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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Toward Transition Modeling in a Hypersonic Boundary Layer at Flight Conditions

An accurate physics-based transition prediction method integrated with computational fluid dynamics (CFD) solvers is pursued for hypersonic boundary layer flows over slender hypersonic vehicles at flight conditions. The geometry and flow conditions are selected to match relevant trajectory locations from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7-degree half-angle cone with 2.5 mm nose radius, freestream Mach numbers in the range of 3.8 – 5.5 and freestream unit Reynolds numbers in the range of 3.3 × 10(exp 6) – 21.4 × 10(exp 6) m(exp -1). Earlier research had shown that the onset of transition during the HIFiRE-1 flight experiment correlated with an amplification factor of N ≈ 13.5 for the planar Mack modes. However, to incorporate the N-factor correlations into a CFD code, we investigate surrogate models for disturbance amplification that avoid the direct computation of stability characteristics. A commonly used approach for low-speed flows is based on an a priori database of stability characteristics for locally similar profiles. However, the results presented in this paper demonstrate that the application of this approach to hypersonic boundary layers over blunt spherical nose-tip cones leads to large, unacceptable errors in the predictions of amplification factors, mainly due to its failure in accounting for the effects of the entropy layer on the boundary-layer profiles along the length of the model. We propose and demonstrate an alternate approach that employs the stability computations for a canonical set of blunt cone configurations to train a physics-informed convolutional neural network model that is shown to provide substantially improved transition predictions for hypersonic flow configurations with entropy-layer effects. Furthermore, the excellent performance of the neural network model is also confirmed for cone configurations with nose radius and half-angle values that do not correspond to those used to build the database. Finally, the convolutional neural network model is shown to outperform the linear stability calculations for underresolved basic states.

Pedro Paredes↗
DOE OSTI2023

Connecting Electric Vehicle Charging Infrastructure to Commercial Buildings

Electric vehicles (EVs) are growing in popularity and gaining meaningful market share with record sales year over year in the last decade. EV charging equipment, also known as EV chargers (EVC) or EV supply equipment (EVSE), must proportionally match the growing number of new EVs on the road for a comparable experience to gas-powered vehicles. The majority of EV charging currently happens at residential buildings. However, demand for EV charging at commercial buildings will significantly increase with wider mainstream EV adoption and as businesses return to more normal operation following COVID-19 pandemic disruptions. Charging equipment can include various sub-systems like power conditioning module, control software, safety devices, metering, communication, cooling, connectors, and its wiring. EV charging at commercial buildings could be used for public, workplace, and commercial fleet charging. This document aims to describe how EVC can be connected to commercial buildings, including considerations for facility managers, and the effects that charging will have on the buildings electrical distribution system. More specifically, this resource provides an overview of: understanding EV charging basics: how charging equipment connects to the building and to EVs; required infrastructure updates needed at the building site to connect EVC to existing distribution systems; network strategies for cost-effective operation; metering and utility considerations for billing and incentives; charging equipment ownership options; future trends in EVC connection to buildings.

ADVANCED PROPULSION SYSTEMS,ENERGY CONSERVATION, C↗
NASA NTRS2017

Aerodynamic Coefficients from Aeroballistic Range Testing of Deployed- and Stowed-SIAD SFDT Models

This report documents a ballistic-range test campaign conducted in 2012 in order to estimate the aerodynamic stability characteristics of two configurations of the Supersonic Flight Dynamics Test (SFDT) vehicle prior to its initial flight in 2014. The SFDT vehicle was a test bed for demonstrating several new aerodynamic decelerator technologies then being developed under the Low-Density Supersonic Decelerator (LDSD) Project. Of particular interest here is the Supersonic Inflatable Aerodynamic Decelerator (SIAD), an inflatable attached torus used to increase the drag surface area of an entry vehicle during the supersonic portion of the entry trajectory. Two model configurations were tested in the ballistic range: one representing the SFDT vehicle prior to deployment of the SIAD, and the other representing the nominal shape with the SIAD inflated. Both models were fabricated from solid metal, and therefore, the effects of the flexibility of the inflatable decelerator were not considered. The test conditions were chosen to match, as close as possible, the Mach number, Reynolds number, and motion dynamics expected for the SFDT vehicle in flight, both with the SIAD stowed and deployed. For SFDT models with the SIAD stowed, 12 shots were performed covering a Mach number range of 3.2 to 3.7. For models representing the deployed SIAD, 37 shots were performed over a Mach number range of 2.0 to 3.8. Pitch oscillation amplitudes covered a range from 0.7 to 20.6 degrees RMS. Portions of this report (data analysis approach, aerodynamic modeling, and resulting aerodynamic coefficients) were originally published as an internal LDSD Project report [1] in 2012. In addition, this report provides a description of the test design approach, the test facility, and experimental procedures. Estimated non-linear aerodynamic coefficients, including pitch damping, for both model configurations are reported, and the shot-by-shot trajectory measurements, plotted in comparison with calculated trajectories based on the derived non-linear aerodynamic coefficients, are provided as appendices. Since the completion of these tests, two full-scale SFDT flights have been successfully conducted: one in June 2014 [2, 3], and one in June 2015 [3].

Ground Test↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASAs Space Launch System

The engineering development of the National Aeronautics and Space Administration's (NASA) new Space Launch System (SLS) requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The nominal and off-nominal characteristics of SLS's elements and subsystems must be understood and matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex systems engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model-based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model-based algorithms and their development lifecycle from inception through FSW certification are an important focus of SLS's development effort to further ensure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. To test and validate these M&FM algorithms a dedicated test-bed was developed for full Vehicle Management End-to-End Testing (VMET). For addressing fault management (FM) early in the development lifecycle for the SLS program, NASA formed the M&FM team as part of the Integrated Systems Health Management and Automation Branch under the Spacecraft Vehicle Systems Department at the Marshall Space Flight Center (MSFC). To support the development of the FM algorithms, the VMET developed by the M&FM team provides the ability to integrate the algorithms, perform test cases, and integrate vendor-supplied physics-based launch vehicle (LV) subsystem models. Additionally, the team has developed processes for implementing and validating the M&FM algorithms for concept validation and risk reduction. The flexibility of the VMET capabilities enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS, GNC, and others. One of the principal functions of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software test and validation processes. In any software development process there is inherent risk in the interpretation and implementation of concepts from requirements and test cases into flight software compounded with potential human errors throughout the development and regression testing lifecycle. Risk reduction is addressed by the M&FM group but in particular by the Analysis Team working with other organizations such as S&MA, Structures and Environments, GNC, Orion, Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission (LOM) and Loss of Crew (LOC) probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses to be tested in VMET to ensure reliable failure detection, and confirm responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - the ARINC 6535-partitioned Operating System, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by FSW. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure their effectiveness and performance in the exterior FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗
NASA NTRS2009

L(sub 1) Adaptive Control Design for NASA AirSTAR Flight Test Vehicle

In this paper we present a new L(sub 1) adaptive control architecture that directly compensates for matched as well as unmatched system uncertainty. To evaluate the L(sub 1) adaptive controller, we take advantage of the flexible research environment with rapid prototyping and testing of control laws in the Airborne Subscale Transport Aircraft Research system at the NASA Langley Research Center. We apply the L(sub 1) adaptive control laws to the subscale turbine powered Generic Transport Model. The presented results are from a full nonlinear simulation of the Generic Transport Model and some preliminary pilot evaluations of the L(sub 1) adaptive control law.

Gregory, Irene M.↗
DOE OSTI2021

Development of in-use engine speed/torque heat maps across multiple heavy-duty commercial vehicle vocations

The U.S. Department of Energy (DOE) established the SuperTruck program with the goal of achieving brake thermal efficiency (BTE) greater than or equal to 55% as demonstrated in an operational heavy-duty (HD) diesel engine at a 65-miles-per-hour (mph) cruise point. Beyond the line-haul application, HD engines operate in a wide range of speed and torque conditions that are unlikely to yield the same efficiency under real-world operation. Thereby, the in-use engine heat maps described in this paper are a valuable tool to illustrate whether the engine-efficiency “sweet spot” matches the most frequent operating conditions. In this study, NREL developed engine heat maps to quantify the important operating points for various vocations using our Fleet DNA database of commercial fleet vehicle operations data. These heat maps clearly show that high-frequency operating points vary significantly according to vehicle vocation, while only a few of them match the sweet spot. Beyond the illustration, engine in-use heat maps can also be leveraged to build up reduced-order engine-efficiency models, needed by many rapid powertrain simulations. As case studies, nine reduced-order models – including line-haul truck, transfer truck, transit bus, transit bus with compressed natural gas (CNG) engine, drayage, refuse pickup, local delivery, utility truck, and school bus with CNG engine – using a trust-region reflective algorithm to fit the on-road data extracted based on the engine in-use heat maps.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Multi-modal Energy-optimal Trip Scheduling in Real-time (METS-R) for Transportation Hubs (Final Report)

This report summarizes the work performed under the award number EE0008524. The project develops the Multi-modal Energy-optimal Trip Scheduling in Real-time (METS-R) platform as the next-generation transportation solution based on autonomous electric vehicles (AEV) serving passenger trips from and to urban transportation hubs, to substantially reduce transportation energy consumption. Extensive data collection and analyses were first conducted to understand the demand patterns and energy consumption of hub-based on-road trips. Then, a data-driven framework that consists of an analytical module and a simulation module was proposed. For the analytical module, five planning + operation tools were developed to support the planning and energy-efficient operations of urban AEV services: the charging station planning that robotically allocates charging supplies based on the stationary charging demand distribution; the transit planning and demand adaptive scheduling model that efficiently generates\ candidate transit routes from hubs to other places and dynamically adjusts the transit time table to fit the current demand; the online energy-efficient routing that learns the energy-optimal paths from observations of link-level energy consumption in real-time; the hub-based ridesharing that matches trip requests together with account for the uncertainty of future trip demand and vehicle supply; and finally, the integrated demand prediction and anomaly detection pipeline that leverages the flight/train time table and support other planning/operation tools. To demonstrate the performance of these tools, a scalable high-performance agent-based simulator was built. We divided the urban space into multiple service zones where each zone was considered as an agent for passenger generation and vehicle charging. Two types of AEV agents were coded to model two types of mobility services: AEV taxi and AEV transit. For the AEV taxi, the team implemented the functions of pickup/drop-off passengers, energy-efficient routing, ridesharing, fleet rebalancing, and recharging. For the AEV bus, the team implemented the functions of demand-adaptive route scheduling, passenger boarding, and recharging. A high-performance computing framework was introduced to receive various profiling information (such as link energy updates, vehicle speed) from the simulator instances and communicate the operational commands back to the instances. The numerical experiments show that each of the proposed operational algorithms can reduce energy consumption and improve system efficiency. Furthermore, there exists the need to collectively consider multiple planning + operational strategies as multiple strategies can influence each other in terms of performance impacts. Recommendations for future work related to AEV planning and simulation are discussed.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS2005

Hyper-X Mach 7 Scramjet Design, Ground Test and Flight Results

The successful Mach 7 flight test of the Hyper-X (X-43) research vehicle has provided the major, essential demonstration of the capability of the airframe integrated scramjet engine. This flight was a crucial first step toward realizing the potential for airbreathing hypersonic propulsion for application to space launch vehicles. However, it is not sufficient to have just achieved a successful flight. The more useful knowledge gained from the flight is how well the prediction methods matched the actual test results in order to have confidence that these methods can be applied to the design of other scramjet engines and powered vehicles. The propulsion predictions for the Mach 7 flight test were calculated using the computer code, SRGULL, with input from computational fluid dynamics (CFD) and wind tunnel tests. This paper will discuss the evolution of the Mach 7 Hyper-X engine, ground wind tunnel experiments, propulsion prediction methodology, flight results and validation of design methods.

Ferlemann, Shelly M.↗
DOE OSTI2023

Decoupling Accurate Electrochemical Behaviors for High-Capacity Electrodes via Reviving Three-Electrode Vehicles

Developing high-capacity electrodes requires the evaluation of electrochemical behaviors with an increasing current density. Currently, the current density for evaluation of high-capacity electrodes has reached a new stage where the polarization at the lithium counter electrode has become a technical barrier for the accurate evaluation of battery electrodes, resulting in severe performance and mechanism mischaracterizations. Here, the accurate electrochemical behavior for high-capacity electrodes via a single-channel three-electrode vehicle is decoupled, by which the impact of lithium counter electrode is minimized. The testing high-capacity graphite electrode is capable of delivering an excellent rate capability with 81.7% capacity retention at 0.3 C, as well as stable cycling performance retaining 97.5% practical reversible capacity after 225 cycles, much higher than the graphite electrode tested with traditional half-cell testing vehicle but in close agreement with the results obtained from a well-matched full cell, reflecting accurate electrochemical performance evaluations of high-capacity electrodes. Moreover, detailed electrochemical mechanisms of impedance and diffusion properties for working electrodes are also successfully decoupled individually. Here, this work uncovers the mismatch between traditional evaluation configuration and increasing testing current density and provides a guideline for accurate electrochemical evaluation for ever-increasing high-capacity electrodes, which is of great significance for high-energy lithium or other alkali-metal ion batteries.

25 ENERGY STORAGE↗
NASA NTRS2022

Aerothermodynamic Measurements of Hypersonic Non-Equilibrium Flows

High enthalpy arc-jets are unique facilities particularly suited for producing complex flows in the aerospace field, such as the aerothermodynamics of a re-entry vehicle. Arc-jets are often used to evaluate important design factors that include heat shield materials and vehicle design. Characterization of these facilities is important, as studies often aim to match specific in-flight environments during experiments. Due to the complex environment produced by an arc-jet, with effects such as thermodynamic and chemical non-equilibrium occurring in the flow, characterization experiments are significantly more difficult than in conventional blow-down wind tunnels. The current work aims to characterize an arc-jet facility through spatially-resolved measurements of flow unsteadiness, temperature, and velocity. To achieve this goal, a non-intrusive imaging technique called “planar laser-induced fluorescence” was performed in the NASA Langley Hypersonic Materials Environmental Test System arc-jet facility. The experimental data was analysed to produce the quantitative measurements in multiple regions of the flow around a blunt body specimen. A three-temperature low fidelity numerical solver was created to simulate the flow in order to investigate thermal non-equilibrium effects occurring outside the imaging region in the arc-jet nozzle. Unsteadiness in the test section of the arc-jet was minimized by analyzing a subset of data assessing the gas injection configuration. Radial velocity, rotational temperature and translational temperature measurements are provided that can be used to validate future computational studies. The temperature measurements revealed rotational non-equilibrium occurring behind the bow-shock near the specimen surface. Computational results show the facility is capable of producing thermal non-equilibrium flow in the arc-jet nozzle. This work provides the first experimental and computational evidence of thermal trans-rotational non-equilibrium occurring in multiple regions of this arc-jet facility. Significant improvements to the methodology are also identified as recommendations for future arc-jet characterization studies.

Laser induced fluorescence↗
NASA NTRS2010

Turbofan Volume Dynamics Model for Investigations of Aero-Propulso-Servo-Elastic Effects in a Supersonic Commercial Transport

A turbofan simulation has been developed for use in aero-propulso-servo-elastic coupling studies, on supersonic vehicles. A one-dimensional lumped volume approach is used whereby each component (fan, high-pressure compressor, combustor, etc.) is represented as a single volume using characteristic performance maps and conservation equations for continuity, momentum and energy. The simulation is developed in the MATLAB/SIMULINK (The MathWorks, Inc.) environment in order to facilitate controls development, and ease of integration with a future aero-servo-elastic vehicle model being developed at NASA Langley. The complete simulation demonstrated steady state results that closely match a proposed engine suitable for a supersonic business jet at the cruise condition. Preliminary investigation of the transient simulation revealed expected trends for fuel flow disturbances as well as upstream pressure disturbances. A framework for system identification enables development of linear models for controller design. Utilizing this framework, a transfer function modeling an upstream pressure disturbance s impacts on the engine speed is developed as an illustrative case of the system identification. This work will eventually enable an overall vehicle aero-propulso-servo-elastic model

Connolly, Joseph W.↗
DOE OSTI2024

Electric Vehicle Supply Equipment (EVSE) Study for Vernon County, Wisconsin [Slides]

Viroqua is a town in Wisconsin with a population of approximately 4,500. The Vernon County Energy district is a local nonprofit in Viroqua that provides energy education, individualized energy consulting and coaching to residents and businesses. They have a very good relationship with our county government and wish to support their efforts. The Vernon County government is currently working on a comprehensive plan and would like to include planning for electric vehicle (EV) charging infrastructure in the plan. They are seeking guidance on logical phases for implementation and identifying the best locations for Level 2 and Level 3 EV chargers. NREL provided technical input on strategic planning for electric vehicle (EV) adoption and electric vehicle supply equipment (EVSE) expansion in Vernon County through the Clean Energy to Communities (C2C) Expert Match technical assistance program. NREL provided strategic planning support for EV expansion planning in Vernon County and siting considerations for locating EVSE.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1972

Flight-determined derivatives and dynamic characteristics for the HL-10 lifting body vehicle at subsonic and transonic Mach numbers

The HL-10 lifting body stability and control derivatives were determined by using an analog-matching technique and compared with derivatives obtained from wind-tunnel results. The flight derivatives were determined as a function of angle of attack for a subsonic configuration at Mach 0.7 and for a transonic configuration at Mach 0.7, 0.9, and 1.2. At an angle of attack of 14 deg, data were obtained for a Mach number range from 0.6 to 1.4. The flight and wind-tunnel derivatives were in general agreement, with the possible exception of the longitudinal and lateral damping derivatives. Some differences were noted between the vehicle dynamic response characteristics calculated from flight-determined derivatives and those predicted by the wind-tunnel results. However, the only difference the pilots noted between the response of the vehicle in flight and the response of a simulator programed with wind-tunnel-predicted data was that the damping generally was higher in the flight vehicle.

Strutz, L. W.↗
NASA NTRS2007

Rapid Contingency Simulation Modeling of the NASA Crew Launch Vehicle

The NASA Crew Launch Vehicle is a two-stage orbital launcher designed to meet NASA's current as well as future needs for human space flight. In order to free the designers to explore more possibilities during the design phase, a need exists for the ability to quickly perform simulation on both the baseline vehicle as well as the vehicle after proposed changes due to mission planning, vehicle configuration and avionics changes, proposed new guidance and control algorithms, and any other contingencies the designers may wish to consider. Further, after the vehicle is designed and built, the need will remain for such analysis in the event of future mission planning. An easily reconfigurable, modular, nonlinear six-degree-of-freedom simulation matching NASA Marshall's in-house high-fidelity simulator is created with the ability to quickly perform simulation and analysis of the Crew Launch Vehicle throughout the entire launch profile. Simulation results are presented and discussed, and an example comparison fly-off between two candidate controllers is presented.

Betts, Kevin M.↗
NASA NTRS1976

Organizing for low cost space operations - Status and plans

Design features of the Space Transportation System (vehicle reuse, low cost expendable components, simple payload interfaces, standard support systems) must be matched by economical operational methods to achieve low operating and payload costs. Users will be responsible for their own payloads and will be charged according to the services they require. Efficient use of manpower, simple documentation, simplified test, checkout, and flight planning are firm goals, together with flexibility for quick response to varying user needs. Status of the Shuttle hardware, plans for establishing low cost procedures, and the policy for user charges are discussed.

Lee, C.↗
NASA NTRS1991

Automated site characterization for robotic sample acquisition systems

A mobile, semi-autonomous vehicle with multiple sensors and on-board intelligence is proposed for performing preliminary scientific investigations on extraterrestrial bodies prior to human exploration. Two technologies, a hybrid optical-digital computer system based on optical correlator technology and an image and instrument data analysis system, provide complementary capabilities which might be part of an instrument package for an intelligent robotic vehicle. The hybrid digital-optical vision system could perform real-time image classification tasks using an optical correlator with programmable matched filters under control of a digital microcomputer. The data analysis system would analyze visible and multiband imagery to extract mineral composition and textural information for geologic characterization. Together these technologies would support the site characterization needs of a robotic vehicle for both navigational and scientific purposes.

Scholl, Marija S.↗
NASA NTRS1992

Evaluation of an optimal guidance algorithm for aero-assisted orbit transfer

A detailed evaluation is performed of a guidance algorithm for aeroassisted orbit transfer that was developed earlier based on the method of matched asymptotic expansions. It is shown that, by exploiting the structure of the matched asymptotic expansion solution procedure, the original problem which requires the solution of a set of 20 implicit algebraic equations can be reduced to a problem of six implicit equations in six unknowns. The main contribution here is that it was possible to obtain a solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the matched asymptotic expansion problem to obtain the feedback controls.

Melamed, N.↗
NASA NTRS1982

Coupled rotor/airframe vibration analysis

A coupled rotor/airframe vibration analysis developed as a design tool for predicting helicopter vibrations and a research tool to quantify the effects of structural properties, aerodynamic interactions, and vibration reduction devices on vehicle vibration levels is described. The analysis consists of a base program utilizing an impedance matching technique to represent the coupled rotor/airframe dynamics of the system supported by inputs from several external programs supplying sophisticated rotor and airframe aerodynamic and structural dynamic representation. The theoretical background, computer program capabilities and limited correlation results are presented in this report. Correlation results using scale model wind tunnel results show that the analysis can adequately predict trends of vibration variations with airspeed and higher harmonic control effects. Predictions of absolute values of vibration levels were found to be very sensitive to modal characteristics and results were not representative of measured values.

Sopher, R.↗