## Publications

102 results found

Pepper N, Montomoli F, Sharma S, 2021, Identification of missing input distributions with an inverse multi-modal polynomial chaos approach based on scarce data, *Probabilistic Engineering Mechanics*, ISSN: 0266-8920

Pepper N, Montomoli F, sharma S, 2021, Data fusion for Uncertainty Quantification with Non-intrusive Polynomial Chaos, *Computer Methods in Applied Mechanics and Engineering*, Vol: 374, ISSN: 0045-7825

This work presents a framework for updating an estimate of a probability distribution, arising from an uncertainty propagation using Non-intrusive Polynomial Chaos (NIPC), with scarce experimental measurements of a Quantity of Interest (QoI). In recent years much work has been directed towards developing methods of combining models of different accuracies in order to propagate uncertainty, but the problem of improving uncertainty propagations by considering evidence from both computational models and experiments has received less attention.The framework described here uses the Maximum Entropy Principle (MEP) to find an updated, least biased estimate of a probability distribution by maximising the entropy between the original and updated estimates. A constrained optimisation is performed to find the coefficients of a Polynomial Chaos Expansion (PCE) that minimise the Kullback–Leibler (KL) divergence between estimates, while ensuring that the new estimate conforms to constraints imposed by the available experimental measurements of the QoI. In this work a novel constraint is used, based upon the Dvoretzky–Kiefer–Wolfowitz inequality and the Massart bound (DKWM), as opposed to the more commonly used moment-based constraints. Such a constraint allows scarce experimental data to be used in informing the updated estimate of the probability distribution.

Voet L, Ahlfeld R, Gaymann A,
et al., 2021, A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling, *Applied Mathematical Modelling: simulation and computation for engineering and environmental systems*, Vol: 89, Pages: 885-906, ISSN: 0307-904X

Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable. UQ based only on RANS simulations or on DNS thus leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

Tagarielli V, Gauch H, Bisio V,
et al., 2020, Predictions of the transient loading exerted on circular cylinders by arbitrary pressure waves in air, *Journal of Fluid Mechanics*, Vol: 901, ISSN: 0022-1120

This study investigates the transient loading exerted on rigid circular cylinders by impinging pressure waves of arbitrary shape, amplitude, and time duration. Numerical calculations are used to predict the transient flow around the cylinder for wide ranges of geometric and loading parameters. An analytical model is developed to predict the transient loading history on the cylinder and this is found in good agreement with the results of the numerical calculations. Both models are used to identify and explore the different loading regimes, and to construct non16 dimensional maps to allow direct application of the findings of this study to the design of structures exposed to the threat of pressure wave loading.

Cavazzini G, Giacomel F, Ardizzon G,
et al., 2020, CFD-based optimization of scroll compressor design and uncertainty quantification of the performance under geometrical variations, *ENERGY*, Vol: 209, ISSN: 0360-5442

Hammond J, Montomoli F, Pietropaoli M, et al., 2020, MACHINE LEARNING FOR THE DEVELOPMENT OF DATA DRIVEN TURBULENCE CLOSURES IN COOLANT SYSTEMS, ASME Turbo Expo

Pietropaoli M, Gaymann A, Montomoli F, 2020, Three-Dimensional Fluid Topology Optimization and Validation of a Heat Exchanger With Turbulent Flow, ASME IGTI 2020

Friso R, Casari N, Pinelli M, et al., 2020, Uncertainty Analysis of Inflow Conditions on an HPT Gas Turbine Nozzle: Effect on Particle Deposition, ASME IGTI 2020

Pepper N, Montomoli F, Giacomel F, et al., 2020, Uncertainty Quantification and Missing Data for Turbomachinery With Probabilistic Equivalence and Arbitrary Polynomial Chaos, Applied to Scroll Compressors, ASME IGTI 2020

Antorkas S, Montomoli F, Massini M, 2020, Topology Optimization of Gas Turbine Blades for Additive Manufacturing, GPPS 2020

Pepper N, Montomoli F, Sharma S, 2019, Multiscale uncertainty quantification with arbitrary polynomial chaos, *Computer Methods in Applied Mechanics and Engineering*, Vol: 357, Pages: 1-20, ISSN: 0045-7825

This work presents a framework for upscaling uncertainty in multiscale models. The problem is relevant to aerospace applications where it is necessary to estimate the reliability of a complete part such as an aeroplane wing from experimental data on coupons. A particular aspect relevant to aerospace is the scarcity of data available.The framework needs two main aspects: an upscaling equivalence in a probabilistic sense and an efficient (sparse) Non-Intrusive Polynomial Chaos formulation able to deal with scarce data. The upscaling equivalence is defined by a Probability Density Function (PDF) matching approach. By representing the inputs of a coarse-scale model with a generalised Polynomial Chaos Expansion (gPCE) the stochastic upscaling problem can be recast as an optimisation problem. In order to define a data driven framework able to deal with scarce data a Sparse Approximation for Moment Based Arbitrary Polynomial Chaos is used. Sparsity allows the solution of this optimisation problem to be made less computationally intensive than upscaling methods relying on Monte Carlo sampling. Moreover this makes the PDF matching method more viable for industrial applications where individual simulation runs may be computationally expensive. Arbitrary Polynomial Chaos is used to allow the framework to use directly experimental data. Finally, the difference between the distributions is quantified using the Kolmogorov–Smirnov (KS) distance and the method of moments in the case of a multi-objective optimisation. It is shown that filtering of dynamical information contained in the fine-scale by the coarse model may be avoided through the construction of a low-fidelity, high-order model.

Pepper N, Gerardo-Giorda L, Montomoli F, 2019, Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal, *Scientific Reports*, Vol: 9, ISSN: 2045-2322

Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporaldynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematicalapproaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on theassumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can beconsidered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in differentsituations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC)to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suitedto handle important landscape heterogeneities as elevation and the complex geometries associated with the boundariesof an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing theuncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.

Gaymann A, Montomoli F, 2019, Deep neural network and Monte Carlo tree search applied to fluid-structure topology optimization, *Scientific Reports*, Vol: 9, ISSN: 2045-2322

This paper shows the application of Deep Neural Network algorithms for Fluid-Structure Topology Optimization. The strategy offered is a new concept which can be added to the current process used to study Topology Optimization with Cellular Automata, Adjoint and Level-Set methods. The design space is described by a computational grid where every cell can be in two states: fluid or solid. The system does not require human intervention and learns through an algorithm based on Deep Neural Network and Monte Carlo Tree Search. In this work the objective function for the optimization is an incompressible fluid solver but the overall optimization process is independent from the solver. The test case used is a standard duct with back facing step where the optimizer aims at minimizing the pressure losses between inlet and outlet. The results obtained with the proposed approach are compared to the solution via a classical adjoint topology optimization code.

Gaymann A, Montomoli F, Pietropaoli M, 2019, Fluid topology optimization: Bio-inspired valves for aircraft engines, *International Journal of Heat and Fluid Flow*, Vol: 79, Pages: 1-7, ISSN: 0142-727X

This work shows the introduction of three dimensional fluid topology optimization for the design of valves without moving parts that can be manufactured through 3D printing and used in aircraft engines. The design obtained is inherently safer than standard design with moving parts and it resembles closely to biological structures.A new three dimensional fluid topology optimization formulation to achieve such geometries is shown. The novelty of the method is linked to the applicability to realistic high Reynolds numbers, as in aircraft engines. This is the first time that such geometries are obtained for realistic operating conditions that are applicable to gas turbines.The optimal geometries are validated by using Computational Fluid Dynamics

Tagarielli V, Gauch H, Montomoli F,
et al., 2019, Predictions of the transient loading on box-like objects by arbitrary pressure waves in air, *Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, Vol: 475, ISSN: 1364-5021

This study investigates the transient loading on rigid, isolated, box-like objects by impinging pressure waves of variable intensity and time duration. A numerical solver is used to predict the transient flow around the object and theconsequent pressure on the object’s surface. An analytical model is developed which is capable of predicting the transient loading history on the faces of a box-like object; it was found in good agreement with the numerical predictions.The numerical and analytical models are then used to construct non-dimensional design maps. Different regimes ofloading are identified and explored.

Salvadori S, Carnevale M, Fanciulli A,
et al., 2019, Uncertainty Quantification of Non-Dimensional Parameters for a Film Cooling Configuration in Supersonic Conditions, *FLUIDS*, Vol: 4

Suman A, Casari N, Fabbri E,
et al., 2019, Generalization of particle impact behavior in gas turbine via non-dimensional grouping, *Progress in Energy and Combustion Science*, Vol: 74, Pages: 103-151, ISSN: 1873-216X

Fouling in gas turbines is caused by airborne contaminants which, under certain conditions, adhere to aerodynamicsurfaces upon impact. The growth of solid deposits causes geometric modifications of the blades in terms of bothmean shape and roughness level. The consequences of particle deposition range from performance deterioration tolife reduction to complete loss of power. Due to the importance of the phenomenon, several methods to model particlesticking have been proposed in literature. Most models are based on the idea of a sticking probability, defined as thelikelihood a particle has to stick to a surface upon impact. Other models investigate the phenomenon from adeterministic point of view by calculating the energy available before and after the impact. The nature of the materialsencountered within this environment does not lend itself to a very precise characterization, consequently, it is difficultto establish the limits of validity of sticking models based on field data or even laboratory scale experiments. As aresult, predicting the growth of solid deposits in gas turbines is still a task fraught with difficulty. In this work, two nondimensionalparameters are defined to describe the interaction between incident particles and a substrate, withparticular reference to sticking behavior in a gas turbine. In the first part of the work, historical experimental data onparticle adhesion under gas turbine-like conditions are analyzed by means of relevant dimensional quantities (e.g.particle viscosity, surface tension, and kinetic energy). After a dimensional analysis, the data then are classified usingnon-dimensional groups and a universal threshold for the transition from erosion to deposition and from fragmentationto splashing based on particle properties and impact conditions is identified. The relation between particle kineticenergy/surface energy and the particle temperature normalized by the softening temperature represents the originalnon-dimensional groups

Gauch HL, Bisio V, Rossin S, et al., 2019, Transient Loading on Turbomachinery Packages due to Pressure Waves Caused by Accidental Deflagration Events, ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, Publisher: American Society of Mechanical Engineers

<jats:title>Abstract</jats:title> <jats:p>In this study we present the application of numerical and analytical models to predict the transient loading of structures by impinging pressure and shock waves in air, which have been recently developed by the authors. Non-dimensional design maps are provided which yield predictions of the maximum loads on structures as a function of the problem parameters. Practical example applications, with reference to typical structures used in turbomachinery packages, are presented. These examples demonstrate the superiority of the new modelling techniques to current industrial design guidelines which are mostly extrapolated from simplified methods developed for shock waves. Finally, conclusions are drawn regarding the nature of the loading exerted on the structure in different regimes of problem parameters.</jats:p>

Friso R, Casari N, Suman A, et al., 2019, A Design for Fouling Oriented Optimization of an HPT Nozzle, ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, Publisher: American Society of Mechanical Engineers

<jats:title>Abstract</jats:title> <jats:p>Fouling and erosion are two problems that severely affect gas turbines. The shape of the blade, its roughness, and its structural stability can vary as a consequence of these phenomena. The outcomes of this occurrence can span from the efficiency reduction to the engine shut down according to the nature of the material ingested, to the concentration of contaminants in the air, the cleanliness of fuel and to the particular design of the machine.</jats:p> <jats:p>In this work, an axial turbine airfoil is modified according to the requirement of less sensibility to the phenomena above mentioned, utilizing an automatic optimization algorithm. An artificial neural network surrogate approach is used for searching the optimal shape, minimizing the computational cost of the entire process. The optimum design of the blade is therefore achieved, in order to reduce the effects of deposition on the performance.</jats:p> <jats:p>The methodology here proposed is fully general and it is applied to an HPT nozzle in the present analysis.</jats:p>

Ahlfeld R, Ciampoli F, Pietropaoli M,
et al., 2019, Data-driven uncertainty quantification for Formula 1: Diffuser, wing tip and front wing variations, *Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering*, ISSN: 0954-4070

© IMechE 2019. This work introduces a new uncertainty quantification method to better deal with scarce data and long simulation run times in Formula 1 design. Race cars are produced in low quantities and for maximum performance. Thus, their designing process is characterised by manufacturing data shortage and complex Computational Fluid Dynamics simulations with long run times. Their car aerodynamics is subject to many random variables that introduce uncertainty into the down-force and drag performance, such as variations in ride height, front wing direction and pitch angle. To accurately predict the car performance during a race, it is important to study the effect of these random variables. This assessment cannot be performed with the standard deterministic Computational Fluid Dynamics approaches used in Formula 1. Even with regard to stochastic approaches, no efficient method has so far been suggested that addresses the problem of data scarcity. The reason for this is that most efficient uncertainty quantification methods fit probability distributions to the scarce data. It is shown in this work that probability distribution fitting can create a significant error using a simple two-dimensional diffuser example. Subsequently, the use of a new data-driven Polynomial Chaos method and its sparse multi-dimensional extension is suggested and demonstrated for Formula 1 to reduce such errors. This method allows to avoid distribution fitting because it is based on pure data. SAMBA’s general formulation also makes it easier to combine any possible inputs within a sparse description for problems with many variables. SAMBA is applied to two realistic car three-dimensional Computational Fluid Dynamics simulations: a NACA 0012 tip wing and the front part of a Formula 1 car. The probabilistic variations of the lift and drag of these two configurations are calculated using SAMBA and shown to be significant.

Suman A, Casari N, Fabbri E,
et al., 2019, Gas Turbine Fouling Tests: Review, Critical Analysis, and Particle Impact Behavior Map, *Journal of Engineering for Gas Turbines and Power*, Vol: 141, ISSN: 0742-4795

© Copyright 2019 by ASME. Fouling affects gas turbine operation, and airborne or fuel contaminants, under certain conditions, become very likely to adhere to surfaces if impact takes place. Particle sticking implies the change in shape in terms of roughness of the impinged surface. The consequences of these deposits could be dramatic: these effects can shut an aircraft engine down or derate a land-based power unit. This occurrence may happen due to the reduction of the compressor flow rate and the turbine capacity, caused by a variation in the HPT nozzle throat area (geometric blockage due to the thickness of the deposited layer and the aerodynamic blockage due to the increased roughness, and in turn boundary layer). Several methods to quantify particle sticking have been proposed in literature so far, and the experimental data used for their validation vary in a wide range of materials and conditions. The experimental analyzes have been supported by (and have given inspiration to) increasingly realistic mathematical models. Experimental tests have been carried out on (i) a full scale gas turbine unit, (ii) wind tunnel testing or hot gas facilities using stationary cascades, able to reproduce the same conditions of gas turbine nozzle operation and finally, (iii) wind tunnel testing or hot gas facilities using a coupon as the target. In this review, the whole variety of experimental tests performed are gathered and classified according to composition, size, temperature, and particle impact velocity. Using particle viscosity and sticking prediction models, over seventy (70) tests are compared with each other and with the model previsions providing a useful starting point for a comprehensive critical analysis. Due to the variety of test conditions, the related results are difficult to be pieced together due to differences in particle material and properties. The historical data of particle deposition obtained over thirty (30) years are classified using particle ki

Pietropaoli M, Montomoli F, Gaymann A, 2019, Three dimensional fluid topology optimization for heat transfer, *Structural and Multidisciplinary Optimization*, Vol: 59, Pages: 801-812, ISSN: 1615-147X

In this work, an in house topology optimization (TO) solver is developed to optimize a conjugate heat transfer problem: realizing more complex and efficient coolant systems by minimizing pressure losses and maximizing the heat transfer. The TO method consists in an idealized sedimentation process in which a design variable, in this case impermeability, is iteratively updated across the domain. The optimal solution is the solidified region uniquely defined by the final distribution of impermeability. Due to the geometrical complexity of the optimal solutions obtained, this design method is not always suitable for classic manufacturing methods (molding, stamping....) On the contrary, it can be thought as an approach to better and fully exploit the flexibility offered by additive manufacturing (AM), still often used on old and less efficient design techniques. In the present article, the proposed method is developed using a Lagrangian optimization approach to minimize stagnation pressure dissipation while maximizing heat transfer between fluid and solid region. An impermeability dependent thermal conductivity is included and a smoother operator is adopted to bound thermal diffusivity gradients across solid and fluid. Simulations are performed on a straight squared duct domain. The variability of the results is shown on the basis of different weights of the objective functions. The solver builds automatically three-dimensional structures enhancing the heat transfer level between the walls and the flow through the generation of pairs of counter rotating vortices. This is consistent to solution proposed in literature like v-shaped ribs, even if the geometry generated is more complex and more efficient. It is possible to define the desired level of heat transfer and losses and obtain the closest optimal solution. It is the first time that a conjugate heat transfer optimization problem, with these constraints, has been tackled with this approach for three-dimensional geomet

Suman A, Casari N, Fabbri E, et al., 2019, A Non-Dimensional Approach for Generalizing the Particle Impact Behavior of Gas Turbine Fouling, ASME Turbo Expo: Turbomachinery Technical Conference and Exposition, Publisher: AMER SOC MECHANICAL ENGINEERS

Gaymann A, Schiaffini G, Massini M, et al., 2019, Neural network topology for wind turbine analysis

Copyright © by the Authors. In this work Artificial Neural Networks (ANN) are used for a multi-target optimization of the aerodynamics of a wind turbine blade. The Artificial Neural Network is used to build a meta-model of the blade, which is then optimized according to the imposed criteria. The neural networks are trained with a data set built by a series of CFD simulations and their configuration (number of neurons and layers) selected to improve performances and avoid over-fitting. The basic configuration of the airfoil is the profile S809, which is commonly used in horizontal axis wind turbines (HAWT), equipped with a Coanda jet. The design position and momentum of the jet are optimized to maximize aerodynamic efficiency and minimize the power required to activate the Coanda Jet.

Mazzoni CM, Ahlfeld R, Rosic B, et al., 2019, Uncertainty quantification of leakages in a multistage simulation and comparison with experiments

© Open Archives of the 16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC 2016. All rights reserved. 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.

Sakuma M, Pepper N, Kodakkal A, et al., 2019, Multi-fidelity uncertainty quantification of the flow around a rectangular 5:1 cylinder, Pages: 420-431

© 2019 Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019. All rights reserved. This work shows the application of Multi-fidelity Uncertainty Quantification to Wind Engineering problems. As test case a rectangular shape is used, with a fillet radius, in order to represent the geometrical variations that can affect buildings or other bluff bodies. The rectangular cylinder used has a chord-to-thickness ratio 5:1. This rectangular shape is an important basic shape for wind engineering tasks, e.g. in case of buildings or other bluff bodies exposed to the flow. Moreover it is well investigated and documented. Coarse and fine meshes are used as low and high fidelity models respectively. To perform CFD simulations, the stabilized finite element methods are used in both the high and low fidelity model with a CFD code developed by TUM and the International Center for Numerical Methods in Engineering. The underlying UQ framework is based on a Sparse Arbitrary Moment Based Algorithm (SAMBA) developed at ICL. In the formulation the number of simulations is reduced using a Smolyak sparsity model. The multi-fidelity extension, with application to wind engineering problems is discussed and presented in this work. The overall goal of such formulation is to gain an accuracy of mixed lowhigh fidelity simulations comparable to the ones obtained with only high fidelity simulations, at a fraction of the computational cost.

Cassinelli A, Xu H, Montomoli F, et al., 2019, ON THE EFFECT OF INFLOW DISTURBANCES ON THE FLOW PAST A LINEAR LPT VANE USING SPECTRAL/HP ELEMENT METHODS, ASME Turbo Expo: Turbomachinery Technical Conference and Exposition, Publisher: AMER SOC MECHANICAL ENGINEERS

Sakai E, Meng B, Ahlfeld R,
et al., 2018, Bi-fidelity UQ with Combination of co-Kriging and Arbitrary Polynomial Chaos: Film Cooling with Back Facing Step using RANS and DES, *International Journal of Heat and Mass Transfer*, ISSN: 0017-9310

Griffini D, Salvadori S, Carnevale M,
et al., 2018, Uncertainty Quantification in Hydrodynamic Bearings, *Energy Procedia*, ISSN: 1876-6102

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