Lagrangian Dynamic Subgrid-scale Model Research Articles

Turbulent structures of buoyant jet in cross-flow studied through large-eddy simulation

In the present paper we study buoyant (plume) and non-buoyant (jet) fluid injection in a neutrally stratified uniform cross-flow. Both cases are of practical importance in environmental fluid mechanics. The study is carried out numerically, using highly resolved large-eddy simulation in conjunction with the Lagrangian dynamic sub-grid scale model for both momentum and scalar transport equations. The velocity ratio is $$\kappa =8$$ . In the plume case, the Froude number is $$F=10$$ , such to allow the use of the Boussinesq approximation. The simulations are successfully validated against experimental data and well established semi-empirical relations. The study shows the existence of three different regions as regards the plume evolution, each of them characterised by different peculiarities: in momentum-buoyancy region the plume exhibits an almost steady cylindrical shape with relative small turbulence structures; in deflection region the plume is deviated horizontally and a high shear rate is detected; in entrainment region the vortex pair develops, along with the sausage-like turbulent structure. The comparison between the plume and the jet case shows that the latter has a higher eccentricity while its trajectory height is sensibly lower. Also, the sausage-like structures are not present. Finally, an empirical formula for the jet trajectory is given, although its full validation will require additional studies.

Interaction of inner and outer layers in plane and radial wall jets

Large eddy simulations of turbulent radial and plane wall jets were performed at different Reynolds numbers using the Lagrangian dynamic eddy viscosity subgrid-scale model. The results were validated with experimental data available in the literature. Compared to the plane ones, the radial wall jets have an extra direction for expansion, which causes faster decay rates. Thus, the resulting pressure gradient distributions are different. However, the comparison of the results with the turbulent boundary layers under adverse and favourable pressure gradients reveals that these pressure gradients are not strong enough to cause any fundamental physical difference between plane and radial wall jets. In both cases, the local Reynolds number is an important determining factor in characterisation of the flow. The joint probability density function analysis shows that the local Reynolds number determines the level of intrusion of the outer layer into the inner layer: the lower the local Reynolds number, the stronger is the interaction of the inner and outer layers. These results can be used to clarify the scatter of the reported log-law constants in the literature.

효율적인 해양구조물 유동 해석을 위한 직교좌표계 기반의 코드 개발 - AMR, VOF, IBM, VIV, LES의 통합

Simulation of flow past a complex marine structure requires a fine resolution in the vicinity of the structure, whereas a coarse resolution is enough far away from it. Therefore, a lot of grid cells may be wasted, when a simple Cartesian grid system is used for an Immersed Boundary Method (IBM). To alleviate this problems while maintaining the Cartesian frame work, we adopted an Adaptive Mesh Refinement (AMR) scheme where the grid system dynamically and locally refines as needed. In this study, We implemented a moving IBM and an AMR technique in our basic 3D incompressible Navier-Stokes solver. A Volume Of Fluid (VOF) method was used to effectively treat the free surface, and a recently developed Lagrangian Dynamic Subgrid-scale Model (LDSM) was incorporated in the code for accurate turbulence modeling. To capture vortex induced vibration accurately, the equation for the structure movement and the governing equations for fluid flow were solved at the same time implicitly. Also, We have developed an interface by using AutoLISP, which can properly distribute marker particles for IBM, compute the geometrical information of the object, and transfer it to the solver for the main simulation. To verify our numerical methodology, our results were compared with other authors’ numerical and experimental results for the benchmark problems, revealing excellent agreement. Using the verified code, we investigated the following cases. (1) simulating flow around a floating sphere. (2) simulating flow past a marine structure.

Reynolds and froude number effect on the flow past an interface-piercing circular cylinder

The two-phase turbulent flow past an interface-piercing circular cylinder is studied using a high-fidelity orthogonal curvilinear grid solver with a Lagrangian dynamic subgrid-scale model for large-eddy simulation and a coupled level set and volume of fluid method for air-water interface tracking. The simulations cover the sub-critical and critical and post critical regimes of the Reynolds and sub and super-critical Froude numbers in order to investigate the effect of both dimensionless parameters on the flow. Significant changes in flow features near the air-water interface were observed as the Reynolds number was increased from the sub-critical to the critical regime. The interface makes the separation point near the interface much delayed for all Reynolds numbers. The separation region at intermediate depths is remarkably reduced for the critical Reynolds number regime. The deep flow resembles the single-phase turbulent flow past a circular cylinder, but includes the effect of the free-surface and the limited span length for sub-critical Reynolds numbers. At different Froude numbers, the air-water interface exhibits significantly changed structures, including breaking bow waves with splashes and bubbles at high Froude numbers. Instantaneous and mean flow features such as interface structures, vortex shedding, Reynolds stresses, and vorticity transport are also analyzed. The results are compared with reference experimental data available in the literature. The deep flow is also compared with the single-phase turbulent flow past a circular cylinder in the similar ranges of Reynolds numbers. Discussion is provided concerning the limitations of the current simulations and available experimental data along with future research.

Turbulent plane wall jets over smooth and rough surfaces

Large-eddy simulations were carried out to study the effects of surface roughness on a plane wall-jet using the Lagrangian dynamic eddy-viscosity subgrid-scale model, at Re = 7500 (based on the jet bulk velocity and height). Results over both smooth and rough surfaces were validated by experimental data at the same Reynolds number. As the jet is injected into the still environment, large-scale rollers are generated in the shear layer between the high-momentum fluid of the jet and the surrounding and are convected downstream with the flow. To understand the extent to which the outer-layer structures modify the flow in the inner layer and the extent to which the effect of roughness spreads away from the wall, both instantaneous and mean flow fields were investigated. The results revealed that, for the Reynolds number and roughness height considered in this study, the effect of roughness is mostly confined to the near-wall region of the wall jet. There is no structural difference between the outer layer of the wall jet over the smooth and rough surfaces. Roughness does not affect the size of the outer-layer structures or the scaling of the profiles of Reynolds stresses in the outer layer. However, in the inner layer, roughness redistributes stresses from streamwise to wall-normal and spanwise directions toward isotropy. Contours of joint probability-density function of the streamwise and wall-normal velocity fluctuations at the bottom of the logarithmic region match those of the turbulent boundary layer at the same height; while the traces of the outer-layer structure were detected at the top of the logarithmic region, indicating that they do not affect the flow very close to the wall, but still modify a major portion of the inner layer. This modification must be taken into consideration when the inner layer of a wall jet is compared with the conventional turbulent boundary layer.

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics

AbstractWe performed large-eddy simulations of flow over a series of three-dimensional dunes at laboratory scale (Reynolds number based on the average channel depth and streamwise velocity was 18 900) using the Lagrangian dynamic eddy-viscosity subgrid-scale model. The bedform three-dimensionality was imposed by shifting a standard two-dimensional dune shape in the streamwise direction according to a sine wave. The statistics of the flow are discussed in 10 cases with in-phase and staggered crestlines, different deformation amplitudes and wavelengths. The results are validated qualitatively against experiments. The three-dimensional separation of flow at the crestline alters the distribution of wall pressure, which in turn may cause secondary flow across the stream, which directs low-momentum fluid, near the bed, toward the lobe (the most downstream point on the crestline) and high-momentum fluid, near the top surface, toward the saddle (the most upstream point on the crestline). The mean flow is characterized by a pair of counter-rotating streamwise vortices, with core radius of the order of the flow depth. However, for wavelengths smaller than the flow depth, the secondary flow exists only near the bed and the mean flow away from the bed resembles the two-dimensional case. Staggering the crestlines alters the secondary motion; the fastest flow occurs between the lobe and the saddle planes, and two pairs of streamwise vortices appear (a strong one, centred about the lobe, and a weaker one, coming from the previous dune, centred around the saddle). The distribution of the wall stress and the focal points of separation and attachment on the bed are discussed. The sensitivity of the average reattachment length, depends on the induced secondary flow, the streamwise and spanwise components of the channel resistance (the skin friction and the form drag), and the contribution of the form drag to the total resistance are also studied. Three-dimensionality of the bed increases the drag in the channel; the form drag contributes more than in the two-dimensional case to the resistance, except for the staggered-crest case. Turbulent-kinetic energy is increased in the separated shear layer by the introduction of three-dimensionality, but its value normalized by the plane-averaged wall stress is lower than in the corresponding two-dimensional dunes. The upward flow on the stoss side and higher deceleration of flow on the lee side over the lobe plane lift and broaden the separated shear layer, respectively, affecting the turbulent kinetic energy.

Large Eddy Simulation of Unstably Stratified Turbulent Flow over Urban-Like Building Arrays

Thermal instability induced by solar radiation is the most common condition of urban atmosphere in daytime. Compared to researches under neutral conditions, only a few numerical works studied the unstable urban boundary layer and the effect of buoyancy force is unclear. In this paper, unstably stratified turbulent boundary layer flow over three-dimensional urban-like building arrays with ground heating is simulated. Large eddy simulation is applied to capture main turbulence structures and the effect of buoyancy force on turbulence can be investigated. Lagrangian dynamic subgrid scale model is used for complex flow together with a wall function, taking into account the large pressure gradient near buildings. The numerical model and method are verified with the results measured in wind tunnel experiment. The simulated results satisfy well with the experiment in mean velocity and temperature, as well as turbulent intensities. Mean flow structure inside canopy layer varies with thermal instability, while no large secondary vortex is observed. Turbulent intensities are enhanced, as buoyancy force contributes to the production of turbulent kinetic energy.

Heat transfer in rotor/stator cavity

In the paper we analyze the results of DNS/LES of the flow with heat transfer in the rotor/stator cavity. The rotor and the outer cylinder are heated. Computations have been performed for wide range of Reynolds numbers and aspect ratios. Computations are based on the efficient pseudo-spectral Chebyshev-Fourier method. In LES we used a Lagrangian dynamic subgrid-scale model of turbulence. Analysis allowed to check the influence of the aspect ratio and Reynolds number on the statistics and the structure of the flow. We analyzed all six Reynolds stress tensor components, turbulent fluctuations, three turbulent heat fluxes and different structural parameters which can be useful for modeling purposes. The distributions of Nusselt numbers obtained for different Re and aspect rations along disks are given. We also investigated influence of thermal Rosssby number as well as distributions of temperature along heated disk on statistics. Computations have shown that turbulence is mostly concentrated in the stator boundary layer with a maximum at the junction between the stator and the outer cylinder. The results are compared to the experimental and numerical data taken from literature.

Heat and fluid flow in cylindrical and conical annular flow-passages with through flow and inner-wall rotation

The flow and heat transfer in cylindrical and conical annular flow-passages with through flow and inner-wall rotation have been numerically simulated by using the large eddy simulation with a Lagrangian dynamic subgrid-scale model. Inlet through-flow Reynolds number was 1000 and the Taylor number was set at 0, 1000, 2000, and 4000. In the conical flow passage, when the inner-wall rotation speed was increased, at first spiral vortices in the downstream region and then much more complicated vortices appeared. The vortices for Ta = 4000 changed the structure in both through-flow and wall-normal directions in the downstream half of the passage. The flow structure and heat transfer of the conical case were completely different from those of the cylindrical case. It was because of the three factors: the expansion of the flow passage, the rotation radius change in the through-flow direction, and the centrifugally driven through-flow. The last factor is due to the acute angle between the centrifugal and through-flow directions.

Large-eddy simulation of two-dimensional dunes in a steady, unidirectional flow

We performed large-eddy simulations of the flow over a typical two-dimensional dune geometry at laboratory scale (the Reynolds number based on the average channel height and mean velocity is 18,900) using the Lagrangian dynamic eddy-viscosity subgrid-scale model. The results are validated by comparison with simulations and experiments in the literature. The flow separates at the dune crest, generating a shear layer that plays a crucial role in the transport of momentum and energy, and the generation of coherent structures. The turbulent kinetic energy budgets show the importance of the turbulent transport and mean-flow advection in the bulk flow above the shear layer. In the recirculation zone and in the attached boundary layers production and dissipation are the most important terms. Large, coherent structures of various types can be observed. Spanwise vortices are generated in the separated shear layer due to the Kelvin–Helmholtz instability; as they are advected, they undergo lateral instabilities and develop into horseshoe-like structures, are tilted downward, and finally reach the surface. The ejection that occurs between the legs of the vortex creates the upwelling and downdrafting events on the free surface known as “boils.” Near-wall turbulence, after the reattachment point, is affected by large streamwise Taylor–Görtler vortices generated on the concave part of the stoss side, which affect the distribution of the near-wall streaks.

Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations

Large-eddy simulation (LES), coupled with a wind-turbine model, is used to investigate the characteristics of a wind-turbine wake in a neutral turbulent boundary-layer flow. The tuning-free Lagrangian scale-dependent dynamic subgrid-scale (SGS) model is used for the parametrisation of the SGS stresses. The turbine-induced forces (e.g., thrust, lift and drag) are parametrised using two models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses the blade-element theory to calculate the lift and drag forces (that produce both thrust and rotation), and distribute them over the rotor disk based on the local blade and flow characteristics. Simulation results are compared to high-resolution measurements collected with hot-wire anemometry in the wake of a miniature wind turbine at the St. Anthony Falls Laboratory atmospheric boundary-layer wind tunnel. In general, the characteristics of the wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. The ADM-R yields improved predictions compared with the ADM-NR in the near-wake region, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces appear to be important. Our results also show that the Lagrangian scale-dependent dynamic SGS model is able to account, without any tuning, for the effects of local shear and flow anisotropy on the distribution of the SGS model coefficient.

The effect of air–water interface on the vortex shedding from a vertical circular cylinder

The flow past an interface piercing circular cylinder at the Reynolds number Re=2.7×10 4 and the Froude numbers Fr=0.2 and 0.8 is investigated using large-eddy simulation. A Lagrangian dynamic subgrid-scale model and a level set based sharp interface method are used for the spatially filtered turbulence closure and the air–water interface treatment, respectively. The mean interface elevation and the rms of interface fluctuations from the simulation are in excellent agreement with the available experimental data. The organized periodic vortex shedding observed in the deep flow is attenuated and replaced by small-scale vortices at the interface. The streamwise vorticity and the outward transverse velocity generated near the edge of the separated region, which enforces the separated shear layers to deviate from each other and restrains their interaction, are primarily responsible for the devitalization of the periodic vortex shedding at the interface. The lateral gradient of the difference between the vertical and transverse Reynolds normal stresses, increasing with the Froude number, is the main source of the streamwise vorticity and the outward transverse velocity at the interface.

LES and DNS of the Flow with Heat Transfer in Rotating Cavity

In the present paper we summarized our numerical investigations on the flow with heat transfer in rotating cavity performed by DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation). We considered different geometrical configurations and different flow and thermal conditions. All presented computations have been performed in Poznan Supercomputing and Networking Center. The objective of our investigations was to analyze the coherent structures of transitional and turbulent flows and to compute statistical parameters, i.e. turbulent heat fluxes, the Reynolds stress tensor components, the turbulent Prandtl number and others. In the LES we used a version of the dynamic Smagorinsky eddy viscosity model proposed by Meneveau et al. (A Lagrangian dynamic subgrid-scale model of turbulence, J. Fluid Mech., vol. 319, 1996), in which the Smagorinsky coefficient at a given position x depends on the history of the flow along the fluid particle pathline.

Sharp interface immersed-boundary/level-set method for wave–body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost–fluid method for solid–fluid and fluid–fluid interface treatments, respectively. A four-step fractional-step method is used for velocity–pressure coupling, and a Lagrangian dynamic Smagorinsky subgrid-scale model is adopted for large-eddy simulations. A simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed. A variety of test cases of different scales ranging from bubble dynamics, water entry and exit, landslide-generated waves, to ship hydrodynamics are performed for validation. Extensions for high Reynolds number ship flows using wall-layer models are also considered.

LES of the non-isothermal transitional flow in rotating cavity

The paper presents the 3D LES study of the non-isothermal transitional and turbulent flow in rotor/stator sealed cavity with a rotating inner and a stationary outer cylinder. The stator and the outer cylinder are warmer than the rotor and the inner cylinder. Computations have been performed for the cavity of aspect ratio L = ( R 1 − R 0)/2 h = 5, curvature parameter Rm = ( R 1 + R 0)/( R 1 − R 0) = 3, Reynolds numbers Re = Ω R 1 2 / ν = 75 , 000 – 300 , 000 , thermal Rossby numbers B = β( T 2 − T 1) = 0.01–0.4, and for the cavity ( L = 9, Rm = 1.5, Re = 100,000–150,000, B = 0.01–0.4). Computations we based on the efficient pseudo-spectral Chebyshev–Fourier method (Serre, E., Pulicani, J.P., 2001. A three-dimensional pseudospectral method for rotating flows in a cylinder. Computers and Fluids, 30, 491). In Large Eddy Simulations we used a version of the dynamic Smagorinsky eddy viscosity model proposed by Meneveau (Meneveau, C., Lund, T.S., Cabot, W.H., 1996, A Lagrangian dynamic subgrid-scale model of turbulence. Journal of Fluid Mechanics, 319, 353–385), in which the averaging is performed over the particle pathline. This approach allowed us to perform computations for higher Reynolds numbers for confined rotating flows, which are strongly inhomogeneous and anisotropic. Results showed that the turbulence is concentrated mostly in the stator boundary layer with a maximum at the junction between the stator and the outer cylinder. For the cavity of aspect ratio L = 5 the stator boundary layer was fully turbulent for Re ⩾ 100,000, whereas the rotor boundary layer was still laminar. The influence of the thermal Rossby number on the flow structure and the basic state was not significant. The correlation formulas, for predicting the distribution of local Nusselt numbers along disks as well as the correlation formulas for the averaged Nusselt numbers depending on the Reynolds numbers are given on the basis of our results.

On the Parameterization of Surface Roughness at Regional Scales

Abstract A parameterization for surface roughness and blending height at regional scales, under neutral atmospheric stability, is studied and tested. The analysis is based on a suite of large-eddy simulations (LES) over surfaces with varying roughness height and multiple variability scales. The LES are based on the scale-dependent Lagrangian dynamic subgrid-scale model, and the surface roughnesses at the ground are imposed using the rough-wall logarithmic law. Several patterns of roughness distribution are considered, including random tiling of patches with a wide distribution of length scales. An integral length scale, based on the one-dimensional structure function of the spatially variable roughness height, is used to define the characteristic surface variability scale, which is a critical input in many regional parameterization schemes. Properties of the simulated flow are discussed with special emphasis on the turbulence properties over patches of unequal roughness. The simulations are then used to assess a generalized form of the parameterization for the blending height and the equivalent surface roughness at regional scales that has been developed earlier for regular patterns of surface roughness (regular stripes). The results are also compared with other parameterizations proposed in the literature. Good agreement is found between the simulations and the regional-scale parameterization for the surface roughness and the blending height when this parameterization is combined with the characteristic surface variability scale proposed in this paper.

Large-eddy simulation of the flow in an S-duct

Large-eddy simulations of the flow in an S-shaped, two-dimensional duct were conducted using a Lagrangian dynamic eddy viscosity subgrid-scale model and a non-orthogonal grid system. The simulations were performed at Re b = 13,800 and 30,800, using up to 13.4 million grid nodes. The results show that two factors affect the boundary layer: the concave or convex wall curvature (which, respectively, enhances or dampens the turbulent motions) and the favourable or adverse pressure gradient in the regions of curvature change, which accelerates or decelerates the boundary layer. In the presence of an adverse pressure gradient the boundary layer can separate intermittently, which also enhances the turbulent motions. The strongest separation occurs between the two curves and affects the flow not only in the following curve but also in the recovery region. The flow near the walls displays a logarithmic behaviour, but its slope and intercept vary with curvature and pressure gradient. Taylor–Görtler vortices are observed near the concave surfaces; they are responsible for strong organization of the streamwise and wall-normal velocity fluctuations, and contribute significantly to the Reynolds stresses. The turbulent kinetic energy budgets show that the production and dissipation are similarly affected by the wall curvature as the turbulent motions: they are increased by the concave wall and decreased by the convex. The mean flow advection transports turbulent kinetic energy from the region with concave curvature to the region with convex curvature.

Effect of rib orientation and channel rotation on turbulent heat transfer in a two-pass square channel with sharp 180° turns investigated by using large eddy simulation

Effect of rib orientation and channel rotation on heat transfer in a two-pass square channel with 180° sharp turns was numerically investigated by using the large eddy simulation with a Lagrangian dynamic subgrid-scale model. In the stationary condition, the heat transfer in and after the turn was increased, and it was dominated by the sharp-turn induced flow field. In the rotating condition, the highest rotating speed caused deteriorated heat transfer on the pressure surface of the straight pass. The friction factor was much more sensitive to both the rib arrangement and channel rotation than the heat transfer.

Large eddy simulation of turbulent heat transfer in a rotating two-pass smooth square channel with sharp 180° turns

Heat transfer in a rotating two-pass square channel with 180° sharp turns was numerically simulated by using the large eddy simulation with a Lagrangian dynamic subgrid-scale model. In the stationary condition, the heat transfer in and after the turn was increased due to the flow impingement, the flow separation and reattachment, and the reversed flow at the second outer corner. In the rotating condition, the high momentum fluid on the upstream pressure side formed one strong vortex in the turn that transported the high momentum and low temperature fluid to the suction surface side where the heat transfer became high.

Effect of cross-sectional aspect ratio on turbulent heat transfer in an orthogonally rotating rectangular duct with angled rib turbulators

Heat transfer in a rotating rib-roughened rectangular duct was numerically simulated by using the large eddy simulation with a Lagrangian dynamic subgrid-scale model. The rotation number and the duct cross-sectional aspect ratio (0.25, 0.5, 1.0, 2.0, and 4.0) were varied for a friction Reynolds number of 350 and rib angle of 60°. The present results clearly showed the locally high heat transfer at several locations and how it was changed by the duct aspect ratio. The dissimilarity between the streamwise velocity and temperature was observed for all the aspect ratio cases in the rotating case.