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DOE OSTI2021

Exactness of OPF Relaxation on Three-phase Radial Networks with Delta Connections

Simulations have shown that while semi-definite relaxations of AC optimal power flow (AC-OPF) on three-phase radial networks with only wye connections tend to be exact, the presence of delta connections seem to render them inexact. This paper shows that such inexactness originates from the non-uniqueness of relaxation solutions and numerical errors amplified by the non-uniqueness. This finding motivates two algorithms to recover the exact solution of AC-OPF in unbalanced distribution networks featuring both wye and delta connections. In simulations using IEEE 13, 37 and 123-bus systems, the proposed algorithms provide exact optimal solutions up to numerical precision.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2001

Sedimentation along the Eastern Chenier Plain Coast: Down Drift Impact of a Delta Complex Shift

The Mississippi River Chenier Plain is a shore parallel landform (down-drift from the Atchafalaya distributary of the Mississippi River) consisting of an alternating series of transgressive sand-shell ridges and regressive, progradational mudflats. The late 1940s shift of 1/3 of the flow of the Mississippi to the newly developing Atchafalaya delta complex to the west has resulted in injection of the river waters and suspended sediment into the westward flowing currents of the coastal current system. This has reactivated the dormant processes of mud accumulation along this coast. These environmental circumstances have provided the opportunity to: (1) investigate the depositional processes of the prograding, fine grained, mud flat facies of the open Chenier main coast and (2) to test the hypothesis that the impacts of the frequent cold front passages of fall, winter and spring exceed those of the occasional and more localized hurricane in shaping the coast and powering the dominant sedimentary processes. We conducted field investigations with the benefit of multi - scale, time series environmental surveillance by remote sensing systems, including airborne and satellite sensors. These systems provided invaluable new information on areal geomorphic patterns and the behavior of the coastal waters. This is a classic case of weather impacting inner shelf waters and sediments and causing the development of a new landform. It is clear that mud flats of the eastern chenier plain are prograding seaward, as well as progressively growing in a westerly direction.

Huh, Oscar K.↗

NASA NTRS2001

Environmental Assessments in the Riparian Corridor of the Colorado River Delta

We will develop remote sensing methods to conduct environmental assessments in the riparian corridor of the Colorado River delta, shared by the United States and Mexico. This important regional ecosystem is dependent upon US water flows, yet the most important wildlife habitats are in Mexico. The delta region is poorly known and difficult to monitor on the ground. We will use ground-validated, aerial and satellite methods to develop accurate vegetation and habitat maps and predictive hydrological and vegetation models of this ecosystem in response to US flood releases. The work products will advance our understanding of water resource issues in dryland climates and provide a specific application tool for a critical binational natural resource area.

Source record↗

NASA NTRS1994

Axis switching and spreading of an asymmetric jet: Role of vorticity dynamics

The effects of vortex generators and periodic excitation on vorticity dynamics and the phenomenon of axis switching in a free asymmetric jet are studied experimentally. Most of the data reported are for a 3:1 rectangular jet at a Reynolds number of 450,000 and a Mach number of 0.31. The vortex generators are in the form of 'delta tabs', triangular shaped protrusions into the flow, placed at the nozzle exit. With suitable placement of the tabs, axis switching could be either stopped or augmented. Two mechanisms are identified governing the phenomenon. One, as described by previous researchers and referred to here as the omega(sub theta)-induced dynamics, is due to difference in induced velocities for different segments of a rolled up azimuthal vortical structure. The other, omega(sub x)-induced dynamics, is due to the induced velocities of streamwise vortex pairs in the flow. Both dynamics can be active in a natural asymmetric jet; the tendency for axis switching caused by the omega(sub theta)-induced dynamics may be, depending on the streamwise vorticity distribution, either resisted or enhanced by the omega(sub x)-induced dynamics. While this simple framework qualitatively explains the various observations made on axis switching, mechanisms actually in play may be much more complex. The two dynamics are not independent as the flow field is replete with both azimuthal and streamwise vortical structures which continually interact. Phase averaged flow field data for a periodically forced case, over a volume of the flow field, are presented and discussed in an effort to gain insight into the dynamics of these vortical structures.

Zaman, K. B. M. Q.↗

NASA NTRS1995

The decay of longitudinal vortices shed from airfoil vortex generators

An experimental study is conducted to examine the crossplane structure and streamwise decay of vortices shed from airfoil-type vortex generators. The vortex generators are set in a counter-rotating array spanning the full circumference of a straight pipe. The span of the vortex generators above the duct surface, h, is approximately equal to the local turbulent boundary layer thickness, delta. Measurement of three-component mean flow velocity in downstream crossplanes are used to characterize the structure of the shed vortices. Measurements in adjacent crossplanes (closely spaced along the streamwise coordinate) characterize the interaction and decay of the embedded vortices. A model constructed by the superposition of Oseen vortices is compared to the data for one test case.

Wendt, Bruce J.↗

NASA NTRS2008

Nonstandard Analysis and Jump Conditions for Converging Shock Waves

Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.

Baty, Roy S.↗

NASA NTRS2008

Compressible Boundary Layer Predictions at High Reynolds Number using Hybrid LES/RANS Methods

Simulations of compressible boundary layer flow at three different Reynolds numbers (Re(sub delta) = 5.59x10(exp 4), 1.78x10(exp 5), and 1.58x10(exp 6) are performed using a hybrid large-eddy/Reynolds-averaged Navier-Stokes method. Variations in the recycling/rescaling method, the higher-order extension, the choice of primitive variables, the RANS/LES transition parameters, and the mesh resolution are considered in order to assess the model. The results indicate that the present model can provide good predictions of the mean flow properties and second-moment statistics of the boundary layers considered. Normalized Reynolds stresses in the outer layer are found to be independent of Reynolds number, similar to incompressible turbulent boundary layers.

Choi, Jung-Il↗

NASA NTRS1981

A numerical simulation of hypersonic viscous flow over arbitrary geometries at angle of attack

An implicit conservative, noniterative, finite-difference algorithm that predicts the supersonic, laminar or turbulent viscous flow about arbitrary geometries at large angles of attack is presented. The three-dimensional parabolized form of the thin-layer Navier-Stokes equations are written in generalized coordinates. These equations are solved using the delta form of the Beam-Warming implicit algorithm. Flow field simulations have been obtained for a blunt biconic with windward and leeward cuts and an X-24C lifting body for both laminar and turbulent flow at various Mach numbers and angles of attack. When compared with experiment or with previous theories, these computational predictions show good agreement.

Chaussee, D. S.↗

NASA NTRS1975

Wall-wake velocity profile for compressible non-adiabatic flows

A form of the wall-wake profile, which is applicable to flows with heat transfer, and for which a variation in y = O at y = delta, was suggested. The modified profile, which takes into account the effect of turbulent Prandtl number, was found to provide a good representation of experimental data for a wide range numbers and heat transfer. The Cf values which are determined by a least squares fit of the profile to the data agree well with values which were measured by the floating element technique. In addition, the values of delta determined by the fit correspond more closely to the outer edge of the viscous flow region than those obtained with earlier versions of the wall-wake profile.

Sun, C. C.↗

NASA NTRS1996

Studies of Radiation-Driven and Buoyancy-Driven Fluid Flows and Transport

It is well known that radiative heat transport influences many types of buoyant flows due to its effect on the temperature and thus density field in the fluid medium. It is of interest to study gaseous flows driven solely by radiation in the absence of buoyancy, particularly because of its application to astrophysical flows that are well known from astronomical observations and numerical simulation. However, no laboratory-scale experiments of this phenomenon have ever been conducted. To study the possibility of obtaining such flows in the laboratory, an apparatus was built to produce large temperature differences (Delta (T)) up to 300 K in a gas confined between flat parallel plates. SF6 was used as the radiatively-active gas because its Planck absorption length is much shorter than that of any other common non-reactive gas. The NASA-Lewis 2.2 second drop tower was used to obtain reduced gravity in order to suppress buoyancy effects. To image the resulting flows, a laser shearing interferometer was employed. Initial results indicate the presence of flow that does not appear to be attributable to the residual flow resulting from buoyancy influences before the drop. For Delta(T) greater than 70 K, slight deformations in the interferometer fringes seen at lower Delta(T) became large unsteady swirls. Such behavior did not occur for radiatively-inactive gases, suggesting that a flow driven solely by radiation was obtained in SF6 and to a lesser extent in CO2. This was more pronounced at higher pressures and plate spacings, consistent with our scaling predictions.

Ronney, Paul D.↗

NASA NTRS1994

Studies of Radiation-Driven and Buoyancy-Driven Fluid Flows and Transport

It is well known that radiative heat transport influences many types of buoyant flows due to its effect on the temperature and thus density field in the fluid medium. It is of interest to study gaseous flows driven solely by radiation in the absence of buoyancy, particularly because of its application to astrophysical flows that are well known from astronomical observations and numerical simulation. However, no laboratory-scale experiments of this phenomenon have ever been conducted. To study the possibility of obtaining such flows in the laboratory, an apparatus was built to produce large temperature differences (Delta T) up to 300 K in a gas confined between flat parallel plates. SF6 was used as the radiatively-active gas because its Planck absorption length is much shorter than that of any other common non-reactive gas. The NASA-Lewis 2.2 second drop tower was used to obtain reduced gravity in order to suppress buoyancy effects. To image the resulting flows, a laser shearing interferometer was employed. Initial results indicate the presence of flow that does not appear to be attributable to the residual flow resulting from buoyancy influences before the drop. For Delta T greater than 70 K, slight deformations in the interferometer fringes seen at lower Delta T became large unsteady swirls. Such behavior did not occur for radiatively-inactive gases, suggesting that a flow driven solely by radiation was obtained in SF6 and to a lesser extent in CO2 This was more pronounced at higher pressures and plate spacings, consistent with our scaling predictions.

Ronney, Paul D.↗

DOE OSTI2021

Hyperdiffusion of dust particles in a turbulent tokamak plasma

The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number $St\propto a_d/n_0$, with $a_d$ the dust radius and $n_0$ the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories $\Delta r^2$ is shown to depend on the ratio $Ku/St$, with $Ku\propto u_{rms}$ the Kubo number and $u_{rms}$ the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting $\Delta r^2\propto (Ku/St)^2t^3$, or $\Delta r^2\propto (u_{rms}n_0/a_d)^2t^3$. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.

dust↗

NASA NTRS1987

Some features of surface pressure fluctuations in turbulent boundary layers with zero and favorable pressure gradients

Measurements of surface pressure fluctuation spectra, coherence and convective wave speeds from zero and favorable pressure gradient turbulent boundary layers are reported for momentum Reynolds numbers from 3000 to 18,800. The acceleration parameter K is near 2 x 10 to the -7 power for the favorable pressure gradient flow. The outer variables, U sub e, tau sub w and delta sub 1 non-dimensionalize and collapse the spectra for the low to middle range of frequencies for most test cases. The grouping using the inner variable, U sub tau and gamma, collapse the spectra for the middle to high range of frequencies for all test cases. The value of p'/tau sub w was near 3.8 and 2.8 for the smallest values of d+ in the zero and favorable pressure gradient flows, respectively. The coherence exhibits a decay that is not exponential in some cases, but the Corcos similarity parameters omega Delta x/U sub c and omega Delta z/U sub c collapse the data for all test cases. The ratio of U sub c/U sub e increases with omega delta sub 1/U sub e up to omega delta sub 1/U sub e on the order of unity, where U sub c/U sub e becomes nearly constant. This was observed in the present results for both streamwise pressure gradient flows. The experimental results presented show good agreement with previous research.

Mcgrath, B. E.↗

NASA NTRS1982

Turbine heat transfer

Objectives and approaches to research in turbine heat transfer are discussed. Generally, improvements in the method of determining the hot gas flow through the turbine passage is one area of concern, as is the cooling air flow inside the airfoil, and the methods of predicting the heat transfer rates on the hot gas side and on the coolant side of the airfoil. More specific areas of research are: (1) local hot gas recovery temperatures along the airfoil surfaces; (2) local airfoil wall temperature; (3) local hot gas side heat transfer coefficients on the airfoil surfaces; (4) local coolant side heat transfer coefficients inside the airfoils; (5) local hot gas flow velocities and secondary flows at real engine conditions; and (6) local delta strain range of the airfoil walls.

Rohde, J. E.↗

NASA NTRS1985

Inferred flows of electric currents in solar active regions

Techniques to identify sources of major current systems in active regions and their channels of flow are explored. Measured photospheric vector magnetic fields together with high resolution white light and H-alpha photographs provide the data base to derive the current systems in the photosphere and chromosphere of a solar active region. Simple mathematical constructions of active region fields and currents are used to interpret these data under the assumptions that the fields in the lower atmosphere (below 200 km) may not be force free but those in the chromosphere and higher are. The results obtained for the complex active region AR 2372 are: (1) Spots exhibiting significant spiral structure in the penumbral filaments were the source of vertical currents at the photospheric surface; (2) Magnetic neutral lines where the transverse magnetic field was strongly sheared were channels along which a strong current system flowed; (3) The inferred current systems produced a neutral sheet and oppositely-flowing currents in the area of the magnetic delta configuration that was the site of flaring.

Ding, Y. J.↗

NASA NTRS1985

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

The surface temperature distributions due to thermocapillary convections in a thin liquid layer with heat fluxes imposed on the free surface were investigated. The nondimensional analysis predicts that, when convection is important, the characteristics length scale in the flow direction L, and the characteristic temperature difference delta T sub o can be represented by L and delta T sub o approx. (A2Ma)/1/4 delta T sub R, respectively, where L sub R and delta sub R are the reference scales used in the conduction dominant situations with A denoting the aspect ratio and Ma the Marangoni number. Having L and delta sub o defined, the global surface temperature gradient delta sub o/L, the global thermocapillary driving force, and other interesting features can be determined. Numerical calculations involving a Gaussian heat flux distribution are presented to justify these two relations.

Lai, C. L.↗

NASA NTRS1985

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

Lai, C.-L.↗

NASA NTRS1991

Late-time cosmological phase transitions

It is shown that the potential galaxy formation and large scale structure problems of objects existing at high redshifts (Z approx. greater than 5), structures existing on scales of 100 M pc as well as velocity flows on such scales, and minimal microwave anisotropies ((Delta)T/T) (approx. less than 10(exp -5)) can be solved if the seeds needed to generate structure form in a vacuum phase transition after decoupling. It is argued that the basic physics of such a phase transition is no more exotic than that utilized in the more traditional GUT scale phase transitions, and that, just as in the GUT case, significant random Gaussian fluctuations and/or topological defects can form. Scale lengths of approx. 100 M pc for large scale structure as well as approx. 1 M pc for galaxy formation occur naturally. Possible support for new physics that might be associated with such a late-time transition comes from the preliminary results of the SAGE solar neutrino experiment, implying neutrino flavor mixing with values similar to those required for a late-time transition. It is also noted that a see-saw model for the neutrino masses might also imply a tau neutrino mass that is an ideal hot dark matter candidate. However, in general either hot or cold dark matter can be consistent with a late-time transition.

Schramm, David N.↗