Smooth Bundles Research Articles

Investigation of Heat Transfer in a Large-Scale External Heat Exchanger with Horizontal Smooth Tube Bundle

In the research work, energy transport between a dense fluidized bed and submerged horizontal tube bundle is analyzed in the commercial external heat exchanger (EHE). In order to investigate the heat transfer behavior, the authors carried out eight performance tests in a fluidized bed heat exchange chamber with a cross-section of 2.7 × 2.3 m in depth and width and a height of 1.3 m. The authors have been developing a mechanistic model for the prediction of the average heat transfer coefficient, which includes the effect of the geometric structure of the tube bundle and the location of the heat transfer surface on the heat transfer rate. The computational results depict that the average heat transfer coefficient is essentially affected by superficial gas velocity and suspension density rather than bed particle size. The empirical correlations have been proposed for predicting heat transfer data since the existing literature data is not sufficient for industrial fluidized bed heat exchangers. On the basis of the evaluated operating conditions of an external heat exchanger, the optimal conditions where heat transfer occurs could be deduced. The developed mechanistic heat transfer model is validated by experimental data under the examined conditions.

Morphological, histochemical and histological study of the ileum in the Iraqi Black Partridge (Francolinus francolinus)

Objective: This project aimed to study the morphological description and histological structure of ileum in Iraqi black partridge (Francolinus francolinus). Methods: To conduct this investigation, 20 healthy Iraqi black partridge were collected from local suppliers. Birds were euthanized, dissected and then specimens were processed for histological and histochemical staining techniques. Results: A morphological study showed that the ileum appears as a short narrow tubular structure. It extends from the wide end of the jejunum and ends in the Ileo-caecal junction region. Histologically, the wall ileum consists of four tunica mucosa, submucosa, muscularis and serosa. The mucosa was lined by simple columnar epithelium with goblet cells. The muscularis mucosa is arranged in two thick layers of smooth muscle fibers, outer longitudinal and inner circular bundles. The tunica submucosa was a thin layer of fibrous connective tissue. Tunica serosa was loose connective tissue covered by mesothelium. The goblet cells gave a positive reaction with PAS stain. Conclusion: Goblet cells neutral mucopolysaccharide secretions; in fact, the latter stain is an indicator mucin substance which are very important in digestion and absorption and subsequent body growth of the bird.

Smooth classifying spaces

We develop the theory of smooth principal bundles for a smooth group G, using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bundles cannot be classified, we define D-numerable bundles, the smooth analogs of numerable bundles from topology, and prove that pulling back a D-numerable bundle along smoothly homotopic maps gives isomorphic pullbacks. We then define smooth structures on Milnor’s spaces EG and BG, show that EG → BG is a D-numerable principal bundle, and prove that it classifies all D-numerable principal bundles over any diffeological space. We deduce analogous classification results for D-numerable diffeological bundles and vector bundles.

Bundles with Non-multiplicative Â-Genus and Spaces of Metrics with Lower Curvature Bounds

Abstract We construct smooth bundles with base and fiber products of two spheres whose total spaces have nonvanishing $\hat{A}$-genus. We then use these bundles to locate nontrivial rational homotopy groups of spaces of Riemannian metrics with lower curvature bounds for all ${{\operatorname{Spin}}}$ manifolds of dimension 6 or at least 10, which admit such a metric and are a connected sum of some manifold and $S^n \times S^n$ or $S^n \times S^{n+1}$, respectively. We also construct manifolds $M$ whose spaces of Riemannian metrics of positive scalar curvature have homotopy groups that contain elements of infinite order that lie in the image of the orbit map induced by the push-forward action of the diffeomorphism group of $M$.

Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

Let $K$ be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber $K$ are non-zero. As a consequence, we fill a gap in a paper of the first author, and prove that the homomorphism $Diff(K)\to \pi_0 Diff(K)$ does not split. One of the two methods of proof uses a result of Franke on the stable cohomology of arithmetic groups that strengthens work of Borel, and may be of independent interest.

A NOTE ON RATIONAL HOMOLOGICAL STABILITY OF AUTOMORPHISMS OF MANIFOLDS

AbstractBy work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre $D^{2n}\sharp (S^n\times S^n)^{\sharp g}$, relative to the boundary, are for $2n\ge 6$ independent of $g$ in degrees $*\le (g-6)/2$. In this note, we explain how this range can be improved to $*\le g-2$ using cohomological vanishing results due to Borel and the classical invariant theory. This implies that the analogous ring for smooth bundles is independent of $g$ in the same range, provided the degree is small compared to the dimension.

Characteristic numbers of manifold bundles over surfaces with highly connected fibers

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases, these conditions are also sufficient. Using this, we determine the characteristic numbers realized by total spaces of bundles of this type, deduce divisibility constraints on their signatures and $\hat{A}$-genera, and compute the second integral cohomology of ${\rm BDiff}^+(M)$ up to torsion in terms of generalized Miller--Morita--Mumford classes. We also prove analogous results for topological bundles over surfaces with fiber $M$ and discuss the resulting obstructions to smoothing them.

Enhancing Energy Saving in Air Cooling Devices by Intensifying External Heat Transfer

The aerodynamic processes of heated air in the ventilation shaft installed above the heat transferring bundle of bimetallic finned tubes are studied. The regions of suppressed natural, steady, and unsteady mixed air convection in the bundle depending on the degree of narrowing of the outlet section of the ventilation shaft are determined. The maximum Nusselt numbers for multi-row bundles and their corresponding optimum parameters of the degree of narrowing of the outlet section of the ventilation shaft are determined. A method is proposed for determining the Reynolds numbers and the average air velocity during free convection for contracted smooth and finned tube bundles, which will allow optimization of heat transfer processes. The practical effectiveness of single- and two-row bimetallic finned tube bundles with a finning factor φ = 21 and an intertube spacing of 58 mm in air cooling and similar aircooled heat exchangers having a ventilation shaft is scientifically proved.

Connections on smooth Lie algebra bundles

We define the notion of Lie Ehresmann connection on Lie algebra bundles and show that a Lie connection on a Lie algebra bundle induces a Lie Ehresmann connection. The converse is proved for normed Lie algebra bundles. We then show that the connection on adjoint bundle corresponding to the connection on principal G—bundle to which it is associated is a Lie Ehresmann connection. Further it is shown that the Lie Ehresmann connection on adjoint bundle induced by a universal G-connection is universal over the family of adjoint bundles associated to G-bundles.

Effects of vacuum or sous-vide cooking methods on the quality of largemouth bass (Micropterus salmoides)

In order to estimate the effects of vacuum (Vacuum boiling (VB), Vacuum steaming (VS)) or sous-vide cooking (SV) methods on the quality of largemouth bass compared with traditional cooking methods (Boiling (BT), Steaming (ST)), the pH, cooking loss, color and texture indicator were used to evaluate physicochemical changes. The thiobarbituric acid (TBA) was used to analyze lipid oxidation. The low-field nuclear magnetic resonance (LF-NMR) was used to explore the water migration and distribution. The scanning electron microscopy (SEM) was used to observe the microstructure. Raman spectroscopy was carried out to determine the structural changes. The results showed that the VS and SV samples had desired quality, showing more stable protein secondary structure and lower lipid oxidation. In addition, the VS and SV samples had more regular and smooth myofibril bundles compared with other cooked samples. Thus, the VS and SV cooking methods could be used to better maintain the quality of fillets.

Heat transfer in rod bundles cooled by supercritical water – Experimental data and correlations

The paper presents the results of a comparative evaluation of existing correlations for the prediction of heat transfer to supercritical pressure water against experimental data for bundles of heated rods. It is shown that the method, developed by the authors for the engineering calculation of the heat transfer coefficient in the supercritical region of the coolant parameters, makes it possible to describe the experimental data for smooth rod bundles with an error of less than 15%. In the case of rod bundles with wrapped wire, the same method gives values of the heat transfer coefficient, which are on average about 8% lower compared to the experimental data obtained. This is connected with the intensification of heat transfer due to swirling the flow and can be considered as a margin when estimating the limiting temperature of the heat transfer wall. Based on the comparison of the calculation results by different methods, the problems of choosing the ratio for determining the heat transfer coefficient in fuel assemblies of reactors with supercritical pressure water are discussed.

A mathematical model of forced convection condensation of steam on smooth horizontal tubes and tube bundles in the presence of noncondensables

This paper presents a description and the results of verification of an unsteady model for forced convection condensation on a smooth single horizontal tube in the presence of noncondensables. The external flow is described by the two-dimensional (2D) unsteady Navier–Stokes equations for a laminar regime or by the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for a turbulent regime, and the condensate film is considered using a one-dimensional model. Details of the numerical implementation of the developed algorithm are described. The available literature data were employed to verify the proposed model for forced convection condensation for an arbitrary flow direction of vapour with and without noncondensables. The numerical results are in good agreement with the published experimental data. In the proposed model, condensation influences the air-vapour mixture flow only through the boundary condition; therefore, this model can be easily implemented using different computational fluid dynamics (CFD) codes (in this work, an “in-house” CFD code ANES) for modelling more complex configurations, like tube bundles. Results for condensation on five tubes in a tube bundle are also presented in this work. The influence of mutual irrigation of pipes by drops coming off was also approximated.

On the rationality problem for quadric bundles

We classify all positive integers n and r such that (stably) non-rational complex r-fold quadric bundles over rational n-folds exist. We show in particular that for any n and r, a wide class of smooth r-fold quadric bundles over projective n-space are not stably rational if r lies in the interval from $2^{n-1}-1$ to $2^{n}-2$. In our proofs we introduce a generalization of the specialization method of Voisin and Colliot-Th\'el\`ene--Pirutka which avoids universally $CH_0$-trivial resolutions of singularities.

Transverse Transport and Heat Transfer in Smooth VVER Fuel-Rod Bundle with Cellular Spacer Grid

The results of the numerical modeling of flow and heat transfer in a bundle of smooth fuel rods spaced by a cellular grid in application to VVER are presented. The results are analyzed and compared with computational-experimental studies in the homegrown and foreign nuclear power industries. The computational region simulating a VVER FA fragment, a mathematical model, and the boundary conditions are described. The results of a calculation of the coolant flow velocity field and the temperature field for the fuel-rod cladding under conditions of stabilized heat transfer in the bundle and on a section of stabilization beyond the cellular spacer grid are presented. Flow in the bundle and the mechanisms of interchannel transfer are described. Recommendations are given for taking account of the grid effect on intensification of heat transfer in the bundle, and a comparison is made with data obtained for plate-shaped spacer grids in PWR.

Tautological classes and smooth bundles over BSU(2)

For a Lie group G and a smooth manifold W, we study the difference between smooth actions of G on W and bundles over the classifying space of G with fiber W and structure group Diff(W). In particular, we exhibit smooth manifold bundles over BSU(2) that are not induced by an action. The main tool for reaching this goal is a technical result that gives a constraint for the values of tautological classes pulled back to the cohomology of BSU(2) along a map induced by an action.

Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds

We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle [Formula: see text] defined over the scalar manifold [Formula: see text]. The construction uses a taming of [Formula: see text], which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of [Formula: see text] to the bundle [Formula: see text] and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over [Formula: see text] and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from [Formula: see text] supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.

Location-dependent correlation between tissue structure and the mechanical behaviour of the urinary bladder

The mechanical properties of the urinary bladder wall are important to understand its filling-voiding cycle in health and disease. However, much remains unknown about its mechanical properties, especially regarding regional heterogeneities and wall microstructure. The present study aimed to assess the regional differences in the mechanical properties and microstructure of the urinary bladder wall. Ninety (n=90) samples of porcine urinary bladder wall (ten samples from nine different locations) were mechanically and histologically analysed. Half of the samples (n=45) were equibiaxially tested within physiological conditions, and the other half, matching the sample location of the mechanical tests, was frozen, cryosectioned, and stained with Picro-Sirius red to differentiate smooth muscle cells, extracellular matrix, and fat. The bladder wall shows a non-linear stress-stretch relationship with hysteresis and softening effects. Regional differences were found in the mechanical response and in the microstructure. The trigone region presents higher peak stresses and thinner muscularis layer compared to the rest of the bladder. Furthermore, the ventral side of the bladder presents anisotropic characteristics, whereas the dorsal side features perfect isotropic behaviour. This response matches the smooth muscle fibre bundle orientation within the tunica muscularis. This layer, comprising approximately 78% of the wall thickness, is composed of two fibre bundle arrangements that are cross-oriented, one with respect to the other, varying the angle between them across the organ. That is, the ventral side presents a 60°/120° cross-orientation structure, while the muscle bundles were oriented perpendicular in the dorsal side. Statement of SignificanceIn the present study, we demonstrate that the mechanical properties and the microstructure of the urinary bladder wall are heterogeneous across the organ. The mechanical properties and the microstructure of the urinary bladder wall within nine specific locations matching explicitly the mechanical and structural variations have been examined. On the one hand, the results of this study contribute to the understanding of bladder mechanics and thus to their functional understanding of bladder filling and voiding. On the other hand, they are relevant to the fields of constitutive formulation of bladder tissue, whole bladder mechanics, and bladder-derived scaffolds i.e., tissue-engineering grafts.

Group actions, non-Kähler complex manifolds and SKT structures

Abstract We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.

The diffeology of Milnor's classifying space

We define a diffeology on the Milnor classifying space of a diffeological group G, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth principal bundles, we prove the existence of a diffeological connection on any principal bundle (with mild conditions on the bundles and groups), and apply the theory to some examples, including some infinite-dimensional groups, as well as irrational tori.

Axioms for higher twisted torsion invariants of smooth bundles

This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes. We will give a system of axioms that we require these cohomology classes to satisfy. Higher Franz Reidemeister torsion and twisted versions of the higher Miller-Morita-Mumford classes will satisfy these axioms. We will show that the space oftwisted torsion invariants is two dimensional or one dimensional depending on the torsion degree and spanned by these two classes. The proof will greatly depend on results on the equivariant Hatcher constructions developed in a separate paper.