optimization of the material and electrical properties of the ferroelectric films, without degrading those of the HTS film; is required. Hence, aspects such as the appropriate type of ferroelectric and optimization of the deposition conditions (e.g., deposition temperature) should be carefully considered. The tunability range as well as the microwave losses of the desired varactor (i.e., tunable component) are also dependent on the geometry chosen (e.g., parallel plate capacitor, interdigital capacitor, coplanar waveguide, etc.). In addition, the performance of the circuit is dependent on the location of the varactor in the circuit and the biasing circuitry. In this paper, we will present our results on the study of the SrTiO3/YBa2Cu3O(7-delta)/LaAl03 (STO/YBCO/LAO) and the Ba(x)Sr(1-x)TiO3/YBa2Cu3O(7-delta)/LaAl03(BSTO/YBCO/ILAO) HTS/FE multilayered structures. We have observed that the amount of variation of the dielectric constant upon the application of a dc electric field is closely related to the microstructure of the film. The largest tuning of the STO/YBCO/LAO structure corresponded to single-phased, epitaxial STO films deposited at 800 C and with a thickness of 500 nm. Higher temperatures resulted in interfacial degradation and poor film quality, while lower deposition temperatures resulted in films with lower dielectric constants, lower tunabilities, and higher losses. For STO/LAO multilayer structures having STO film of similar quality we have observed that interdigital capacitor configurations allow for higher tunabilities and lower losses than parallel plate configurations, but required higher dc voltage. Results on the use of these geometries in working microwave components such as filters and stabilizing resonators for local oscillators (LO) will be discussed.

Miranda, Felix A.↗

Secondary Wing System for Use on an Aircraft

A secondary wing system for use on an aircraft augments the lift, stability, and control of the aircraft at subsonic speeds. The secondary wing system includes a mechanism that allows the canard to be retracted within the contour of the aircraft fuselage from an operational position to a stowed position. The top surface of the canard is exposed to air flow in the stowed position, and is contoured to integrate aerodynamically and smoothly within the contour of the fuselage when the canard is retracted for high speed flight. The bottom portion of the canard is substantially flat for rotation into a storage recess within the fuselage. The single canard rotates about a vertical axis at its spanwise midpoint. The canard can be positioned between a range of sweep angles during flight and a stowed position in which its span is substantially parallel to the aircraft fuselage. The canard can be deployed and retracted during flight. The deployment mechanism includes a circular mounting ring and drive mechanism that connects the canard with the fuselage and permits it to rotate and to change incidence. The deployment mechanism further includes retractable fairings which serve to streamline the wing when it is retracted into the top of the fuselage.

Smith, Brian E.↗

Receptivity of Hypersonic Boundary Layers Due to Acoustic Disturbances over Blunt Cone

The transition process induced by the interaction of acoustic disturbances in the free-stream with boundary layers over a 5-degree straight cone and a wedge with blunt tips is numerically investigated at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves the Navier-Stokes equations are solved in axisymmetric coordinates. The governing equations are solved using the 5th -order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, acoustic disturbances are introduced at the outer boundary of the computational domain and unsteady simulations are performed. Generation and evolution of instability waves and the receptivity of boundary layer to slow and fast acoustic waves are investigated. The mean flow data are compared with the experimental results. The results show that the instability waves are generated near the leading edge and the non-parallel effects are stronger near the nose region for the flow over the cone than that over a wedge. It is also found that the boundary layer is much more receptive to slow acoustic wave (by almost a factor of 67) as compared to the fast wave.

Kara, K.↗

NASA Tech Briefs, November 1995

The contents include: 1) Mission Accomplished; 2) Resource Report: Marshall Space Flight Center; 3) NASA 1995 Software of the Year Award; 4) Microbolometers Based on Epitaxial YBa2Cu3O(sub 7-x) Thin Films; 5) Garnet Random-Access Memory; 6) Fabrication of SNS Weak Links on SOS Substrates; 7) High-Voltage MOSFET Switching Circuit; 8) Asymmetric Switching for a PWM H-Bridge Power Circuit; 9) Better Ohmic Contacts for InP Semiconductor Devices; 10) Low-Bandgap Thermovoltaic Materials and Devices; 11) Digital Frequency-Differencing Circuit; 12) Imaging Magnetometer; 13) Computer-Assisted Monitoring of a Complex System; 14) Buffered Telemetry Demodulator; 15) Compact Multifunction Inspection Head; 16) Optical Detection of Fractures in Ceramic Diaphragms; 17) Eddy-Current Detection of Cracks in Reinforced Carbon/Carbon; 18) Apparent Thermal Conductivity of Multilayer Insulation; 19) Optimizing Misch-Metal Compositions in Metal Hydride Anodes; 20) Device for Sampling Surface Contamination; 21) Probabilistic Failure Assessment for Fatigue; 22) Probabilistic Fatigue and Flaw-Propagation Analysis; 23) Windows Program for Driving the TDU-850 Printer; 24) Subband/Transform MATLAB Functions for Processing Images; 25) Computing Equilibrium Chemical Compositions; 26) Program Processes Thermocouple Readings; 27) ICAN-Second-Generation Integrated Composite Analyzer; 28) Integrated Composite Analyzer with Damping Capabilities; 29) Computing Efficiency of Transfer of Microwave Power; 30) Program Calculates Power Demands of Electronic Designs; 31) Cost-Estimation Program; 32) Program Estimates Areas Required by Electronic Designs; 33) Program to Balance Mapped Turbopump Assemblies; 34) BiblioTech; 35) Controlling Mirror Tilt With a Bimorph Actuator; 36) Burst-Disk Device Simulates Effect of Pyrotechnic Device; 37) Bearing-Mounting Concept Accommodates Thermal Expansion; 38) Parallel-Plate Acoustic Absorbers for Hot Environments; 39) Adjustable-Length Strut Withstands Large Cyclic Loads; 40) Tool Indicates Contact Angles in Bearing Raceways; 41) Gravity Slides With Magnetic Braking; 42) High-Torque, Lightweight, Pneumatically Driven Wrench for Small Spaces; 43) Device for Testing Compatibility of an O-Ring; 44) Magnetic Heat Pump Containing Flow Diverters; 45) Variable-Tilt Helicopter Rotor Mast; 46) "Beach-Ball" Robotic Rovers; 47) Apparatus Would Measure Temperatures of Ball Bearings; 48) Flexible Borescope for Inspecting Ducts; 49) Texturing Copper To Reduce Secondary Emission of Electrons; 50) Automated Laser Cutting in Three Dimensions; 51) Algorithm Helps Monitor Engine Operation; 52) Flexible Revision of Data-Processing Communications; 53) Software for Managing the Use of Land; 54) Thermal Strap Increases Cryocooling Efficiency; 55) Reversible Nut With Engagement Indication; 56) Control Algorithms for Kinematically Redundant Manipulators; 57) Computed Hydrogen-Flow Splits in a Rocket Engine; 58) Pressure and Thermal Modeling of Rocket Launches; 59) Field of View of a Spacecraft Antenna: Analysis and Software; 60) Digital Controller for Laser-Beam-Steering Subsystem; 61) More About Beam-Steering Subsystem for Laser Communication; 62) Digital Controller for Laser-Beam-Steering Subsystem: Part 2; 63) Interface Circuit Board for Space-Shuttle Communications; 64) Automated Planning of Spacecraft Telecommunications; 65) Artifacts of Spectral Analysis of Instrument Readings; 66) Neural-Network Controller for Vibration Suppression; 67) Adaptive Finite-Element Computation in Fracture Mechanics; 68) Attitude Control for the Cassini Spacecraft; 69) Analytical Model for Fluid Dynamics in a Microgravity Environment; 70) Study of Rocket-Engine Joints Bonded by NVCU/NARloy-Z; 71) Improved Silicon Nitride for Advanced Heat Engines; 72) Parameters for Welding Aluminum/Lithium Alloys; 73) Lightweight Composite Intertank Structure; 74) Foil Patches Seal Small Vacuum Leaks; 75) Data Base on Cables and Connectors; 76) Effect of Clock Mode on Radiation Hardnessf an ADC; and 77) Fault-Tolerant Control for a Robotic Inspection System.

Source record↗

Space Launch Systems Block 1B Preliminary Navigation System Design

NASA is currently building the Space Launch Systems (SLS) Block 1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. In parallel, NASA is also designing the Block 1B launch vehicle. The Block 1B vehicle is an evolution of the Block 1 vehicle and extends the capability of the NASA launch vehicle. This evolution replaces the Interim Cryogenic Propulsive Stage (ICPS) with the Exploration Upper Stage (EUS). As the vehicle evolves to provide greater lift capability, increased robustness for manned missions, and the capability to execute more demanding missions so must the SLS Integrated Navigation System evolved to support those missions. This paper describes the preliminary navigation systems design for the SLS Block 1B vehicle. The evolution of the navigation hard-ware and algorithms from an inertial-only navigation system for Block 1 ascent flight to a tightly coupled GPS-aided inertial navigation system for Block 1B is described. The Block 1 GN&C system has been designed to meet a LEO insertion target with a specified accuracy. The Block 1B vehicle navigation system is de-signed to support the Block 1 LEO target accuracy as well as trans-lunar or trans-planetary injection accuracy. Additionally, the Block 1B vehicle is designed to support human exploration and thus is designed to minimize the probability of Loss of Crew (LOC) through high-quality inertial instruments and robust algorithm design, including Fault Detection, Isolation, and Recovery (FDIR) logic.

Oliver, T. Emerson↗

An Integrated Circuit for Radio Astronomy Correlators Supporting Large Arrays of Antennas

Radio telescopes that employ arrays of many antennas are in operation, and ever larger ones are being designed and proposed. Signals from the antennas are combined by cross-correlation. While the cost of most components of the telescope is proportional to the number of antennas N, the cost and power consumption of cross-correlationare proportional to N2 and dominate at sufficiently large N. Here we report the design of an integrated circuit (IC) that performs digital cross-correlations for arbitrarily many antennas in a power-efficient way. It uses an intrinsically low-power architecture in which the movement of data between devices is minimized. In a large system, each IC performs correlations for all pairs of antennas but for a portion of the telescope's bandwidth (the so-called "FX" structure). In our design, the correlations are performed in an array of 4096 complex multiply-accumulate (CMAC) units. This is sufficient to perform all correlations in parallel for 64 signals (N=32 antennas with 2 opposite-polarization signals per antenna). When N is larger, the input data are buffered in an on-chipmemory and the CMACs are re-used as many times as needed to compute all correlations. The design has been synthesized and simulated so as to obtain accurate estimates of the IC's size and power consumption. It isintended for fabrication in a 32 nm silicon-on-insulator process, where it will require less than 12mm2 of silicon area and achieve an energy efficiency of 1.76 to 3.3 pJ per CMAC operation, depending on the number of antennas. Operation has been analyzed in detail up to N = 4096. The system-level energy efficiency, including board-levelI/O, power supplies, and controls, is expected to be 5 to 7 pJ per CMAC operation. Existing correlators for the JVLA (N = 32) and ALMA (N = 64) telescopes achieve about 5000 pJ and 1000 pJ respectively usingapplication-specific ICs in older technologies. To our knowledge, the largest-N existing correlator is LEDA atN = 256; it uses GPUs built in 28 nm technology and achieves about 1000 pJ. Correlators being designed for the SKA telescopes (N = 128 and N = 512) using FPGAs in 16nm technology are predicted to achieve about 100 pJ.

ASIC↗

Analysis of face deformation effects on gas film seal performance

Analyses are presented for compressible fluid flow across shaft face seals with face deformation. The solutions are obtained from an approximate integral analysis. The models, used in this analysis, can predict gas film seal behavior operating at subsonic or choked flow conditions. The flow regime can either be laminar or turbulent. Entrance losses can also be accounted for. When fluid inertia effects are negligible and the sealing faces are slightly deformed, the following results are found for both laminar and turbulent flows: (1) The pressure profiles are independent of fluid properties; and (2) the parallel film leakage equation can be used, provided a characteristic film thickness is used. Pressure profiles are presented for both divergent and convergent seal faces under choked flow conditions.

Zuk, J.↗

A crack problem with four distinct harmonic functions

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered. A closed form solution using four distinct harmonic functions (none of which can be taken arbitrarily) is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically. An example is presented, which is in contrast with the conclusion established in the literature that one of the four Papkovich-Neuber functions in three-dimensional elasticity may be arbitrarily set to zero.

Sih, G. C.↗

Radiative cooling of a hydrogen plasma in a shock tube

A method of computing radiative cooling of a hydrogen plasma assuming quasi-isothermal radiative transfer is described. A comparison with nonisothermal calculations for a plane parallel slab indicates good agreement for temperature gradients up to 300 K/cm. The calculations are compared with shock-tube data obtained in the JPL high-performance shock-tube facility. The calculations agreed with the data for one run but were 20 percent high for the other. Due to greater radiative cooling at the test slug boundaries a lateral temperature variation typically exists. This would cause the intensity measurement, which is integrated across the diameter of the test slug, to be below the prediction.

Stickford, G. H., Jr.↗

Morphological study of the innervation pattern of the rabbit sinoatrial node

The pattern of sinoatrial (SA) node innervations in rabbit was elucidated using a newly developed highly reproducible cholinesterase/silver impregnation staining procedure which made it possible to delineate large nerves, fine processes, and ganglion cells. The SA node and dominant pacemaker sites were identified by microelectrode recording. A generalized pattern of innnervation was recognized, which includes a large ganglionic complex inferior to the SA node; two or more moderately large nerves traversing the SA node parallel to the crista terminalis; nerves entering the intercaval region from the septum, the superior vena cava, and the inferior vena cava to impinge on the SA node; and a fine network of nerve processes, which was particularly dense in the SA node. From the location and distribution of the nerves and ganglionic branches, it can be inferred that the neural network in the intercaval region is capable of performing complex modulatory and integrative functions among the structures within this region.

Roberts, L. A.↗

Concept of Operations for Commercial and Business Aircraft Synthetic Vision Systems

A concept of operations (CONOPS) for the Commercial and Business (CaB) aircraft synthetic vision systems (SVS) is described. The CaB SVS is expected to provide increased safety and operational benefits in normal and low visibility conditions. Providing operational benefits will promote SVS implementation in the Net, improve aviation safety, and assist in meeting the national aviation safety goal. SVS will enhance safety and enable consistent gate-to-gate aircraft operations in normal and low visibility conditions. The goal for developing SVS is to support operational minima as low as Category 3b in a variety of environments. For departure and ground operations, the SVS goal is to enable operations with a runway visual range of 300 feet. The system is an integrated display concept that provides a virtual visual environment. The SVS virtual visual environment is composed of three components: an enhanced intuitive view of the flight environment, hazard and obstacle defection and display, and precision navigation guidance. The virtual visual environment will support enhanced operations procedures during all phases of flight - ground operations, departure, en route, and arrival. The applications selected for emphasis in this document include low visibility departures and arrivals including parallel runway operations, and low visibility airport surface operations. These particular applications were selected because of significant potential benefits afforded by SVS.

Williams Daniel M.↗

Changes in Black Carbon Deposition to Antarctica from Two Ice Core Records, A.D. 1850-2000

Continuous flow analysis was based on a steady sample flow and in-line detection of BC and other chemical substances as described in McConnell et al. (2007). In the cold room, previously cut one meter ice core sticks of 3x3cm, are melted continuously on a heated melter head specifically designed to eliminate contamination from the atmosphere or by the external parts of the ice. The melted ice from the most inner part of the ice stick is continuously pumped by a peristaltic pump and carried to a clean lab by Teflon lines. The recorded signal is continuous, integrating a sample volume of about 0.05 mL, for which the temporal resolution depends on the speed of melting, ice density and snow accumulation rate at the ice core drilling site. For annual accumulation derived from the WAIS and Law Dome ice cores, we assumed ~3.1 cm water equivalent uncertainty in each year's accumulation from short scale spatial variability (glaciological noise) which was determined from several measurements of annual accumulation in multiple parallel ice cores notably from the WAIS Divide ice core site (Banta et al., 2008) and from South Pole site (McConnell et al., 1997; McConnell et al., 2000). Refractory black carbon (rBC) concentrations were determined using the same method as in (Bisiaux et al., 2011) and adapted to continuous flow measurements as described by (McConnell et al., 2007). The technique uses a single particle intracavity laser induced incandescence photometer (SP2, Droplet Measurement Technologies, Boulder, Colorado) coupled to an ultrasonic nebulizer/desolvation (CETAC UT5000) Flow Injection Analysis (FIA). All analyses, sample preparation etc, were performed in a class 100 cleanroom using anti contamination "clean techniques". The samples were not acidified.

Bisiaux, Marion M.↗

Cryogenic performance of slotted brazed Rene 41 honeycomb panels

Two brazed Rene 41 honeycomb panels that would incorporate a frame element were designed, fabricated and tested. The panels were representative of the lower surface of an advanced space transportation vehicle. The first panel was a two span panel supported by a center frame and on edges parallel to it. The second panel was a two span panel supported by a center frame and on edges parallel to it. The second panel was a three span panel supported on two frames and on edges parallel to the frames. Each panel had its outer skin slotted to reduce the thermal stresses of the panel skins. The first panel was tested under simulated boost conditions that included liquid hydrogen exposure of the frame and inner skin and radiant heat to 478K on the outer skins. The first panel was tested to investigate the effect of thermal stresses in skins and core caused by the panel being restrained by a cold integral frame and to observe the effects of frost formation and possible liquid air development in and around outer skin slots.

Hepler, A. K.↗

Compressibility effects in turbulence modeling

Numerical turbulence modeling is discussed with attention given to fluid property variations caused by compressibility in an adiabatic flow. The models are considered in terms of integral quantities expressed by ordinary differential equations and by those formulated as partial differential equations. Compressibility corrections for both integral and partial differential methods are reviewed. Eddy-viscosity models are explored for their capability to characterize the mass-weighted Reynolds stress, which can be accounted for with primitive and/or mass-weighted variables. Compressible flow simulations are currently constrained to low Re and zero mean dilation. The effects of compressibility are defined in wave number space by resolving the Fourier transforms of the velocity vectors into components which are perpendicular and parallel to the wave number vector. Statistical correlations then permit obtaining a value for each contribution.

Rubesin, M. W.↗