Film-cooling performance in supersonic flows: Effect of shock impingement

High pressure turbine stages work in transonic regimes and then shock waves, shed by the trailing edge, impinge on the suction side modifying the flow structures. Gas turbine entry temperature is much higher than the allowable material limit and the hot components can survive only using advanced film-cooling systems. Unfortunately these systems are designed without taking into account the interaction with the shock waves and this article would like to address this problem and to evaluate if this assumption is correct or not. A correct prediction and understanding of the interaction between the ejected coolant and the shock waves is crucial in order to achieve an optimal distribution of the coolant and to increase the components life. In this work, the numerical investigation of a film-cooling test case, investigated experimentally by the University of Karlsruhe, is shown. An in-house computational fluid dynamics solver is used for the numerical analysis. The test rig consists of a converging-diverging nozzle that accelerates the incoming flow up to supersonic conditions and an oblique shock is generated at the nozzle exit section. Three cases have been studied, where the cooling holes have been positioned before, near and after the shock impingement. The results obtained considering four blowing ratios are presented and compared with the available experimental data. The local adiabatic effectiveness is affected by the shock-coolant interaction and this effect has been observed for all the blowing ratios investigated. A similar trend is observed in the experimental data even if the numerical simulations over-predict the impact of the interaction. © IMechE 2013

Hopf bifurcation and related stability problems for periodic differential systems

This paper deals with 2π-periodic one parameter differential systems in the plane. Those systems all admit the null solution which is asymptotically stable for a fixed value, say μ=0, and completely unstable for μ>0 small. We find that for the perturbed systems 2π-periodic solutions occur only if another parameter ε which regulates the angular velocity is involved. In any other case an annulus which is asimptotically stable replaces the 2π-periodic solutions

Thermo-Hydrodynamic Analysis of Plain and Tilting Pad Bearings

Abstract The demand for higher efficiency and increased equipment compactness is pushing industrial compressors' designers towards the choice of higher rotor peripheral speed. As a consequence, modern bearing-rotor systems are subject to complex thermal phenomena inducing a renewed interest on their real working conditions. This work is about the validation of the in-house numerical code TILTPAD developed at the Department of Industrial Engineering of the University of Florence for the thermo-hydrodynamic analysis of both plain and tilting pad journal bearings performance. TILTPAD is a steady-state code based on a 2D thin-film approach able to find either the resulting hydrodynamic load using the shaft equilibrium position and the rotational speed (i.e., direct problem) or the shaft equilibrium position once the load and the rotational speed are prescribed (i.e., inverse problem). In order to calculate pads' pressure distribution a finite element approach is used to solve the Reynolds equation together with a mixed procedure to evaluate pads equilibrium positions. Two steady-state energy equations based on a Petroff-type simplification are implemented in the code. The first one is proposed in the work of Balbahadur and Kirk [1] while the second one is based on an improved mixing model and a temperature dependent viscosity. An iterative procedure is used between Reynolds and energy equations to account for the dependence of the dynamic viscosity on the temperature field. Super-laminar flow regimes are also modeled in the code by means of a simplified approach able to represents, with reasonable accuracy, the effects of Taylor-Couette vortex flows and of the transitional regimes up to the onset of a fully turbulent state. Under these hypotheses, the pressure field is slightly affected by the viscosity variation while dissipative effects are enhanced. The code has been validated by means of comparison with available experimental data. Particular attention is devoted to static working parameters (i.e., equilibrium position and frictional power loss), reproducing the global behavior of the bearing, although some local characteristic is also considered

On the return period and design in a multivariate framework

Abstract. Calculating return periods and design quantiles in a multivariate environment is a difficult problem: this paper tries to make the issue clear. First, we outline a possible way to introduce a consistent theoretical framework for the calculation of the return period in a multi-dimensional environment, based on Copulas and the Kendall's measure. Secondly, we introduce several approaches for the identification of suitable design events: these latter quantities are of utmost importance in practical applications, but their calculation is yet limited, due to the lack of an adequate theoretical environment where to embed the problem. Throughout the paper, a case study involving the behavior of a dam is used to illustrate the new concepts outlined in this work

The Brightest Lyα\alpha Emitter: Pop III or Black Hole?

CR7 is the brightest $z=6.6 \, {\rm Ly}\alpha$ emitter (LAE) known to date, and spectroscopic follow-up by Sobral et al. (2015) suggests that CR7 might host Population (Pop) III stars. We examine this interpretation using cosmological hydrodynamical simulations. Several simulated galaxies show the same "Pop III wave" pattern observed in CR7. However, to reproduce the extreme CR7 ${\rm Ly}\alpha$/HeII1640 line luminosities ($L_{\rm \alpha/He II}$) a top-heavy IMF and a massive ($>10^{7}{\rm M}_{\odot}$) PopIII burst with age $<2$ Myr are required. Assuming that the observed properties of ${\rm Ly}\alpha$ and HeII emission are typical for Pop III, we predict that in the COSMOS/UDS/SA22 fields, 14 out of the 30 LAEs at $z=6.6$ with $L_{\alpha} >10^{43.3}{\rm erg}\,{\rm s}^{-1}$ should also host Pop III stars producing an observable $L_{\rm He II}>10^{42.7}{\rm erg}\,{\rm s}^{-1}$. As an alternate explanation, we explore the possibility that CR7 is instead powered by accretion onto a Direct Collapse Black Hole (DCBH). Our model predicts $L_{\alpha}$, $L_{\rm He II}$, and X-ray luminosities that are in agreement with the observations. In any case, the observed properties of CR7 indicate that this galaxy is most likely powered by sources formed from pristine gas. We propose that further X-ray observations can distinguish between the two above scenarios.Comment: 6 pages, 4 figure

A Comparative Study of RANS, URANS and NLES Approaches for Flow Prediction in Pin Fin Array

Gas Turbine are nowadays largely used for aircraft propulsion and land-based power generation. The increased attention to environmental aspects has promoted research and development efforts both from manufacturers and research centres. The latest developments in turbinecooling technologies play a critical role in the attempt to increase the efficiency and the specific power of the most advanced designs. Pin fin arrays, in particular, are widely used in jet engine application because of their ability to enhance cooling by providing extended surfaces for conduction and convection. They are also known to be an effective means to create turbulence which naturally increases heat transfer. Pin fin turbulators are typically located inside the trailing edge of high pressure turbine blade where they also act as a structural support. The optimum shapes and spacing of such elements are usually determined experimentally, or more recently, by using Computational Fluid Dynamics (CFD). On the other hand, the comprehension of the real physics controlling the heat transfer enhancement process and the role played by the large scale vortical structures generated by the inserts, still represent a great challenge for fluid mechanic researchers. The problem has been intensively investigated by Ames et al. (2005) by means of an experimental campaign on pin fin matrix. From the numerical point of view, the principal bottleneck of the CFD approach as applied to this kind of massively unsteady flow is related to the high computational cost and to the reliability of the turbulence models. The main objective of this work is to offer a critical analysis of the performance of a cooling device consisting of a pin fin turbulators geometry, as predicted by different CFD models of various complexity, using similar computational technology to integrate the corresponding governing equations. Local velocity and turbulence distributions are presented and compared with available experimental data

Cross-Border Investment, Conflict of Laws, and the Privatization of Securities Law

The rapid acceleration of transnational investing is occurring in an environment in which emerging markets, and foreign interest in these markets, are exploding. The issues involved with cross-border investment, conflict of laws and the privatization of securities law are examined

Stochastic Variation of the Aero-Thermal Flow Field in a Cooled High-Pressure Transonic Vane Configuration

In transonic high-pressure turbine stages, oblique shocks originated from vane trailing edges impact the rear suction side of each adjacent vane. High-pressure vanes are usually cooled to tolerate the combustor exit temperature levels, which would reduce dramatically the residual life of a solid vane. Then, it is highly probable that shock impingement will occur in proximity of one of the coolant rows. It has already been observed that the presence of an adverse pressure gradient generates non-negligible effects on heat load due to the increase in boundary layer thickness and turbulence level, with a detrimental impact on the local adiabatic effectiveness values. Furthermore, the generation of a tornado-like vortex has been recently observed that could further decrease the efficacy of the cooling system by moving cold flow far from the vane wall. It must be also underlined that manufacturing deviations and in-service degradation are responsible for the stochastic variation of geometrical parameters. This latter phenomenon greatly alters the unsteady location of the shock impingement and the time-dependent thermal load on the vane. Present work starts from what is shown in literature and provides a highly-detailed description of the aero-thermal field that occurs on a model that represents the flow conditions occurring on the rear suction side of a cooled vane. The numerical model is initially validated against the experimental data obtained by the University of Karlsruhe during TATEF2 EU project, and then an uncertainty quantification methodology based on the probabilistic collocation method and on Padè's polynomials is used to consider the probability distribution of the geometrical parameters. The choice of aleatory unknowns allows to consider the mutual effects between shock-waves, trailing edge thickness and hole diameter. Turbulence is modelled by using the Reynolds Stress Model already implemented in ANSYS® Fluent®. Special attention is paid to the description of the flow field in the shock/boundary layer interaction region, where the presence of a secondary effects will completely change the local adiabatic effectiveness values