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Average and reject logic control system provides an average of the output signals of transducers measuring critical parameters. It uses a circuit that compares each signal against an average, rejects any signal that departs significantly from the average, and supplies an average of the acceptable signals.
A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.
Recent advancement in the molecular Rayleigh scattering based technique allowed for simultaneous measurement of velocity and density fluctuations with high sampling rates. The technique was used to investigate unheated high subsonic and supersonic fully expanded free jets in the Mach number range of 0.8 to 1.8. The difference between the Favre averaged and Reynolds averaged axial velocity and axial component of the turbulent kinetic energy is found to be small. Estimates based on the Morkovin's "Strong Reynolds Analogy" were found to provide lower values of turbulent density fluctuations than the measured data.
For abstract, see N78-28147.
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Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.
It is often desirable to characterize a turbomachinery flow field with a few lumped parameters such as total pressure ratio or stage efficiency. Various averaging schemes may be used to compute these parameters. Here three averaging schemes, the momentum, energy, and area averaging schemes, are described and compared for two computed solutions of the midspan section of a transonic fan stage: a steady averaging-plane solution in which average rotor outflow conditions were used as stator inflow conditions and an unsteady rotor-stator interaction solution. The unsteady solution is described, some unsteady flow phenomena are discussed and the steady pressure distributions are compared. Despite large unsteady pressure fluctuations on the stator surface, the steady pressure distribution matched the average unsteady distribution almost exactly. Stator wake profiles, stator loss coefficient, and stage efficiency were computed for the two solutions with the three averaging schemes and are compared. In general the energy averaging scheme gave good agreement between the averaging-plane solution and the time-averaged unsteady solution, even though certain phenomena due to unsteady wake migration were neglected.
The Monthly TOA/Surface Averages (SRBAVG) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The SRBAVG is also produced for combinations of scanner instruments. The monthly average regional flux is estimated using diurnal models and the 1-degree regional fluxes at the hour of observation from the CERES SFC product. A second set of monthly average fluxes are estimated using concurrent diurnal information from geostationary satellites. These fluxes are given for both clear-sky and total-sky scenes and are spatially averaged from 1-degree regions to 1-degree zonal averages and a global average. For each region, the SRBAVG also contains hourly average fluxes for the month and an overall monthly average. The cloud properties from SFC are column averaged and are included on the SRBAVG. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-02-01; Stop_Date=2000-03-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1 degree; Longitude_Resolution=1 degree; Horizontal_Resolution_Range=100 km - < 250 km or approximately 1 degree - < 2.5 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
The Monthly TOA/Surface Averages (SRBAVG) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The SRBAVG is also produced for combinations of scanner instruments. The monthly average regional flux is estimated using diurnal models and the 1-degree regional fluxes at the hour of observation from the CERES SFC product. A second set of monthly average fluxes are estimated using concurrent diurnal information from geostationary satellites. These fluxes are given for both clear-sky and total-sky scenes and are spatially averaged from 1-degree regions to 1-degree zonal averages and a global average. For each region, the SRBAVG also contains hourly average fluxes for the month and an overall monthly average. The cloud properties from SFC are column averaged and are included on the SRBAVG. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-02-01; Stop_Date=2003-02-28] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1 degree; Longitude_Resolution=1 degree; Horizontal_Resolution_Range=100 km - < 250 km or approximately 1 degree - < 2.5 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
The Monthly TOA/Surface Averages (SRBAVG) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The SRBAVG is also produced for combinations of scanner instruments. The monthly average regional flux is estimated using diurnal models and the 1-degree regional fluxes at the hour of observation from the CERES SFC product. A second set of monthly average fluxes are estimated using concurrent diurnal information from geostationary satellites. These fluxes are given for both clear-sky and total-sky scenes and are spatially averaged from 1-degree regions to 1-degree zonal averages and a global average. For each region, the SRBAVG also contains hourly average fluxes for the month and an overall monthly average. The cloud properties from SFC are column averaged and are included on the SRBAVG. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-02-01; Stop_Date=2003-02-28] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1 degree; Longitude_Resolution=1 degree; Horizontal_Resolution_Range=100 km - < 250 km or approximately 1 degree - < 2.5 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
The Monthly TOA/Surface Averages (SRBAVG) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The SRBAVG is also produced for combinations of scanner instruments. The monthly average regional flux is estimated using diurnal models and the 1-degree regional fluxes at the hour of observation from the CERES SFC product. A second set of monthly average fluxes are estimated using concurrent diurnal information from geostationary satellites. These fluxes are given for both clear-sky and total-sky scenes and are spatially averaged from 1-degree regions to 1-degree zonal averages and a global average. For each region, the SRBAVG also contains hourly average fluxes for the month and an overall monthly average. The cloud properties from SFC are column averaged and are included on the SRBAVG. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-02-01; Stop_Date=2004-05-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1 degree; Longitude_Resolution=1 degree; Horizontal_Resolution_Range=100 km - < 250 km or approximately 1 degree - < 2.5 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
The Monthly TOA/Surface Averages (SRBAVG) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The SRBAVG is also produced for combinations of scanner instruments. The monthly average regional flux is estimated using diurnal models and the 1-degree regional fluxes at the hour of observation from the CERES SFC product. A second set of monthly average fluxes are estimated using concurrent diurnal information from geostationary satellites. These fluxes are given for both clear-sky and total-sky scenes and are spatially averaged from 1-degree regions to 1-degree zonal averages and a global average. For each region, the SRBAVG also contains hourly average fluxes for the month and an overall monthly average. The cloud properties from SFC are column averaged and are included on the SRBAVG. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-02-01; Stop_Date=2004-05-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1 degree; Longitude_Resolution=1 degree; Horizontal_Resolution_Range=100 km - < 250 km or approximately 1 degree - < 2.5 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its area‐to‐mass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average cross‐sectional area in the calculation of the area‐to‐mass ratio. The average cross‐sectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to one‐fourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average cross‐sectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a space‐carving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average cross‐sectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed cross‐sectional area projections and then averages them to determine the average cross‐sectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average cross‐sectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions.
It is often desirable to characterize a turbomachinery flow field with a few lumped parameters such as total pressure ratio or stage efficiency. Various averaging schemes may be used to compute these parameters. The momentum, energy, and area averaging schemes are described and compared. The schemes were compared for two computed solutions of the midspan section of a transonic fan stage: a steady averaging-plane solution in which average rotor outflow conditions were used as stator inflow conditions, and an unsteady rotor-stator interaction solution. The solutions were computed on identical grids using similar Navier-Stokes codes and an algebraic turbulence model. The unsteady solution is described, some unsteady flow phenomena are discussed, and the steady pressure distributions are compared. Despite large unsteady pressure fluctuations on the stator surface, the steady pressure distribution matched the average unsteady distribution almost exactly. Stator wake profiles, stator loss coefficient, and stage efficiency were computed for the two solutions with the three averaging schemes and are compared. In general, the energy averaging scheme gave good agreement between the averaging-plane solution and the time-averaged unsteady solution, even though certain phenomena due to unsteady wake migration were neglected.
A characteristic feature of rainfall statistics is that they in general depend on the space and time scales over which rain data are averaged. As a part of an earlier effort to determine the sampling error of satellite rain averages, a space-time model of rainfall statistics was developed to describe the statistics of gridded rain observed in GATE. The model allows one to compute the second moment statistics of space- and time-averaged rain rate which can be fitted to satellite or rain gauge data to determine the four model parameters appearing in the precipitation spectrum - an overall strength parameter, a characteristic length separating the long and short wavelength regimes and a characteristic relaxation time for decay of the autocorrelation of the instantaneous local rain rate and a certain 'fractal' power law exponent. For area-averaged instantaneous rain rate, this exponent governs the power law dependence of these statistics on the averaging length scale $L$ predicted by the model in the limit of small $L$. In particular, the variance of rain rate averaged over an $L \times L$ area exhibits a power law singularity as $L \rightarrow 0$. In the present work the model is used to investigate how the statistics of area-averaged rain rate over the tropical Western Pacific measured with ship borne radar during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean Atmospheric Response Experiment) and gridded on a 2 km grid depends on the size of the spatial averaging scale. Good agreement is found between the data and predictions from the model over a wide range of averaging length scales.
Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds-averaged Navier Stokes equations. The first scheme is a hybrid Reynolds-averaged- Navier Stokes/large-eddy-simulation model using the two-equation k(epsilon) model with a Reynolds-averaged-Navier Stokes/large-eddy-simulation transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier Stokes model in which the unresolved kinetic energy parameter f(sub k) is allowed to vary as a function of grid spacing and the turbulence length scale. This parameter is estimated based on a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for partially averaged Navier Stokes. It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The parameter f(sub k) varies between zero and one and is equal to one in the viscous sublayer and when the Reynolds-averaged Navier Stokes turbulent viscosity becomes smaller than the large-eddy-simulation viscosity. The formulation, usage methodology, and validation examples are presented to demonstrate the enhancement of PAB3D's time-accurate turbulence modeling capabilities. The accurate simulations of flow and turbulent quantities will provide a valuable tool for accurate jet noise predictions. Solutions from these models are compared with Reynolds-averaged Navier Stokes results and experimental data for high-temperature jet flows. The current results show promise for the capability of hybrid Reynolds-averaged Navier Stokes and large eddy simulation and partially averaged Navier Stokes in simulating such flow phenomena.
Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.
The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-10-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].