Multi-fidelity Deep Learning-based methodology for epistemic uncertainty quantification of turbulence models

Computational Fluid Dynamics (CFD) simulations using turbulence models are commonly used in engineering design. Of the different turbulence modeling approaches that are available, eddy viscosity based models are the most common for their computational economy. Eddy viscosity based models utilize many simplifications for this economy such as the gradient diffusion and the isotropic eddy viscosity hypotheses. These simplifications limit the degree to which eddy viscosity models can replicate turbulence physics and lead to model form uncertainty. The Eigenspace Perturbation Method (EPM) has been developed for purely physics based estimates of this model form uncertainty in turbulence model predictions. Due to its physics based nature, the EPM weighs all physically possible outcomes equally leading to overly conservative uncertainty estimates in many cases. In this investigation we use data driven Machine Learning (ML) approaches to address this limitation. Using ML models, we can weigh the physically possible outcomes by their likelihood leading to better calibration of the uncertainty estimates. Specifically, we use ML models to predict the degree of perturbations in the EPM over the flow domain. This work focuses on a Convolutional Neural Network (CNN) based model to learn the discrepancy between Reynolds Averaged Navier Stokes (RANS) and Direct Numerical Simulation (DNS) predictions. This model acts as a marker function, modulating the degree of perturbations in the EPM. We show that this physics constrained machine learning framework performs better than the purely physics or purely ML alternatives, and leads to less conservative uncertainty bounds with improved calibration.Comment: arXiv admin note: text overlap with arXiv:2301.1184

Thermal-hydraulic analysis of gas-cooled reactor core flows

In this thesis a numerical study has been undertaken to investigate turbulent flow and heat transfer in a number of flow problems, representing the gas-cooled reactor core flows. The first part of the research consisted of a meticulous assessment of various advanced RANS models of fluid turbulence against experimental and numerical data for buoyancy-modified mixed convection flows, such flows being representative of low-flow-rate flows in the cores of nuclear reactors, both presently-operating Advanced Gas-cooled Reactors (AGRs) and proposed ‘Generation IV’ designs. For this part of the project, an in-house code (‘CONVERT’), a commercial CFD package (‘STAR-CD’) and an industrial code (‘Code_Saturne’) were used to generate results. Wide variations in turbulence model performance were identified. Comparison with the DNS data showed that the Launder-Sharma model best captures the phenomenon of heat transfer impairment that occurs in the ascending flow case; v^2-f formulations also performed well. The k-omega-SST model was found to be in the poorest agreement with the data. Cross-code comparison was also carried out and satisfactory agreement was found between the results.The research described above concerned flow in smooth passages; a second distinct contribution made in this thesis concerned the thermal-hydraulic performance of rib-roughened surfaces, these being representative of the fuel elements employed in the UK fleet of AGRs. All computations in this part of the study were undertaken using STAR-CD. This part of the research took four continuous and four discrete design factors into consideration including the effects of rib profile, rib height-to-channel height ratio, rib width-to-height ratio, rib pitch-to-height ratio, and Reynolds number. For each design factor, the optimum configuration was identified using the ‘efficiency index’. Through comparison with experimental data, the performance of different RANS turbulence models was also assessed. Of the four models, the v^2-f was found to be in the best agreement with the experimental data as, to a somewhat lesser degree were the results of the k-omega-SST model. The k-epsilon and Suga models, however, performed poorly. Structured and unstructured meshes were also compared, where some discrepancies were found, especially in the heat transfer results. The final stage of the study involved a simulation of a simplified 3-dimensional representation of an AGR fuel element using a 30 degree sector configuration. The v^2-f model was employed and comparison was made against the results of a 2D rib-roughened channel in order to assess the validity and relevance of the precursor 2D simulations of rib-roughened channels. It was shown that although a 2D approach is extremely useful and economical for ‘parametric studies’, it does not provide an accurate representation of a 3D fuel element configuration, especially for the velocity and pressure coefficient distributions, where large discrepancies were found between the results of the 2D channel and azimuthal planes of the 3D configuration.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research CouncilGBUnited Kingdo

Age Effects on Iron-Based Pipes in Water Distribution Systems

Pipes in water distribution systems may change as they age. The accumulation of corrosion byproducts and suspended particles on the inside wall of aged pipes can increase pipe roughness and reduce pipe diameter. To quantify the hydraulic effects of irregular accumulation on the pipe walls, eleven aged pipes ranging in diameter from 0.020-m (0.75-in) to 0.100-m (4-in) and with varying degrees of turberculation were located and subjected to laboratory testing. The laboratory test results were used to determine a relationship between pipe diameter reduction and Hazen-Williams C. This relationship, combined with a manipulation of the Hazen-Williams equation, provided a simple and direct method for correcting the diameters of aged pipes in distribution models. Using EPANET 2, the importance of correcting pipe diameters when modeling water distribution systems containing aged pipes was investigated. Correcting the pipe diameters in the sample network reduced the modeled water age by up to 10% and changed the pattern of fluctuating water age that occurred as waters with different sources moved through the pipe network. In addition, two of the aforementioned aged pipes with diameters of 0.025-m (1-in) and 0.050-m (2-in) were modeled using Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling. Flow was computed at Reynolds numbers ranging from 6700 to 31,000 using three turbulence models including a 4-equation v2-f model, and 2-equation realizable k-e; and k-ω models. In comparing the RANS results to the laboratory testing, the v2-f model was found to be most accurate, producing Darcy-Weisbach friction factors from 5% higher to 15% lower than laboratory-obtained values. The capability of RANS modeling to provide a detailed characterization of the flow in aged pipes was demonstrated. Large eddy simulation (LES) was also performed on a single 0.050-m (2-in) pipe at a Reynolds number of 6800. The Darcy-Weisbach friction factor calculated using LES was 20% less than obtained from experimental tests. Roughness elements smaller than the grid scale and deficiencies in the subgrid-scale model at modeling the complex three-dimensional flow structures due to the irregular pipe boundary were identified as likely sources of error. Even so, the utility of LES for describing complex flows was established

Simulations des grandes échelles pour la prédiction des écoulements de refroidissement des pales de turbines

Les concepteurs de moteurs aéronautiques sont constamment sujets à la demande d’augmentation de puissance de la part des constructeurs d’aéronefs. Pour satisfaire à cette exigence, la température de sortie de la chambre de combustion peut être augmentée pour améliorer le rendement et la puissance de sortie du moteur. Cette élévation de température peut toutefois dépasser le point de fusion du matériau et, pour éviter les pannes de moteur, l’intégrité des aubes de la turbine repose notamment sur des systèmes de refroidissement internes,prélevant de l'air froid du compresseur. La conception de ces systèmes revient donc à maximiser l’amélioration du transfert de chaleur tout en minimisant le débit d’air via les pertes de charge afin d’éviter des pénalités de puissance du moteur. Or ces écoulements en canaux internes sont encore largement incontrôlés et mal compris. Dans le but de mieux comprendre ces écoulements en rotation se développant spatialement, ce travail porte sur l’étude via simulations numériques d’un canal de refroidissement droit, perturbé, en rotation. La configuration consiste en un canal carré équipé de 8 perturbateurs placés avec un angle de 90 degrés par rapport à l’écoulement principal. Pour les cas étudiés, des mesures PIV temporelles ont été effectuées à l'Institut VanKarman (VKI). Les conditions adiabatiques et isothermes ont été étudiées pour évaluer l’impact dela température de la paroi sur l’écoulement, en particulier dans les configurations en rotation. Les canaux statiques ainsi qu’en rotation positive et négative sont comparés avec, dans chaque cas,une prédiction d’écoulement adiabatique ou isotherme. Dans ce travail, les résultats de simulations aux grandes échelles (SGE) montrent que le modèle CFD haute fidélité est capable de reproduire les différences induites par la flottabilité sur la topologie de l'écoulement dans la région proche. Le modèle parvient également à prévoir l'augmentation (la diminution) de la turbulence autour des perturbateurs en rotation déstabilisante (stabilisante). Enfin et grâce à la SGE spatiale et temporelle complète, le développement spatial et l’instationnarité des écoulements secondaires sont analysés pour mieux comprendre leur origine et leurs différences potentielles entre les cas. Cette étude montre que la topologie du flux thermique en parois est déterminée par la structure des écoulements secondaires alors que l’intensité du flux thermique aux parois est déterminée par le niveau de fluctuations de l’écoulement dans l’espace interperturbateu

Large-eddy simulation of turbulent flows with heat transfer in simple and complex geometries

Some basic aspects of turbulence, transition to turbulence, and turbulence modelling, are summarized in Chapter 1 (Introduction). Emphasis is put on the increasing understanding of turbulent phenomena made possible by recent advances in the theory of dynamical systems; on the concept of "coherent structure"; and on the parallel evolution of computing power and computational fluid dynamics. Chapter 2 is a survey of the turbulence modelling technique known as Large Eddy Simulation (LES). The equations governing fluid flow and scalar transport are introduced; the direct simulation of turbulent flows and its limitations are briefly outlined; and the concept of LES, with the related topics of decomposition, filtering and subgrid modelling, is discussed. The state of the art in LES is reviewed in the last three sections, under the separate headings of proposed subgrid models; wall boundary conditions; and applications presented in the literature. An attempt is made to give the most complete and updated possible account of the subject; work carried out from the early 'Seventies up to now is considered. Emphasis is put more on physical models and corresponding performances than on numerical methods and computational details. In Chapter 3, the finite-volume numerical techniques used in the present work are presented and discussed. Emphasis is put on those aspects and options which bear more relevance for the accuracy and quality of the results, such as the pressure-velocity coupling algorithm, the discretization of advective terms and the treatment of centred (co-located), body-fitted grids. The architecture and the basic features of the computer code Harwell-FL0W3D, Release 2, are outlined, while the modifications introduced in order to implement the Smagorinsky subgrid model and the appropriate boundary conditions for LES are described in detail. In Chapters 4-6 results are presented and discussed for the basic geometries studied. Chapter 4 deals with the flow between indefinite parallel plates (plane channel), one of which heated with a uniform heat flux. For this basic geometry, a detailed study is presented on the influence of numerical options (grid size, time step and time-stepping method, pressure-velocity coupling, discretization of the advective terms); model parameters (Smagorinsky constant, subgrid Prandtl number, near-wall damping); Reynolds number; and alternative wall boundary conditions. The issues of initial conditions, numerical transients and statistical processing of the results are also discussed with some depth. In Chapter 5, computations are presented for a plane channel having one of the walls roughened by transverse square ribs. An extensive literature review of experimental and numerical studies on this geometry is included. The parametrical study is limited here to the influence of grid size and Reynolds number; LES results are presented in detail for a reference case, and are compared with experimental flow and heat transfer data. Chapter 6 is dedicated to the geometry of cross-corrugated ducts, representative of storage-type air preheaters for fossil-fuelled power stations. Flow and heat transfer predictions from direct simulation and LES are presented; they are compared with experimental results and with numerical predictions obtained by a standard and a low-Reynolds number version of the k-s turbulence model. Finally, Chapter 7 summarizes the main conclusions which can be drawn from the above studies. Emphasis is put on the basic issue of LES applicability to engineering problems of practical interest, and of its feasibility using a commercial, general-purpose (though highly sophisticated) computer code. A critical comparison with more conventional turbulence modelling approaches is outlined, and 'weak spots', or issues requiring further clarifications, are pointed out for future studies. The work includes an extensive bibliography with almost 400 references, and an appendix on the tensorial formulation of the governing equations of fluid dynamics in general domains

A Corpus of Roman Pottery from Lincoln (Volume 6)

This is the first major analysis of the Roman pottery from excavations in Lincoln (comprising more than 150,000 sherds). The pottery is presented in seven major ware groups. Fine wares include a modest range of imports and are dominated by Nene Valley products. Oxidised wares are mostly local products with a few imports as are the shell- and calcite-tempered wares and reduced wares. The final three are the standard specialised wares: mortaria, mostly of German and Mancetter-Hartshill manufacture; amphorae (80% Spanish Dressel 20) and samian, mostly from Les Martres/Lezoux and 75% undecorated! The discussion explores the chronological range of the entire ceramic assemblage across the three discrete parts of the Roman fortress and later colonia

Forecasting through deep learning and modal decomposition in multi-phase concentric jets

This work presents a set of neural network (NN) models specifically designed for accurate and efficient fluid dynamics forecasting. In this work, we show how neural networks training can be improved by reducing data complexity through a modal decomposition technique called higher order dynamic mode decomposition (HODMD), which identifies the main structures inside flow dynamics and reconstructs the original flow using only these main structures. This reconstruction has the same number of samples and spatial dimension as the original flow, but with a less complex dynamics and preserving its main features. We also show the low computational cost required by the proposed NN models, both in their training and inference phases. The core idea of this work is to test the limits of applicability of deep learning models to data forecasting in complex fluid dynamics problems. Generalization capabilities of the models are demonstrated by using the same neural network architectures to forecast the future dynamics of four different multi-phase flows. Data sets used to train and test these deep learning models come from Direct Numerical Simulations (DNS) of these flows.Comment: 46 pages, 20 figures. Submitted to Expert Systems with Application

Simulation and optimization of steam-cracking processes

Thermal cracking is an industrial process sensitive to both temperature and pressure operating conditions. The use of internally ribbed reactors is a passive method to enhance the chemical selectivity of the process, thanks to a significant increase of heat transfer. However, this method also induces an increase in pressure loss, which is damageable to the chemical yield and must be quantified. Because of the complexity of turbulence and chemical kinetics, and as detailed experimental measurements are difficult to conduct, the real advantage of such geometries in terms of selectivity is however poorly known and difficult to assess. This work aims both at evaluating the real benefits of internally ribbed reactors in terms of chemical yields and at proposing innovative and optimized reactor designs. This is made possible using the Large Eddy Simulation (LES) approach, which allows to study in detail the reactive flow inside several reactor geometries. The AVBP code, which solves the Navier-Stokes compressible equations for turbulent flows, is used in order to simulate thermal cracking thanks to a dedicated numerical methodology. In particular, the effect of pressure loss and heat transfer on chemical conversion is compared for both a smooth and a ribbed reactor in order to conclude about the impact of wall roughness in industrial operating conditions. An optimization methodology, based on series of LES and Gaussian process, is finally developed and an innovative reactor design for thermal cracking applications, which maximizes the chemical yield, is propose