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Large eddy simulation is performed in heat transfer of turbulent pipe flow with NEK5000 code based on spectral element method to study uncertainty quantification by Grid Convergence Index. The turb...

In the present study, 2-D large eddy simulations (LES) are conducted for flow past a porous circular array with a solid volume fraction (SVF) of 8.8%, 15.4% and 21.5%. Such simulations are relevant to understanding flow in natural streams and channels containing patches of emerged vegetation. In the simulations discussed in the paper, the porous cylinder of diameter D contains a variable number of identical solid circular cylinders (rigid plant stems) of diameter d = 0.048D. Most of the simulations are conducted at a Reynolds number of 2 100 based on the diameter D and the velocity of the steady uniform incoming flow. Though in all cases wake billows are shed in the regions where the separated shear layers (SSLs) forming on the sides of the porous cylinder interact, the effect of these wake billows on the mean drag is different. While in the high SVF case (21.5%), the total drag force oscillates quasi-regularly in time, similar to the canonical case of a large solid cylinder, in the cases with a lower SVF the shedding of the wake billows takes place sufficiently far from the cylinder such that the unsteady component of the total drag force is negligible. The mean amplitude of the oscillations of the drag force on the individual cylinders is the largest in a streamwise band centered around the center of the porous cylinder, where the wake to wake interactions are the strongest. In all cases the maximum drag force on the individual cylinders is the largest for the cylinders directly exposed to the flow, but this force is always smaller than the one induced on a small isolated cylinder and the average magnitude of the force on the cylinders directly exposed to the flow decreases monotonically with the increase in the SVF. Predictions of the global drag coefficients, Strouhal numbers associated with the wake vortex shedding and individual forces on the cylinders in the array from the present LES are in very good agreement with those of 2-D direct numerical simulations conducted on finer meshes, which suggests LES is a better option to numerically investigate flow in channels containing canopy patches, given that LES is computationally much less expensive than DNS at high Reynolds number. To prove this point, the paper also discusses results of 2-D LES conducted at a much higher Reynolds number, where the near-wake flow is strongly turbulent. For the higher Reynolds number cases, where the influence of the turbulence model is important, the effect of the sub-grid scale model and the predictive capabilities of the unsteady Reynolds averaged Navier-Stokes (RANS) approach to predict flow past porous cylinders are discussed.

Owing to their frequent occurrence in the natural environment, there has been significant interest in refining our understanding of flow over dunes and other bedforms. Recent work in this area has focused, in particular, on their shear-layer characteristics and the manner by which flow structures are generated. However, field-based studies, are reliant on single-, or multi-point measurements, rather than delimiting flow structures from the velocity gradient tensor, as is possible in numerical work. Here, we extract pointwise time series from a well-resolved large eddy simulation as a means to connect these two approaches. The at-a-point analysis technique is termed the velocity-intermittency quadrant method and relates the fluctuating, longitudinal velocity, $u_{1}^{\prime }(t)$, to its fluctuating pointwise Hölder regularity, $\unicode[STIX]{x1D6FC}_{1}^{\prime }(t)$. Despite the difference in boundary conditions, our results agree very well with previous experiments that show the importance, in the region above the dunes, of a quadrant 3 ($u_{1}^{\prime }, $\unicode[STIX]{x1D6FC}_{1}^{\prime }) flow configuration. Our higher density of sampling beneath the shear layer and close to the bedforms relative to experimental work reveals a negative correlation between $u_{1}^{\prime }(t)$ and $\unicode[STIX]{x1D6FC}_{1}^{\prime }(t)$ in this region. This consists of two distinct layers, with quadrant 4 ($u_{1}^{\prime }>0$, $\unicode[STIX]{x1D6FC}_{1}^{\prime }) dominant near the wall and quadrant 2 ($u_{1}^{\prime }, $\unicode[STIX]{x1D6FC}_{1}^{\prime }>0$) dominant close to the lower part of the separated shear layer. These results are consistent with a near-wall advection of vorticity into a region downstream of a temporarily foreshortened reattachment region, and the entrainment of slow moving and quiescent fluid into a faster, more turbulent shear layer. A comparison of instantaneous vorticity fields to the velocity-intermittency analysis shows how the pointwise results reflect larger-scale organisation of the flow. We illustrate this using results from two instantaneous datasets. In the former, extreme velocity-intermittency events corresponding to a foreshortened recirculation region (and high pressures on the stoss slope of the dune immediately downstream) arise, and the development of intense flow structures occurs as a consequence. In the other case, development of a ‘skimming flow’ with relatively little exchange between the inner and outer regions results in exceedances because of the coherence associated with this high velocity, high turbulence outer region. Thus, our results shed further light on the characteristics of dune flow in the near-wall region and, importantly for field-based research, show that useful information on flow structure can be obtained from single-point single velocity component measurements.

This numerical study investigates flow and turbulence structure through and around a circular array of solid circular cylinders of diameter$d$. The region containing the array of rigid cylinders resembles a porous circular cylinder of diameter$D$. The porous cylinder Reynolds number defined with the steady incoming flow velocity is$\mathit{Re}_{D}=10\,000$. Fully three-dimensional (3D) large eddy simulations (LES) are conducted to study the effects of the volume fraction of solids of the porous cylinder ($0.023) and$d/D$on the temporal variation and mean values of the drag/lift forces acting on the solid cylinders and on the porous cylinder. The effects of the bleeding flow through the circular porous cylinder on the wake structure and the influence of the SVF and$d/D$on the onset of flow three-dimensionality within or downstream of the porous cylinder and transition to turbulence are discussed. Results are compared with experimental data, predictions of theoretical models available in the literature and also with the canonical case of a solid cylinder ($\text{SVF}=1,d/D=1$). Three-dimensional LES predict that large-scale wake billows are shed in the wake of the porous cylinder for$\text{SVF}>0.05$, similar to the von Karman vortex street observed for solid cylinders. As the SVF decreases, the length of the separated shear layers (SSLs) of the porous cylinder and the distance from the back of the porous cylinder at which wake billows form increase. For sufficiently low volume fractions of solids (e.g. $\text{SVF}=0.05$, 0.023), no wake billows are shed and the interactions among the wakes of the solid cylinders are weak. Even for$\text{SVF}=0.023$, SSLs containing large-scale turbulent eddies form on the two sides of the porous cylinder, but their ends cannot interact to generate wake billows. In both regimes, the force acting on some of the solid cylinders within the array is highly unsteady. As opposed to results obtained based on 2D simulations, no intermediate regime in which the force acting on the solid cylinders is close to steady is present. Interestingly, an energetic low frequency corresponding to a Strouhal number defined with the diameter of the porous cylinder of approximately 0.2 is present within the porous cylinder and near-wake regions not only for cases where wake billows are generated but also for cases where no wake billows form. In the latter cases, this frequency is due to an instability acting on the SSLs which induces in-phase large-scale undulatory deformations of the two SSLs. A combined drag parameter for the porous cylinder${\it\Gamma}_{D}=\overline{C}_{d}\,aD/(1-\text{SVF})$is introduced, where$aD$is the non-dimensional frontal area per unit volume of the porous cylinder. This parameter characterizes by how much the velocity of the bleeding flow at the back of the porous cylinder is reduced compared with the incoming flow velocity for a given total drag force acting on the porous cylinder. Results from simulations conducted with different values of the SVF,$d/D$and mean time-averaged solid cylinder streamwise drag parameter,$\overline{C}_{d}$, show that${\it\Gamma}_{D}$increases monotonically with increasing$aD$. Several ways of defining the spatial extent of the wake region in a less ambiguous way are proposed.

A numerical simulation for a nonslender BWB UCAV configuration with a rounded leading edge and span of 1.0 m was performed to analyze its aerodynamic characteristics. Numerical results were compared with experimental data obtained at a free stream velocity of 50 m/s and at angles of attack from -4 to 26°. The Reynolds number, based on the mean chord length, is 1.25×106. 3D multi-block hexahedral grids are used to guarantee good grid quality and to efficiently resolve the boundary layer. Menter’s shear stress transport model and two transition models (γ-Reθ model and γ model) were used to assess the effect of the laminar/turbulent transition on the flow characteristics. Aerodynamic coefficients, such as drag, lift, and the pitching moment, were compared with experimental data. Drag and lift coefficients of the UCAV were predicted well while the pitching moment coefficient was underpredicted at high angles of attack and influenced strongly by the selected turbulent models. After assessing the pressure distribution, skin friction lines and velocity field around UCAV configuration, it was found that the transition effect should be considered in the prediction of aerodynamic characteristics of vortical flow fields.

A computational simulation for a nonslender BWB UCAV configuration with rounded leading edge and span of 1.0m was performed to analyze its aerodynamic characteristics. The freestream is 50m/s over –4 to 26 degree A.o.A.s. Reynolds number based on the mean chord length is × . 3D multi block hexahedral grids are used which allow good grid quality and ease to capture boundary layer.  model as well as  SST model is employed to assess the effect of transition for flow behavior. Drag and lift of the UCAV were well predicted while  is under predicted at high angle of attacks and influenced by the turbulence models strongly. After assessing pressure distribution, skin friction lines and velocity field around the UCAV configuration, it was found that transition effect should be considered to enhance the prediction of aerodynamic behavior by a vortical flowfield.

Turbulent flows with wavy wall are simulated using Residual-based Variational Multiscale Method (RB-VMS) which is proposed by Bazilves et al(2007) as new Large Eddy Simulation methodology. Incompressible Navier-Stokes equations are integrated using Isogeometric analysis which adopt the basis function as NURBS. The Reynolds number is 6760 based on the bulk velocity and averaged channel height. And the amplitude (

The three-dimensional (3D) incompressible flow past an open cavity in a channel is predicted using the Spalart–Almaras (SA) and the shear-stress-transport model (SST) based versions of detached eddy simulation (DES). The flow upstream of the cavity is fully turbulent. In the baseline case the length to depth (L∕D) ratio of the cavity is 2 and the Reynolds number ReD=3360. Unsteady RANS (URANS) is performed to better estimate the performance of DES using the same code and meshes employed in DES. The capabilities of DES and URANS to predict the mean flow, velocity spectra, Reynolds stresses, and the temporal decay of the mass of a passive contaminant introduced instantaneously inside the cavity are assessed based on comparisons with results from a well resolved large eddy simulation (LES) simulation of the same flow conducted on a very fine mesh and with experimental data. It is found that the SA-DES simulation with turbulent fluctuations at the inlet gives the best overall predictions for the flow statistics and mass exchange coefficient characterizing the decay of scalar mass inside the cavity. The presence of inflow fluctuations in DES is found to break the large coherence of the vortices shed in the separated shear layer that are present in the simulations with steady inflow conditions and to generate a wider range of 3D eddies inside the cavity, similar to LES. The predictions of the mean velocity field from URANS and DES are similar. However, URANS predictions show poorer agreement with LES and experiment compared to DES for the turbulence quantities. Additionally, simulations with a higher Reynolds number (ReD=33,600) and with a larger length to depth ratio (L∕D=4) are conducted to study the changes in the flow and shear-layer characteristics, and their influence on the ejection of the passive contaminant from the cavity.

The flow past two-dimensional (2D) channel cavities along with the removal of neutrally buoyant or dense miscible contaminants introduced instantaneously inside the cavity are studied using eddy resolving techniques. In the simulations, the incoming boundary layer is laminar and the flow is observed not to transition to turbulence as it is convected over the cavity. As for these flow conditions the main coherent structures in the separated shear layer over the cavity are quasi-dimensional, 2D simulations are performed. It is found that the mechanism of removal of the contaminant is very different between the neutrally buoyant and buoyant cases. In the neutrally buoyant case the contaminant is purged from the cavity mostly due to the interactions between the vortices shed in the separated shear layer with the main recirculation eddies inside the cavity and with the trailing edge corner. In the simulations in which a dense contaminant is introduced inside the cavity, after the initial stages of the mass exc...

Fully three-dimensional (3D) large-eddy simulation calculations of the flow past two-dimensional cavities for the case in which the incoming flow is fully turbulent are conducted to study the purging of neutrally buoyant or dense miscible contaminants introduced instantaneously inside the cavity. 3D simulations are needed because in the turbulent case (TC), as opposed to the laminar inflow case (LC) considered in the companion paper, the interactions between the coherent structures advected from the incoming channel and the eddies inside the cavity are highly 3D and have a nonnegligible effect on the mass exchange processes between the cavity and channel. Similar to the LC, it is found that the mechanism of removal of the contaminant is very different between the neutrally buoyant and buoyant cases. In the neutrally buoyant TC simulation the contaminant is ejected from the cavity due to the interactions among the large scale eddies in the separated shear layer, the coherent structures convected from the upstream channel over the cavity, and the main recirculation eddies inside the cavity. In the TC simulation with a negatively buoyant contaminant, internal wave breaking is observed to occur over the initial phases of the mixing which, along with other turbulent mixing phenomena, reduces the mean density gradient across the density interface. In the later stages, the contaminant removal and mixing processes are controlled by the interactions of the trailing edge vortex with the bottom layer containing denser contaminant beneath it and upstream of it (for the final stages when the vortex touches the cavity bottom). The oscillations in the size, position, and intensity of the trailing edge vortex are larger than the ones observed in the LC. As expected, turbulent mixing accelerates the purging process in the TC simulations.

The three-dimensional incompressible flow past a rectangular two-dimensional shallow cavity in a channel is investigated using large-eddy simulation (LES). The aspect ratio (length/depth) of the cavity is L/D = 2 and the Reynolds number defined with the cavity depth and the mean velocity in the upstream channel is 3360. The sensitivity of the flow around the cavity to the characteristics of the upstream flow is studied by considering two extreme cases: a developing laminar boundary layer upstream of the cavity and when the upstream flow is fully turbulent. The two simulations are compared in terms of the mean statistics and temporal physics of the flow, including the dynamics of the coherent structures in the region surrounding the cavity. For the laminar inflow case it is found that the flow becomes unstable but remains laminar as it is convected over the cavity. Due to the three-dimensional flow instabilities and the interaction of the jet-like flow inside the recirculation region with the separated shear layer, the spanwise vortices that are shed regularly from the leading cavity edge are disturbed in the spanwise direction and, as they approach the trailing-edge corner, break into an array of hairpin-like vortices that is convected downstream the cavity close to the channel bottom. In the fully turbulent inflow case in which the momentum thickness of the incoming boundary layer is much larger compared to the laminar inflow case, the jittering of the shear layer on top of the cavity by the incoming near-wall coherent structures strongly influences the formation and convection of the eddies inside the separated shear layer. The mass exchange between the cavity and the main channel is investigated by considering the ejection of a passive scalar that is introduced instantaneously inside the cavity. As expected, it is found that the ejection is faster when the incoming flow is turbulent due to the interaction between the turbulent eddies convected from upstream of the cavity with the separated shear layer and also to the increased diffusion induced by the broader range of scales that populate the cavity. In the turbulent case it is shown that the eddies convected from upstream of the cavity can play an important role in accelerating the extraction of high-concentration fluid from inside the cavity. For both laminar and turbulent inflow cases it is shown that the scalar ejection can be described using simple dead-zone theory models in which a single-valued global mass exchange coefficient can be used to describe the scalar mass decay inside cavity over the whole ejection process.