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Fixed interface and free interface methods of substructure coupling for dynamic analysis are discussed. Three methods for reducing the number of coordinates required by fixed interface methods are introduced. Matrix ordinary differential equations are employed to improve accuracy in free interface substructure coupling methods.
Analysis of coupled roll-spiral-mode, pilot induced oscillation occurring with M-2F2 lifting body
Hurty (1965) has conducted a dynamic analysis of structural systems using component modes. The component mode synthesis (CMS) procedure considered by him represents a form of substructure coupling analysis which is often utilized in structural dynamics. Time-domain CMS methods employing real modes are discussed, taking into account real component modes, normal modes, redundant constraint modes, rigid-body modes, attachment modes, inertia-relief modes, statically-complete interface mode sets, dynamic component mode supersets, component modal models, the coupling of components, and the classification of methods. Attention is also given to the experimental determination of component mode synthesis parameters, time-domain CMS methods for damped systems, and frequency-domain CMS methods for damped systems.
This paper presents a modeling methodology used to predict the performance of a flexible structure, such as a space telescope, in the presence of an on-board vibrational disturbance source, such as a reaction wheel assembly (RWA). Both decoupled and coupled analysis methods are presented. The decoupled method relies on blocked RWA disturbances, measured with the RWA hardmounted to a rigid surface. The coupled method corrects the blocked RWA disturbance boundary conditions using "force filters," which depend on estimates of the interface accelerances of the RWA and space-craft. Both methods were validated on the Micro-Precision Interferometer testbed at the Jet Propulsion Laboratory. Experimental results are encouraging, indicating that both methods provide sufficient accuracy compared to measured values; however, the coupled method provides the best results when the gyroscopic nature of the spinning RWA is captured in the RWA accelerance model. Additionally, the RWA disturbance cross spectral density terms are found to be influential.
Reanalysis is the process whereby an unchanging data assimilation system is used to provide a consistent reprocessing of observations, typically spanning an extended segment of the historical data record. The process relies on an underlying model to combine often-disparate observations in a physically consistent manner, enabling production of gridded data sets for a broad range of applications including the study of historical weather events, preparation of climatologies, business sector development and, more recently, climate monitoring. Over the last few decades, several generations of reanalyses of the global atmosphere have been produced by various operational and research centers, focusing more or less on the period of regular conventional and satellite observations beginning in the mid to late twentieth century. There have also been successful efforts to extend atmospheric reanalyses back to the late nineteenth and early twentieth centuries, using mostly surface observations. Much progress has resulted from (and contributed to) advancements in numerical weather prediction, especially improved models and data assimilation techniques, increased computing capacity, the availability of new observation types and efforts to recover and improve the quality of historical ones. The recent extension of forecast systems that allow integrated modeling of meteorological, oceanic, land surface, and chemical variables provide the basic elements for coupled data assimilation. This has opened the door to the development of a new generation of coupled reanalyses of the Earth system, or integrated Earth system analyses (IESA). Evidence so far suggests that this approach can improve the analysis of currently uncoupled components of the Earth system, especially at their interface, and lead to increased predictability. However, extensive analysis coupling as envisioned for IESA, while progressing, still presents significant challenges. These include model biases that can be exacerbated when coupled, component systems with different physical characteristics and different spatial and temporal scales, and component observations in different media with different spatial and temporal frequencies and different latencies. Quantification of uncertainty in reanalyses is also a critical challenge and is important for expanding their utility as a tool for climate change assessment. This talk provides a brief overview of the progress of reanalysis development during recent decades, and describes remaining challenges in the progression toward coupled Earth system reanalyses.
Composite loads spectra (CLS) were applied to generate probabilistic loads for use in the PSAM nonlinear evaluation of stochastic structures under stress (NESSUS) finite element code. The CLS approach allows for quantifying loads as mean values and distributions around a central value rather than maximum or enveloped values typically used in deterministic analysis. NESSUS uses these loads to determine mean and perturbation responses. These results are probabilistically evaluated with the distributional information from CLS using a fast probabilistic integration (FPI) technique to define response distributions. The main example discussed describes a method of obtaining load descriptions and stress response of the second-stage turbine blade of the Space Shuttle Main Engine (SSME) high-pressure fuel turbopump (HPFTP). Additional information is presented on the on-going analysis of the high pressure oxidizer turbopump discharge duct (HPOTP) where probabilistic dynamic loads have been generated and are in the process of being used for dynamic analysis. Example comparisons of load analysis and engine data are furnished for partial verification and/or justification for the methodology.
Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and λ as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.
A numerical procedure has been developed to calculate the flow fields resulting from the viscous-inviscid interactions that occur when a strong jet exhaust and aircraft flow field coupling exists. The approach used in the current procedure is to divide the interaction region into zones which are either predominantly viscous or inviscid. The flow in the inviscid zone, which surrounds most of the aircraft, is calculated using an existing linearized potential flow code. The viscous flow zone, which encompasses the jet plume, is modeled using a parabolized Navier-Stokes code. The key feature of the present procedure is the coupling of the zonal solutions such that sufficient information is transferred between the zones to preserve the effects of the interactions. The zonal boundaries overlap with the boundary conditions being the information link between zones. An iteraction scheme iterates the coupled analysis until convergence has been obtained. The procedure has been successfully used for several test cases for which the computed results are presented.
An innovative concept utilizing the natural porosity of refractory-composite materials and hydrogen coolant to provide CONvective and TRANspiration (CONTRAN) cooling and oxidation protection has been numerically studied for surfaces exposed to a high heat flux high temperature environment such as hypersonic vehicle engine combustor walls. A boundary layer code and a porous media finite difference code were utilized to analyze the effect of convection and transpiration cooling on surface heat flux and temperature. The boundary layer code determined that transpiration flow is able to provide blocking of the surface heat flux only if it is above a minimum level due to heat addition from combustion of the hydrogen transpirant. The porous media analysis indicated that cooling of the surface is attained with coolant flow rates that are in the same range as those required for blocking, indicating that a coupled analysis would be beneficial.
An innovative concept utilizing the natural porosity of refractory-composite materials and hydrogen coolant to provide CONvective and TRANspiration (CONTRAN) cooling and oxidation protection has been numerically studied for surfaces exposed to a high heat flux, high temperature environment such as hypersonic vehicle engine combustor walls. A boundary layer code and a porous media finite difference code were utilized to analyze the effect of convection and transpiration cooling on surface heat flux and temperature. The boundary, layer code determined that transpiration flow is able to provide blocking of the surface heat flux only if it is above a minimum level due to heat addition from combustion of the hydrogen transpirant. The porous media analysis indicated that cooling of the surface is attained with coolant flow rates that are in the same range as those required for blocking, indicating that a coupled analysis would be beneficial.
Structural finite element (FE) models naturally output displacement or acceleration response data. However, they can also be used to compute stress, internal forces, and strain response. When coupled with a boundary element model (BEM) of the fluid surrounding the structure, a fully coupled analysis can be performed. Modeling a diffuse acoustic field in the BEM fluid provides an excitation like that found when the structure is placed in a reverberation chamber. Fully coupling the structural FE model to the acoustic BEM model provides a means to predict not only the acceleration response of the panel to diffuse field loading, but also the ability to predict the dynamic stress and strain response. This type of model has been available with current predictive tools, but experimental validation of the prediction of dynamic stress or strain is difficult to find. An aluminum panel was instrumented with accelerometers and strain gages and hung in a reverberation room and subjected to a diffuse acoustic field. This paper presents the comparison of the experimental and predicted results.
NASA’s Global Modeling and Assimilation Office (GMAO) is establishing coupled Earth system capabilities using the Joint Effort for Data Assimilation Integration (JEDI) framework, developed in collaboration with the Joint Center for Satellite Data Assimilation(JCSDA). Marine and atmospheric components will utilize a weakly-coupled data assimilation approach. The implementation of the sea-ice, ocean, and coupled analysis (SOCA) component of JEDI is highlighted here, while parallel work on atmospheric data assimilation is also in progress. Improvements to the ocean data assimilation system (ODAS) include: 1) adopting the JEDI framework, 2) a new coupled GCM, and 3) incorporation of new observation sources.
The NASA GEOS-S2S-2 system (Molod et al., 2020) uses the SST relaxation with the Level-4 SST products while the latest GEOS GEOS-S2S-3 system directly assimilates the Level-4 SST in the data assimilation step, yet no study has been conducted to understand the impact of this switch on the GEOS coupled analysis and short-range forecast. In addition, the GEOS-S2S-2/3 systems use the ocean model MOM5. Recently, the ocean model MOM6 is added to the GEOS ESM. This poster presents results of the first coupling of the ensemble data assimilation system to the GEOS MOM6.
The chemical, structural and microstructural behavior of steels (304, 316 and A36), titanium-aluminum alloy (Ti-Al, (6Al-4V)), aluminum-magnesium alloy (Al-Mg, 6061), and coatings (Silcolloy and Dursan (SilcoTek Corporation)) were probed after exposure to iodine laminar flow. Exposures were carried out in a custom-built Iodine Vapor RIG (IVR) at 300 degrees C to an iodine laminar vapor flow of 1 mg min(exp. -1), carried by 145 mL-min(exp. -1) argon gas, for 5, 15 and 30 days. Samples were characterized before and after the experiment by gravimetric analysis, X-ray diffraction (XRD) and cross section electron microscopy analysis coupled with energy dispersive X-ray spectroscopy (EDS). All steels exposed for 30 days formed scales consisting mainly of metal (Cr, Fe, Ni) oxides showing different chemistry, microstructure and crystalline phases. Elemental iodine was only detected by EDS analysis in the scales of stainless steels 304 and 316. After 30 days, the Ti-Al exhibited no detectable scale, suggesting only a very thin film was formed. A scale consisting mainly of aluminum, iodine, and oxygen formed on the Al-Mg sample exposed to 30 days. Some pockets rich in magnesium, iodine and oxygen also formed in this Al-Mg alloy. Stainless steel 316, low carbon steel A36 and Ti-Al alloy coated with Silcolloy and stainless steel 304 coated with Dursan that were exposed for 30 days exhibited no oxidation. Stainless steel 304 coated with Silcolloy exposed for 30 days did not exhibit corrosion although the sample gained weight and the coating exhibited expansion. The weight gain per area performance of the materials exposed in iodine lamina flow containing oxygen at impurity level for 10, 15 and 30 days are reported from the lowest to the highest weight gain per area as follows: Steels: Less than 316 less than 304 less than A36; Ti-Al-Mg based alloys: Al-Mg less than Ti-Al: Considering the experimental uncertainties, no weight change was observed for Stainless steel 316, low carbon steel A36 and Ti-Al alloy coated with Silcolloy and stainless steel 304 coated with Dursan. The corrosion of the alloys is catalyzed by iodine in the presence of oxygen as impurity.
A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.
The feasibility of using boundary layer control (BLC) on a high speed civil transport (HSCT) high lift configuration for low speed performance improvement is studied. The possibility of using a part of the suction system previously designed for cruise laminar flow control (LFC) for low speed BLC mode was explored. A suction scheme for BLC was devised for the HSCT high lift configuration. The extent of the suction regions and levels were determined via panel method based inviscid flow analysis coupled with three-dimensional boundary layer analyses. The compatibility of the BLC suction requirements was assessed, and the modifications necessary to operate the system in both modes of operation, were determined. An assessment of the potential aerodynamic performance improvement resulting from an implementation of the BLC concept compared to an optimized simple flap configuration without BLC was made by an Euler code analysis of the simple flap configuration.
Details relating to the design and subsequent vibration and shock tests of a spacecraft component for a severe vibration and shock environment are presented. The design process and analysis method involve the use of finite element analysis coupled with the Modal Strain Energy method with risk graphs to determine the adequacy of the design. The vibration levels experienced by box parts are reduced by the application of passive constrained layer viscoelastic treatments that significantly improve component reliability. All significant internal components were fully instrumented in both the random vibration and shock tests, the latter being done on a mechanical impact pyro simulator. Correlation between analysis and test data is good, validating the modeling and analysis techniques.
The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.