Imperial College London

Prof Francesco Montomoli

Faculty of EngineeringDepartment of Aeronautics

Professor in Computational Aerodynamics
 
 
 
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Contact

 

+44 (0)20 7594 5151f.montomoli Website

 
 
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Location

 

215City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

137 results found

Li Z, Montomoli F, 2024, Aleatory uncertainty quantification based on multi-fidelity deep neural networks, Reliability Engineering and System Safety, Vol: 245, ISSN: 0951-8320

Traditional methods for uncertainty quantification (UQ) struggle with the curse of dimensionality when dealing with high-dimensional problems. One approach to address this challenge is to leverage the potent approximation capabilities of deep neural networks (DNNs). However, conventional DNNs often demand a substantial amount of high-fidelity (HF) training data to ensure precise predictions. Unfortunately, the availability of such data is limited due to computational or experimental constraints, primarily driven by associated costs. To mitigate these training expenses, this research introduces multi-fidelity deep neural networks (MF-DNNs), wherein a sub-network is constructed to simultaneously capture both linear and non-linear correlations between HF- and low-fidelity (LF) data. The efficacy of MF-DNNs is initially demonstrated by accurately approximating diverse benchmark functions. Subsequently, the developed MF-DNNs are employed for the first time to simulate the aleatory uncertainty propagation in 1-, 32-, and 100-dimensional contexts, considering either uniform or Gaussian distributions of input uncertainties. The UQ results affirm that MF-DNNs adeptly predict probability density distributions of quantities of interest (QoI) and their statistical moments without significant compromise of accuracy. Furthermore, MF-DNNs are applied to model the physical flow inside an aircraft propulsion system while accounting for aleatory uncertainties originating from experimental measurement errors. The distributions of isentropic Mach number are accurately predicted by MF-DNNs based on the 2D Euler flow field and few experimental data points. In conclusion, the proposed MF-DNN framework exhibits significant promise in addressing UQ and robust optimization challenges in practical engineering applications, particularly when dealing with multi-fidelity data sources.

Journal article

Bisio V, Montomoli F, Rossin S, Tagarielli VLet al., 2024, On the pressure wave emanating from a deflagration flame front, Heliyon, Vol: 10, ISSN: 2405-8440

We consider a spherical flame expanding from an ignition point through a homogeneous, flammable gaseous mixture. We analytically predict the transient pressure and velocity fields ahead of the flame as a function of the flame front position, which is assumed to evolve in time according to a power-law relation. The predictions are successfully validated by CFD simulations. We show that the model is also effective for analyzing real deflagration problems, by predicting measurements taken in hydrocarbon deflagration tests.

Journal article

Li Z, Montomoli F, Casari N, Pinelli Met al., 2023, High-Dimensional Uncertainty Quantification of High-Pressure Turbine Vane Based on Multifidelity Deep Neural Networks, JOURNAL OF TURBOMACHINERY-TRANSACTIONS OF THE ASME, Vol: 145, ISSN: 0889-504X

Journal article

Baker CM, Blonda P, Casella F, Diele F, Marangi C, Martiradonna A, Montomoli F, Pepper N, Tamborrino C, Tarantino Cet al., 2023, Using remote sensing data within an optimal spatiotemporal model for invasive plant management: the case of Ailanthus altissima in the Alta Murgia National Park, Scientific Reports, Vol: 13, Pages: 1-14, ISSN: 2045-2322

We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction–diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density. Remote sensing and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. The approach has been applied to the plant species Ailanthus altissima (Mill.) Swingle within the Alta Murgia National Park. This area is one of the Natura 2000 sites under the study of the ongoing National Biodiversity Future Center (NBFC) funded by the Italian National Recovery and Resilience Plan (NRRP), and pilot site of the finished H2020 project ECOPOTENTIAL, which aimed at the integration of modeling tools and Earth Observations for a sustainable management of protected areas. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data provided by the EU Life Alta Murgia Project (LIFE12 BIO/IT/000213), a project aimed at the eradication of A. altissima in the Alta Murgia National Park.

Journal article

Vivarelli G, Isler JA, Williams TS, Montomoli F, Sherwin SJ, Wilson M, Adami P, Vazquez-Diaz Ret al., 2023, ON THE EFFECT OF CURVATURE AND COMPRESSIBILITY IN LAMINAR BOUNDARY LAYERS OVER FAN BLADES

During the early phases of the turbomachinery design process, it is often the case that various simplifications and assumptions are made to understand boundary layer behaviour subject to pressure gradients. For example, simplified boundary-layer models can be employed to appreciate losses incurred in flows over gas turbine components. These neglect the effect of surface curvature and/or density, while retaining the surface pressure distribution. This paper's objective is to assess the implication of those simplifications by studying a realistic fan loading and the status of the boundary layer just upstream of a shock. A set of 2D aerofoils, representing the pressure distribution found at 70% and 90% span of a modern low-speed fan, are analysed at cruise conditions. In order to investigate compressibility, the two profiles were redesigned to achieve exactly the same pressure loading at incompressible conditions. On the other hand, curvature effects were studied by means of a comparison of incompressible flow over the symmetric aerofoil and a convergent-convergent nozzle, once again with the same loading. The resulting laminar boundary layer quantities were compared explaining the necessary scaling required along with the reasons behind the discrepancies, such as the effect of density and curvature variations. All test-cases were analysed deploying Nektar++. This is a high-order spectral h/p element solver having both compressible and incompressible formulations.

Conference paper

Isler J, Vivarelli G, Montomoli F, Sherwin S, Adami P, Vazquez Ret al., 2023, High Fidelity Compressible and Incompressible Flow Simulations of an Engine Intake Pressure Distribution

In this work, we investigated the impact of compressibility of an engine intake pressure distribution at high Reynolds numbers in absence of transonic effects and under strong adverse pressure gradients on a flate plate by means of computational simulations. In order to assess the compressibility effects in the vicinity and over the flat plate surface, compressible and incompressible high-order Implicit Large Eddy Simulations (iLES) of the Navier-Stokes (NS) equations were performed using the Nektar++ framework. With this methodology, we were able to assert what are the physical mechanisms behind the turbulent transition processes. In addition, and crucially, what role the compressibility is playing in this flow configuration, in order to promote the design of improved geometries using high-order methods. Therefore, a consistent investigation of the density variation effects and boundary layer behaviours of the compressible and incompressible solutions provided the necessary understanding of the viscous driven separation that governs the flow in an engine intake at moderate fan speed.

Conference paper

Marioni YF, Adami P, Montomoli F, Vázquez-Díaz R, Sherwin Set al., 2023, MACHINE-LEARNT TURBULENCE CLOSURES FOR AXIAL COMPRESSOR CASCADE WITH CORNER SEPARATION

Corner separation in axial compressors is a complex phenomenon, which is hardly well captured by traditional steady RANS calculations, primarily because of the deficiencies of the Reynolds stress tensor formulations. In this work a Machine Learning (ML) framework is applied to Large-Eddy Simulation (LES) data to develop non-linear turbulence stress closures. Two linear compressor cascade LES calculations are run with the Rolls-Royce solver HYDRA: one at nominal incidence condition, for which no corner separation is observed, and one at high incidence, where more complex secondary flow structures and recirculation appear. The two cases are validated against experiments performed in the linear cascade facility at LMFA, Lyon. A transitional variant of Wilcox's k−ω SST is used as baseline turbulence model and traditional closures are found to perform well at nominal conditions, but poorly at higher incidence, as they strongly over-predict losses and secondary flows. The coefficients of an Explicit Algebraic Reynolds Stress Model (EARSM) are trained using Artificial Neural Networks (ANN) on the high incidence dataset. When tested in HYDRA, improvements are observed in the prediction of end-wall losses, as well as vorticity and Reynolds stress contours downstream of the separation region. The model also performs well at nominal incidence. The importance of a near-wall coefficient damping is discussed. Finally, end-wall loss polars are computed and compared for different non-linear constitutive relationships.

Conference paper

Li Z, Montomoli F, Casari N, Pinelli Met al., 2023, HIGH-DIMENSIONAL UNCERTAINTY QUANTIFICATION OF HIGH-PRESSURE TURBINE VANE BASED ON MULTI-FIDELITY DEEP NEURAL NETWORKS

In this work a new multi-fidelity (MF) uncertainty quantification (UQ) framework is presented and applied to LS89 nozzle modified by fouling. Geometrical uncertainties significantly influence aerodynamic performance of gas turbines. One representative example is given by the airfoil shape modified by fouling deposition, as in turbine nozzle vanes, which generates high-dimensional input uncertainties. However, the traditional UQ approaches suffer from the curse of dimensionality phenomenon in predicting the influence of high-dimensional uncertainties. Thus, a new approach based on multi-fidelity deep neural networks (MF-DNN) was proposed in this paper to solve the high-dimensional UQ problem. The basic idea of MF-DNN is to ensure the approximation capability of neural networks based on abundant low-fidelity (LF) data and few high-fidelity (HF) data. The prediction accuracy of MF-DNN was first evaluated using a 15-dimensional benchmark function. An affordable turbomachinery UQ framework was then built based on the MF-DNN model, the sampling-, the parameterization- and the statistical processing modules. The impact of fouling deposition on LS89 nozzle vane flow was investigated using the proposed UQ framework. In detail, the MF-DNN was fine-tuned based on bi-level numerical simulation results: the 2D Euler flow field as low-fidelity data and the 3D Reynolds-Averaged Navier-Stokes (RANS) flow field as high-fidelity data. The UQ results show that the total pressure loss of LS89 vane is increased by at most 17.1 % or reduced by at most 4.3 %, while the mean value of loss is increased by 3.4 % compared to the baseline. The main reason for relative changes in turbine nozzle performance is that the geometric uncertainties induced by fouling deposition significantly alter the intensity of shock waves near the throat area and trailing edge. The developed UQ framework could provide a useful tool in the design and optimization of advanced turbomachinery considering high-dimensio

Conference paper

Marioni YF, Adami P, Montomoli F, Vázquez-Díaz R, Sherwin Set al., 2023, MACHINE-LEARNT TURBULENCE CLOSURES FOR AXIAL COMPRESSOR CASCADE WITH CORNER SEPARATION, ISSN: 2313-0067

Corner separation in axial compressors is a complex phenomenon, which is hardly well captured by traditional steady RANS calculations, primarily because of the deficiencies of the Reynolds stress tensor formulations. In this work a Machine Learning (ML) framework is applied to Large-Eddy Simulation (LES) data to develop non-linear turbulence stress closures. Two linear compressor cascade LES calculations are run with the Rolls-Royce solver HYDRA: one at nominal incidence condition, for which no corner separation is observed, and one at high incidence, where more complex secondary flow structures and recirculation appear. The two cases are validated against experiments performed in the linear cascade facility at LMFA, Lyon. A transitional variant of Wilcox's k−ω SST is used as baseline turbulence model and traditional closures are found to perform well at nominal conditions, but poorly at higher incidence, as they strongly over-predict losses and secondary flows. The coefficients of an Explicit Algebraic Reynolds Stress Model (EARSM) are trained using Artificial Neural Networks (ANN) on the high incidence dataset. When tested in HYDRA, improvements are observed in the prediction of end-wall losses, as well as vorticity and Reynolds stress contours downstream of the separation region. The model also performs well at nominal incidence. The importance of a near-wall coefficient damping is discussed. Finally, end-wall loss polars are computed and compared for different non-linear constitutive relationships.

Conference paper

Isler J, Vivarelli G, Montomoli F, Sherwin S, Adami P, Vazquez Ret al., 2023, High Fidelity Compressible and Incompressible Flow Simulations of an Engine Intake Pressure Distribution, ISSN: 2313-0067

In this work, we investigated the impact of compressibility of an engine intake pressure distribution at high Reynolds numbers in absence of transonic effects and under strong adverse pressure gradients on a flate plate by means of computational simulations. In order to assess the compressibility effects in the vicinity and over the flat plate surface, compressible and incompressible high-order Implicit Large Eddy Simulations (iLES) of the Navier-Stokes (NS) equations were performed using the Nektar++ framework. With this methodology, we were able to assert what are the physical mechanisms behind the turbulent transition processes. In addition, and crucially, what role the compressibility is playing in this flow configuration, in order to promote the design of improved geometries using high-order methods. Therefore, a consistent investigation of the density variation effects and boundary layer behaviours of the compressible and incompressible solutions provided the necessary understanding of the viscous driven separation that governs the flow in an engine intake at moderate fan speed.

Conference paper

Vivarelli G, Isler JA, Williams TS, Montomoli F, Sherwin SJ, Wilson M, Adami P, Vazquez-Diaz Ret al., 2023, ON THE EFFECT OF CURVATURE AND COMPRESSIBILITY IN LAMINAR BOUNDARY LAYERS OVER FAN BLADES, ISSN: 2313-0067

During the early phases of the turbomachinery design process, it is often the case that various simplifications and assumptions are made to understand boundary layer behaviour subject to pressure gradients. For example, simplified boundary-layer models can be employed to appreciate losses incurred in flows over gas turbine components. These neglect the effect of surface curvature and/or density, while retaining the surface pressure distribution. This paper's objective is to assess the implication of those simplifications by studying a realistic fan loading and the status of the boundary layer just upstream of a shock. A set of 2D aerofoils, representing the pressure distribution found at 70% and 90% span of a modern low-speed fan, are analysed at cruise conditions. In order to investigate compressibility, the two profiles were redesigned to achieve exactly the same pressure loading at incompressible conditions. On the other hand, curvature effects were studied by means of a comparison of incompressible flow over the symmetric aerofoil and a convergent-convergent nozzle, once again with the same loading. The resulting laminar boundary layer quantities were compared explaining the necessary scaling required along with the reasons behind the discrepancies, such as the effect of density and curvature variations. All test-cases were analysed deploying Nektar++. This is a high-order spectral h/p element solver having both compressible and incompressible formulations.

Conference paper

Hammond J, Pietropaoli M, Montomoli F, 2022, Robust data-driven turbulence closures for improved heat transfer prediction in complex geometries, INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW, Vol: 98, ISSN: 0142-727X

Journal article

Pepper N, Crespo L, Montomoli F, 2022, Adaptive learning for reliability analysis using Support Vector Machines, RELIABILITY ENGINEERING & SYSTEM SAFETY, Vol: 226, ISSN: 0951-8320

Journal article

Pepper N, Montomoli F, Sharma S, 2022, A Non-Parametric Histogram Interpolation Method for Design Space Exploration, JOURNAL OF MECHANICAL DESIGN, Vol: 144, ISSN: 1050-0472

Journal article

Hammond J, Montomoli F, Pietropaoli M, Sandberg RD, Michelassi Vet al., 2022, Machine Learning for the Development of Data-Driven Turbulence Closures in Coolant Systems, JOURNAL OF TURBOMACHINERY-TRANSACTIONS OF THE ASME, Vol: 144, ISSN: 0889-504X

Journal article

Hammond J, Marioni YF, Montomoli F, 2022, Error Quantification for the Assessment of Data-Driven Turbulence Models, FLOW TURBULENCE AND COMBUSTION, Vol: 109, Pages: 1-26, ISSN: 1386-6184

Journal article

Hammond J, Pepper N, Montomoli F, Michelassi Vet al., 2022, Machine Learning Methods in CFD for Turbomachinery: A Review, INTERNATIONAL JOURNAL OF TURBOMACHINERY PROPULSION AND POWER, Vol: 7

Journal article

Cassinelli A, Mateo Gabín A, Montomoli F, Adami P, Vázquez Díaz R, Sherwin SJet al., 2022, Reynolds sensitivity of the wake passing effect on a LPT cascade using spectral/hp element methods, International Journal of Turbomachinery, Propulsion and Power, Vol: 7, Pages: 8-8, ISSN: 2504-186X

Reynolds-Averaged Navier–Stokes (RANS) methods continue to be the backbone of CFD-based design; however, the recent development of high-order unstructured solvers and meshing algorithms, combined with the lowering cost of HPC infrastructures, has the potential to allow for the introduction of high-fidelity simulations in the design loop, taking the role of a virtual wind tunnel. Extensive validation and verification is required over a broad design space. This is challenging for a number of reasons, including the range of operating conditions, the complexity of industrial geometries and their relative motion. A representative industrial low pressure turbine (LPT) cascade subject to wake passing interactions is analysed, adopting the incompressible Navier–Stokes solver implemented in the spectral/hp element framework Nektar++. The bar passing effect is modelled by leveraging a spectral-element/Fourier Smoothed Profile Method. The Reynolds sensitivity is analysed, focusing in detail on the dynamics of the separation bubble on the suction surface as well as the mean flow properties, wake profiles and loss estimations. The main findings are compared with experimental data, showing agreement in the prediction of wake traverses and losses across the entire range of flow regimes, the latter within 5% of the experimental measurements.

Journal article

Bisio V, Montomoli F, Rossin S, Ruggiero M, Tagarielli VLet al., 2022, Predictions and uncertainty quantification of the loading induced by deflagration events on surrounding structures, Process Safety and Environmental Protection, Vol: 158, Pages: 445-460, ISSN: 0957-5820

The threat of accidental hydrocarbon explosions is of major concern to industrial operations; in particular, there is a need for design tools to assess and quantify the effects of potential deflagration events. Here we present a design methodology based on analytical models that allow assessing the loading and structural response of objects exposed to pressure waves generated by deflagration events. The models allow determining: i) the importance of Fluid-Structure Interaction (FSI) effects; ii) the transient pressure histories on box-like or circular cylindrical objects, including the effects of pressure clearing; iii) the dynamic response of structural components that can be idealised as fully clamped beams. We illustrate by three case studies the complete design methodology and validate the analytical models by comparing their predictions to those of detailed CFD and FE simulations. We employ the validated analytical models to perform Monte Carlo analyses to quantify, for box-like structures, how the uncertainty in input design variables propagates through to the expected maximum force and impulse. We present this information in the form of non-dimensional uncertainty maps.

Journal article

Hammond J, Pietropaoli M, Montomoli F, 2022, Topology optimisation of turbulent flow using data-driven modelling, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, Vol: 65, ISSN: 1615-147X

Journal article

Sakuma M, Pepper N, Warnakulasuriya S, Montomoli F, Wuech-ner R, Bletzinger K-Uet al., 2022, Multi-fidelity uncertainty quantification of high Reynolds number turbulent flow around a rectangular 5:1 cylinder, 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, Publisher: Techno Press, Pages: 127-136, ISSN: 1226-6116

This work shows the application of Multi-fidelity Uncertainty Quantification to WindEngineering problems. As test case a rectangular shape is used, with a fillet radius, in orderto represent the geometrical variations that can affect buildings or other bluff bodies. Therectangular cylinder used has a chord-to-thickness ratio 5:1. This rectangular shape is animportant basic shape for wind engineering tasks, e.g. in case of buildings or other bluff bodiesexposed to the flow. Moreover it is well investigated and documented.Coarse and fine meshes are used as low and high fidelity models respectively. To performCFD simulations, the stabilized finite element methods are used in both the high and low fidelitymodel with a CFD code developed by TUM and the International Center for Numerical Methodsin Engineering. The underlying UQ framework is based on a Sparse Arbitrary Moment BasedAlgorithm (SAMBA) developed at ICL. In the formulation the number of simulations is reducedusing a Smolyak sparsity model.The multi-fidelity extension, with application to wind engineering problems is discussed andpresented 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, ata fraction of the computational cost.

Conference paper

Raske N, Gonzalez OA, Furino S, Pietropaoli M, Shahpar S, Montomoli Fet al., 2022, THERMAL MANAGEMENT FOR ELECTRIFICATION IN AIRCRAFT ENGINES: OPTIMIZATION OF COOLANT SYSTEM

This work shows the application of fluid Topology Optimization for the thermal management of electric parts in aircraft engines. There is a growing trend in electrification of current engines, but this requires higher power to be dissipated. Standard coolant systems based on serpentines are not effective enough to remove the heat produced by these systems. In this work a new solution is shown which has a higher heat dissipation, lower pressure loss and a reduction in the mass of the heat exchanger. The optimization is carried out with the commercial solver TOffee. Manufacturing constraints allow the part to be manufacturable using two different methods: additive manufacturing and milling with diffusion bonding. Overall, the optimized geometry, a nearly 2D coldplate with extruded channels, shows higher heat dissipation and a reduction of weight of 38.5% if compared with the baseline heat exchanger. The overall pressure drop has been also reduced by 65%.

Conference paper

Lahooti M, Vivarelli G, Montomoli F, Sherwin SJet al., 2022, Under-resolved direct numerical simulation of naca0012 at stall

In this work a high-order spectral-h/p element solver is employed to efficiently but accurately resolve the flow field around the NACA0012 aerofoil. In particular, the conditions considered are a Reynolds number of 150000 and three angles of attack, namely 9◦, 10◦ and 12◦. This particular study aims at providing the necessary preliminary insight into the flow dynamics of the turbulent transition at near-post stall with very well resolved Large Eddy Simulation range if not Direct Numerical Simulation. Therefore, the first step consists of determining the mesh resolution required and the spanwise length. Our results repeatedly demonstrate the possible existence of a large-scale low-frequency 2D dominant flow structure over the span where. It was found that employing a single chord length in z is not sufficient to capture it. Concerning the flow behaviour, it is observed that a laminar separation bubble forms at the aerofoil leading edge. This tends to move upstream, shorten in length and increase in height as the angle of attack is increased. Mild three-dimensional behaviour is seen right from the beginning of the aerofoil suction surface with turbulent transition occurring just after the reattachment point. In particular, this is seen to happen sooner with higher aerofoil inclination. Finally, our results indicate an interaction of large-scale structures with the boundary layer.

Conference paper

Vivarelli G, Isler JA, Montomoli F, Sherwin SJ, Adami Pet al., 2022, HIGH-ORDER SPECTRAL/HP COMPRESSIBLE AND INCOMPRESSIBLE COMPARISON OF TRANSITIONAL BOUNDARY-LAYERS SUBJECT TO A REALISTIC PRESSURE GRADIENT AND HIGH REYNOLDS NUMBER

Within the literature, there are limited high-order results concerning large Reynolds number flows under the influence of strong adverse pressure gradients, mainly due to the computational expense involved. The main advantage in employing high-order methodologies over standard second-order finite-volume solvers, relates to their ability to increase accuracy with a significantly lower number of degrees of freedom. In theory, this would permit Direct Numerical Simulation sort of analysis. Yet, there is still a significant computational cost involved. For this reason, an efficient approach to analyse such flows by means of a Nektar++ high-order Implicit Large Eddy Simulation is proposed. The flow conditions considered in this case cause a separation bubble to form with consequent turbulent transition. In particular, Tollmien-Schlichting instabilities trigger Kelvin-Helmholtz behaviour, which in turn cause the turbulent transition. The bulk of the study will be carried out with the incompressible flow solver, as it is assumed that compressibility effects are negligible within the boundary layer. An initial 2D analysis will be conducted to determine the necessary spatial resolution and whether it is possible to consider a subset of the overall simulation domain to reduce the computational expense. Once this will have been established, the 3D results will be achieved by Fourier expansion in the cross-flow direction. These results will prove the cost-effectiveness of the methodology, that could be used within an industrial setting with a limited turn-around time. Additionally, a comparison between the results achieved by means of the Nektar++ compressible flow solver in 2D and 3D will be provided, to assess any differences that may be present.

Conference paper

Marioni YF, Cassinelli A, Adami P, Sherwin S, Diaz RV, Montomoli Fet al., 2022, DEVELOPMENT OF MACHINE-LEARNT TURBULENCE CLOSURES FOR WAKE MIXING PREDICTIONS IN LOW-PRESSURE TURBINES

In this work, a DNS – Machine Learning (ML) framework is developed for low-pressure turbine (LPT) profiles to inform turbulence closures in Reynolds-Averaged Navier–Stokes (RANS) calculations. This is done by training the coefficients of Explicit Algebraic Reynolds Stress Models (EARSM) with shallow artificial neural networks (ANN) as a function of input flow features. DNS data are generated with the incompressible Navier–Stokes solver in Nektar++ and validated against experiments. All calculations include moving bars upstream of the profile to capture the effect of incoming wakes. The resulting formulations are then implemented in the Rolls-Royce solver HYDRA and tested a posteriori. The aim is to improve mixing predictions in LPT wakes, compared to the baseline model, Wilcox’s k− ω SST, in terms of velocity profiles, turbulent kinetic energy (TKE) production and mixing losses. LPT calculations are run at Reynolds numbers spanning from ≈ 80k to ≈ 300k, to cover the range of aircraft engine applications. Models for the low and high Reynolds datasets are trained separately and a method is developed to merge the two together. The resulting model is tested on an intermediate Reynolds case. This process is followed for two computational domains: one starting downstream of the profile trailing edge and one including the last portion of the profile. Finally, the developed closures are tested on the entire profile, to confirm the validity of the improvements when the additional effect of transition is included in the simulation. This work explains the methodology used to develop ML-driven closures and shows how it is possible to combine models trained on different datasets.

Conference paper

Frey Marioni Y, de Toledo Ortiz EA, Cassinelli A, Montomoli F, Adami P, Vazquez Ret al., 2021, A Machine Learning Approach to Improve Turbulence Modelling from DNS Data Using Neural Networks, INTERNATIONAL JOURNAL OF TURBOMACHINERY PROPULSION AND POWER, Vol: 6

Journal article

Pepper N, Gaymann A, Montomoli F, Sharma Set al., 2021, Local bi-fidelity field approximation with knowledge based neural networks for computational fluid dynamics, Scientific Reports, Vol: 11, Pages: 1-11, ISSN: 2045-2322

This work presents a machine learning based method for bi-fidelity modelling. The method, a Knowledge Based Neural Network (KBaNN), performs a local, additive correction to the outputs of a coarse computational model and can be used to emulate either experimental data or the output of a more accurate, but expensive, computational model. An advantage of the method is that it can scale easily with the number of input and output features. This allows bi-fidelity modelling approaches to be applied to a wide variety of problems, for instance in the bi-fidelity modelling of fields. We demonstrate this aspect in this work through an application to Computational Fluid Dynamics, in which local corrections to a velocity field are performed by the KBaNN to account for mesh effects. KBaNNs were trained to make corrections to the free-stream velocity field and the boundary layer. They were trained on a limited data-set consisting of simple two-dimensional flows. The KBaNNs were then tested on a flow over a more complex geometry, a NACA 2412 airfoil. It was demonstrated that the KBaNNs were still able to provide a local correction to the velocity field which improved its accuracy. The ability of the KBaNNs to generalise to flows around new geometries that share similar physics is encouraging. Through knowledge based neural networks it may be possible to develop a system for bi-fidelity, computer based design which uses data from past simulations to inform its predictions.

Journal article

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

Journal article

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.

Journal article

Fadiga E, Casari N, Suman A, Pinelli M, Montomoli Fet al., 2021, Design considerations and numerical simulations of variable thickness scroll geometries, Pages: 1626-1636

Among the suitable expanders for small scale Organic Rankine Cycles (ORCs), scrolls are one of the most frequent solutions. The main advantages related to such machines are cost-effectiveness, high efficiency, silent operation, small size and high reliability. The great majority of scroll machines available on the market is designed using a spiral profile generated by the involute of a circle, resulting in a constant wall thickness. The main consequence of this approach is that an increase in the volume ratio has to be obtained with an increase in the scroll length, resulting in a machine augmented size. Currently, the state of the art in scroll expanders for small size ORC is to revert a compressor in its operation. Variable thickness geometries offer an alternative way to modify the expansion ratio of the machine, with no modifications on the scroll length. In this work, the authors have investigated a scroll geometry derived from a curvature radius parametrized with involute angle, firstly introduced by Gravesen and Henriksen (2001). In the beginning, the influence of the parameterization on the volume ratio has been deeply analyzed. At a later stage, a noteworthy geometry has been simulated using an extension of the OpenFOAM C++ toolbox for Computational Fluid Dynamics.

Conference paper

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