This article establishes a data-driven modeling framework for lean hydrogen ($ {\mathrm{H}}_2 $)-air reaction rates for the Large Eddy Simulation (LES) of turbulent reactive flows. This is particularly challenging since $ {\mathrm{H}}_2 $ molecules diffuse much faster than heat, leading to large variations in burning rates, thermodiffusive instabilities at the subfilter scale, and complex turbulence-chemistry interactions. Our data-driven approach leverages a Convolutional Neural Network (CNN), trained to approximate filtered burning rates from emulated LES data. First, five different lean premixed turbulent $ {\mathrm{H}}_2 $-air flame Direct Numerical Simulations (DNSs) are computed each with a unique global equivalence ratio. Second, DNS snapshots are filtered and downsampled to emulate LES data. Third, a CNN is trained to approximate the filtered burning rates as a function of LES scalar quantities: progress variable, local equivalence ratio, and flame thickening due to filtering. Finally, the performances of the CNN model are assessed on test solutions never seen during training. The model retrieves burning rates with very high accuracy. It is also tested on two filter and downsampling parameters and two global equivalence ratios between those used during training. For these interpolation cases, the model approximates burning rates with low error even though the cases were not included in the training dataset. This a priori study shows that the proposed data-driven machine learning framework is able to address the challenge of modeling lean premixed $ {\mathrm{H}}_2 $-air burning rates. It paves the way for a new modeling paradigm for the simulation of carbon-free hydrogen combustion systems.

Propulsive fuselage aircraft complement the two under-wing turbofans of current aircraft with an embedded propulsion system within the airframe to ingest the energy-rich fuselage boundary layer. The key design features of this embedding are examined and related to an aero-propulsive performance assessment undertaken in the absolute reference frame which is believed to best evaluate these effects with intuitive physics-based interpretations. First, this study completes previous investigations on the potential for energy recovery for different fuselage slenderness ratios to characterise the aerodynamics sensitivity to morphed fuselage-tail design changes and potential performance before integrating fully circumferential propulsors. Its installation design space is then explored with macro design parameters (position, size and operating conditions) where an optimum suggests up to 11% fuel savings during cruise and up to 16% when introducing compact nacelles and re-scaling of the under-wing turbofans. Overall, this work provides valuable insights for designers and aerodynamicists on the potential performance of their concepts to meet the environmental targets of future aircraft.

In several problems involving fluid flows, computational fluid dynamics (CFD) provides detailed quantitative information and allows the designer to successfully optimize the system by minimizing a cost function. Sometimes, however, one cannot improve the system with CFD alone, because a suitable cost function is not readily available; one notable example is diagnosis in medicine. The application considered here belongs to the field of rhinology; a correct air flow is key for the functioning of the human nose, yet the notion of a functionally normal nose is not available and a cost function cannot be written. An alternative and attractive pathway to diagnosis and surgery planning is offered by data-driven methods. In this work, we consider the machine learning study of nasal impairment caused by anatomic malformations, with the aim of understanding whether fluid dynamic features, available after a CFD analysis, are more effective than purely geometric features at the training of a neural network for regression. Our experiments are carried out on an extremely simplified anatomic model and a correspondingly simple CFD approach; nevertheless, they show that flow-based features perform better than geometry-based ones and allow the training of a neural network with fewer inputs, a crucial advantage in fields like medicine.

Compressible anisothermal flows, which are commonly found in industrial settings such as combustion chambers and heat exchangers, are characterized by significant variations in density, viscosity, and heat conductivity with temperature. These variations lead to a strong interaction between the temperature and velocity fields that impacts the near-wall profiles of both quantities. Wall-modeled large-eddy simulations (LESs) rely on a wall model to provide a boundary condition, for example, the shear stress and the heat flux that accurately represents this interaction despite the use of coarse cells near the wall, and thereby achieve a good balance between computational cost and accuracy. In this article, the use of graph neural networks for wall modeling in LES is assessed for compressible anisothermal flow. Graph neural networks are a type of machine learning model that can learn from data and operate directly on complex unstructured meshes. Previous work has shown the effectiveness of graph neural network wall modeling for isothermal incompressible flows. This article develops the graph neural network architecture and training to extend their applicability to compressible anisothermal flows. The model is trained and tested a priori using a database of both incompressible isothermal and compressible anisothermal flows. The model is finally tested a posteriori for the wall-modeled LES of a channel flow and a turbine blade, both of which were not seen during training.

Deep reinforcement learning (DRL) is promising for solving control problems in fluid mechanics, but it is a new field with many open questions. Possibilities are numerous and guidelines are rare concerning the choice of algorithms or best formulations for a given problem. Besides, DRL algorithms learn a control policy by collecting samples from an environment, which may be very costly when used with Computational Fluid Dynamics (CFD) solvers. Algorithms must therefore minimize the number of samples required for learning (sample efficiency) and generate a usable policy from each training (reliability). This paper aims to (a) evaluate three existing algorithms (DDPG, TD3, and SAC) on a fluid mechanics problem with respect to reliability and sample efficiency across a range of training configurations, (b) establish a fluid mechanics benchmark of increasing data collection cost, and (c) provide practical guidelines and insights for the fluid dynamics practitioner. The benchmark consists in controlling an airfoil to reach a target. The problem is solved with either a low-cost low-order model or with a high-fidelity CFD approach. The study found that DDPG and TD3 have learning stability issues highly dependent on DRL hyperparameters and reward formulation, requiring therefore significant tuning. In contrast, SAC is shown to be both reliable and sample efficient across a wide range of parameter setups, making it well suited to solve fluid mechanics problems and set up new cases without tremendous effort. In particular, SAC is resistant to small replay buffers, which could be critical if full-flow fields were to be stored.

This paper presents some of the first results of global linear stability analyses performed using a bespoke eigensolver that has recently been implemented in the next generation flow solver framework CODA. The eigensolver benefits from the automatic differentiation capability of CODA that allows computation of the exact product of the Jacobian matrix with an arbitrary complex vector. It implements the Krylov–Schur algorithm for solving the eigenvalue problem. The bespoke tool has been validated for the case of laminar flow past a circular cylinder with numerical results computed using the TAU code and those reported in the literature. It has been applied with both second-order finite volume and high-order discontinuous Galerkin schemes for the case of laminar flow past a square cylinder. It has been demonstrated that using high-order schemes on coarser grids leads to well-converged eigenmodes with a shorter computation time compared to using second-order schemes on finer grids.

As the Reynolds number increases, the large-eddy simulation (LES) of complex flows becomes increasingly intractable because near-wall turbulent structures become increasingly small. Wall modeling reduces the computational requirements of LES by enabling the use of coarser cells at the walls. This paper presents a machine-learning methodology to develop data-driven wall-shear-stress models that can directly operate, a posteriori, on the unstructured grid of the simulation. The model architecture is based on graph neural networks. The model is trained on a database which includes fully developed boundary layers, adverse pressure gradients, separated boundary layers, and laminar–turbulent transition. The relevance of the trained model is verified a posteriori for the simulation of a channel flow, a backward-facing step and a linear blade cascade.

This paper presents progress towards a transition modelling capability for use in the numerical solution of the Reynolds-averaged Navier-Stokes equations that provides accurate predictions for transonic flows and is thus suitable for use in the design of wings for aircraft flying at transonic speeds. To this end, compressibility corrections are developed and investigated to extend commonly used empirical correlations to transonic flight conditions while retaining their accuracy at low speeds. A compressibility correction for Tollmien-Schlichting instabilities is developed and applied to a smooth local correlation-based transition model and a stationary crossflow instability compressibility correction is included by adding a new crossflow source term function. Two- and three-dimensional transonic transition test cases demonstrate that the Tollmien-Schlichting compressibility correction produces substantially improved agreement with the experimental transition locations, particularly for higher Reynolds number applications where the effects of flow compressibility are expected to be more significant, such as the NASA CRM-NLF wing-body configuration, while the crossflow compressibility correction prevents an inaccurate, upstream transition front. The compressibility corrections and modifications do not significantly affect the numerical behaviour of the model, which provides an efficient alternative to non-local and higher-fidelity approaches, and can be applied to other transport-equation-based transition models with low-speed empirical correlations without affecting their predictive capability in the incompressible regime.

The use of topology optimization in the design of fluid dynamics systems is still in its infancy. With the decreasing cost of additive manufacture, the application of topology optimization in the design of structural components has begun to increase. This paper provides a method for using topology optimization to reduce the power dissipation of fluid dynamics systems, with the novelty of it being the first application of stochastic mechanisms in the design of 3D fluid–solid geometrical interfaces. The optimization algorithm uses the continuous adjoint method for sensitivity analysis and is optimized against an objective function for fluid power dissipation. The paper details the methodology behind a vanilla gradient descent approach before introducing stochastic behavior through a minibatch-based system. Both algorithms are then applied to a novel case study for an internal combustion engine's piston cooling gallery before the performance of each algorithm's resulting geometry is analyzed and compared. The vanilla gradient descent algorithm achieves an 8.9% improvement in pressure loss through the case study, and this is surpassed by the stochastic descent algorithm which achieved a 9.9% improvement, however this improvement came with a large time cost. Both approaches produced similarly unintuitive geometry solutions to successfully improve the performance of the cooling gallery.

This paper presents a relative fuel burn evaluation of the transonic strut-braced-wing configuration for the regional aircraft class in comparison to an equivalent conventional tube-and-wing aircraft. This is accomplished through multipoint aerodynamic shape optimisation based on the Reynolds-averaged Navier-Stokes equations. Aircraft concepts are first developed through low-order multidisciplinary design optimisation based on the design missions and top-level aircraft requirements of the Embraer E190-E2. High-fidelity aerodynamic shape shape optimisation is then applied to wing–body–tail models of each aircraft, with the objective of minimising the weighted-average cruise drag over a five-point operating envelope that includes the nominal design point, design points at $\pm 10\%$ nominal $C_L$ at Mach 0.78, and two high-speed cruise points at Mach 0.81. Design variables include angle-of-attack, wing (and strut) twist and section shape degrees of freedom, and horizontal tail incidence, while nonlinear constraints include constant lift, zero pitching moment, minimum wing and strut volume, and minimum maximum thickness-to-chord ratios. Results show that the multipoint optimised strut-braced wing maintains similar features to those of the single-point optimum, and compromises on-design performance by only two drag counts to achieve up to 11.6% reductions in drag at the off-design conditions. Introducing low-order estimates for approximating full aircraft performance, results indicate that the multipoint optimised strut-braced-wing regional jet offers a 13.1% improvement in cruise lift-to-drag ratio and a 7.8% reduction in block fuel over a 500nmi nominal mission when compared to the similarly optimised Embraer E190-E2-like conventional tube-and-wing aircraft.

As the key part for energy amplification of high-power laser systems, disk amplifiers must work in an extremely clean environment. Different from the traditional cleanliness control scheme of active intake and passive exhaust (AIPE), a new method of active exhaust and passive intake (AEPI) is proposed in this paper. Combined with computational fluid dynamics (CFD) technology, through the optimization design of the sizes, shapes, and locations of different outlets and inlets, the turbulence that is unfavorable to cleanliness control is effectively avoided in the disk amplifier cavity during the process of AEPI. Finally, the cleanliness control of the cavity of the disk amplifier can be realized just by once exhaust. Meanwhile, the micro negative pressure environment in the amplifier cavity produced during the exhaust process reduces the requirement for sealing. This method is simple, time saving, gas saving, efficient, and safe. It is also suitable for the cleanliness control of similar amplifiers.

Gas turbine engines for fixed-wing or rotary-wing aircraft are operated in a variety of harsh weather environments ranging from arctic, volcanic zones, to desert conditions. Operation under these degraded conditions leads to the undesired entrainment of complex particulates resulting in drastic performance losses. Hence, there is a critical need to understand the governing mechanisms to inform the development of durable thermal and environmental barrier coatings. The objective of the current work is to present a novel multiscale physics-based approach to study two-phase flows that take into account the underpinning particle transport and deposition dynamics. Sessile droplet models are presented and used to compute the contact angle at high temperatures and compared with experiments. The study also investigates the sensitivity of deposition patterns to the Stokes number and the results identify local vulnerability regions. The analysis suggests that particle size distributions and the initial trajectories of the particles are critically important in predicting the final deposition pattern.

In chemical process engineering, surrogate models of complex systems are often necessary for tasks of domain exploration, sensitivity analysis of the design parameters, and optimization. A suite of computational fluid dynamics (CFD) simulations geared toward chemical process equipment modeling has been developed and validated with experimental results from the literature. Various regression-based active learning strategies are explored with these CFD simulators in-the-loop under the constraints of a limited function evaluation budget. Specifically, five different sampling strategies and five regression techniques are compared, considering a set of four test cases of industrial significance and varying complexity. Gaussian process regression was observed to have a consistently good performance for these applications. The present quantitative study outlines the pros and cons of the different available techniques and highlights the best practices for their adoption. The test cases and tools are available with an open-source license to ensure reproducibility and engage the wider research community in contributing to both the CFD models and developing and benchmarking new improved algorithms tailored to this field.

Existing numerical schemes used to solve the governing equations for compressible flow suffer from dissipation errors which tend to smear out sharp discontinuities. Hybrid schemes show potential improvements in this challenging problem; however, the solution quality of a hybrid scheme heavily depends on the criterion to switch between the different candidate reconstruction functions. This work presents a new type of switching criterion (or selector) using machine learning techniques. The selector is trained with randomly generated samples of continuous and discontinuous data profiles, using the exact solution of the governing equation as a reference. Neural networks and random forests were used as the machine learning frameworks to train the selector, and it was later implemented as the indicator function in a hybrid scheme which includes THINC and WENO-Z as the candidate reconstruction functions. The trained selector has been verified to be effective as a reliable switching criterion in the hybrid scheme, which significantly improves the solution quality for both advection and Euler equations.

RANS models remain an attractive turbulence simulation method which could provide some open jet aerofoil interaction analysis at a fraction of the cost of a high-fidelity LES approach. The present work explores the potential and limitations of RANS in this context by simulating an open jet aerofoil noise experiment using the aerospace oriented Menter SST RANS model. This model’s tendency to transition at a critical Reynolds number lower than the experimental value was found to impact the boundary layer development. However, the introduction of a low-Re correction improved the prediction of surface pressure and skin friction, enabling the suction surface separation bubble to be captured. The free shear layer’s virtual origin characteristics exhibited sensitivity to the interaction with the aerofoil, which can be developed into a metric of the interaction. The main challenge for RANS was accounting for the rise in background disturbance level in the working section, which is caused by the high-turbulence intensity in the free shear layers.