Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case

We develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p

Acoustics Research of Propulsion Systems

The liftoff phase induces high acoustic loading over a broad frequency range for a launch vehicle. These external acoustic environments are used in the prediction of the internal vibration responses of the vehicle and components. Present liftoff vehicle acoustic environment prediction methods utilize stationary data from previously conducted hold-down tests to generate 1/3 octave band Sound Pressure Level (SPL) spectra. In an effort to update the accuracy and quality of liftoff acoustic loading predictions, non-stationary flight data from the Ares I-X were processed in PC-Signal in two flight phases: simulated hold-down and liftoff. In conjunction, the Prediction of Acoustic Vehicle Environments (PAVE) program was developed in MATLAB to allow for efficient predictions of sound pressure levels (SPLs) as a function of station number along the vehicle using semi-empirical methods. This consisted of generating the Dimensionless Spectrum Function (DSF) and Dimensionless Source Location (DSL) curves from the Ares I-X flight data. These are then used in the MATLAB program to generate the 1/3 octave band SPL spectra. Concluding results show major differences in SPLs between the hold-down test data and the processed Ares I-X flight data making the Ares I-X flight data more practical for future vehicle acoustic environment predictions

Infrared Imagery of Solid Rocket Exhaust Plumes

The Ares I Scale Model Acoustic Test program consisted of a series of 18 solid rocket motor static firings, simulating the liftoff conditions of the Ares I five-segment Reusable Solid Rocket Motor Vehicle. Primary test objectives included acquiring acoustic and pressure data which will be used to validate analytical models for the prediction of Ares 1 liftoff acoustics and ignition overpressure environments. The test article consisted of a 5% scale Ares I vehicle and launch tower mounted on the Mobile Launch Pad. The testing also incorporated several Water Sound Suppression Systems. Infrared imagery was employed during the solid rocket testing to support the validation or improvement of analytical models, and identify corollaries between rocket plume size or shape and the accompanying measured level of noise suppression obtained by water sound suppression systems

Verification of Ares I Liftoff Acoustic Environments via the Ares Scale Model Acoustic Test

Launch environments, such as Liftoff Acoustic (LOA) and Ignition Overpressure (IOP), are important design factors for any vehicle and are dependent upon the design of both the vehicle and the ground systems. The NASA Constellation Program had several risks to the development of the Ares I vehicle linked to LOA which are used in the development of the vibro-acoustic environments. The risks included cost, schedule and technical impacts for component qualification due to high predicted vibro-acoustic environments. One solution is to mitigate the environment at the component level. However, where the environment is too severe to mitigate at the component level, reduction of the launch environments is required. The Ares I Scale Model Acoustic Test (ASMAT) program was implemented to verify the predicted Ares I launch environments and to determine the acoustic reduction for the LOA environment with an above deck water sound suppression system. The test article included a 5% scale Ares I vehicle model, tower and Mobile Launcher. Acoustic and pressure data were measured by approximately 200 instruments. The ASMAT results are compared to the Ares I LOA predictions and water suppression effectiveness results are presented

Subscale Acoustic Testing: Comparison of ALAT and ASMAT

The liftoff phase induces acoustic loading over a broad frequency range for a launch vehicle. These external acoustic environments are then used in the prediction of internal vibration responses of the vehicle and components which result in the qualification levels. Thus, predicting these liftoff acoustic environments is critical to the design requirements of any launch vehicle. If there is a significant amount of uncertainty in the predictions or if acoustic mitigation options must be implemented, a subscale acoustic test is a feasible pre-launch test option. This paper compares the acoustic measurements of two different subscale tests: the 2% Ares Liftoff Acoustic Test conducted at Stennis Space Center and the 5% Ares I Scale Model Acoustic Test conducted at Marshall Space Flight Center

Scale Model Acoustic Test Overview

Launch environments, such as liftoff acoustic (LOA) and ignition overpressure (IOP), are important design factors for any vehicle and are dependent upon the design of both the vehicle and the ground systems. LOA environments are used directly in the development of vehicle vibro-acoustic environments and IOP is used in the loads assessment. The Scale Model Acoustic Test (SMAT) program was implemented to verify the Space Launch Systems LOA and IOP environments for the vehicle and ground systems including the Mobile Launcher (ML) and tower. The SMAT is currently in the design and fabrication phase. The SMAT program is described in this presentation

SLS Scale Model Acoustic Test Liftoff Results and Comparisons

The liftoff phase induces acoustic loading over a broad frequency range for a launch vehicle. These external acoustic environments are then used in the prediction of internal vibration responses of the vehicle and components which result in the qualification levels. Thus, predicting these liftoff acoustic (LOA) environments is critical to the design requirements of any launch vehicle. If there is a significant amount of uncertainty in the predictions or if acoustic mitigation options must be implemented, a subscale acoustic test is a feasible design phase test option to verify the LOA environments. The NASA Space Launch System (SLS) program initiated the Scale Model Acoustic Test (SMAT) to verify the predicted SLS LOA environments

ATK Launch Vehicle (ALV-X1) Liftoff Acoustic Environments: Prediction vs. Measurement

The ATK Launch Vehicle (ALV-X1) provided an opportunity to measure liftoff acoustic noise data. NASA Marshall Space Flight Center (MSFC) engineers were interested in the ALV-X1 launch because the First Stage motor and launch pad conditions, including a relativity short deflector ducting, provide a potential analogue to future Ares I launches. This paper presents the measured liftoff acoustics on the vehicle and tower. Those measured results are compared to predictions based upon the method described in NASA SP-8072 "Acoustic Loads Generated by the Propulsion System" and the Vehicle Acoustic Environment Prediction Program (VAEPP) which was developed by MSFC acoustics engineers. One-third octave band sound pressure levels will be presented. This data is useful for the ALV-X1 in validating the pre-launch environments and loads predictions. Additionally, the ALV-X1 liftoff data can be scaled to define liftoff environments for the NASA Constellation program Ares vehicles. Vehicle liftoff noise is caused by the supersonic jet flow interaction with surrounding atmosphere or more simply, jet noise. As the vehicle's First Stage motor is ignited, an acoustic noise field is generated by the exhaust. This noise field persists due to the supersonic jet noise and reflections from the launch pad and tower, then changes as the vehicle begins to liftoff from the launch pad. Depending on launch pad and adjacent tower configurations, the liftoff noise is generally very high near the nozzle exit and decreases rapidly away from the nozzle. The liftoff acoustic time range of interest is typically 0 to 20 seconds after ignition. The exhaust plume thermo-fluid mechanics generates sound at approx.10 Hz to 20 kHz. Liftoff acoustic noise is usually the most severe dynamic environment for a launch vehicle or payload in the mid to high frequency range (approx.50 to 2000 Hz). This noise environment can induce high-level vibrations along the external surfaces of the vehicle and surrounding launch facility structures. The acoustic pressure fluctuations will induce severe vibrations in relatively large lightweight structures. Consequently, there is the potential for failure of the structure or attached electrical components. Due to these potential failures, the liftoff acoustic noise is one of the noise source inputs used to determine the vibro-acoustic qualification environment for a launch vehicle and its components

Ares I Scale Model Acoustic Test Liftoff Acoustic Results and Comparisons

Conclusions: Ares I-X flight data validated the ASMAT LOA results. Ares I Liftoff acoustic environments were verified with scale model test results. Results showed that data book environments were under-conservative for Frustum (Zone 5). Recommendations: Data book environments can be updated with scale model test and flight data. Subscale acoustic model testing useful for future vehicle environment assessments

Overview of the Ares I Scale Model Acoustic Test Program

Launch environments, such as lift-off acoustic (LOA) and ignition overpressure (IOP), are important design factors for any vehicle and are dependent upon the design of both the vehicle and the ground systems. LOA environments are used directly in the development of vehicle vibro-acoustic environments and IOP is used in the loads assessment. The NASA Constellation Program had several risks to the development of the Ares I vehicle linked to LOA. The risks included cost, schedule and technical impacts for component qualification due to high predicted vibro-acoustic environments. One solution is to mitigate the environment at the component level. However, where the environment is too severe for component survivability, reduction of the environment itself is required. The Ares I Scale Model Acoustic Test (ASMAT) program was implemented to verify the Ares I LOA and IOP environments for the vehicle and ground systems including the Mobile Launcher (ML) and tower. An additional objective was to determine the acoustic reduction for the LOA environment with an above deck water sound suppression system. ASMAT was a development test performed at the Marshall Space Flight Center (MSFC) East Test Area (ETA) Test Stand 116 (TS 116). The ASMAT program is described in this presentation