Large eddy simulation of turbulent horizontal buoyant jets

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10^?4, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.     

Evolution of an asymmetric turbulent shear layer in a thermocline

Large eddy simulations are used to examine the evolution of a shear layer in a thermocline with non-uniform density stratification. Unlike previous studies, the density in the present study is continuously stratified and has stratification in the upper half different from the lower half of the shear layer. The stratification in the upper half is fixed at J_u = 0.05, while the stratification in the lower half is increased to J_d = 0.05, 0.15, 0.25 and 0.35, leading to a progressively stronger asymmetry of the Ri_g profile in the four cases. Here, J is the bulk Richardson number and Ri_g is the gradient Richardson number. The type of shear instability and the properties of the ensuing turbulence are found to depend strongly on the degree of asymmetry in stratification. The shear instability changes from a Kelvin–Helmholtz (KH) mode at J_d = 0.05 to a Holmboe (H) mode at J_d = 0.35 and exhibits characteristics of both KH and H modes at intermediate values of J_d. Differences in the evolution among the cases are quantified using density visualisations and statistics such as mean shear, mean stratification and turbulent kinetic energy.     

Subgrid-scale dynamics and model test in a turbulent stratified jet with coexistence of stable and unstable stratification

The subgrid-scale dynamics of stratified flows is studied in a horizontally introduced turbulent jet with coexistence of stable and unstable stratification of a low Richardson number case and a high Richardson number case. The positive production of subgrid-scale kinetic energy and the production of scalar variance suggest the forward energy cascade. The subgrid-scale buoyant destruction plays a role as a sink of subgrid-scale kinetic energy in the stable stratification while holds a role of turbulent generation in the unstable stratification. The role-switch of buoyant destruction in the stable stratification of high-Ri case implies the occurrence of a destabilising process triggered by the coupled instability mechanisms. The energy balance assumption related to the production of and the dissipation of subgrid-scale kinetic energy as well as the subgrid-scale buoyant destruction may fail. The a-priori test suggests the scale-invariant dynamic and standard Smagorinsky models not to work properly here, while the scale-dependent dynamic model gives a decent performance but with restrictions of the ratio between two testing filter scales.     

On the relationship between the gradient and the bulk Richardson number for the atmospheric surface layer

Summary Semi-empirical formulations which have been proposed to describe the wind and potential temperature profiles are used to derive relationships between the gradient Richardson number, Ri, the finite-difference layer Richardson number, Ri_b, the surface layer Richardson number, Ri_s, and the bulk Richardson number,B, through the atmospheric surface layer. The theoretical analysis for stable conditions indicates that Ri (z ₃)=Ri_b, wherez ₃=(z ₂−z ₁)/ln(z ₂/z ₁), andz ₂;z ₁=upper and lower levels at which temperature and wind speed are specified. It is also found that, during stable conditions, the wind profile power law exponent,p, is computed at the heightz ₃, instead of the widely used geometric mean height,z _m, between top (z ₂) and bottom (z ₁) of the layer considered.     

Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid

Mixed convection flow of Cu–water nanofluid inside a lid-driven square cavity with adiabatic horizontal walls and sinusoidal heating on sidewalls has been investigated numerically. The effects of increase in shear force for a fixed buoyancy force and effects of increase in buoyancy force for a fixed shear force were investigated. Effects of variations of Richardson number, phase deviation of sinusoidal heating, and volume fraction of nanoparticles on flow and temperature field were studied. The obtained results showed that for a constant Grashof number at all Richardson numbers, a clockwise eddy was developed inside the cavity, also the rate of heat transfer increases with decrease in Richardson number and increase of volume fraction of nanoparticles. For a constant Reynolds number the clockwise eddy is observed up to Ri = 1. For Ri = 10 a multicellular flow pattern is formed inside the cavity. Moreover it was found that when the Reynolds number is kept constant, the rate of heat transfer increases with increase in Richardson number.     

Lock-exchange flows in inclined pipes: the relevance of the Prandtl mixing length model

We examine the applicability of the Prandtl mixing length model to transverse momentum and mass flux in strongly confined, stably stratified turbulent shear flows. These fluxes were measured in the vertical diametral plane of lock-exchange flows in an inclined pipe by the simultaneous use of planar laser-induced fluorescence and particle image velocimetry at local Reynolds numbers ranging from Re = 580 to 1770 and Richardson numbers ranging from Ri = 0.26 and 1.6. Measurements indicate that the eddy diffusivities of mass and momentum are symmetric about the pipe axis, with their maximum at the axis. The corresponding Prandtl mixing lengths decrease with increasing distance from the pipe axis within the central 60% of the pipe cross-section. Within the range of experimental conditions, the mixing lengths at the axis increase linearly with Ri so that the corresponding turbulent Prandtl number Pr_t decreases with Ri. In contrast, Pr_t and the mixing lengths do not display a systematic dependence on Re. Comparison with unbounded and semi-bound shear flows suggests that the strong confinement imposed by the pipe wall may be constraining the integral length scale and Prandtl mixing lengths.     

Conditional statistics of inert droplet effects on turbulent combustion in reacting mixing layers

Direct numerical simulation (DNS) of turbulent reacting mixing layers laden with evaporating inert droplets is used to assess the droplet effects in the context of the conditional moment closure (CMC) for multiphase turbulent combustion. The temporally developing mixing layer has an initial Reynolds number of 1000 based on the vorticity thickness with more than 16 million Lagrangian droplets traced. An equivalent mixture fraction incorporating the inert vapour mass fractions clearly demonstrates the effects of vapour dilution on the mixture. Instantaneous fields and conditional statistics, such as the singly conditioned scalar dissipation rate, the gas temperature 〈 T _g|η 〉, conditional variance of the gas temperature 〈 T _g ^”2|η 〉 and conditional covariance between the fuel mass fraction and gas temperature 〈 Y _f ^” T _g ^”|η 〉 show considerable droplet effects. Comparison between the droplet-free and droplet-laden reacting mixing layer cases suggests significant extinction in the latter case. The resulting large conditional fluctuations around the conditional means contradict the basic assumption behind the first-order singly conditioned CMC. More sophisticated CMC approaches, such as doubly conditioned or second-order CMCs are, in principle, better able to incorporate the effects of evaporating droplets, but significant modelling challenges exist. The scalar dissipation rate doubly conditioned on the mixture fraction and a normalized gas temperature 〈 χ | η, ζ 〉 exemplifies the modelling complexity in the CMC of multiphase combustion.     

On the theoretical relationship between the Monin-Obukhov stability parameter and the bulk Richardson number

Summary Nomograms were constructed to determine relations among different stability parameters in the surface layer. The variables interrelated were the Monin-Obukhov stability parameter, ξ=z/L, the bulk Richardson number, Ri_b, and the PasquillA-F stability classes. Also, the nomograms were used to estimate the Monin-Obukhov length variation, with respect to changes in surface roughness and atmospheric stability.     

On the analytical solutions of unstable surface layer similarity equations

Summary An approximate relationship between the gradient, Ri, and the bulk Richardson number, Ri_b, for unstable atmospheric conditions, is suggested. The proposed relation shows much better agreement with the estimation provided by a numerical iterative method than the usual approximations suggested by Louis and Byun.     

Three-dimensional vortex visualization in stratified spin-up

Abstract  

We present the results of three-dimensional time-dependent numerical simulations of incremental spin-up of a thermally stratified fluid. The fluid inside a vertical cylindrical container of radius R and height 2H is water characterized by the kinematic viscosity ν and thermal diffusivity κ. Initially, its density (temperature) varies linearly with height and is characterized by a constant buoyancy frequency N, which is proportional to the density gradient. The system undergoes an abrupt change in the rotation rate from its initial value Ω_i, when the fluid is in a solid-body rotation state, to the final value Ω_f. The aim of this contribution is to show the formation of columnar vortices in a high Rossby number spin-up flow.     

Density and velocity statistics in variable density turbulent mixing

We experimentally study variable–density mixing of miscible gases in an open-circuit wind tunnel using simultaneous particle image velocimetry and planar laser-induced fluorescence. Experiments of a high Atwood number (0.6) and low Atwood number (0.1) are performed to compare non-Boussinesq cases with the Boussinesq limit. The higher density gas is injected into the wind tunnel co-flow using a round jet configuration, and near-field and far-field measurements are performed to examine mixing in both momentum and buoyancy-dominated regimes. The effects of buoyancy are measurable and important in both large-scale mixing features and in turbulence quantities. The low Atwood number PDFs (probability density functions) show fast and uniform mixing. The high Atwood number PDFs of density have skewness towards the larger densities, indicating less mixing of the heavy fluid due to its inertia. The skewness in the density gradient PDFs at high Atwood number displays strong density local variations that can enhance mixing at molecular scales. Turbulent kinetic energy decreases with streamwise distance from the jet for low Atwood number but increases for high Atwood number due to larger buoyancy and density-driven shear. Over 3000 experimental realisations are used to calculate statistical characteristics of the mixing, including valuable and rarely given data such as Favre-averaged turbulent quantities: mass flux velocity, Reynolds stress, turbulent kinetic energy, and density-specific volume correlation. Buoyancy effects are observed in these quantities and the trends are compared qualitatively with direct numerical simulations.     

Aspect ratio effects in turbulent duct flows studied through direct numerical simulation

Three-dimensional effects in turbulent duct flows, i.e., sidewall boundary layers and secondary motions, are studied by means of direct numerical simulation (DNS). The spectral element code Nek5000 is used to compute turbulent duct flows with aspect ratios 1–7 (at Re_{b, c} = 2800, Re_{τ, c} ? 180) and aspect ratio 1 (at Re_{b, c} = 5600, Re_{τ, c} ? 330), in streamwise-periodic boxes of length 25h. The total number of grid points ranges from 28 to 145 million, and the pressure gradient is adjusted iteratively in order to keep the same bulk Reynolds number in the centreplane with changing aspect ratio. Turbulence is initiated via a trip forcing active during the initial stages of the simulation, and the statistical convergence of the data is discussed both in terms of transient approach and averaging period. Spanwise variations in wall shear, mean-flow profiles, and turbulence statistics are analysed as a function of aspect ratio, and also compared with the spanwise-periodic channel (as idealisation of an infinite aspect ratio duct). The computations show good agreement with experimental measurements carried out in parallel at the Illinois Institute of Technology (IIT) in Chicago, and highlight the relevance of sidewall boundary layers and secondary vortices in the physics of the duct flow. The rich array of secondary vortices extending throughout the upper and lower walls of the duct, and their dependence on Reynolds number and aspect ratio, had not been reported in the literature before.     

Large-eddy simulations of temporally accelerating turbulent channel flow

The unsteady turbulent channel flow subject to the temporal acceleration is considered in this study. Large-eddy simulations were performed to study the response of the turbulent flow to the temporal acceleration. The simulations were started with the fully developed turbulent channel flow at an initial Reynolds number of Re₀ = 3500 (based on the channel half-height and the bulk-mean velocity), and then a constant temporal acceleration was applied. During the acceleration, the Reynolds number of the channel flow increased linearly from the initial Reynolds number to the final Reynolds number of Re₁ = 22,600. The effect of grid resolution, domain size, time step size on the simulation results was assessed in a preliminary study using simulations of the accelerating turbulent flow as well as simulations of the steady turbulent channel flow at various Reynolds numbers. Simulation parameters were carefully chosen from the preliminary study to ascertain the accuracy of the simulation. From the accelerating turbulent flow simulations, the delays in the response of various flow properties to the temporal acceleration were measured. The distinctive features of the delays responsible for turbulence production, energy redistribution, and radial propagation were identified. Detailed turbulence statistics including the wall shear stress response during the acceleration were examined. The results reveal the changes in the near-wall structures during the acceleration. A self-sustaining mechanism of turbulence is proposed to explain the response of the turbulent flow to the temporal acceleration. Although the overall flow characteristics are similar between the channel and pipe flows, some differences were observed between the two flows.     

Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

An Effective Field Theory Approach to f 0(980)–a 0(980) Mixing

We consider the problem of mixing in the f ₀(980)–a ₀(980) system when width effects are taken into account. By explicit calculation we show that two mixing angles are necessary to describe the phenomenon.     

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u_∞ / v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.     

FRICTIONAL FLOW CHARACTERISTICS OF WATER FLOWING THROUGH RECTANGULAR MICROCHANNELS

Experiments were conducted to investigate the flow characteristics of water flowing through rectangular microchannels having hydraulic diameters of 0.133-0.367 mm and H/W ratios of 0.333-1. Experimental results indicated that the laminar flow transition occurred at Reynolds numbers of 200-700. This critical Re for the laminar transition was strongly affected by the hydraulic diameter, decreasing with corresponding decreases in the microchannel. In addition, the size of the transition range was diminished and fully developed turbulent flow also occurred at much lower Re. The friction behavior of both the laminar and turbulent flow was found to depart from the classical thermqfluid correlations. lite friction factor, f, was found to be proportional to Re^?1.98 rather than Re for the laminar condition, and proportional to Re^?1.72i for turbulent flow. The geometric parameters, hydraulic diameter, and H/W were found to be the most important parameters and had a critical effect on the flow. Generally, increasing the ratio H/W increases the friction factor. The reduction of the microchannel hydraulic radius decreases the friction factor significantly for a given H/W. There exists a special range of ratio H/W (approximately 0.5 mm) at which the experimental data are lower than the predictions obtained from classical correlations. Continued reduction of channel size increases the difference between f_I,expf_1,theo at RE_cri, and the quantity of f_I,exp becomes smaller within the region adjacent to H/W = 0.5, and larger when H /Wis out of this region.     

Effective eddy viscosity in stratified turbulence

This paper investigates the effective eddy viscosity inferred from direct numerical simulations of decaying stratified and non-stratified turbulence. It is shown that stratification affects the horizontal eddy viscosity dramatically, by increasing non-local energy transfer between large and small horizontal scales. This non-local horizontal energy transfer is around 20% of the local horizontal energy transfer at the cutoff wavenumber k_c = 40. The non-local horizontal energy transfer occurs at large vertical wavenumbers, which may be larger than the buoyancy wavenumber k_b = N/u_rms, where N is the buoyancy frequency and u_rms is the root-mean-square velocity. By increasing the value of the test cutoff wavenumber k_c from large scales to the dissipation range, the non-local horizontal eddy viscosity decreases and the local eddy viscosity is dominant. Overall, the presence of stratification can significantly change the features of subgrid-scale (SGS) motions. Current SGS models should, therefore, be modified for use in large-eddy simulation of stratified turbulence.     

A quark model study of semileptonic baryon decays in the electronic decay modes

A relativistic quark model based on Dirac equation with the independent-quark confining potential of the form (1 +γ ⁰)[a ln(r/b)] is used to compute the weak electric and magnetic form factors for semileptonic baryonic decays in the electronic decay modes. The values obtained for (g ₂/g ₁) agree with the non relativistic results and those for (f ₂/f ₁) agree with the MIT bag model values of Donoghue and Holstein. The SU(3) symmetry breaking does not generate appreciable departures in (f ₂/f ₁) values from corresponding Cabibbo values.