Similarity solutions of a Blasius flow with variable fluid properties and viscous dissipation

An analytical model of the Blasius flow is studied including temperature-dependent fluid properties and viscous dissipation. The friction coefficient and Nusselt number at the wall are calculated from the resulting dimensionless velocity and temperature fields. The variable properties model is compared to a constant properties model to verify if and under which conditions this simplification is valid. Air, water and oil are analyzed as fluids over a representative operating regime, respectively. For air, the variable properties do not influence the friction coefficient and the Nusselt number. For water, the influence of the variable properties is present for both parameters but limited since no large temperature difference can occur in water without a phase change. New correlations for the friction coefficient and Nusselt number were derived for water and oil over a large range of operating conditions. Viscous dissipation does not significantly affect these parameters for air and water because of their relatively low Prandtl numbers. The high Prandtl number of oil in combination with a viscosity that is strongly decreasing with increasing temperature, leads to a more complex behavior. The friction coefficient as well as the Nusselt number are strongly dependent on the fluid properties. Dissipation effects cannot be neglected above an Eckert number of around 0.01. The superposition principle to evaluate wall heat flux in experiments is based on the assumption of constant fluid properties. It can be used without restrictions for air but should be thoroughly checked for all other fluids, especially liquids, using the presented methodology

Experimental investigation of the oil jet heat transfer on meshing spur gears

Designing an adequate cooling system for a high-speed high-power gearbox of a geared turbofan requires a thorough understanding of the cooling capabilities of the utilized oil jet impingement. An experimental setup is employed to determine the heat transfer coefficient on gear teeth in various non-meshing and meshing configurations, which incorporate inclined jets with varying distances between the impingement and the meshing zones. The direction of heat transfer is inverted in the experiments to allow for a feasible setup with the rotating gears, where impinging oil jets heat the hollow instrumented gear as its inner surface is cooled via air jet impingement. Measurements with varying oil volume flow rates and rotational speeds are carried out. The losses are analyzed to enable an isolated investigation of the heat transfer between the oil and the gear via measured temperatures on the gear teeth. Heat transfer coefficients are compared at the lower rotational speed with relatively small meshing losses. The meshing in the experimental setup does not have a significant influence on the mean heat transfer coefficient. The spatial distribution of the heat transfer coefficient is slightly affected by the meshing teeth as the distribution gets more uniform with decreasing distance between the impingement and meshing zones

Experimental Investigation of the Oil Jet Heat Transfer for an Aero Engine Gearbox

Geared turbofan engines have the potential to propel future civil aircraft engines more efficiently. A planetary gearbox between the low-pressure turbine and the fan enables the operation of both components at their respective optimum rotational speeds. This makes it possible to achieve higher bypass ratios and thus a better propulsion efficiency. A crucial part of the planetary gearbox design is the cooling and lubrication of the gears. Sufficient heat removal from the gear tooth flanks is necessary to ensure reliable operation without the risk of gear failure through pitting or scoring. Fast rotating and highly loaded gears are cooled with impinging oil jets according to current design guidelines. This impingement cooling process comprises a complex, multi-phase flow with heat transfer. Previous experimental, numerical and analytical investigations have shown that the cooling process depends both on the highly unsteady liquid flow dynamics and on the heat conduction in the oil film formed on the gear tooth flank. In this study, the gear is replaced by a cylinder in order to be able to study the impingement cooling on a rotating surface without the influence of unsteady flow phenomena. A hollow cylinder is instrumented with 42 thermocouples across the surface, which are all connected to a telemetry system. A single oil jet is directed radially onto the outer cylinder surface. The measured temperatures are subsequently corrected using a new algorithm to reduce systematic measurement errors without distorting the data. The corrected temperatures are used to calculate the Nusselt number distribution across the cylinder surface by means of a finite element analysis. A parameter study is performed to identify the influence of the parameters oil flow rate, oil viscosity and rotational speed of the cylinder on the heat transfer. The fundamental results of the present study enable a better understanding of the heat transfer on impingement cooled cylinders and spur gears

CFD study of oil-jet gear interaction flow phenomena in spur gears

Oil-jet lubrication and cooling of high-speed gears is frequently employed in aeronautical systems, such as novel high-bypass civil aero engines based on the geared turbofan technology. Using such oil-jet system, practitioners aim to achieve high cooling rates on the flanks of the highly thermally loaded gears with minimum oil usage. Thus, for an optimal design, detailed knowledge about the flow processes is desired. These involve the oil exiting the nozzle, the oil impacting on the gear teeth, the oil spreading on the flanks, the subsequent oil fling-off, as well as the effect of the design parameters on the oil flow. Better understanding of these processes will improve the nozzle design phase, e.g. regarding the nozzle positioning and orientation, as well as the nozzle sizing and operation. Most related studies focus on the impingement depth to characterize the two-phase flow. However, the level of information of this scalar value is rather low for a complete description of the highly dynamic three-dimensional flow. Motivated by the advancements in numerical methods and the computational resources available nowadays, the investigation of the oil-jet gear interaction by means of computational fluid dynamics (CFD) has come into focus lately. In this work, a numerical setup based on the volume-of-fluid method is presented and employed to investigate the two-phase flow phenomena occurring in the vicinity of the gear teeth. The setup consists of a single oil-jet impinging on a single rotating spur gear. By introducing new metrics for characterizing the flow phenomena, extensive use of the possibilities of modern CFD is made, allowing a detailed transient and spatially resolved flow analysis. Thus, not only the impingement depth, but also the temporal and spatial evolution of wetted areas on the gear flanks, as well as the evolution of the oil volume in contact with the gear flanks are extracted from the simulation data and compared in a CFD study. The study consists of 21 different simulation cases, whereby the effect of varying the jet velocity, the jet inclination angle, the jet diameter, and the gear speed are examined. Consistent results compared to a simplified analytical approach for the impinging depth are obtained and the results for the newly introduced metrics are presented

Heat Transfer by Impingement Cooling of Spur Gears

Lower specific fuel consumption as well as noise reduction are the main goals in the sector of civilaeronautics engineering nowadays. One prominent concept of achieving these goals is the gearedturbofan engine, in which a planetary gear box is installed between the low pressure spool and thefan. This allows the low pressure turbine as well as the fan to rotate at optimum speeds. This way, thesame power can be generated by fewer stages in the faster rotating turbine, which in turn compensatesthe additional weight of the gear box. The main advantage of the geared turbofan is the possibilityto further increase the fan diameter and therefore improve the propulsion efficiency by means of ahigher bypass ratio. One crucial feature of the gear box is the cooling system needed to ensure safeoperating conditions during all phases of the flight envelope. For an efficient cooling system, optimizedwith respect to weight and cost, the heat transfer between the cooling fluid and the gears needs tobe understood thoroughly. In this study, the impingement cooling of spur gears by oil jets is forthe first time examined analytically and compared to experimental results. This provides knowledgeabout the evolution of the heat transfer coefficient distribution resulting from the cooling fluid flowrate and the gear speed, as well as a deep understanding of the underlying phenomena causing thisbehavior. The analytical solution process comprises of two calculation steps. First, the size of the oilfilm is calculated and secondly, the heat transfer across this surface is evaluated while the oil film isflung off the tooth flank by centrifugal forces. The parameters varied in this study were the oil flowrate, the rotational speed of the spur gear and the oil jet angle. The theoretical results are in goodagreement with the experimental data. The theoretical approach can therefore be applied as a newand efficient tool to estimate the global heat transfer coefficient of impingement cooled spur gears.Furthermore, the validated tool can be used as boundary condition for thermal models of spur gearsand help optimize the impingement cooling oil systems

The 12,460-Year Hohenheim Oak and Pine Tree-Ring Chronology from Central Europe—A Unique Annual Record for Radiocarbon Calibration and Paleoenvironment Reconstructions

ABSTRACT. The combined oak and pine tree-ring chronologies of Hohenheim University are the backbone of the Holocene radiocarbon calibration for central Europe. Here, we present the revised Holocene oak chronology (HOC) and the Preboreal pine chronology (PPC) with respect to revisions, critical links, and extensions. Since 1998, the HOC has been strengthened by new trees starting at 10,429 BP (8480 BC). Oaks affected by cockchafer have been identified and discarded from the chro-nology. The formerly floating PPC has been cross-matched dendrochronologically to the absolutely dated oak chronology, which revealed a difference of only 8 yr to the published 14C wiggle-match position used for IntCal98. The 2 parts of the PPC, which were linked tentatively at 11,250 BP, have been revised and strengthened by new trees, which enabled us to link both parts of the PPC dendrochronologically. Including the 8-yr shift of the oak-pine link, the older part of the PPC (pre-11,250 BP) needs to be shifted 70 yr to older ages with respect to the published data (Spurk 1998). The southern German part of the PPC now covers 2103 yr from 11,993–9891 BP (10,044–7942 BC). In addition, the PPC was extended significantly by new pine chronologies from other regions. A pine chronology from Avenches and Zürich, Switzerland, and another from the Younger Dryas forest of Cottbus, eastern Germany, could be crossdated and dendrochronologically matched to the PPC. The abso-lutely dated tree-ring chronology now extends back to 12,410 cal BP (10,461 BC). Therefore, the tree-ring-based 14C calibra-tion now reaches back into the Central Younger Dryas. With respect to the Younger Dryas-Preboreal transition identified in the ring width of our pines at 11,590 BP, the absolute tree-ring chronology now covers the entire Holocene and 820 yr of th

Can the envisaged reductions of fossil fuel CO2 emissions be detected by atmospheric observations?

The lower troposphere is an excellent receptacle, which integrates anthropogenic greenhouse gases emissions over large areas. Therefore, atmospheric concentration observations over populated regions would provide the ultimate proof if sustained emissions changes have occurred. The most important anthropogenic greenhouse gas, carbon dioxide (CO2), also shows large natural concentration variations, which need to be disentangled from anthropogenic signals to assess changes in associated emissions. This is in principle possible for the fossil fuel CO2 component (FFCO2) by high-precision radiocarbon (14C) analyses because FFCO2 is free of radiocarbon. Long-term observations of 14CO2 conducted at two sites in south-western Germany do not yet reveal any significant trends in the regional fossil fuel CO2 component. We rather observe strong inter-annual variations, which are largely imprinted by changes of atmospheric transport as supported by dedicated transport model simulations of fossil fuel CO2. In this paper, we show that, depending on the remoteness of the site, changes of about 7–26% in fossil fuel emissions in respective catchment areas could be detected with confidence by high-precision atmospheric 14CO2 measurements when comparing 5-year averages if these inter-annual variations were taken into account. This perspective constitutes the urgently needed tool for validation of fossil fuel CO2 emissions changes in the framework of the Kyoto protocol and successive climate initiatives

IntCal09 and Marine09 radiocarbon age calibration curves, 0-50,000yeats cal BP

The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the 14C and calendar timescales as established in 2002. No change was made to the curves from 0–12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org