Assessment of Five SGS Models for Low-Rem MHD Turbulence

Assessment of three regularization-based and two eddy-viscosity-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are carried out in the context of magnetohydrodynamic (MHD) decaying homogeneous turbulence (DHT) with a Taylor scale Reynolds number (Re_λ) of 120 and a MHD transition-to-turbulence Taylor-Green vortex (TGV) problems with a Reynolds number of 3000, through direct comparisons to direct numerical simulations (DNS). Simulations are conducted using the low-magnetic Reynolds number approximation (Re_m<<1). LES predictions using the regularization-based Leray- α,LANS- α, and Clark- α SGS models, along with the eddy viscosity-based non-dynamic Smagorinsky and the dynamic Smagorinsky models are compared to in-house DNS for DHT and previous results for TGV. With regard to the regularization models, this work represents their first application to MHD turbulence. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields made between the varying magnetic field cases demonstrated that the regularization models performed poorly compared to the eddy-viscosity models for all MHD cases, but the comparisons improved with increase in magnitude of magnetic field, due to a decrease in the population of SGS eddies within the flow field.     

Effects of Lewis Number on Head on Quenching of Turbulent Premixed Flames: A Direct Numerical Simulation Analysis

The head on quenching of statistically planar turbulent premixed flames by an isothermal inert wall has been analysed using three-dimensional Direct Numerical Simulation (DNS) data for different values of global Lewis number Le(0.8, 1.0 and 1.2) and turbulent Reynolds number Re_t. The statistics of head on quenching have been analysed in terms of the wall Peclet number Pe (i.e. distance of the flame from the wall normalised by the Zel’dovich flame thickness) and the normalised wall heat flux Φ. It has been found that the maximum (minimum) value of Φ(Pe) for the turbulent Le=0.8 cases are greater (smaller) than the corresponding laminar value, whereas both Pe and Φ in turbulent cases remain comparable to the corresponding laminar values for Le=1.0 and 1.2. Detailed physical explanations are provided for the observed Le dependences of Pe and Φ. The existing closure of mean reaction rate \(\overline {\dot {\omega }}\) using the scalar dissipation rate (SDR) in the near wall region has been assessed based on a-priori analysis of DNS data and modifications to the existing closures of mean reaction rate and SDR have been suggested to account for the wall effects in such a manner that the modified closures perform well both near to and away from the wall.     

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured,Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re =?5000, the turbulent channel flow at Re_τ =?587, the circular cylinder in cross-flow at Re_D =?3900, the square cylinder in cross-flow at Re_D =?22400 and the channel with periodic constrictions at Re_h =?10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.     

Study of the Spectral Difference Numerical Dissipation for Turbulent Flows Using Unstructured Grids

In this paper, the numerical dissipation properties of the Spectral Difference (SD) method are studied in the context of vortex dominated flows and wall-bounded turbulence, using uniform and distorted grids. First, the validity of using the SD numerical dissipation as the only source of subgrid dissipation (the so-called Implicit-LES approach) is assessed on regular grids using various polynomial degrees (namely, p = 3, p = 4, p = 5) for the Taylor-Green vortex flow configuration at R e = 5 000. It is shown that the levels of numerical dissipation greatly depend on the order of accuracy chosen and, in turn, lead to an incorrect estimation of the viscous dissipation levels. The influence of grid distortion on the numerical dissipation is then assessed in the context of finite Reynolds number freely-decaying and wall-bounded turbulence. Tests involving different amplitudes of distortion show that highly skewed grids lead to the presence of small-scale, noisy structures, emphasizing the need of explicit subgrid modeling or regularization procedures when considering coarse, high-order SD computations on unstructured grids. Under-resolved, high-order computations of the turbulent channel flow at R e _τ = 1000 using highly-skewed grids are considered as well and present a qualitatively similar agreement to results obtained on a regular grid.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer

This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e _?? = 1000 based on the momentum thickness or R e _τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.     

Kovasznay Mode Decomposition of Velocity-Temperature Correlation in Canonical Shock-Turbulence Interaction

The correlation coefficient R_uT between the streamwise velocity and temperature is investigated for the case of canonical shock-turbulence interaction, motivated by the fact that this correlation is an important component in compressible turbulence models. The variation of R_uT with the Mach number, the turbulent Mach number, and the Reynolds number is predicted using linear inviscid theory and compared to data from DNS. The contributions from the individual Kovasznay modes are quantified. At low Mach numbers, the peak post-shock R_uT is determined by the acoustic mode, which is correctly predicted by the linear theory. At high Mach numbers, it is determined primarily by the vorticity and entropy modes, which are strongly affected by nonlinear and viscous effects, and thus less well predicted by the linear theory.     

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating

In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90 ^° pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (R e _d =32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of ΔT=50 K and ΔT=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10^°. Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward.     

Turbulent Drag Reduction by a Near Wall Surface Tension Active Interface

In this work we study the turbulence modulation in a viscosity-stratified two-phase flow using Direct Numerical Simulation (DNS) of turbulence and the Phase Field Method (PFM) to simulate the interfacial phenomena. Specifically we consider the case of two immiscible fluid layers driven in a closed rectangular channel by an imposed mean pressure gradient. The present problem, which may mimic the behaviour of an oil flowing under a thin layer of different oil, thickness ratio h₂/h₁ =?9, is described by three main flow parameters: the shear Reynolds number Re _τ (which quantifies the importance of inertia compared to viscous effects), the Weber number We (which quantifies surface tension effects) and the viscosity ratio λ = ν₁/ν₂ between the two fluids. For this first study, the density ratio of the two fluid layers is the same (ρ₂ = ρ₁), we keep Re _τ and We constant, but we consider three different values for the viscosity ratio: λ =?1, λ =?0.875 and λ =?0.75. Compared to a single phase flow at the same shear Reynolds number (Re _τ =?100), in the two phase flow case we observe a decrease of the wall-shear stress and a strong turbulence modulation in particular in the proximity of the interface. Interestingly, we observe that the modulation of turbulence by the liquid-liquid interface extends up to the top wall (i.e. the closest to the interface) and produces local shear stress inversions and flow recirculation regions. The observed results depend primarily on the interface deformability and on the viscosity ratio between the two fluids (λ).     

Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

A scale-similarity model of a two-point two-time Lagrangian velocity correlation(LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows(HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80, 066313(2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity V. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values(R_λ = 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity.Moreover, the dispersion velocity V normalized by the Kolmogorov velocity V_η≡η/τ_η in which η and τ_η are the Kolmogorov space and time scales, respectively, scales with the Reynolds number R_λ as V/V_η∝ R_λ~(1.39) obtained from the numerical data.     

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section

A direct numerical simulation database of the flow around a NACA4412 wing section at R e _c = 400,000 and 5^° angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117–128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter β ranges from ? 0 and 85 on the suction side, and from 0 to ? 0.25 on the pressure side of the wing. The maximum R e _?? and R e _τ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at β values of around 4 for λ _z ? 0.65δ ₉₉, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher R e _?? . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.     

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU _w ≡ 2U _w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity u _τ , and h is the half-height of the channel. This leads to a one-parameter family of one-dimensional flows of varying Reynolds number Re ≡ U _w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of two each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend’s hypothesis of universal behavior for the velocity and shear stress, when they are normalized with u _τ and h; on the other hand universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford’s conjectures, suggesting that at least in this idealized flow turbulence theory is successful like it was for the classical logarithmic law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, that again does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.     

Numerical Simulation of Two Phase Turbulent Flow of Nanofluids in Confined Slot Impinging Jet

In this article, a numerical investigation is performed on flow and heat transfer of confined impinging slot jet, with a mixture of water and Al₂O₃ nanoparticles as the working fluid. Two-dimensional turbulent flow is considered and a constant temperature is applied on the impingement surface. The k ? ω turbulence model is used for the turbulence computations. Two-phase mixture model is implemented to study such a flow field. The governing equations are solved using the finite volume method. In order to consider the effect of obstacle angle on temperature fields in the channel, the numerical simulations were performed for different obstacle angles of 0° ? 60°. Also different geometrical parameters, volume fractions and Reynolds numbers have been considered to study the behavior of the system in terms of stagnation point, average and local Nusselt number and stream function contours. The results showed that the intensity and size of the vortex structures depend on jet- impingement surface distance ratio (H/W) and volume fraction. The maximum Nusselt number occurs at the stagnation point with the highest values at about H/W = 1. Increasing obstacle angle, from 15° to 60°, enhances the heat transfer rate. It was also revealed that the minimum value of average Nusselt number occurs in higher H/W ratios with decreasing the channel length.     

Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer

A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of R e _θ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for \(\lambda _{z}^{+} > 1000\) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.     

Mixing and Bimolecular Reaction Kinetics in a Plane Poisseulle Flow

Mixing and a nonlinear bimolecular chemical reaction (reactant A + reactant B → product; reaction rate r?=?κc ₁ c ₂) in laminar shear flow are investigated. It is found that asymptotically the dominant balance between the rates of production and dissipation of the mean-squared concentration fluctuations \((\sigma_{c_1 }^2 ,\sigma_{c_2 }^2)\) and cross-covariance of concentration fluctuations \((\overline {c_1 c_2 })\) occurs under nonreactive and reactive conditions. Longitudinal dispersion of the cross-sectional averages (C ₁, C ₂), and variances and the cross-covariance of reactant concentrations can be asymptotically quantified by the classic Taylor dispersion coefficient (D) even under reactive conditions. The characteristic time-scale (τ) over which molecular diffusion dissipates concentration variance and the cross-covariance of reactant concentrations is also shown to be the same under nonreactive and reactive conditions. A variational estimate of τ is shown to be close to the values inferred from detailed numerical simulation. The production-dissipation balance implies that the cross-sectional averaged reaction rate follows \(\overline r =\kappa_{eff} C_1 C_2 \) and \(\kappa _{eff} \approx \kappa \left[ {1+2D\tau \left( {{\partial \ln C_1 } \mathord{\left/ {\vphantom {{\partial \ln C_1 } {\partial x}}} \right. \kern-\nulldelimiterspace} {\partial x}} \right)\left( {{\partial \ln C_2 } \mathord{\left/ {\vphantom {{\partial \ln C_2 } {\partial x}}} \right. \kern-\nulldelimiterspace} {\partial x}} \right)} \right]\). The effective reaction rate parameter (κ _eff ) is higher than that of well-mixed batch test reaction rate constant (κ) for initially overlapping species and κ _eff is smaller than κ for initially non-overlapping species.     

Experimental and Theoretical Sensitivity Analysis of Turbulent Flow Past a Square Cylinder

The Siemens SGT-800 3^rd generation DLE burner fitted to an atmospheric combustion rig has been numerically investigated. Pure methane and methane enriched by 80 vol% hydrogen flames have been considered. A URANS (Unsteady Reynolds Averaged Navier-Stokes) approach was used in this study along with the k ? ω SST and the k ? ω SST-SAS models for the turbulence transport. The chemistry is coupled to the turbulent flow simulations by the use of a laminar flamelet library combined with a presumed PDF. The effect of the mesh density in the mixing and the flame region and the effect of the turbulence model and reaction rate model constant are first investigated for the methane/air flame case. The results from the k ? ω SST-SAS along with flamelet libraries are shown to be in excellent agreement with experimental data, whereas the k ? ω SST model is too dissipative and cannot capture the unsteady motion of the flame. The k ? ω SST-SAS model is used for simulation of the 80 vol% hydrogen enriched flame case without further adjusting the model constants. The global features of the hydrogen enrichment are very well captured in the simulations using the SST-SAS model. With the hydrogen enrichment the time averaged flame front location moves upstream towards the burner exit nozzle. The results are consistent with the experimental observations. The model captures the three dominant low frequency unsteady motion observed in the experiments, indicating that the URANS/LES hybrid model indeed is capable of capturing complex, time dependent, features such as an interaction between a PVC and the flame front.     

Effects of Permeable Cylinder on the Flow Structure in Deep Water

Flow behaviors around permeable cylinders were investigated using Particle Image Velocimetry technique in deep water. The height of deep water and free stream velocity were kept constant as h_w = 340 mm and U = 156 mm/s. To find out the effect of the permeable cylinders on the flow structure, eight different porosities (β = 0.4, 0.5, 0.6, 0.65, 0.7, 0.75, 0.8, and 0.85) were used. The results have indicated that the permeable cylinders are effective on the control of large-scale vortical structures downstream of the permeable cylinder. As the porosity increases, turbulent kinetic energy and Reynolds shear stress decrease. This means that the fluctuations in the wake region are significantly weakened by permeable cylinders. The permeable cylinders having the porosity higher than 0.6 do not pose an obstacle in the flow. Furthermore, for all diameter values of permeable cylinders, it can be concluded that the flow structures downstream of the permeable cylinder show similar trend with each other.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Globally Stoichiometric Stratified Mixtures: a Numerical Investigation

The influences of fuel Lewis number Le_F on localised forced ignition of globally stoichiometric stratified mixtures have been analysed using three-dimensional compressible Direct Numerical Simulations (DNS) for cases with Le_F ranging from 0.8 to 1.2. The globally stoichiometric stratified mixtures with different values of root-mean-square (rms) equivalence ratio fluctuation (i.e. ?^′= 0.2, 0.4 and 0.6) and the Taylor micro-scale l_? of equivalence ratio ? variation (i.e. l_?/l_f= 2.1, 5.5 and 8.3 with l_f being the Zel’dovich flame thickness of the stoichiometric laminar premixed flame) have been considered for different initial rms values of turbulent velocity u^′. A pseudo-spectral method is used to initialise the equivalence ratio variation following a presumed bi-modal distribution for prescribed values of ?^′ and l_?/l_f for global mean equivalence ratio 〈?〉=1.0. The localised ignition is accounted for by a source term in the energy transport equation that deposits energy for a stipulated time interval. It has been observed that the maximum values of temperature and the fuel reaction rate magnitude increase with decreasing Le_F during the period of external energy deposition. The initial values of Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f have been found to have significant effects on the extent of burning of the stratified mixtures following localised ignition. For a given value of u^′/S_b(?=1), the extent of burning decreases with increasing Le_F. An increase in u^′ leads to a monotonic reduction in the burned gas mass for all values of Le_F in all stratified mixture cases but an opposite trend is observed for the Le_F=0.8 homogeneous mixture. It has been found that an increase in ?^′ has adverse effects on the burned gas mass, whereas the effects of l_?/l_f on the extent of burning are non-monotonic and dependent on ?^′ and Le_F. Detailed physical explanations have been provided for the observed Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f dependences.