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NASA NTRS2006

Mode I Toughness Measurements of Core/Facesheet Bonds in Honeycomb Sandwich Structures

Composite sandwich structures will be used in many future applications in aerospace, marine and offshore industries due to the fact that the strength and stiffness to mass ratios surpass any other structural type. Sandwich structure also offers advantages over traditional stiffened panels such as ease of manufacturing and repair. During the last three decades, sandwich structure has been used extensively for secondary structure in aircraft (fuselage floors, rudders and radome structure). Sandwich structure is also used as primary structure in rotorcraft, the most common example being the trailing edge of rotor blades. As with other types of composite construction, sandwich structure exhibits several types of failure mode such as facesheet wrinkling, core crushing and sandwich buckling. Facesheet/core debonding has also been observed in the marine and aerospace industry. During this failure mode, peel stresses applied to an existing facesheet/core debond or an interface low in toughness, results in the facesheet being peeled from the core material, possibly leading to a significant loss in structural integrity of the sandwich panel. In an incident during a test on a liquid hydrogen fuel tank of the X-33 prototype vehicle, the outer graphite/epoxy facesheet and honeycomb core became debonded from the inner facesheet along significant areas, leading to failure of the tank. As a consequence of the accident; significant efforts were made to characterize the toughness of the facesheet/core bond. Currently, the only standardized method available for assessing the quality of the facesheet/core interface is the climbing drum peel test (ASTM D1781). During this test a sandwich beam is removed from a panel and the lip of one of the facesheets is attached to a drum, as shown in Fig. 1. The drum is then rotated along the sandwich beam, causing the facesheet to peel from the core. This method has two major drawbacks. First, it is not possible to obtain quantitative fracture data from the test and so the results can only be used in a qualitative manner. Second, only sandwich structure with thin facesheets can be tested (to facilitate wrapping of the facesheet around the climbing drum). In recognition of the need for a more quantitative facesheet/core fracture test, several workers have devised experimental techniques for characterizing the toughness of the facesheet/core interface. In all of these cases, the tests are designed to yield a mode I-dominated fracture toughness of the facesheet/core interface in a manner similar to that used to determine mode I fracture toughness of composite laminates. In the current work, a modified double cantilever beam is used to measure the mode I-dominated fracture toughness of the interface in a sandwich consisting of glass/phenolic honeycomb core reinforced with graphite epoxy facesheets. Two specimen configurations were tested as shown in Fig 2. The first configuration consisted of reinforcing the facesheets with aluminum blocks (Fig. 2a). In the second configuration unreinforced specimens were tested (Fig. 2b). Climbing drum peel tests were also conducted to compare the fracture behavior observed between this test and the modified double cantilever beam. This paper outlines the test procedures and data reduction strategies used to compute fracture toughness values from the tests. The effect of specimen reinforcement on fracture toughness of the facesheet/core interface is discussed.

Nettles, Alan T.↗
NASA NTRS2006

Phase Calibration of Microphones by Measurement in the Free-field

Over the past several years, significant effort has been expended at NASA Langley developing new Micro-Electro-Mechanical System (MEMS)-based microphone directional array instrumentation for high-frequency aeroacoustic measurements in wind tunnels. This new type of array construction solves two challenges which have limited the widespread use of large channel-count arrays, namely by providing a lower cost-per-channel and a simpler method for mounting microphones in wind tunnels and in field-deployable arrays. The current generation of array instrumentation is capable of extracting accurate noise source location and directivity on a variety of airframe components using sophisticated data reduction algorithms [1-2]. Commercially-available MEMS microphones are condenser-type devices and have some desirable characteristics when compared with conventional condenser-type microphones. The most important advantages of MEMS microphones are their size, price, and power consumption. However, the commercially-available units suffer from certain important shortcomings. Based on experiments with array prototypes, it was found that both the bandwidth and the sound pressure limit of the microphones should be increased significantly to improve the performance and flexibility of the microphone array [3]. It was also desired to modify the packaging to eliminate unwanted Helmholtz resonance s exhibited by the commercial devices. Thus, new requirements were defined as follows: Frequency response: 100 Hz to 100 KHz (+/-3dB) Upper sound pressure limit: Design 1: 130 dB SPL (THD less than 5%) Design 2: 150-160 dB SPL (THD less than 5%) Packaging: 3.73 x 6.13 x 1.3 mm can with laser-etched lid. In collaboration with Novusonic Acoustic Innovation, NASA modified a Knowles SiSonic MEMS design to meet these new requirements. Coupled with the design of the enhanced MEMS microphones was the development of a new calibration method for simultaneously obtaining the sensitivity and phase response of the devices over their entire broadband frequency range. Traditionally, electrostatic actuators (EA) have been used to characterize air-condenser microphones; however, MEMS microphones are not adaptable to the EA method due to their construction and very small diaphragm size [4]. Hence a substitution based, free-field method was developed to calibrate these microphones at frequencies up to 80 kHz. The technique relied on the use of a random, ultrasonic broadband centrifugal sound source located in a small anechoic chamber. The free-field sensitivity (voltage per unit sound pressure) was obtained using the procedure outlined in reference 4. Phase calibrations of the MEMS microphones were derived from cross spectral phase comparisons between the reference and test substitution microphones and an adjacent and invariant grazing-incidence 1/8-inch standard microphone. The free-field calibration procedure along with representative sensitivity and phase responses for the new high-frequency MEMS microphones are presented here.

Shams, Qamar A.↗
NASA NTRS2006

SIMsim: An End-to-end Simulator for the SIM Mission

In this paper we discuss the use of an innovative SIM simulator, called SIMsim, to perform end-to end simulations of the SIM mission. The inputs to the simulator are a physically-based parameterization of the major SIM error sources and the output is the mission astrometric accuracy for various observing scenarios such as narrow-angle (NA) and wide-angle (WA) observations. The primary role of SIMsim is to validate the SIM astrometric error budget (AEB), bit it is also being used to study a variety of mission performance issues as well as being a test-bed for prototype data reduction algorithms. SIMsim is giving us confidence that the SIM AEB is a valid estimate of mission performance. It also is illustrating where analytical formulas for estimating certain effects breakdown and a numerical approach has to be adopted.

sumulation↗
NASA NTRS2004

Experimentally Determined Plasma Parameters in a 30 cm Ion Engine

Single planar Langmuir probes and fiber optic probes are used to concurrently measure the plasma properties and neutral density variation in a 30cm diameter ion engine discharge chamber, from the immediate vicinity of the keeper to the near grid plasma region. The fiber optic probe consists of a collimated optical fiber recessed into a double bore ceramic tube fitted with a stainless steel light-limiting window. The optical fiber probe is used to measure the emission intensity of excited neutral xenon for a small volume of plasma, at various radial and axial locations. The single Langmuir probes, are used to generate current-voltage characteristics at a total of 140 spatial locations inside the discharge chamber. Assuming a maxwellian distribution for the electron population, the Langmuir probe traces provide spatially resolved measurements of plasma potential, electron temperature, and plasma density. Data reduction for the NSTAR TH8 and TH15 throttle points indicates an electron temperature range of 1 to 7.9 eV and an electron density range of 4e10 to le13 cm(sup -3), throughout the discharge chamber, consistent with the results in the literature. Plasma potential estimates, computed from the first derivative of the probe characteristic, indicate potential from 0.5V to 11V above the discharge voltage along the thruster centerline. These values are believed to be excessively high due to the sampling of the primary electron population along the thruster centerline. Relative neutral density profiles are also obtained with a fiber optic probe sampling photon flux from the 823.1 nm excited to ground state transition. Plasma parameter measurements and neutral density profiles will be presented as a function of probe location and engine discharge conditions. A discussion of the measured electron energy distribution function will also be presented, with regards to variation from pure maxwellian. It has been found that there is a distinct primary population found along the thruster centerline, which causes estimates of electron temperature, electron density, and plasma potential, to err on the high side, due this energetic population. Computation of the energy distribution fimction of the plasma clearly indicates the presence of primaries, whose presence become less obvious with radial distance from the main discharge plume.

near grid plasma↗
NASA NTRS2007

Hardware Outgassing Certification

This course will provide students with the understanding necessary to calculate certification requirements for and interpret the data from hardware undergoing vacuum bakeout. The fundamental physics that driv e hardware outgassing and contaminant deposition will be explained, a nd data reduction techniques will be applied to examples.

Hughes, David W.↗
NASA NTRS2006

Overview of Dynamic Test Techniques for Flight Dynamics Research at NASA LaRC (Invited)

An overview of dynamic test techniques used at NASA Langley Research Center on scale models to obtain a comprehensive flight dynamics characterization of aerospace vehicles is presented. Dynamic test techniques have been used at Langley Research Center since the 1920s. This paper will provide a partial overview of the current techniques available at Langley Research Center. The paper will discuss the dynamic scaling necessary to address the often hard-to-achieve similitude requirements for these techniques. Dynamic test techniques are categorized as captive, wind tunnel single degree-of-freedom and free-flying, and outside free-flying. The test facilities, technique specifications, data reduction, issues and future work are presented for each technique. The battery of tests conducted using the Blended Wing Body aircraft serves to illustrate how the techniques, when used together, are capable of characterizing the flight dynamics of a vehicle over a large range of critical flight conditions.

Owens, D. Bruce↗
NASA NTRS2006

Nonlinear Spring Finite Elements for Predicting Mode I-Dominated Delamination Growth in Laminated Structure with Through-Thickness reinforcement

One particular concern of polymer matrix composite laminates is the relatively low resistance to delamination cracking, in particular when the dominant type of failure is mode I opening. One method proposed for alleviating this problem involves the insertion pultruded carbon pins through the laminate thickness. The pins, known as z-pins, are inserted into the prepreg laminate using an ultrasonic hammer prior to the curing process, resulting in a field of pins embedded normal to the laminate plane as illustrated in Figure. 1. Pin diameters range between 0.28-mm to 0.5-mm and standard areal densities range from 0.5% to 4%. The z-pins are provided by the manufacturer, Aztex(Registered TradeMark) , in a low-density foam preform, which acts to stabilize orientation of the pins during the insertion process [1-3]. Typical pin materials include boron and carbon fibers embedded in a polymer matrix. A number of methods have been developed for predicting delamination growth in laminates reinforced with z-pins. During a study on the effect of z-pin reinforcement on mode I delamination resistance, finite element analyses of z-pin reinforced double cantilever beam (DCB) specimens were performed by Cartie and Partridge [4]. The z-pin bridging stresses were modeled by applying equivalent forces at the pin locations. Single z-pin pull-out tests were performed to characterize the traction law of the pins under mode I loading conditions. Analytical solutions for delamination growth in z-pin reinforced DCB specimens were independently derived by Robinson and Das [5] and Ratcliffe and O'Brien [6]. In the former case, pin bridging stresses were modeled using a distributed load and in the latter example the bridging stresses were discretely modeled by way of grounded springs. Additionally, Robinson and Das developed a data reduction strategy for calculating mode I fracture toughness, G(sub Ic), from a z-pin reinforced DCB specimen test [5]. In both cases a traction law similar to that adopted by Cartie and Partridge was used to represent z-pin failure under mode I loading conditions. In the current work spring elements available in most commercial finite element codes were used to model z-pins. The traction law used in previous analyses [4-6] was employed to represent z-pin damage. This method is intended for and is limited to simulating z-pins in composite laminate structure containing mode I-dominated delamination cracking. The current technique differs from previous analyses in that spring finite elements (available in commercial codes) are employed for simulating zpins, reducing the complexity of the analysis construction process. Furthermore, the analysis method can be applied to general structure that experiences mode I-dominated delamination cracking, in contrast to existing analytical solutions that are only applicable to coupon DCB specimens.

Ratcliffe, James G.↗
NASA NTRS2008

Enhanced Flight Termination System (EFTS): Flight Demonstration and Results

The Enhanced Flight Termination System (EFTS) program was initiated and propelled due to the inadvertent terminations of Global Hawk and the Strategic Target System and the NASA Inspector General's assessment letter and recommendations regarding the exploration of low-cost, lightweight space COMSEC for FTS. Additionally, the standard analog and high alphabet systems most commonly used in FTS are secure, but not encrypted. A study group was initiated to select and document a robust, affordable, reliable technology that provides encrypted FTS capability. A flight demonstration was conducted to gain experience using EFTS in an operational environment, provide confidence in the use of the EFTS components, integrate EFTS into an existing range infrastructure to demonstrate the scalability of system components, to provide a command controller that generated the EFTS waveform using an existing range infrastructure, and to provide a report documenting the results of the demonstration. The primary goal of the demonstration was to obtain operational experience with EFTS. Areas of operational experience include: mission planning, pre-flight configuration and testing, mission monitoring and recording, vehicle termination, developing mission procedures. and post mission data reduction and other post mission activities. An Advanced Medium-Range Air-to-Air Missile (AMRAAM) was selected to support the EFTS demonstration due to interest in future use of EFTS by the AMRAAM program, familiarity of EFTS by range personnel, and the availability of existing operational environment to support EFTS testing with available program funding. For demonstration purposes, the AMRAAM was successfully terminated using an EFTS receiver and successfully demonstrating EFTS. The EFTS monitoring software with spectrum analyzer and digital graphical display of aircraft, missile, and target were also demonstrated.

Tow, David↗
NASA NTRS2008

Integrated Vehicle Ground Vibration Testing of Manned Spacecraft: Historical Precedent

For the first time in nearly 30 years, NASA is developing a new manned space flight launch system. The Ares I will carry crew and cargo to not only the International Space Station, but onward for the future exploration of the Moon and Mars. The Ares I control system and structural designs use complex computer models for their development. An Integrated Vehicle Ground Vibration Test (IVGVT) will validate the efficacy of these computer models. The IVGVT will reduce the technical risk of unexpected conditions that could place the vehicle or crew in jeopardy. The Ares Project Office's Flight and Integrated Test Office commissioned a study to determine how historical programs, such as Saturn and Space Shuttle, validated the structural dynamics of an integrated flight vehicle. The study methodology was to examine the historical record and seek out members of the engineering community who recall the development of historic manned launch vehicles. These records and interviews provided insight into the best practices and lessons learned from these historic development programs. The information that was gathered allowed the creation of timelines of the historic development programs. The timelines trace the programs from the development of test articles through test preparation, test operations, and test data reduction efforts. These timelines also demonstrate how the historical tests fit within their overall vehicle development programs. Finally, the study was able to quantify approximate staffing levels during historic development programs. Using this study, the Flight and Integrated Test Office was able to evaluate the Ares I Integrated Vehicle Ground Vibration Test schedule and workforce budgets in light of the historical precedents to determine if the test had schedule or cost risks associated with it.

Lemke, Paul R.↗
NASA NTRS2007

A Catalog of Galaxy Clusters Observed by XMM-Newton

Images and the radial profiles of the temperature, abundance, and brightness for 70 clusters of galaxies observed by XMM-Newton are presented along with a detailed discussion of the data reduction and analysis methods, including background modeling, which were used in the processing. Proper consideration of the various background components is vital to extend the reliable determination of cluster parameters to the largest possible cluster radii. The various components of the background including the quiescent particle background, cosmic diffuse emission, soft proton contamination, and solar wind charge exchange emission are discussed along with suggested means of their identification, filtering, and/or their modeling and subtraction. Every component is spectrally variable, sometimes significantly so, and all components except the cosmic background are temporally variable as well. The distributions of the events over the FOV vary between the components, and some distributions vary with energy. The scientific results from observations of low surface brightness objects and the diffuse background itself can be strongly affected by these background components and therefore great care should be taken in their consideration.

Snowden, S. L.↗
NASA NTRS2008

Ultraviolet Imaging of the Cen-A Jet

We present GALEX ultraviolet (125-300nm) images of Centaurus A over a 1.1 degree field. We detect UV emission from young stars and shocks at the interface between the outer jet and an HI cloud, at locations where the inner jet bends or is disrupted, and in the central disk. Although some of these star-forming regions were previously imaged with HST, not all have been. We also detect faint, diffuse UV emission from several regions where young stars are not obviously present. New radio images of the Northern Middle Lobe of Cen A may also be presented, depending on the progress of data reduction.

Neff, Susan↗
NASA NTRS2009

Experimental Studies of the Aerothermal Characteristics of the Project Orion CEV heat Shield in High Speed Transitional and Turbulent Flows

An experimental program has been completed by CUBRC exploring laminar, transitional, and turbulent flows over a 7.0% scale model of the Project ORION CEV geometry. This program was executed primarily to answer questions concerning the increase in heat transfer on the windward, or "hot shoulder" of the CEV heat shield from laminar to turbulent flow. To answer these questions CUBRC constructed and instrumented a 14.0 inch diameter Project ORION CEV model and ran a range of Reynolds numbers based on diameter from 1.0 to over 40 million at a Mach number of 8.0. These Reynolds numbers were selected to cover laminar to turbulent heating data on the "hot shoulder". Data obtained during these runs will be used to guide design decisions as they apply to heat shield thickness and extent. Several experiments at higher enthalpies were achieved to obtain data for code validation with real gas effects and transition. CUBRC also performed computation studies of these experiments to aid in the data reduction process and study turbulence modeling.

Wadhams, T.P.↗
NASA NTRS2009

Design and Calibration of a Flowfield Survey Rake for Inlet Flight Research

The Propulsion Flight Test Fixture at the NASA Dryden Flight Research Center is a unique test platform available for use on NASA's F-15B aircraft, tail number 836, as a modular host for a variety of aerodynamics and propulsion research. For future flight data from this platform to be valid, more information must be gathered concerning the quality of the airflow underneath the body of the F-15B at various flight conditions, especially supersonic conditions. The flow angularity and Mach number must be known at multiple locations on any test article interface plane for measurement data at these locations to be valid. To determine this prerequisite information, flight data will be gathered in the Rake Airflow Gauge Experiment using a custom-designed flowfield rake to probe the airflow underneath the F-15B at the desired flight conditions. This paper addresses the design considerations of the rake and probe assembly, including the loads and stress analysis using analytical methods, computational fluid dynamics, and finite element analysis. It also details the flow calibration procedure, including the completed wind-tunnel test and posttest data reduction, calibration verification, and preparation for flight-testing.

Flynn, Darin C.↗
NASA NTRS2009

The Capillary Flow Experiments Aboard the International Space Station: Increments 9-15

This report provides a summary of the experimental, analytical, and numerical results of the Capillary Flow Experiment (CFE) performed aboard the International Space Station (ISS). The experiments were conducted in space beginning with Increment 9 through Increment 16, beginning August 2004 and ending December 2007. Both primary and extra science experiments were conducted during 19 operations performed by 7 astronauts including: M. Fincke, W. McArthur, J. Williams, S. Williams, M. Lopez-Alegria, C. Anderson, and P. Whitson. CFE consists of 6 approximately 1 to 2 kg handheld experiment units designed to investigate a selection of capillary phenomena of fundamental and applied importance, such as large length scale contact line dynamics (CFE-Contact Line), critical wetting in discontinuous structures (CFE-Vane Gap), and capillary flows and passive phase separations in complex containers (CFE-Interior Corner Flow). Highly quantitative video from the simply performed flight experiments provide data helpful in benchmarking numerical methods, confirming theoretical models, and guiding new model development. In an extensive executive summary, a brief history of the experiment is reviewed before introducing the science investigated. A selection of experimental results and comparisons with both analytic and numerical predictions is given. The subsequent chapters provide additional details of the experimental and analytical methods developed and employed. These include current presentations of the state of the data reduction which we anticipate will continue throughout the year and culminate in several more publications. An extensive appendix is used to provide support material such as an experiment history, dissemination items to date (CFE publication, etc.), detailed design drawings, and crew procedures. Despite the simple nature of the experiments and procedures, many of the experimental results may be practically employed to enhance the design of spacecraft engineering systems involving capillary interface dynamics.

Jenson, Ryan M.↗
NASA NTRS2010

Throttling Characteristics of the RL10 Derivative Common Extensible Cryogenic Engine -- Demo 1.6 and 1.7 Test Results

The Common Extensible Cryogenic Engine (CECE) is a deep throttling cryogenic Lunar Module Descent Engine (LMDE) technology development demonstrator based on the Pratt & Whitney Rocketdyne (PWR) RL10 engine. Previous testing on this engine occurred during 2006 as Demo 1.0, then Demo 1.5 in 2007, Demo 1.6 in 2008 and finally Demo 1.7 in 2010. A review of Demo 1.0, 1.5, and preliminary results of 1.6 were reported in previous JANNAF papers. Demo 1.6 was tested at the PWR E-6 test facility in November 2008. The primary goal of this series was to mitigate low frequency combustion instability observed at low power levels. To mitigate the chug, the Demo 1.6 injector was modified from the previous configurations to include an approximately 0.050 inch thick teflon-type spray-on insulation to reduce heat transfer to the LOX manifold, which was believed to be a significant contributor to the low power instability. In addition, gaseous helium injection into the LOX manifold was used as a means to stabilize the system. Also explored in this test series was mitigation for a low power 1 Hz fuel system oscillation caused by sub-critical hydrogen boiling in the chamber cooling jacket. Reduced area gas venturis were utilized to avoid the 1 Hz fuel-size oscillation by keeping the cooling jacket supercritical down to lower engine power levels. Demo 1.7 began testing in March 2010. Its primary objectives were to demonstrate closed loop control capability on mixture ratio and chamber pressure, start to lower power levels and increased throttling ramp rates. Secondary test objectives that are discussed include multiple engine starts, higher mixture ratio excursions and additional time at low power level. While the complete test series and data reduction is not yet complete for Demo 1.7, an overview and up-to-date status is provided.

Devine, Matthew K.↗
NASA NTRS2010

Sizing Single Cantilever Beam Specimens for Characterizing Facesheet/Core Peel Debonding in Sandwich Structure

This paper details part of an effort focused on the development of a standardized facesheet/core peel debonding test procedure. The purpose of the test is to characterize facesheet/core peel in sandwich structure, accomplished through the measurement of the critical strain energy release rate associated with the debonding process. The specific test method selected for the standardized test procedure utilizes a single cantilever beam (SCB) specimen configuration. The objective of the current work is to develop a method for establishing SCB specimen dimensions. This is achieved by imposing specific limitations on specimen dimensions, with the objectives of promoting a linear elastic specimen response, and simplifying the data reduction method required for computing the critical strain energy release rate associated with debonding. The sizing method is also designed to be suitable for incorporation into a standardized test protocol. Preliminary application of the resulting sizing method yields practical specimen dimensions.

Ratcliffe, James G.↗
NASA NTRS2010

Cosmic Infrared Background Fluctuations in Deep Spitzer Infrared Array Camera Images: Data Processing and Analysis

This paper provides a detailed description of the data reduction and analysis procedures that have been employed in our previous studies of spatial fluctuation of the cosmic infrared background (CIB) using deep Spitzer Infrared Array Camera observations. The self-calibration we apply removes a strong instrumental signal from the fluctuations that would otherwise corrupt the results. The procedures and results for masking bright sources and modeling faint sources down to levels set by the instrumental noise are presented. Various tests are performed to demonstrate that the resulting power spectra of these fields are not dominated by instrumental or procedural effects. These tests indicate that the large-scale ([greater, similar]30') fluctuations that remain in the deepest fields are not directly related to the galaxies that are bright enough to be individually detected. We provide the parameterization of these power spectra in terms of separate instrument noise, shot noise, and power-law components. We discuss the relationship between fluctuations measured at different wavelengths and depths, and the relations between constraints on the mean intensity of the CIB and its fluctuation spectrum. Consistent with growing evidence that the [approx]1-5 [mu]m mean intensity of the CIB may not be as far above the integrated emission of resolved galaxies as has been reported in some analyses of DIRBE and IRTS observations, our measurements of spatial fluctuations of the CIB intensity indicate the mean emission from the objects producing the fluctuations is quite low ([greater, similar]1 nW m-2 sr-1 at 3-5 [mu]m), and thus consistent with current [gamma]-ray absorption constraints. The source of the fluctuations may be high-z Population III objects, or a more local component of very low luminosity objects with clustering properties that differ from the resolved galaxies. Finally, we discuss the prospects of the upcoming space-based surveys to directly measure the epochs inhabited by the populations producing these source-subtracted CIB fluctuations, and to isolate the individual fluxes of these populations.

Arendt, Richard↗
NASA NTRS2010

Methodology for the Assessment of 3D Conduction Effects in an Aerothermal Wind Tunnel Test

This slide presentation reviews a method for the assessment of three-dimensional conduction effects during test in a Aerothermal Wind Tunnel. The test objectives were to duplicate and extend tests that were performed during the 1960's on thermal conduction on proturberance on a flat plate. Slides review the 1D versus 3D conduction data reduction error, the analysis process, CFD-based analysis, loose coupling method that simulates a wind tunnel test run, verification of the CFD solution, Grid convergence, Mach number trend, size trends, and a Sumary of the CFD conduction analysis. Other slides show comparisons to pretest CFD at Mach 1.5 and 2.16 and the geometries of the models and grids.

Oliver, Anthony Brandon↗