Graphical techniques to assist in pointing and control studies of orbiting spacecraft

Computer generated graphics are developed to assist in the modeling and assessment of pointing and control systems of orbiting spacecraft. Three-dimensional diagrams are constructed of the Earth and of geometrical models which resemble the spacecraft of interest. Orbital positioning of the spacecraft model relative to the Earth and the orbital ground track are then displayed. A star data base is also available which may be used for telescope pointing and star tracker field-of-views to visually assist in spacecraft pointing and control studies. A geometrical model of the Hubble Space Telescope (HST) is constructed and placed in Earth orbit to demonstrate the use of these programs. Simulated star patterns are then displayed corresponding to the primary mirror's FOV and the telescope's star trackers for various telescope orientations with respect to the celestial sphere

NASA/MSFC's Calculation for Test Case 1a of ATAC-FSDC Workshop on After-body and Nozzle Flows

Mr. Ruf of NASA/MSFC executed the CHEM computational fluid dynamics (CFD) code to provide a prediction of the test case 1 a for the ATAC-FSDC Workshop on After-body and Nozzle Flows. CHEM is used extensively at MSFC for a wide variety of fluid dynamic problems. These problems include; injector element flows, nozzle flows, feed line flows, turbomachinery flows, solid rocket motor internal flows, plume vehicle flow interactions, etc

Weak tail conditions for local martingales

© Institute of Mathematical Statistics, 2019. The following conditions are necessary and jointly sufficient for an arbitrary càdlàg local martingale to be a uniformly integrable martingale: (A) The weak tail of the supremum of its modulus is zero; (B) its jumps at the first-exit times from compact intervals converge to zero in L 1 on the events that those times are finite; and (C) its almost sure limit is an integrable random variable

Axisymmetric computational fluid dynamics analysis of Saturn V/S1-C/F1 nozzle and plume

An axisymmetric single engine Computational Fluid Dynamics calculation of the Saturn V/S 1-C vehicle base region and F1 engine plume is described. There were two objectives of this work, the first was to calculate an axisymmetric approximation of the nozzle, plume and base region flow fields of S1-C/F1, relate/scale this to flight data and apply this scaling factor to a NLS/STME axisymmetric calculations from a parallel effort. The second was to assess the differences in F1 and STME plume shear layer development and concentration of combustible gases. This second piece of information was to be input/supporting data for assumptions made in NLS2 base temperature scaling methodology from which the vehicle base thermal environments were being generated. The F1 calculations started at the main combustion chamber faceplate and incorporated the turbine exhaust dump/nozzle film coolant. The plume and base region calculations were made for ten thousand feet and 57 thousand feet altitude at vehicle flight velocity and in stagnant freestream. FDNS was implemented with a 14 species, 28 reaction finite rate chemistry model plus a soot burning model for the RP-1/LOX chemistry. Nozzle and plume flow fields are shown, the plume shear layer constituents are compared to a STME plume. Conclusions are made about the validity and status of the analysis and NLS2 vehicle base thermal environment definition methodology

Modeling of Supersonic Film Cooling on the J-2X Nozzle Extension

Supersonic film cooling (SSFC) of nozzles has been used in several liquid rocket engine designs, and is being applied to the nozzle extension (NE) of the J-2X upper stage engine currently under development. Turbine exhaust gas (TEG) is injected tangentially from a manifold along the NE, and provides a thermal barrier from the core nozzle flow for the NE. As the TEG stream mixes with the nozzle flow, the effectiveness of the thermal barrier is reduced. This paper documents computational fluid dynamics (CFD) analysis work performed by NASA Marshall Space Flight Center (MSFC) to model the flow of the TEG through the manifold, into the nozzle, and the subsequent mixing of the TEG stream with the core flow. The geometry and grid of the TEG manifold, structural support ribs, and the NE wall will be shown, and the CFD boundary conditions described. The Loci-CHEM CFD code used in this work will also be briefly described. A unique approach to modeling the combined TEG manifold/thrust chamber assembly (TCA) was employed, as it was not practical to model the entire 360 circumferential range in one simulation. Prior CFD validation work modeling Calspan SSFC experiments in the early 1990s, documented in a previous AIAA paper, will also be briefly discussed. The fluid dynamics of the TEG flow through the manifold, into and between the structural support ribs, and into the nozzlette that feeds the TCA will be described. Significant swirl and non-uniformities are present, which along with the wakes from the ribs, act to degrade the film cooling effectiveness compared to idealized injection of TEG gas. The effect of these flow characteristics on the adiabatic wall temperature profile on the NE will be discussed

Validation of Supersonic Film Cooling Modeling for Liquid Rocket Engine Applications

Topics include: upper stage engine key requirements and design drivers; Calspan "stage 1" results, He slot injection into hypersonic flow (air); test articles for shock generator diagram, slot injector details, and instrumentation positions; test conditions; modeling approach; 2-d grid used for film cooling simulations of test article; heat flux profiles from 2-d flat plate simulations (run #4); heat flux profiles from 2-d backward facing step simulations (run #43); isometric sketch of single coolant nozzle, and x-z grid of half-nozzle domain; comparison of 2-d and 3-d simulations of coolant nozzles (run #45); flowfield properties along coolant nozzle centerline (run #45); comparison of 3-d CFD nozzle flow calculations with experimental data; nozzle exit plane reduced to linear profile for use in 2-d film-cooling simulations (run #45); synthetic Schlieren image of coolant injection region (run #45); axial velocity profiles from 2-d film-cooling simulation (run #45); coolant mass fraction profiles from 2-d film-cooling simulation (run #45); heat flux profiles from 2-d film cooling simulations (run #45); heat flux profiles from 2-d film cooling simulations (runs #47, #45, and #47); 3-d grid used for film cooling simulations of test article; heat flux contours from 3-d film-cooling simulation (run #45); and heat flux profiles from 3-d and 2-d film cooling simulations (runs #44, #46, and #47)

Altitude Compensating Nozzle

The dual-bell nozzle (fig. 1) is an altitude-compensating nozzle that has an inner contour consisting of two overlapped bells. At low altitudes, the dual-bell nozzle operates in mode 1, only utilizing the smaller, first bell of the nozzle. In mode 1, the nozzle flow separates from the wall at the inflection point between the two bell contours. As the vehicle reaches higher altitudes, the dual-bell nozzle flow transitions to mode 2, to flow full into the second, larger bell. This dual-mode operation allows near optimal expansion at two altitudes, enabling a higher mission average specific impulse (Isp) relative to that of a conventional, single-bell nozzle. Dual-bell nozzles have been studied analytically and subscale nozzle tests have been completed.1 This higher mission averaged Isp can provide up to a 5% increase2 in payload to orbit for existing launch vehicles. The next important step for the dual-bell nozzle is to confirm its potential in a relevant flight environment. Toward this end, NASA Marshall Space Flight Center (MSFC) and Armstrong Flight Research Center (AFRC) have been working to develop a subscale, hot-fire, dual-bell nozzle test article for flight testing on AFRC's F15-D flight test bed (figs. 2 and 3). Flight test data demonstrating a dual-bell ability to control the mode transition and result in a sufficient increase in a rocket's mission averaged Isp should help convince the launch service providers that the dual-bell nozzle would provide a return on the required investment to bring a dual-bell into flight operation. The Game Changing Department provided 0.2 FTE to ER42 for this effort in 2014

Visualizing particle networks in granular media by in situ X-ray computed tomography

In this contribution, cylindrical samples consisting of monodisperse soft (rubber) and stiff (glass) particles are pre-stressed under uniaxial compression. Acoustic P-waves at ultrasound frequencies are superimposed into prepared samples with different soft-stiff volume fractions. Earlier investigations showed the importance of particles networks, i.e. force chains, in controlling the effective mechanical properties of particulate systems. Measured P-wave modulus showed a significant decline while more soft particles are added due to a change in microstructure. However, for small contents of soft particles, it could be observed that the P-wave modulus is increasing. For the understanding of such kinds of effects, detailed insight into the microstructure of the system is required. To gain this information and link it to the effective properties, we made use of high-resolution micro X-ray Computed Tomography (micro-XRCT) imaging and combined it with the classical stiffness characterization. Both performed in situ meaning inside the laboratory-based XRCT scanner. With micro-XRCT imaging, the granular microstructure can be visualized in 3d and characterized subsequently. By post-processing of the data, the individual grains of the particulate systems could be uniquely identified. Finally, the contact network of the packings which connects the center of particles was established to demonstrate the network transition from stiff- to soft-dominated regimes. This has allowed for unprecedented observations and a renewed understanding of particulate systems. It has been demonstrated that micro-XRCT scans of particles packings can be analyzed and compared in 3d to gain extensive information on the scale of the single particles. Here, the in situ setup and workflow from the start of acquiring images in situ till the post-processing of the image data is explained and demonstrated by selected results.Comment: 17 pages, 10 figures, submitted to Survey for Applied Mathematics and Mechanics (GAMM Mitteilungen

Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type

The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of functions that satisfy the Dirichlet boundary conditions and whose derivatives are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into manifolds of codimension 1 in X. If f''0, the set C_j is shown to be non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure