Physics

Linear instability of high-speed boundary layers is routinely examined assuming quiescent edge conditions, without reference to the internal structure of shocks or to instabilities potentially generated in them. Our recent work has shown that the kinetically modeled internal nonequilibrium zone of straight shocks away from solid boundaries exhibits low-frequency molecular fluctuations. The presence of the dominant low frequencies observed using the Direct Simulation Monte Carlo (DSMC) method has been explained as a consequence of the well-known bimodal probability density function (PDF) of the energy of particles inside a shock. Here, PDFs of particle energies are derived in the upstream and downstream equilibrium regions, as well as inside shocks, and it is shown for the first time that they have the form of the non-central chi-squared (NCCS) distributions. A linear correlation is proposed to relate the change in the shape of the analytical PDFs as a function of Mach number, within the range 3?�M??0 , with the DSMC-derived average characteristic low-frequency of shocks, as computed in our earlier work. At a given Mach number M=7.2 , varying the input translational temperature in the range 89??T tr,1 /(K)??420 , it is shown that the variation in DSMC-derived low-frequencies is correlated with the change in most-probable-speed inside shocks at the location of maximum bulk velocity gradient. Using the proposed linear functions, average low-frequencies are estimated within the examined ranges of Mach number and input temperature and a semi-empirical relationship is derived to predict low-frequency oscillations in shocks. Our model can be used to provide realistic physics-based boundary conditions in receptivity and linear stability analysis studies of laminar-turbulent transition in high-speed flows.

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. When the advected particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. Here we investigate the behavior of neutrally buoyant particles in 2-dimensional chaotic flows, combining numerical simulations and laboratory experiments. We show that depending on the particles shape and size, the underlying Lagrangian coherent structures can be altered, resulting in distinct dispersion phenomena within the same flow field. Experiments performed in a two-dimensional cellular flow, exhibited a focusing effect in vortex cores of particles with anisotropic shape. In agreement with our numerical model, neutrally buoyant ellipsoidal particles display markedly different trajectories and overall organization than spherical particles, with a clustering in vortices that changes accordingly with the aspect ratio of the particles.

Discrete mechanics is presented as an alternative to the equations of fluid mechanics, in particular to the Navier-Stokes equation. The derivation of the discrete equation of motion is built from the intuitions of Galileo, the principles of Galilean equivalence and relativity. Other more recent concepts such as the equivalence between mass and energy and the Helmholtz-Hodge decomposition complete the formal framework used to write a fundamental law of motion such as the conservation of accelerations, the intrinsic acceleration of the material medium, and the sum of the accelerations applied to it. The two scalar and vector potentials of the acceleration resulting from the decomposition into two contributions, to curl-free and to divergence-free, represent the energies per unit of mass of compression and shear. The solutions obtained by the incompressible Navier-Stokes equation and the discrete equation of motion are the same, with constant physical properties. This new formulation of the equation of motion makes it possible to significantly modify the treatment of surface discontinuities, thanks to the intrinsic properties established from the outset for a discrete geometrical description directly linked to the decomposition of acceleration. The treatment of the jump conditions of density, viscosity and capillary pressure is explained in order to understand the two-phase flows. The choice of the examples retained, mainly of the exact solutions of the continuous equations, serves to show that the treatment of the conditions of jumps does not affect the precision of the method of resolution.

Bayesian optimization (BO) based on Gaussian process regression (GPR) is applied to different CFD (computational fluid dynamics) problems which can be of practical relevance. The problems are i) shape optimization in a lid-driven cavity to minimize or maximize the energy dissipation, ii) shape optimization of the wall of a channel flow in order to obtain a desired pressure-gradient distribution along the edge of the turbulent boundary layer formed on the other wall, and finally, iii) optimization of the controlling parameters of a spoiler-ice model to attain the aerodynamic characteristics of the airfoil with an actual surface ice. The diversity of the optimization problems, independence of the optimization approach from any adjoint information, the ease of employing different CFD solvers in the optimization loop, and more importantly, the relatively small number of the required flow simulations reveal the flexibility, efficiency, and versatility of the BO-GPR approach in CFD applications. It is shown that to ensure finding the global optimum of the design parameters of the size up to 8, less than 90 executions of the CFD solvers are needed. Furthermore, it is observed that the number of flow simulations does not significantly increase with the number of design parameters. The associated computational cost of these simulations can be affordable for many optimization cases with practical relevance.

This paper presents a lattice Boltzmann model to simulate the aqueous humor (AH) dynamics in the human eyes by involving incompressible Navier-Stokes flow, heat convection and diffusion, and Darcy seepage flow. Verifying simulations indicate that the model is stable, convergent and robust. Further investigations were carried out, including the effects of heat convection and buoyancy, AH production rate, permeability of trabecular meshwork, viscosity of AH and anterior chamber angle on intraocular pressure (IOP). The heat convection and diffusion can significantly affect the flow patterns in the healthy eye, and the IOP can be controlled by increasing the anterior chamber angle or decreasing the secretion rate, the drainage resistance and viscosity of AH. However, the IOP is insensitive to the viscosity of the AH, which may be one of the causes that the viscosity would not have been considered as a factor for controlling the IOP. It's interesting that all these factors have more significant influences on the IOP in pathologic eyes than healthy ones. The temperature difference and the eye-orientation have obvious influence on the cornea and iris wall shear stresses. The present model and simulation results are expected to provide an alternative tool and theoretical reference for the study of AH dynamics.

A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by artificial neural network (ANN) based on the local coordinate system which is orthogonal to the curved walls. We verify the proposed model for the flows over periodic hills. The correlation coefficients of the RANS unclosed terms predicted by the LANN model can be made larger than 0.96 in an a priori analysis, and the relative error of the unclosed terms can be made smaller than 18%. In an a posteriori analysis, detailed comparisons are made on the results of RANS simulations using the LANN and Spalart-Allmaras (SA) models. It is shown that the LANN model performs better than the SA model in the prediction of the average velocity, wall-shear stress and average pressure, which gives the results that are essentially indistinguishable from the direct numerical simulation (DNS) data. The LANN model trained in low Reynolds number Re = 2800 can be directly applied in the cases of high Reynolds numbers Re = 5600, 10595, 19000, 37000 with accurate predictions. Furthermore, the LANN model is verified for flows over periodic hills with varying slopes. These results suggest that the LANN framework has a great potential to be applied to complex turbulent flows with curved walls.

Iceberg meltwater is a critical freshwater flux from the cryosphere to the oceans. Global climate simulations therefore require simple and accurate parameterisations of iceberg melting. Iceberg shape is an important but often neglected aspect of iceberg melting. Icebergs have an enormous range of shapes and sizes, and distinct processes dominate basal and side melting. We show how different iceberg aspect ratios and relative ambient water velocities affect melting using a combined experimental and numerical study. The experimental results show significant variations in melting between different iceberg faces, as well as within each iceberg face. These findings are reproduced and explained with novel multiphysics numerical simulations. At high relative ambient velocities melting is largest on the side facing the flow, and mixing during vortex generation causes local increases in basal melt rates of over 50%. Double-diffusive buoyancy effects become significant when the relative ambient velocity is low. Existing melting parameterisations do not reproduce our findings. We propose several corrections to capture the influence of aspect ratio on iceberg melting.

Implementing multicomponent diffusion models in numerical combustion studies is computationally expensive; to reduce cost, numerical simulations commonly use mixture-averaged diffusion treatments or simpler models. However, the accuracy and appropriateness of mixture-averaged diffusion has not been verified for three-dimensional, turbulent, premixed flames. In this study we evaluated the role of multicomponent mass diffusion in premixed, three-dimensional high Karlovitz-number hydrogen, n-heptane, and toluene flames, representing a range of fuel Lewis numbers. We also studied a premixed, unstable two-dimensional hydrogen flame due to the importance of diffusion effects in such cases. Our comparison of diffusion flux vectors revealed differences of 10-20% on average between the mixture-averaged and multicomponent diffusion models, and greater than 40% in regions of high flame curvature. Overall, however, the mixture-averaged model produces small differences in diffusion flux compared with global turbulent flame statistics. To evaluate the impact of these differences between the two models, we compared normalized turbulent flame speeds and conditional means of species mass fraction and source term. We found differences of 5-20% in the mean normalized turbulent flame speeds, which seem to correspond to differences of 5-10% in the peak fuel source terms. Our results motivate further study into whether the mixture-averaged diffusion model is always appropriate for DNS of premixed turbulent flames.

The present paper reports on the assessment of different turbulence-chemistry interaction closures for modeling turbulent combustion in the Moderate and Intense Low oxygen Dilution combustion regime. 2D RANS simulations have been carried out to model flames issuing from two burners DJHC burner and Adelaide JHC burner which imitate the MILD combustion. In order to model these flames, two different approaches of turbulence-chemistry interaction models are considered; while in the PDF based modeling, two different variants are invoked to understand the applicability of the PDF based models in the MILD regime: one is based on presumed shape PDF approach and the other one is transported PDF approach. A comprehensive study has been carried out by comparing the results obtained from these different models. For the DJHC burner, the computations are carried out for a jet speed corresponding to Reynolds numbers of Re=4100, whereas the Adelaide JHC burner computations are performed for a jet speed corresponding to Reynolds number of Re=10000. The effects of molecular diffusion on the flame characteristics are also studied by using different micro-mixing models. In the case of DJHC burner, it has been observed that the mean axial velocity and the turbulent kinetic energy profiles are in good agreement with the measurements. However, the temperature profiles are over-predicted in the downstream region by both EDC and the PDF based models. In the context of Adelaide JHC burner, the profiles of the temperature and the mass fraction of major species (CH4, H2, O2, H2O, CO2) obtained using LPDF approach are in better agreement with the measurements compared to those obtained using EDC model; although, both the solution approaches fail to capture CO and OH radical profiles.

In this paper, we present two deep learning-based hybrid data-driven reduced order models for the prediction of unsteady fluid flows. The first model projects the high-fidelity time series data from a finite element Navier-Stokes solver to a low-dimensional subspace via proper orthogonal decomposition (POD). The time-dependent coefficients in the POD subspace are propagated by the recurrent net (closed-loop encoder-decoder updates) and mapped to a high-dimensional state via the mean flow field and POD basis vectors. This model is referred as POD-RNN. The second model, referred to as convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (CNN) as layers of linear kernels with nonlinear activations, to extract low-dimensional features from flow field snapshots. The flattened features are advanced using a recurrent (closed-loop manner) net and up-sampled (transpose convoluted) gradually to high-dimensional snapshots. Two benchmark problems of the flow past a cylinder and flow past a side-by-side cylinder are selected as the test problems to assess the efficacy of these models. For the problem of flow past a single cylinder, the performance of both the models is satisfactory, with CRAN being a bit overkill. However, it completely outperforms the POD-RNN model for a more complicated problem of flow past side-by-side cylinders. Owing to the scalability of CRAN, we briefly introduce an observer-corrector method for the calculation of integrated pressure force coefficients on the fluid-solid boundary on a reference grid. This reference grid, typically a structured and uniform grid, is used to interpolate scattered high-dimensional field data as snapshot images. These input images are convenient in training CRAN. This motivates us to further explore the application of CRAN models for the prediction of fluid flows.