Bundle Geometry Research Articles

Jet bundle geometry of scalar field theories

Jet bundle geometry of scalar field theories

Numerical simulation of corium flow through rod bundle and/or debris bed geometries with a model based on Lattice Boltzmann method

A new model is proposed to investigate the relocation and the distribution of hot corium flows in different configurations (rod bundle, porous debris bed) representative of a severe accident in a Light Water Reactor (LWR). Our model relies on the coupling between a modified Lattice Boltzmann Method (LBM), called Free-Surface LBM, that solves hydrodynamics of unsaturated corium and a Finite Volume Method (FVM) that solves heat transfers. Corium solidification and melting are addressed by implementing a correlation between the temperature and the viscosity. Several simulations on representative elementary volumes were performed, varying configurations (debris bed, rod bundle with and without grid). From the results, it is possible to capture important details of the flow at a scale lower than the pore scale and, at the same time, it is possible to take into account the average effects at the scale of several pores. Presented as a proof of concept these preliminary studies show the interest of this kind of CFD approach to identify which parameters at microstructure scale can potentially govern the corium relocation kinetics at macroscopic scale. It will provide useful information that might improve core degradation models in severe accident codes, such as ASTEC.

Effect of artificial lung fiber bundle geometric design on micro‐ and macro‐scale clot formation

AbstractThe hollow fiber membrane bundle is the functional component of artificial lungs, transferring oxygen to and carbon dioxide from the blood. It is also the primary location of blood clot formation and propagation in these devices. The geometric design of fiber bundles is defined by a narrow set of parameters that determine gas exchange efficiency and blood flow resistance, principally: fiber packing density, path length, and frontal area. These same parameters also affect thrombosis. This study investigated the effect of these parameters on clot formation using 3D printed flow chambers that mimic the geometry and blood flow patterns of fiber bundles. Hollow fibers were represented by an array of vertical micro‐rods (380 μm diameter) arranged with three packing densities (40%, 50%, and 60%) and two path lengths (2 and 4 cm). Blood was pumped through these devices corresponding to three mean blood flow velocities (16, 20, and 25 cm/min). Results showed that (1) clot formation decreases dramatically with decreasing packing density and increasing blood flow velocity, (2) clot formation at the outlet of the fiber bundle enhances deposition upstream, and consequently (3) greater path length provides greater clot‐free fiber surface area for gas exchange than a shorter path length. These results can help guide the design of less thrombogenic, more efficient artificial lung designs.

The dressing field method for diffeomorphisms: a relational framework

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M) -invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic ‘extended bracket’ for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Frölicher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M) -theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent ( diff(M) ) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M) -invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the ‘dressed’ (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.

Algebra and geometry of irreducible toric vector bundles of rank n on [formula omitted]

We construct a presentation for the Cox ring of the projectivization PE of any rank n irreducible toric vector bundle on Pn. We use this presentation to show that PE always satisfies Fujita's freeness and ampleness conjectures.

Improvement of macroscopic turbulence model for subchannel analysis in the rod bundle array

The PRIUS program was established to generate an experimental database for the 6 × 4 and 12 × 6 rod bundle geometry. The database will be used to address the subchannel and CFD code analysis required for modeling and validation. This is necessary because Small Break Loss of Coolant Accident (SBLOCA) and Intermediate Break Loss of Coolant Accident (IBLOCA) present three-dimensional phenomena in the core due to the radial power profile, crossflow, and diffusion-dispersion. Therefore, specific experimental programs are required, especially during core reflooding, to investigate the large-scale three-dimensional effects. However, validating each sensitive model of the code separately in the presence of 3D effects is not possible due to the inability to implement instrumentation at high pressure and temperature steam-water flow conditions. The PRIUS test program uses a single-phase flow test to simulate a non-homogeneous velocity distribution and provide information on crossflow with radial mixing effects between subchannels. The CUPID code, which uses a macroscopic turbulence model, has been validated using the PRIUS-II experimental database. Existing macroscopic turbulence models were also validated for their prediction capabilities with different inlet flow conditions. However, the validation revealed significant errors in the shear region between subchannels. An improved macroscopic turbulence model showed promising results in predicting turbulence kinetic energy in porous media analysis.

Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces

We classify equivariant harmonic maps of the complex projective spaces CPm into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective line, we have one parameter family of those maps. (This result is already shown in [2] and [4] in other ways). However, when m≧2, we will obtain the rigidity results.

Comparative analysis of tube designs in heat exchangers: A numerical simulation study for enhanced thermal-flow efficiency, "optimizing wavy tubes bundle geometries for enhanced heat transfer in underwater applications"

With the growing challenges of heat transfer in marine vehicles and underwater power stations, the demand for an effective tube heat exchanger has surged. Numerical simulations were conducted on the constant, laminar flow of an incompressible viscous fluid inside a wavy tube while keeping the wall temperature consistent. The laminar flow was modeled in two dimensions using ANSYS FLUENT 19.2. For the water fluid model, an integrated algorithm was used to link the pressure and velocity fields. Primarily examined were circular tube banks organized in a staggered arrangement. The primary equations were approached via a finite volume method based on a combined technique. This study aimed to evaluate and contrast the heat exchange and flow traits of four distinct tube designs: asteroid (ASTB), hypotrochoid (HTB), Wavy edge circle (WCTB), and mixed bundle (MBT). The influence of tube design on a heat exchanger’s thermal-flow efficiency was measured across Reynolds numbers ranging from 100 to 400. The results indicated an improved Colburn factor and a decrease in both the friction factor and tube performance for all scenarios examined. Three key metrics determined the optimal tube design: the performance evaluation criterion (PEC), the global performance criterion (GPC), and the average Nusselt number (Nu). Regardless of the Reynolds number, the conventional HC had the least efficient PEC, while the STB registered the peak PEC value. The highest GPC was attained with the STB. Nu values remained relatively consistent for ASTB, HTB, WCTB, and MBT. In evaluating the average Nusselt number, the ASTB outperformed the STB (92–106% higher), HTB (36–48% higher), WCTB (21–32% higher), and MBT (57–64% higher).

Thermal-hydraulic analysis of a full-scale lead-bismuth cooled fast reactor core considering inter-wrapper flow

The Lead-bismuth cooled Fast Reactors (LFR) utilizes wrapped hexagonal fuel assemblies arranged in a honeycomb pattern. The inter-wrapper flow (IWF) between adjacent assemblies has a significant influence on the core thermal-hydraulics. In this paper, the LFR core assembly analysis model, inter-wrapper flow and heat transfer model, and multi-scale coupling analysis model were developed and were implemented into the previously self-developed subchannel-level three-dimensional thermal hydraulic analysis code CorTAF-LBE for whole core of LFR, which is based on the OpenFOAM computational fluid dynamics simulation platform. The inter-wrapper flow and heat transfer model was validated against the KALLA-IWF experiment. Whole core steady state operating condition and low flow rate condition simulations were performed with reference to the 19-rod bundle geometry from KALLA laboratory and typical LFR core assembly arrangement. The whole core steady state distribution laws of key thermal-hydraulic parameters were obtained, and the influence of low flow rate operation on safety parameters such as cladding and pellet temperatures was analyzed. Under low flow rate operating conditions, the IWF heat transfer was accounted for 4.87% of the core thermal power, which was 315.6 kW higher than that under normal operating conditions, playing an important role in core heat removal and safe operation. This work provides important insights into LFR core design and the assessment of the role of IWF under low flow rate conditions.

Multimedia Photogrammetry for Automated 3D Monitoring in Archaeological Waterlogged Wood Conservation

Abstract. This study addresses the challenges inherent in preserving archaeological waterlogged wood, which is prone to deformation and decay if not stabilized immediately after recovery. Conventional preservation methods, such as impregnation with polyethylene glycol (PEG) solutions, often result in undesirable dimensional changes. To obtain exact spatio-temporal information on the deformations during the conservation process, a photogrammetric monitoring system, utilizing a stereo camera facing from air into the liquid, attached to an automated biaxial measurement unit is proposed. Special target heads were developed and attached to the wood to provide deformation points. Refraction correction was applied to the imaging model by ray tracing, and indirect flat lighting was used to mitigate turbidity. The system observed logs from a wooden track from the first century, subject to conservation. Subject of investigation were the influence of refraction negligence and scale definition in a bundle geometry, similar to bathymetric aerial setups. Results show that refraction correction is imperative for good results. Furthermore, scale definition with highly accurately determined scale bars and inclusion of relative orientation constraints provide further accuracy improvements.

Graded jet geometry

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of Lagrangian mechanics and the calculus of variations. It is thus only natural to require their generalization in geometry of Z-graded manifolds and vector bundles.Our aim is to construct the k-th order jet bundle JEk of an arbitrary Z-graded vector bundle E over an arbitrary Z-graded manifold M. We do so by directly constructing its sheaf of sections, which allows one to quickly prove all its usual properties. It turns out that it is convenient to start with the construction of the graded vector bundle of k-th order (linear) differential operators DEk on E. In the process, we discuss (principal) symbol maps and a subclass of differential operators whose symbols correspond to completely symmetric k-vector fields, thus finding a graded version of Atiyah Lie algebroid. Necessary rudiments of geometry of Z-graded vector bundles over Z-graded manifolds are recalled.

Notes on the geometry of cotangent bundle and unit cotangent sphere bundle

Let $(\mathtt{N},\mathfrak{g})$ be a Riemannian manifold, by using the musical isomorphisms ♪ and $\natural$ induced by $\mathfrak{g}$, we built a bridge between the geometry of the tangent bundle $\mathtt{TN}$ (resp. the unit tangent sphere bundle $\mathtt{T}_{1}\mathtt{N}$) equipped with the Sasaki metric $\mathfrak{g}_{S}$ (resp. the induced Sasaki metric $\bar{\mathfrak{g}}_{S}$) and that of the cotangent bundle $\mathtt{T}^{\ast}\mathtt{N}$ (resp. the unit cotangent sphere bundle $\mathtt{T}_{1}^{\ast}\mathtt{N}$) endowed with the Sasaki metric $\mathfrak{g}_{\widetilde{S}}$ (resp. the induced Sasaki metric $\tilde{\mathfrak{g}}_{\widetilde{S}}$). Moreover, we prove that $\mathtt{T}_{1}^{\ast}\mathtt{N}$ carries a contact metric structure and study some of its proprieties.

Experimental investigation of local boron concentration in a 2 × 2 rod bundle channel under subcooled boiling flow

During the operation of pressured water reactors (PWRs), subcooled boiling occurring at the upper-span region of the fuel assembly causes migration of the boron concentration in the coolant. The distribution of boron concentration in the coolant is essential to predict the boron hideout within the Corrosion Related Unidentified Deposition (CRUD) and crud-induced power shift (CIPS). However, experimental data on local boron concentration of rod bundle geometries in subcooled boiling conditions are not available. In this paper, a vertical test channel is constructed to determine the distribution of the local boron concentration of a 2 × 2 rod bundle channel under subcooled boiling conditions. The bubble-boron concentration simultaneous measurement device is developed and calibrated to measure the local two-phase flow parameters and boron concentrations under the subcooled boiling conditions. The experimental results indicate that the boron concentration is highest near the narrowest gap and decreases toward the subchannel center or subchannel wall. The boron concentration increases linearly with void fraction in the central subchannel, while the boron concentration first increases rapidly and then slowly in the wall channel. The underlying mechanism for the boron concentration distribution is revealed by considering the boron enrichment on the bubble–liquid interface, diffusion of the boron concentration, boron mixing induced by bubble wake, and boron dilution caused by bubble condensation. On the basis of that, a boron equilibrium model considering the evaporation and condensation of bubbles is developed. The experimental data is used to support the development and validation of the boron equilibrium model. The comparison results show that the boron equilibrium model can predict the performance of the boron concentration in the rod bundle channel with an accuracy of 20 %.

Multiscale Modeling of Flow in Rod Bundles: From Direct Numerical Simulation and Subchannel to Coarse-Mesh CFD

Fast and accurate evaluation of flow and heat transfer phenomena in rod bundles is a problem of long-standing interest in nuclear engineering. Computational fluid dynamics (CFD) can provide accurate but relatively time-intensive estimates, such that simulations of very long transients with high spatial detail are infeasible. On the other hand, subchannel codes require relatively low computational time and can provide pin-level estimates, but have substantial empiricism in evaluating aspects such as crossflows and turbulent mixing coefficients. A multiscale method (SC+) for bridging this accuracy/speed gap, based on the Subchannel CFD (SubChCFD) method of Liu et al. [Nucl. Eng. Design, Vol. 355, paper 110318 (2019)], is demonstrated and developed here with a focus on a 5 × 5 square rod bundle geometry. The method has been newly implemented into the commercial code STAR-CCM+ and benchmarked against Liu et al.’s data. The 5 × 5 geometry was chosen in part due to the availability of direct numerical simulation (DNS) data at a relevant Reynolds number of a similar configuration for comparison. The SC+ results are variously compared against results from DNS, large eddy simulation, wall-resolved Reynolds-averaged Navier-Stokes, and coarse-mesh CFD methods. As an expansion to the original SubChCFD approach, a simple Hi2Lo approach is demonstrated using the DNS data as a correction to the original friction factor correlations employed. This is verified to improve the predictions. Additional test cases with geometric perturbations are pursued, illustrating the flexibility of SC+. The potential of this method for modeling the narrow gap vortex instability, which would represent an advancement over standard subchannel approaches, is also assessed. The method is expanded to include transverse flow losses, which was found to improve the results for modeling the gap instability. Initial extensions of SC+ for hexagonal rod bundles are also presented; some inaccuracies for the coarsest meshes prompted a detailed investigation of the mesh convergence behavior of the method. Geometric correction factors were devised that provided substantial improvement on these very coarse meshes, improving the prospects of SC+ for wider usage. Future work plans are to expand the methodology to wire-wrapped rod bundles and to implement the method into Pronghorn, with a unified pipeline via the Cardinal wrapper between the codes NekRS, Pronghorn, and BISON, to solve fuel performance problems of direct interest to industry.

On Calderon's problem for the connection Laplacian

We consider Calderón's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry of a vector bundle up to a gauge transformation and an isometry of the base manifold.

On the birational geometry of conic bundles over the projective space

AbstractLet be a general minimal ‐fold conic bundle with a hypersurface of degree as discriminant. We prove that if , then is not pseudo‐effective, and that if , then none of the integral multiples of is effective. Finally, we provide examples of smooth unirational ‐fold conic bundles with a discriminant of arbitrarily high degree.

Tube bundle evaporators with LGWP refrigerant R1234ze(E)

With new low-GWP HFO refrigerants, the heat transfer performances and methods for decreasing system refrigerant inventory are receiving increasing interest. In shell-and-tube heat exchangers, refrigerant distribution via pressurized liquid spray has the potential for high heat transfer performance while reducing refrigerant charge. However, no published studies have investigated LGWP refrigerants with spray evaporation on tube bundles. A test apparatus was constructed to measure the shell-side heat transfer coefficients of R1234ze(E) on bundles of tubes with two different enhanced-surface types and in two different bundle geometries at various refrigerant saturation temperatures. The results showed strong dependence on refrigerant properties, tube heat flux, enhanced-surface type, bundle geometry, and refrigerant inlet subcooling. The bundle heat transfer coefficients of R1234ze(E) were similar to that of R134a in the same test setup, usually within ±15% for similar conditions. In both cases, they first increased with the heat flux until a local maximum value was achieved. A localized dryout of the tubes at the bottom of the bundle penalized the overall bundle heat transfer coefficient at very high heat flux. For the condensing surface, bundle heat transfer coefficients rarely exceeded 10 kW/m2-K, whereas values in excess of 30 kW/m2-K were sometimes seen for the evaporating surface.

On the Geometry of the Null Tangent Bundle of a Pseudo-Riemannian Manifold

When we consider a non-definite pseudo-Riemannian manifold, we obtain lightlike tangent vectors that constitute the null tangent bundle, whose fibers are lightlike cones in the corresponding tangent spaces. In this paper, we define and study a class of “g-natural” metrics on the tangent bundle of a pseudo-Riemannian manifold and we investigate the geometry of the null tangent bundle as a lightlike hypersurface equipped with an induced g-natural metric.

Hierarchical multi-scale analysis of the effect of varying fiber bundle geometric properties on the mechanical properties of 3D braided composites

A hierarchical multi-scale numerical model is developed to predict the effect of cross-sectional geometric properties on the mechanical response of three-dimensional (3D) braided composites. In this model, the effective properties are transferred from the fiber bundle scale to the mesoscale, and the finite element and analytical methods are used to predict the macroscopic mechanical properties. Damage evolution was evaluated, based on a continuous damage mechanics approach. A user-defined material subroutine (UMAT), in a nonlinear finite element analysis, has been developed to implement the proposed model and further determine the response and subsequent damage evolution in 3D braided composites subjected to quasi-static tension. The elastic properties of the composites are predicted using a hybrid multi-scale model. The agreement between the numerical simulations and the experimental results is good. It has been shown that the cross-sectional geometry of the fiber bundle properties has a significant influence on the tensile behavior of the composite, which is captured by the proposed multi-scale damage model. This research offers a theoretical analysis for selecting the optimized fiber bundle geometry for using in FE predictions of 3D braided composites.

Sheaves and symplectic geometry of cotangent bundles

Sheaves and symplectic geometry of cotangent bundles