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At least 523 records · Page 29

Subleading corrections in $ \mathcal{N} $ = 3 Gaiotto-Tomasiello theory

We study subleading corrections to the genus-zero free energy of the N = 3 Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar resolvent, up to exponentially suppressed corrections. In the particular case that the two gauge groups in the quiver are of equal rank, we find an explicit (perturbative) expansion for the free energy. If, additionally, both groups have equal levels, then we find the full expression for the genus-zero free energy, modulo exponentially suppressed corrections. We also verify our results numerically.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Calculation of the lateral-dynamic stability of aircraft

Graphs and formulas are given with the aid of which all the aerodynamic coefficients required for computing the lateral dynamic stability can be determined. A number of numerical examples are given for obtaining the stability derivatives and solving the characteristic-stability equation. Approximate formulas are derived with the aid of which rapid preliminary computations may be made and the stability coefficients corrected for certain modifications of the airplane. A derivation of the lateral-dynamic-stability equations is included.

STABILITY, LATERAL - DYNAMIC↗

A pressure based method for the solution of viscous incompressible turbomachinery flows

A new technique was developed for the solution of the incompressible Navier-Stokes equations. The numerical technique, derived from a pressure substitution method (PSM), overcomes many of the deficiencies of the pressure correction method. This technique allows for the direct solution of the actual pressure in the form of a Poisson equation which is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. Two dimensional internal flows are computed with this method. The prediction of cascade performance is presented. The extention of the pressure correction method for the solution of three dimensional flows is also presented.

Hobson, Garth Victor↗

Recent Turbulence Model Advances Applied to Multielement Airfoil Computations

A one-equation linear turbulence model and a two-equation nonlinear explicit algebraic stress model (EASM) are applied to the flow over a multielement airfoil. The effect of the K-epsilon and K-omega forms of the two-equation model are explored, and the K-epsilon form is shown to be deficient in the wall-bounded regions of adverse pressure gradient flows. A new K-omega form of EASM is introduced. Nonlinear terms present in EASM are shown to improve predictions of turbulent shear stress behind the trailing edge of the main element and near midflap. Curvature corrections are applied to both the one- and two-equation turbulence models and yield only relatively small local differences in the flap region, where the flow field undergoes the greatest curvature. Predictions of maximum lift are essentially unaffected by the turbulence model variations studied.

Rumsey, Christopher L.↗

Another look at North Sea pole tide dynamics

The mechanism proposed by Wunsch (1974) to explain pole tide observations in the North Sea is evaluated. Wunsch's equations governing pole tide in the North Sea are presented, and solutions for correcting the depth, stream function, and deviation of the tidal height from the equilibrium values are described. The similarity between the Stokes paradox and the tidal equations of the North Sea, and the need for inclusion of inertial terms in the tidal equations are discussed.

Dickman, S. R.↗

Prediction of Airfoil Characteristics With Higher Order Turbulence Models

This study focuses on the prediction of airfoil characteristics, including lift and drag over a range of Reynolds numbers. Two different turbulence models, which represent two different types of models, are tested. The first is a standard isotropic eddy-viscosity two-equation model, and the second is an explicit algebraic stress model (EASM). The turbulent flow field over a general-aviation airfoil (GA(W)-2) at three Reynolds numbers is studied. At each Reynolds number, predicted lift and drag values at different angles of attack are compared with experimental results, and predicted variations of stall locations with Reynolds number are compared with experimental data. Finally, the size of the separation zone predicted by each model is analyzed, and correlated with the behavior of the lift coefficient near stall. In summary, the EASM model is able to predict the lift and drag coefficients over a wider range of angles of attack than the two-equation model for the three Reynolds numbers studied. However, both models are unable to predict the correct lift and drag behavior near the stall angle, and for the lowest Reynolds number case, the two-equation model did not predict separation on the airfoil near stall.

Gatski, Thomas B.↗

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Taylor, Arthur C., III↗

Orbit improvement from satellite imaging data obtainable from outer planet missions.

Equations of motion are established for a dynamical system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in a simultaneous orbit correction of n interacting bodies, a notably compact set of variational equations is derived. The above system of differential equations is integrated numerically on a computer. Spacecraft-satellite direction measurements accurate to plus or minus 10 sec were simulated along three representative trajectories (Mariner/Jupiter/Saturn 1977 missions) approaching Io, Titan, and Iapetus to within 41000, 13000, and 7000 km, respectively. The paper concludes with a brief discussion of the need for future work on the orbits of the satellites of the outer planets.

Aksnes, K.↗

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work have been limited. Here, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. Boiling involves both fluid flow and heat transfer and thus requires the solution of the Navier-Stokes and the energy equations. The numerical method is based on writing one set of governing transport equations which is valid in both the liquid and vapor phases. This local, single-field formulation incorporates the effect of the interface in the governing equations as source terms acting only at the interface. These sources account for surface tension and latent heat in the equations for conservation of momentum and energy as well as mass transfer across the interface due to phase change. The single-field formulation naturally incorporates the correct mass, momentum and energy balances across the interface. Integration of the conservation equations across the interface directly yields the jump conditions derived in the local instant formulation for two-phase systems. In the numerical implementation, the conservation equations for the whole computational domain (both vapor and liquid) are solved using a stationary grid and the phase boundary is followed by a moving unstructured two-dimensional grid. While two-dimensional simulations have been used for preliminary studies and to examine the resolution requirement, the focus is on fully three-dimensional simulations. The numerical methodology, including the parallelization and grid refinement strategy is discussed, and preliminary results shown. For buoyancy driven flow, the heat transfer is in good agreement with experimental correlations. The changes when gravity is turned off and/or fluid shear is added are discussed, as well as the difference between simulations of a layer freely releasing bubbles versus simulations using only one wavelength initial perturbation. Figure 1 shows the early stages of the formation of a three-dimensional bubble from a thin vapor layer. The boundary conditions are periodic in the x and y direction, the bottom is a hot and the top allows a free outflow. The jagged edge of the surface close to the bottom of the computational domain is due to some of the surface elements being on the other side of the domain and some elements not plotted by our plotting routine. In the second figure, we show the temperature distribution through two perpendicular planes.

Tryggvason, G.↗

Sharply curved turn around duct flow predictions using spectral partitioning of the turbulent kinetic energy and a pressure modified wall law

Computational predictions of turbulent flow in sharply curved 180 degree turn around ducts are presented. The CNS2D computer code is used to solve the equations of motion for two-dimensional incompressible flows transformed to a nonorthogonal body-fitted coordinate system. This procedure incorporates the pressure velocity correction algorithm SIMPLE-C to iteratively solve a discretized form of the transformed equations. A multiple scale turbulence model based on simplified spectral partitioning is employed to obtain closure. Flow field predictions utilizing the multiple scale model are compared to features predicted by the traditional single scale k-epsilon model. Tuning parameter sensitivities of the multiple scale model applied to turn around duct flows are also determined. In addition, a wall function approach based on a wall law suitable for incompressible turbulent boundary layers under strong adverse pressure gradients is tested. Turn around duct flow characteristics utilizing this modified wall law are presented and compared to results based on a standard wall treatment.

Santi, L. Michael↗

Effects of truncation in modal representations of thermal convection

The Galerkin equations for convection in a sphere are examined to determine which physical processes are neglected by the severe truncation of the equations of motion. It is demonstrated that the gross features of the flow are affected by truncation in the horizontal direction, with all of the models considered being well resolved in the vertical direction. One of the effects of truncation is to enhance the high-wave number end of the kinetic energy and thermal variance spectra. The examples cited indicate that as long as the kinetic energy spectrum decreases with wave number, a truncation gives a qualitatively correct solution. Conclusions are tested by calculating solutions to the equations of motion for several values of the Rayleigh number and the limit of horizontal spatial resolution.

Marcus, P. S.↗

Textbook Multigrid Efficiency for the Steady Euler Equations

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

Roberts, Thomas W.↗

Physics-Informed Deep Learning-Based Proof-of-Concept Study of a Novel Elastohydrodynamic Seal for Supercritical CO 2 Turbomachinery

Supercritical carbon dioxide (sCO 2 ) power cycles show promising potential of higher plant efficiencies and power densities for a wide range of power generation applications such as fossil fuel power plants, nuclear power production, solar power, and geothermal power generation. sCO 2 leakage through the turbomachinery has been one of the main concerns in such applications. To offer a potential solution, we propose an elastohydrodynamic (EHD) seal that can work at elevated pressures and temperatures with low leakage and minimal wear. The EHD seal has a very simple, sleeve-like structure, wrapping on the rotor with minimal initial clearance at micron levels. Here, in this work, a proof-of-concept study for the proposed EHD seal was presented by using the simplified Reynolds equation and Lame’s formula for the fluid flow in the clearance and for seal deformation, respectively. The set of nonlinear equations was solved by using both the conventional Prediction–Correction (PC) method and modern Physics-Informed Neural Network (PINN). It was shown that the physics-informed deep learning method provided good computational efficiency in resolving the steep pressure gradient in the clearance with good accuracy. The results showed that the leakage rates increased quadratically with working pressures and reached a steady-state at high-pressure values of 15~20 MPa, where Q = 300 g/s at 20 MPa for an initial seal clearance of 255 μm. This indicates that the EHD seal could be tailored to become a potential solution to minimize the sCO 2 discharge in power plants.

30 DIRECT ENERGY CONVERSION↗

Flux-corrected transport techniques for transient calculations of strongly shocked flows

New flux-corrected transport algorithms are described for solving generalized continuity equations. These techniques were developed by requiring that the finite difference formulas used ensure positivity for an initially positive convected quantity. Thus FCT is particularly valuable for fluid-like problems with strong gradients or shocks. Repeated application of the same subroutine to mass, momentum, and energy conservation equations gives a simple solution of the coupled time-dependent equations of ideal compressible fluid dynamics without introducing an artificial viscosity. FCT algorithms span Eulerian, sliding-rezone, and Lagrangian finite difference grids in several coordinate systems. The latest FCT techniques are fully vectorized for parallel/pipeline processing.

Boris, J. P.↗

The determination of transport parameters of minority carriers in n-p junctions by means of an electron microscope - Critique of recent developments

It has recently been shown that amplitude modulated electron beams provide a novel means for the determination of minority carrier lifetimes, diffusion lengths, etc., in n-p junctions. In this paper it is shown that: (1) a recently published analysis based on a cylindrically symmetric configuration is incorrect, (2) the correct approach leads to a system of dual integral equations for which the formal solution is given, (3) in general, the short circuit current can only be determined by means of extensive computer calculations except in the case of large front surface recombination velocities, and (4) the difficulties encountered with cylindrically symmetric configurations (circular ohmic contacts and the like) are completely avoided with a choice of a planar geometry since simple closed form expressions for the short circuit current are readily available in this case.

Von Roos, O.↗

A natural conservative flux difference splitting for the hyperbolic systems of gasdynamics

Gasdynamic hyperbolic systems are treated by a novel conservative flux difference splitting upwind method which is applicable to explicit or implicit and iterative or direct schemes, for marching in time or space with the Euler or compressible Navier-Stokes equations. The method is able to capture sharp shocks correctly by maintaining global conservation. The embedded characteristics formulation is cast in the volumetric internal energy primitive variable, which is effective for real as well as perfect gases. Higher order upwind formulae are constructed from the distribution of pieces of the simple internal flux difference splitting, and the method reverts to first order at the appropriate points in order not to violate the domain of dependence by differencing across discontinuities. At insignificant computational overhead, switching is done by simple algebraic extensions of the truth functions that determine upwind direction for the first order scheme.

Lombard, C. K.↗

New Directions in Asymptotically Stable Finite-dimensional Adaptive Control of Linear Distributed Parameter Systems

Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.

Balas, M. J.↗

MAGSAT scalar anomaly map of South America

A scalar magnetic anomaly map was prepared for South America and adjacent marine areas directly from original MAGSAT orbits. The preparation of the map poses special problems, notably in the separation of external field and crustal anomalies, and in the reduction of data to a common altitude. External fields are manifested in a long-wavelength ring current effect, a medium-wavelength equatorial electrojet, and short-wavelength noise. The noise is reduced by selecting profiles from quiet periods, and since the electrojet is confined primarily to dusk profiles, its effect is minimized by drawing the data set from dawn profiles only. The ring current is corrected through the use of the standard ring current equation, augmented by further filtering with a Butterworth bandpass filter. Under the assumption that the time-variant ring current is best removed when a replication of redundant profiles is achieved, a test set of 25 groups of 3 nearly coincident orbits per group is set up for filtering with a range of long-wavelength cutoffs to determine which cutoff best replicates the residual profiles. Altitude differences are then normalized by an inversion of the profile data onto a grid of equivalent point dipoles, and recalculated at an altitude of 350 km. The resulting map, when compared to the 2 deg averaged map, shows more coherent anomalies, with notable differences in the region affected by the electrojet.

Ridgway, J. R.↗