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The Role of Aspect Ratio and Beta in H-mode Confinement Scalings

Description: The addition of high power, low aspect ratio data from the NSTX and MAST experiments have motivated a new investigation of the effect of aspect ratio on confinement scaling. Various statistical methods, including those that incorporate estimates of measurement error, have been applied to datasets constrained by the standard set of criteria in addition to the range of ? and M(sub)eff appropriate to ITER operation. Development of scalings using engineering parameters as predictor variables results in ?-scaling coefficients that range from 0.38 to 1.29; the transformation of these scalings to physics variables results in an unfavorable dependence of ?? on ?, but a favorable dependence on ?. Because the low aspect ratio devices operate at low ?(sub)T and therefore high ?(sub)T, a strong correlation exists between ? and ?, and this makes scalings based on physics variables imprecise.
Date: October 20, 2005
Creator: Kaye, S. M.; Valovic, M.; Chudnovskiy, A.; Cordey, J. G.; McDonald, D.; Meakins, A. et al.
Partner: UNT Libraries Government Documents Department

Characteristics of Low-Aspect-Ratio Wings at Supercritical Mach Numbers

Description: "The separation of the flow over wings precipitated by the compression shock that forms as speeds are increased into the supercritical Mach number range has imposed serious difficulties in the improvement of aircraft performance. Three difficulties rise principally as a consequence of the rapid drag rise and the loss of lift that causes serious stability changes when the wing shock-stalls. Favorable relieving effects due to the three-dimensional flow around the tips were obtained and these effects were of such magnitude that it is indicated that low-aspect-ratio wings offer a possible solution of the problems encountered" (p. 1).
Date: 1949
Creator: Stack, John & Lindsey, W. F.
Partner: UNT Libraries Government Documents Department

Lift, Drag, and Pitching Moment of Low-Aspect-Ratio Wings at Subsonic and Supersonic Speeds : Plane Tapered Wing of Aspect Ratio 3.1 with 3-Percent-Thick, Biconvex Section

Description: "A wing-body combination having a plane tapered wing of aspect ratio 3.1 and 3-percent-thick, biconvex sections in streamwise planes has been investigated at both subsonic and supersonic Mach numbers. The lift, drag, and pitching moment of the model are presented for Mach numbers from 0.60 to 0.925 and 1.20 to 1.90 at a Reynolds number of 2.4 million. Results are also presented for Mach numbers from 0.60 to 0.925 and 1.20 to 1.50 at Reynolds numbers of 1.5 million and 3.8 million" (p. 1).
Date: January 30, 1951
Creator: Reese, David E. & Phelps, E. Ray
Partner: UNT Libraries Government Documents Department

Spherical Torus Center Stack Design

Description: The low aspect ratio spherical torus (ST) configuration requires that the center stack design be optimized within a limited available space, using materials within their established allowables. This paper presents center stack design methods developed by the National Spherical Torus Experiment (NSTX) Project Team during the initial design of NSTX, and more recently for studies of a possible next-step ST (NSST) device.
Date: January 18, 2002
Creator: Neumeyer, C.; Heitzenroeder, P.; Kessel, C.; Ono, M.; Peng, M.; Schmidt, J. et al.
Partner: UNT Libraries Government Documents Department

Stability and control characteristics of a free-flying model with an unswept wing of aspect ratio 3 (XS-3)

Description: The results of power-off force tests and flight tests of a model with a thin unswept low-aspect-ratio wing are presented. The tests were made with the flaps retracted and deflected. The effects on the lateral flight characteristics of decreasing directional stability were noted.
Date: November 15, 1948
Creator: Bennett, Charles V. & Hassell, James L., Jr.
Partner: UNT Libraries Government Documents Department

Inf-sup estimates for the Stokes problem in a periodic channel

Description: We derive estimates of the Babuska-Brezzi inf-sup constant {beta} for two-dimensional incompressible flow in a periodic channel with one flat boundary and the other given by a periodic, Lipschitz continuous function h. If h is a constant function (so the domain is rectangular), we show that periodicity in one direction but not the other leads to an interesting connection between {beta} and the unitary operator mapping the Fourier sine coefficients of a function to its Fourier cosine coefficients. We exploit this connection to determine the dependence of {beta} on the aspect ratio of the rectangle. We then show how to transfer this result to the case that h is C{sup 1,1} or even C{sup 0,1} by a change of variables. We avoid non-constructive theorems of functional analysis in order to explicitly exhibit the dependence of {beta} on features of the geometry such as the aspect ratio, the maximum slope, and the minimum gap thickness (if h passes near the substrate). We give an example to show that our estimates are optimal in their dependence on the minimum gap thickness in the C{sup 1,1} case, and nearly optimal in the Lipschitz case.
Date: December 10, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Inf-sup estimates for the Stokes problem in a periodic channel

Description: We derive estimates of the Babuska-Brezzi inf-sup constant {beta} for two-dimensional incompressible flow in a periodic channel with one flat boundary and the other given by a periodic, Lipschitz continuous function h. If h is a constant function (so the domain is rectangular), we show that periodicity in one direction but not the other leads to an interesting connection between {beta} and the unitary operator mapping the Fourier sine coefficients of a function to its Fourier cosine coefficients. We exploit this connection to determine the dependence of {beta} on the aspect ratio of the rectangle. We then show how to transfer this result to the case that h is C{sup 1,1} or even C{sup 0,1} by a change of variables. We avoid non-constructive theorems of functional analysis in order to explicitly exhibit the dependence of {beta} on features of the geometry such as the aspect ratio, the maximum slope, and the minimum gap thickness (if h passes near the substrate). We give an example to show that our estimates are optimal in their dependence on the minimum gap thickness in the C{sup 1,1} case, and nearly optimal in the Lipschitz case.
Date: June 27, 2007
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Approximating spheroid inductive responses using spheres

Description: The response of high permeability ({mu}{sub r} {ge} 50) conductive spheroids of moderate aspect ratios (0.25 to 4) to excitation by uniform magnetic fields in the axial or transverse directions is approximated by the response of spheres of appropriate diameters, of the same conductivity and permeability, with magnitude rescaled based on the differing volumes, D.C. magnetizations, and high frequency limit responses of the spheres and modeled spheroids.
Date: December 12, 2003
Creator: Smith, J. Torquil & Morrison, H. Frank
Partner: UNT Libraries Government Documents Department

Wind-Tunnel Investigation at Low Speeds of the Pitching Derivatives of Untapered Swept Wings

Description: Report presenting a wing-tunnel investigation in straight and pitching flow to determine the effects of independently varying aspect ratio and angle of sweep on the longitudinal rotary stability characteristics of a series of ten untapered wings. The investigation showed that an interdependent relationship existed between the effects of aspect ratio and sweep. Results regarding pitching moment due to pitching velocity and lift due to pitching velocity are provided.
Date: September 29, 1948
Creator: MacLachlan, Robert & Fisher, Lewis R.
Partner: UNT Libraries Government Documents Department

Characteristics of Low-Aspect Ratio Wings at Supercritical Mach Numbers

Description: Note presenting experiments to study the characteristics of low-aspect-ratio wings at supercritical Mach numbers. The experiments consisted of tests of wings of aspect ratios ranging from infinity to 2. The results indicate that the detrimental effects of compressibility in the supercritical speed range on the stability and performance of aircraft are alleviated to a great degree by the use of low-aspect-ratio lifting surfaces.
Date: August 1948
Creator: Stack, John & Lindsey, W. F.
Partner: UNT Libraries Government Documents Department

Modular Coil Design for the Ultra-low Aspect Ratio Quasi-axially Symmetric Stellarator MHH2

Description: A family of two field-period quasi-axisymmetric stellarators generally known as MHH2 with aspect ratios of only {approx}2.5 was found. These configurations have low field ripples and excellent confinement of {alpha} particles. This discovery raises the hope that a compact stellarator reactor may eventually be designed with the property of tokamak transport and stellarator stability. In this paper we demonstrate that smooth modular coils may be designed for this family of configurations that not only yield plasmas with good physics properties but also possess engineering properties desirable for compact power producing reactors. We show designs featuring 16 modular coils with ratios of major radius to minimum coil-plasma separation {approx}5.5, major radius to minimum coil-coil separation {approx}10 and the maximum field in coil bodies to the field on axis {approx}2 for 0.2 m{sup 2} conductors. These coils is expected to allow plasmas operated at 5% {beta} with {alpha} energy loss < 10% for a reactor of major radius <9 m at 5 T.
Date: September 27, 2005
Creator: Ku LP, the ARIES-CS Team
Partner: UNT Libraries Government Documents Department

Effect of Pressure with Wall Heating in Annular Two-Phase Flow

Description: The local distributions of void fraction, interfacial frequency and velocity have been measured in annular flow of R-134a through a wall-heated, high aspect ratio duct. High aspect ratio ducts provide superior optical access to tubes or irregular geometries. This work expands upon earlier experiments conducted with adiabatic flows in the same test section. Use of thin, transparent heater films on quartz windows provided sufficient electrical power capacity to produce the full range of two-phase conditions of interest. With wall vapor generation, the system pressure was varied from 0.9 to 2.4 MPa, thus allowing the investigation of flows with liquid-to-vapor density ratios covering the range of about 7 to 27, far less than studied in air-water and similar systems. There is evidence that for a given cross-sectional average void fraction, the local phase distributions can be different depending on whether the vapor phase is generated at the wall, or upstream of the test section inlet. In wall-heated flows, local void fraction profiles measured across both the wide and narrow test section dimensions illustrate the profound effect that pressure has on the local flow structure; notably, increasing pressure appears to thin the wall-bounded liquid films and redistribute liquid toward the edges of the test section. This general trend is also manifested in the distributions of mean droplet diameter and interfacial area density, which are inferred from local measurements of void fraction, droplet frequency and velocity. At high pressure, the interfacial area density is increased due to the significant enhancement in droplet concentration.
Date: October 31, 2000
Creator: Kumar, R. & Trabold, T.A.
Partner: UNT Libraries Government Documents Department

OPTIMUM PLASMA STATES FOR NEXT STEP TOKAMAKS

Description: OAK A271 OPTIMUM PLASMA STATES FOR NEXT STEP TOKAMAKS. The dependence of the ideal ballooning {beta} limit on aspect ratio, A, and elongation {kappa} is systematically explored for nearly 100% bootstrap current driven tokamak equilibria in a wide range of the shape parameters (A = 1.2-7.0, {kappa} = 1.5-6.0 with triangularity {delta} = 0.5). The critical {beta}{sub N} is shown to be optimal at {kappa} = 3.0-4.0 for all A studied and increases as A decreases with a dependence close to A{sup -0.5}. The results obtained can be used as a theoretical basis for the choice of optimum aspect ratio and elongation of next step burning plasma tokamaks or tokamak reactors.
Date: November 1, 2002
Creator: LIN-LIU,YR & STAMBAUGH,RD
Partner: UNT Libraries Government Documents Department

Electron cyclotron heating and current drive approach for low-temperature startup plasmas using O-X-EBW mode conversion

Description: A mechanism for heating and driving currents in very overdense plasmas is considered based on a double-mode conversion: Ordinary mode to Extraordinary mode to electron Bernstein wave. The possibility of using this mechanism for plasma buildup and current ramp in the National Spherical Torus Experiment is investigated.
Date: June 1, 1997
Creator: Batchelor, D.B. & Bigelow, T.S.
Partner: UNT Libraries Government Documents Department

Multiplicity of low-shear toroidal Alfven eigenmodes

Description: An enlarged spectrum of ideal toroidal Alfven eigenmodes is demonstrated to exist within a toroidicity-induced Alfven gap when the inverse aspect ratio is comparable to or larger than the value of the magnetic shear. This limit is appropriate for the low-shear region in most tokamaks, especially those with low aspect ratio. The new modes may be destabilized by fusion-product alpha particles more easily than the standard toroidal Alfven eigenmodes.
Date: January 1, 1996
Creator: Candy, J.; Breizman, B.N.; Van Dam, J.W. & Ozeki, T.
Partner: UNT Libraries Government Documents Department

Stable bootstrap-current driven equilibria for low aspect ratio tokamaks

Description: Low aspect ratio tokamaks can potentially provide a high ratio of plasma pressure to magnetic pressure {beta} and high plasma current I at a modest size, ultimately leading to a high power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma current. A high value of the Troyon factor {beta}{sub N} and strong shaping are required to allow simultaneous operation at high {beta} and high bootstrap current fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect ratio 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both {beta}{sub N} and {beta} are defined in terms of the vacuum toroidal field. Equilibria with {beta}{sub N} {ge} 8 and {beta} - 35% to 55% exist which are stable to n = {infinity} ballooning modes, and stable to n = 0, 1,2,3 kink modes with a conducting wall. The dependence of {beta} and {beta}{sub N} with respect to aspect ratio is also considered.
Date: August 1, 1996
Creator: Miller, R.L.; Lin-Liu, Y.R.; Turnbull, A.D.; Chan, V.S.; Pearlstein, L.D.; Sauter, O. et al.
Partner: UNT Libraries Government Documents Department

A numerical investigation of scale-up effects on coke yields of a thermal cracking Riser reactor

Description: A validated computational fluid dynamics (CFD) computer code, ICRKFLO, was used to investigate the scale-up effects on the coke yields of thermal cracking riser factors. Comparisons were made for calculated coke yields of pilot- and commercial-scales riser units. Computational results show that the riser aspect ratio, reaction temperature, particle residence time, and particle/oil ratio have major impacts on the coke yield. A computational experiment was conducted to determine optimal operating conditions for a conceptual design of a commercial-scale riser unit. This experiment showed that the performance loss in scale-up from pilot to commercial scale may be almost completely recovered through optimizing the operating conditions after scale-up using the CFD simulations as a guide.
Date: May 1, 1995
Creator: Chang, S.L.; Lottes, S.A. & Petrick, M.
Partner: UNT Libraries Government Documents Department

MECHANICAL TESTING OF EPON SU-8 WITH SIEM

Description: High aspect ratio structures are often present in MEMS devices and EPON SU-8 is often used to produce such structures because of its low cost. It is essential to know the mechanical properties of SU-8 for producing reliable MEMS products. However, the mechanical properties of SU-8 may depend on the manufacturing process and the size of the structure, which is in the micron domain. Hence, one needs to test specimens that are similar in size to MEMS structures to determine if the mechanical properties change with processing protocol. In this work, the authors applied the newly developed technique SIEM (Speckle Interferometry with Electron Microscopy) to the determination of SU-8's mechanical properties.
Date: June 8, 2000
Creator: CHANG,S.; WARREN,J. & CHIANG,F.P.
Partner: UNT Libraries Government Documents Department

Ohmic Flux Consumption During Initial Operation of the NSTX Spherical Torus

Description: The spherical tokamak (ST), because of its slender central column, has very limited volt-second capability relative to a standard aspect ratio tokamak of similar plasma cross-section. Recent experiments on the National Spherical Torus Experiment (NSTX) have begun to quantify and optimize the ohmic current drive efficiency in a MA-class ST device. Sustainable ramp-rates in excess of 5MA/sec during the current rise phase have been achieved on NSTX, while faster ramps generate significant MHD activity. Discharges with Ip exceeding 1MA have been achieved in NSTX with nominal parameters: aspect ratio A=1.3--1.4, elongation k=2--2.2, triangularity d=0.4, internal inductance li=0.6, and Ejima coefficient CE=0.35. Flux consumption efficiency results, performance improvements associated with first boronization, and comparisons to neoclassical resistivity are described.
Date: October 5, 2000
Creator: Menard, J.; LeBlanc, B.; Sabbagh, S.A.; Bell, M.; Bell, R.; Fredrickson, E. et al.
Partner: UNT Libraries Government Documents Department

Physics Issues in the Design of Low Aspect-Ratio, High-Beta, Quasi-Axisymmetric Stellarators

Description: Compact stellarators have the potential to combine the best features of the stellarator and the advanced tokamak, offering steady state operation without current drive and potentially without disruptions at an aspect ratio similar to tokamaks. A quasi-axisymmetric stellarator is developed that is consistent with the boot-strap current and passively stable to the ballooning, kink, Mercier, vertical, and neoclassical tearing modes at b=4.1 % without need for conducting walls or external feedback. The configuration has good flux surfaces and fast ion confinement. Thermal transport analysis indicates that the confinement should be similar to tokamaks of the same size, allowing access to the b-limit with moderate power. Coils have been designed to reproduce the physics properties. Initial analysis indicates the coils have considerable flexibility to manipulate the configuration properties. Simulations of the current evolution indicate the kink-mode can remain stable during the approach to h igh-beta.
Date: November 16, 2000
Creator: Zarnstorff, M.C.; Berry, L.A.; Boozer, A.; Brooks, A.; Cooper, W.A. & al, et
Partner: UNT Libraries Government Documents Department

Initial Physics Results From the National Spherical Torus Experiment

Description: The mission of the National Spherical Torus Experiment (NSTX) is to extend the understanding of toroidal physics to low aspect ratio (R/a approximately equal to 1.25) in low collisionality regimes. NSTX is designed to operate with up to 6 MW of High Harmonic Fast Wave (HHFW) heating and current drive, 5 MW of Neutral Beam Injection (NBI) and Co-Axial Helicity Injection (CHI) for non-inductive startup. Initial experiments focused on establishing conditions that will allow NSTX to achieve its aims of simultaneous high-bt and high-bootstrap current fraction, and to develop methods for non-inductive operation, which will be necessary for Spherical Torus power plants. Ohmic discharges with plasma currents up to 1 MA and with a range of shapes and configurations were produced. Density limits in deuterium and helium reached 80% and 120% of the Greenwald limit respectively. Significant electron heating was observed with up to 2.3 MW of HHFW. Up to 270 kA of toroidal current for up to 200 msec was produced noninductively using CHI. Initial NBI experiments were carried out with up to two beam sources (3.2 MW). Plasmas with stored energies of up to 140 kJ and bt =21% were produced.
Date: January 3, 2001
Creator: Kaye, S.M.; Bell, M.G.; Bell, R.E. & Bialek, J.
Partner: UNT Libraries Government Documents Department

Engineering design of the National Spherical Torus Experiment

Description: NSTX is a proof-of-principle experiment aimed at exploring the physics of the ``spherical torus'' (ST) configuration, which is predicted to exhibit more efficient magnetic confinement than conventional large aspect ratio tokamaks, amongst other advantages. The low aspect ratio (R/a, typically 1.2--2 in ST designs compared to 4--5 in conventional tokamaks) decreases the available cross sectional area through the center of the torus for toroidal and poloidal field coil conductors, vacuum vessel wall, plasma facing components, etc., thus increasing the need to deploy all components within the so-called ``center stack'' in the most efficient manner possible. Several unique design features have been developed for the NSTX center stack, and careful engineering of this region of the machine, utilizing materials up to their engineering allowables, has been key to meeting the desired objectives. The design and construction of the machine has been accomplished in a rapid and cost effective manner thanks to the availability of extensive facilities, a strong experience base from the TFTR era, and good cooperation between institutions.
Date: May 11, 2000
Creator: Neumeyer, C.; Heitzenroeder, P.; J. Spitzer, J. Chrzanowski & al, et
Partner: UNT Libraries Government Documents Department

Physics Results from the National Spherical Torus Experiment

Description: The National Spherical Torus Experiment (NSTX) at the Princeton Plasma Physics Laboratory is designed for studying toroidal plasma confinement at very low aspect-ratio, A = R/a = 0.85m/0.68m {approximately} 1.25, with cross-section elongation up to 2.2 and triangularity up to 0.5, for plasma currents up to 1 MA and vacuum toroidal magnetic fields up to 0.6 T on axis. Conducting plates are installed close to the plasma on the outboard side to stabilize kink modes. This should permit operation with toroidal-{beta} approaching 40% [1]. The plasmas will be heated by up to 6 MW High-Harmonic Fast Waves (HHFW) at a frequency 30 MHz and by 5 MW of 80 keV deuterium Neutral Beam Injection. Inductive plasma startup can be supplemented by the process of Coaxial Helicity Injection (CHI).
Date: June 13, 2000
Creator: Bell, M. G.
Partner: UNT Libraries Government Documents Department

Diagnostic Development on NSTX

Description: Diagnostics are described which are currently installed or under active development for the newly commissioned NSTX device. The low aspect ratio (R/a less than or equal to 1.3) and low toroidal field (0.1-0.3T) used in this device dictate adaptations in many standard diagnostic techniques. Technical summaries of each diagnostic are given, and adaptations, where significant, are highlighted.
Date: December 16, 1999
Creator: Roquemore, A.L.; Johnson, D.; Kaita, R. & al, et
Partner: UNT Libraries Government Documents Department