Data-Driven Isogeometric Design Space Exploration

With improvements in computational hardware and the increasing role of numerical simulations for product design, interactive real-time design space exploration harbors the potential for revolutionalizing the industrial design process. Isogeometric analysis overcomes the time-consuming meshing step and bridges the gap between geometric design and computational analysis of the design. However, isogeometric analysis for a single geometric design could be expensive and thereby prohibits its use for real-time analysis. Therefore, surrogate models are essential for bridging the gap between design parameterization and real-time exploration of geometric design spaces. In this thesis, three surrogate modeling approaches, namely modal expansion, artificial neural networks and Gaussian process regression, are assessed for suitability for geometric design space exploration. The cost of surrogate modeling training for artificial neural networks with physics-based and data-based loss function approaches is theoretically estimated and compared. This theoretical analysis indicated that data-based loss function approaches are less expensive to train and thereby selected for surrogate modeling demonstration in this thesis. The performance of the three surrogate modeling approaches is compared for two problems: a plate with a hole and an L-bracket. The error in model approximation for differing numbers of training design points is used to assess the cost-accuracy trade-off. The low dimensionality of the geometric design space for the plate with a hole problem makes the modal approximation-based approaches more favorable than the other two approaches. On the other hand, as the L-bracket problem involves 17 geometric design parameters, a higher error is observed for the modal approximation approach, especially when the extent of design space is large. For this scenario, artificial neural networks give results nearly independent of the extent of geometric design space and are more accurate than the other two surrogate modeling approaches. Even though Gaussian process regression leads to less accurate and more expensive models, it estimates model uncertainty. These estimates are beneficial for scenarios where high-fidelity results may not be available to validate important regions of the design space, and uncertainty bounds are the only metric of confidence in results. Lastly, the applicability of modal expansion and artificial neural network-based surrogate modeling approaches for geometric design shape optimization problems is also demonstrated.</p

Scale-Resolving Simulations and Data-Driven Subgrid Modeling for Complex Turbulent Boundary Layer Flows

With the advancements in computational hardware and numerical algorithms, scale-resolving simulations of complex turbulent flows are becoming increasingly possible. Turbulent boundary layers are one such flow of immense interest to the aerospace sector. Advancements in modeling and controlling turbulent boundary layers would lead to efficient, sustainable and safer operation of aircraft, gas turbines and wind turbines. Despite decades of research on turbulent boundary layers, the onset of turbulent flow separation for a smooth body separation problem governed by the dynamics of the incoming boundary layer is poorly understood. The upstream boundary layer, before separating, often encounters non-equilibrium pressure gradient and curvature effects for such flows. A lack of understanding of these non-equilibrium effects has cascaded to immature turbulence models for smooth body separation problems. Inspired by this research challenge, this dissertation has two main goals: 1) Advance the understanding of the physical behavior of turbulent boundary layers in the presence of pressure gradients and 2) Improve existing and develop new data-driven subgrid models for scale-resolving simulation of turbulent flows. For the first goal, direct numerical simulation was performed for a turbulent boundary layer over the Boeing speed bump. This flow exhibits varying pressure gradients and curvature effects, which leads to flow separation. The statistics of turbulent boundary layer leading to flow separation was studied and integral analysis was performed to determine the scaling of the Reynolds stresses in the inner and outer regions of the turbulent boundary layer. For the second goal, a framework for embedding physical invariance properties for data-driven subgrid stress models was proposed. Furthermore, a method for extending traditional and data-driven subgrid stress models for anisotropic grids was also proposed. Lastly, an optimal clipping procedure that ensures theoretical numerical stability without significant loss in subgrid stress model prediction accuracy was proposed. These advancements in subgrid stress models were demonstrated to improve predictions for several turbulent flows.</p

Atomistic Simulations of Basal Dislocations Interacting with Mg17_{17}Al12_{12} Precipitates in Mg

The mechanical properties of Mg-Al alloys are greatly influenced by the complex intermetallic phase Mg$_{17}$Al$_{12}$, which is the most dominant precipitate found in this alloy system. The interaction of basal edge and 30$^\text{o}$ dislocations with Mg$_{17}$Al$_{12}$ precipitates is studied by molecular dynamics and statics simulations, varying the inter-precipitate spacing ($L$), and size ($D$), shape and orientation of the precipitates. The critical resolved shear stress $\tau_c$ to pass an array of precipitates follows the usual $\ln((1/D + 1/L)^{-1})$ proportionality. In all cases but the smallest precipitate, the dislocations pass the obstacles by depositing dislocation segments in the disordered interphase boundary rather than shearing the precipitate or leaving Orowan loops in the matrix around the precipitate. An absorbed dislocation increases the stress necessary for a second dislocation to pass the precipitate also by absorbing dislocation segments into the boundary. Replacing the precipitate with a void of identical size and shape decreases the critical passing stress and work hardening contribution while an artificially impenetrable Mg$_{17}$Al$_{12}$ precipitate increases both. These insights will help improve mesoscale models of hardening by incoherent particles.Comment: 13 pages with 9 figures and 2 tables. Supplementary materia

RANS Computation of Heat Transfer Over Rough Surfaces

RÉSUMÉ Un modèle précis de simulation de la résistance au frottement et du transfert de chaleur sur des surfaces rugueuses est une exigence importante dans les domaines de la conception pour plusieurs industries. La résolution des équations RANS est une des méthodes de modélisation les plus réalisables dans le contexte industriel actuel et nécessite l'extension des modèles de turbulence RANS afin d'intégrer l'effet de rugosité. Le présent travail étudie les approches issues de la littérature du modèle de turbulence à faible nombre de Reynolds et à nombre de Reynolds élevé (lois de paroi) pour simuler l'effet de la rugosité. Le transfert de chaleur sur les surfaces lisses est modélisé sur la base de l'hypothèse d'analogie de Reynolds. L'hypothèse n'est pas valable pour les surfaces rugueuses et conduit à une prédiction excessive du nombre de Stanton. L'objectif de ce mémoire est d'intégrer la correction thermique pour surmonter cette hypothèse dans les deux approches et améliorer la prévision du transfert de chaleur sur des surfaces rugueuses. Tout d'abord, différentes extensions de rugosité pour les modèles de turbulence Spalart-Allmaras et k-ω SST sont implémentées dans le solveur RANS interne. La précision et la robustesse numérique de ces extensions sont discutées. La correction thermique par Aupoix est mise en œuvre pour surmonter l'hypothèse de l'analogie de Reynolds et l'amélioration des prévisions de transfert de chaleur est évaluée. La correction conduit à une meilleure cohérence dans la prédiction du coefficient de frottement et du nombre de Stanton. Deuxièmement, les lois de paroi basées sur la loi logarithmique sont appliquées et étendues pour modéliser le flux et le transfert de chaleur sur des surfaces rugueuses. La mise en œuvre de lois de paroi rugueuses est compatible avec l’extension de rugosité du modèle de turbulence à faible nombre de Reynolds. La dépendance des lois de paroi à l'espacement par rapport à la paroi est évaluée pour des surfaces lisses et rugueuses avec une hauteur de rugosité variable. On observe que la loi de paroi ressemble au comportement physique attendu. La formulation actuelle de la loi de paroi donne des résultats supérieurs indépendants de l'espacement près de la paroi pour les surfaces rugueuses par rapport à d'autres formulations de lois de paroi rugueuses. Trois variantes de conditions aux limites approximatives pour le modèle de turbulence k-ω SST sont analysées et il est observé que la cohérence des variables de turbulence conduit à une amélioration des résultats. Le travail montre que l'hypothèse de l'analogie de Reynolds peut être utilisée comme stratégie efficace pour vérifier l'extension de la rugosité des lois de paroi. Trois corrections thermiques sont explorées pour améliorer la prévision du transfert de chaleur sur des surfaces rugueuses. La correction thermique de Aupoix est étendue à l’approche de loi de paroi. L'approche actuelle surmonte quelques restrictions offertes par l'approche de la loi de paroi analytique. Les deux autres corrections reposent uniquement sur une échelle de rugosité c'est-à-dire une rugosité équivalente avec grains de sable, qui n'est pas adéquate pour modéliser avec précision le frottement et le transfert de chaleur. Ceci est exploré en considérant un cas avec deux types de rugosité différents produisant le même coefficient de frottement mais avec des nombres de Stanton différents. Il est observé que la correction Aupoix nécessite un paramètre physique supplémentaire en entrée et capture plus précisément la physique du transfert de chaleur. Cependant, la nécessité de paramètres physiques supplémentaires pourrait poser des problèmes de modélisation lorsque les données expérimentales sur la distribution de la rugosité ne sont pas disponibles. Les deux autres corrections ont montré un bon accord avec plusieurs cas expérimentaux et ont pu être utilisées en l'absence de données de géométrie de rugosité. La discussion se termine en mentionnant les nombreuses limitations et difficultés numériques rencontrées lors de la modélisation de l'écoulement sur des surfaces rugueuses. Les futures orientations pour faire avancer les frontières de la recherche sont finalement proposées.----------ABSTRACT An accurate model for simulating friction drag and heat transfer over rough surfaces is a major requirement in the design and development domain of several industries. Computational modeling via RANS equations is the most computationally feasible in today’s industrial scenario and requires the extension of RANS turbulence models to incorporate the effect of roughness. The present work discusses both the low-Reynolds and high-Reynolds number (Wall function) turbulence model approaches to simulate the effect of roughness. Heat transfer over smooth surfaces is modeled based on the Reynolds analogy assumption. The assumption does not hold over rough surfaces and leads to an overprediction of Stanton number. The objective of this thesis is to incorporate the thermal correction overcoming the assumption in both approaches and improve the heat transfer prediction over rough surfaces. Firstly, different roughness extensions proposed in the literature for the Spalart-Allmaras and k-ω SST turbulence models are implemented in an in-house RANS solver. The accuracy and numerical robustness of these extensions are discussed. The thermal correction by Aupoix is implemented to overcome the assumption of Reynolds analogy and the improvement in predictions of heat transfer is assessed. The correction leads to consistency in the prediction of the skin-friction coefficient and Stanton number. Secondly, the log-law based wall functions are implemented and extended to model flow and heat transfer over rough walls. The implementation of rough wall functions is consistent with the low-Reynolds number turbulence model roughness extension. The near-wall spacing dependence characteristics of wall functions are assessed for smooth and rough walls with varying roughness heights. It is observed that the wall functions resemble the expected physical behavior. The present wall function formulation gives superior near-wall spacing independent results for rough walls compared to other rough wall function formulations. Three variants of rough boundary conditions for the k-ω SST turbulence model are analyzed, and it is observed that the consistency of turbulence variables leads to improved results. The work shows that the Reynolds analogy assumption can be used as an effective strategy to verify the roughness extension of wall functions. Three thermal corrections are explored to improve the heat transfer prediction over rough surfaces. The Aupoix thermal correction is extended to the wall function approach. The present approach overcomes a few restrictions offered by the Analytical Wall Function (AWF) approach. The other two corrections rely only on one roughness scale (equivalent sand-grain roughness) which is not adequate for accurate modeling of both friction drag and heat transfer. This is explored by considering a case with two different roughness types resulting in same skin-friction coefficients but different Stanton numbers. It is observed that the Aupoix correction requires an additional physical parameter as input and captures the physics of heat transfer more accurately. However, the requirement of additional physical parameters could pose modeling constraints when the experimental roughness distribution data is not available. The other two corrections showed good agreement with several other experimental cases and could be used in the absence of roughness geometry data. The discussion concludes by mentioning the several limitations and numerical difficulties experienced while modeling flows over rough surfaces. Future directions to advance the research frontiers are proposed

Turbulent boundary layer with strong favorable pressure gradient and curvature effects: Streamline coordinate and scaling analysis

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favorable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterized and compared to a lower Reynolds number flow over the same geometry. The momentum budgets are analyzed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral analysis-based scalings for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. These proposed scalings exhibit a better collapse of Reynolds stress profiles compared to friction velocity scaling and Zagarola-Smits scaling in the strong favorable pressure gradient region and in the mild adverse pressure region that precedes it in this flow

Detectability of QCD phase transitions in binary neutron star mergers: Bayesian inference with the next generation gravitational wave detectors

We study the detectability of postmerger QCD phase transitions in neutron star binaries with next-generation gravitational-wave detectors Cosmic Explorer and Einstein Telescope. We perform numerical relativity simulations of neutron star mergers with equations of state that include a quark deconfinement phase transition through either a Gibbs or Maxwell construction. These are followed by Bayesian parameter estimation of the associated gravitational-wave signals using the $\tt{NRPMw}$ waveform model, with priors inferred from the analysis of the inspiral signal. We assess the ability of the model to measure the postmerger peak frequency $f_2^{\rm peak}$ and identify aspects that should be improved in the model. We show that, even at postmerger signal to noise ratios as low as 10, the model can distinguish (at the 90% level) $f_2^{\rm peak}$ between binaries with and without a phase transition in most cases. Phase-transition induced deviations in the $f_2^{\rm peak}$ from the predictions of equation-of-state insensitive relations can also be detected if they exceed $1.6\,\sigma$. Our results suggest that next-generation gravitational wave detectors can measure phase transition effects in binary neutron star mergers. However, unless the phase transition is ``strong'', disentangling it from other hadronic physics uncertainties will require significant theory improvements

Numerical Relativity Simulations of the Neutron Star Merger GW170817: Long-Term Remnant Evolutions, Winds, Remnant Disks, and Nucleosynthesis

We present a systematic numerical-relativity study of the dynamical ejecta, winds and nucleosynthesis in neutron star merger remnants. Binaries with the chirp mass compatible with GW170817, different mass ratios, and five microphysical equations of state (EOS) are simulated with an approximate neutrino transport and a subgrid model for magnetohydrodynamics turbulence up to 100 milliseconds postmerger. Spiral density waves propagating from the neutron star remnant to the disk trigger a wind with mass flux ${\sim}0.1{-}0.5\,{\rm M_\odot/s}$ persisting for the entire simulation as long as the remnant does not collapse to black hole. This wind has average electron fraction $\gtrsim 0.3$ and average velocity ${\sim}0.1-0.17\,$c and thus is a site for the production of weak $r$-process elements (mass number $A<195$). Disks around long-lived remnants have masses ${\sim}0.1{-}0.2\,{\rm M_\odot}$, temperatures peaking at $\lesssim10\,$MeV near the inner edge, and a characteristic double-peak distribution in entropy resulting from shocks propagating through the disk. The dynamical and spiral-wave ejecta computed in our targeted simulations are not compatible with those inferred from AT2017gfo using two-components kilonova models. Rather, they indicate that multi-component kilonova models including disk winds are necessary to interpret AT2017gfo. The nucleosynthesis in the combined dynamical ejecta and spiral-wave wind in the comparable-mass long-lived mergers robustly accounts for all the $r$-process peaks, from mass number ${\sim}75$ to actinides in terms of solar abundances. Total abundandes are weakly dependent on the EOS, while the mass ratio affect the production of first peak elements.Comment: 20 pages, 13 figures, 3 table