Eddy Model Research Articles

Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y(+) less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y(+) less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the filtered Navier-Stokes equations. Results presented include the distribution of velocity, the decay law of the mean velocity along the jet axis, self-similar characteristics and volume flux per unit width. In particular, the role of coherent structures on the momentum transfer along the jet centerline and the jet instantaneous characteristics in JONSWAP waves are a special focus of this research. The numerical results obtained are of great theoretical importance in understanding the behavior of turbulent jets in random wave environments.

Direct Numerical Simulation of Gas Transfer at the Air-Water Interface

A direct numerical simulation is made to investigate the gas transfer at the air-water interface in an open channel flow. The numerical results show the interfacial gas flux to increase intensively in large positive surface divergence regions. This means that the surface divergence model is effective for evaluating the gas transfer velocity at the air-water interface. Scaling relations for turbulence controlling the gas transfer are examined from view points of the surface divergence model. The scale of the surface divergence can be expressed by the Taylor microscale, not macro turbulent scales. We found a dimensionless gas transfer velocity to depend on the -1/4 power of a turbulent Reynolds number. The divergence model shows formally the same Reynolds number dependence as the small eddy model based on the Kolmogorov scaling.

A novel dynamic coherent eddy model and its application to LES of a turbulent jet with free surface

We has developed a novel dynamic coherent eddy model, in which the coherent structure—Q criterion introduced by Hunt et al (1988)—is taken into account in the subgrid-scale turbulent viscosity based on the eddy viscosity model. One proposed method is to combine the resolved-scale velocity-gradient tensor in the classical Smagorinsky model with Q criterion weighted. A kind of dynamic procedure which was averaged in a general process at temporal direction based on the autocorrelations of the characteristic resolved scales of turbulence was taken for the coefficient of subgrid model. The model is implemented in the σ-coordinate and the filtered Navier-Stokes equations are solved by the operator splitting method. The validation was explored to 2-D turbulent slot jet both in ambient environment and in regular waves. The prediction of the present model was compared with the experiment data, including the averaged velocity profiles, the velocity fluctuations and the Reynolds stress. The model performance is shown to be satisfactory.

Wet scavenging of SO<sub>2</sub> emissions around India's largest lignite based power plant

Abstract. The Neyveli Lignite Corporation (NLC) is among the largest lignite based power plants in South East Asia. The four elevated stacks from this power plant emanate a substantial amount of sulphur dioxide into a tropical boundary layer. Sulphur dioxide being a soluble pollutant gas is absorbed by falling raindrops. This is a first study that quantifies the scavenging action of the North Eastern monsoonal rains from a lignite based power plant. We find that although the North Eastern monsoonal rains have a preponderance of very large droplets, the contribution of the small droplets cannot be neglected. We expect that the estimated scavenging coefficients can be used by large eddy and climate models.

Simulations of the effects of surface heat flux anomalies on stratification, convective growth, and vertical transport within the Saharan boundary layer

Using two cases based on observations from the Geostationary Earth Radiation Budget Intercomparison of Longwave and Shortwave Radiation field campaign, large eddy model (LEM) simulations have been used to investigate the effects of surface flux anomalies on the growth of the summertime Saharan convective boundary layer (CBL) into the Saharan Residual Layer (SRL) above and transport from the CBL into the SRL. Hot surface anomalies generated updrafts and convergence in the CBL that increased transport from the CBL into the SRL. The induced subsidence in regions away from the anomalies inhibited growth of the CBL there. If the domain‐averaged surface fluxes were kept constant, this led to a shallower, cooler CBL. If fluxes outside the anomalies were kept constant so that stronger anomalies led to increased domain‐averaged fluxes, this gave a warmer, shallower CBL. These effects were larger for wider, stronger anomalies with low winds. The low‐level wind speed variations induced by the anomalies were also shown to affect dust uplift rates. Previous observations have shown that the summertime SRL, which often contains sublayers of varying humidity and dust content, can persist until late in the afternoon. The LEM simulations presented show that mesoscale variations in surface fluxes can contribute both to inhibiting the growth of the Saharan CBL into the SRL and to generating layerings within the SRL.

Estimation of mass transfer velocity based on measured turbulence parameters

AbstractThe aim of this study is to quantify the mass transfer velocity using turbulence parameters from simultaneous measurements of oxygen concentration fields and velocity fields. The surface divergence model was considered in more detail, using data obtained for the lower range of β (surface divergence). It is shown that the existing models that use the divergence concept furnish good predictions for the transfer velocity also for low values of β, in the range of this study. Additionally, traditional conceptual models, such as the film model, the penetration‐renewal model, and the large eddy model, were tested using the simultaneous information of concentration and velocity fields. It is shown that the film and the surface divergence models predicted the mass transfer velocity for all the range of the equipment Reynolds number used here. The velocity measurements showed viscosity effects close to the surface, which indicates that the surface was contaminated with some surfactant. Considering the results, this contamination can be considered slight for the mass transfer predictions. © 2009 American Institute of Chemical Engineers AIChE J, 2010

The impact of resolution on ship plume simulations with NO<sub>x</sub> chemistry

Abstract. A high resolution chemical transport model of the marine boundary layer is designed in order to investigate the detailed chemical evolution of a ship plume in a tropical location. To estimate systematic errors due to finite model resolution, otherwise identical simulations are run at a range of model resolutions. Notably, to obtain comparable plumes in the different simulations, it is found necessary to use an advection scheme consistent with the Large Eddy Model representation of sub-grid winds for those simulations with degraded resolution. Our simulations show that OH concentration, NOx lifetime and ozone production efficiency of the model change by 8%, 32% and 31% respectively between the highest (200 m×200 m×40 m) and lowest resolution (9600 m×9600 m×1920 m) simulations. Interpolating to the resolution of a typical global composition transport model (CTM, 5°×5°), suggests that a CTM overestimates OH, NOx lifetime and ozone production efficiency by approximately 15%, 55% and 59% respectively. For the first time, by explicitly degrading the model spatial resolution we show that there is a significant reduction in model skill in accurately simulating the aforementioned quantities due to the coarse resolution of these CTMs and the non-linear nature of atmospheric chemistry. These results are significant for the assessment and forecasting of the climate impact of ship NOx and indicate that for realistic representation of ship plume emissions in CTMs, some suitable parametrisation is necessary at current global model resolutions.

TYPE Ia SUPERNOVAE: CALCULATIONS OF TURBULENT FLAMES USING THE LINEAR EDDY MODEL

The nature of carbon burning flames in Type Ia supernovae is explored as they interact with Kolmogorov turbulence. One-dimensional calculations using the Linear Eddy Model of Kerstein elucidate three regimes of turbulent burning. In the simplest case, large-scale turbulence folds and deforms thin laminar flamelets to produce a flame brush with a total burning rate given approximately by the speed of turbulent fluctuations on the integral scale, UL , This is the regime where the supernova explosion begins and where most of its pre-detonation burning occurs. As the density declines, turbulence starts to tear the individual flamelets, making broader structures that move faster. For a brief time, these turbulent flamelets are still narrow compared to their spacing and the concept of a flame brush moving with an overall speed of UL remains valid. However, the typical width of the individual flamelets, which is given by the condition that their turnover time equals their burning time, continues to increase as the density declines. Eventually, mixed regions almost as large as the integral scale itself are transiently formed. At that point, a transition to detonation can occur. The conditions for such a transition are explored numerically and it is estimated that the transition will occur for densities near 1 × 107 g cm–3, provided the turbulent speed on the integral scale exceeds about 20% sonic. An example calculation shows the details of a detonation actually developing.

Simulating dynamic stall in a two‐dimensional vertical‐axis wind turbine: verification and validation with particle image velocimetry data

AbstractThe implementation of wind energy conversion systems in the built environment has renewed the interest and the research on Vertical Axis Wind Turbines (VAWTs).The VAWT has an inherent unsteady aerodynamic behavior due to the variation of angle of attack and perceived velocity with azimuth angle. The phenomenon of dynamic stall is then an intrinsic effect of the operation at low tip speed ratios, impacting both loads and power.The complexity of the problem and the need for new design approaches for VAWTs for the built environment have driven the authors to focus this research on the CFD modeling of VAWTs on: Comparing the results between commonly used turbulence models: Unsteady Reynolds Averaged Navier‐Stokes – URANS (Spalart‐Allmaras and k‐ϵ) and large eddy models (Large Eddy Simulation and Detached Eddy Simulation). Verifying the sensitivity of the model to its grid refinement (space and time). Evaluating the suitability of using Particle Image Velocimetry (PIV) experimental data for model validation. The current work investigates the impact of accurately modeling the separated shed wake resulting from dynamic stall, and the importance of validation of the flow field rather than validation with only load data.The structure and magnitude of the wake are validated with PIV results, and it demonstrated that the accuracy of the different models in simulating a correct wake structure has a large impact in loads.

Investigation of Jet Break-Up Process in Diesel Engine Spray Modelling

Fluid mechanical or CFD simulation is playing an increasingly important role in the simulation of engine processes, as it makes possible the most detailed physical description of the relevant processes. The objective of this work is to simulate spray flow with different break-up models and investigate the effect of these models on DI diesel engine combustion and performance. In this simulation, the 3-Dimensional Naiver-Stokes equation is solved with SIMPLEC algorithm. An eddy break-up combustion model and a diesel auto-ignition model were implemented to simulate the ignition and combustion process in a diesel engine. All the simulations were carried out by the use of FIRE CFD tool. Results were validated with available experimental data for OM_355 DI diesel engine for mean cylinder pressure. The results show that there have been good agreements between experiments and the CFD calculations. The research demonstrated that multidimensional modeling is useful for diesel engine spray modeling and optimization.

Synoptic eddies of the Subantarctic and Agulhas fronts and generation of the Antarctic Intermediate Water in the Atlantic Ocean

The concept developed in [9] and [10], according to which the Antarctic Intermediate Water is generated owing to the formation and subsequent decay of cyclonic eddies of the Subantarctic Front, is tested for the Atlantic Ocean. The cross frontal water and salt transport by the Subantarctic Front eddies and the Agulhas Front anticyclones is estimated by developing cinematic eddy models and analyzing satellite altimetry maps. Calculations of the water and salt balance for a box in the South Atlantic based on these results and various experimental data confirmed the above-mentioned concept.

A Comparison of Roll and Nonroll Convection and the Subsequent Deepening Moist Convection: An LEM Case Study Based on SCMS Data

Abstract Rolls observed during the Small Cumulus Microphysical Study (SCMS) field campaign are simulated using a large eddy model (LEM). The simulated boundary layer properties were in a good agreement with sounding profiles and aircraft observations, and the observed boundary layer rolls were reproduced by the model. Rolls started to decay when −Zi/L exceeded a threshold, with a value between 5 and 45. Here Zi and L refer to the height of the top of convective boundary layer and the Monin–Obukhov length, respectively. This value was found to depend on a nondimensional combination of the low-level wind shear, the height of the CBL, and the eddy velocity scale. Larger surface buoyancy fluxes and smaller shears gave higher thresholds. For the case modeled, rolls persisted for surface buoyancy fluxes less than 110 W m−2, and formed for boundary layer wind shears greater than 5 × 10−3 s−1, which is consistent with previous studies. The simulated roll convection was compared with a nonroll simulation, which was identical except for the wind and the wind shear used. In both the roll and nonroll cases the variability in convective inhibition (CIN) was dominated by the variability in the source air, rather than the lifting of the top of the boundary layer by the convection. Stronger moist updrafts existed in the nonroll convection, whereas roll convection gave a more symmetrical distribution of up and downdrafts, with stronger downdrafts than the nonroll case. The nonroll convection simulations have lower minimum values of CIN and clouds develop 15 min earlier in this case.

Observations of mesoscale and boundary-layer scale circulations affecting dust transport and uplift over the Sahara

Abstract. Observations of the Saharan boundary layer, made during the GERBILS field campaign, show that mesoscale land surface temperature variations (which were related to albedo variations) induced mesoscale circulations. With weak winds along the aircraft track, land surface temperature anomalies with scales of greater than 10 km are shown to significantly affect boundary-layer temperatures and winds. Such anomalies are expected to affect the vertical mixing of the dusty and weakly stratified Saharan Residual Layer (SRL). Mesoscale variations in winds are also shown to affect dust loadings in the boundary layer. Using the aircraft observations and data from the COSMO model, a region of local dust uplift, with strong along-track winds, was identified in one low-level flight. Large eddy model (LEM) simulations based on this location showed linearly organised boundary-layer convection. Calculating dust uplift rates from the LEM wind field showed that the boundary-layer convection increased uplift by approximately 30%, compared with the uplift rate calculated neglecting the convection. The modelled effects of boundary-layer convection on uplift are shown to be larger when the boundary-layer wind is decreased, and most significant when the mean wind is below the threshold for dust uplift and the boundary-layer convection leads to uplift which would not otherwise occur. Both the coupling of albedo features to the atmosphere on the mesoscale, and the enhancement of dust uplift by boundary-layer convection are unrepresented in many climate models, but may have significant impacts on the vertical transport and uplift of desert dust. Mesoscale effects in particular tend to be difficult to parametrise.

A tabulated closure for turbulent non-premixed combustion based on the linear eddy model

A tabulated closure based on conditional statistics from fully-resolved one-dimensional scalar profiles has been formulated for application using the large eddy simulation technique. These scalar profiles are obtained from both experiments (i.e., line imaging of Raman/Rayleigh/CO-LIF) and from the simulations of linear eddy model. Such profiles provide a local description of species and temperature evolution due to the full range of turbulent scales in the predominant direction of scalar transport. Instantaneous realizations of these scalar profiles are processed as a function of pre-determined filter widths in space to obtain the conditional statistics of filtered scalars. Key statistical quantities needed for LES, are then parameterized as a function of a unique filtered state vector. Here, we use the filtered mixture fraction Z∼, filtered scalar dissipation rate χ∼, and the subgrid Reynolds number ReΔ as the filtered state vector. Conditional PDF’s of temperature P(T|Z∼,χ∼,ReΔ), species mass fractions P(Yi|Z∼,χ∼,ReΔ), and relevant thermodynamic and transport properties are tabulated as a function of Z∼, χ∼, and ReΔ. A thermo-chemical state library is then constructed in a manner directly analogous to the conventional flamelet-library approach. The potentially novel feature of this approach is that the relation between filtered and instantaneous quantities is known directly. This eliminates the need for a posteriori models that link these quantities. An a priori analysis of the proposed model was carried out for non-premixed combustion using measurements obtained from CH4/H2/N2 jet flames at a Reynolds numbers of 15,200. This flame exhibits an interesting range of Damköhler and Schmidt numbers through local extinction, reignition, and differential diffusion. Results show good quantitative agreement with measurements.

Turbulent fluctuations above the buffer layer of wall-bounded flows

The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Reτ≤2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are ‘attached’ in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at http://torroja.dmt.upm.es/ftp/channels/.

Effect of Mesoscale eddies on underwater sound propagation

The effects of sound speed variables induced by an anticyclonic eddy and a field of three cyclonic eddies on long-range sound propagation are investigated respectively. A deep-sea analytical eddy model [Henrick RF, Siegmann WL, Jacobson MJ. General analysis of ocean eddy effects for sound transmission applications. J Acoust Soc Am 1977;62:860–870] is used to determined sound speed distributions produced by warm-core ring in the southwest of South China Sea. Furthermore, the above analytical eddy model is generalize to include the azimuth angle variation and is used to determined sound speed distributions produced by Gulf Stream rings with different strengths. The theoretical temperature fluctuations induced by the warm eddy and a eddy field including three cyclonic eddies agree qualitatively with the in situ investigation data. The transmission loss of acoustic energy through the cross section of the warm-core ring center and three cyclonic eddy centers is simulated using 2-D parabolic-equation (PE) numerical modeling. It is found that the acoustic field has a significant change with variation of the location of SOFAR axis in the presence of the warm eddy and three cyclonic eddies comparing with the scenario of no eddies. When the source is located in the outside of the warm-core eddy and three cyclonic eddies respectively, and the receiver is located in outside of the eddy, the transmission loss as a function of range is investigated at different receive depth. It is shown that the changes of transmission loss caused by the warm-core eddy and three cyclonic eddies are as much as 20 dB than that of no-eddy situation. In the case of three cyclonic eddies, the largest discrepancy of transmission loss is about 40 dB near the range of 45 km for a 25-Hz source being located at a depth of 1500 m.

On the use of the notion of suitable weak solutions in CFD

AbstractThe notion of suitable weak solutions for the three‐dimensional incompressible Navier–Stokes equations together with some standard regularization techniques for constructing these solutions is reviewed. The novel result presented in this paper is that Faedo–Galerkin weak solutions to the Navier–Stokes equations are suitable provided they are constructed using finite‐dimensional spaces having a discrete commutator property and satisfying a proper inf–sup condition. Low‐order mixed finite element spaces appear to be acceptable for this purpose. Connections between the notion of suitable solutions and LES modeling are investigated. A proposal for a large eddy scale model based on the notion of suitable solutions is made and numerically illustrated. Copyright © 2008 John Wiley & Sons, Ltd.

Numerical simulation of low Mach number reacting flows

The explosion of a Type Ia supernova (SNIa) begins as a turbulent flame deep within a 1.4 solar-mass white dwarf. Initially the burning happens in the flamelet regime where turbulence serves only to wrinkle and fold an essentially laminar burning front. As the star expands and the flame moves outwards, however, it encounters regions of lower density. At ∼ 2 × 107 g cm-3, the flame transitions to a distributed burning regime. Here individual flamelets are disrupted by turbulent eddies, resulting in a fundamental change in the character of the burning. Detonation does not occur immediately because the turbulently broadened flamelets are still too thin. As the density declines further, however, each flamelet thickens and moves faster until only a few structures are contained within the ∼ 10 km integral scale of the SN turbulence. It is here that detonation may occur. We present simulations using both a three-dimensional low Mach number model and a one-dimensional linear eddy model to explore the structure of these flames and quantify their scaling behavior. Our results suggest that detonation may be possible at a density near 1.0 × 107 g cm-3.

Investigation of autoignition under thermal stratification using linear eddy modeling

The influence of thermal stratification on autoignition at constant volume and high pressure is investigated under turbulent conditions using the one-dimensional linear eddy model (LEM) and detailed hydrogen/air chemistry. Results are presented for the influence of initial temperature inhomogeneities on the heat release rate and the relative importance of diffusion and chemical reactions. The predicted heat release rates are compared with heat release rates of recent published studies obtained by two-dimensional direct numerical simulations (DNS). Using the definition of Chen et al. [Combust. Flame 145 (2006) 145–159] for the displacement speed of the H 2 mass fraction tracked at the location of maximum heat release, and a comparison of budget terms, different combustion modes including ignition-front propagation and deflagration waves are identified and the results are compared to the DNS data. The LEM approach shows qualitatively and quantitatively reasonable agreement with the DNS data over the whole range of investigated temperature fluctuations. The results presented in this work suggest that LEM is a potential candidate as a submodel for CFD calculations of HCCI engines.