Uncertainty Quantification in Hydrodynamic Bearings

Although it is possible to imagine a strong sensitivity of hydrodynamic bearings performance to geometrical and fluid dynamic uncertainties, a small amount of scientific contributions have been found in literature about the use of uncertainty quantification techniques for the numerical modeling of bearings. In the present paper we aim at quantifying the effects of the aleatory uncertainty of some relevant input values on key parameters related to rotordynamic effects in turbomachinery, and in particular on the rotor thermal instability problem (e.g. the equilibrium position and the dynamic coefficients). A methodology is initially developed in order to study the propagation of the uncertainties in the numerical analysis of Tilting Pad Journal Bearings (TPJB). Due to the characteristics of the in-house finite element code TILTPAD considered for the UQ analysis, the Monte Carlo method has been selected among the possible approaches. The analysis here presented considers the effects of both manufacturing tolerances on the assembled bearing clearance and of the tolerances adopted for the characterization of the viscosity grade of the oil. The test case adopted for the analysis is the Kingsbury D-140 TPJB. Considering the individual variation of the selected parameters, it is possible to observe that the standard deviation (STD) of the the non-dimensional dynamic coefficients is up to 2.1% in case of viscosity variation and up to 9.1% in case of clearance variation. The STD of the frictional power losses is about 2.2% and 1.4% respectively. Considering the simultaneous variation of the selected parameters, it is possible to observe a STD of the non-dimensional dynamic coefficients comprised between 6.4% and 9.4%, while the STD of the frictional power losses is about 2.7%

On the Assessment of an Unstructured Finite-Volume DES/LES Solver for Turbomachinery Applications

Improvements in mean flow and performances simulation in turbomachinery has brought research to focus more demanding topics like turbulence effects on turbines. Although overall performances are well predicted by Unsteady-RANS, other phenomena such as aerodynamic noise or transition need more accurate prediction of turbulent flow features. Thus different kinds of equation modeling other than URANS are needed to cope with this issue. The success of Detached-Eddy Simulation and Large-Eddy Simulation applications in reproducing physical behavior of flow turbulence is well documented in literature. Despite that, LES simulations are still computationally very expensive and their use for investigating industrial configurations requires a careful assessment of both numerical and closure modeling techniques. Moreover LES solvers are usually developed on a structured mesh topology for sake of simplicity of high-order schemes implementation. Application to complex geometries like those of turbomachinery is therefore difficult. The present work addresses this issue considering the feasibility of converting an operative in-house URANS solver, widely validated for applicative purposes, into higher resolution DES and LES, in order to face turbulence computation of turbomachinery technical cases. The solver presents a 3D unstructured finite-volume formulation, which is kept in LES approach in order to handle complex geometries and it is developed to perform unsteady simulations on turbine stages. Preliminary assessment of the solver has been performed to evaluate and improve the accuracy of the convective fluxes discretization on an inviscid bump test case. First a DES-based approach has been implemented, as it is less computationally challenging and numerically demanding than LES. A square cylinder test case has been assessed and compared with experiments. Then, a pure LES with a Smagorinsky sub-grid scale model has been evaluated on the test case of incompressible periodic channel flow in order to assess the capability of the solver to correctly sustain a time developing turbulent field

Uncertainty Quantification of Non-Dimensional Parameters for a Film Cooling Configuration in Supersonic Conditions

In transonic high-pressure turbine stages, oblique shocks originating from vane trailing edges impact the suction side of each adjacent vane. High-pressure vanes are cooled to tolerate the combustor exit-temperature levels, then it is highly probable that shock impingement will occur in proximity to a row of cooling holes. The presence of such a shock, together with the inevitable manufacturing deviations, alters the location of the shock impingement and of the performance parameters of each cooling hole. The present work provides a general description of the aero-thermal field that occurs on the rear suction side of a cooled vane. Computational Fluid Dynamics (CFD) is used to evaluate the deterministic response of the selected configurations in terms of adiabatic effectiveness, discharge coefficient, blowing ratio, density ratio, and momentum ratio. Turbulence is modelled by using both the Shear Stress Transport method (SST) and the Reynolds Stress Model (RSM) implemented in ANSYS® FLUENT®. The obtained results are compared with the experimental data obtained by the Institut für Thermische Strömungsmaschinen in Karlsruhe. Two uncertainty quantification methodologies based on Hermite polynomials and Padè–Legendre approximants are used to consider the probability distribution of the geometrical parameters and to evaluate the response surfaces for the system response quantities. Trailing-edge and cooling-hole diameters have been considered to be aleatory unknowns. Uncertainty quantification analysis allows for the assessment of the mutual effects on global and local parameters of the cooling device. Obtained results demonstrate that most of the parameters are independent by the variation of the aleatory unknowns while the standard deviation of the blowing ratio associated with the hole diameter uncertainty is around 12%, with no impact by the trailing-edge thickness. No relevant advantages are found using either SST model or RSM in combination with Hermite polynomials and Padè–Legendre approximants

The origin of dust in high redshift QSOs: the case of SDSS J1148+5251

We present a semi-analytical model for the formation and evolution of a high redshift quasar (QSO). We reconstruct a set of hierarchical merger histories of a 10^13 Msun dark matter halo and model the evolution of the corresponding galaxy and of its central super massive black hole. The code GAMETE/QSODUST consistently follows: the black hole assembly via both coalescence with other black holes and gas accretion; the build up and star formation history of the quasar host galaxy, driven by binary mergers and mass accretion; the evolution of gas, stars, metals in the interstellar medium (ISM), accounting for mass exchanges with the external medium (infall and outflow processes); dust formation in Supernova (SN) ejecta and in the stellar atmosphere of Asymptotic Giant Branch (AGB) stars, dust destruction by interstellar shocks and grain growth in molecular clouds; the AGN feedback which powers a galactic-scale wind, self-regulating the black hole growth and eventually halting star formation.We use this model to study the case of SDSS J1148+5251 observed at redshift 6.4, exploring different star formation histories for the QSO host galaxy.Comment: 20 pages, 15 figures, accepted for publication in MNRA

Effects of realistic inflow conditions on the aero-thermal performance of a film-cooled vane

A high-pressure vane equipped with a realistic film-cooling configuration has been studied. The vane is characterized by the presence of multiple rows of fan-shaped holes along pressure and suction side while the leading edge is protected by a showerhead system of cylindrical holes. Steady three-dimensional Reynolds-Averaged Navier-Stokes simulations have been performed. A preliminary grid sensitivity analysis has been performed with uniform inlet flow to quantify the effect of the spatial resolution. Turbulence model has been assessed in comparison with available experimental data. The effects of a realistic inflow condition on the thermal behaviour of the cooled vane are then investigated by means of comparison between two conjugate heat transfer simulations. The first one is characterized by a uniform inlet flow while the second one presents a temperature distortion and a superimposed aggressive swirl derived from the EU- funded TATEF2 project. The effect of the swirling flow in determining the metal temperature distribution is investigated with particular attention to the consequences on the operation of the film cooling system

On the Effect of an Aggressive Inlet Swirl Profile on the Aero-thermal Performance of a Cooled Vane

AbstractA high-pressure vane equipped with a realistic film-cooling configuration has been studied. The vane is characterized by the presence of multiple rows of fan-shaped holes along pressure and suction side while the leading edge is protected by a showerhead system. Steady three-dimensional Reynolds-Averaged Navier-Stokes (RANS) simulations have been performed. A preliminary grid sensitivity analysis has been performed (with uniform inlet flow) to quantify the effect of the spatial resolution. Turbulence model has been assessed in comparison with available experiment data. The effects of a realistic inlet swirl on the aero-thermal performance of the cooling system are then investigated by means of comparison between two different kinds of simulations. The first one using a uniform inlet flow while the second one with aggressive swirl derived from the EU-funded project TATEF2. Clocking effects are also accounted for. The effect of the swirling flow in determining the coolant transport are investigated, evidencing the key role that these phenomena have in determining the effectiveness of the cooling

Film Cooling Performance in a Transonic High-pressure Vane: Decoupled Simulation and Conjugate Heat Transfer Analysis☆

Abstract The continuous demand for increased performance and reliability of gas turbines leads to the improvement of prediction tools. Having regard to the effects of heat transfer on the residual life of gas turbine components, it is necessary to achieve a high level of accuracy in the evaluation of thermal loads. Computational fluid dynamics is able to provide reliable data in a limited lapse of time. In this paper, the numerical analysis of the cooled vane of the MT1 high-pressure turbine stage is presented. A grid dependence analysis based on the evaluation of the aero-thermal characteristics of the vane has been performed. Turbulence is modeled using the kT-kL-ω method whose performance in this kind of configuration is rarely debated in the scientific literature. Model parameters have been tuned to match the experimental data. The final objective of the present activity is to assess the capability of numerical methods to deal with an annular, transonic high-pressure vane with a realistic film cooling configuration. Adiabatic effectiveness, heat transfer coefficient and net heat flux reduction distributions have been evaluated, the latter providing relevant information on the performance of the cooling system. The coupled fluid-solid simulation of the cooled configuration has also been performed to evaluate the impact of conjugate heat transfer on the prediction of thermal loads. Results show a non-negligible difference in the wall temperature evaluation between the decoupled and the coupled approach, mainly caused by the heat conduction in the solid

Effects of Inflow Condition on RANS and LES Predictions of the Flow around a High-Rise Building

An increasing number of engineering applications require accurate predictions of the flow around buildings to guarantee performance and safety. This paper investigates the effects of variations in the turbulent inflow, as predicted in different numerical simulations, on the flow pattern prediction around buildings, compared to wind tunnel tests. Turbulence characteristics were assessed at several locations around a model square high-rise building, namely, above the roof region, at the pedestrian level, and in the wake. Both Reynolds-averaged Navier–Stokes (RANS, where turbulence is fully modelled) equations and large-eddy simulation (LES, where turbulence is partially resolved) were used to model an experimental setup providing validation for the roof region. The performances of both techniques were compared in ability to predict the flow features. It was found that RANS provides reliable results in regions of the flow heavily influenced by the building model, and it is unreliable where the flow is influenced by ambient conditions. In contrast, LES is generally reliable, provided that a suitable turbulent inflow is included in the simulation. RANS also benefits when a turbulent inflow is provided in simulations. In general, LES should be the methodology of choice if engineering applications are involved with the highly separated and turbulent flow features around the building, and RANS provides reliable information when regions of high wind speed and low turbulence are investigated

Uncertainty Quantification of the Effects of Blade Damage on the Actual Energy Production of Modern Wind Turbines

Wind turbine blade deterioration issues have come to the attention of researchers and manufacturers due to the relevant impact they can have on the actual annual energy production (AEP). Research has shown how after prolonged exposure to hail, rain, insects or other abrasive particles, the outer surface of wind turbine blades deteriorates. This leads to increased surface roughness and material loss. The trailing edge (TE) of the blade is also often damaged during assembly and transportation according to industry veterans. This study aims at investigating the loss of AEP and efficiency of modern multi-MW wind turbines due to such issues using uncertainty quantification. Such an approach is justified by the stochastic and widely different environmental conditions in which wind turbines are installed. These cause uncertainties regarding the blade's conditions. To this end, the test case selected for the study is the DTU 10 MW reference wind turbine (RWT), a modern reference turbine with a rated power of 10 MW. Blade damage is modelled through shape modification of the turbine's airfoils. This is done with a purposely developed numerical tool. Lift and drag coefficients for the damaged airfoils are calculated using computational fluid dynamics. The resulting lift and drag coefficients are used in an aero-servo-elastic model of the wind turbine using NREL's code OpenFAST. An arbitrary polynomial chaos expansion method is used to estimate the probability distributions of AEP and power output of the model when blade damage is present. Average AEP losses of around 1% are predicted mainly due to leading-edge blade damage. Results show that the proposed method is able to account for the uncertainties and to give more meaningful information with respect to the simulation of a single test case