Bundle Geometry Research Articles

Optimal selection and positioning of conductors in multi-circuit overhead transmission lines using evolutionary computing

This paper presents a new approach for designing transmission lines to transmit more power in a narrower space. Multi-circuits lines are a good alternative to attain this objective. However, the optimum solution is not obtained by just positioning several regular single-circuit transmission lines in a single tower structure. Although double-circuit and multi-circuit transmission lines have been used over the last years, there are not many studies about non-conventional multi-circuit transmission lines. Thus, in this research a mathematical model to represent the problem related to increasing the surge impedance loading level of each circuit, and reducing the costs, the ROW and the height of the towers by optimizing their bundle geometry and conductor type by applying genetic algorithms is proposed. The overall transmission lines presented as examples have an improvement between 52% and 149% in the objective function.

Some properties of Riemannian geometry of the tangent bundle of Lie groups

We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam. We investigate Einstein-like, Ricci soliton, and Yamabe soliton structures on TG. Then we study some geometrical tensors on TG such as Cotton, Schouten, Weyl, and Bach tensors, and we also compute projective and concircular and m-projective curvatures on TG. Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.

Numerical investigation of flow-induced forces in the rods bundle

The numerical modelling of cross-flow through the rods bundle with triangular arrangement has been done to analyse flow-induced forces on the rod located in the middle of the bundle. Significant problems of rods in the bundle during the operational time of the system can be caused by the cross-flow. At the same time, it is known that the behaviour of the system is strongly related to many parameters such as bundle geometry, flow, rods support and others. Therefore, there is needed to investigate characteristics of each type of typical bundles. In this paper is analysed flow-induced hydrodynamic forces in closely-packed rods bundle using Computational Fluid Dynamics. Unsteady Reynolds Averaged Navier-Stokes equations were solved using Finite Volume discretization. The impact of the size of the computational domain and the number of rows in it was investigated to find the optimal case for the numerical modelling. Obtained results were compared with references from literature and experimental data. Reynolds number effect on the test cylinder depending on the domain size and the bundle asymmetry impact on flow-induced force were investigated as well.

Geometrodynamic Models of Continuum Mesomechanics: Dynamic Degrees of Freedom with Non-Eulerian Space-Time Evolution

The paper proposes a Lagrangian formalism for describing the space-time dynamics of complex continuum motion with addition variables—non-Eulerian dynamic degrees of freedom. The new variables are interpreted in terms of mechanics and geometry, and principles are suggested for their tracking in experiments. The formalism offers invariant tensor representations of Lagrangians in a system with an extended set of independent variables, explains the mechanical meaning of their respective coefficients, and gives Euler—Lagrange equations for this type of multidimensional variational problems. It is hypothesized that the bundle geometry of dynamic degrees of freedom is a generalized structure for fluctuation and other models of complex continuum evolution. The proposed method is analyzed as applied to dynamic equations of developed turbulence, and an interpretation on its basis is given to turbulence degeneration into unsteady Euler fields.

Assessment of heat transfer correlations in the sub-channels of proposed rod bundle geometry for supercritical water reactor

There are heat transfer correlations for heat transfer analysis in single tube geometries after several experimental and theoretical heat transfer studies in these single tube geometries. This is not the case for heat transfer analysis in rod bundle geometry with regard to proposed square fuel assembly of the Supercritical-Water-Cooled Reactor (SCWR) European Atomic Energy (EURATOM) design. Thus limited heat transfer studies exist on rod bundle geometry at supercritical pressures. Heat transfer correlations with accurate prediction capabilities of coolant and wall temperatures will be helpful in carrying out heat transfer studies at supercritical pressures. This paper presents the performance of twelve selected heat transfer correlations assessed on the 1/8th bare square fuel assembly of the SCWR EURATOM design using Simulation of Turbulent flow in Arbitrary Regions Computational Continuum Mechanics C ++ based code (STAR-CCM + CFD code). The obtained numerical results were compared with the results obtained by Waata numerical experimentation. Overall, the Cheng et al. correlation provided the most satisfying prediction for the wall temperatures in all the sub-channels and captured closely Wataa's Numerical data. The maximum wall temperature was obtained in sub-channel 9, the hottest sub-channel and exceeded the design limit 620 °C by 60 °C for the Cheng correlation. The difference in temperature between the hottest and coldest sub-channels 9 and 1 respectively was approximately 80 °C. It was found that Cheng correlation is best suited for heat transfer prediction in rod bundle geometry at supercritical pressures with regard to the proposed square fuel assembly of the SCWR EURATOM design. It was also found that the different numerical tools adopted for this study and Waata study were able to capture the trends of normal, enhanced and deteriorated heat transfer regimes normally observed at supercritical pressures. Nevertheless, experimental investigations involving rod bundles adopted in this study should be conducted to validate the results obtained numerically and address the inconsistency of the conclusions drawn when compared with Waata data and other similar studies.

Petrov type D equation on horizons of nontrivial bundle topology

We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov type D equation introduced and studied in previous works \cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view, solutions to that equation define isolated horizons embeddable in vacuum spacetimes (with cosmological constant) as Killing horizons to the second order such that the spacetime Weyl tensor at the horizon is of the Petrov type D. From the point of view of the $U(1)$-bundle structure, the equation couples a $U(1)$-connection, a metric tensor defined on the base manifold and the surface gravity in a very nontrivial way. We focus on the $U(1)$-bundles over $2$-dimensional manifolds diffeomorphic to $2$-sphere. We have derived all the axisymmetric solutions to the Petrov type D equation. For a fixed value of the cosmological constant they set a $3$-dimensional family as one could expect. A surprising result is, that generically our horizons are not embeddable in the known exact solutions to Einstein's equations. It means that among the exact type D spacetimes there exists a new family of spacetimes that generalize the properties of the Kerr- (anti) de Sitter black holes on one hand and the Taub-NUT spacetimes on the other hand.

Void fractions in a rod bundle geometry at high pressure–part Ⅰ: Experimental study

An investigation of void fraction measurement and prediction in a triangular-array rod bundle geometry was carried out under high pressure conditions (P = 5–9 MPa and G = 100–350 kg·m−2·s−1). The aims of this work were to expand the existing database and assess and modify the predictive models. The present paper is the Part I of this study, where the experimental work was presented to measure local, chordal and area-average void fractions respectively by a comprehensive measuring system composed by optical probes and gamma-ray densitometry. Non-uniform distribution of void fraction was investigated by local-to-local and local-to-average comparisons of void fractions. The results indicated that non-uniform distribution was not only related to the geometry, but also affected by the transition of flow regimes in rod bundle. The effects of pressure and mass flux on void fractions were also analyzed in detail in consideration of variations of fluid properties and drift-flux parameters. Additionally, both void fraction and interface frequency were compared with the flow regime map in TRACE code. The variation of interface frequency indicated that the droplet entrainment would occur in annular flow at high mass flux. In the Part Ⅱ of this study, an assessment of existing models for void fraction prediction in rod bundles was carried out according to the present data and a newly-developed drift-flux model was proposed.

Extension of the standard model of electroweak interaction and Dark Matter in the tangent bundle geometry

A generalized theory of electroweak interaction is developed based on the underlying geometrical structure of the tangent bundle with symmetries arising from transformations of tangent vectors along the fiber axis at a fixed spacetime point given by the SO(3,1) group. Electroweak interaction beyond the standard model (SM) is described by the little groups SU(2)otimes E^{c}(2) (E^{c}(2) is the central extended Euclidian group) which includes the group SU(2)otimes U(1) as a limit case. In addition to isospin and hypercharge, two additional quantum numbers arise which explain the existence of families in the SM. The connection coefficients yield the SM gauge potentials but also hypothetical gauge bosons and other hypothetical particles as a Higgs family as well as candidate Dark Matter particles are predicted. Several important consequences for the interaction between dark fermions, dark scalars or dark vector gauge bosons with each other and with SM Higgs and Z-bosons are described.

Experimental investigation on the influence of gap vortex streets on fluid-structure interactions in hexagonal bundle geometries

Gap vortex streets characterise many industrial applications involving rod bundle flows, such as heat exchangers and nuclear reactors. These structures, known as gap vortex streets, may excite the structural components of the bundle to resonance, leading to fretting and fatigue. This work aims to measure these coherent structures and the resulting displacement and oscillation frequency of the neighbouring rod, to provide unique data for fluid-structure interaction studies and to develop a general correlation for estimating the coherent structure’s wavelength. A water loop was built to host a hexagonal rod bundle. Fluorinated Ethylene Prophylene (FEP), a refractive index matching (RIM) material, was used to have undisturbed optical access in the area around the central rod. The flow was measured with Laser Doppler Anemometry (LDA) to detect coherent structures, while the vibrations were measured with a high speed camera. A new correlation for estimating the wavelength of the coherent structures is derived with dimensional analysis based on experimental evidence. The correlation is tested on different geometries: rectangular channels with single or half-rods, and two rod bundles, within the pitch-to-diameter ratio (P/D) range 1.02–1.2. Moreover fluctuations in the flow, given by the detected coherent structures, govern the structural response of the rod. The rod is excited to resonance if these fluctuations match twice the natural frequency of the rod.

Local liquid film behavior of annular two-phase flow on rod-bundle geometry – II. Modeling and verification

Local liquid film behavior of annular flow on rod bundle geometry is vital for accurate prediction of dryout. This paper is the Part II of a two-part study devoting to modelling and prediction of local liquid film behavior of annular flow on rod bundle geometry based on the unique feature of experimental phenomenon in Part I of this work. In this paper, a mechanism model is developed to predict the local liquid film thickness of annular two-phase flow on rod bundle geometry, in which the spatial distribution of gas flow in the cross-section of rod bundle is specified, and the local velocity of liquid film is obtained by employing the triangular relationship that taking into account properly the momentum and mass balances for the liquid film and the gas core. Ordinary differential equation (ODE) for the liquid film thickness is developed according to the Navier-Stokes equations for momentum balance of film flow on a rod to analyze the spatial characteristic of film thickness, in which the droplet entrainment-deposition process and the effect of circumferential shear stress are considered as boundary conditions during mass transfer at the gas-liquid interface. The present model predicts the experimental local liquid film thickness with the maximum relative error of ±10%. Circumferential coherent wave structure is formed by the combination effect of transversal stress gradient in the wave, droplet redeposition and film flow by circumferential shear stress, and the circumferential shear stress reduces the relative importance of the droplet redeposition with respect to the transversal stress gradient making the peripheral distribution of film thickness more uniform.

Long‐duration fully autonomous operation of rotorcraft unmanned aerial systems for remote‐sensing data acquisition

AbstractRecent applications of unmanned aerial systems (UAS) to precision agriculture have shown increased ease and efficiency in data collection at precise remote locations. However, further enhancement of the field requires operation over long periods of time, for example, days or weeks. This has so far been impractical due to the limited flight times of such platforms and the requirement of humans in the loop for operation. To overcome these limitations, we propose a fully autonomous rotorcraft UAS that is capable of performing repeated flights for long‐term observation missions without any human intervention. We address two key technologies that are critical for such a system: full platform autonomy to enable mission execution independently from human operators and the ability of vision‐based precision landing on a recharging station for automated energy replenishment. High‐level autonomous decision making is implemented as a hierarchy of master and slave state machines. Vision‐based precision landing is enabled by estimating the landing pad's pose using a bundle of AprilTag fiducials configured for detection from a wide range of altitudes. We provide an extensive evaluation of the landing pad pose estimation accuracy as a function of the bundle's geometry. The functionality of the complete system is demonstrated through two indoor experiments with duration of 11 and 10.6 hr, and one outdoor experiment with a duration of 4 hr. The UAS executed 16, 48, and 22 flights, respectively, during these experiments. In the outdoor experiment, the ratio between flying to collect data and charging was 1–10, which is similar to past work in this domain. All flights were fully autonomous with no human in the loop. To our best knowledge, this is the first research publication about the long‐term outdoor operation of a quadrotor system with no human interaction.

Monitoring of the Process of Immersion Optical Clearing of Collagen Bundles Using Optical Coherence Tomography

Future development of the method of immersion optical clearing of biological tissues—this method is widely used in the study of the morphology and pathologies of tissues in vitro and considered promising for in vivo applications in biophysical research and medicine—requires knowledge of the details of interaction of immersion liquids with the tissue, in particular, the characteristics both of the tissue dehydration process, which is caused by the osmotic effect of the immersion liquid, and the process of diffusion of the immersion agent (IA) into the tissue. The optical properties of skin dermis, eye sclera, tendon, and many other tissues are determined by the properties of collagen bundles, abundant in these tissues. In the present work, a convenient and reliable technique for monitoring the optical properties and geometry of collagen bundles in the course of their immersion clearing in vitro, based on optical coherence tomography (OCT), is proposed. The main advantage of this technique is that it allows one to monitor changes in the geometric and optical properties of the tissue simultaneously, without interrupting the natural course of the immersion clearing process, and to obtain reliable estimates of the characteristic times and rates of both the process of tissue dehydration and process of diffusion of the IA into the tissue.

Computational Fluid Dynamics Simulation of Flow-Mixing and Heat Transfer in 4 × 4 Rod Bundle With a Twist-Vane Spacer Grid

The clearance between fuel rods is maintained by spacer grid or helical wire wrap. Thermal-hydraulic characteristics inside fuel rod bundle are strongly influenced by the spacer grid geometry and the bundle pitch-to-diameter (P/D) ratio. This includes the maximum fuel temperature, critical heat flux, as well as pressure drop through the fuel bundle. An understanding of the detailed structure of flow mixing and heat transfer in a fuel rod bundle geometry is therefore an important aspect of reactor core design, both in terms of the reactor's safe and reliable operation, and with regard to optimum power extraction. In this study, computational fluid dynamics (CFD) simulations are performed to investigate isothermal turbulent flow mixing and heat transfer behavior in 4 × 4 rod bundle with twist-vane spacer grid with P/D ratio of 1.35. This work is carried out under International Atomic Energy Agency (IAEA) co-ordinated research project titled as “Application of Computational Fluid Dynamics (CFD) Codes for Nuclear Power Plant Design.” CFD simulations are performed using open source CFD code OpenFOAM. Numerical results are compared with experimental data from Korea Atomic Energy Research Institute (KAERI) and found to be in good agreement.

Physically Based Modeling of Hand-Assembled Wire Bundles for Accurate EMC Prediction

In this paper, a new modeling approach to generate wire bundles with geometry accurately mimicking the random displacements of the wires in real, hand-assembled bundles is proposed. To this end, the wire trajectories are modeled by three-dimensional (3-D) curves that retain continuity of the wire path and its first derivative, allow enforcing random fluctuations of wire position in the bundle cross section and controlling bundle density. An iterative algorithm involving both local and global perturbations of initially generated trajectories is used to prevent wire overlapping. As a whole, the proposed modeling approach is able to reproduce (through the use of a limited number of parameters) the main physical properties of real hand-assembled wire bundles. In order to get either deterministic or statistical estimates of the electromagnetic compatibility performance, the obtained bundle geometry can be easily imported into 3-D electromagnetic solvers or modeled as a multiconductor transmission line by approximating the nonuniform wire paths as a sequence of uniform cascaded sections. Application examples aimed at the prediction of crosstalk and field-to-wire coupling are used to prove the importance of accurate modeling of the bundle geometry and proper digitization of the bundle along its length for prediction at high frequencies of the electromagnetic noise induced in the terminal units.

Local liquid film behavior of annular two-phase flow on rod-bundle geometry-I. Experimental phenomenon and analysis

Local liquid film behavior of annular flow on rod bundle geometry is vital for accurate prediction of dryout. This paper is the first part of a two-part study concerning measurement and analysis of local liquid film behavior of annular flow on rod bundle geometry. In this paper, air-water annular flow experiments have been performed at different gas and liquid superficial velocity conditions in a 3 × 3 simulating PWR fuel rod-bundle test-section, and a conductivity-based technique is developed to measure the local dynamical liquid film thickness. Large amplitude disturbance waves appear at all low liquid phase superficial velocity conditions through down-burst mechanism caused by the highly turbulent gas flow and strong inter-subchannel interaction. Wave shapes do not change drastically by the variation of superficial liquid velocity since liquid flow tends to fill out the rod bundle corner due to the nature of annular flow. For disturbance wave dominating the film flow case, secondary flow in subchannel produces a circumferential force to shear off the liquid film, and the liquid droplets are redistributed, resulting in the liquid film thickness for the central region being thicker than that of gap region. Cross-correlation analysis indicates that gap and central regions are in possession of circumferential coherent wave structure with the same interfacial velocity, and the wave position for the central region is a little ahead of that for gap region since a higher wave has a longer leeward and upwind faces. The current study on local liquid film behaviors for rod bundle and the possible mechanisms that causing the discrepancies in local liquid film structures can be further used for the mechanism model development for the liquid film flow on the rod bundle. Part II of this study will introduce a mechanism model as an alternative approach to local liquid film thickness prediction for annular flow in rod bundle geometry.

Invariant analysis of the Reynolds stress tensor for a nuclear fuel assembly with spacer grid and split type vanes

Invariant analysis of the Reynolds stress tensor anisotropy can give an accurate and deep intuitive understanding of the turbulent structure of a turbulent flow. Lumley's triangle has proven to be a powerful representation of the invariant analysis of the second-order statistics collection provided by the Reynolds stress tensor. In the present work the spectral element code Nek5000 has been used to investigate the turbulent structure of the flow across a pressurized water reactor spacer grid with split type mixing vanes. Wall-resolved large eddy simulation of the flow in a prototypical rod bundle geometry at Re = 14,000 and P/D = 1.32 are performed and validated against particle image velocimetry data. The results are then used to perform an in-depth invariant analysis. The results show a reorganization of the Reynolds stresses components in the downstream region of the spacer grid. The mixing vanes orientation produces a symmetric behavior between sub-channels. The turbulent structure in the fully developed region has the typical behavior of fully-developed channel flow turbulence. When averaging the state across regions of the sub-channels, we observed a transition from disk-like turbulence in the mixing vanes region to rod-like turbulence in the fully developed region.

Development of a two-phase flow mass quality correlation in the post-dryout DFFB regime during reflood transients

A new semi-empirical two-phase flow mass quality correlation was developed for the post-dryout dispersed flow film boiling (DFFB) regime in a 7 × 7 rod bundle geometry. Starting from the fundamental physics describing the two-phase flow in the dispersed droplet flow regime, one-dimensional conservation governing equations were formulated for the liquid and vapor phases by considering a detailed characterization of the liquid droplet phase, based on which the liquid phase velocity was related to the key flow parameters. A scaling analysis was then performed within a sub-channel of the rod bundle to obtain an expression for the vapor drift velocity, from which a suitable relationship for the two-phase flow quality was derived using the drift flux model. It was found that the vapor drift velocity in the DFFB regime is affected by many variables including: the droplet size, velocities of the liquid and vapor phases, void fraction, vapor superheat and fluid properties, all of which are important in characterizing the dispersed droplet flow. Based on the results of the RBHT reflood tests, which simulate the reflood transients of a LWR during an accident scenario, a new mass quality correlation was developed that is applicable to the conditions with system pressure ranging from 138 to 414 kPa, rod bundle peak power between 0.98 and 1.97 kW/m, inlet liquid subcooling temperature from 11 to 83 K, and inlet flooding rate ranging from 0.0191 to 0.0508 m/s. Comparisons with experimental data indicated that the new correlation is able to predict the actual mass quality in the post-dryout two-phase flow regime with significantly improved accuracy not only for the rod bundle geometry but also for the tube geometry.

Elastohydrodynamics of swimming helices: Effects of flexibility and confinement

Motivated by bacterial transport through porous media, here we study the swimming of an actuated, flexible helical filament in both three-dimensional free space and within a cylindrical tube whose diameter is much smaller than the length of the helix. The filament, at rest, has a native helical shape modeled after the geometry of a typical bacterial flagellar bundle. The finite length filament is a free swimmer, and is driven by an applied torque as well as a counter-torque (of equal strength and opposite direction) that represents a virtual cell body. We use a regularized Stokeslet framework to examine the shape changes of the flexible filament in response to the actuation as well as the swimming performance as a function of the nondimensional Sperm number that characterizes the elastohydrodynamic system. We also show that a modified Sperm number may be defined to characterize the swimming progression within a tube. Finally, we demonstrate that a helical filament whose axis is not aligned with the tube axis can exhibit centering behavior in the narrowest tubes.

Laminar Natural Convection Heat Transfer From Vertical 7 × 7 Rod Bundles in Liquid Sodium

Laminar natural convection heat transfer from vertical 7 × 7 rod bundle in liquid sodium was numerically analyzed to optimize the thermal–hydraulic design for the bundle geometry with equilateral square array (ESA). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The code of the parabolic hyperbolic or elliptic numerical integration code series (PHOENICS) was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 7 × 7 heated rods for diameter (D = 0.0076 m), length (L = 0.2 m) and L/D (=26.32) were used in this work. The surface heat fluxes for each cylinder, which was uniformly heated along the length, were equally given for a modified Rayleigh number, (Raf,L)ij and (Raf,L)Nx×Ny,S/D, ranging from 3.08 × 104 to 4.28 × 107 (q = 1 × 104∼7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of ratio of the diagonal center-line distance between rods for bundle geometry to the rod diameter (S/D) for vertical 7 × 7 rod bundle were ranged from 1.8 to 6 on the bundle geometry with ESA. The spatial distribution of average Nusselt numbers for a vertical single cylinder of a rod bundle, (Nuav)ij, and average Nusselt numbers for a vertical rod bundle, (Nuav,B)Nx×Ny,S/D, were clarified. The average values of Nusselt number, (Nuav)ij and (Nuav,B)Nx×Ny,S/D, for the bundle geometry with various values of S/D were calculated to examine the effect of array size, bundle geometry, S/D, (Raf,L)ij and (Raf,L)Nx×Ny,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)Nx×Ny,S/D value under the condition of S/D = constant was examined. The general correlations for natural convection heat transfer from a vertical Nx×Ny rod bundle with the ESA and equilateral triangle array (ETA), including the effects of array size, (Raf,L)Nx×Ny,S/D and S/D were derived. The correlations for vertical Nx×Ny rod bundles can describe the theoretical values of (Nuav,B)Nx×Ny,S/D for each bundle geometry in the wide analytical range of S/D (=1.8–6) and the modified Rayleigh number ((Raf,L)Nx×Ny,S/D = 3.08 × 104 to 4.28 × 107) within −9.49 to 10.6% differences.

Effect of bundle geometries on the detonation velocity behaviors in stoichiometric hydrogen-air mixture

In this study, the effects of pipe bundle geometries on the detonation velocity behaviors are examined systematically in a circular tube with 6 m long and an inner diameter of 90 mm. The tube bundle structures are created by inserting several small pipes (20 mm outer diameter, 2 mm wall thickness) into the tube. Three different bundle structures can be obtained by varying the number of small pipes n of 3, 4 and 5. The ionization probes and pressure transducers (PCB102B06) are used to determine the average velocity while the smoked foil technique is employed to register the detonation cellular structures. The experimental results indicate that detonation can propagate at about the theoretical CJ velocity with a small deficit when the initial pressure (P0) is greater than the critical value (Pc). The average velocity gradually decreases and deviates from the CJ value as the approaches of critical condition by gradually decreasing the initial pressure. The failure of detonation can be observed below the critical pressure. In the smooth tube, three different propagation mechanisms can be observed, i.e., super-critical condition, critical condition and sub-critical condition. After the bundle structures are introduced into the tube, a sudden velocity drop is seen at the critical pressure. Moreover, the detonation re-initiation phenomenon occurs with the velocity from the flame back to over-driven state quickly. Of note is that nearly no difference is seen between n = 3 and 4. However, in the case of n = 5, the detonation velocity experiences a more violent fluctuation with a high frequency, and the critical pressure is also increased to 28 kPa sharply. Finally, the critical condition analysis of detonation successful transmission is performed. The critical condition can be quantified as DH/λ > 1. However, the critical values of DH/λ are not uniform among various bundle geometries, but in a small range, i.e., from 1.52 to 1.97.