Multiscale simulations and experiments on water jet atomization

Numerical simulation of primary atomization at high Reynolds number is still a challenging problem. In this work a multiscale approach for the numerical simulation of liquid jet primary atomization is applied, using an Eulerian-Lagrangian coupling. In this approach, an Eulerian volume of fluid (VOF) method, where the Reynolds stresses are closed by a Reynolds stress model is applied to model the global spreading of the liquid jet. The formation of the micro-scale droplets, which are usually smaller than the grid spacing in the computational domain, is modelled by an energy-based sub-grid model. Where the disruptive forces (turbulence and surface pressure) of turbulent eddies near the surface of the jet overcome the capillary forces, droplets are released with the local properties of the corresponding eddies. The dynamics of the generated droplets are modelled using Lagrangian particle tracking (LPT). A numerical coupling between the Eulerian and Lagrangian frames is then established via source terms in conservation equations. As a follow-up study to our investigation in Saeedipour et al. (2016a), the present paper aims at modelling drop formation from liquid jets at high Reynolds numbers in the atomization regime and validating the simulation results against in-house experiments. For this purpose, phase-Doppler anemometry (PDA) was used to measure the droplet size and velocity distributions in sprays produced by water jet breakup at different Reynolds numbers in the atomization regime. The spray properties, such as droplet size spectra, local and global Sauter-mean drop sizes and velocity distributions obtained from the simulations are compared with experiment at various locations with very good agreement.     

Numerical investigation of turbulent-jet primary breakup using one-dimensional turbulence

Primary breakup to form droplets at liquid surfaces is an important fundamental process to study as it determines the initial properties of the dispersed phase, which affect mixing rates, secondary breakup, droplet collisions, and flow separation within the dispersed flow region. Primary breakup can be regarded as one of the least developed model components for simulating and predicting liquid jet breakup. However, it is of paramount importance in many technical applications, e.g. fuel injection in engines and spray painting. This paper presents a numerical investigation of primary breakup of a turbulent liquid jet in still air at standard conditions using the one-dimensional turbulence (ODT) modeling framework. ODT is a stochastic model that simulates turbulent flow evolution along a notional 1D line of sight by applying instantaneous maps to represent the effect of individual turbulent eddies on property profiles. An important feature of ODT is the resolution of all relevant scales, both temporal and spatial. The restriction to one spatial dimension in ODT permits affordable high resolution of interfacial and single-phase property gradients, which is key to capturing the local behavior of the breakup process and allows simulations at high Reynolds and Weber numbers that are currently not accessible to direct numerical simulations (DNS).This paper summarizes our extensions of the ODT model to simulate geometrically simple jet breakup problems, including representations of Rayleigh wave breakup, turbulent breakup, and shear-driven breakup. Each jet breakup simulation consists of a short temporal channel section to initialize a turbulent velocity profile at the nozzle exit followed by an adjacent jet section. The simulations are carried out for jet exit Reynolds number of 11,500, 23,000, 46,000 and 92,000 while the Weber number is varied within the range 10²–10⁷. We present results on breakup statistics including spatial locations of droplet release, droplet sizes and liquid core length. The results on primary breakup are compared to experimental results and models.     

Numerical Simulation of Single-Stream Jets from a Serrated Nozzle

Hybrid large-eddy type simulations for cold jet flows from a serrated nozzle are performed at an acoustic Mach number Ma _ac ?=?0.9 and Re?=?1.03×10⁶. Since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES) or implicit LES (ILES) reminiscent procedure. To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended to the LES making a hybrid RANS-ILES. The geometric complexity of the serrated nozzle is fully considered without simplification or emulation. An improved but still modest hexahedral multi-block grid with circa 20 million grid points (with respect to 12.5 million in Xia et al., Int J Heat Fluid Flow 30:1067–1079, 2009) is used. Despite the modest grid size, encouraging and improved results are obtained. Directly resolved mean and second-order fluctuating quantities along the jet centerline and in the jet shear layer compare favorably with measurements. The radiated far-field sound predicted using the Ffowcs Williams and Hawkings (FW-H) surface integral method shows good agreement with the measurements in directivity and sound spectra.     

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle-plate distances H/D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k-ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k-ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k-ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model.The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle-plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle-plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement.All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle-plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle-plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.     

Development of an efficient statistical volumes of fluid–Lagrangian particle tracking coupling method

The breakup of a liquid jet into irregular liquid structures and droplets leading to the formation of a dilute spray has been simulated numerically. To overcome the shortcomings of certain numerical methods in specific flow regimes, a combined approach has been chosen. The intact liquid core, its primary breakup and the dense spray regime are simulated using the volumes of fluid (VOF) method in combination with LES, whereas the Lagrangian particle tracking (LPT) approach in the LES context is applied to the dilute spray regime and the secondary breakup of droplets. A method has been developed to couple both simulation types on a statistical basis. This statistical coupling approach (SCA) reflects the dominating physical mechanisms of the two‐phase flow in each regime to a high degree. The main benefit of the SCA is computational efficiency as compared with the more straightforward approach where one follows each structure, denoted here as the direct coupling approach. The computational benefits stem from the reduction of computational time since the VOF simulation is run only until statistical convergence and not during the whole spray development. A second benefit using the SCA is the possibility to use the stochastic parcel method in the LPT simulation whereby a large number of droplets may be handled. The coupling approach is applied to the atomization of a fuel jet in a high pressure chamber, demonstrating the gain of efficiency of the SCA as compared with direct coupling approach. Copyright © 2014 The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons Ltd.     

Large eddy simulation of fuel injection and mixing process in a diesel engine

The large eddy simulation(LES) approach implemented in the KIVA-3V code and based on one-equation sub-grid turbulent kinetic energy model are employed for numerical computation of diesel sprays in a constant volume vessel and in a Caterpillar 3400 series diesel engine.Computational results are compared with those obtained by an RANS(RNG k-ε) model as well as with experimental data.The sensitivity of the LES results to mesh resolution is also discussed.The results show that LES generally provides flow and spray characteristics in better agreement with experimental data than RANS;and that small-scale random vortical structures of the in-cylinder turbulent spray field can be captured by LES.Furthermore,the penetrations of fuel droplets and vapors calculated by LES are larger than the RANS result,and the sub-grid turbulent kinetic energy and sub-grid turbulent viscosity provided by the LES model are evidently less than those calculated by the RANS model.Finally,it is found that the initial swirl significantly affects the spray penetration and the distribution of fuel vapor within the combustion chamber.     

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re _n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.     

Determination of the aerodynamic droplet breakup boundaries based on a total force approach

The determination of the critical We_g number separating the different breakup regimes has been extensively studied in several experimental and numerical works, while empirical and semi-analytical approaches have been proposed to relate the critical We_g number with the Oh_l number. Nevertheless, under certain conditions, the Re_g number and the density ratio ε may become important. The present work provides a simple but reliable enough methodology to determine the critical We_g number as a function of the aforementioned parameters in an effort to fill this gap in knowledge. It considers the main forces acting on the droplet (aerodynamic, surface tension and viscous) and provides a general criterion for breakup to occur but also for the transition among the different breakup regimes. In this light, the present work proposes the introduction of a new set of parameters named as We_g,eff and Ca_l monitored in a new breakup plane. This plane provides a direct relation between gas inertia and liquid viscosity forces, while the secondary effects of Re_g number and density ratio have been embedded inside the effective We_g number (We_g,eff)     

Computations of breakup modes in laminar compound liquid jets in a coflowing fluid

We present a numerical investigation of breakup modes of an axisymmetric, laminar compound jet of immiscible fluids, which flows in a coflowing immiscible outer fluid. We use a front-tracking/finite difference method to track the unsteady evolution and breakup of the compound jet, which is governed by the Navier–Stokes equations for incompressible Newtonian fluids. Numerical results show that depending on parameters such as the Reynolds number Re (in the range of 5–30) and Weber Number We (in the range of 0.1–0.7), based on the inner jet radius and inner fluid properties, the compound jet can break up into drops in various modes: inner dripping–outer dripping (dripping), inner jetting–outer jetting (jetting), and mixed dripping–jetting. Decreasing Re or increasing We promotes the jetting mode. The transition from dripping to jetting is also strongly affected by the velocity ratios, U₂₁ (intermediate to inner velocities) and U₃₁ (outer to inner velocities). Increasing U₂₁ makes the inner jet thinner and stretches the outer jet and thus promotes jetting. In contrast, increasing U₃₁ thins the outer jet, and thus, when the inner jet is dripping, the outer jet can break up into drops in the mixed dripping–jetting mode. Continuously increasing U₃₁ results in thinning both inner and outer jets and thus produces small drops in the jetting mode. In addition, starting from dripping, a decrease in the interfacial tension ratio of the outer to inner interfaces results in the mixed dripping–jetting and jetting modes. These modes produce various types of drops: simple drops, and compound drops with a single inner drop (single-core compound drops) or a few inner drops (multi-core compound drops).     

Droplet impact dynamics for two liquids impinging on anisotropic superhydrophobic surfaces

Droplet impingement experiments were performed on grooved hydrophobic surfaces with cavity fractions of 0, 80, and 93?% using droplets of water and a 50?%/50?% water/glycerol mixture. The influence of liquid viscosity, cavity fraction, and spreading direction, relative to the surface grooves, is explored qualitatively and quantitatively. The maximum droplet spread diameter, velocity of the rebounding jet, and the time delay between droplet impact and jet emission were characterized for Weber numbers, We, based on droplet impact speed and diameter, up to 500. The unequal shear stresses and contact angles influence the maximum spread diameters in the two primary spread directions. At We?>?100, the ratio of the spread diameter along the direction of the grooves to the spread diameter perpendicular to the grooves increases above unity with increasing We. The maximum droplet spread diameter is compared to recent predictive models, and the data reveal differing behavior for the two fluids considered. The results also reveal the existence of very high relative jet velocities in the range 5????We????15 for water droplets, while such jets were not observed for the more viscous mixture. Further, in the range 115????We????265, the water/glycerol jet formation dynamics are radically different from the water behavior. Most evident is the existence of two-pronged jets, which arise from the anisotropy of the surface and the unequal shear stresses and contact angles that prevail on the surfaces. It is these influences that give rise to differences in the maximum spread diameters in the two primary spread directions. Similar two-pronged jet emission was observed for water over the very narrow range of We from 91 to 96. The issuing jet velocities were also observed to increase with increasing cavity fraction for both fluids and over the entire range of We explored. Lastly, the elapsed time between droplet impact and jet emission decreased with increasing cavity fraction.     

Hybrid RANS/LES computations of plane impinging jets with DES and PANS models

The qualities of a DES (Detached Eddy Simulation) and a PANS (Partially-Averaged Navier–Stokes) hybrid RANS/LES model, both based on the k–ω RANS turbulence model of Wilcox (2008, “Formulation of the k–ω turbulence model revisited” AIAA J., 46: 2823–2838), are analysed for simulation of plane impinging jets at a high nozzle-plate distance (H/B = 10, Re = 13,500; H is nozzle-plate distance, B is slot width; Reynolds number based on slot width and maximum velocity at nozzle exit) and a low nozzle-plate distance (H/B = 4, Re = 20,000). The mean velocity field, fluctuating velocity components, Reynolds stresses and skin friction at the impingement plate are compared with experimental data and LES (Large Eddy Simulation) results. The k–ω DES model is a double substitution type, following Davidson and Peng (2003, “Hybrid LES–RANS modelling: a one-equation SGS model combined with a k–ω model for predicting recirculating flows” Int. J. Numer. Meth. Fluids, 43: 1003–1018). This means that the turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the eddy viscosity formula. The k–ω PANS model is derived following Girimaji (2006, “Partially-Averaged Navier–Stokes model for turbulence: a Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation bridging method” J. Appl. Mech., 73: 413–421). The turbulent length scale in the PANS model is constructed from the total turbulent kinetic energy and the sub-filter dissipation rate. Both hybrid models change between RANS (Reynolds-Averaged Navier–Stokes) and LES based on the cube root of the cell volume. The hybrid techniques, in contrast to RANS, are able to reproduce the turbulent flow dynamics in the shear layers of the impacting jet. The change from RANS to LES is much slower however for the PANS model than for the DES model on fine enough grids. This delays the break-up process of the vortices generated in the shear layers with as a consequence that the DES model produces better results than the PANS model.     

A Hybrid-Filter Approach to Turbulence Simulation

Germano (Theor Comput Fluid Dyn 17:225–331, 2004) proposed a hybrid-filter approach, which additively combines an LES-like filter operator (F) and a RANS-like statistical operator (E) using a blending function k: H?=?kF?+?(1???k)E. Using turbulent channel flow as an example, we first conducted a priori tests in order to gain some insights into this hybrid-filter approach, and then performed full simulations to further assess the approach in actual simulations. For a priori tests, two separate simulations, RANS (E) and LES (F), were performed using the same grid in order to construct a hybrid-filtered field (H). It was shown that the extra terms arising out of the hybrid-filtered Navier–Stokes (HFNS) equations provided additional energy transfer from the RANS region to the LES region, thus alleviating the need for the ad hoc forcing term that has been used by some investigators. The complexity of the governing equations necessitated several modifications in order to render it suitable for a full numerical simulation. Despite some issues associated with the numerical implementation, good results were obtained for the mean velocity and skin friction coefficient. The mean velocity profile did not have an overshoot in the logarithmic region for most blending functions, confirming that proper energy transfer from the RANS to the LES region was a key to successful hybrid models. It is shown that Germano’s hybrid-filter approach is a viable and mathematically more appealing approach to simulate high Reynolds number turbulent flows.     

Recent improvements in the Zonal Detached Eddy Simulation (ZDES) formulation

An efficient generalized Zonal Detached Eddy Simulation method (ZDES) is presented, which aims at performing hybrid Reynolds Averaged Numerical Simulation (RANS)/Large Eddy Simulation (LES) calculations for both internal and external aerodynamics problems. It is based on a zonal formulation of the hybrid length scale that allows to combine the zonal approach with the best features of Delayed Detached Eddy Simulation (DDES) (Spalart et?al. Theor Comput Fluid Dyn 20:181–195, 2006). In other words, the presumed weak point of a zonal approach, namely that the location of separation has to be known in advance, is now overcome. What is more, the problem of slow LES content development in mixing layers when they are treated neither in RANS nor in LES mode is investigated. It is argued that the subgrid length scale Δ_max?=?max(Δx, Δy, Δz) entering DDES is physically justified to shield the boundary layer but is definitely not a good subgrid length scale in LES mode. Remedies are proposed based on new zonal subgrid length scales that depend not only on the grid spacing but also on the flow solution and especially on the local vorticity vector. The method is validated on a spatially developing mixing layer as well as in a backward facing step flow and then applied to a three-element airfoil. It is argued in this latter case that a precise control of the RANS mode thanks to a zonal approach is essential. More generally, in all simulated cases in this study, ZDES has proven to be very efficient as regards the behavior in LES mode while retaining the strongest asset of DDES, namely the treatment of the attached boundary layer in RANS mode. The issue of zonal or non-zonal treatment of turbulent flows is also briefly discussed.     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

Collision dynamics of high-speed droplets upon layers of variable thickness

The collision dynamics between a droplet and a film has been studied with high-impact energy that can be grouped in a dimensionless Weber number, We, as normalized by surface energy. To accomplish this, we have developed a technique based on cutting of a high-speed jet, which can generate a single droplet with speed up to 23 m/s and We on the order of thousands. It was found that the boundaries indicating the occurrence of a central jet and that of a secondary droplet disintegrated from the jet decreased monotonically with increased dimensionless film thickness, H, and remained constant when the film thickness was larger than the crater depth. However, the transition designating multiple droplets that are originated from a central jet shows a non-monotonic trend with the variation of H, with a minimum We being at H ≈ 3, which is about the maximum crater depth, owing to a tuning behavior. The critical We for splashing that occurs at an early phase immediately after the impact is relatively sensitive to the film thickness only when H is between 1 and 2, which increases with reduced H. At large We (≳2,570 for high H), the ejected crown is closed to form a bubble and the transition boundary reveals a similar dependence on H as that for creation of a central jet.     

Scrutinizing URANS in Shedding Flows: The Case of Cylinder in Cross-Flow in the Subcritical Regime

To unravel the widespread perception that the RANS (Reynolds-averaged Navier-Stokes) concept is unreliable in predicting the dynamics of separated flows, we assessed the performance of two RANS closure levels, the linear eddy-viscosity (LEVM) and the second-moment (Reynolds stress, RSM) approaches in a massively separated generic flow over a bluff body. Considered is the canonical, zero-turbulence, cross-flow over an infinite cylinder with reference to our LES and the available DNS and experiments at two Reynolds numbers, Re = 3.9 × 10³ and 1.4 × 10⁵, both within the sub-critical regime with laminar separation. Both models capture successfully the vortex shedding frequency, but the low frequency modulations are detected only by the RSM. At high Reynolds numbers the RSM is markedly superior to the LEVM showing very good agreement with the LES and experimental data. The RSM, accounting naturally for the stress anisotropy and phase lag between the stress and strain eigenvectors, is especially successful in reproducing the growth rate of the turbulent kinetic energy in the initial shear layer which proved to be crucial for accurate prediction of the separation-induced transition. A scrutiny of the unsteady RANS (URANS) stress terms based on the conditional phase-averaged LES data shows a remarkable similarity of the normalized coherent and stochastic (modeled) stress components for the two Reynolds numbers considered. The mixed (cross) correlations, while non-negligible at the low Re number, diminish fast relative to the stochastic ones with increasing Reynolds number and, in the whole, are not significant to undermine the URANS concept and its applicability to high Re flows of industrial relevance.     

Numerical simulation of the deformation and breakup of a two-core compound droplet in an axisymmetric T-junction channel

The rheological behaviors of a compound droplet in a confined geometry are of importance in many industrial and natural processes. However, a detailed numerical simulation of the finite deformation and its transition to the breakup of the multi-core compound droplet in an axisymmetric T-junction channel is still lacking. The present study is to fill this gap through the numerical simulations of a two-core compound droplet that deforms and breaks up in this channel configuration. The numerical results are obtained by the axisymmetric front-tracking method. Our new finding is that the compound droplet in the channel can experience the finite deformation or the breakup depending on the flow condition or the configuration of the channel. In the finite deformation mode (i.e. non-breakup mode), the droplet rapidly reaches the maximum deformation before approaching the perpendicular rigid wall. The most deformation occurs with the outer droplet, and the inner droplet closer to the wall is less deformed than the other inner core droplet. In the breakup mode, three breakup patterns are recognized: (i) breakup type I occurring when breaking up only the outer droplet; (ii) breakup type 2 occurring when breaking up only the inner droplets; (iii) breakup type 3 occurring when breaking up both inner and outer droplets. The transition from the non-breakup mode to the breakup mode is available when increasing the Reynolds number Re (from 0.16 to 40.0), the capillary number Ca (from 0.04 to 4.0), the size R_o of the outer droplet and the middle-to-outer fluid viscosity ratio μ₂₁, or decreasing the size R_i of the inner droplets, the radial size C₂ of the channel (normalized by the channel axial size C₁) and the interfacial tension ratio of the inner to the outer droplets. The transition diagrams based on some of these parameters are also proposed to provide a more complete picture of the two-core compound droplet behaving in the axisymmetric T-junction channel..     

High-order Large Eddy Simulations of Confined Rotor-Stator Flows

In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a secondary flow in the meridian plane composed of two thin boundary layers along the disks separated by a non-viscous geostrophic core. Most numerical simulations have been performed using RANS and URANS modelling, and very few investigations have been performed using LES. This paper reports on quantitative comparisons of two high-order LES methods to predict a turbulent rotor-stator flow at the rotational Reynolds number Re(=?Ωb ²/ν)?=4 × 10⁵. The classical dynamic Smagorinsky model for the subgrid-scale stress (Germano et al., Phys Fluids A 3(7):1760–1765, 1991) is compared to a spectral vanishing viscosity technique (Séverac & Serre, J Comp Phys 226(2):1234–1255, 2007). Numerical results include both instantaneous data and post-processed statistics. The results show that both LES methods are able to accurately describe the unsteady flow structures and to satisfactorily predict mean velocities as well as Reynolds stress tensor components. A slight advantage is given to the spectral SVV approach in terms of accuracy and CPU cost. The strong improvements obtained in the present results with respect to RANS results confirm that LES is the appropriate level of modelling for flows in which fully turbulent and transition regimes are involved.     

Feedback-controlled forcing in hybrid LES/RANS

The computational cost of large eddy simulation (LES) increases rapidly with the Reynolds number when applied to attached boundary layers. This problem can be avoided by use of a Reynolds-averaged Navier–Stokes (RANS) model in the inner part of the boundary layer, which reduces the computational cost drastically. Such hybrid LES/RANS methods yield accurate results in general, but suffer from an artificial buffer layer and a shift in the velocity profile around the modeling interface. This velocity shift can be removed by use of additional forcing, but the results are very sensitive to the forcing amplitude.

The present paper proposes a feedback algorithm which efficiently finds the appropriate amplitude and thus yields accurate flow statistics. The feedback algorithm is relatively robust, both in that it is insensitive to the values of the parameters involved and that it yields accurate results with different forcing fields and for different Reynolds numbers. It is argued that the feedback algorithm is consistent with the underlying assumptions of hybrid LES/RANS and that it does not introduce additional empiricism into the method.