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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment.

Park, Michael A.↗
NASA NTRS1983

The value of residential photovoltaic systems: A comprehensive assessment

Utility-interactive photovoltaic (PV) arrays on residential rooftops appear to be a potentially attractive, large-scale application of PV technology. Results of a comprehensive assessment of the value (i.e., break-even cost) of utility-grid connected residential photovoltaic power systems under a variety of technological and economic assumptions are presented. A wide range of allowable PV system costs are calculated for small (4.34 kW (p) sub ac) residential PV systems in various locales across the United States. Primary factor in this variation are differences in local weather conditions, utility-specific electric generation capacity, fuel types, and customer-load profiles that effect purchase and sell-back rates, and non-uniform state tax considerations. Additional results from this analysis are: locations having the highest insolation values are not necessary the most economically attractive sites; residential PV systems connected in parallel to the utility demonstrate high percentages of energy sold back to the grid, and owner financial and tax assumptions cause large variations in break-even costs. Significant cost reduction and aggressive resolution of potential institutional impediments (e.g., liability, standards, metering, and technical integration) are required for a residential PV marker to become a major electric-grid-connected energy-generation source.

Borden, C. S.↗
NASA NTRS1999

Thermal Analysis of Magnetically-Coupled Pump for Cryogenic Applications

Magnetically-coupled pump is under evaluation at Kennedy Space Center for possible cryogenic applications. A major concern is the impact of low temperature fluid flows on the pump performance. As a first step toward addressing this and related issues, a computational fluid dynamics and heat transfer tool has been adopted in a pump geometry. The computational tool includes (i) a commercial grid generator to handle multiple grid blocks and complicated geometric definitions, and (ii) an in-house computational fluid dynamics and heat transfer software developed in the Principal Investigator's group at the University of Florida. Both pure-conduction and combined convection-conduction computations have been conducted. A pure-conduction analysis gives insufficient information about the overall thermal distribution. Combined convection-conduction analysis indicates the significant influence of the coolant over the entire flow path. Since 2-D simulation is of limited help, future work on full 3-D modeling of the pump using multi-materials is needed. A comprehensive and accurate model can be developed to take into account the effect of multi-phase flow in the cooling flow loop, and the magnetic interactions.

Senocak, Inanc↗
NASA NTRS1992

Application of engineering codes to the assessment of spacecraft charging induced hazards

One of the major hurdles to developing a better understanding of the environmentally induced interactions in spacecraft systems (spacecraft charging) is the lack of simple tools to analyze the behavior of the spacecraft in a sub-storm environment. The available tool, NASA Charging Analyzer Program (NASCAP), is expensive to use and treats only half of the problem - surface effects only. In response to this need, we have developed, under our IRAD Program, a set of engineering tools that operate on personal computers and addresses both the surface and bulk charging aspects of the interactions. These engineering codes utilize circuit analysis techniques and model simplifications to allow rapid computations. The codes were compared to both NASCAP predictions and to bulk charging data with excellent agreement for both phenomena. The models used in our engineering codes are shown, and in the engineering codes, the models are defined in terms of plates or triangles in an unconfined space. The predictions are based upon current balances to each plate. The code has routines to allow interactions between the plates to simulate 'barrier' effects. The agreement for the predicted differential surface voltages for the model is given. In conducting the comparison of engineering codes to NASCAP predictions, it was found that some inconsistencies existed in the NASCAP code that are not obvious to the user. The use of the grid imposes constraints that voltage gradients exist between the grid points. This allows the existence of voltage gradients in conductors and influences surface resistivity predictions. These points are discussed along with the predictions for treating these inconsistencies properly. The model predictions for a variable intensity substorm is also presented.

Stevens, N. J.↗
NASA NTRS1996

High-Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

This research program dealt with the application of high-performance computing methods to the numerical simulation of complete jet engines. The program was initiated in January 1993 by applying two-dimensional parallel aeroelastic codes to the interior gas flow problem of a bypass jet engine. The fluid mesh generation, domain decomposition and solution capabilities were successfully tested. Attention was then focused on methodology for the partitioned analysis of the interaction of the gas flow with a flexible structure and with the fluid mesh motion driven by these structural displacements. The latter is treated by a ALE technique that models the fluid mesh motion as that of a fictitious mechanical network laid along the edges of near-field fluid elements. New partitioned analysis procedures to treat this coupled three-component problem were developed during 1994 and 1995. These procedures involved delayed corrections and subcycling, and have been successfully tested on several massively parallel computers, including the iPSC-860, Paragon XP/S and the IBM SP2. For the global steady-state axisymmetric analysis of a complete engine we have decided to use the NASA-sponsored ENG10 program, which uses a regular FV-multiblock-grid discretization in conjunction with circumferential averaging to include effects of blade forces, loss, combustor heat addition, blockage, bleeds and convective mixing. A load-balancing preprocessor tor parallel versions of ENG10 was developed. During 1995 and 1996 we developed the capability tor the first full 3D aeroelastic simulation of a multirow engine stage. This capability was tested on the IBM SP2 parallel supercomputer at NASA Ames. Benchmark results were presented at the 1196 Computational Aeroscience meeting.

Felippa, C. A.↗
NASA NTRS2002

A Three-Dimensional Parallel Time-Accurate Turbopump Simulation Procedure Using Overset Grid System

The objective of the current effort is to provide a computational framework for design and analysis of the entire fuel supply system of a liquid rocket engine, including high-fidelity unsteady turbopump flow analysis. This capability is needed to support the design of pump sub-systems for advanced space transportation vehicles that are likely to involve liquid propulsion systems. To date, computational tools for design/analysis of turbopump flows are based on relatively lower fidelity methods. An unsteady, three-dimensional viscous flow analysis tool involving stationary and rotational components for the entire turbopump assembly has not been available for real-world engineering applications. The present effort provides developers with information such as transient flow phenomena at start up, and nonuniform inflows, and will eventually impact on system vibration and structures. In the proposed paper, the progress toward the capability of complete simulation of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of the hybrid MPI/Open-MP and MLP versions of the INS3D code. CAD to solution auto-scripting capability is being developed for turbopump applications. The relative motion of the grid systems for the rotor-stator interaction was obtained using overset grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on Origin 3000 systems at NASA Ames Research Center. Results from these time-accurate simulations with moving boundary capability are presented along with the performance of parallel versions of the code.

Kiris, Cetin↗
NASA NTRS1995

Progress in Integrated Fluid/Structure/Controls Computations Using High Fidelity Equations

Aeroelasticity that involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of aircraft which can experience complex flow/structure interactions. Supersonic transports can experience vortex induced aeroelastic oscillations whereas subsonic transports can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Using these high fidelity methods, design quantities such as structural stresses can be directly computed. Computations using these high fidelity equations require state-of-the-art large computational resources. This paper will describe the transition from potential equations to Euler/Navier-Stokes equations for fluids and from modal equations to finite element equations for structures. Complexities associated with grids for moving control surfaces will be discussed. All contents of the paper will be limited to those already presented at domestic conferences within U.S. such as those sponsored by AIAA. It will not include any materials related to HPCCP computational work.

Guruswamy, Guru P.↗
NASA NTRS2001

A Three Dimensional Parallel Time Accurate Turbopump Simulation Procedure Using Overset Grid Systems

The objective of the current effort is to provide a computational framework for design and analysis of the entire fuel supply system of a liquid rocket engine, including high-fidelity unsteady turbopump flow analysis. This capability is needed to support the design of pump sub-systems for advanced space transportation vehicles that are likely to involve liquid propulsion systems. To date, computational tools for design/analysis of turbopump flows are based on relatively lower fidelity methods. An unsteady, three-dimensional viscous flow analysis tool involving stationary and rotational components for the entire turbopump assembly has not been available for real-world engineering applications. The present effort provides developers with information such as transient flow phenomena at start up, and non-uniform inflows, and will eventually impact on system vibration and structures. In the proposed paper, the progress toward the capability of complete simulation of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of the hybrid MPI/Open-MP and MLP versions of the INS3D code. CAD to solution auto-scripting capability is being developed for turbopump applications. The relative motion of the grid systems for the rotor-stator interaction was obtained using overset grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on Origin 3000 systems at NASA Ames Research Center. Results from these time-accurate simulations with moving boundary capability will be presented along with the performance of parallel versions of the code.

Kiris, Cetin↗
NASA NTRS2001

Coupled-Flow Simulation of HP-LP Turbines Has Resulted in Significant Fuel Savings

Our objective was to create a high-fidelity Navier-Stokes computer simulation of the flow through the turbines of a modern high-bypass-ratio turbofan engine. The simulation would have to capture the aerodynamic interactions between closely coupled high- and low-pressure turbines. A computer simulation of the flow in the GE90 turbofan engine's high-pressure (HP) and low-pressure (LP) turbines was created at GE Aircraft Engines under contract with the NASA Glenn Research Center. The three-dimensional steady-state computer simulation was performed using Glenn's average-passage approach named APNASA. The areas upstream and downstream of each blade row mutually interact with each other during engine operation. The embedded blade row operating conditions are modeled since the average passage equations in APNASA actively include the effects of the adjacent blade rows. The turbine airfoils, platforms, and casing are actively cooled by compressor bleed air. Hot gas leaks around the tips of rotors through labyrinth seals. The flow exiting the high work HP turbines is partially transonic and, therefore, has a strong shock system in the transition region. The simulation was done using 121 processors of a Silicon Graphics Origin 2000 (NAS 02K) cluster at the NASA Ames Research Center, with a parallel efficiency of 87 percent in 15 hr. The typical average-passage analysis mesh size per blade row was 280 by 45 by 55, or approx.700,000 grid points. The total number of blade rows was 18 for a combined HP and LP turbine system including the struts in the transition duct and exit guide vane, which contain 12.6 million grid points. Design cycle turnaround time requirements ran typically from 24 to 48 hr of wall clock time. The number of iterations for convergence was 10,000 at 8.03x10(exp -5) sec/iteration/grid point (NAS O2K). Parallel processing by up to 40 processors is required to meet the design cycle time constraints. This is the first-ever flow simulation of an HP and LP turbine. In addition, it includes the struts in the transition duct and exit guide vanes.

Veres, Joseph P.↗
NASA NTRS2007

Modeling and Grid Generation of Iced Airfoils

SmaggIce Version 2.0 is a software toolkit for geometric modeling and grid generation for two-dimensional, singleand multi-element, clean and iced airfoils. A previous version of SmaggIce was described in Preparing and Analyzing Iced Airfoils, NASA Tech Briefs, Vol. 28, No. 8 (August 2004), page 32. To recapitulate: Ice shapes make it difficult to generate quality grids around airfoils, yet these grids are essential for predicting ice-induced complex flow. This software efficiently creates high-quality structured grids with tools that are uniquely tailored for various ice shapes. SmaggIce Version 2.0 significantly enhances the previous version primarily by adding the capability to generate grids for multi-element airfoils. This version of the software is an important step in streamlining the aeronautical analysis of ice airfoils using computational fluid dynamics (CFD) tools. The user may prepare the ice shape, define the flow domain, decompose it into blocks, generate grids, modify/divide/merge blocks, and control grid density and smoothness. All these steps may be performed efficiently even for the difficult glaze and rime ice shapes. Providing the means to generate highly controlled grids near rough ice, the software includes the creation of a wrap-around block (called the "viscous sublayer block"), which is a thin, C-type block around the wake line and iced airfoil. For multi-element airfoils, the software makes use of grids that wrap around and fill in the areas between the viscous sub-layer blocks for all elements that make up the airfoil. A scripting feature records the history of interactive steps, which can be edited and replayed later to produce other grids. Using this version of SmaggIce, ice shape handling and grid generation can become a practical engineering process, rather than a laborious research effort.

Vickerman, Mary B.↗
NASA NTRS1999

Impact of a Merged Precipitation Data on Global Soil Moisture Variability

Accurate soil moisture information has proved to be important to climate simulations and climate and weather forecasts. However, many difficulties exist that limit our understanding of soil moisture distribution and variability. One of them is the lack of accurate precipitation with appropriate spatial and temporal resolution. Precipitation as an input forcing to the land surface greatly influences soil moisture characteristics and variability. To improve precipitation data quality, an algorithm has been developed to generate a spatially and temporally continuous 3-hourly global precipitation data for the period of 1987 to present. This precipitation product is a combination of the precipitation from Special Sensor Microwave Imager (SSMI) with the Goddard Earth Observing System-1 Data Assimilation System (GEOS-1 DAS) employing a Physical-space Statistical Analysis System (PSAS). In this study we investigate the impact of this merged/analyzed precipitation data on the global soil moisture variability using an Off-line Land-surface GEOS Assimilation (OLGA) system. Two OLGA integrations starting from 1987 to 1993 are performed forced with the analyzed and GEOS-1 DAS precipitation respectively. We examine the spatial and temporal characteristics of soil moisture variability in response to the analyzed precipitation. The influence of this merged precipitation on the soil moisture variability and regional hydrological budget is estimated throughout the comparison with the results forced with the GEOS-1 DAS precipitation only. In the OLGA the sut@-grid scale horizontal heterogeneity is explicitly represented on the tile space. This provides a means to assess the role of the surface moisture heterogeneity in the interaction with the surface atmosphere and surface hydrological budget, and to validate OLGA results at tile space with in situ observation. ABRACOS (Anglo-Brazilian Amazonian Climate Observation Study), FIFE (First ISLSCP Field Experiment) I and HAPEX data will be used in the validation.

Yang, Runhua↗
NASA NTRS1995

Remote Visualization and Remote Collaboration On Computational Fluid Dynamics

A new technology has been developed for remote visualization that provides remote, 3D, high resolution, dynamic, interactive viewing of scientific data (such as fluid dynamics simulations or measurements). Based on this technology, some World Wide Web sites on the Internet are providing fluid dynamics data for educational or testing purposes. This technology is also being used for remote collaboration in joint university, industry, and NASA projects in computational fluid dynamics and wind tunnel testing. Previously, remote visualization of dynamic data was done using video format (transmitting pixel information) such as video conferencing or MPEG movies on the Internet. The concept for this new technology is to send the raw data (e.g., grids, vectors, and scalars) along with viewing scripts over the Internet and have the pixels generated by a visualization tool running on the viewer's local workstation. The visualization tool that is currently used is FAST (Flow Analysis Software Toolkit).

Watson, Val↗
NASA NTRS1987

Finite element methods of analysis for high speed viscous flows

Over the past three years a finite element based procedure for the solution of high speed viscous compressible flows was developed. The approach followed was to compute steady state solutions via a false transient, using an explicit time stepping scheme, and to attempt to improve the solution quality by incorporating adaptive mesh procedures. The main thrust of the work was to continue on the extension of the approach to the solution of some realistic compressible viscous flows. When flows at high Reynolds number are investigated, is soon becomes apparent that explicit techniwues have to be supplemented if they are to deal effectively with the large variations in element size and aspect ratio which characterize the computational grids necessary for adequate resolutin of the primary flow features. For this reason, the Taylor-Galerkin solution algorithm was rewritten in an explicit/implicit form. Solutions were computed for the problems of a flow past a flat plate, M-3, Re-100; shock/boundary layer interaction, M-2, Re-296000; flow over a compression corner, M-11.68, Re246000; and unifrom flow past a circular cylinder, M-6.34, Re-39770. A summary of the results is included and demonstrates the numerical performance of the scheme.

Source record↗
NASA NTRS1992

Dynamic interactions between hypersonic vehicle aerodynamics and propulsion system performance

Described here is the development of a flexible simulation model for scramjet hypersonic propulsion systems. The primary goal is determination of sensitivity of the thrust vector and other system parameters to angle of attack changes of the vehicle. Such information is crucial in design and analysis of control system performance for hypersonic vehicles. The code is also intended to be a key element in carrying out dynamic interaction studies involving the influence of vehicle vibrations on propulsion system/control system coupling and flight stability. Simple models are employed to represent the various processes comprising the propulsion system. A method of characteristics (MOC) approach is used to solve the forebody and external nozzle flow fields. This results in a very fast computational algorithm capable of carrying out the vast number of simulation computations needed in guidance, stability, and control studies. The three-dimensional fore- and aft body (nozzle) geometry is characterized by the centerline profiles as represented by a series of coordinate points and body cross-section curvature. The engine module geometry is represented by an adjustable vertical grid to accommodate variations of the field parameters throughout the inlet and combustor. The scramjet inlet is modeled as a two-dimensional supersonic flow containing adjustable sidewall wedges and multiple fuel injection struts. The inlet geometry including the sidewall wedge angles, the number of injection struts, their sweepback relative to the vehicle reference line, and strut cross-section are user selectable. Combustion is currently represented by a Rayleigh line calculation including corrections for variable gas properties; improved models are being developed for this important element of the propulsion flow field. The program generates (1) variation of thrust magnitude and direction with angle of attack, (2) pitching moment and line of action of the thrust vector, (3) pressure and temperature distributions throughout the system, and (4) performance parameters such as thrust coefficient, specific impulse, mass flow rates, and equivalence ratio. Preliminary results are in good agreement with available performance data for systems resembling the NASP vehicle configuration.

Flandro, G. A.↗
NASA NTRS2012

Evaluation of the Relative Contribution of Observing Systems in Reanalyses: Aircraft Temperature Bias and Analysis Innovations

Reanalyses have become important sources of data in weather and climate research. While observations are the most crucial component of the systems, few research projects consider carefully the multitudes of assimilated observations and their impact on the results. This is partly due to the diversity of observations and their individual complexity, but also due to the unfriendly nature of the data formats. Here, we discuss the NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) and a companion dataset, the Gridded Innovations and Observations (GIO). GIO is simply a post-processing of the assimilated observations and their innovations (forecast error and analysis error) to a common spatio-temporal grid, following that of the MERRA analysis fields. This data includes in situ, retrieved and radiance observations that are assimilated and used in the reanalysis. While all these disparate observations and statistics are in a uniform easily accessible format, there are some limitations. Similar observations are binned to the grid, so that multiple observations are combined in the gridding process. The data is then implicitly thinned. Some details in the meta data may also be lost (e.g. aircraft or station ID). Nonetheless, the gridded observations should provide easy access to all the observations input to the reanalysis. To provide an example of the GIO data, a case study evaluating observing systems over the United States and statistics is presented, and demonstrates the evaluation of the observations and the data assimilation. The GIO data is used to collocate 200mb Radiosonde and Aircraft temperature measurements from 1979-2009. A known warm bias of the aircraft measurements is apparent compared to the radiosonde data. However, when larger quantities of aircraft data are available, they dominate the analysis and the radiosonde data become biased against the forecast. When AMSU radiances become available the radiosonde and aircraft analysis and forecast error take on an annual cycle. While this supports results of previous work that recommend bias corrections for the aircraft measurements, the interactions with AMSU radiances will also require further investigation. This also provides an example for reanalysis users in examining the available observations and their impact on the analysis. GIO data is presently available alongside the MERRA reanalysis.

Bosilovich, Michael G.↗
NASA NTRS2001

Unsteady Turbopump Flow Simulations

The objective of the current effort is two-fold: 1) to provide a computational framework for design and analysis of the entire fuel supply system of a liquid rocket engine; and 2) to provide high-fidelity unsteady turbopump flow analysis capability to support the design of pump sub-systems for advanced space transportation vehicle. Since the space launch systems in the near future are likely to involve liquid propulsion system, increasing the efficiency and reliability of the turbopump components is an important task. To date, computational tools for design/analysis of turbopump flow are based on relatively lower fidelity methods. Unsteady, three-dimensional viscous flow analysis tool involving stationary and rotational components for the entire turbopump assembly has not been available, at least, for real-world engineering applications. Present effort is an attempt to provide this capability so that developers of the vehicle will be able to extract such information as transient flow phenomena for start up, impact of non-uniform inflow, system vibration and impact on the structure. Those quantities are not readily available from simplified design tools. In this presentation, the progress being made toward complete turbo-pump simulation capability for a liquid rocket engine is reported. Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for the performance evaluation of the hybrid MPI/Open-MP and MLP versions of the INS3D code. Relative motion of the grid system for rotor-stator interaction was obtained by employing overset grid techniques. Time-accuracy of the scheme has been evaluated by using simple test cases. Unsteady computations for SSME turbopump, which contains 106 zones with 34.5 Million grid points, are currently underway on Origin 2000 systems at NASA Ames Research Center. Results from these time-accurate simulations with moving boundary capability and the performance of the parallel versions of the code will be presented.

Centin, Kiris C.↗
NASA NTRS2013

Remote Data Exploration with the Interactive Data Language (IDL)

A difficulty for many NASA researchers is that often the data to analyze is located remotely from the scientist and the data is too large to transfer for local analysis. Researchers have developed the Data Access Protocol (DAP) for accessing remote data. Presently one can use DAP from within IDL, but the IDL-DAP interface is both limited and cumbersome. A more powerful and user-friendly interface to DAP for IDL has been developed. Users are able to browse remote data sets graphically, select partial data to retrieve, import that data and make customized plots, and have an interactive IDL command line session simultaneous with the remote visualization. All of these IDL-DAP tools are usable easily and seamlessly for any IDL user. IDL and DAP are both widely used in science, but were not easily used together. The IDL DAP bindings were incomplete and had numerous bugs that prevented their serious use. For example, the existing bindings did not read DAP Grid data, which is the organization of nearly all NASA datasets currently served via DAP. This project uniquely provides a fully featured, user-friendly interface to DAP from IDL, both from the command line and a GUI application. The DAP Explorer GUI application makes browsing a dataset more user-friendly, while also providing the capability to run user-defined functions on specified data. Methods for running remote functions on the DAP server were investigated, and a technique for accomplishing this task was decided upon.

Galloy, Michael↗
NASA NTRS1994

Unsteady aerodynamic analyses for turbomachinery aeroelastic predictions

Applications for unsteady aerodynamics analysis in this report are: (1) aeroelastic: blade flutter and forced vibration; (2) aeroacoustic: noise generation; (3) vibration and noise control; and (4) effects of unsteadiness on performance. This requires that the numerical simulations and analytical modeling be accurate and efficient and contain realistic operating conditions and arbitrary modes of unsteady excitation. The assumptions of this application contend that: (1) turbulence and transition can be modeled with the Reynolds averaged and using Navier-Stokes equations; (2) 'attached' flow with high Reynolds number will require thin-layer Navier-Stokes equations, or inviscid/viscid interaction analyses; (3) small-amplitude unsteady excitations will need nonlinear steady and linearized unsteady analyses; and (4) Re to infinity will concern inviscid flow. Several computer programs (LINFLO, CLT, UNSVIS, AND SFLOW-IVI) are utilized for these analyses. Results and computerized grid examples are shown. This report was given during NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Verdon, Joseph M.↗