Direct Numerical Simulations Simulations Research Articles

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM + . For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed.The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. Given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

Modeling of high-speed, methane–air, turbulent combustion, Part I: One-dimensional turbulence modeling with comparison to DNS

The ability of the one-dimensional turbulence (ODT) model to serve as a surrogate direct numerical simulation (DNS) is assessed for highly turbulent flames. The ODT model is applied to freely propagating premixed methane–air flames at Karlovitz numbers 10, 102, 103, and 104, and results are compared with DNS. The ODT model solves the conservation equations for momentum, energy, and species on a one-dimensional domain, which corresponds to a streamwise line of sight spanning the DNS domain. The effects of turbulent advection are modeled via a stochastic process, in which the Kolmogorov and reactive length and time scales are explicitly resolved. Molecular transport and chemical kinetics are concurrently advanced in time. Both the ODT and DNS simulations use a 21-species skeletal chemical model for methane combustion. The accuracy of the ODT model is assessed by comparing its predictions of several key characteristics of the flames for each Karlovitz number tested, including the turbulent flame speed and width and the joint probability density functions (jPDFs) of major and selected minor species as well as the heat release rate conditioned on temperature with the results of DNS under comparable conditions. The ODT model is shown to yield qualitative and quantitative agreement with the DNS data for most of the above flame characteristics. Discrepancies are observed primarily for the jPDFs of several minor species examined. Overall, the ODT approach is shown to be an effective surrogate of DNS, potentially useful for guiding chemical reaction model reduction and for assessing the sensitivities of the flame structure and the burning rate to chemistry under highly turbulent conditions.Novelty and Significance:The direct numerical simulations (DNS) of premixed turbulent methane–air flames presented in this work span a uniquely wide range of turbulent intensities, from relatively modest corresponding to Karlovitz number Ka=10 to ultra-high intensities at Ka=104. This represents virtually the entire range of turbulent intensities that could be encountered in any realistic situation. This is also the first time that such a wide range of conditions is probed for methane in high-fidelity, fully resolved simulations, which use a fully compressible set of flow equations. The one-dimensional turbulence (ODT) model utilizes the same forcing that is present in the DNS enabling a direct comparison between the ODT and DNS. The results show that ODT captures the key features of the DNS results. ODT is shown to be an effective surrogate for DNS and may be useful in guiding chemical reaction model reduction, where many simulations are required.

Droplet characterization of a pressure-swirl atomizer by means of high-fidelity modelling based on DNS simulations

Liquid injection optimization is key to enhance the efficiency of many processes in a wide variety of fields. Combustion processes are one of the most challenging ones, due to the direct emissions and greenhouse gases implications. This work aims at studying the external two-phase flow produced when injecting fuel with a pressure-swirl atomizer in an operating condition typical of an academic burner. The main objective is to have a better comprehension of the atomization process in this type of nozzles, getting information on the droplets’ characteristic size and how they are produced and arranged. For that regard, a high-fidelity Direct Numerical Simulation (DNS) is used to analyse the very near field of the spray produced, where primary atomization takes place. Pre-processing tasks are explained in terms of geometry comprehension, computational domain and mesh selection, boundary conditions and main simulation setup parameters. Then, through post-processing tasks, both quantitative and qualitative results are extracted, which will serve to validate the modelling against previous works and to provide novel data about the atomization process in pressure-swirl atomizers. Results show that smaller droplets predominate over bigger ones as expected, since just the first millimetres of the spray are modelled. However, there is a clear trend of droplet’s size growing when increasing both axial and radial distances, indicating coalescence in regions relatively far from the nozzle. The achieved results, together with results from simulating the injection event with other fuels or at other operating conditions, can be used to develop a phenomenological model able to predict how atomization is going to be as a function of the non-dimensional Reynolds and Weber numbers that could be implemented in lower-resolution RANS and LES codes for modelling atomization. This investigation proves that it is possible to faithfully predict the near field of these sprays through DNS simulation, getting similar trends to those of the experimental data, and that the study through numerical models is necessary in the investigation process. The information they can bring, together with the experimental knowledge, can make a good synergy that will eventually lead to a better understanding of this type of atomizers.

Numerical simulation of turbulent, plane parallel Couette–Poiseuille flow

We present numerical simulation and mean-flow modelling of statistically stationary plane Couette–Poiseuille flow in a parameter space $(Re,\theta )$ with $Re=\sqrt {Re_c^2+Re_M^2}$ and $\theta =\arctan (Re_M/Re_c)$ , where $Re_c,Re_M$ are independent Reynolds numbers based on the plate speed $U_c$ and the volume flow rate per unit span, respectively. The database comprises direct numerical simulations (DNS) at $Re=4000,6000$ , wall-resolved large-eddy simulations at $Re = 10\,000, 20\,000$ , and some wall-modelled large-eddy simulations (WMLES) up to $Re=10^{10}$ . Attention is focused on the transition (from Couette-type to Poiseuille-type flow), defined as where the mean skin-friction Reynolds number on the bottom wall $Re_{\tau,b}$ changes sign at $\theta =\theta _c(Re)$ . The mean flow in the $(Re,\theta )$ plane is modelled with combinations of patched classical log-wake profiles. Several model versions with different structures are constructed in both the Couette-type and Poiseuille-type flow regions. Model calculations of $Re_{\tau,b}(Re,\theta )$ , $Re_{\tau,t}(Re,\theta )$ (the skin-friction Reynolds number on the top wall) and $\theta _c$ show general agreement with both DNS and large-eddy simulations. Both model and simulation indicate that, as $\theta$ is increased at fixed $Re$ , $Re_{\tau,t}$ passes through a peak at approximately $\theta = 45^{\circ }$ , while $Re_{\tau,b}$ increases monotonically. Near the bottom wall, the flow laminarizes as $\theta$ passes through $\theta _c$ and then re-transitions to turbulence. As $Re$ increases, $\theta _c$ increases monotonically. The transition from Couette-type to Poiseuille-type flow is accompanied by the rapid attenuation of streamwise rolls observed in pure Couette flow. A subclass of flows with $Re_{\tau,b}=0$ is investigated. Combined WMLES with modelling for these flows enables exploration of the $Re\to \infty$ limit, giving $\theta _c \to 45^\circ$ as $Re\to \infty$ .

Status, perspectives, and added value of high fidelity simulations for safety and design

With the increase in computational power, High Fidelity (HiFi) simulations become increasingly important to nuclear thermal hydraulics for fundamental understanding of turbulent flow and heat transfer phenomena and for further development and validation of engineering CFD models. We consider Direct Numerical Simulations (DNS) and Large Eddy Simulation (LES) as HiFi analyses. In this paper, we present an overview of single-phase and two-phase flow DNS simulations relevant for nuclear reactor safety and design purposes. In order to limit the scope, this overview has a focus on DNS simulations of fully turbulent non-reacting incompressible flows. LES approaches are briefly mentioned in certain areas, where LES-to-DNS upgrade is expected to happen in the near future.We first explain the concept of DNS and related concepts like Under-resolved DNS (UDNS) and quasi-DNS (q-DNS). Subsequently, we present the numerical methods which are generally used for HiFi simulations. A wider span of numerical methods can be observed in single-phase flow simulations than in two-phase flow simulations, where the later require additional algorithms for tracking of the interfaces between the two phases. Consequently, two-phase DNS simulations are not immune to modelling errors, and are much more complex than their single-phase counterparts. Next, an overview is given of single-phase flow DNS simulations. We start with basic cases like turbulent channel and pipe flows, which are mainly useful for development and validation of less detailed engineering CFD models. We continue with more recent and more complex cases like, e.g., flows in a rod bundle and a pebble bed, which are directly applicable in nuclear engineering. Next, an overview of two-phase flow HiFi simulations is presented in a similar fashion. The importance of the availability of the presented HiFi simulations is explained by addressing their role for further development and validation of engineering CFD models which are used for the eventual industrial applications. The importance of HiFi simulation data, complementary to experimental data, for uncertainty quantification and machine learning is explained. Finally, future challenges for HiFi simulations, especially for two-phase flow, are elucidated.

Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.

Possibility for survival of macroscopic turbulence in porous media with high porosity

The direct numerical simulation (DNS) study by Jin et al. (J. Fluid Mech, vol. 766, 2015, pp. 76–103) shows that the turbulent structures are generally restricted in size to the pore scale, leading to the pore-scale prevalence hypothesis (PSPH). Although the PSPH has been validated under most conditions, it might become invalid as the porosity approaches unity. In order to investigate the valid domain of the PSPH, we have studied the turbulent flows in porous matrices which have one or two length scales using DNS and macroscopic simulation methods. The large porous elements are made of staggered arrays of square cylinders, which might stimulate strong macroscopic (large-scale) turbulence. The small porous elements are made of aligned arrays of spheres or cubes, which suppress the macroscopic turbulence. The analyses are performed for various values of the Reynolds number, Darcy number, pore-scale ratio and porosity. Turbulent two-point correlations, integral length scales and premultiplied energy spectra are calculated from the DNS and macroscopic simulation results to determine the length scale of the turbulent structures. Our numerical results show that the flow becomes turbulent when the Reynolds number is sufficiently large. However, the length scale of turbulence is not considerably affected by the Reynolds number, Darcy number and pore-scale geometry. The PSPH is valid when the porosity has small or medium values. At a sufficiently large Reynolds number, large-scale turbulence survives if the porosity is larger than a critical value. Our DNS and macroscopic simulation results show that this critical value is in the range 0.93–0.98 for porous matrices with large Darcy numbers (0.3–1.26 using the definition in this study). The dependence of the critical porosity on the pore-scale geometry still needs to be further investigated.

Particle‐resolved turbulent flow in a packed bed: RANS, LES, and DNS simulations

AbstractPacked bed reactors are widely used to perform solid‐catalyzed gas‐phase reactions and local turbulence is known to influence heat and mass transfer characteristics. We have investigated turbulence characteristics in a packed bed of 113 spherical particles by performing particle‐resolved Reynolds‐averaged Navier–Stokes (RANS) simulations, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). The predictions of the RANS and LES simulations are validated with the lattice Boltzmann method (LBM)–based DNS at particle Reynolds number (Rep) of 600. The RANS and LES simulations can predict the velocity, strain rate, and vorticity with a reasonable accuracy. Due to the dominance of enhanced wall‐function treatment, the turbulence characteristics predicted by the ε‐based models are found to be in a good agreement with the DNS. The ω‐based models under‐predicted the turbulence quantities by several orders of magnitude due to their inadequacy in handling strongly wall‐dominated flows at low Rep. Using the DNS performed at different Rep, we also show that the onset of turbulence occurs between .

Flow through an elbow: A direct numerical simulation investigating turbulent flow quantities

Turbulent flow in a sharp 90° elbow in a square duct was numerically investigated by performing a direct numerical simulation (DNS) and the results were compared to experimental and Reynolds Averaged Navier–Stokes (RANS) data. This is the first part of an effort to expand the understanding of particle transport in complex geometries. The paper is divided into two parts: a validation of the flow, and then a discussion of additional flow quantities that are important for modeling particles but were not measured experimentally. In the validation section the DNS results were compared to experimental and RANS data at a Reynolds number of 11,500. Profiles of the mean and root-mean-square (RMS) fluctuating velocities were compared at various points along the elbow’s midplane. Upstream of the bend, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing only slightly near the walls. Downstream of the bend the DNS and the experimental results were virtually identical, varying by no more than 2%. However, the RANS results deviated, showing a more extended region of flow re-circulation, causing the mean and RMS velocities to differ by as much as 40%. After the validation, one of the additional quantities was the secondary flow structures in the plane perpendicular to the mean flow direction. The RANS and DNS showed similar results upstream of the bend, exhibiting in-plane vortices of the second-kind. Downstream, the vortical flows of the first-kind were observed with a magnitude of about 40% of the mean flow and differed by about 5% between the DNS and the RANS. Eulerian time scales at different locations upstream and downstream of the elbow were also evaluated. The upstream Eulerian time scales showed trends similar to channel flow data, with maximum time scales near the wall. The downstream time scales were qualitatively different showing non monotonic behavior across the channel and values that were significantly different than a channel flow.

Extracting signature responses from respiratory flows: Low-dimensional analyses on Direct Numerical Simulation-predicted wakes of a flapping uvula.

Uvula-induced snoring and associated obstructive sleep apnea is a complex phenomenon characterized by vibrating structures and highly transient vortex dynamics. This study aimed to extract signature features of uvula wake flows of different pathological origins and develop a linear reduced-order surrogate model for flow control. Six airway models were developed with two uvula kinematics and three pharynx constriction levels. A direct numerical simulation (DNS) flow solver based on the immersed boundary method was utilized to resolve the wake flows induced by the flapping uvula. Key spatial and temporal responses of the flow to uvula kinematics and pharynx constriction were investigated using continuous wavelet transform (CWT), proper orthogonal decomposition (POD), and dynamic mode decomposition (DMD). Results showed highly complex patterns in flow topologies. CWT analysis revealed multiscale correlations in both time and space between the flapping uvular and wake flows. POD analysis successfully separated the flows among the six models by projecting the datasets in the vector space spanned by the first three eigenmodes. Perceivable differences were also captured in the time evolution of the DMD modes among the six models. A linear reduced-order surrogate model was constructed from the predominant eigenmodes obtained from the DMD analysis and predicted vortex patterns from this surrogate model agreed well with the corresponding DNS simulations. The computational and analytical platform presented in this study could bring a variety of applications in breathing-related disorders and beyond. The computational efficiency of surrogate modeling makes it well suited for flow control, forecasting, and uncertainty analyses.

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable. UQ based only on RANS simulations or on DNS thus leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model

Abstract. This paper presents a novel methodology to use direct numerical simulation (DNS) to study the impact of isotropic homogeneous turbulence on the condensational growth of cloud droplets. As shown by previous DNS studies, the impact of turbulence increases with the computational domain size, that is, with the Reynolds number, because larger eddies generate higher and longer-lasting supersaturation fluctuations that affect growth of individual cloud droplets. The traditional DNS can only simulate a limited range of scales because of the excessive computational cost that comes from resolving all scales involved, that is, from large scales at which the turbulent kinetic energy (TKE) is introduced down to the Kolmogorov microscale, and from following every single droplet. The novel approach is referred to as the “scaled-up DNS”. The scaling up is done in two parts, first by increasing both the computational domain and the Kolmogorov microscale and second by using super-droplets instead of real droplets. To ensure proper dissipation of TKE and scalar variance at small scales, molecular transport coefficients are appropriately scaled up with the grid length. For the scaled-up domains, say, meters and tens of meters, one needs to follow billions of real droplets. This is not computationally feasible, and so-called super-droplets are applied in scaled-up DNS simulations. Each super-droplet represents an ensemble of identical real droplets, and the number of real droplets represented by a super-droplet is referred to as the multiplicity attribute. After simple tests showing the validity of the methodology, scaled-up DNS simulations are conducted for five domains, the largest of 643 m3 volume using a DNS of 2563 grid points and various multiplicities. All simulations are carried out with vanishing mean vertical velocity and with no mean supersaturation, similarly to past DNS studies. As expected, the supersaturation fluctuations as well as the spread in droplet size distribution increase with the domain size, with the droplet radius variance increasing in time t as t1∕2 as identified in previous DNS studies. Scaled-up simulations with different multiplicities document numerical convergence of the scaled-up solutions. Finally, we compare the scaled-up DNS results with a simple stochastic model that calculates supersaturation fluctuations based on the vertical velocity fluctuations updated using the Langevin equation. Overall, the results document similar scaling to previous small-domain DNS simulations and support the notion that the stochastic subgrid-scale model is a valuable tool for the multi-scale simulation of droplet spectral evolution applying a large-eddy simulation model.

Recent advances in high-fidelity simulations of pulverized coal combustion

Although renewable energy has recently attracted a lot of attention, coal-fired power plants will still play an important role in electricity production in the future due to coal’s abundance in the world. However, combustion of pulverized coal is extremely complex which makes experimental measurements very challenging even impossible. As an alternative, computational fluid dynamics (CFD) is a powerful tool to investigate pulverized coal combustion (PCC), and can help to design and develop advanced coal-fired facilities. With the development of computational capacity, high-fidelity simulations of PCC have been developed and significant achievements have been obtained in the recent years. In this review, the recent advances in CFD of PCC, especially in fully-resolved direct numerical simulation (DNS), point-particle DNS and large eddy simulation (LES) of PCC are summarized. The progresses on both numerical methods and coal combustion models are highlighted. The state-of-the-art applications of these high-fidelity simulations are also reviewed, including the investigation of combustion characteristics of pulverized coals, the development of advanced coal combustion models, and the development of clean coal technologies. It is concluded that fully-resolved DNS, point-particle DNS, and LES have their merits and demerits, so the optimal use of each approach depends on specific research purpose. For coal devolatilization and char-oxidation models, the combined models in which advanced models are used to calibrate the kinetic parameters of simple models are quite attractive in terms of computational accuracy and computational burden. For chemical reactions, the flamelet model is popular, but the predictive capability and robustness need to be further improved. Besides, LES is rapidly approaching to simulate industrial PCC. However, the computational cost is still quite expensive, and more efficient algorithms and sub-grid models are required. To this end, DNS database, benchmark measurements, and international collaborations are important. Machine learning may also play an important role in promoting the development of high-fidelity simulations of PCC in the future.

Direct Numerical Simulation of Laminar Natural Convection in a Square Cavity at Different Inclination Angle

The effect of angle of rotation on laminar natural convection inside the square cavity have been observed in this research. It was assumed that left and right walls heated isothermally, whereas other two walls act as adiabatic. This problem was solved by assuming 2-D and by Direct Numerical Simulation (DNS) method using ANSYS Fluent 16.0. A series of DNS simulation were carried out for different inclination angle (𝜃 = 0°~90°) of the cavity at Ra = 103 & 104. It was observed that at average Nusselt number increase up to some value of angle of inclination after that it decrease though this variation is not significant.

Modeling Turbulent Flows in Porous Media

Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this review, we summarize the current state of the literature on methods to model such flows. We focus on a range of Reynolds numbers, covering the inertial regime through the asymptotic turbulent regime. The review emphasizes both numerical modeling and the development of averaged (spatially filtered) balances over representative volumes of media. For modeling the pore scale, we examine the recent literature on Reynolds-averaged Navier–Stokes (RANS) models, large-eddy simulation (LES) models, and direct numerical simulations (DNS). We focus on the role of DNS and discuss how spatially averaged models might be closed using data computed from DNS simulations. A Darcy–Forchheimer-type law is derived, and a prior computation of the permeability and Forchheimer coefficient is presented and compared with existing data.

Fractal Reconstruction of Sub-Grid Scales for Large Eddy Simulation

In this work, the reconstruction of sub-grid scales in large eddy simulation (LES) of turbulent flows in stratocumulus clouds is addressed. The approach is based on the fractality assumption of turbulent velocity field. The fractal model reconstructs sub-grid velocity field from known filtered values on LES grid, by means of fractal interpolation, proposed by Scotti and Meneveau (Physica D 127, 198–232 1999). The characteristics of the reconstructed signal depend on the stretching parameter d, which is related to the fractal dimension of the signal. In many previous studies, the stretching parameter values were assumed to be constant in space and time. To improve the fractal interpolation approach, we account for the stretching parameter variability. The local stretching parameter is calculated from direct numerical simulation (DNS) data with an algorithm proposed by Mazel and Hayes (IEEE Trans. Signal Process 40(7), 1724–1734, 1992), and its probability density function (PDF) is determined. It is found that the PDFs of d have a universal form when the velocity field is filtered to wave-numbers within the inertial range. In order to investigate Reynolds number (Re) dependence, we compare the inertial-range PDFs of d in DNS and large eddy simulation (LES) of stratocumulus cloud-top and experimental airborne data from Physics of Stratocumulus Top (POST) research campaign. Next, fractal reconstruction of the subgrid velocity is performed and energy spectra and statistics of velocity increments are compared with DNS data. It is assumed that the stretching parameter d is a random variable with the prescribed PDF. We show that the agreement with the DNS is in such case better and the error in mass conservation is smaller compared to the use of constant values of d. The motivation of this study is to reproduce effect of sub-grid scales on a motion of Lagrangian particles (e.g. droplets) in clouds.

DNS and LST stability analysis of Oldroyd-B fluid in a flow between two parallel plates

Several flows of practical interest are of viscoelastic fluids and it is desirable to know if these flows are in a laminar or turbulent state. In this paper, the laminar-turbulent transition is studied in which the convection of Tollmien–Schlichting waves is investigated for the incompressible two-dimensional flow between two parallel plates. The viscoelastic fluid adopted is modeled by the Oldroyd-B constitutive equation. Direct Numerical Simulation (DNS) and Linear Stability Theory (LST) were used to verify the stability of the viscoelastic fluid flow to unsteady disturbances. In the DNS formulation, the governing equations are discretized by high-order compact finite difference schemes for the spatial derivatives, while time integrations are carried out by a fourth order Runge–Kutta method. For the LST analysis, the Orr–Sommerfeld equation is modified to include viscoelastic effects and solved by a shooting method. In order to evaluate the flow stability when submitted to unsteady disturbances and to find the neutral stability curves, a range of numerical simulations was performed with different dimensionless parameters for the viscoelastic fluid flow and the results were compared with the Newtonian fluid flow. The influence of the elastic forces and the amount of the polymer concentration in the fluid were investigated. A wide range of polymer concentration was studied. The results show that the variation of the critical Reynolds number may be monotonic for certain conditions. The DNS simulations were carried out, and the amplification rates obtained were compared with the LST results, with a very good agreement. The DNS results allow also the visualization of the disturbances variation in streamwise and wall-normal directions, showing the behavior of the velocity components, vorticity and the non-Newtonian extra-stress tensor components. The DNS results show a significant change in flow structure for certain combinations of the polymer concentration and elastic forces parameters.

Effects of Rotation on Turbulence Production

Direct numerical simulations (DNS) of non-rotating and rotating turbulent channel flow were conducted. The data base obtained from these DNS simulations was used to investigate the prominent coherent structures involved in the turbulence generation cycle. Predictions from three theoretical models concerning the formation and evolution of sublayer streaks, three-dimensional hairpin vortices and propagating plane waves were validated using visualizations from the present DNS data. Quadrant analysis was used to determine a phase shift between the fluctuating streamwise and wall-normal velocities as a characteristic of turbulence production in the suction region at a low rotation number.

Air Entrainment and Surface Fluctuations in a Turbulent Ship Hull Boundary Layer

The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations. In the experiments, a laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. To complement the experiments, Direct Numerical Simulations (DNS) of the two-phase boundary layer problem were carried out with the domain including a streamwise belt section simulated with periodic boundary conditions. Cinematic Laser-Induced Fluorescence (LIF) measurements of water surface profiles in two vertical planes oriented parallel to the belt surface (wall-parallel profiles) are presented and compared to previous measurements of profiles in a vertical plane oriented normal to the belt surface (wall-normal profiles). Additionally, photographic observations of air entrainment and measurements of air bubble size distributions and motions are reported herein. The bubble entrainment mechanisms are studied in detail through the results obtained by the DNS simulations. Free surface features resembling breaking waves and traveling parallel to the belt are observed in the wall-parallel LIF movies. These breaking events are thought to be one of the mechanisms by which the air is entrained into the underlying flow. The bubble size distribution is found to have a characteristic break in slope, similar to the Hinze scale previously observed in breaking waves. Finally, several entrainment mechanisms are found in the simulations and their prevalence in the free surface boundary layer is assessed.

Direct Numerical Simulation Code Validation for Compressible Shear Flows Using Linear Stability Theory

In order to simulate compressible shear flow stability and aeroacoustic problems, a numerical code must be able to capture how a baseflow behaves when submitted to small disturbances. If the disturbances are amplified, the flow is unstable. The linear stability theory (LST) provides a framework to obtain information about the growth rate in relation to the excitation frequency for a given baseflow. A linear direct numerical simulation (DNS) should capture the same growth rate as the LST, providing a severe test for the code. In the present study, DNS simulations of a two-dimensional compressible mixing layer and of a two-dimensional compressible plane jet are performed. Disturbances are introduced at the domain inflow and spatial growth rates obtained with a DNS code are compared with growth rates obtained from LST analyses, for each baseflow, in order to verify and validate the DNS code. The good comparison between DNS simulations and LST results indicates that the code is able to simulate compressible flow problems and it is possible to use it to perform numerical simulation of instability and aeroacoustic problems.