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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Natural Frequency Testing and Model Correlation of Rocket Engine Structures in Liquid Hydrogen - Phase I, Cantilever Beam

Many structures in the launch vehicle industry operate in liquid hydrogen (LH2), from the hydrogen fuel tanks through the ducts and valves and into the pump sides of the turbopumps. Calculating the structural dynamic response of these structures is critical for successful qualification of this hardware, but accurate knowledge of the natural frequencies is based entirely on numerical or analytical predictions of frequency reduction due to the added-fluid-mass effect because testing in LH2 has always been considered too difficult and dangerous. This fluid effect is predicted to be approximately 4-5% using analytical formulations for simple cantilever beams. As part of a comprehensive test/analysis program to more accurately assess pump inducers operating in LH2, a series of frequency tests in LH2 were performed at NASA/Marshall Space Flight Center's unique cryogenic test facility. These frequency tests are coupled with modal tests in air and water to provide critical information not only on the mass effect of LH2, but also the cryogenic temperature effect on Young's Modulus for which the data is not extensive. The authors are unaware of any other reported natural frequency testing in this media. In addition to the inducer, a simple cantilever beam was also tested in the tank to provide a more easily modeled geometry as well as one that has an analytical solution for the mass effect. This data will prove critical for accurate structural dynamic analysis of these structures, which operate in a highly-dynamic environment.

Brown, Andrew M.↗
NASA NTRS2020

Optically targeted search for gravitational waves emitted by core-collapse supernovae during the first and second observing runs of advanced LIGO and advanced Virgo

We present the results from a search for gravitational-wave transients associated with core-collapse supernovae observed within a source distance of approximately 20 Mpc during the first and second observing runs of Advanced LIGO and Advanced Virgo. No significant gravitational-wave candidate was detected. We report the detection efficiencies as a function of the distance for waveforms derived from multidimensional numerical simulations and phenomenological extreme emission models. The sources with neutrino-driven explosions are detectable at the distances approaching 5 kpc, and for magnetorotationally driven explosions the distances are up to 54 kpc. However, waveforms for extreme emission models are detectable up to 28 Mpc. For the first time, the gravitational-wave data enabled us to exclude part of the parameter spaces of two extreme emission models with confidence up to 83%, limited by coincident data coverage. Besides, using ad hoc harmonic signals windowed with Gaussian envelopes, we constrained the gravitational-wave energy emitted during core collapse at the levels of 4.27 × 10^(−4) Mꙩc^(2) and 1.28 × 10^(−1) Mꙩc^(2) for emissions at 235 and 1304 Hz, respectively. These constraints are 2 orders of magnitude more stringent than previously derived in the corresponding analysis using initial LIGO, initial Virgo, and GEO 600 data.

B. P. Abbott↗
NASA NTRS1998

Absolute Rovibrational Intensities of C-12O2-16 Absorption Bands in the 3090-3850/ CM Spectral Region

A multispectrum nonlinear least-squares fitting technique has been used to determine the absolute intensities for approximately 1500 spectral lines in 36 vibration - rotation bands Of C-12O2-16 between 3090 and 3850/ cm. A total of six absorption spectra of a high- purity (99.995% minimum) natural sample of carbon dioxide were used in the analysis. The spectral data (0.01/cm resolution) were recorded at room temperature and low pressure (1 to 10 Torr) using the McMath-Pierce Fourier transform spectrometer of the National Solar Observatory (NSO) on Kitt Peak. The absorption path lengths for these spectra varied between 24.86 and 385.76 m. The first experimental determination of the intensity of the theoretically predicted 2(nu)(sub 2, sup 2) + nu(sub 3) "forbidden" band has been made. The measured line intensities obtained for each band have been analyzed to determine the vibrational band intensity, S(sub nu), in /cm/( molecule/sq cm) at 296 K, square of the rotationless transition dipole moment |R|(exp 2) in Debye, as well as the nonrigid rotor coefficients. The results are compared to the values listed in the 1996 HITRAN database which are obtained using the direct numerical diagonalization (DND) technique as well as to other published values where available.

Devi, V. Malathy↗
NASA NTRS2010

Aero-Heating of Shallow Cavities in Hypersonic Freestream Flow

The purpose of these experiments and analysis was to augment the heating database and tools used for assessment of impact-induced shallow-cavity damage to the thermal protection system of the Space Shuttle Orbiter. The effect of length and depth on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These rapid-response experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated immediately prior to the launch of STS-114, the initial flight in the Space Shuttle Return-To-Flight Program, and continued during the first week of the mission. Previously-designed and numerically-characterized blunted-nose baseline flat plates were used as the test surfaces. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process and the two-dimensional flow assumptions used for the data analysis. The experimental boundary layer state conditions were inferred using the measured heating distributions on a no-cavity test article. Two test plates were developed, each containing 4 equally-spaced spanwise-distributed cavities. The first test plate contained cavities with a constant length-to-depth ratio of 8 with design point depth-to-boundary-layer-thickness ratios of 0.1, 0.2, 0.35, and 0.5. The second test plate contained cavities with a constant design point depth-to-boundary-layer-thickness ratio of 0.35 with length-to-depth ratios of 8, 12, 16, and 20. Cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary results indicate that the floor-averaged Bump Factor (local heating rate nondimensionalized by upstream reference) at the tested conditions is approximately 0.3 with a standard deviation of 0.04 for laminar-in/laminar-out conditions when the cavity length-to-boundary-layer thickness is between 2.5 and 10 and for cavities in the depth-to-boundary-layer-thickness range of 0.3 to 0.8. Over this same range of conditions and parameters, preliminary results also indicate that the maximum Bump Factor on the cavity centerline falls between 2.0 and 2.75, as long as the cavity-exit conditions remain laminar. Cavities with length-to-boundary-layer-thickness ratio less than 2.5 can not be easily classified with this approach and require further analysis.

Everhart, Joel L.↗
NASA NTRS1993

Geologic mapping of Northern Atla Regio on Venus: Preliminary data

The Northern part of Atla Regio within the frame of C1-formate Magellan photo map 15N197 was mapped geologically at scale 1:8,000,000. This is a part of Russia's contribution into C1 geologic mapping efforts. The map is reproduced here being reduced about twice. The map shows that the Northern Atla area is predominantly a volcanic plain with numerous volcanic features: shield volcanoes, domes and hills with various morphology, corona-like constructions, radar bright and dark spots often with flow-like outlines. Relatively small areas of tessera occurred in the area are mainly semi-flooded with the plain material. Tesserae are considered to be the oldest terrains within the map sheet. There are many lineated terrains in the region. They are interpreted as the old, almost-buried tesserae (those with crossed lineaments) or partly buried ridge belts (those with parallel lineaments). These lineated terrains have an intermediate age between the young volcanic plains and the old tessera areas. Two prominent high volcanic shields are located within the region - Ozza Mons and Sapas Mona. The most prominent structure in Northern Atla is Ganis Chasma rift. The rift cuts volcanic plain and is considered to be under formation during approximately the same time with Ozza Mons shield. Ganis Chasma rift valley is highly fractured and bounded with fault scarps. Rift shoulder uplifts are typical for Ganis Chasma. There are few relatively young volcanic features inside the rift valley. The analysis of fracturing and rift valley geometry shows the rift originated due to 5-10 percent crustal extention followed by the crustal subsidence. The age sequence summary for the main terrain types in the region is (from older to younger ones): tesserae; lineated terrains with crossed lineaments; lineated terrains with parallel lineaments; volcanic plains; and prominent volcanic shields and Ganis Chasma rift valley. The geologic structure of Atla Regio as it appeared now with the Magellan high resolution images is very close to that of Beta Regio. Such conclusion coincide with the earlier ones based on the coarser data.

Nikishin, A. M.↗
NASA NTRS2020

Streak Instabilities on HIFiRE-5 Elliptic Cone

The Hypersonic International Flight Research and Experimentation (HIFiRE) 5 flight experiment by the Air Force Research Laboratories and Australian Defense Science and Technology Organization yielded inflight, hypersonic transition data for a canonical, 3D configuration in the form of an elliptic cone at various combinations of angle-of-attack and yaw. Previous analysis has shown that boundary-layer stability calculations for the as-flown, zero-yaw flight conditions are able to capture the second mode dominated transition along the attachment line as well as the crossflow induced transition in between the attachment line and the minor axis symmetry plane. However, there is still a need to understand the transition in the vicinity of the minor axis plane of symmetry, where the boundary layer thickness exhibits an azimuthally compact bulge due to the collision of the secondary flow approaching from the attachment lines on both sides. This paper reports a computational analysis of the stability of the boundary layer flow along the bulge regions on both the leeward and windward sides of the vehicle surface. At a representative flight condition corresponding to a time instant of t = 514.813 seconds, computations are performed to identify several different unstable modes within the bulge regions, with the eventual goal of developing a linear stability correlation for the transition onset near the minor axis symmetry plane. The most amplified flow instabilities in the pretransitional region correspond to a “stem” mode that is concentrated within a pair of nearly vertical shear layers below the cap of the mushroom shaped bulge in the mean velocity contours. An excellent agreement is found between the predictions of instability amplification based on the plane marching parabolized stability equations (PSE) and the direct numerical solutions (DNS). Given the large number of unstable modes within the bulge region, the observed agreement demonstrates, for first time, that the PSE can provide accurate predictions for the development of flow instabilities in streak-like flow features over three-dimensional bodies. The peak N-factor of approximately 15 at the transition location estimated from the thermocouple measurements along the leeward centerline is close to the transition N-factor for Mack mode transition during the HIFiRE-1 circular cone flight experiment with nearly zero degrees angle of attack.

Meelan Choudhari↗
NASA NTRS2016

Analysis of Summer-Time Ozone and Precursor Species in the Southeast United States

Ozone (O3) is a greenhouse gas and toxic pollutant which plays a major role in air quality and atmospheric chemistry. The understanding and ability to model the horizontal and vertical structure of O3 mixing ratios is difficult due to the complex formation/destruction processes and transport pathways that cause large variability of O3. The Environmental Protection Agency has National Ambient Air Quality Standards for O3 set at 75 ppb with future standards proposed to be as low as 65 ppb. These lower values emphasize the need to better understand/simulate the transport processes, emission sources, and chemical processes controlling precursor species (e.g., NOx, VOCs, and CO) which influence O3 mixing ratios. The uncertainty of these controlling variables is particularly large in the southeast United States (US) which is a region impacted by multiple different emission sources of precursor species (anthropogenic and biogenic) and transport processes resulting in complex spatio-temporal O3 patterns. During this work we will evaluate O3 and precursor species in the southeast US applying models, ground-based and airborne in situ data, and lidar observations. In the summer of 2013, the UAH O3 Differential Absorption Lidar (DIAL) (part of the Tropospheric Ozone Lidar Network (TOLNet)) measured vertical O3 profiles from the surface up to approximately 12 km. During this period, the lidar observed numerous periods of dynamic temporal and vertical O3 structures. In order to determine the sources/processes impacting these O3 mixing ratios we will apply the CTM GEOS-Chem (v9-02) at a 0.25 deg x 0.3125 deg resolution. Using in situ ground-based (e.g., SEARCH Network, CASTNET), airborne (e.g., NOAA WP-3D - SENEX 2013, DC-8 - SEAC4RS), and TOLNet lidar data we will first evaluate the model to determine the capability of GEOS-Chem to simulate the spatio-temporal variability of O3 in the southeast US. Secondly, we will perform model sensitivity studies in order to quantify which emission sources (e.g., anthropogenic, biogenic, lighting, wildfire) and transport processes (e.g., stratospheric, long-range, local scale) are contributing to these TOLNet-observed dynamic O3 patterns. Results from the evaluation of the model and the study of sources/processes impacting observed O3 mixing ratios will be presented.

Optical Radar↗
NASA NTRS1994

Generation of gear tooth surfaces by application of CNC machines

This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.

Litvin, F. L.↗
NASA NTRS2023

An Analysis of Degradation in Low-Cost Particulate Matter Sensors

Low-cost sensors (LCSs) are increasingly being used to measure fine particulate matter (PM 2.5 ) concentrations in cities around the world. One of the most commonly deployed LCSs is PurpleAir with ∼15 000 sensors deployed in the United States, alone. PurpleAir measurements are widely used by the public to evaluate PM 2.5 levels in their neighborhoods. PurpleAir measurements are also increasingly being integrated into models by researchers to develop large-scale estimates of PM 2.5 . However, the change in sensor performance over time has not been well studied. It is important to understand the lifespan of these sensors to determine when they should be serviced or replaced, and when measurements from these devices should or should not be used for various applications. This paper fills this gap by leveraging the fact that: (1) each PurpleAir sensor is composed of two identical sensors and the divergence between their measurements can be observed, and (2) there are numerous PurpleAir sensors within 50 meters of regulatory monitors allowing for the comparison of measurements between these instruments. We propose empirically-derived degradation outcomes for the PurpleAir sensors and evaluate how these outcomes change over time. On average, we find that the number of ‘flagged’ measurements, where the two sensors within each PurpleAir sensor disagree, increases with time to ∼4% after 4 years of operation. Approximately, 2 percent of all PurpleAir sensors were permanently degraded. The largest fraction of permanently degraded PurpleAir sensors appeared to be in the hot and humid climate zone, suggesting that sensors in these locations may need to be replaced more frequently. We also find that the bias of PurpleAir sensors, or the difference between corrected PM2.5 levels and the corresponding reference measurements, changed over time by −0.12 μg m −3 (95% CI: −0.13 μg m −3 , −0.10 μg m −3 ) per year. The average bias increases dramatically after 3.5 years. Further, climate zone is a significant modifier of the association between degradation outcomes and time.

Priyanka deSouza↗
NASA NTRS1995

Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields

A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.

Tweedt, Daniel L.↗
NASA NTRS2017

Online Visualization and Value Added Services of MERRA-2 Data at GES DISC

NASA climate reanalysis datasets from MERRA-2, distributed at the Goddard Earth Sciences Data and Information Services Center (GES DISC), have been used in broad research areas, such as climate variations, extreme weather, agriculture, renewable energy, and air quality, etc. The datasets contain numerous variables for atmosphere, land, and ocean, grouped into 95 products. The total archived volume is approximately 337 TB ( approximately 562K files) at the end of October 2017. Due to the large number of products and files, and large data volumes, it may be a challenge for a user to find and download the data of interest. The support team at GES DISC, working closely with the MERRA-2 science team, has created and is continuing to work on value added data services to best meet the needs of a broad user community. This presentation, using aerosol over Asia Monsoon as an example, provides an overview of the MERRA-2 data services at GES DISC, including: How to find the data? How many data access methods are provided? What are the best data access methods for me? How do download the subsetted (parameter, spatial, temporal) data and save in preferred spatial resolution and data format? How to visualize and explore the data online? In addition, we introduce a future online analytic tool designed for supporting application research, focusing on long-term hourly time-series data access and analysis.

Shen, Suhung↗
NASA NTRS1968

Predicted vibration responses of Apollo structure and effects of pressure correlation lengths on response

Progressive wove and reverberant acoustic fields ore often used in the laboratory for qualification testing of aerospace structures that are subjected to unsteady aerodynamic environments which occur during flight through the atmosphere. Acoustic simulation of these in-flight environments i s achieved i f the structural vibration response to acoustic excitation is equivalent, over the frequency range of interest, to the response caused by aerodynamic turbulence. To determine the degree of response simulation that could be expected for such qualification testing of the Apollo Spacecraft, responses of a segment of the Apollo structure were estimated theoretically for both acoustic and flight environments. The vibration analysis presented in this report was performed for the Spacecraft Lunar Module Adaptor; and the three environments treated are turbulence at Mach 1 and Mach 2, a reverberant acoustic field, and a modified acoustic progressive wave field. The progressive wave field is assumed to be generated within a specially designed shroud of sixteen axially oriented ducts which is constructed around and contoured to the external skin of the vehicle. Each duct is open on the side adjacent to the skin and is driven acoustically at one end by an independent noise source, thus allowing for different pressure correlation patterns around the circumference of the vehicle. The purpose of the analysis was to determine the effects of surface pressure correlation lengths on the response characteristics of representative Apollo structure, and to select on this basis, the optimum acoustic environment for structural vibration qualification tests of the Apollo in the Spacecraft Acoustic Laboratory at MSC. The method of analysis employed consists of determining, independently, the space average, mean-square acceleration spectral density for each of the significant modes of vibration of an equivalent cylindrical shell, and then expressing the total structural response as a linear summation of these modal responses. Approximately 570 classical modes of a pinned-end cylinder were used in order to find the spectral response characteristics of the structure throughout the frequency range of 10 - 1,000 Hz. The effective forcing functions or joint acceptances of the various modes of vibration were computed and are presented graphically for each of the pressure excitation environments. A brief development of the response equations used is presented in the report. Space average acceleration response spectra were computed for twelve different cases including aerodynamic turbulence at Mach 1 and Mach 2, reverberant acoustic field, five duct correlation patterns, two cases of an axially damped progressive wave field, and two cases in which the structural damping constant was varied from the expected value. The response spectra were computed and plotted by a high speed digital computer far a flat excitation pressure spectrum; and the response spectra were numerically integrated to give one-third octave bond average responses. A complete set of digital computer programs has been developed for both flat plate and cylindrical shell structures for the above environments, and each requires run times of three minutes or less. Thus, the work presented herein, along with the results, constitutes a practical advancement to the existing state-of-the-art of vibration prediction.

R W White↗
NASA NTRS1989

Space station contamination modeling

Current plans for the operation of Space Station Freedom allow the orbit to decay to approximately an altitude of 200 km before reboosting to approximately 450 km. The Space Station will encounter dramatically increasing ambient and induced environmental effects as the orbit decays. Unfortunately, Shuttle docking, which has been of concern as a high contamination period, will likely occur during the time when the station is in the lowest orbit. The combination of ambient and induced environments along with the presence of the docked Shuttle could cause very severe contamination conditions at the lower orbital altitudes prior to Space Station reboost. The purpose here is to determine the effects on the induced external environment of Space Station Freedom with regard to the proposed changes in altitude. The change in the induced environment will be manifest in several parameters. The ambient density buildup in front of ram facing surfaces will change. The source of such contaminants can be outgassing/offgassing surfaces, leakage from the pressurized modules or experiments, purposeful venting, and thruster firings. The third induced environment parameter with altitude dependence is the glow. In order to determine the altitude dependence of the induced environment parameters, researchers used the integrated Spacecraft Environment Model (ISEM) which was developed for Marshall Space Flight Center. The analysis required numerous ISEM runs. The assumptions and limitations for the ISEM runs are described.

Gordon, T. D.↗
NASA NTRS1946

Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.

LOADS - FUSELAGES↗
NASA NTRS1997

Analytical Studies of Boundary Layer Generated Aircraft Interior Noise

An analysis is made of the "interior noise" produced by high, subsonic turbulent flow over a thin elastic plate partitioned into "panels" by straight edges transverse to the mean flow direction. This configuration models a section of an aircraft fuselage that may be regarded as locally flat. The analytical problem can be solved in closed form to represent the acoustic radiation in terms of prescribed turbulent boundary layer pressure fluctuations. Two cases are considered: (i) the production of sound at an isolated panel edge (i.e., in the approximation in which the correlation between sound and vibrations generated at neighboring edges is neglected), and (ii) the sound generated by a periodic arrangement of identical panels. The latter problem is amenable to exact analytical treatment provided the panel edge conditions are the same for all panels. Detailed predictions of the interior noise depend on a knowledge of the turbulent boundary layer wall pressure spectrum, and are given here in terms of an empirical spectrum proposed by Laganelli and Wolfe. It is expected that these analytical representations of the sound generated by simplified models of fluid-structure interactions can used to validate more general numerical schemes.

Howe, M. S.↗
NASA NTRS1996

Application of the kappa-omega Turbulence Model to Quasi-Three-Dimensional Turbomachinery Flows

Many computational fluid dynamics codes for turbomachinery use the Baldwin-Lomax (B-L) turbulence model. It is easy to implement in two dimensions and works well for predicting overall turbomachinery performance. However, it is awkward to implement in three dimensions, often has difficulty finding the length scale, has a crude transition model, and neglects freestream turbulence, surface roughness, and mass injection. The kappa-omega model developed by Wilcox is an appealing alternative for several reasons. First, it is the only two-equation model that can be integrated to the wall without requiring damping functions or the distance to the wall, and hence, should behave well numerically. Second, the effects of freestream turbulence, surface roughness, and mass injection are easily included in the model. Finally, transition can be simulated using the low Reynolds number version of the model. Menter applied the kappa-model to external flows and showed very good results for flows with adverse pressure gradients. Liu and Zheng described their implementation of the kappa-model in a cascade code that included an area change term to account for endwall convergence. They validated the model for a flat plate, and compared the B-L and kappa-models to measured surface pressures for a low-pressure turbine cascade. Since they did not use the low Reynolds number version of the model, their results showed problems resulting from early transition. In this Note the low Reynolds number kappa-model was incorporated in the author's quasi-three-dimensional turbomachinery analysis code. The code includes the effects of rotation, radius change, and stream-surface thickness variation, and also includes the B-L turbulence model. The kappa-omega model was implemented using many of Menter's recommendations and an implicit approximate-factorization scheme described by Baldwin and Barth. The model was tested for a transonic compressor with rotation and variable stream-surface radius and height, and for a transonic turbine vane with transition and heat transfer. Results were compared to the B-L model and to experimental data.

Chima, Rodrick V.↗
NASA NTRS2005

Baseline Computational Fluid Dynamics Methodology for Longitudinal-Mode Liquid-Propellant Rocket Combustion Instability

A computational method for the analysis of longitudinal-mode liquid rocket combustion instability has been developed based on the unsteady, quasi-one-dimensional Euler equations where the combustion process source terms were introduced through the incorporation of a two-zone, linearized representation: (1) A two-parameter collapsed combustion zone at the injector face, and (2) a two-parameter distributed combustion zone based on a Lagrangian treatment of the propellant spray. The unsteady Euler equations in inhomogeneous form retain full hyperbolicity and are integrated implicitly in time using second-order, high-resolution, characteristic-based, flux-differencing spatial discretization with Roe-averaging of the Jacobian matrix. This method was initially validated against an analytical solution for nonreacting, isentropic duct acoustics with specified admittances at the inflow and outflow boundaries. For small amplitude perturbations, numerical predictions for the amplification coefficient and oscillation period were found to compare favorably with predictions from linearized small-disturbance theory as long as the grid exceeded a critical density (100 nodes/wavelength). The numerical methodology was then exercised on a generic combustor configuration using both collapsed and distributed combustion zone models with a short nozzle admittance approximation for the outflow boundary. In these cases, the response parameters were varied to determine stability limits defining resonant coupling onset.

Litchford, R. J.↗
NASA NTRS1996

Electron Flow to a Satellite at High Positive Potential

The Tethered Satellite System (TSS) is designed to deploy a 1.6 m diameter spherical satellite a distance of 20 km above the space shuttle orbiter on an insulated conducting tether. Because of the passage of the conducting tether through the earth's magnetic field, an emf is generated producing a positive satellite potential of about 5000 V. Electron flow under the influence of this high positive potential is the focus of the present analysis. The ionospheric parameters at TSS orbit altitude are; thermal velocity of electrons, 1.9 x 10(exp 5) M/S, thermal velocity of the ions, 1.1 x 10(exp 3) m/s, velocity of the satellite 8 x 10(exp 3) m/s. The electrons, with a Debye length, lambda(D) = 0.49 cm, spiral about the earth's magnetic field lines (0.4 Gauss) with a radius of about 3 cm and the ions spiral with a radius of 5 m. Under these conditions, the electron thermal energy, kT is 0.17 eV. The TSS satellite radius, r(p) is 163 Debye lengths. There is an extensive literature on the interaction of satellites with the near-earth ionospheric plasma. The space charge limitation to the electron current collected by a sphere at positive electrical potential was calculated by Langmuir and Blodgett (1924). Parker and Murphy (1967) recognized the importance of the influence of the earth's magnetic field and used the guiding center approximation to calculate the electron current collected by a positive charged satellite. More recently Ma and Schunk (1989) have calculated the time dependent flow of electrons to a spherical satellite at positive potential utilizing numerical methods and Sheldon (1994) used similar methods to solve this problem for the steady state. In order to analyze some of the phenomena that occurred in the ionosphere during the TSS flights, it would be useful to have analytic expressions for these electron flows. The governing equations are very complex and an exact analytical solution is not likely. An approximate analytical solution is feasible however, and the results of one attempt are presented herein.

Sheldon, John W.↗