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At least 199 records · Page 11

CFD Study of Turbo-Ramjet Interactions in Hypersonic Airbreathing Propulsion System

Advanced airbreathing propulsion systems used in Mach 4-6 mission scenarios, usually involve turbo-ramjet configurations. As the engines transition from turbojet to ramjet, there is an operational envelope where both engines operate simultaneously. In the first phase of our study, an over/under nozzle configuration was analyzed. The two plumes from the turbojet and ramjet interact at the end of a common 2-D cowl, where they both reach an approximate Mach 3.0 condition and then jointly expand to Mach 3.6 at the common nozzle exit plane. For the problem analyzed, the turbojet engine operates at a higher nozzle pressure ratio than the ramjet, causes the turbojet plume overpowers the ramjet plume, deflecting it approximately 12 degrees downward and in turn the turbojet plume is deflected 6 degrees upward. In the process, shocks were formed at the deflections and a shear layer formed at the confluence of the two jets. This particular case was experimentally tested and the data were used to compare with a computational fluid dynamics (CFD) study using the PARC2D code. The CFD results were in good agreement with both static pressure distributions on the cowl separator and on nozzle walls. The thrust coefficients were also in reasonable agreement. In addition, inviscid relationships were developed around the confluence point, where the two exhaust jets meet, and these results compared favorably with the CFD results. In the second phase of our study, a 3-D CFD solution was generated to compare with the 2-D solution. The major difference between the 2-D and 3-D solutions was the interaction of the shock waves, generated by the plume interactions, on the sidewall. When a shock wave interacts with a sidewall and sidewall boundary layer, it is called a glancing shock sidewall interaction. These interactions entrain boundary layer flow down the shockline into a vortical flow pattern. The 3-D plots show the streamlines being entrained down the shockline. The pressure of the flow also decreases slightly as the sidewall is approached. Other difference between the 2-D and 3-D solutions were a lowering of the nozzle thrust coefficient value from 0.9850 (2-D) to 0.9807 (3-D), where the experimental value was 0.9790. In the third phase of our study, a different turbo-ramjet configuration was analyzed. The confluence of a supersonic turbojet and a subsonic ramjet in the turbine based combined-cycle (TBCC) propulsion system was studied by a 2-D CFD code. In the analysis, Mach 1.4 primary turbojet was mixed with the subsonic ramjet secondary flow in an ejector mode operation. Reasonable agreements were obtained with the supplied I-D TBCC solutions. For low downstream backpressure, the Fabri choke condition (Break-Point condition) was observed in the secondary flow within mixing zone. For sufficient high downstream backpressure, the Fabri choke no longer exist, the ramjet flow was reduced and the ejector flow became backpressure dependent. Highly non-uniform flow at ejector exit were observed, indicated that for smooth downstream combustion, the mixing of the two streams probably required some physical devices.

Chang, Ing↗

Characterization and Optimization of the Fitting of Quantum Correlation Functions

This case study presents a characterization and optimization of an application code for extracting parton distribution functions from high energy electron-proton scattering data. Profiling this application code reveals that the phase-space density computation accounts for 93% of the overall execution time for a single iteration on a single core. When executing multiple iterations in parallel on a multicore system, the application spends 78% of its overall execution time idling due to load imbalance. We address these issues by first transforming the application code from Python to C++ and then tackling the application load imbalance via a hybrid scheduling strategy that combines dynamic and static scheduling. These techniques result in a 62% reduction in CPU idle time and a 2.46x speedup in overall execution time per node. In addition, the typically enabled power-management mechanisms in supercomputers (e.g., AMD Turbo Core, Intel Turbo Boost, and RAPL) can significantly impact intra-node scalability when more than 50% of the CPU cores are used. This finding underscores the importance of understanding system interactions with power management, as they can adversely impact application performance, and highlights the necessity of intra-node scaling tests to identify performance degradation that inter-node scaling tests might otherwise overlook.

Chuang, Pi-Yueh [Virginia Tech,Dept. of Computer S↗

The Attenuation of a Detonation Wave by an Aircraft Engine Axial Turbine Stage

A Constant Volume Combustion Cycle Engine concept consisting of a Pulse Detonation Combustor (PDC) followed by a conventional axial turbine was simulated numerically to determine the attenuation and reflection of a notional PDC pulse by the turbine. The multi-stage, time-accurate, turbomachinery solver TURBO was used to perform the calculation. The solution domain consisted of one notional detonation tube coupled to 5 vane passages and 8 rotor passages representing 1/8th of the annulus. The detonation tube was implemented as an initial value problem with the thermodynamic state of the tube contents, when the detonation wave is about to exit, provided by a 1D code. Pressure time history data from the numerical simulation was compared to experimental data from a similar configuration to verify that the simulation is giving reasonable results. Analysis of the pressure data showed a spectrally averaged attenuation of about 15 dB across the turbine stage. An evaluation of turbine performance is also presented.

VanZante, Dale↗

A CCIR-based prediction model for Earth-Space propagation

At present there is no single 'best way' to predict propagation impairments to an Earth-Space path. However, there is an internationally accepted way, namely that given in the most recent version of CCIR Report 564 of Study Group 5. This paper treats a computer code conforming as far as possible to Report 564. It was prepared for an IBM PS/2 using a 386 chip and for Macintosh SE or Mach II. It is designed to be easy to write and read, easy to modify, fast, have strong graphic capability, contain adequate functions, have dialog capability and windows capability. Computer languages considered included the following: (1) Turbo BASIC, (2) Turbo PASCAL, (3) FORTRAN, (4) SMALL TALK, (5) C++, (6) MS SPREADSHEET, (7) MS Excel-Macro, (8) SIMSCRIPT II.5, and (9) WINGZ.

Zhang, Zengjun↗

NNEPEQ: Chemical equilibrium version of the Navy/NASA Engine Program

The Navy NASA Engine Program, NNEP, currently is in use at a large number of government agencies, commercial companies and universities. This computer code has bee used extensively to calculate the design and off-design (matched) performance of a broad range of turbine engines, ranging from subsonic turboprops to variable cycle engines for supersonic transports. Recently, there has been increased interest in applications for which NNEP was not capable of simulating, namely, high Mach applications, alternate fuels including cryogenics, and cycles such as the gas generator air-turbo-rocker (ATR). In addition, there is interest in cycles employing ejectors such as for military fighters. New engine component models had to be created for incorporation into NNEP, and it was found necessary to include chemical dissociation effects of high temperature gases. The incorporation of these extended capabilities into NNEP is discussed and some of the effects of these changes are illustrated.

Fishbach, Laurence H.↗

NNEPEQ - Chemical equilibrium version of the Navy/NASA Engine Program

The Navy NASA Engine Program, NNEP, currently is in use at a large number of government agencies, commercial companies and universities. This computer code has been used extensively to calculate the design and off-design (matched) performance of a broad range of turbine engines, ranging from subsonic turboprops to variable cycle engines for supersonic transports. Recently, there has been increased interest in applications for which NNEP was not capable of simulating, namely, high Mach applications, alternate fuels including cryogenics, and cycles such as the gas generator air-turbo-rocker (ATR). In addition, there is interest in cycles employing ejectors such as for military fighters. New engine component models had to be created for incorporation into NNEP, and it was found necessary to include chemical dissociation effects of high temperature gases. The incorporation of these extended capabilities into NNEP is discussed and some of the effects of these changes are illustrated.

Fishbach, L. H.↗

Analysis of HolosGen Sub-Scale Simulator with Plant Dynamics Code

The Subcritical Power Module Sub-scale Simulator (SPM-SS) has been designed and constructed by HolosGen LLC under the ARPA-E MEITNER program to simulate the thermal-hydraulic and heat transfer behavior of the full-scale Holos-Quad Subcritical Power Modules (SPMs). Four coupled SPMs, each rated at 5.5MW, form the Holos-Quad gas-cooled microreactor design. The SPM-SS represents a substantially scaled-down system with a power rating less than 40 kW, equipped with an electrically heated fuel cartridge heat exchanger, an electrically heated compressor heat exchanger, and a valve actuated turbine heat exchanger, in addition to a recuperator and a cooler heat exchanger. The fuel cartridge represents a portion of the full-scale SPM core, the compressor heat exchanger mimics the temperature changes resulting from the compressor’s turbomachinery inefficiencies, the turbine heat exchanger mimics the expansion process normally occurring through the turbine, while the recuperator and cooler heat exchangers complete the subscale simulator loop. The heaters equipping the fuel cartridge and the compressor heat exchangers are electronically controlled to simulate normal and off-normal SPM operating conditions. The full-scale Holos-Quad SPM design eliminates the traditional balance of plant and executes thermal-to-electric energy conversion by means of an intercooled Brayton cycle with decoupled compressor-turbine turbomachinery. The Holos-Quad full-scale design is equipped with a multi-stage axial Low- and High-Pressure compressor, and a multistage axial turbine. The SPM-SS is designed for testing and validation of selected components which are instead coupled by a traditional balance of plant. The SPMSS is not equipped with turbo-machinery (compressor and turbine) as the development of these components were excluded from the scope of work under the ARPA-E MEITNER funding program. The SPM-SS balance of plant enables modifications, replacement and testing of individual components with different working fluids and is designed to include the turbo-machinery components that will be developed in future research . The SPM-SS can be operated with different gases, variable mass-flow-rates, pressures, and temperatures to obtain test data for selected components, whose performance can be scaled to validate the computer model of the full-scale SPM at various conditions (e.g., start-up, transients conditions). The SPM-SS can operate at the maximum Holos-Quad design pressure of 7 MPa, and a maximum temperature limited to 650 °C by the electrical heaters. Several SPM-SS tests have been conducted and analyzed with the Plant Dynamics Code (PDC) developed at the Argonne National Laboratory (ANL). These tests aimed at validating the PDC modeled predictions of the full-scale Holos-Quad design with data from selected SPM-SS components. In order to address SPM-SS specific characteristics, such as components heat losses and absence of turbomachinery components, some modifications to the PDC have been implemented to factor the design differences from the full-scale Holos-Quad SPM to the SPM-SS. As the PDC offers capabilities to analyze systems with different working fluids, air, nitrogen, and helium were utilized as the SPM-SS working fluids. Air was utilized to fine-tune the SPM-SS Systems Structures and Components (SSCs), nitrogen was utilized to pressure test the SPM-SS loop at the SPMs design maximum pressure of 7MPa. Helium was utilized as the working fluid circulating through the SPM-SS SSCs for specific tests to validate the PDC predictions of the fuel cartridge heat exchanger. SPM-SS tests data were also analyzed with both the steady-state and transient analysis capabilities offered by the PDC. This report describes the PDC analysis of the SPM-SS tests data, including the necessary code modifications and comparison of the code results with the experimental data. Based on the results, a discussion is presented on how the analysis supports design and transient calculations of the full-scale Holos-Quad microreactor. Also based on the results of this work, recommendations are made for future optimizations of the SPM-SS components and PDC model development needs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Montgomery, Matthew D.↗

Flight evaluation of differential GPS aided inertial navigation systems

Algorithms are described for integration of Differential Global Positioning System (DGPS) data with Inertial Navigation System (INS) data to provide an integrated DGPS/INS navigation system. The objective is to establish the benefits that can be achieved through various levels of integration of DGPS with INS for precision navigation. An eight state Kalman filter integration was implemented in real-time on a twin turbo-prop transport aircraft to evaluate system performance during terminal approach and landing operations. A fully integrated DGPS/INS system is also presented which models accelerometer and rate-gyro measurement errors plus position, velocity, and attitude errors. The fully integrated system was implemented off-line using range-domain (seventeen-state) and position domain (fifteen-state) Kalman filters. Both filter integration approaches were evaluated using data collected during the flight test. Flight-test data consisted of measurements from a 5 channel Precision Code GPS receiver, a strap-down Inertial Navigation Unit (INU), and GPS satellite differential range corrections from a ground reference station. The aircraft was laser tracked to determine its true position. Results indicate that there is no significant improvement in positioning accuracy with the higher levels of DGPS/INS integration. All three systems provided high-frequency (e.g., 20 Hz) estimates of position and velocity. The fully integrated system provided estimates of inertial sensor errors which may be used to improve INS navigation accuracy should GPS become unavailable, and improved estimates of acceleration, attitude, and body rates which can be used for guidance and control. Precision Code DGPS/INS positioning accuracy (root-mean-square) was 1.0 m cross-track and 3.0 m vertical. (This AGARDograph was sponsored by the Guidance and Control Panel.)

Mcnally, B. David↗

CFD simulation of coaxial injectors

The development of improved performance models for the Space Shuttle Main Engine (SSME) is an important, ongoing program at NASA MSFC. These models allow prediction of overall system performance, as well as analysis of run-time anomalies which might adversely affect engine performance or safety. Due to the complexity of the flow fields associated with the SSME, NASA has increasingly turned to Computational Fluid Dynamics (CFD) techniques as modeling tools. An important component of the SSME system is the fuel preburner, which consists of a cylindrical chamber with a plate containing 264 coaxial injector elements at one end. A fuel rich mixture of gaseous hydrogen and liquid oxygen is injected and combusted in the chamber. This process preheats the hydrogen fuel before it enters the main combustion chamber, powers the hydrogen turbo-pump, and provides a heat dump for nozzle cooling. Issues of interest include the temperature and pressure fields at the turbine inlet and the thermal compatibility between the preburner chamber and injector plate. Performance anomalies can occur due to incomplete combustion, blocked injector ports, etc. The performance model should include the capability to simulate the effects of these anomalies. The current approach to the numerical simulation of the SSME fuel preburner flow field is to use a global model based on the MSFC sponsored FNDS code. This code does not have the capabilities of modeling several aspects of the problem such as detailed modeling of the coaxial injectors. Therefore, an effort has been initiated to develop a detailed simulation of the preburner coaxial injectors and provide gas phase boundary conditions just downstream of the injector face as input to the FDNS code. This simulation should include three-dimensional geometric effects such as proximity of injectors to baffles and chamber walls and interaction between injectors. This report describes an investigation into the numerical simulation of GH2/LOX coaxial injectors. The following sections will discuss the physical aspects of injectors, the CFD code employed, and preliminary results of a simulation of a single coaxial injector for which experimental data is available. It is hoped that this work will lay the foundation for the development of a unique and useful tool to support the SSME program.

Landrum, D. Brian↗

Advanced Noise Control Fan: A 20-Year Retrospective

The ANCF test bed is used for evaluating fan noise reduction concepts, developing noise measurement technologies, and providing a database for Aero-acoustic code development. Rig Capabilities: 4 foot 16 bladed rotor @ 2500 rpm, Auxiliary air delivery system (3 lbm/sec @ 6/12 psi), Variable configuration (rotor pitch angle, stator count/position, duct length), synthetic acoustic noise generation (tone/broadband). Measurement Capabilities: 112 channels dynamic data system, Unique rotating rake mode measuremen, Farfield (variable radius), Duct wall microphones, Stator vane microphones, Two component CTA w/ traversing, ESP for static pressures.

turbo fan↗

System Decommutes And Displays Telemetry Data

TDPlus computer program software system for decommutation of pulse-code-modulation (PCM) telemetry signals. Provides synchronization, conversion into engineering units, and display of serial bit streams. Transforms IBM PC-compatible computer into PCM-telemetry-decommutation system. Synchronizes telemetric signals data and enables conversion back into such meaningful forms as voltage, current, pressure, and the like. Also controls operation of digital-to-analog converters to ship data to paper strip charts or to parallel digital ports for offloading to other computers. Software used to process actual data only when telemetry-data-processing computer modified in accordance with specifications contained in "TDPlus TM Data Processor" (GSC-13291). Written in Turbo C and 8088 Assembly language.

Massey, D. E.↗

Nonlinear Dynamic Analysis of Disordered Bladed-Disk Assemblies

In a effort to address current needs for efficient, air propulsion systems, we have developed some new analytical predictive tools for understanding and alleviating aircraft engine instabilities which have led to accelerated high cycle fatigue and catastrophic failures of these machines during flight. A frequent cause of failure in Jets engines is excessive resonant vibrations and stall flutter instabilities. The likelihood of these phenomena is reduced when designers employ the analytical models we have developed. These prediction models will ultimately increase the nation's competitiveness in producing high performance Jets engines with enhanced operability, energy economy, and safety. The objectives of our current threads of research in the final year are directed along two lines. First, we want to improve the current state of blade stress and aeromechanical reduced-ordered modeling of high bypass engine fans, Specifically, a new reduced-order iterative redesign tool for passively controlling the mechanical authority of shroudless, wide chord, laminated composite transonic bypass engine fans has been developed. Second, we aim to advance current understanding of aeromechanical feedback control of dynamic flow instabilities in axial flow compressors. A systematic theoretical evaluation of several approaches to aeromechanical feedback control of rotating stall in axial compressors has been conducted. Attached are abstracts of two .papers under preparation for the 1998 ASME Turbo Expo in Stockholm, Sweden sponsored under Grant No. NAG3-1571. Our goals during the final year under Grant No. NAG3-1571 is to enhance NASA's capabilities of forced response of turbomachines (such as NASA FREPS). We with continue our development of the reduced-ordered, three-dimensional component synthesis models for aeromechanical evaluation of integrated bladeddisk assemblies (i.e., the disk, non-identical bladeing etc.). We will complete our development of component systems design optimization strategies for specified vibratory stresses and increased fatigue life prediction of assembly components, and for specified frequency margins on the Campbell diagrams of turbomachines. Finally, we will integrate the developed codes with NASA's turbomachinery aeromechanics prediction capability (such as NASA FREPS).

McGee, Oliver G., III↗

Turbo-Design: Open-Source Radial Equilibrium Turbomachinery Solver: Part I - Turbines

Advances in 3D Geometrical Designs and Cooling have played a significant role in improving the efficiency of turbomachinery. However, these advancements must be effectively translated back to the modeler. Machine learning can facilitate this transition. Specifically, machine learning–based loss models can bridge the gap between 3D and 1D designs, enabling modelers not only to predict velocity triangles but also to extract additional geometric features. Currently, the design tools used at NASA have not been updated to support such integration—until now. TurboDesign is an open-source, Python-based framework that replaces TD2 (LEW-11029-1) and AXOD2 (LEW-16323-1), both of which are radial equilibrium solvers for axial turbines. The goal of this update is to enable the integration of machine learning loss models into radial equilibrium equations. Additionally, TurboDesign is designed to support radial machines. This paper presents the governing equations, the assumptions underlying the code, the integration of legacy loss models, an example of machine learning model integration, and a validation comparison with CFD. All code, tutorials, and documentation are available at: https://www.github.com/nasa/turbo-design

Radial Equilibrium↗

Towards Rocket Engine Components with Increased Strength and Robust Operating Characteristics

High-energy rotating machines, powering liquid propellant rocket engines, are subject to various sources of high and low cycle fatigue generated by unsteady flow phenomena. Given the tremendous need for reliability in a sustainable space exploration program, a fundamental change in the design methodology for engine components is required for both launch and space based systems. A design optimization system based on neural-networks has been applied and demonstrated in the redesign of the Space Shuttle Main Engine (SSME) Low Pressure Oxidizer Turbo Pump (LPOTP) turbine nozzle. One objective of the redesign effort was to increase airfoil thickness and thus increase its strength while at the same time detuning the vane natural frequency modes from the vortex shedding frequency. The second objective was to reduce the vortex shedding amplitude. The third objective was to maintain this low shedding amplitude even in the presence of large manufacturing tolerances. All of these objectives were achieved without generating any detrimental effects on the downstream flow through the turbine, and without introducing any penalty in performance. The airfoil redesign and preliminary assessment was performed in the Exploration Technology Directorate at NASA ARC. Boeing/Rocketdyne and NASA MSFC independently performed final CFD assessments of the design. Four different CFD codes were used in this process. They include WIL DCA T/CORSAIR (NASA), FLUENT (commercial), TIDAL (Boeing Rocketdyne) and, a new family (AardvarWPhantom) of CFD analysis codes developed at NASA MSFC employing LOX fluid properties and a Generalized Equation Set formulation. Extensive aerodynamic performance analysis and stress analysis carried out at Boeing Rocketdyne and NASA MSFC indicate that the redesign objectives have been fully met. The paper presents the results of the assessment analysis and discusses the future potential of robust optimal design for rocket engine components.

Marcu, Bogdan↗

Current Issues in Unsteady Turbomachinery Flows (Images)

Among the numerous causes for unsteadiness in turbo machinery flows are turbulence and flow environment, wakes from stationary and rotating vanes, boundary layer separation, boundary layer/shear layer instabilities, presence of shock waves and deliberate unsteadiness for flow control purposes. These unsteady phenomena may lead to flow-structure interactions such as flutter and forced vibration as well as system instabilities such as stall and surge. A major issue of unsteadiness relates to the fact that a fundamental understanding of unsteady flow physics is lacking and requires continued attention. Accurate simulations and sufficient high fidelity experimental data are not available. The Glenn Research Center plan for Engine Component Flow Physics Modeling is part of the NASA 21st Century Aircraft Program. The main components of the plan include Low Pressure Turbine National Combustor Code. The goals, technical output and benefits/impacts of each element are described in the presentation. The specific areas selected for discussion in this presentation are blade wake interactions, flow control, and combustor exit turbulence and modeling.

Povinelli, Louis↗

Jet-Surface Interaction: High Aspect Ratio Nozzle Test, Nozzle Design and Preliminary Data

The Jet-Surface Interaction High Aspect Ratio (JSI-HAR) nozzle test is part of an ongoing effort to measure and predict the noise created when an aircraft engine exhausts close to an airframe surface. The JSI-HAR test is focused on parameters derived from the Turbo-electric Distributed Propulsion (TeDP) concept aircraft which include a high-aspect ratio mailslot exhaust nozzle, internal septa, and an aft deck. The size and mass flow rate limits of the test rig also limited the test nozzle to a 16:1 aspect ratio, half the approximately 32:1 on the TeDP concept. Also, unlike the aircraft, the test nozzle must transition from a single round duct on the High Flow Jet Exit Rig, located in the AeroAcoustic Propulsion Laboratory at the NASA Glenn Research Center, to the rectangular shape at the nozzle exit. A parametric nozzle design method was developed to design three low noise round-to-rectangular transitions, with 8:1, 12:1, and 16: aspect ratios, that minimizes flow separations and shocks while providing a flat flow profile at the nozzle exit. These designs validated using the WIND-US CFD code. A preliminary analysis of the test data shows that the actual flow profile is close to that predicted and that the noise results appear consistent with data from previous, smaller scale, tests. The JSI-HAR test is ongoing through October 2015. The results shown in the presentation are intended to provide an overview of the test and a first look at the preliminary results.

Aeroacoustics↗

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗