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NASA NTRS1998

Some Results Relevant to Statistical Closures for Compressible Turbulence

For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.

Ristorcelli, J. R.↗

NASA NTRS1999

Human Mars Mission Performance Crew Taxi Profile

Using the results from Integrated Mission Program (IMP), a simulation language and code used to model present and future Earth Moon, or Mars missions, this report presents six different case studies of a manned Mars mission. The mission profiles, timelines, propellant requirements, feasibility and perturbation analysis is presented for two aborted, two delayed rendezvous, and two normal rendezvous cases for a future Mars mission.

Duaro, Vince A.↗

NASA NTRS2007

Small Scale Response and Modeling of Periodically Forced Turbulence

The response of the small scales of isotropic turbulence to periodic large scale forcing is studied using two-point closures. The frequency response of the turbulent kinetic energy and dissipation rate, and the phase shifts between production, energy and dissipation are determined as functions of Reynolds number. It is observed that the amplitude and phase of the dissipation exhibit nontrivial frequency and Reynolds number dependence that reveals a filtering effect of the energy cascade. Perturbation analysis is applied to understand this behavior which is shown to depend on distant interactions between widely separated scales of motion. Finally, the extent to which finite dimensional models (standard two-equation models and various generalizations) can reproduce the observed behavior is discussed.

Bos, Wouter↗

NASA NTRS2010

Optimal Control Modification Adaptive Law for Time-Scale Separated Systems

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

Nguyen, Nhan T.↗

NASA NTRS2009

Optimal Control Modification for Robust Adaptation of Singularly Perturbed Systems with Slow Actuators

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. The model matching conditions in the transformed time coordinate results in increase in the feedback gain and modification of the adaptive law.

Nguyen, Nhan T.↗

NASA NTRS2011

Parametric Modeling of the Safety Effects of NextGen Terminal Maneuvering Area Conflict Scenarios

The goal of this work was to analytically identify and quantify the issues, challenges, technical hurdles, and pilot-vehicle interface issues associated with conflict detection and resolution (CD&R)in emerging operational concepts for a NextGen terminal aneuvering area, including surface operations. To this end, the work entailed analytical and trade studies focused on modeling the achievable safety benefits of different CD&R strategies and concepts in the current and future airport environment. In addition, crew-vehicle interface and pilot performance enhancements and potential issues were analyzed based on review of envisioned NextGen operations, expected equipage advances, and human factors expertise. The results of perturbation analysis, which quantify the high-level performance impact of changes to key parameters such as median response time and surveillance position error, show that the analytical model developed could be useful in making technology investment decisions.

Rogers, William H.↗

NASA NTRS2012

Optimal Control Modification for Time-Scale Separated Systems

Adaptive Control↗

NASA NTRS2016

The Effects of Magnetic-Field Geometry on Longitudinal Oscillations of Solar Prominences: Cross-Sectional Area Variation for Thin Tubes

Solar prominences are subject to both field-aligned (longitudinal) and transverse oscillatory motions, as evidenced by an increasing number of observations. Large-amplitude longitudinal motions provide valuable information on the geometry of the filament channel magnetic structure that supports the cool prominence plasma against gravity. Our pendulum model, in which the restoring force is the gravity projected along the dipped field lines of the magnetic structure, best explains these oscillations. However, several factors can influence the longitudinal oscillations, potentially invalidating the pendulum model. Aims. The aim of this work is to study the influence of large-scale variations in the magnetic field strength along the field lines, i.e., variations of the cross-sectional area along the flux tubes supporting prominence threads. Methods. We studied the normal modes of several flux tube configurations, using linear perturbation analysis, to assess the influence of different geometrical parameters on the oscillation properties. Results. We found that the influence of the symmetric and asymmetric expansion factors on longitudinal oscillations is small.Conclusions. We conclude that the longitudinal oscillations are not significantly influenced by variations of the cross-section of the flux tubes, validating the pendulum model in this context.

Luna, M.↗

NASA NTRS2018

Changes in Earth’s Energy Budget during and after the “Pause” in Global Warming: An Observational Perspective

This study examines changes in Earth’s energy budget during and after the global warming “pause” (or “hiatus”) using observations from the Clouds and the Earth’s Radiant Energy System. We find a marked 0.83±0.41 Wm−2 reduction in global mean reflected shortwave (SW) top-of-atmosphere (TOA) flux during the three years following the hiatus that results in an increase in net energy into the climate system. A partial radiative perturbation analysis reveals that decreases in low cloud cover are the primary driver of the decrease in SW TOA flux. The regional distribution of the SW TOA flux changes associated with the decreases in low cloud cover closely matches that of sea-surface temperature warming, which shows a pattern typical of the positive phase of the Pacific Decadal Oscillation. Large reductions in clear-sky SW TOA flux are also found over much of the Pacific and Atlantic Oceans in the northern hemisphere. These are associated with a reduction in aerosol optical depth consistent with stricter pollution controls in China and North America. A simple energy budget framework is used to show that TOA radiation (particularly in the SW) likely played a dominant role in driving the marked increase in temperature tendency during the post-hiatus period.

Norman G Loeb↗

NASA NTRSDate not supplied

Diagnosing Changes In Earth's Top-Of-Atmosphere Radiation Budget Since 2000

Earth’s radiation budget (ERB) is a key indicator of the climate system as it describes the delicate balance between how much of the sun’s energy reaching Earth is absorbed and how much thermal infrared radiation is emitted back to space. It is now well established that there is a positive net imbalance in ERB of 0.5-1 Wm-2. This imbalance, referred to as Earth’s Energy Imbalance (EEI), is shaped by natural and anthropogenic climate forcings and the climate system’s response to the forcing.When averaged over a long period, a positive EEI leads to an increase in surface temperature, sea levelrise, ocean heat content, melting of snow and sea-ice, and an acceleration of the hydrological cycle.EEI is also influenced by internal climate variability at interannual (e.g., El Niño/Southern Oscillation(ENSO)) and longer timescales (e.g., Pacific Decadal Oscillation (PDO)). Here we use CERES data toshow that since 2000, EEI has been increasing at a rate of 0.04+-0.03 Wm-2 per yr, corresponding to 0.8 Wm-1 over the 20-year CERES record. To understand the underlying causes for this increase, we analyze the CERES data in the context of internal climate variability indices and regional pattern changes. We also perform a partial radiative perturbation analysis that decomposes the TOA SW and LW radiation variations in terms of contributions by clouds, aerosols, surface albedo, temperature,water vapor and other gases (e.g., ozone, carbon dioxide, methane, etc.).

Norman G Loeb↗

NASA NTRS1977

Computation of unsteady transonic flows through rotating and stationary cascades. 3: Acoustic far-field analysis

A small perturbation type analysis has been developed for the acoustic far field in an infinite duct extending upstream and downstream of an axial turbomachinery stage. The analysis is designed to interface with a numerical solution of the near field of the blade rows and, thereby, to provide the necessary closure condition to complete the statement of infinite duct boundary conditions for the subject problem. The present analysis differs from conventional inlet duct analyses in that a simple harmonic time dependence was not assumed, since a transient signal is generated by the numerical near-field solution and periodicity is attained only asymptotically. A description of the computer code developed to carry out the necessary convolutions numerically is included, as well as the results of a sample application using an impulsively initiated harmonic signal.

Slutsky, S.↗

DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1984

Large perturbation flow field analysis and simulation for supersonic inlets

An analysis technique for simulation of supersonic mixed compression inlets with large flow field perturbations is presented. The approach is based upon a quasi-one-dimensional inviscid unsteady formulation which includes engineering models of unstart/restart, bleed, bypass, and geometry effects. Numerical solution of the governing time dependent equations of motion is accomplished through a shock capturing finite difference algorithm, of which five separate approaches are evaluated. Comparison with experimental supersonic wind tunnel data is presented to verify the present approach for a wide range of transient inlet flow conditions.

Varner, M. O.↗

NASA NTRS1983

Analysis of structural perturbations in systems via cost decomposition methods

It has long been common practice to analyze linear dynamic systems by decomposing the total response in terms of individual contributions which are easier to analyze. Examples of this philosophy include the expansion of transfer functions using: (1) the superposition principle, (2) residue theory and partial fraction expansions, (3) Markov parameters, Hankel matrices, and (4) regular and singular perturbations. This paper summarizes a new and different kind of expansion designed to decompose the norm of the response vector rather than the response vector itself. This is referred to as "cost-decomposition' of the system. The notable advantages of this type of decomposition are: (a) easy application to multi-input, multi-output systems, (b) natural compatibility with Linear Quadratic Gaussian Theory, (c) applicability to the analysis of more general types of structural perturbations involving inputs, outputs, states, parameters. Property (c) makes the method suitable for problems in model reduction, measurement/actuator selections, and sensitivity analysis.

Skelton, R. E.↗

NASA NTRS2008

Radiative Susceptibility of Cloudy Atmospheres to Droplet Number Perturbations: 1. Theoretical Analysis and Examples from MODIS

Theoretical and satellite-based assessments of the sensitivity of broadband shortwave radiative fluxes in cloudy atmospheres to small perturbations in the cloud droplet number concentration (N) of liquid water clouds under constant water conditions are performed. Two approaches to study this sensitivity are adopted: absolute increases in N, for which the radiative response is referred to as absolute cloud susceptibility, and relative increases in N or relative cloud susceptibility. Estimating the former is more challenging as it requires an assumed value for either cloud liquid water content or geometrical thickness; both susceptibilities require an assumed relationship between the droplet volume and effective radius. Expanding upon previous susceptibility studies, present radiative calculations include the effect of AN perturbations on droplet asymmetry parameter and single-scattering albedo, in addition to extinction. Absolute cloud susceptibility has a strong nonlinear dependence on the droplet effective radius as expected, while relative cloud susceptibility is primarily dependent on optical thickness. Molecular absorption and reflecting surfaces both reduce the relative contribution of the cloud to the top-of-atmosphere (TOA) flux and therefore also reduce the TOA albedo susceptibility. Transmittance susceptibilities are negative with absolute values similar to albedo susceptibility, while atmospheric absorptance susceptibilities are about an order of magnitude smaller than albedo susceptibilities and can be either positive or negative. Observation-based susceptibility calculations are derived from MODIS pixel-level retrievals of liquid water cloud optical thickness, effective radius, and cloud top temperature; two data granule examples are shown. Susceptibility quantifies the aerosol indirect effect sensitivity in a way that can be easily computed from model fields. As such, susceptibilities derived from MODIS observations provide a higher-order test of model cloud properties used for indirect effect studies. MODIS-derived global distributions of cloud susceptibility and radiative forcing calculations are presented in a companion paper.

Platnick, Steven↗

NASA NTRS2008

Radiative Susceptibility of Cloudy Atmospheres to Droplet Number Perturbations: 2. Global analysis from MODIS

Global distributions of albedo susceptibility for areas covered by liquid clouds are presented for 4 months in 2005. The susceptibility estimates are based on expanded definitions presented in a companion paper and include relative cloud droplet number concentration (CDNC) changes, perturbations in cloud droplet asymmetry parameter and single-scattering albedo, atmospheric/surface effects, and incorporation of the full solar spectrum. The cloud properties (optical thickness and effective radius) used as input in the susceptibility calculations come from MODIS Terra and Aqua Collection 5 gridded data. Geographical distributions of susceptibility corresponding to absolute ( absolute cloud susceptibility ) and relative ( relative cloud susceptibility ) CDNC changes are markedly different indicating that the detailed nature of the cloud microphysical perturbation is important for determining the radiative forcing associated with the first indirect aerosol effect. However, both types of susceptibility exhibit common characteristics such as significant reductions when perturbations in single-scattering properties are omitted, significant increases when atmospheric absorption and surface albedo effects are ignored, and the tendency to decrease with latitude, to be higher over ocean than over land, and to be statistically similar between the morning and afternoon MODIS overpasses. The satellite-based susceptibility analysis helps elucidate the role of present-day cloud and land surface properties in indirect aerosol forcing responses. Our realistic yet moderate CDNC perturbations yield forcings on the order of 1-2 W/sq m for cloud optical property distributions and land surface spectral albedos observed by MODIS. Since susceptibilities can potentially be computed from model fields, these results have practical application in assessing the reasonableness of model-generated estimates of the aerosol indirect radiative forcing.

Oreopoulos, Lazaros↗

NASA NTRS1986

Transfer function analysis of thermospheric perturbations

Applying perturbation theory, a spectral model in terms of vectors spherical harmonics (Legendre polynomials) is used to describe the short term thermospheric perturbations originating in the auroral regions. The source may be Joule heating, particle precipitation or ExB ion drift-momentum coupling. A multiconstituent atmosphere is considered, allowing for the collisional momentum exchange between species including Ar, O2, N2, O, He and H. The coupled equations of energy, mass and momentum conservation are solved simultaneously for the major species N2 and O. Applying homogeneous boundary conditions, the integration is carred out from the Earth's surface up to 700 km. In the analysis, the spherical harmonics are treated as eigenfunctions, assuming that the Earth's rotation (and prevailing circulation) do not significantly affect perturbations with periods which are typically much less than one day. Under these simplifying assumptions, and given a particular source distribution in the vertical, a two dimensional transfer function is constructed to describe the three dimensional response of the atmosphere. In the order of increasing horizontal wave numbers (order of polynomials), this transfer function reveals five components. To compile the transfer function, the numerical computations are very time consuming (about 100 hours on a VAX for one particular vertical source distribution). However, given the transfer function, the atmospheric response in space and time (using Fourier integral representation) can be constructed with a few seconds of a central processing unit. This model is applied in a case study of wind and temperature measurements on the Dynamics Explorer B, which show features characteristic of a ringlike excitation source in the auroral oval. The data can be interpreted as gravity waves which are focused (and amplified) in the polar region and then are reflected to propagate toward lower latitudes.

Mayr, H. G.↗

DOE OSTI2020

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗