Uncertainty quantification of leakages in a multistage simulation and comparison with experiments

The present paper presents a numerical study of the impact of tip gap uncertainties in a multistage turbine. It is well known that the rotor gap can change the gas turbine efficiency but the impact of the random variation of the clearance height has not been investigated before. In this paper the radial seals clearance of a datum shroud geometry, representative of steam turbine industrial practice, was systematically varied and numerically tested. By using a Non-Intrusive Uncertainty Quantification simulation based on a Sparse Arbitrary Moment Based Approach, it is possible to predict the radial distribution of uncertainty in stagnation pressure and yaw angle at the exit of the turbine blades. This work shows that the impact of gap uncertainties propagates radially from the tip towards the hub of the turbine and the complete span is affected by a variation of the rotor tip gap. This amplification of the uncertainty is mainly due to the low aspect ratio of the turbine and a similar behavior is expected in high pressure turbines

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms

Uncertainty quantification for fat-tailed probability distributions in aircraft engine simulations

Rare event simulation is vital for industrial design because some events, so-called black swans, can have fatal consequences despite their low probability of occurrence. Finding low-probability events far off the mean design is a challenging task for realistic engineering models because they are characterized by high computational demands, many input variables, and often insufficient statistical information to build parametric probability distributions. Therefore, an adaptive and arbitrary polynomial chaos method, called sparse approximation of moment-based arbitrary polynomial chaos, is suggested in this work. Sparse approximation of moment-based arbitrary polynomial chaos creates custom polynomial basis functions and grids based on statistical moments to avoid incorrect statistical assumptions. The contribution of this work is that it is derived how rare event simulation can conveniently be integrated into adaptive sparse grid methods by calculating polynomial chaos expansions based on the statistical moments of truncated fat-tailed distributions. Moreover, the use of tempered alpha-stable distributions is suggested to avoid discontinuous tail cutoffs. Sparse approximation of moment-based arbitrary polynomial chaos is compared to other statistical methods in two industrial aircraft engine simulations: a simulation of transient cycle temperature in a turbine cavity and hot-gas ingestion in the interwheel region. In both cases, sparse approximation of moment-based arbitrary polynomial chaos agrees with previous results but obtains them with lower computational effort

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

Ueber Verhütung und Behandlung der Dammrisse

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Intrahepatic cholestasis of pregnancy

Intrahepatic cholestasis of pregnancy (ICP) is a cholestatic disorder characterized by (i) pruritus with onset in the second or third trimester of pregnancy, (ii) elevated serum aminotransferases and bile acid levels, and (iii) spontaneous relief of signs and symptoms within two to three weeks after delivery. ICP is observed in 0.4–1% of pregnancies in most areas of Central and Western Europe and North America, while in Chile and Bolivia as well as Scandinavia and the Baltic states roughly 5–15% and 1–2%, respectively, of pregnancies are associated with ICP. Genetic and hormonal factors, but also environmental factors may contribute to the pathogenesis of ICP. Intrahepatic cholestasis of pregnancy increases the risk of preterm delivery (19–60%), meconium staining of amniotic fluid (27%), fetal bradycardia (14%), fetal distress (22–41%), and fetal loss (0.4–4.1%), particularly when associated with fasting serum bile acid levels > 40 μmol/L. The hydrophilic bile acid ursodeoxycholic acid (10–20 mg/kg/d) is today regarded as the first line treatment for intrahepatic cholestasis of pregnancy. Delivery has been recommended in the 38th week when lung maturity has been established

Surface pretreatments for medical application of adhesion

Medical implants and prostheses (artificial hips, tendono- and ligament plasties) usually are multi-component systems that may be machined from one of three material classes: metals, plastics and ceramics. Typically, the body-sided bonding element is bone. The purpose of this contribution is to describe developments carried out to optimize the techniques , connecting prosthesis to bone, to be joined by an adhesive bone cement at their interface. Although bonding of organic polymers to inorganic or organic surfaces and to bone has a long history, there remains a serious obstacle in realizing long-term high-bonding strengths in the in vivo body environment of ever present high humidity. Therefore, different pretreatments, individually adapted to the actual combination of materials, are needed to assure long term adhesive strength and stability against hydrolysis. This pretreatment for metal alloys may be silica layering; for PE-plastics, a specific plasma activation; and for bone, amphiphilic layering systems such that the hydrophilic properties of bone become better adapted to the hydrophobic properties of the bone cement. Amphiphilic layering systems are related to those developed in dentistry for dentine bonding. Specific pretreatment can significantly increase bond strengths, particularly after long term immersion in water under conditions similar to those in the human body. The bond strength between bone and plastic for example can be increased by a factor approaching 50 (pealing work increasing from 30 N/m to 1500 N/m). This review article summarizes the multi-disciplined subject of adhesion and adhesives, considering the technology involved in the formation and mechanical performance of adhesives joints inside the human body