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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

Introduction The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗
NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗
DOE OSTI2022

The role of breakup and coalescence in fine-scale bubble-induced turbulence. I. Dynamics

We study the effect of bubble breakup and coalescence on fine-scale dynamics of bubbly turbulent flows using direct numerical simulations. We perform two different simulations of dilute bubbly flows of void fraction 0.5%: one with bubbles breaking up and coalescing and the other without these physical processes. The volume of the fluid method is used for simulating bubbles undergoing breakup and coalescence while the bubbles are treated as rigid spheres in the immersed boundary method simulation. The energy spectrum in both types of simulation, consistent with previous studies, exhibits a -3 slope. We follow a single infinitesimal fluid element as it evolves to understand velocity gradient dynamics using conditional mean trajectories. We note finite-time divergence when the fluid element evolves under the action of inertial and pressure dynamics. The inertial, pressure, and viscous velocity gradient dynamics, when considered individually, produce the same results for bubble-induced turbulence (BIT) as with the classical homogeneous isotropic turbulence (HIT). Yet when the overall velocity gradient dynamics is considered, BIT results in non-cyclic trajectories moving toward stable node and unstable saddle while classical HIT shows cyclic behavior in their trajectories that move toward the origin. Interestingly, both the volume of fluid and immersed boundary simulations produce similar results. Therefore, there are two main takeaways from this research. First, new velocity gradient models are needed for BIT as their velocity gradients behavior is entirely different from the HIT. Second, we can neglect the bubble topology, breakup, and coalescence while studying or modeling the fine-scale dynamics of BIT.

42 ENGINEERING↗
DOE OSTI2025

Explicit block encodings of boundary value problems for many-body elliptic operators

Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities of block encoding the discretized elliptic operators that arise extensively in numerical simulations for partial differential equations, including high-dimensional instances for many-body simulations. When restricted to rectangular domains with separable boundary conditions, we provide explicit circuits to block encode the many-body Laplacian with separable periodic, Dirichlet, Neumann, and Robin boundary conditions, using standard discretization techniques from low-order finite difference methods. To obtain high-precision, we introduce a scheme based on periodic extensions to solve Dirichlet and Neumann boundary value problems using a high-order finite difference method, with only a constant increase in total circuit depth and subnormalization factor. We then present a scheme to implement block encodings of differential operators acting on more arbitrary domains, inspired by Cartesian immersed boundary methods. We then block encode the many-body convective operator, which describes interacting particles experiencing a force generated by a pair-wise potential given as an inverse power law of the interparticle distance. This work provides concrete recipes that are readily translated into quantum circuits, with depth logarithmic in the total Hilbert space dimension, that block encode operators arising broadly in applications involving the quantum simulation of quantum and classical many-body mechanics.

Kharazi, Tyler [University of California, Berkeley↗
NASA NTRSDate not supplied

Fluid-Structure Interaction Simulations of the ASPIRE SR01 Supersonic Parachute

High-fidelity computational fluid dynamics (CFD) simulations have so far only played exploratory and supporting roles in the study and qualification of parachutes for planetary entry. The last few years have seen the maturation of coupled computational methods that are capable of modeling the complex fluid-structure interactions between a parachute canopy and the supersonic flow in the wake of an entry vehicle in flight conditions. One of the primary goals of these methods is to predict the peak opening load experienced by the parachute during inflation. The Launch, Ascent, and Vehicle Aerodynamics (LAVA)team is developing efficient, high-fidelity numerical methods to perform such challenging fluid-structure interaction simulations. A loose coupling approach is used to advance the solutions of a Cartesian ghost cell immersed boundary method CFD solver and a finite element computational structural dynamics (CSD) solver in space and time. The coupled solver is employed to simulate the ASPIRE SR01 flight test, where a build-to-print version of the Mars Science Laboratory parachute was inflated in supersonic conditions in the upper terrestrial atmosphere. The simulations conducted in the current paper predict a peak opening load that is within 10% of that from the flight test. Grid convergence with respect to the volume and structural domains is demonstrated, and less than 1% variation in the peak opening load is predicted between all grid resolutions.

ARMD↗
DOE OSTI2022

Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces

Here we introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, traction coupling with the surrounding bulk fluid, and thermal fluctuations. For fluid-structure interactions, we introduce Immersed Boundary Methods (IBM) and related Stochastic Eulerian-Lagrangian Methods (SELM) for curved surfaces. We use these approaches to investigate the statistics of surface fluctuating hydrodynamics and microstructures. For velocity autocorrelations, we find characteristic power-law scalings $τ^{-1}, τ^{-2}$, and plateaus can emerge. This depends on the physical regime associated with the geometry, surface viscosity, and bulk viscosity. This differs from the characteristic $τ^{-3/2}$ scaling for bulk three dimensional fluids. We develop theory explaining these observed power-laws associated with time-scales for dissipation within the fluid interface and coupling to the surrounding fluid. We then use our introduced methods to investigate a few example systems and roles of hydrodynamic coupling and thermal fluctuations including for the kinetics of passive particles and active microswimmers in curved fluid interfaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗
DOE OSTI2022

Flash-X: A multiphysics simulation software instrument

Flash-X is a highly composable multiphysics software system that can be used to simulate physical phenomena in several scientific domains. It derives some of its solvers from FLASH, which was first released in 2000. Flash-X has a new framework that relies on abstractions and asynchronous communications for performance portability across a range of increasingly heterogeneous hardware platforms. Flash-X is meant primarily for solving Eulerian formulations of applications with compressible and/or incompressible reactive flows. It also has a built-in, versatile Lagrangian framework that can be used in many different ways, including implementing tracers, particle-in-cell simulations, and immersed boundary methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fluid structure interaction of a subaqueous pendulum: Analyzing the effect of wake correction via large eddy simulations

The dynamic behavior of a subaqueous cylindrical pendulum and corresponding flow dynamics are investigated. The objectives were twofold: (i) to examine whether the two-dimensional model equations sufficiently capture the three-dimensional dynamics and (ii) to investigate the emerging three-dimensional vortical flow structures. Large eddy simulations with two-way coupling fluid structure interaction were carried out using the immersed boundary method to simulate the motion of the pendulum and its interactions with the initially stagnant water. The resulting pendulum motion is compared against measured data obtained in a series of experimental tests to validate the simulation results and the model equations with and without wake corrections. An analysis of the flow vorticity revealed the development of a vortex ring during the first swing and the formation of tip vortices. The evolution of the vortex rings emerging from the motion of the subaqueous cylindrical pendulum was visualized using Q-criteria showing a reasonable agreement with vortical structures observed in the experiment using particle imaging velocimetry. The hydrodynamic moments acting on the simulated pendulum and the moments calculated from the model equations are analyzed. Using the insights from these numerical simulations, a modification of the wake correction is proposed to enhance the accuracy of the rate of decay and period. The transient effect of coherent flow on pendulum dynamics, especially the added mass effect, is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Multi-fidelity modeling to predict the rheological properties of a suspension of fibers using neural networks and Gaussian processes

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications. There are multiple factors, such as fiber aspect ratio and volume fraction, that play a significant role in altering the rheological behavior of suspensions. Three-dimensional (3D) numerical simulations of coupled differential equations of the suspension of fibers are computationally expensive and time-consuming. Machine learning algorithms can be trained on the available data and make predictions for the cases where no numerical data are available. However, some widely used machine learning surrogates, such as neural networks, require a relatively large training dataset to produce accurate predictions. Multi-fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified constitutive equations, can pave the way for more accurate predictions. Here, we focus on neural networks and the Gaussian processes with two levels of fidelity, i.e., high and low fidelity networks, to predict the steady-state rheological properties, and compare them to the single-fidelity network. High-fidelity data are obtained from direct numerical simulations based on an immersed boundary method to couple the fluid and solid motion. The low-fidelity data are produced by using constitutive equations. Multiple neural networks and the Gaussian process structures are used for the hyperparameter tuning purpose. Results indicate that with the best choice of hyperparameters, both the multi-fidelity Gaussian processes and neural networks are capable of making predictions with a high level of accuracy with neural networks demonstrating marginally better performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

The role of breakup and coalescence in fine-scale bubble-induced turbulence. II. Kinematics

This second part of our research explores the kinematic aspect of fine-scale bubble-induced turbulence (BIT) to (i) present the effect of bubble breakup and coalescence and (ii) compare it against the universal kinematic fine-scale turbulence characteristics reported in the literature. To this end, we simulate a dilute bubbly system of 0.5% void fraction using two distinct numerical simulations. In the volume-of-fluid (VoF) simulation, bubbles undergo breakup and coalescence. In the immersed boundary method (IBM) simulation, however, they act as rigid spheres. We also perform a simulation of classical homogeneous isotropic turbulence (HIT). The first important outcome of this study is that BIT is radically different from HIT in terms of its kinematic fine-scale characteristics. In the vorticity-dominating regions, BIT exhibits a weak vortex stretching. This weak vortex stretching is due to (a) the intermediate strain-rate eigenvalues skewed weakly to positive and (b) the extensive strain-rate eigenvector aligning perpendicular to the vorticity vector. The BIT has, on average, not only a weak enstrophy production but also a weak strain production in strain-dominating regions. The weak strain production is due to (a) the presence of vortex stretching in highly strained fluid elements and (b) the absolute magnitude of compressive strain-rate eigenvalue being as close to the extensive strain-rate eigenvalue. Thus, none of the kinematic fine-scale HIT characteristics is noted for BIT. The second important conclusion is that bubble breakup and coalescence play little to no influence on the kinematics of fine-scale BIT as VoF and IBM simulations produce similar results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Numerical simulation of frost formation and heat transfer on fin-and-tube heat exchangers in turbulent cross-flow

Frost formation in fin-and-tube heat exchangers in turbulent cross-flow presents significant challenges in industrial refrigeration applications, affecting heat transfer efficiency and operational reliability. The purpose of this work is to investigate frost deposition and growth on a staggered bank of a fin-and-tube freezer coil under turbulent forced convection conditions. The focus here is on investigating conditions that closely replicate real-world scenarios in large walk-in industrial freezers. Using a direct numerical simulation approach, we examine the flow dynamics and thermal behaviour in the presence of frost, considering turbulent regimes characterized by a Reynolds number in the range 1050 ≤ R e D , avg ≤ 4800 , with the characteristic length being the outer diameter of the tube and the velocity being the bulk fluid velocity between the plates (fins). Computational fluid dynamics simulations are employed to resolve the interactions between turbulent airflow and the frost layer. Our approach incorporates a modified immersed boundary method and a slow-time acceleration technique to address the complex dynamic interface between the continuously evolving frost layer and the flowing air stream. Our findings indicate that frost forms more on the sides of the finned surfaces (plates) and less on the tubes themselves. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.

Science & Technology - Other Topics↗
DOE OSTI2023

Rheology of dense fiber suspensions: Origin of yield stress, shear thinning, and normal stress differences

We explain the origins of yield stress, shear thinning, and normal stress differences in rigid fiber suspensions. We investigate the interplay between the hydrodynamic, noncontact attractive and repulsive, and interfiber contact interactions. The shear-thinning viscosity and finite yield stress obtained from the Immerse Boundary Method simulations are in quantitative agreement with experiential results from the literature. In this study, we show that attractive interactions result in yield stress and shear thinning rheology in the suspensions of rigid fibers. This is an important finding, given the ongoing discussion regarding the origin of the yield stress for suspensions of fibers. Finally, the ability of the proposed model to quantitatively predict the rheology is not limited to only shear thinning and yield stress but also extends to normal stresses.

42 ENGINEERING↗
DOE OSTI2023

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part II: The Effect of Roughness on the Performance of a High-Pressure Turbine Blade

Abstract Turbine blades generally present surface roughness introduced in the manufacturing process or caused by in-service degradation, which can have a significant impact on aero-thermal performance. A better understanding of the fundamental physical mechanisms arising from the interaction between the roughness and the turbine flow at engine-relevant conditions can provide insights for the design of blades with improved efficiency and longer operational life. To this end, a high-fidelity numerical framework combining a well-validated solver for direct numerical simulation and a second-order accurate immersed boundary method is employed to predict roughness-induced aero-thermal effects on an LS89 high-pressure turbine (HPT) blade at engine-relevant conditions. Different amplitudes and distributions of surface roughness are investigated and a reference smooth-blade simulation under the same flow conditions is conducted for comparison. Roughness of increasing amplitude progressively shifts the blade suction side boundary layer transition upstream, producing larger values of the turbulent kinetic energy and higher total wake losses. The on-surface data-capturing capabilities of the numerical framework provide direct measurements of the heat flux and the skin friction coefficient, hence offering quantitative information between the surface topology and engineering-relevant performance parameters. This work may provide a benchmark for future numerical studies of turbomachinery flows with roughness.

Engineering↗
DOE OSTI2022

Evaluation of Turbulence and Dispersion in Multiscale Atmospheric Simulations over Complex Urban Terrain during the Joint Urban 2003 Field Campaign

Abstract This paper evaluates the representation of turbulence and its effect on transport and dispersion within multiscale and microscale-only simulations in an urban environment. These simulations, run using the Weather Research and Forecasting Model with the addition of an immersed boundary method, predict transport and mixing during a controlled tracer release from the Joint Urban 2003 field campaign in Oklahoma City, Oklahoma. This work extends the results of a recent study through analysis of turbulence kinetic energy and turbulence spectra and their role in accurately simulating wind speed, direction, and tracer concentration. The significance and role of surface heat fluxes and use of the cell perturbation method in the numerical simulation setup are also examined. Our previous study detailed the model development necessary for our multiscale simulations, examined model skill at predicting wind speeds and tracer concentrations, and demonstrated that dynamic downscaling from mesoscale to microscale through a sequence of nested simulations can improve predictions of transport and dispersion relative to a microscale-only simulation forced by idealized meteorology. Here, predictions are compared with observations to assess qualitative agreement and statistical model skill at predicting wind speed, wind direction, tracer concentration, and turbulent kinetic energy at locations throughout the city. We also investigate the scale distribution of turbulence and the associated impact on model skill, particularly for predictions of transport and dispersion. Our results show that downscaled large-scale turbulence, which is unique to the multiscale simulations, significantly improves predictions of tracer concentrations in this complex urban environment. Significance Statement Simulations of atmospheric transport and mixing in urban environments have many applications, including pollution modeling for urban planning or informing emergency response following a hazardous release. These applications include phenomena with spatial scales spanning from millimeters to kilometers. Most simulations resolve flow only within the urban area of interest, omitting larger scales of turbulence and regional influences. This study examines a method that resolves both the small and large-scale flow features. We evaluate simulation accuracy by comparing predictions with observations from an experiment involving the release of a tracer gas in Oklahoma City, Oklahoma, with emphasis on correctly modeling turbulent fluctuations. Our results demonstrate the importance of resolving large-scale flow features when predicting transport and dispersion in urban environments.

42 ENGINEERING↗
DOE OSTI2023

Rheology of dense fiber suspensions: Origin of yield stress, shear thinning, and normal stress differences

We use high-fidelity computational model of fiber suspension to investigate suspension rheology. We investigate the interplay between the hydrodynamic, noncontact attractive and repulsive, and interfiber contact interactions. The shear-thinning viscosity and finite yield stress obtained from the Immerse Boundary Method simulations align quantitatively with experimental findings from the literature. The study demonstrates that attractive interactions lead to both yield stress and shear thinning behavior in rigid fiber suspensions. This discovery holds significance as it contributes to the ongoing debate on the source of yield stress in fiber suspensions. The proposed model is used to quantify normal stresses in addition to shear thinning and yield stress.

Ardekani, Arezoo↗
NASA NTRS1998

Annual Research Briefs, 1998

The topics contained in this progress report are direct numerical simulation of turbulent non-premixed combustion with realistic chemistry; LES of non-premixed turbulent reacting flows with conditional source term estimation; measurements of the three-dimensional scalar dissipation rate in gas-phase planar turbulent jets; direct simulation of a jet diffusion flame; on the use of interpolating wavelets in the direct numerical simulation of combustion; on the use of a dynamically adaptive wavelet collocation algorithm in DNS (direct numerical simulation) of non-premixed turbulent combustion; 2D simulations of Hall thrusters; computation of trailing-edge noise at low mach number using LES and acoustic analogy; weakly nonlinear modeling of the early stages of bypass transition; interactions between freestream turbulence and boundary layers; interfaces at the outer boundaries of turbulent motions; largest scales of turbulent wall flows; the instability of streaks in near-wall turbulence; an implementation of the v(sup 2) - f model with application to transonic flows; heat transfer predictions in cavities; a structure-based model with stropholysis effects; modeling a confined swirling coaxial jet; subgrid-scale models based on incremental unknowns for large eddy simulations; subgrid scale modeling taking the numerical error into consideration; towards a near-wall model for LES of a separated diffuser flow; on the feasibility of merging LES with RANS (Reynolds Averaging Numerical simulation) for the near-wall region of attached turbulent flows; large-eddy simulation of a separated boundary layer; numerical study of a channel flow with variable properties; on the construction of high order finite difference schemes on non-uniform meshes with good conservation properties; development of immersed boundary methods for complex geometries; and particle methods for micro and macroscale flow simulations.

Spinks, Debra↗
NASA NTRS2004

Interaction of a Boundary Layer with a Turbulent Wake

The objective of this grant was to study the transition mechanisms on a flat-plate boundary layer interacting with the wake of a bluff body. This is a simplified configuration presented and designed to exemplify the phenomena that occur in multi-element airfoils, in which the wake of an upstream element impinges on a downstream one. Some experimental data is available for this configuration at various Reynolds numbers. The first task carried out was the implementation and validation of the immersed-boundary method. This was achieved by performing calculations of the flow over a cylinder at low and moderate Reynolds numbers. The low-Reynolds number results are discussed, which is enclosed as Appendix A. The high-Reynolds number results are presented in a paper in preparation for the Journal of Fluid Mechanics. We performed calculations of the wake-boundary-layer interaction at two Reynolds numbers, Re approximately equal to 385 and 1155. The first case is discussed and a comparison of the two calculations is reported. The simulations indicate that at the lower Reynolds number the boundary layer is buffeted by the unsteady Karman vortex street shed by the cylinder. This is shown: long streaky structures appear in the boundary layer in correspondence of the three-dimensionalities in the rollers. The fluctuations, however, cannot be self-sustained due to the low Reynolds-number, and the flow does not reach a turbulent state within the computational domain. In contrast, in the higher Reynolds-number case, boundary-layer fluctuations persist after the wake has decayed (due, in part, to the higher values of the local Reynolds number Re achieved in this case); some evidence could be observed that a self-sustaining turbulence generation cycle was beginning to be established. A third simulation was subsequently carried out at a higher Reynolds number, Re=3900. This calculation gave results similar to those of the Re=l155 case. Turbulence was established at fairly low Reynolds number, as a consequence of the high level of the free-stream perturbation. An instantaneous flow visualization for that case is shown. A detailed examination of flow statistics in the transitional and turbulent regions, including the evolution of the turbulent kinetic energy (TKE) budget and frequency spectra showed the formation and evolution of turbulent spots characteristic of the bypass transition mechanism. It was also observed that the turbulent eddies achieved an equilibrium, fully developed turbulent states first, as evidenced by the early agreement achieved by the terms in the TKE budget with those observed in turbulent flows. Once a turbulent Reynolds stress profile had been established, the velocity profile began to resemble a turbulent one, first in the inner region and later in the outer region of the wall layer. An extensive comparison of the three cases, including budgets, mean velocity and Reynolds stress profiles and flow visualization, is included. The results obtained are also presented.

Piomelli, Ugo↗