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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

RSM 1.0 user's guide: A resupply scheduler using integer optimization

The Resupply Scheduling Model (RSM) is a PC based, fully menu-driven computer program. It uses integer programming techniques to determine an optimum schedule to replace components on or before a fixed replacement period, subject to user defined constraints such as transportation mass and volume limits or available repair crew time. Principal input for RSJ includes properties such as mass and volume and an assembly sequence. Resource constraints are entered for each period corresponding to the component properties. Though written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user defined resource constraints. Presented here is a step by step procedure for preparing the input, performing the analysis, and interpreting the results. Instructions for installing the program and information on the algorithms are given.

Viterna, Larry A.↗
NASA NTRS1994

Potential capabilities of Reynolds stress turbulence model in the COMMIX-RSM code

A Reynolds stress turbulence model has been implemented in the COMMIX code, together with transport equations describing turbulent heat fluxes, variance of temperature fluctuations, and dissipation of turbulence kinetic energy. The model has been verified partially by simulating homogeneous turbulent shear flow, and stable and unstable stratified shear flows with strong buoyancy-suppressing or enhancing turbulence. This article outlines the model, explains the verifications performed thus far, and discusses potential applications of the COMMIX-RSM code in several domains, including, but not limited to, analysis of thermal striping in engineering systems, simulation of turbulence in combustors, and predictions of bubbly and particulate flows.

Chang, F. C.↗
NASA NTRS2010

Ocean Turbulence, III: New GISS Vertical Mixing Scheme

We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma-alpha (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation Epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma-alpha s are functions of both Ri and Rq (Richardson number and density ratio representing double diffusion, DD); the Gamma-alpha are different for heat, salt and momentum; in the case of heat, the traditional value Gamma-h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Gamma-h can be three times as large, a result that we reproduce. The salt Gamma-s is given in terms of Gamma-h. The momentum Gamma-m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma-m(Ri,R-rho). Having tested Gamma-h, we then test the momentum Gamma-m by showing that the turbulent Prandtl number Gamma-m/Gamma-h vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean;s bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon/N(exp 2) from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma-alpha = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma-alpha; the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma-h(Ri,Rq). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon (Ri < 1) approximately equals 10epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri much greater than 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve.

Canuto, V. M.↗
NASA NTRS2010

High-Resolution Subtropical Summer Precipitation Derived from Dynamical Downscaling of the NCEP-DOE Reanalysis: How Much Small-Scale Information Is Added by a Regional Model?

This study assesses the regional-scale summer precipitation produced by the dynamical downscaling of analyzed large-scale fields. The main goal of this study is to investigate how much the regional model adds smaller scale precipitation information that the large-scale fields do not resolve. The modeling region for this study covers the southeastern United States (Florida, Georgia, Alabama, South Carolina, and North Carolina) where the summer climate is subtropical in nature, with a heavy influence of regional-scale convection. The coarse resolution (2.5deg latitude/longitude) large-scale atmospheric variables from the National Center for Environmental Prediction (NCEP)/DOE reanalysis (R2) are downscaled using the NCEP Environmental Climate Prediction Center regional spectral model (RSM) to produce precipitation at 20 km resolution for 16 summer seasons (19902005). The RSM produces realistic details in the regional summer precipitation at 20 km resolution. Compared to R2, the RSM-produced monthly precipitation shows better agreement with observations. There is a reduced wet bias and a more realistic spatial pattern of the precipitation climatology compared with the interpolated R2 values. The root mean square errors of the monthly R2 precipitation are reduced over 93 (1,697) of all the grid points in the five states (1,821). The temporal correlation also improves over 92 (1,675) of all grid points such that the domain-averaged correlation increases from 0.38 (R2) to 0.55 (RSM). The RSM accurately reproduces the first two observed eigenmodes, compared with the R2 product for which the second mode is not properly reproduced. The spatial patterns for wet versus dry summer years are also successfully simulated in RSM. For shorter time scales, the RSM resolves heavy rainfall events and their frequency better than R2. Correlation and categorical classification (above/near/below average) for the monthly frequency of heavy precipitation days is also significantly improved by the RSM.

NARR↗
NASA NTRS2002

Runway Safety Monitor Algorithm for Runway Incursion Detection and Alerting

The Runway Safety Monitor (RSM) is an algorithm for runway incursion detection and alerting that was developed in support of NASA's Runway Incursion Prevention System (RIPS) research conducted under the NASA Aviation Safety Program's Synthetic Vision System element. The RSM algorithm provides pilots with enhanced situational awareness and warnings of runway incursions in sufficient time to take evasive action and avoid accidents during landings, takeoffs, or taxiing on the runway. The RSM currently runs as a component of the NASA Integrated Display System, an experimental avionics software system for terminal area and surface operations. However, the RSM algorithm can be implemented as a separate program to run on any aircraft with traffic data link capability. The report documents the RSM software and describes in detail how RSM performs runway incursion detection and alerting functions for NASA RIPS. The report also describes the RIPS flight tests conducted at the Dallas-Ft Worth International Airport (DFW) during September and October of 2000, and the RSM performance results and lessons learned from those flight tests.

Green, David F., Jr.↗
NASA NTRS2003

Response Surface Methods For Spatially-Resolved Optical Measurement Techniques

Response surface methods (or methodology), RSM, have been applied to improve data quality for two vastly different spatially-resolved optical measurement techniques. In the first application, modern design of experiments (MDOE) methods, including RSM, are employed to map the temperature field in a direct-connect supersonic combustion test facility at NASA Langley Research Center. The laser-based measurement technique known as coherent anti-Stokes Raman spectroscopy (CARS) is used to measure temperature at various locations in the combustor. RSM is then used to develop temperature maps of the flow. Even though the temperature fluctuations at a single point in the flowfield have a standard deviation on the order of 300 K, RSM provides analytic fits to the data having 95% confidence interval half width uncertainties in the fit as low as +/- 30 K. Methods of optimizing future CARS experiments are explored. The second application of RSM is to quantify the shape of a 5-meter diameter, ultra-lightweight, inflatable space antenna at NASA Langley Research Center. Photogrammetry is used to simultaneously measure the shape of the antenna at approximately 500 discrete spatial locations. RSM allows an analytic model to be developed that describes the shape of the majority of the antenna with an uncertainty of 0.4 mm, with 95% confidence. This model would allow a quantitative comparison between the actual shape of the antenna and the original design shape. Accurately determining this shape also allows confident interpolation between the measured points. Such a model could, for example, be used for ray tracing of radio-frequency waves up to 95 GHz. to predict the performance of the antenna.

Danehy, P. M.↗
NASA NTRS2002

Measurement of Unsteady Pressure Data on a Large HSCT Semispan Wing and Comparison with Analysis

Experimental data from wind-tunnel tests of the Rigid Semispan Model (RSM) performed at NASA Langley's Transonic Dynamics Tunnel (TDT) are presented. The primary focus of the paper is on data obtained from testing of the RSM on the Oscillating Turntable (OTT). The OTT is capable of oscillating models in pitch at various amplitudes and frequencies about mean angles of attack. Steady and unsteady pressure data obtained during testing of the RSM on the OTT is presented and compared to data obtained from previous tests of the RSM on a load balance and on a Pitch and Plunge Apparatus (PAPA). Testing of the RSM on the PAPA resulted in utter boundaries that were strongly dependent on angle of attack across the Mach number range. Pressure data from all three tests indicates the existence of vortical flows at moderate angles of attack. The correlation between the vortical flows and the unusual utter boundaries from the RSM/PAPA test is discussed. Comparisons of experimental data with analyses using the CFL3Dv6 computational fluid dynamics code are presented.

Scott, Robert C.↗
NASA NTRS2003

Response Surface Methods for Spatially-Resolved Optical Measurement Techniques

Response surface methods (or methodology), RSM, have been applied to improve data quality for two vastly different spatial ly-re solved optical measurement techniques. In the first application, modern design of experiments (MDOE) methods, including RSM, are employed to map the temperature field in a direct-connect supersonic combustion test facility at NASA Langley Research Center. The laser-based measurement technique known as coherent anti-Stokes Raman spectroscopy (CARS) is used to measure temperature at various locations in the combustor. RSM is then used to develop temperature maps of the flow. Even though the temperature fluctuations at a single point in the flowfield have a standard deviation on the order of 300 K, RSM provides analytic fits to the data having 95% confidence interval half width uncertainties in the fit as low as +/-30 K. Methods of optimizing future CARS experiments are explored. The second application of RSM is to quantify the shape of a 5-meter diameter, ultra-light, inflatable space antenna at NASA Langley Research Center.

Danehy, P. M.↗
NASA NTRS2004

Formal Verification of Safety Properties for Aerospace Systems Through Algorithms Based on Exhaustive State-Space Exploration

The Runway Safety Monitor (RSM) designed by Lockheed Martin is part of NASA's effort to reduce aviation accidents. We developed a Petri net model of the RSM protocol and used the model checking functions of our tool SMART to investigate a number of safety properties in RSM. To mitigate the impact of state-space explosion, we built a highly discretized model of the system, obtained by partitioning the monitored runway zone into a grid of smaller volumes and by considering scenarios involving only two aircraft. The model also assumes that there are no communication failures, such as bad input from radar or lack of incoming data, thus it relies on a consistent view of reality by all participants. In spite of these simplifications, we were able to expose potential problems in the RSM conceptual design. Our findings were forwarded to the design engineers, who undertook corrective action. Additionally, the results stress the efficiency attained by the new model checking algorithms implemented in SMART, and demonstrate their applicability to real-world systems. Attempts to verify RSM with NuSMV and SPIN have failed due to excessive memory consumption.

Ciardo, Gianfranco↗
NASA NTRS2006

Runway Safety Monitor Algorithm for Single and Crossing Runway Incursion Detection and Alerting

The Runway Safety Monitor (RSM) is an aircraft based algorithm for runway incursion detection and alerting that was developed in support of NASA's Runway Incursion Prevention System (RIPS) research conducted under the NASA Aviation Safety and Security Program's Synthetic Vision System project. The RSM algorithm provides warnings of runway incursions in sufficient time for pilots to take evasive action and avoid accidents during landings, takeoffs or when taxiing on the runway. The report documents the RSM software and describes in detail how RSM performs runway incursion detection and alerting functions for NASA RIPS. The report also describes the RIPS flight tests conducted at the Reno/Tahoe International Airport (RNO) and the Wallops Flight Facility (WAL) during July and August of 2004, and the RSM performance results and lessons learned from those flight tests.

Green, David F., Jr.↗
NASA NTRS2006

Formal Verification of the Runway Safety Monitor

The Runway Safety Monitor (RSM) designed by Lockheed Martin is part of NASA's effort to reduce runway accidents. We developed a Petri net model of the RSM protocol and used the model checking functions of our tool SMART to investigate a number of safety properties in RSM. To mitigate the impact of state-space explosion, we built a highly discretized model of the system, obtained by partitioning the monitored runway zone into a grid of smaller volumes and by considering scenarios involving only two aircraft. The model also assumes that there are no communication failures, such as bad input from radar or lack of incoming data, thus it relies on a consistent view of reality by all participants. In spite of these simplifications, we were able to expose potential problems in the RSM conceptual design. Our findings were forwarded to the design engineers, who undertook corrective action. Additionally, the results stress the efficiency attained by the new model checking algorithms implemented in SMART, and demonstrate their applicability to real-world systems.

Siminiceanu, Radu↗
NASA NTRS1986

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

Amano, R. S.↗
NASA NTRS1990

Calculation of 3D turbulent jets in crossflow with a multigrid method and a second-moment closure model

A multigrid method is presented for calculating turbulent jets in crossflow. Fairly rapid convergence is obtained with the k-epsilon turbulence model, but computations with a full Reynolds stress turbulence model (RSM) are not yet very efficient. Grid dependency tests show that there are slight differences between results obtained on the two finest grid levels. Computations using the RSM are significantly different from those with k-epsilon model and compare better to experimental data. Some work is still required to improve the efficiency of the computations with the RSM.

Demuren, A. O.↗
NASA NTRS1991

Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow

A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds Stress Model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equations in the latter may be responsible. Computed results with both turbulence models are compared with experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement with mean flow velocity but RSM yields better prediction of the Reynolds stresses.

Demuren, A. O.↗
NASA NTRS1992

Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow

A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds stress model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method to be obtained with both turbulence models. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equation in the latter may be responsible. Computed results with both turbulence models are compared to experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement for the mean flow velocity, but RSM yields better predictions of the Reynolds stresses.

Demuren, A. O.↗
NASA NTRS1993

Space transportation vehicle design evaluation using saturated designs

An important objective in the preliminary design and evaluation of space transportation vehicles is to find the best values of design variables that optimize the performance characteristic (e.g. dry weight). For a given configuration, the vehicle performance can be determined by the use of complex sizing and performance evaluation computer programs. These complex computer programs utilize iterative algorithms and they are generally too expensive and/or difficult to use directly in multidisciplinary design optimization. An alternative is to use response surface methodology (RSM) and obtain quadratic polynomial approximations to the functional relationships between performance characteristics and design variables. In RSM, these approximation models are then used to determine optimum design parameter values and for rapid sensitivity studies. Constructing a second-order model requires that 'n' design parameters be studied at least at 3 levels (values) so that the coefficients in the model can be estimated. There, 3(n) factorial experiments (point designs or observations) may be necessary. For small values of 'n' such as two or three, this design works well. However, when a large number of design parameters are under study, the number of design points required for a full-factorial design may become excessive. Fortunately, these quadratic polynomial approximations can be obtained by selecting an efficient design matrix using central composite designs (CCD) from design of experiments theory. Each unique point design from the CCD matrix is then conducted using computerized analysis tools (e.g. POST, CONSIZ, etc.). In the next step, least squares regression analysis is used to calculate the quadratic polynomial coefficients from the data. However, in some multidisciplinary applications involving a large number of design variables and several disciplines, the computerized performance synthesis programs may get too time consuming and expensive to run even with the use of efficient central composite designs. In such cases, it may be preferable to keep the number of design points to an absolute minimum and trade some model accuracy with cost. For this purpose, another class of experimental designs, called saturated D-optimal designs may be utilized for generating a matrix of vehicle designs. A design is called saturated when the number of design points is exactly equal to the number of terms in the model to be fitted. As a result, saturated designs require the absolute minimum number of design points ((n+1)(n+2)/s) to estimate the quadratic polynomial model coefficients. Saturated designs can be generated using the D-optimality criterion. A good saturated design should give rise to least squares estimates with minimum generalized variance.

Unal, Resit↗