Optimization of the design of recuperative heat exchangers in the exhaust nozzle of an aero engine

Today the needs for safer, cleaner and more affordable civil aero engines are found to be of great importance. Five years ago, the EU initiated an action for the design and the construction of efficient and environmentally friendly aero engines (EEFAE). One of the major European gas turbine industries, MTU, has presented a new technology for an advanced aero engine design, which uses an alternative thermodynamic cycle. The basis of this cycle is the adoption of a recuperation part with the use of a system of heat exchangers, installed in the exhaust nozzle of the aircraft engine. Thermal energy in the turbine exhaust is used in the recuperator to pre-heat the compressor outlet air before combustion. The benefits of this technique are focused on reduced pollutants and decreased fuel consumption. In this work, the procedure of the optimization of this installation, by means of the imposed pressure drop downstream the aircraft engine and the balanced mass inflow to the heat exchangers is presented. The optimization is based on experimental measurements in laboratory conditions and preliminary 2D CFD modeling for the flow inside the exhaust duct and through the heat exchangers. It is shown that with a careful approach, a better arrangement of the heat exchangers can be achieved in order to have a minimum pressure drop in the exhaust nozzle which can positively affect the engine’s performance.     

Doubly stochastic matrices with some equal diagonal sums

Let A be doubly stochastic, and let τ₁,…,τ_m be m mutually disjoint zero diagonals in A, 1?m?n-1. E. T. H. Wang conjectured that if every diagonal in A disjoint from each τ_k (k=1,…,m) has a constant sum, then all entries in A off the m zero diagonals τ_k are equal to (n?m)^-1. Sinkhorn showed the conjecture to be correct. In this paper we generalize this result for arbitrary doubly stochastic zero patterns.     

A logarithmic Hardy inequality

We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy. This inequality differs from standard logarithmic Sobolev inequalities in the sense that the measure is neither Lebesgue's measure nor a probability measure. All terms are scale invariant. After an Emden-Fowler transformation, the inequality can be rewritten as an optimal inequality of logarithmic Sobolev type on the cylinder. Explicit expressions of the sharp constant, as well as minimizers, are established in the radial case. However, when no symmetry is imposed, the sharp constants are not achieved by radial functions, in some range of the parameters.     

A unified approach to improved Hardy inequalities with best constants

We present a unified approach to improved Hardy inequalities in . We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where the distance is taken from a surface of codimension . In our main result, we add to the right hand side of the classical Hardy inequality a weighted norm with optimal weight and best constant. We also prove nonhomogeneous improved Hardy inequalities, where the right hand side involves weighted norms, .

     

On existence of minimizers for the Hardy–Sobolev–Maz’ya inequality

We show existence of minimizers for the Hardy–Sobolev–Maz’ya inequality in when either m > 2, n≥ 1 or m = 1, n≥ 3. The authors expresses their gratitude to the faculties of mathematics departments at Technion - Haifa Institute of Technology, at the University of Crete and at the University of Cyprus for their hospitality. A.T. acknowledges partial support by the RTN European network Fronts–Singularities, HPRN-CT-2002-00274. K.T acknowledges support as a Lady Davis Visiting Professor at Technion and partial support from University of Crete, University of Cyprus and Swedish Research Council.     

Dendritic Domains with Hexagonal Symmetry Formed by X‐Shaped Bolapolyphiles in Lipid Membranes

A novel class of bolapolyphile (BP) molecules are shown to integrate into phospholipid bilayers and self‐assemble into unique sixfold symmetric domains of snowflake‐like dendritic shapes. The BPs comprise three philicities: a lipophilic, rigid, π–π stacking core; two flexible lipophilic side chains; and two hydrophilic, hydrogen‐bonding head groups. Confocal microscopy, differential scanning calorimetry, XRD, and solid‐state NMR spectroscopy confirm BP‐rich domains with transmembrane‐oriented BPs and three to four lipid molecules per BP. Both species remain well organized even above the main 1,2‐dipalmitoyl‐sn‐glycero‐3‐phosphocholine transition. The BP molecules only dissolve in the fluid membrane above 70 °C. Structural variations of the BP demonstrate that head‐group hydrogen bonding is a prerequisite for domain formation. Independent of the head group, the BPs reduce membrane corrugation. In conclusion, the BPs form nanofilaments by π stacking of aromatic cores, which reduce membrane corrugation and possibly fuse into a hexagonal network in the dendritic domains.     

Sharp Two–Sided Heat Kernel Estimates for Critical Schrödinger Operators on Bounded Domains

On a smooth bounded domain \(\Omega \subset {\bf {\rm R}}^N\) we consider the Schrödinger operators ? Δ ? V, with V being either the critical borderline potential V(x) =  (N ? 2)²/4 |x|^?2 or V(x) =  (1/4) dist(x, ?Ω)^?2, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Schrödinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a series of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincaré. As a byproduct of our technique we are able to answer positively to a conjecture of E. B. Davies.     

Dark energy and extending the geodesic equations of motion: its construction and experimental constraints

With the discovery of Dark Energy, Λ_DE, there is now a universal length scale, l_DE=c/(L_DE G)^1/2{\ell_{\rm DE}=c/(\Lambda_{\rm DE} G)^{1/2}}, associated with the universe that allows for an extension of the geodesic equations of motion. In this paper, we will study a specific class of such extensions, and show that contrary to expectations, they are not automatically ruled out by either theoretical considerations or experimental constraints. In particular, we show that while these extensions affect the motion of massive particles, the motion of massless particles are not changed; such phenomena as gravitational lensing remain unchanged. We also show that these extensions do not violate the equivalence principal, and that because l_DE=14010⁸⁰⁰₈₂₀{\ell_{\rm DE}=14010^{800}_{820}} Mpc, a specific choice of this extension can be made so that effects of this extension are not be measurable either from terrestrial experiments, or through observations of the motion of solar system bodies. A lower bound for the only parameter used in this extension is set.     

Simultane Bestimmung freier Ca2+- und Mg2+-Konzentrationen durch Ionenaustausch

Zusammenfassung Die simultane Bestimmung freier Ca²⁺- und Mg²⁺-Konzentrationen in Anwesenheit relativ hoher Konzentrationen einwertiger Kationen mit einem erweiterten Ionenaustauschverfahren wird beschrieben. Die Auswertung der Meßergebnisse beruht auf der Theorie der Ionenaustauschgleichgewichte. Die relativen Fehler von [Ca²⁺] und [Mg²⁺] wurden auf der Basis ihrer Bestimmungsgleichungen für einen großen Konzentrationsbereich abgeschätzt. Bei Na⁺- bzw. K⁺-Konzentrationen zwischen 100 und 200 mmol/l lassen sich freie Ca²⁺- und Mg²⁺- Konzentrationen im Bereich von ca. 0,05–5 mmol/l mit einer relativen Standardabweichung zwischen 2 und 5% bestimmen.

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Simultaneous determination of free Ca²⁺ and Mg²⁺ concentrations by ion-exchange

Summary The simultaneous determination of free Ca²⁺ and Mg²⁺ concentrations in the presence of relatively high concentrations of monovalent cations by an improved ion-exchange method is described. The evaluation of the measured results is based upon the theory of ion-exchange equilibria. Relative errors of [Ca²⁺] and [Mg²⁺] were estimated for large ranges of cation concentrations using the error propagation law. In the presence of 100–200 mmol/l of Na⁺ and/or K⁺, [Ca²⁺] and [Mg²⁺] can be determined in the range of about 0.05–5 mmol/l with relative standard deviations from 2 to 5%.

Wir danken Frau Ingrid Schwabe für die ausgezeichnete technische Mitarbeit, sowie Herrn Dr. Oswald und Herrn Dr. Tietz für die Unterstützung bei elektrometrischen Messungen. Herrn Prof. Dr. H. Frunder danken wir für die Durchsicht des Manuskripts.