Francesco Montomoli

Direct numerical simulations (DNSs) of the T106A low-pressure turbine were conducted for various turbulence intensities and length scales to investigate their effects on flow behaviour and transition. A source-term formulation of the synthetic eddy method (SEM) was implemented in the Nektar++ spectral/hp element framework to introduce anisotropic turbulence into the flow field. A single sponge layer was imposed, which covers the inflow and outflow regions just downstream and upstream of the inflow and outflow boundaries, respectively, to avoid acoustic wave reflections on the boundary conditions. Additionally, in the T106A model, mixed polynomial orders were utilized, as Nektar++ allows different polynomial orders for adjacent elements. A lower polynomial order was employed in the outflow region to further assist the sponge layer by coarsening the mesh and diffusing the turbulence near the outflow boundary. Thus, this study contributes to the development of a more robust and efficient model for high-fidelity simulations of turbine blades by enhancing stability and producing a more accurate flow field. The main findings are compared with experimental and DNS data, showing good agreement and providing new insights into the influence of turbulence length scales on flow separation, transition, wake behaviour, and loss profiles.

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). 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. The aim is to improve mixing predictions in LPT wakes, compared to the baseline k-ω SST, in terms of velocity profiles, turbulent kinetic energy 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, including transition 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.

We illustrate an application of graph neural networks (GNNs) to predict the pressure, temperature and velocity fields induced by a sudden explosion. The aim of the work is to enable accurate simulation of explosion events in large and geometrically complex domains. Such simulations are currently out of the reach of existing CFD solvers, which represents an opportunity to apply machine learning. The training dataset is obtained from the results of URANS analyses in OpenFOAM. We simulate the transient flow following impulsive events in air in atmospheric conditions. The time history of the fields of pressure, temperature and velocity obtained from a set of such simulations is then recorded to serve as a training database. In the training simulations we model a cubic volume of air enclosed within rigid walls, which also encompass rigid obstacles of random shape, position and orientation. A subset of the cubic volume is initialized to have a higher pressure than the rest of the domain. The ensuing shock initiates the propagation of pressure waves and their reflection and diffraction at the obstacles and walls. A recently proposed GNN framework is extended and adapted to this problem. During the training, the model learns the evolution of thermodynamic quantities in time and space, as well as the effect of the boundary conditions. After training, the model can quickly compute such evolution for unseen geometries and arbitrary initial and boundary conditions, exhibiting good generalization capabilities for domains up to 125 times larger than those used in the training simulations.

Trailing edge cutback film cooling flows are ubiquitous in small and medium gas turbines, but they are difficult to predict accurately due to the inherent deterministic and stochastic unsteadiness that controls the effectiveness of the cooling system. To help develop accurate closure models for such flows, the characteristics of both types of unsteadiness and their effects on the mean flows are analyzed in this research. Zonal detached eddy simulation (ZDES) is performed on a trailing edge cutback flow model, and the numerical results are validated against the measured data. Then, by using spectral proper orthogonal decomposition (SPOD) reconstruction, the original dataset is segregated into deterministic and stochastic unsteadiness. The characteristics of the stress tensor and the heat flux of each type of unsteadiness are analyzed in detail, and notable differences between the two unsteadiness are identified in terms of the stress tensor anisotropy and distribution of unsteady kinetic energy and heat flux. By propagating the unsteadiness through the Reynolds-averaged Navier–Stokes (RANS) equations, the effect of different unsteadiness on the mean flow prediction is quantified. An accurate prediction of the total stress tensor reduces the prediction error in the velocity field by 79% and cooling effectiveness by 55%. An accurate prediction of the total heat flux vector reduces the prediction error in cooling effectiveness further by 37%. These findings provide valuable knowledge for the physical understanding, turbulence modeling, and aerothermal design of cutback trailing edge flows.

In this work, a new multifidelity (MF) uncertainty quantification (UQ) framework is presented and applied to the LS89 nozzle modified by fouling. Geometrical uncertainties significantly influence the 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 multifidelity 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 platform was then built based on key components including the MF-DNN model, the sampling module, the parameterization module and the statistical processing module. 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 the 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 platform could provide a useful tool in the design and optimization of advanced turbomachinery considering high-dimensional input uncertainties.

In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor's flow field. PINNs also show obvious advantages over the traditional CFD approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flow field of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.