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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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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Evaluation of historical precipitation interannual variability in CMIP6 over the United States

Interannual precipitation variability profoundly influences society via its effects on agriculture, water resources, infrastructure, and disaster risks. In this study, we use daily in situ precipitation observations from the global historical climatology network-daily (GHCN-D) to assess the ability of 21 Coupled Model Intercomparison Project Phase 6 (CMIP6) models, including the 50-member fifth-generation Canadian Earth System Model single model initial-condition large ensemble (CanESM5_SMILE), to realistically simulate historical interannual precipitation variability trends within 17 regions of the contiguous United States (CONUS). We assess how accurately the CMIP6 simulations align with observational data across annual, summer, and winter periods, focusing on four key hydrometeorological metrics, including interannual precipitation variability, relative interannual precipitation variability (coefficient of variation), annual mean precipitation, and annual wet day frequency. Our findings reveal that CMIP6 ensemble members generally reproduce the spatial patterns of observed trends in annual mean precipitation. In most regions, models agree well with the signs of observed changes in annual mean precipitation, though discrepancies in trend magnitude are evident. Further, observed trends in winter mean precipitation broadly exhibit a spatial pattern similar to that of the observed annual mean. However, analysis of the CanESM5_SMILE shows that trends in precipitation variability may primarily be the result of model-simulated internal variability, suggesting caution in interpreting multi-model single-realization ensemble results. Challenges in accurately simulating interannual precipitation variability underscore the need for ongoing model refinement and validation to enhance climate projections, especially in regions vulnerable to extreme precipitation events.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1982

O1, P1, N2 models of the global ocean tide on an elastic earth plus surface potential and spherical harmonic decompositions for M2, S2, and K1

The models of M2, S2, and K1 presented in Parke and Hendershott (1980) are supplemented with models of O1, P1, and N2. The models satisfy specified elevation boundary conditions and are generated by fighting a small number of test functions to island data. Maps are presented of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each new component. Maps of the tidal potential seen by an observer fixed to the surface of the solid earth are also presented for all six constituents. Spherical harmonic coefficients up to order four and the rms magnitude of the coefficients to order fifteen are presented for each constituent. The rms magnitudes of the P1 and K1 coefficients normalized by their respective equilibrium amplitudes are compared to determine the effect of the diurnal core resonance.

Parke, M. E.↗
NASA NTRS2018

Improved Mars Helicopter Aerodynamic Rotor Model for Comprehensive Analyses

The Mars Helicopter is part of the NASA Mars 2020 rover mission scheduled to launch in July of 2020. Its goal is to demonstrate the viability and potential of heavier-than-air vehicles in the Martian atmosphere. Ultimately, it aims to bridge the resolution gap between orbiters and the rover as well as allow access to otherwise inaccessible regions. The low density of the Martian atmosphere and the relatively small-scale rotor result in very low Reynolds number flows. The low density and low Reynolds numbers reduce the lifting force and lifting efficiency, respectively. This paper describes the generation of the improved Mars Helicopter aerodynamic rotor model. The goal is to generate a performance model for the Mars Helicopter rotor using a free wake analysis, since this has a low computational cost for design. The improvements in the analysis are two-fold and are expanded on from two prior publications. First, the fidelity of the simulations is increased by performing higher-order two-dimensional time-accurate OVERFLOW simulations allowing for higher accuracy aerodynamic coefficients and a better understanding of the boundary layer behavior as well as its transient features. Second, a version of the model is generated to duplicate the exact testing conditions in the 25–ft. diameter Space Simulator at the Jet Propulsion Laboratory, which allows for better correlation of rotor performance figures. Previous work correlated performance with that test, but did not consider the higher temperatures in the experiment compared to those of the Martian atmosphere. The higher temperatures in the experiment are expected to give conservative performance estimates, as they give rise to an increase in speed of sound and decrease in observed Reynolds numbers.

Grip, Håvard F.↗
DOE OSTI2022

Optimization control technology for building energy conservation

A simulation processor generates and stores a simulation model based on conditions associated with a physical structure, such as a building. A neural network processor implements a neural network, having an input layer coupled to receive sensor data from the structure and having an output layer coupled to supply control signals to the at least one electrically operable environmental control device. The neural network is trained using the simulation model. A particle swarm optimization processor programmed to receive the simulation results and perform particle swarm optimization, ascertains optimal parameters for controlling the at least one electrically operable environmental control device and supplies these optimal parameters to the neural network processor. The neural network processor uses the optimal parameters supplied by the particle swarm optimization processor to further train the neural network.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Analysis of contact conditions and microstructure evolution in shear assisted processing and extrusion using smoothed particle hydrodynamics method

Shear assisted processing and extrusion (ShAPE) is a solid-phase processing technique that adds an additional shear force as compared with a conventional extrusion approach. Recently, ShAPE has demonstrated the capability of extruding high-performance aluminum alloy 7075 (AA7075) tubes at speeds up to 12.2 m/min without surface tearing. However, the relationship among the ShAPE processing parameters, thermomechanical conditions, contact conditions, heat generation, and microstructure evolution remains primarily empirical because an insightful understanding of the associated physics is still lacking. To help elucidate these relationships, this work proposes a thermomechanical meshfree model for the first time for ShAPE processing of AA7075 using the smoothed particle hydrodynamics (SPH) method. The meshfree model is first validated thoroughly by experimental data in terms of material flow, die face temperature, and extrusion force with various processing parameters. The validated model is then used to analyze the steady-state contact conditions and heat generation rates during ShAPE processing. Distributions of the average grain size of AA7075 being extruded are calculated using the SPH model output. The meshfree model results reveal that extrusions conducted at lower temperatures and higher strain rates yield more refined grains and possibly higher material strength, which is also consistent with the experimental observations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Model, data, and code for paper "Modeling of streamflow in a 30-kilometer-long reach spanning 5 years using OpenFOAM 5.x"

The data package includes data, model, and code that support the analyses and conclusions in the paper titled “modeling of streamflow in a 30-kilometer-long reach spanning 5 years using OpenFOAM 5.x”. The primary goal of this paper is to demonstrate that key streamflow properties such as water depth, flow velocity, and dynamic pressure in a natural river at 30-kilometer scale over 5 years can be reliably and efficiently modeled using the computational framework presented in this paper. To support the paper, various data types from remote sensing, field observations, and computational models are used. Specific details are described as follows. Firstly, the river bathymetry data was obtained from a Light Detection and Ranging (LiDAR) survey. This data is then converted to a triangulated surface format, STL, for mesh generation in OpenFOAM. The STL data can be found in Model_Setups/BaseCase_2013To2015/constant/triSurface. The OpenFOAM mesh generated using this STL file can be found in constant/polyMesh. Other model setups, boundary and initial conditions can be found in /system and /0.org under folder BaseCase_2013To2015. A similar data structure can also be found in BaseCase_2018To2019 for the simulations during 2018 and 2019. Secondly, the OpenFOAM simulations need the upstream discharge and water depth information at the upstream boundary to drive the model. These data are generated from a one-dimensional hydraulic model and the data can be found under the folder Model_Setups /1D model Mass1 data. The mass1_65.csv and mass1_191.csv files include the results of the 1D model at the model inlet and outlet, respectively. The Matlab source code Mass1ToOFBC20182019.m is used to convert these data into OpenFOAM boundary condition setups.With the above OpenFOAM model, it can generate data for water surface elevation, flow velocity, and dynamic pressure. In this paper, the water surface elevation was measured at 7 locations during different periods between 2011 and 2019. The exact survey locations (see Fig1_SurveyLocations.txt) can be found in folder Fig_1. The variation of water stage over time at the 7 locations can be found in folder /Observation_WSE. The data type include .txt, .csv, .xlsx, and .mat. The .mat data can be loaded by Matlab.We also measured the flow velocities at 12 cross-sections along the river. At each cross-section, we recorded the x, y locations, depth, three velocity components u,v,w. These data are saved to a Matlab format which can be found under folder /Observation_Velocity and /Fig_1. The relative locations of velocity survey locations to the river bathymetry can be found in Figure 1c.The water stage data at the 7 locations from OpenFOAM, 1D, and 2D hydraulic models are also provided to evaluate the long-term performance of 3D models vs 1D/2D models. The water stage data for the 7 locations from OpenFOAM have been saved to .mat format and can be found in /OpenFOAM_WSE. The water stage data from the 1D model are saved in .csv format and can be found in /Mass1_WSE. The water stage from the 2D model is saved as .mat format and can be found in / Mass2_WSEIn addition, the OpenFOAM model outputs the information of hydrostatic and hydrodynamic pressure. They are saved as .mat format under folder /Fig_11/2013_1. As the files are too large, we only uploaded the data for January 2013. The area of different ratio of dynamic pressure to static pressure for all simulation range, i.e., 2013-2015, are saved to .mat format. They can be found in /Fig_11/PA. Further, the data of wall clock time versus the solution time of the OpenFOAM modeling are also saved to .mat format under folder /Fig_13/LogsMat. In summary, the data package contains seven data types, including .txt, .csv, .xlsx, .dat, .stl, .m, and .mat. The former 4 types can be directly open using a text editor or Microsoft Office. The .mat format needs to be read by Matlab. The Matlab source code .m files need to be run with Matlab. The OpenFOAM setups can be visualized in ParaView. The .stl file can be opened in ParaView or Blender. The data in subfolders Fig_1 to Fig_10 and Fig_12 are copied from the aforementioned data folders to generate specific figures for the paper. A readME.txt file is included in each subfolder to further describe how the data in each folder are generated and used to support the paper.Please use the data package's DOI to cite the data package. Please contact yunxiang.chen@pnnl.gov if you need more data related to the paper.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Space Shuttle Main Engine structural analysis and data reduction/evaluation. Volume 2: High pressure oxidizer turbo-pump turbine end bearing analysis

The high-pressure oxidizer turbopump (HPOTP) consists of two centrifugal pumps, on a common shaft, that are directly driven by a hot-gas turbine. Pump shaft axial thrust is balanced in that the double-entry main inducer/impeller is inherently balanced and the thrusts of the preburner pump and turbine are nearly equal but opposite. Residual shaft thrust is controlled by a self-compensating, non-rubbing, balance piston. Shaft hang-up must be avoided if the balance piston is to perform properly. One potential cause of shaft hang-up is contact between the Phase 2 bearing support and axial spring cartridge of the HPOTP main pump housing. The status of the bearing support/axial spring cartridge interface is investigated under current loading conditions. An ANSYS version 4.3, three-dimensional, finite element model was generated on Lockheed's VAX 11/785 computer. A nonlinear thermal analysis was then executed on the Marshall Space Flight Center Engineering Analysis Data System (EADS). These thermal results were then applied along with the interference fit and bolt preloads to the model as load conditions for a static analysis to determine the gap status of the bearing support/axial spring cartridge interface. For possible further analysis of the local regions of HPOTP main pump housing assembly, detailed ANSYS submodels were generated using I-DEAS Geomod and Supertab (Appendix A).

Sisk, Gregory A.↗
NASA NTRS1984

Global matrix of thermospheric density values for selected solar/geomagnetic conditions and spacecraft orbital attitudes

Presented are selected thermospheric/exospheric global mean and extreme density values computed between 130 and 1100 km altitude. These values were generated from the MSFC/J70 reference orbital atmospheric model using different input conditions of solar flux and geomagnetic index, ranging from low to peak. Typical magnitudes of day-night density changes are presented, as an example, for use in space vehicle orbital analyses.

Johnson, D. L.↗
DOE OSTI2023

Deep generative models for vehicle speed trajectories

Generating realistic vehicle speed trajectories is a crucial component in evaluating vehicle fuel economy and in predictive control of self-driving cars. Traditional generative models rely on Markov chain methods and can produce accurate synthetic trajectories but are subject to the curse of dimensionality. They do not allow to include conditional input variables into the generation process. In this paper, we show how extensions to deep generative models allow accurate and scalable generation. Proposed architectures involve recurrent and feed-forward layers and are trained using adversarial techniques. Our models are shown to perform well on generating vehicle trajectories using a model trained on GPS data from Chicago metropolitan area.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS2007

An Update on the Lithium-Ion Cell Low-Earth-Orbit Verification Test Program

A Lithium-Ion Cell Low-Earth-Orbit Verification Test Program is being conducted by NASA Glenn Research Center to assess the performance of lithium-ion (Li-ion) cells over a wide range of low-Earth-orbit (LEO) conditions. The data generated will be used to build an empirical model for Li-ion batteries. The goal of the modeling will be to develop a tool to predict the performance and cycle life of Li-ion batteries operating at a specified set of mission conditions. Using this tool, mission planners will be able to design operation points of the battery system while factoring in mission requirements and the expected life and performance of the batteries. Test conditions for the program were selected via a statistical design of experiments to span a range of feasible operational conditions for LEO aerospace applications. The variables under evaluation are temperature, depth-of-discharge (DOD), and end-of-charge voltage (EOCV). The baseline matrix was formed by generating combinations from a set of three values for each variable. Temperature values are 10 C, 20 C and 30 C. Depth-of-discharge values are 20%, 30% and 40%. EOCV values are 3.85 V, 3.95 V, and 4.05 V. Test conditions for individual cells may vary slightly from the baseline test matrix depending upon the cell manufacturer s recommended operating conditions. Cells from each vendor are being evaluated at each of ten sets of test conditions. Cells from four cell manufacturers are undergoing life cycle tests. Life cycling on the first sets of cells began in September 2004. These cells consist of Saft 40 ampere-hour (Ah) cells and Lith ion 30 Ah cells. These cells have achieved over 10,000 cycles each, equivalent to about 20 months in LEO. In the past year, the test program has expanded to include the evaluation of Mine Safety Appliances (MSA) 50 Ah cells and ABSL battery modules. The MSA cells will begin life cycling in October 2006. The ABSL battery modules consist of commercial Sony hard carbon 18650 lithium-ion cells configured in series and parallel combinations to create nominal 14.4 volt, 3 Ah packs (4s-2p). These modules have accumulated approximately 3000 cycles. Results on the performance of the cells and modules will be presented in this paper. The life prediction and performance model for Li-ion cells in LEO will be built by analyzing the data statistically and performing regression analysis. Cells are being cycled to failure so that differences in performance trends that occur at different stages in the life of the cell can be observed and accurately modeled. Cell testing is being performed at the Naval Surface Warfare Center in Crane, IN.

Reid, Concha M.↗
DOE OSTI2022

Hybrid data-driven and model-informed online tool wear detection in milling machines

Precision machining tool wear is responsible for low product throughput and quality. Monitoring the tool wear online is vital to prevent degradation in machining quality. However, direct real-time tool wear measurement is not practical. This paper presents residual-based anomaly detection models, combining a hybrid model comprised of a physics-based model and a data-driven model (a decision tree or a neural network) to predict signals of interest (e.g., power or forces) under nominal conditions, followed by Page’s cumulative sum test for detecting tool wear on-line using the computer numerical control machine measurements. The most informative features are ranked using dynamic programming and its approximation variants from real-time measurements and machine settings, such as the width of cut, depth of cut, feed rate and spindle speed, that serve as inputs to the predictive models. The baseline nominal model is incrementally updated with experimental data via a gradient boosted adaptation model to generate the residuals that account for discrepancies between the actual machine data under normal conditions and the baseline nominal model predictions. The hybrid model is validated against 20 Mazak milling machine experimental tests and one Haas run-to-failure experiment. The proposed anomaly detector is applied to synthetic data from simulations of the physics-based model at different operating conditions, measurement noise levels, and tool wear levels, and the methods were able to achieve an overall 92% accuracy in data with 1% noise. The anomaly detection methods based on hybrid model reduced the false alarms of either the data-driven or physical-based models alone, and are found to be capable of good online detection of tool wear.

42 ENGINEERING↗
NASA NTRS2022

Hybrid data-driven and model-informed online tool wear detection in milling machines

Precision machining tool wear is responsible for low product throughput and quality. Monitoring the tool wear online is vital to prevent degradation in machining quality. However, direct real-time tool wear measurement is not practical. This paper presents residual-based anomaly detection models, combining a hybrid model comprised of a physics-based model and a data-driven model (a decision tree or a neural network) to predict signals of interest (e.g., power or forces) under nominal conditions, followed by Page’s cumulative sum test for detecting tool wear on-line using the computer numerical control machine measurements. The most informative features are ranked using dynamic programming and its approximation variants from real-time measurements and machine settings, such as the width of cut, depth of cut, feed rate and spindle speed, that serve as inputs to the predictive models. The baseline nominal model is incrementally updated with experimental data via a gradient boosted adaptation model to generate the residuals that account for discrepancies between the actual machine data under normal conditions and the baseline nominal model predictions. The hybrid model is validated against 20 Mazak milling machine experimental tests and one Haas run-to-failure experiment. The proposed anomaly detector is applied to synthetic data from simulations of the physics-based model at different operating conditions, measurement noise levels, and tool wear levels, and the methods were able to achieve an overall 92% accuracy in data with 1% noise. The anomaly detection methods based on hybrid model reduced the false alarms of either the data-driven or physical-based models alone, and are found to be capable of good online detection of tool wear.

Online anomaly detection↗
DOE OSTI2023

Modeling of Vertical Motor-driven Pump for Simulation of a Fault Signature \\ for Condition Monitoring

As part of the ongoing effort to transition from preventive maintenance strategies to condition-based maintenance strategies in nuclear power plants, there is significant reliance on using machine learning techniques. To develop a robust machine learning model that can diagnose all the fault modes of a vertical motor-driven pump, data capturing the unique signature of each fault mode is required. In practice, it is difficult to collect or capture data that captures all the fault modes from a single plant site. So to address this situation, a computational model of a vertical motor-driven pump is developed using the multipurpose finite element software COMSOL Multiphysics. The developed model is used to generate simulated data under normal operation and is compared with the vibration data collected using vibration sensors. Once the simulation model is verified under normal operating condition, simulated data for the fault mode for which minimal or no evidence is available in historical plant process data is developed. This simulated data is used to develop fault signatures to achieve robust predictive models. This paper presents modeling details and verification of the model that can used to generate data for fault modes that are not available at a plant site for condition monitoring purpose.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
NASA NTRS1977

Boundary layer integral matrix procedure: Verification of models

The three turbulent models currently available in the JANNAF version of the Aerotherm Boundary Layer Integral Matrix Procedure (BLIMP-J) code were studied. The BLIMP-J program is the standard prediction method for boundary layer effects in liquid rocket engine thrust chambers. Experimental data from flow fields with large edge-to-wall temperature ratios are compared to the predictions of the three turbulence models contained in BLIMP-J. In addition, test conditions necessary to generate additional data on a flat plate or in a nozzle are given. It is concluded that the Cebeci-Smith turbulence model be the recommended model for the prediction of boundary layer effects in liquid rocket engines. In addition, the effects of homogeneous chemical reaction kinetics were examined for a hydrogen/oxygen system. Results show that for most flows, kinetics are probably only significant for stoichiometric mixture ratios.

Bonnett, W. S.↗
DOE OSTI2022

Automated Control for Nuclear Thermal Propulsion Start-Up using MOOSE-based Applications

This report presents a Griffin/Bison/RELAP-7 numerical model of a prototypical NTP system that features fuel assemblies arranged in rings, and which was designed to simulate rapid startup transients. The physics modeled include full-core neutronics, assembly-wise heat conduction, and conjugate heat transfer, with the balance of plant mainly imposed through boundary conditions. In addition, various forms of automated reactivity control were deployed by using the MOOSE to autonomously drive the model and simulate the reactor transitioning from assumed initial conditions to nominal power in a fraction of a minute. To generate the cross-sections of the neutronics model, and in an effort to simultaneously account for the tremendous axial temperature gradients in the reactor and to limit the number of state points required for cross-section generation, the average component temperatures and hydrogen densities in the cooling channels were correlated to the average fuel and moderator temperatures, and fixed axial profiles were derived for nominal conditions and then used during the transient. With this approximation, a tractable cross-section library tabulated with fuel/moderator temperatures and CD angles was generated using Serpent. The full-core SPH correction procedure and the CD decusping technology in Griffin, respectively, ensure preservation of the multiplication factor and reaction rates at state points, along with a reasonably accurate reactivity worth between tabulated CD angles, despite using a coarse mesh. Feedback from other physics was calculated by modeling one representative fuel assembly per ring, along with the corresponding fuel and moderator cooling channels. To limit power overshoots during startup, another layer of multiphysics coupling was added to the model in order to automatically control the drums. Two different technologies presented herein showed outstanding performance in this regard: (1) a novel hybrid PID controller based on both power and reactivity signals, and (2) a PGC that relies on kinetics parameters and reactivity coefficients to predict future behavior and adjust the desired signal accordingly. A challenging benchmark was devised, featuring a power demand curve that exponentially increases by a factor of 500 within 30 seconds, then levels out after that. Both control approaches create a simulated power curve that closely follows the power demand curve and limits power overshoots to 1% or less. While the former approach requires more tuning of the internal parameters, the latter requires additional knowledge of the reactivity feedback coefficients and rates of change of the corresponding variables, including fuel and moderator temperature, which could be difficult to dynamically measure for a real NTP system. Fortunately, some inaccuracy in these quantities will not drastically degrade the PGC performance. Subsequently, a more realistic startup sequence was considered, in which the mass flow rate and outlet pressures are ramped up to model bootstrap and thrust build-up phases prior to reaching steady-state conditions, demonstrating the ability of the hybrid PID and PGCs to handle such transients, with both types of controllers exhibiting very similar behavior. Nevertheless, a significant chamber temperature overshoot was observed, caused by the demanded power signal and assumed mass flow rate. This issue could be mitigated by deploying a reactor controller that follows the chamber temperature signal and actuates both the control valves and drums (rather than using a power signal based solely on the drums to control reactivity). Enhancement of the hydrogen fluid properties available in MOOSE, as well as a better understanding of prototypical initial conditions, are also needed to further enhance this startup model. Finally, a study was performed to model decay heat post-shutdown, and to prepare for extending this model to predict shutdown behavior and post-shutdown pulsed cooling requirements.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

Modified Paschen curves for pulsed breakdown

The influence of the voltage rise time on the Paschen curves is analyzed using kinetic and fluid models. The Paschen curves, which describe the dependence of the breakdown voltage, U br , on the product pd of gas pressure p and the characteristic length d between the electrodes, have minima that correspond to optimal conditions for plasma generation. It is shown that both kinetic and fluid models predict the experimentally observed shift of the curves toward higher voltages and the shift of the Paschen minima toward higher values of pd with the decreasing voltage rise time τ. On the right branch of the Paschen curves, the agreement between both models is obtained for all τ. We confirm that the minimum of the Paschen curves corresponds to conditions of electron runaway. Finally on the left branch, the electron velocity distribution function is nonlocal in space and also nonlocal in time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Finite element model for piles in liquefiable ground

This paper develops a three dimensional finite element modelling method for piles in liquefiable ground and applies it to the analysis of seismic pile responses. A unified plasticity model for large post-liquefaction shear deformation of sand provides the basis for the effective and efficient modelling of liquefiable ground. Special attention is dedicated towards the modelling of piles and soil-pile interface to accurately reflect the behaviour of piles. A staged modelling procedure is adopted to appropriately generate the initial conditions for the soil and piles and achieve hydrostatic pore pressure prior to seismic loading. Three centrifuge shaking table tests on single piles, both with and without pile cap and superstructure, in level and inclined liquefiable ground are conducted and simulated in validation and application of the proposed method. Further studies to investigate the effects of pile cap, lateral spreading, and non-liquefiable surface layer are undertaken numerically using the validated method. The results show these aforementioned factors to be influential in the dynamic and residual response of piles in liquefiable ground.

Centrifuge test↗
DOE OSTI2015

A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.

42 ENGINEERING↗