Smooth Bundles Research Articles

Discriminant Divisors for Conic Bundles

ABSTRACT We study some foundational properties on discriminant divisors for generically smooth conic bundles. In particular, we extend the formula $\Delta_f \equiv -f_*K_{X/T}^2$ to arbitrary characteristics.

Assessment of Look-up tables for the prediction of heat transfer coefficient distribution in rod bundles cooled by supercritical water

The evaluation of available Look-Up Tables for prediction of heat transfer coefficient distribution in rod bundles cooled by supercritical water with the aim of their further use in computational analyses of various Fuel Assembles of Supercritical Water-Cooled Reactors is made. The comparison between the calculations based on Look-Up Tables with the values from empirical correlations and experimental data for smooth and wire-wrapped rod bundles was presented. The obtained results showed that Look-Up Table of the University of Ottawa, which was created to describe improved and deteriorated heat transfer regimes in round tubes, allows describing available data points with 30 % of the mean square deviation. It is noted that the presence of wire intensifies heat transfer exchange near pseudocritical temperature region but existing versions of Look-Up Tables cannot take into account this effect. Nevertheless, there is potential for further improvement in predicting the heat transfer coefficient using Look-Up Table by introducing additional correction factors.

Investigation of thermo-hydraulics performance and vapour bubble behaviour over 5×3 smooth hybrid elliptical tube bundle under saturated cross flow boiling condition - An experimental study

In the current experimental study, the thermal-hydraulic behaviour of a novel smooth hybrid elliptical tube bundle (TB) is compared with the performance of the corresponding conventional smooth circular TB. The smooth hybrid elliptical tube, made up of AISI-304, is in the form of a conventional elliptical shape from the outside but a circular shape from the inside. The operating parameters encountered in the current investigation are Heat Flux (10–75 kW/m2), Mass Flux (19–100 kg/m2s), and pitch-to-diameter ratio (P/D) (1.25 - 1.95). The outcomes show that the thermal-hydraulics performance in the case of a smooth hybrid elliptical TB is higher than a conventional smooth circular TB. The augmentation in the heat transfer coefficient obtained with a smooth hybrid elliptical TB is limited to 12 % in the entire range. The pressure drop improvement is found to be 48 % to 120 % equated to the conventional smooth circular TB. However, the effective performance of the smooth hybrid elliptical TB measured in terms of H/P ratio (H/P = heat transfer coefficient/total pressure drop) is found to be in the range of 0.3–2.5 compared to the conventional smooth circular TB which is in the range of 0.2–1.1. This is evident from the present experimental study that the employment of the elliptical TB will lead to lower pumping power than a conventional smooth circular TB owing to its lower pressure because of the streamlined surface. The obtained two-phase heat transfer enhancement efficiency based on enhancement factor and pressure drop penalty factor showed a higher gap TB (P/D = 1.95) has higher performance. Moreover, for the first time, an effort has been made to analyze the physics associated with vapor bubble dynamics and interaction along the height of the smooth hybrid elliptical TB.

Heat transfer enhancement of different ribbing pitched semi-closed microstructure tube bundles fabricated by deformational cutting method

The study investigates the limitations posed by low-value heat transfer coefficients and higher wall superheat in conventional tube bundles, which adversely impact the performance of heat exchangers. To address this challenge, semi-closed microstructure tubes, created via deformational cutting at ribbing pitches of 300 µm and 400 µm, are proposed as a potential solution. The research centers on analyzing the two-phase boiling heat transfer performance of these microstructure tubes arranged in 2 × 3 staggered tube bundles. A comparative analysis is conducted, evaluating the thermal effectiveness of the microstructure tube bundles against a 2 × 3 smooth tube bundle and a copper-coated tube bundle under varying mass flux, heat flux, and pitch-to-diameter ratios. The experimental findings indicate the superior heat transfer performance of both microstructure tube bundles, with reduced wall superheat compared to other tube bundles. The findings further indicate that the 2 × 3 semi-closed microstructure tube bundle with a higher ribbing pitch outperforms the microstructure with a lower ribbing pitch. The 2 × 3 high-pitched microstructure tube bundle exhibits a maximum enhancement of 420 % over the 5 × 3 smooth tube bundle and 340 % over the 2 × 3 smooth tube bundle. Moreover, it surpasses the performance of copper-coated tube bundles by 230 % and outperforms its lower-pitch counterpart by 70 %. Particularly, the use of microstructure tube bundles allows for a reduction in the number of tubes required in the heat exchanger configuration without compromising its performance, promoting compactness and cost-effectiveness. Overall, the study highlights the feasibility of implementing these tubes in the two-phase heat exchanger owing to their superior performance compared to conventional tubes.

Prediction and comparison of aerodynamic performance and flow control for smooth and wavy tube banks in crossflow at subcritical Reynolds numbers using a 3D RANS approach

This paper investigates the effects of introducing wavy cylinders of appropriate wavelength into tube bundles for the passive control of flow-induced vibration. The Reynolds-averaged Navier–Stokes approach RANS was used to study the turbulent flow characteristics within staggered tube bundles having transverse and longitudinal pitch-to-diameter ratios of 3.8 and 2.1, respectively. Two wavy models are tested with different wavelength-to-mean diameter ratios, namely: Model-A with [Formula: see text] and Model-B with [Formula: see text], and their performances are compared with those of a smooth circular tube bundle Model-C ([Formula: see text]), in a range of subcritical Reynolds numbers [Formula: see text]. Mean velocity and pressure fields as well as aerodynamic coefficients are presented and compared. According to the obtained results, the wavy tube bundle with [Formula: see text] exhibits the best performance, with slightly smaller [Formula: see text] values than the smooth tube bundle. However, results show that the wavy model with [Formula: see text] is clearly the worst with an increase of [Formula: see text] up to 40%. Numerical outcomes also reveal that the interaction of neighboring rows and columns affects the fluctuation of [Formula: see text] values relative to each tube position. Moreover, [Formula: see text] evolutions depend significantly on the variation of Re as well, where drag reduction is more substantial by increasing Re. Thus, wavy-shaped tubes with optimum parameters could be more suitable for flow control by enhancing the secondary flow, turbulence and fluid mixing.

Development of Nusselt number and friction factor models for rough rod bundles based on wall functions

The fuel assembly in the reactor undergo surface roughening due to fouling deposits and material corrosion, which significantly impact the pressure drop and convective heat transfer performance of the fuel assembly. In this study, new models were developed based on the wall velocity and temperature distribution functions. The Nusselt number and friction factor are obtained by integrating these functions over the flow cross-section. The findings demonstrate the accuracy of the method in predicting the friction factor and Nusselt number for both rough tube and smooth rod bundles. The models developed in this study can be utilized to predict the friction factor and Nusselt number in rod bundles with different relative roughness under turbulent flow states, considering square and hexagonal arrangements with P/D<1.5. The present study reveals that the roughness promotes convective heat transfer to a slightly less extent as the pressure drop.

ALGEBRA ENVIRONMENTS I.

Algebra environments capture properties of non–commutative conditional expectations in a general algebraic setting. Their study relies on algebraic geometry, topology, and differential geometry techniques. The structure algebraic and Banach manifolds of algebra environments and their Zariski and smooth tangent vector bundles are particular objects of interest. A description of derivations on algebra environments compatible with geometric structures is an additional issue. Grassmann and flag manifolds of unital involutive algebras and spaces of projective compact group representations in C∗–algebras are analyzed as structure manifolds of associated algebra environments.

Numerical study of the influence of amplitudes on heat transfer in a tube bundle

The objective of this study is to investigate the impact of different surface roughness levels on a staggered arrangement of tubes in a cross-flow configuration, with water as the fluid being used. The focus lies in comparing the data obtained from the rough surface configuration with that of a smooth cylinder reference point. To assist this comparison, a comprehensive two-dimensional computational fluid dynamics (CFD) model is created, which accurately represents the distinctive characteristics of each surface shape. This study also included modifying the Remax within a range of 10 000–16 000 and analyzing the outcomes of using four different tube types, each with different supernatant thicknesses labeled as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] accordingly. Surprisingly, the tube with a 0.4 wave surface had significantly higher average Nusselt numbers (Nu) compared to the other tubes, indicating superior performance. The ideal tube design was found based on three main metrics: The performance evaluation criterion (PEC), the global performance criterion (GPC) and the average Nu. The performance metrics encompassed the PEC, GPC and the Colburn factor [Formula: see text]. The average Nu of the wavy_0.4 tube was higher than that of the SM by 31.66–32.54%, higher than that of the wavy_0.2 tube by 19.76–20.74%, and higher than that of the wavy_0.1 tube by 9.38–16.58%. According to the statistics, a heat exchanger that cools and has a wave with an amplitude of 0 is the most efficient choice for offshore energy systems. The smooth bundle tube (SBT) demonstrated the most significant increase in GPC, with values of 9.3–12.7% and 20.3–28.3% higher than those of wavy tubes with amplitudes of 0.1 and 0.2, respectively. In addition, correlations for the Nu are given, with results verified using empirical data from Balabani et al.

Experimental study and performance evaluation of an air source heat pump (ASHP) system with a frost-free evaporator

The air source heat pump (ASHP) is operated in a low temperature and high humidity working environment. There is always a lot of frost forming on the outdoor heat exchanger, which hinders the heat transfer rate of the heat exchange surface, leading to the decrease of performance of the ASHP system. This paper presents a new type of frost-free evaporator for ASHP system. The heat transfer zone of the evaporator is composed of three parts: non-packing zone, plain finned-tube falling film zone and horizontal smooth tube bundle falling film zone. The experimental system of the frost-free evaporator is established, and the reliability of the experimental data is verified. The effects of refrigerant flow rate, inlet air temperature, fan frequency and solution spray mode on energy efficiency ratio, heat transfer expansion coefficient, air side pressure drop and exergy loss of the evaporator are studied. The performance of the evaporator is evaluated. The results show that with the increase of inlet air flow and temperature, the energy efficiency ratio of frost-free evaporator increases by about 8%–12%, and the air side pressure drop also increases. As the inlet air temperature increases from −10 to 15 °C, the heat transfer expansion coefficient of evaporator decreases by about 3%–6%, indicating that the increase of inlet air temperature will lead to an increase of sensible heat transfer ratio and a decrease of latent heat transfer ratio. The results also show that compared with no spray mode and continuous spray mode, the intermittent spray mode is more recommended as a feasible operation scheme to realize the continuous, efficient and stable operation of the new evaporator.

On the unirationality of quadric bundles

We prove that a general (n−1)-fold quadric bundle Qn−1→P1, over a number field, with (−KQn−1)n>0 and discriminant of odd degree δQn−1 is unirational, and that the same holds for quadric bundles over an arbitrary infinite field provided that Qn−1 has a point, is otherwise general and n≤5. As a consequence we get the unirationality of any smooth quadric surface bundle Q2→P2, over an algebraically closed field, with δQ2≤12.

H-Principle for Stratified Spaces

Abstract We extend Gromov and Eliashberg–Mishachev’s $h-$principle on manifolds to stratified spaces. This is done in both the sheaf-theoretic framework of Gromov and the smooth jets framework of Eliashberg–Mishachev. The generalization involves developing 1. the notion of stratified continuous sheaves to extend Gromov’s theory, 2. the notion of smooth stratified bundles to extend Eliashberg–Mishachev’s theory. A new feature is the role played by homotopy fiber sheaves. We show, in particular, that stratumwise flexibility of stratified continuous sheaves along with flexibility of homotopy fiber sheaves furnishes the parametric $h$-principle. We extend the Eliashberg–Mishachev holonomic approximation theorem to stratified spaces. We also prove a stratified analog of the Smale–Hirsch immersion theorem.

Geometrical envelopes of fast radio bursts

Aims. Assuming fast radio bursts (FRBs) are produced by matter travelling ultra-relativistically in a localised region of a smooth bundle of streamlines, we study the constraints applied by geometry to the morphology and polarisation of the burst in time and frequency independently of the intrinsic radiative process. Methods. We express the problem only in terms of the local properties of direction and curvature of a streamline. This allows us to cast the general results to any desired geometry. We illustrate by applying this framework to two geometries inspired by pulsar and magnetar magnetospheres, namely the dipolar polar-cap region and a magnetic dipole with an additional toroidal component. Results. Geometry constrains bursts to occur within an envelope in the frequency vs. time plane (dynamic spectrum). This envelope notably characterises spectral occupancy and frequency drifts (both burst-to-burst and within an individual burst). We illustrate how one can simulate bursts by specifying some basic properties of an intrinsic emission process. In particular we show that the typical properties of one-off bursts can be produced in polar-cap geometry by a star with spin period > 1s, while bursts from repeating sources are better accounted for with an additional strong toroidal component and a sub-second spin period. Conclusions. We propose that a relationship between burst morphologies and the properties of the source, such as its spin period and magnetospheric properties, can be established at least qualitatively based on geometrical considerations. Our results favour models where repeaters are younger and faster magnetars with highly twisted magnetospheres.

On the structure group of an infinite dimensional JB-algebra

We extend several results for the structure group of a real Jordan algebra V, to the setting of infinite dimensional JB-algebras. We prove that the structure group Str(V), the cone preserving group G(Ω) and the automorphism group Aut(V) of the algebra V are embedded Banach-Lie groups of GL(V), and that each of the inclusions Aut(V)⊂G(Ω)⊂Str(V) are of embedded Banach-Lie subgroups. We give a full description of the components of Str(V) via cones, isotopes and central projections. We apply these results to V=B(H)sa the special JB-algebra of self-adjoint operators on an infinite dimensional complex Hilbert space, describing the groups Str(V),G(Ω),Aut(V), their Banach-Lie algebras and their connected components. We show that the action of the unitary group of H on Aut(V) has smooth local cross sections, thus Aut(V) is a smooth principal bundle over the unitary group, with structure group S1.

APPLICATION OF DIMPLES AND HELICAL GROOVES ON THE OUTTER SURFACE OF TUBES TO INCREASE THERMAL-HYDRAULIC EFFICIENCY OF TUBE BUNDLES AT CROSS FLOW

The flow structure and thermo-hydraulic efficiency of cross flow of tube bundles with dimples and helical grooves have been analyzed. The Reynolds number range (103-104) was typical for industrial heat exсhangers. It was found that dimples and grooves decrease scientifically the cylinder wake area and reduces the hydraulic losses. The heat transfer augmentation in five-row tube bundle by dimples is 35-40% while pressure drop increase by 10-15%. The hydraulic resistance of two-row bundle of tube with helical grooves is 20% lower than that of a smooth tube bundle, while heat transfer augmentation is absent. The value of Reynolds analogy factor for tube bundles with dimples and helical grooves exceeds unity. The high thermo-hydraulic efficiency of tube bundles with dimples and helical grooves, allows us to recommend it for practical use in the development of modern heat exchange equipment of the tubular type.

Intrinsic Riemannian functional data analysis for sparse longitudinal observations

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from sparsely observed Riemannian functional data, while the covariance vector bundle provides a rigorous mathematical foundation for formulating such smoothing problems. The parallel transport and the bundle metric together make it possible to measure fidelity of fit to the covariance function. They also play a critical role in quantifying the quality of estimators for the covariance function. As an illustration, based on the proposed framework, we develop a local linear smoothing estimator for the covariance function, analyze its theoretical properties and provide numerical demonstration via simulated and real data sets. The intrinsic feature of the framework makes it applicable to not only Euclidean submanifolds but also manifolds without a canonical ambient space.

Modeling of Lateral Flow in CFD for Subchannel Analysis

This paper is aimed at the application of computational fluid dynamics (CFD) calculations for lateral flow modeling in rod bundles of Russian-type pressurized water reactors with hexagonal fuel rod lattice by subchannel analysis under a constant temperature. The subchannel code SUBCAL and CFD code ANSYS Fluent with the Reynolds stress turbulence model, which is capable of solving the anisotropic flow present in rod bundles, are used. Both methods are compared in terms of calculations in rod bundles. The literature review of available experiments of rod bundles suitable for CFD calculation validation follows. This paper describes the created CFD models on a triangular lattice, which are subsequently validated on selected experimental data in a wide range of Reynolds numbers and geometry (pitch-to–rod diameter ratio) together with mesh sensitivity analysis. The main part of this work is to develop a new equation for the lateral flow resistance coefficient for the subchannel code based on CFD calculations. Within these calculations, the turbulent mixing coefficient β for hydraulically smooth rod bundles, which is related to the geometry, and the momentum-energy transfer analogy correction factor ε are also evaluated and for which the equation is subsequently proposed.

Simulation of convective heat transfer of a bank of pipes when using turbulators with cutouts

The article discusses the mathematical modeling of the intensification of convective heat transfer of a smooth tube bundle. Turbulators with cutouts were used as heat transfer intensifiers. The mathematical model of the heat exchanger consisted of a section of a rectangular channel with a turbulator device. To solve the differential equation, the finite difference method was used, approximated by difference equations. On the basis of the calculations, for the purpose of choosing the size of the experimental object, the profiles of the velocity distribution before and after the turbulizer were obtained. Keywords: m

Smooth loops and loop bundles

A loop is a rather general algebraic structure that has an identity element and division, but is not necessarily associative. Smooth loops are a direct generalization of Lie groups. A key example of a non-Lie smooth loop is the loop of unit octonions. In this paper, we study properties of smooth loops and their associated tangent algebras, including a loop analog of the Maurer-Cartan equation. Then, given a manifold, we introduce a loop bundle as an associated bundle to a particular principal bundle. Given a connection on the principal bundle, we define the torsion of a loop bundle structure and show how it relates to the curvature, and also develop aspects of a non-associative gauge theory. Throughout, we see how some of the known properties of G2-structures can be seen from this more general setting.

Study on enhanced heat transfer characteristics of metal foam solar receiver in Solar Power Tower plants

In order to explore the mechanism of heat and mass transfer of metal foam absorber based on electrodeposition, the numerical simulation study of metal foam absorbers with different structures was carried out, and the heat transfer model of the coated metal foam tube bundle with a tube spacing of 3D × 1.5D was analyzed and established. Compared with the smooth tube bundle, with the Re number varying from 100 to 1500, the Rext of the tube bundle coated with stainless steel foam decreased from 0.061 K/W to 0.009 K/W, and the thermal resistance ratio outside the tube increased from 2.75 to 4.76. The pressure loss of the tube rose from 1.89 Pa to 80.10 Pa, and the pressure loss outside the tube dropped from 5.15 to 3.12. The overall performance index PEC of the tube increased from 1.59 to 3.26. Compared with rows of staggered tube bundles from 2.5D to 2.2D, the heat transfer coefficient can reach 4621 W/m2/K and the pressure loss is 1.67%.

Bundles with even-dimensional spherical space form as fibers and fiberwise quarter pinched Riemannian metrics

Let E E be a smooth bundle with fiber an n n -dimensional real projective space R P n \mathbb {R}P^n . We show that, if every fiber carries a positively curved pointwise strongly 1 / 4 1/4 -pinched Riemannian metric that varies continuously with respect to its base point, then the structure group of the bundle reduces to the isometry group of the standard round metric on R P n \mathbb {R}P^n .