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NASA NTRS1990

Non-linear dynamic analysis of geared systems, part 2

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Singh, Rajendra↗

NASA NTRS1991

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.

Thompson, C. P.↗

NASA NTRS1991

Grid generation about complex three-dimensional aircraft configurations

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

Klopfer, Goetz H.↗

NASA NTRS2012

Implementation of a Smeared Crack Band Model in a Micromechanics Framework

The smeared crack band theory is implemented within the generalized method of cells and high-fidelity generalized method of cells micromechanics models to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. An repeating unit cell containing 13 randomly arranged fibers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verified against experimental data (where available), and an equivalent finite element model utilizing the same implementation of the crack band theory. To evaluate the performance of the crack band theory within a repeating unit cell that is more amenable to a multiscale implementation, a single fiber is modeled with generalized method of cells and high-fidelity generalized method of cells using a relatively coarse subcell mesh which is subjected to the same loading scenarios as the multiple fiber repeating unit cell. The generalized method of cells and high-fidelity generalized method of cells models are validated against a very refined finite element model.

Pineda, Evan J.↗

NASA NTRS2012

Progressive Failure of a Unidirectional Fiber-Reinforced Composite Using the Method of Cells: Discretization Objective Computational Results

Pineda, Evan J.↗

NASA NTRS1980

Thermally induced response of flexible structures - A method for analysis

The phenomenon of a thermally induced spacecraft instability became apparent during the flight of the OGO-IV spacecraft in the late 1960s. The paper presents a generalized approach to the problem of obtaining a computationally practical simulation model for a thermally driven structure. The formulation is such that it can be utilized in a stand-along manner or be meshed into a general multibody simulation model such as that reported by Bodley et al. (1978). As presented, the formulation is restricted to the dynamic range for which linearized radiation is a valid assumption.

Frisch, H. P.↗

NASA NTRS1991

Multigrid calculation of three-dimensional viscous cascade flows

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

NASA NTRS1994

Evaluating success levels of mega-projects

Today's mega-projects transcend the traditional trajectories traced within national and technological limitations. Powers unleashed by internationalization of initiatives, in for example space exploration and environmental protection, are arguably only temporarily suppressed by narrower national, economic, and professional disagreements as to how best they should be harnessed. While the world gets its act together there is time to develop the technologies of such supra-mega-project management that will synergize truly diverse resources and smoothly mesh their interfaces. Such mega-projects and their management need to be realistically evaluated, when implementing such improvements. This paper examines current approaches to evaluating mega-projects and questions the validity of extrapolations to the supra-mega-projects of the future. Alternatives to improve such evaluations are proposed and described.

Kumaraswamy, Mohan M.↗

NASA NTRS1995

Implicit method for the computation of unsteady flows on unstructured grids

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Venkatakrishnan, V.↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRSDate not supplied

CFD Modeling & Validation of Single Bubble Growth During Cavitation in Zero Gravity

Cryogenic Fluid Management (CFM) in zero gravity represents a vital area of research as NASA pursues future long-duration space missions. Success of these missions relies heavily on the ability to store and transfer the cryogenic liquid fuels efficiently and safely. In the Zero Boil-Off Tank (ZBOT-1) Experiment in 2018, unexpected and intense phase change occurred at the screened Liquid Acquisition Device (LAD) during tank pressure control that was later attributed to cavitation. The cavitation ultimately resulted in pump failure. Since cryogen cavitation during storage and transfer of propellants in microgravity has been a source of serious concern for the aerospace community, a series of drop tower experiments with liquid methane were also performed at the University of Bremen to carefully study cavitation from a single bubble nucleus in an engineered micron-sized wall cavity. As the test cell is depressurized during the 10-second drop, cavitation causes bubble growth from the nucleus. Here, in a collaboration between the Case Western Reserve University and University of Bremen, we present a two-phase Computational Fluid Dynamics (CFD) model of bubble growth from a single wall cavity during depressurization in microgravity. Both 2D axisymmetric and 3D parametric simulation case studies are performed to show the evolution of the bubble growth. The model uses a Volume of Fluid (VOF) approach with and without adaptive mesh refinement and adaptive time stepping to capture the growth dynamics using an explicit formulation with algebraic reconstruction of the interface. CFD results show good agreement with corresponding experiment. Based on the velocity, temperature, and volume fraction fields generated by the validation case studies, detailed discussion and analysis of fluid flow and heat transfer during bubble growth process are presented to delineate the intricacies of the cavitation process. Strengths and shortcomings of the present numerical approach in capturing this phenomenon are also highlighted.

Two Phase Flow↗

NASA NTRS1991

Multigrid calculation of three-dimensional viscous cascade flows

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

NASA NTRS2012

An Analysis Technique/Automated Tool for Comparing and Tracking Analysis Modes of Different Finite Element Models

An analysis technique was developed to compare and track mode shapes for different Finite Element Models. The technique may be applied to a variety of structural dynamics analyses, including model reduction validation (comparing unreduced and reduced models), mode tracking for various parametric analyses (e.g., launch vehicle model dispersion analysis to identify sensitivities to modal gain for Guidance, Navigation, and Control), comparing models of different mesh fidelity (e.g., a coarse model for a preliminary analysis compared to a higher-fidelity model for a detailed analysis) and mode tracking for a structure with properties that change over time (e.g., a launch vehicle from liftoff through end-of-burn, with propellant being expended during the flight). Mode shapes for different models are compared and tracked using several numerical indicators, including traditional Cross-Orthogonality and Modal Assurance Criteria approaches, as well as numerical indicators obtained by comparing modal strain energy and kinetic energy distributions. This analysis technique has been used to reliably identify correlated mode shapes for complex Finite Element Models that would otherwise be difficult to compare using traditional techniques. This improved approach also utilizes an adaptive mode tracking algorithm that allows for automated tracking when working with complex models and/or comparing a large group of models.

Towner, Robert L.↗

NASA NTRS1995

Simulation of patch and slot antennas using FEM with prismatic elements and investigations of artificial absorber mesh termination schemes

Year 1 progress can be characterized with four major achievements which are crucial toward the development of robust, easy to use antenna analysis code on doubly conformal platforms. (1) A new FEM code was developed using prismatic meshes. This code is based on a new edge based distorted prism and is particularly attractive for growing meshes associated with printed slot and patch antennas on doubly conformal platforms. It is anticipated that this technology will lead to interactive, simple to use codes for a large class of antenna geometries. Moreover, the codes can be expanded to include modeling of the circuit characteristics. An attached report describes the theory and validation of the new prismatic code using reference calculations and measured data collected at the NASA Langley facilities. The agreement between the measured and calculated data is impressive even for the coated patch configuration. (2) A scheme was developed for improved feed modeling in the context of FEM. A new approach based on the voltage continuity condition was devised and successfully tested in modeling coax cables and aperture fed antennas. An important aspect of this new feed modeling approach is the ability to completely separate the feed and antenna mesh regions. In this manner, different elements can be used in each of the regions leading to substantially improved accuracy and meshing simplicity. (3) A most important development this year has been the introduction of the perfectly matched interface (PMI) layer for truncating finite element meshes. So far the robust boundary integral method has been used for truncating the finite element meshes. However, this approach is not suitable for antennas on nonplanar platforms. The PMI layer is a lossy anisotropic absorber with zero reflection at its interface. (4) We were able to interface our antenna code FEMA_CYL (for antennas on cylindrical platforms) with a standard high frequency code. This interface was achieved by first generating equivalent magnetic currents across the antenna aperture using the FEM code. These currents were employed as the sources in the high frequency code.

Gong, J.↗

NASA NTRS2011

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

Berger, Marsha↗

NASA NTRS2018

Systems Engineering for the PRANDTL-D 3c Aircraft

The purpose of the Preliminary Research in AerodyNamicDesign to Lower Drag (PRANDTL-D) project is to show that birds fly using a "bell" shaped spanload rather than using an elliptical shaped spanload and to demonstrate the extensive benefits of this alternative spanload. This validation is done by flying a research glider with a twenty five foot wingspan that collects a range of parameters in flight. To ensure the data collection computers and suite of sensors work together and mesh well with the aircraft, systems engineering principles are applied. Needs for new one-off parts require a systems engineering approach as all the criteria of the plane, such as aerodynamics, structures, and avionics, must be taken into account when making decisions. The result of this approach were effective solutions that had a minimal negative impact on other systems that were not related to the original problem.

Larson, James G.↗

NASA NTRS1986

Computer models of the spacecraft wake

Until recently, computations of space plasma flow over a spacecraft have been unstable for ratios of spacecraft dimension to Debye length typical of the low Earth orbit environment. Calculations are presented of the spacecraft/environment interaction based on two computer codes, MACH and POLAR. MACH, an inside-out particle tracking code, was developed for the purpose of validating the physics of POLAR in regimes where these are no comprehensive theoretical or experimental results. While the spacecraft which can be treated by MACH are restricted to simple geometries, the methodology is more fundamental than POLAR. MACH generates self-consistent solutions within the context of quasisteady Vlasov plasma flow and achieves Debye ratios previously unobtainable. POLAR uses a three-dimensional finite-element representation of the vehicle in a staggered mesh. The plasma sheath is modeled by outside-in particle tracking. Solutions for the plasma flow, wake and vehicle charging are obtained by Vlasov-Poisson iteration; charge stabilization techniques make the results virtually insensitive to the Debye ratio. POLAR reproduces the Laframboise static plasma solutions for sperical probes and fits the Makita-Kuriki probe data for spheres in a flowing plasma in regions where comparisons are valid. POLAR and MACH solutions for the particle and electrostatic potential structure of the wake of a charged disk in a low-altitude flow are shown for Mach numbers 4, 5, and 8. New features of the solutions include ion focussing in the wake and a definitive determination of the sheath edge in the wake which shows that the sheath is not an equipotential.

Rubin, A. G.↗

NASA NTRS1991

The aerodynamic characteristics of vortex ingestion for the F/A-18 inlet duct

A Reduced Navier-Stokes (RNS) solution technique was successfully combined with the concept of partitioned geometry and mesh generation to form a very efficient 3D RNS code aimed at the analysis-design engineering environment. Partitioned geometry and mesh generation is a pre-processor to augment existing geometry and grid generation programs which allows the solver to (1) recluster an existing gridlife mesh lattice, and (2) perturb an existing gridfile definition to alter the cross-sectional shape and inlet duct centerline distribution without returning to the external geometry and grid generator. The present results provide a quantitative validation of the initial value space marching 3D RNS procedure and demonstrates accurate predictions of the engine face flow field, with a separation present in the inlet duct as well as when vortex generators are installed to supress flow separation. The present results also demonstrate the ability of the 3D RNS procedure to analyze the flow physics associated with vortex ingestion in general geometry ducts such as the F/A-18 inlet. At the conditions investigated, these interactions are basically inviscid like, i.e., the dominant aerodynamic characteristics have their origin in inviscid flow theory.

Anderson, Bernhard H.↗