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NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗

NASA NTRSDate not supplied

Developing Procedures to Implement Geometric Imperfections Beyond Right Circular Cylindrical Shells in Finite Element Method Models

Analysis of aerospace structures is frequently conducted using nominal dimensions and frequently assumes ideal conditions in loading, contact, constraints, et cetera. Off-nominal dimensions and nonideal conditions, however, are present in all structures. These are the result of widely ranging causes from coefficient of thermal expansion mismatches, manufacturing tooling anomalies, to assembly procedures that inadvertently alter the structure. Specifically, geometric imperfections can have potentially significant influence on the response of a structural test article observed in an experiment versus the response given by a numerical simulation. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS) was previously presented as a set of Python scripts to calculate and implement as-manufactured geometric midsurface and thickness imperfections into finite element method (FEM) shell models of nominally right circular cylinders. By taking advantage of the simple shape of a right circular cylinder, interpolations of the measured data points were able to be performed along directions that aligned to the cylindrical coordinate system axes of the entire structure. By taking advantage of the shell representation of the real structure as opposed to modeling using a continuum representation, the thickness variation was able to be implemented by shell section definitions instead of having to modify the position of multiple nodes in the thickness direction. Py_TIGIRS is a useful tool that established a procedural example on how to implement geometric imperfections in right circular cylindrical shell structures. Three new procedures, each expanded from concepts established in Py_TIGIRS, are proposed for various test-article designs and are intended to broaden the range of structures that can be modeled with measured geometric imperfections in the structural analysis community. Each test-article design introduces new challenges to successfully implement geometric imperfections into a FEM model. The first test-article design consists of a carbon fiber reinforced polymer square plate with a hat-shaped stiffener co-cured on one side. This test-article design was for a novel seven-point bend test that was also previously presented. Manufacturing and cure-cycle imperfections are observed using digital image correlation (DIC) techniques. As thermal expansion coefficient mismatches between the plate and stiffener materials were anticipated, a thermal analysis study with continuum shell and solid elements was conducted to capture the global shape observed prior to testing. The second test-article design is of a similar hat-stiffened plate configuration, but with a side length ratio near 3:1 with elongation in the stiffener direction. The test article was used to characterize the response to uniaxial compressive loading in the direction of the stiffener. Due to differing manufacturing steps, a thermal analysis like the one developed for the seven-point bend configuration was unable to mimic the observed geometric imperfections. Instead, a strategy based on applying deformations directly to the structure during analysis was developed for continuum shell and solid element representation of a stiffened panel.

Geometric imperfections↗

NASA NTRS2012

Projections of Declining Surface-Water Availability for the Southwestern United States

16 of the CMIP5 models had all the data needed for this work for at least one simulation that was continuous from 1950 to 2040. Details of the models analyzed here are provided in Table S1. The model data analyzed here are available at http://strega.ldeo.columbia.edu:81/expert/home/.naomi/.AR5/.v2/.historical:rcp85/.mmm16/ a. Assessing the climatology of the models Despite increases in horizontal resolution of many models compared to their CMIP3 counterparts none of these models can adequately resolve the topography of the south west United States, such as the Sierra Nevada and Rocky Mountains and the associated orographic precipitation. This requires that caution be used when interpreting the results presented here. To assess the ability of the models to simulate the current hydroclimate, in Figure S1 we show the observed (from the Global Precipitation Climatology Centre gridded rain gauge data, (1)) monthly climatology of precipitation and the same for all the models and the multimodel mean for the California-Nevada, Colorado headwaters and Texas regions. The GPCC data uses rain gauges only and interpolates to regular grids of which we used the 1◦ by 1◦ one. Details of the data set can be found in (2). While the models apparently overestimate precipitation in California and Nevada the seasonal cycle with wet winters and dry summers is very well represented. It is also possible that the rain gauge observations are biased low by inadequately sampling the higher mountain regions. How ever the models might also be expected to underestimate orographic precipitation due to inadequate horizontal resolution. The 25 models are also too wet in the Colorado headwaters region but correctly represent the quite even distribution though the year. The bimodal distribution of precipitation in Texas, with peaks in May and September, and the absolute amounts, are well modeled but with the September peak too weak. The positive precipitation bias translates into a positive runoff bias for the Colorado headwaters as also shown in Figure S1. Here the observed runoff values are taken from simulations of the Variable Infiltration Capacity (VIC) land surface-hydrology model (3) forced by observed meteorology (5) that were conducted as part of the North American Land Data Assimilation System project phase 2 ( (NLDAS-2), http://www.emc.ncep.noaa.gov/mmb/nldas/. Runoff for California-Nevada is better simulated but there is a positive bias over Texas despite no strong precipitation bias. To check whether regional climate models better simulate P and runoff in these regions we analyzed the historical simulation with the Regional Climate Model version 3 driven by the National Centers for Environmental Prediction-Department of Energy Reanalysis 2 available from the North American Regional Climate Change Assessment Program (http://www.narccap.ucar.edu). This model configuration retained these biases in P and runoff although they were reduced in amplitude. Given these varying biases we plot P and P − E changes in actual values but apply the simplest bias correction possible to the runoff and soil moisture values and show the modeled changes in terms of percentages of the 20th Century model climatologies. A thorough assessment of the simulation of North American climate in CMIP5 models is conducted in Sheffield at al. (North American Climate in CMIP5 Experiments. Part I: Evaluation of 20th Century Continental and Regional Climatology, manuscript submit ted to J. Climate, available at http://www.climate.noaa.gov/index.jsp?pg=./cpo pa/ mapp/cmip5 publications.html). Sheffield et al. analyze the climatology of precipitation, surface air temperature, low level winds, moisture fluxes, runoff etc. and conclude that the main features of the hydrological cycle, including characteristics of the atmospheric moisture balance and its seasonality, are captured in the CMP5 models subject to biases in total precipitation amounts. We chose to use all available models instead of selecting some and rejecting others based on an assessment of model realism. This is in accord with the suggestions of Mote et al. for CMIP3 (4) but future work needs to revisit this matter for the case of the CMIP5 ensemble.

Seager, Richard↗

NASA NTRS2020

The AERONET Version 3 Aerosol Retrieval Algorithm, Associated Uncertainties and Comparisons to Version 2

The Aerosol Robotic Network (AERONET) Version 3 (V3) aerosol retrieval algorithm is described, which is based on the Version 2 (V2) algorithm with numerous updates. Comparisons of V3 aerosol retrievals to those of V2 are presented, along with a new approach to estimate uncertainties in many of the retrieved aerosol parameters. Changes in the V3 aerosol retrieval algorithm include (1) a new polarized radiative transfer code (RTC), which replaced the scalar RTC of V2, (2) detailed characterization of gas absorption by adding NO2 and H2O to specify total gas absorption in the atmospheric column, specification of vertical profiles of all the atmospheric species, (3) new bidirectional reflectance distribution function (BRDF) parameters for land sites adopted from the MODIS BRDF/Albedo product, (4) a new version of the extraterrestrial solar flux spectrum, and (5) a new temperature correction procedure of both direct Sun and sky radiance measurements. The potential effect of each change in V3 on single scattering albedo (SSA) retrievals was analyzed. The operational almucantar retrievals of V2 versus V3 were compared for four AERONET sites: GSFC, Mezaira, Mongu, and Kanpur. Analysis showed very good agreement in retrieved parameters of the size distributions. Comparisons of SSA retrievals for dust aerosols (Mezaira) showed a good agreement in 440 nm SSA, while for longer wavelengths V3 SSAs are systematically higher than those of V2, with the largest mean difference at 675 nm due to cumulative effects of both extraterrestrial solar flux and BRDF changes. For non-dust aerosols, the largest SSA deviation is at 675 nm due to differences in extraterrestrial solar flux spectrums used in each version. Further, the SSA 675 nm mean differences are very different for weakly (GSFC) and strongly (Mongu) absorbing aerosols, which is explained by the lower sensitivity to a bias in aerosol scattering optical depth by less absorbing aerosols. A new hybrid (HYB) sky radiance measurement scan is introduced and discussed. The HYB combines features of scans in two different planes to maximize the range of scattering angles and achieve scan symmetry, thereby allowing for cloud screening and spatial averaging, which is an advantage over the principal plane scan that lacks robust symmetry. We show that due to an extended range of scattering angles, HYB SSA retrievals for dust aerosols exhibit smaller variability with solar zenith angles (SZAs) than those of almucantar (ALM), which allows extension of HYB SSA retrievals to SZAs less than 50∘ to as small as 25∘. The comparison of SSA retrievals from closely time-matched HYB and ALM scans in the 50 to 75∘ SZA range showed good agreement with the differences below ∼0.005. We also present an approach to estimate retrieval uncertainties which utilizes the variability in retrieved parameters generated by perturbing both measurements and auxiliary input parameters as a proxy for retrieval uncertainty. The perturbations in measurements and auxiliary inputs are assumed as estimated biases in aerosol optical depth (AOD), radiometric calibration of sky radiances combined with solar spectral irradiance, and surface reflectance. For each set of Level 2 Sun/sky radiometer observations, 27 inputs corresponding to 27 combinations of biases were produced and separately inverted to generate the following statistics of the inversion results: average, standard deviation, minimum and maximum values. From these statistics, standard deviation (labeled U27) is used as a proxy for estimated uncertainty, and a lookup table (LUT) approach was implemented to reduce the computational time. The U27 climatological LUT was generated from the entire AERONET almucantar (1993–2018) and hybrid (2014–2018) scan databases by binning U27s in AOD (440 nm), Angström exponent (AE, 440–870 nm), and SSA (440, 675, 870, 1020 nm). Using this LUT approach, the uncertainty estimates U27 for each individual V3 Level 2 retrieval can be obtained by interpolation using the corresponding measured and inverted combination of AOD, AE, and SSA.

Aliaksandr Siniuk↗