Well-resolved Large-eddy Simulations Research Articles

The skin-friction coefficient of a turbulent boundary layer modified by a large-eddy break-up device

A computational study based on well-resolved large-eddy simulations is performed to study the skin friction modification by a large-eddy breakup device (LEBU) in a zero-pressure-gradient turbulent boundary layer. The LEBU was modeled using an immersed boundary method. It is observed that the presence of the device leads to the generation of wake vortices, which propagate downstream from the LEBU and toward the wall. A skin friction decomposition procedure is utilized to study different physical mechanisms of the observed skin friction reduction. From the skin friction decomposition, it is found that the skin friction reduction can be characterized by three universal regions of different changes for the skin friction contributions. The first region is predominantly associated with the formation of the wake vortices and the reduction of Reynolds shear stress. In the second region, the mean streamwise velocity fields show that a region of velocity deficit formed downstream of the LEBU propagates toward the wall and leads to turbulence reduction due to wake wall interactions, which also induces a local maximum skin friction reduction. In the third region, the dissipation of wake vortices leads to the regeneration of Reynolds shear stress. A quadrant analysis of the Reynolds shear stress contribution reveals that the LEBU increases the Q2 and Q4 contributions and attenuates the Q1 and Q3 contributions in the first region, followed by an onset of Reynolds shear stress further downstream.

Assessment of the wall-adapting local eddy-viscosity model in transitional boundary layer

The main idea of this manuscript is to assess the wall-adapting local eddy-viscosity (WALE) model, which is designed for large-eddy simulation (LES) of turbulent boundary layer, in transitional flow. In contrast to many other sub-grid-scale (SGS) models, the WALE model demonstrates the asymptotic decay of the eddy viscosity in the vicinity of a solid wall in turbulent boundary layer without relying on a dynamic procedure on the SGS model coefficient. Furthermore, the WALE model yields zero eddy viscosity in pure shear flow. Such features are attractive for LES of laminar-to-turbulent transition, yet the WALE model has not been thoroughly investigated in transitional boundary layer flow. Well-resolved LES is conducted for canonical boundary layer transition triggered by sub-harmonic resonance. The model formulation is thoroughly analyzed in the transition process. The asymptotic behavior of the two major tensors, i.e., the strain rate tensor and the traceless tensor of the velocity gradient squared, are confirmed in the current well-resolved LES. The cubic decay of the eddy viscosity in the wall distance is confirmed from the asymptotic analysis on the transitional flow. The presence of the strain rate in the model formulation generates practically zero eddy viscosity in the pre-transition region, allowing interactions of small-amplitude instabilities. The traceless tensor of the velocity gradient squared escalates if small-scale eddies appear, leading to sizable eddy viscosity particularly in the log-law layer in turbulent flow. The response of the WALE model to grid resolution is also discussed. The performance of the WALE model is compared to two other SGS models, Smagorinsky and Vreman models with a constant coefficient, in the current transitional wall-bounded flow.

Enabling Adaptive Mesh Refinement for Spectral-Element Simulations of Turbulence Around Wing Sections

The implementation of adaptive mesh refinement (AMR) in the spectral-element method code Nek5000 is used for the first time on the well-resolved large-eddy simulation of the turbulent flow over wings. In particular, the flow over a NACA4412 profile with a 5^circ angle of attack at chord-based Reynolds number {text {Re}}_c=200{,}000 is analyzed in the present work and compared with a previous conformal simulation used as baseline. The mesh, starting from a coarse resolution, is progressively and automatically refined by means of AMR, which allows for high resolution near the wall and wake whereas significantly larger elements are used in the far-field. The resulting mesh, which remains unchanged in the production runs (i.e. AMR is used to create the final mesh, which is then fixed), is of higher resolution than those in previous conformal cases, and it allows for the use of larger computational domains, avoiding the use of precursor RANS simulations to determine the boundary conditions. This is achieved with, approximately, 2 times lower total number of grid points if the same spanwise length is used. Turbulence statistics obtained in the AMR simulation show good agreement with the ones obtained with the conformal mesh, and the pressure-coefficient distribution along the wing surface matches pressure-scan experimental data obtained in the MTL wind tunnel at KTH. The use of AMR is therefore expected to enable the simulation of high-Reynolds numbers turbulent flows over complex geometries (such as wings), thus allowing the study of pressure-gradient effects at high Reynolds numbers relevant for practical applications.

Influence of upstream disturbances on the primary and secondary instabilities in a supersonic separated flow over a backward-facing step

The development of primary and secondary instabilities is investigated numerically for a supersonic transitional flow over a backward-facing step at Ma = 1.7 and Reδ0=13 718. Oblique Tollmien–Schlichting (T–S) waves with properties according to linear stability theory (LST) are introduced at the domain inlet with zero, low, or high amplitude (cases ZA, LA, and HA). A well-resolved large eddy simulation (LES) is carried out for the three cases to characterize the transition process from laminar to turbulent flow. The results for the HA case show a rapid transition due to the high initial disturbance level such that the non-linear interactions already occur upstream of the step, before the Kelvin–Helmholtz (K–H) instability could get involved. In contrast, cases ZA and LA share a similar transition road map in which transition occurs in the separated shear flow behind the step. Case LA is analyzed in detail based on the results from LST and LES to scrutinize the evolution of T–S, K–H, and secondary instabilities, as well as their interactions. Upstream of the step, the linear growth of the oblique T–S waves is the prevailing instability. Both T–S and K–H modes act as the primary mode within a short distance behind the step and undergo a quasi-linear growth with a weak coupling. Upon pairing of the large K–H vortices, subharmonic waves are produced, and secondary instabilities begin to dominate the transition. Simultaneously, the growth of T–S waves is retarded by the slow resonance between subharmonic K–H and secondary instabilities. The vortex breakdown and reattachment downstream further contribute to the development of the turbulent boundary layer.

Dynamic mode decomposition of supersonic turbulent pipe flow with and without shock train

ABSTRACTLow frequency dynamics of shock–turbulence interactions in constant area pipe flow with centre-line Mach number of 1.7 and friction Reynolds number of 245 is analysed using dynamic mode decomposition (DMD) of well-resolved large eddy simulation (LES) data. Two flow cases – one with a shock train and the other without shocks – are analysed. The dominant DMD modes show the near-wall sweep-ejection activity especially for the flow without shocks and also show the influence of the shocks on the near-wall organisation of the flow. The DMD modes also demonstrate a reasonable correlation between the near-wall coherent structures and the shock train for some of the modes.

Effect of adverse pressure gradients on turbulent wing boundary layers

The characteristics of turbulent boundary layers (TBLs) subjected to adverse pressure gradients are analysed through well-resolved large-eddy simulations. The geometries under study are the NACA0012 and NACA4412 wing sections, at and angle of attack, respectively, both of them at a Reynolds number based on inflow velocity and chord length of . The turbulence statistics show that adverse pressure gradients (APGs) have a significant effect on the mean velocity, velocity fluctuations and turbulent kinetic energy budget, and this effect is more prominent on the outer region of the boundary layer. Furthermore, the effect of flow history is assessed by means of an integrated Clauser pressure-gradient parameter (Vinuesa et al., Flow Turbul. Combust., vol. 99, 2017, pp. 565–587), through the study of cases with matching local values of and the friction Reynolds number to isolate this effect. Our results show a noticeable effect of the flow history on the outer region, however the differences in the near-wall peak of the tangential velocity fluctuations appear to be mostly produced by the local APG magnitude. The one-dimensional power-spectral density shows energetic small scales in the outer region of APG TBLs, whereas these energetic scales do not appear in zero-pressure-gradient (ZPG) TBLs, suggesting that small scales near the wall are advected towards the outer layer by the APG. Moreover, the linear coherence spectra show that the spectral outer peak of high-Reynolds-number ZPG TBLs is highly correlated with the near-wall region (Baars et al., J. Fluid Mech., vol. 823, 2017, R2), unlike APG TBLs which do not show such a correlation. This result, together with the different two-dimensional spectra of APG and high-Reynolds-number ZPG TBLs, suggests different energisation mechanisms due to APG and increase in Reynolds number. To the authors’ knowledge, this is the first in-depth analysis of the TBL characteristics over wings, including detailed single-point statistics, spectra and coherence.

The influence of thermal boundary conditions on turbulent forced convection pipe flow at two Prandtl numbers

Different types of thermal boundary conditions are conceivable in numerical simulations of convective heat transfer problems. Isoflux, isothermal and a mixed-type boundary condition are compared by means of direct numerical simulations (for the lowest Reynolds number) and well-resolved large-eddy simulations of a turbulent forced convection pipe flow over a range of bulk Reynolds numbers from Reb=5300 to Reb=37700, at two Prandtl numbers, i.e. Pr=0.71 and Pr=0.025. It is found that, while for Pr=0.71 the Nusselt number is hardly affected by the type of thermal boundary condition, for Pr=0.025 the isothermal boundary condition yields ≈20% lower Nusselt numbers compared to isoflux and mixed-type over the whole range of Reynolds numbers. A decomposition of the Nusselt number is derived. In particular, we decompose it into four contributions: laminar, radial and streamwise turbulent heat flux as well as a contribution due to the turbulent velocity field. For Pr=0.71 the contribution due to the radial turbulent heat flux is dominant, whereas for Pr=0.025 the contribution due to the turbulent velocity field is dominant. Only at a moderately high Reynolds number, such as Reb=37700, both turbulent contributions are of similar magnitude. A comparison of first- and second-order thermal statistics between the different types of thermal boundary conditions shows that the statistics are not only influenced in the near-wall region but also in the core region of the flow. Power spectral densities illustrate large thermal structures in low-Prandtl-number fluids as well as thermal structures located right at the wall, only present for the isoflux boundary condition.A database including the first- and second-order statistics together with individual contributions to the budget equations of the temperature variance and turbulent heat fluxes is hosted in the open access repository KITopen (DOI:https://doi.org/10.5445/IR/1000096346).

Large-eddy simulation of turbulent flow over a parametric set of bumps

Turbulent flow over a series of increasingly high, two-dimensional bumps is studied by well-resolved large-eddy simulation. The mean flow and Reynolds stresses for the lowest bump are in good agreement with experimental data. The flow encounters a favourable pressure gradient over the windward side of the bump, but does not relaminarize, as is evident from near-wall fluctuations. A patch of high turbulent kinetic energy forms in the lee of the bump and extends into the wake. It originates near the surface, before flow separation, and has a significant influence on flow development. The highest bumps create a small separation bubble, whereas flow over the lowest bump does not separate. The log law is absent over the entire bump, evidencing strong disequilibrium. This dataset was created for data-driven modelling. An optimization method is used to extract fields of variables that are used in turbulence closure models. From this, it is shown how these models fail to correctly predict the behaviour of these variables near to the surface. The discrepancies extend further away from the wall in the adverse pressure gradient and recovery regions than in the favourable pressure gradient region.

Qualitative assessment of the bi-stable states in the wake of a finite-width double backward facing step

The flow past a simplified frigate shape model which is analogous to a finite-width double backward facing step is investigated numerically using well-resolved large eddy simulations at Re≃8×104. The geometric configuration of this model permits the occurrence of bi-stable flow states, with an asymmetrical flow topology being observed in the lateral midplane behind each step. In each flow state, the flow at the top step is anti-symmetrical to that observed on the bottom step, and the two flow states are anti-symmetrical to each other. Furthermore, incorporating a base cavity on the top step leads to the suppression of the asymmetrical flow topology on both the steps. The recirculation bubble formed by the downwash at each step is elongated when the base cavity is used, as compared to that observed in either of the two flow states, resulting in a decrease of the drag coefficient. In each of the two flow states, the unequal strength of the streamwise vortices close to the lateral edges on the top step has been identified as the likely cause of the asymmetrical flow on the bottom step.

Quantification of amplitude modulation in wall-bounded turbulence

Many recent investigations on the scale interactions in wall-bounded turbulent flows focus on describing so-called amplitude modulation, the phenomenon that deals with the influence of large scales in the outer region on the amplitude of the small-scale fluctuations in the near-wall region. The present study revisits this phenomenon regarding two aspects, namely the method for decomposing the scales and the quantification of the modulation. First, the paper presents a summary of the literature that has dealt with either or both aspects. Second, for decomposing the scales, different spectral filters (temporal, spatial or both) and empirical mode decomposition (EMD) are evaluated and compared. The common data set is a well-resolved large-eddy simulation that offers a wide range of Reynolds numbers spanning Reθ = 880–8200. The quantification of the amplitude modulation is discussed for the resulting scale components. Particular focus is given to evaluate the efficacy of the various filters to separate scales for the range of Reynolds numbers of interest. Different to previous studies, the different methods have been evaluated using the same data set, thereby allowing a fair comparison between the various approaches. It is observed that using a spectral filter in the spanwise direction is an effective approach to separate the small and large scales in the flow, even at comparably low Reynolds numbers, whereas filtering in time should be approached with caution in the low-to-moderate Re range. Additionally, using filters in both spanwise and time directions, which would separate both wide and long-living structures from the small and fast scales, gives a cleaner image for the small-scales although the contribution to the scales interaction from that filter implementation has been found negligible. Applying EMD to decompose the scales gives similar results to Fourier filters for the energy content of the scales and thereby for the quantification of the amplitude modulation using the decomposed scales. No direct advantage of EMD over classical Fourier filters could be seen. Potential issues regarding different decomposition methods and different definitions of the amplitude modulation are also discussed.

LARGE-EDDY SIMULATION OF OSCILLATORY FLOW, SEDIMENT TRANSPORT AND MORPHODYNAMICS OVER RIPPLES

In the present study, a well-resolved large-eddy simulation was coupled to a morphodynamical model in order to study the sediment dynamics induced by an oscillatory flow over a sandy bed, as well as the creation/evolution of ripples under hydrodynamic forcing. The simulations were based on the numerical solution of the Navier-Stokes equations for the flow, empirical formulas for the bed load, and the advection-diffusion equation for the suspended sediment. The evolution of the bed form was obtained by the numerical solution of the conservation of sediment mass equation. The Immersed Boundary method was implemented for the imposition of fluid and sediment boundary conditions on the moving bed surface. The model was effectively validated against laboratory measurements. Results are presented for ripple creation and propagation from a quasi-flat bed, as well as results of ripples adapting to water conditions.

Turbulent flow through a high aspect ratio cooling duct with asymmetric wall heating

We present well-resolved large-eddy simulations of turbulent flow through a straight, high aspect ratio cooling duct operated with water at a bulk Reynolds number of $Re_{b}=110\times 10^{3}$ and an average Nusselt number of $Nu_{xz}=371$. The geometry and boundary conditions follow an experimental reference case and good agreement with the experimental results is achieved. The current investigation focuses on the influence of asymmetric wall heating on the duct flow field, specifically on the interaction of turbulence-induced secondary flow and turbulent heat transfer, and the associated spatial development of the thermal boundary layer and the inferred viscosity variation. The viscosity reduction towards the heated wall causes a decrease in turbulent mixing, turbulent length scales and turbulence anisotropy as well as a weakening of turbulent ejections. Overall, the secondary flow strength becomes increasingly less intense along the length of the spatially resolved heated duct as compared to an adiabatic duct. Furthermore, we show that the assumption of a constant turbulent Prandtl number is invalid for turbulent heat transfer in an asymmetrically heated duct.

An LES Investigation of the Near-Wake Flow Topology of a Simplified Heavy Vehicle

Recent experimental investigations by McArthur et al. (J. Fluids Struct. 66, 293–314, 2016) in the wake of a simplified heavy vehicle or commonly known as the ground transportation system (GTS) model has shown that the flow topology is invariant over a large range of Reynolds numbers [2.7 × 104 − 2 × 106]. Numerical simulations are performed to investigate the initial flow topology at a Reynolds number of 2.7 × 104, using well-resolved large eddy simulations (LES). In the vertical midplane behind the GTS, a flow state which is anti-symmetric to that reported in McArthur et al. (J. Fluids Struct. 66, 293–314, 2016) is observed here, thereby, confirming the possibility of occurrence of the complementary bi-stable flow state. The occurrence of this bi-stable state does not depend on the ground clearance between the GTS and the ground plane, as a similar flow topology is observed at both small and large gap heights. Furthermore, the flow topology in the vertical midplane is also found to be insensitive to the incoming flow for small yaw angles. However, complex flow behaviour is observed in the wake for larger yaw angles, where the flow topology in the vertical midplane becomes nearly symmetric, while an asymmetric flow topology is now observed in the lateral midplane in the near wake. Furthermore, the corner vortices which originate from either side at the front of the model merge in the far wake, leading to a large vortex structure nearly equal to the height of the model. The near-wake topology of the GTS is analysed and compared with previous studies for a range of scenarios, and the forces on the GTS are computed.

LES grid resolution requirements for the modelling of gravity currents

The influence of the grid resolution on the large eddy simulation (LES) of a lock-exchange turbidity current is investigated. The simulations are performed using a finite volume Boussinesq code with a Smagorinsky turbulence model for a range of buoyancy Reynolds numbers, ranging from transitional currents (Reb=1,000) to fully-developed turbulence (Reb=60,000). The general features of the flow and the relative independence of the current front for Reb>10,000 are correctly predicted. In agreement with previous research, the spanwise two-point correlations are found to be the most useful quantities to assess the mesh resolution. In addition, velocity power spectrum densities are used to provide information on the maximum cell size required to ensure the LES filter cutoff wavelength is inside the inertial range of the turbulence spectra. We show that at low Reynolds numbers, the turbulence model is too restrictive and direct resolution (DNS) is preferable. For 10,000<Reb<60,000, the combination of the different criteria lead to a minimum resolution of 1140 × 37 × 74 cells for coarse LES, and 1925 × 62 × 125 cells for well-resolved LES, regardless of the Reynolds number. Finally, recommendations are made on how to achieve a well-resolved LES based on examination of the vertical profiles of the ratio of SGS viscosity to molecular viscosity, and of the SGS shear-stress to the resolved Reynolds stress.

Turbulent boundary layers around wing sections up to [formula omitted

Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Rec=100,000 to 1,000,000, all of them with 5° angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressure-gradient parameter β). Comparisons of the wing profiles with zero-pressure-gradient (ZPG) data at matched friction Reynolds numbers reveal that, for approximately the same β distribution, the lower-Reynolds-number boundary layers are more sensitive to pressure-gradient effects. This is reflected in the values of the inner-scaled edge velocity Ue+, the shape factor H, the components of the Reynolds-stress tensor in the outer region and the outer-region production of turbulent kinetic energy. This conclusion is supported by the larger wall-normal velocities and outer-scaled fluctuations observed in the lower-Rec cases. Thus, our results suggest that two complementing mechanisms contribute to the development of the outer region in TBLs and the formation of large-scale energetic structures: one mechanism associated with the increase in Reynolds number, and another one connected to the APG. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and increasing Reynolds number.

Large Eddy Simulations of Electromagnetic Braking Effects on Argon Bubble Transport and Capture in a Steel Continuous Casting Mold

In continuous casting of steel, argon gas is often injected to prevent clogging of the nozzle, but the bubbles affect the flow pattern, and may become entrapped to form defects in the final product. Further, an electromagnetic field is frequently applied to induce a braking effect on the flow field and modify the inclusion transport. In this study, a previously validated GPU-based in-house code CUFLOW is used to investigate the effect of electromagnetic braking on turbulent flow, bubble transport, and capture. Well-resolved large eddy simulations are combined with two-way coupled Lagrangian computations of the bubbles. The drag coefficient on the bubbles is modified to account for the effects of the magnetic field. The distribution of the argon bubbles, capture, and escape rates, are presented and compared with and without the magnetic field. The bubble capture patterns are also compared with results of a previous RANS model as well as with plant measurements.

Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A

We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component subcritical two-phase states via a homogeneous mixture approach. Well-resolved LES results for the Spray A benchmark case of the Engine Combustion Network (ECN) and three additional operating conditions are found to agree very well with available experimental data. We also address well-known numerical challenges of trans- and supercritical fluid mixing and compare a fully conservative formulation to a quasi-conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi-conservative formulation on typical LES grids.

Large-eddy simulations of heat transfer in asymmetric rib-roughened ducts: Effects of rotation

We report on large-eddy simulations (LES) of the effects of system rotation on heat transfer in a fully-developed flow in an asymmetrically-ribbed rectangular duct at Re=DhU0ν=15000 where Dh is the hydraulic diameter and U0 the bulk flow velocity. The bottom duct wall, ribbed by flow-normal, equally-distanced square-sectioned ribs, was uniformly heated (except for the ribs) with an imposed constant heat flux. The duct was rotated with a spanwise angular velocity Ω corresponding to two rotation number Ro=ΩDhU0=±0.3, destabilising and stabilising respectively the ribbed-wall adjacent flow. The computational method and the treatment of heat transfer were verified and validated in prior simulations of generic well-documented reference configurations, rotating plane channel and non-ribbed duct flows. The well-resolved LES gave some new insight into the rotation effects on flow and heat transfer, providing information that are not easily accessible to experiments. An attempt is made to identify and distinguish the physical mechanisms of heat transfer enhancement and suppression by system rotation, rib-induced modifications of secondary motion, and the direct effects on the turbulence statistics, especially on the budgets of the turbulent kinetic energy, temperature variance and turbulent heat flux components.

Influence of a Large-Eddy-Breakup-Device on the Turbulent Interface of Boundary Layers

The effects of implementing a large-eddy break-up device (LEBU) in a turbulent boundary layer on the interaction with the boundary layer is investigated with particular emphasis on the turbulent/non-turbulent interface (TNTI). The simulation data is taken from a recent well-resolved large eddy simulation (Chin et al. Flow Turb. Combust. 98, 445–460 2017), where the LEBU was implemented at a wall-normal distance of 0.8 δ (local boundary layer thickness) from the wall. A comparison of the TNTI statistics is performed between a zero-pressure-gradient boundary layer with and without the LEBU. The LEBU is found to delay the growth of the turbulent boundary layer and also attenuates the fluctuations of the TNTI. The LEBU appears to alter the structure size at the interface, resulting in a narrower and shorter dominant structure (in an average sense). Further analysis beneath the TNTI using two-point correlations shows that the LEBU affects the turbulent structures in excess of 100 δ downstream of the LEBU.

LARGE-EDDY SIMULATION OF OSCILLATORY FLOW AND MORPHODYNAMICS OVER RIPPLES

The objective of the present study was to study the morphodynamical development of ripples in a movable bed. The methodology is based on the coupling of fluid flow, sediment transport and morphodynamics. A well-resolved large-eddy simulation (LES) is employed for the simulation of the three-dimensional turbulent oscillatory flow and the corresponding bed and suspended sediment transport over a rippled bed. The evolution of the bed form is obtained by the numerical solution of the Exner equation based on the spanwise-mean flow and sediment transport conditions. The Immersed Boundary method is implemented for the imposition of fluid and sediment boundary conditions on the moving bed surface. Results are presented for ripple creation and propagation from a quasi-flat bed, as well as results of initially sinusoidal ripples adapting to water conditions, based on the mobility number, ψ. The numerical model demonstrates phenomena of ripple creation, propagation and migration, resulting in ripple lengths in agreement with those predicted by empirical equations. It was shown that under the same hydrodynamic forcing, the bed tends to reach the same equilibrium state, regardless of the initial bed form.