LES validation of urban flow,part II: eddy statistics and flow structures

Time-dependent three-dimensional numerical simulations such as large-eddy simulation (LES) play an important role in fundamental research and practical applications in meteorology and wind engineering. Whether these simulations provide a sufficiently accurate picture of the time-dependent structure of the flow, however, is often not determined in enough detail. We propose an application-specific validation procedure for LES that focuses on the time dependent nature of mechanically induced shear-layer turbulence to derive information about strengths and limitations of the model. The validation procedure is tested for LES of turbulent flow in a complex city, for which reference data from wind-tunnel experiments are available. An initial comparison of mean flow statistics and frequency distributions was presented in part I. Part II focuses on comparing eddy statistics and flow structures. Analyses of integral time scales and auto-spectral energy densities show that the tested LES reproduces the temporal characteristics of energy-dominant and flux-carrying eddies accurately. Quadrant analysis of the vertical turbulent momentum flux reveals strong similarities between instantaneous ejection-sweep patterns in the LES and the laboratory flow, also showing comparable occurrence statistics of rare but strong flux events. A further comparison of wavelet-coefficient frequency distributions and associated high-order statistics reveals a strong agreement of location-dependent intermittency patterns induced by resolved eddies in the energy-production range. The validation concept enables wide-ranging conclusions to be drawn about the skill of turbulence-resolving simulations than the traditional approach of comparing only mean flow and turbulence statistics. Based on the accuracy levels determined, it can be stated that the tested LES is sufficiently accurate for its purpose of generating realistic urban wind fields that can be used to drive simpler dispersion models.     

Turbulent kinetic energy budgets in a model canopy: comparisons between LES and wind-tunnel experiments

A comparative study of turbulence in a wind-tunnel model canopy is performed, using Large eddy simulation (LES) and experimental data from PIV and hot-wire anemometry measurements. The model canopy is composed of thin cylindrical stalks. In the LES, these are represented using a plant-scale approach, while the scale-dependent Lagrangian dynamic model is used as subgrid-scale model. LES predictions of turbulence statistics and energy spectra are found to be in good agreement with the experimental data. Turbulent kinetic energy (TKE) budgets from the LES simulation are analyzed to provide more information absent in the measurements. Results confirm that sloshing motions at the low levels of the canopy are mainly driven by pressure fluctuations. A difference between the energy flux obtained from the energy spectrum and the SGS dissipation rate is observed, consistent with a spectral bypass mechanism in which the real spectral flux due to cascade is smaller than that implied by the energy-spectrum level, due to direct drain by the canopy.     

Simulation of Ekman Boundary Layers by Large Eddy Model with Dynamic Mixed Subfilter Closure

Theoretical analysis of boundary layer turbulence has suggested a feasibility of sufficiently accurate turbulence resolving simulations at relatively coarse meshes. However, large eddy simulation (LES) codes, which employ traditional eddy-viscosity turbulence closures, fail to provide adequate turbulence statistics at coarse meshes especially within a surface layer. Manual tuning of parameters in these turbulence closures may correct low order turbulence statistics but severely harms spectra of turbulence kinetic energy (TKE). For more than decade, engineering LES codes successfully employ dynamic turbulence closures. A dynamic Smagorinsky turbulence closure (DSM) has been already tried in environmental LES. The DSM is able to provide adequate turbulence statistics at coarse meshes but it is not completely consistent with the LES equations. This paper investigates applicability of an advanced dynamic mixed turbulence closure (DMM) to simulations of Ekman boundary layers of high Reynolds number flows. The DMM differs from the DSM by explicit calculation of the Leonard term in the turbulence stress tensor. The Horizontal Array Turbulence Study (HATS) field program has revealed that the Leonard term is indeed an important component of the real turbulence stress tensor. This paper presents validation of a new LES code LESNIC. The study shows that the LES code with the DMM provides rather accurate low order turbulence statistics and the TKE spectra at very coarse meshes. These coarse LES maintain more energetic small scale fluctuations of velocity especially within the surface layer. This is critically important for success of simulations. Accurate representation of higher order turbulence statistics, however, requires essentially better LES resolution. The study also shows that LES of the Ekman boundary layer cannot be directly compared with conventionally neutral atmospheric boundary layers. The depth of the boundary layer is an important scaling parameter for turbulence statistics.     

Embedded large eddy simulation approach for pollutant dispersion around a model building in atmospheric boundary layer

In the present article, the potential of embedded large eddy simulation (ELES) approach to reliably predict pollutant dispersion around a model building in atmospheric boundary layer is assessed. The performance of ELES in comparison with large eddy simulation (LES) is evaluated in several ways. These include a number of qualitative and quantitative comparisons of time-averaged and instantaneous results with wind tunnel measurements supplemented by statistical data analyses using scatter plots and standard evaluation metrics. Results obtained by both LES and ELES approaches show very good agreement with the experiment. However, addition of turbulence to mean flow at Reynolds averaged Navier–Stokes (RANS)–LES interface in ELES approach not only increases the turbulence intensity, it also results in larger values of turbulent kinetic energy (TKE) as well as a shorter reattachment length in the wake region. Accordingly, higher levels of TKE predicted by ELES increase the local intensity of concentration leading to shorter plume shapes as compared with LES. In general, ELES shows better agreement with experiment on the surfaces of model building and also in the downstream wake region. In terms of computational costs, the CPU time required to obtain statistical values in ELES is about 49 % lower than that of LES and the number of iterations per time step is also reduced by 55 % as compared with LES.     

Large-eddy simulation of turbulent flow and dispersion over a complex urban street canyon

Turbulent flow and dispersion characteristics over a complex urban street canyon are investigated by large-eddy simulation using a modified version of the Fire Dynamics Simulator. Two kinds of subgrid scale (SGS) models, the constant coefficient Smagorinsky model and the Vreman model, are assessed. Turbulent statistics, particularly turbulent stresses and wake patterns, are compared between the two SGS models for three different wind directions. We found that while the role of the SGS model is small on average, the local or instantaneous contribution to total stress near the surface or edge of the buildings is not negligible. By yielding a smaller eddy viscosity near solid surfaces, the Vreman model appears to be more appropriate for the simulation of a flow in a complex urban street canyon. Depending on wind direction, wind fields, turbulence statistics, and dispersion patterns show very different characteristics. Particularly, tall buildings near the street canyon predominantly generate turbulence, leading to homogenization of the mean flow inside the street canyon. Furthermore, the release position of pollutants sensitively determines subsequent dispersion characteristics.     

Numerical simulation of water mixing and renewals in the Barcelona harbour area: the winter season

In the present paper, we use numerical simulation to investigate currents, mixing and water renewal in Barcelona harbour under typical conditions of wind forcing for the winter season. This site is of particular importance due to the interplay between touristic and commercial activities, requiring detailed and high-definition studies of water quality within the harbour. We use Large Eddy Simulation (LES) which directly resolves the anisotropic and energetic large scales of motion and parametrizes the small, dissipative, ones. Small-scale turbulence is modelled by the anisotropic Smagorinsky model (ASM) to be employed in presence of large cell anisotropy. The complexity of the harbour is modelled using a combination of curvilinear, structured, non-staggered grid and the immersed boundary method. Boundary conditions for wind and currents at the inlets of the port are obtained from in-situ measurements. Analysis of the numerical results is carried out based on both instantaneous and time-averaged velocity fields. First- and second-order statistics, such as turbulent kinetic energy and horizontal and vertical eddy viscosities, are calculated and their spatial distribution is discussed. The study shows the presence of intense current in the narrow and elongated part of the harbour together with sub-surface along-shore elongated rolling structures (with a time scale of a few hours), and they contribute to the vertical water mixing. Time-averaged velocity field reveals intense upwelling and downwelling zones along the walls of the harbour. The analysis of second-order statistics shows strong inhomogeneity of turbulent kinetic energy and horizontal and vertical eddy viscosities in the horizontal plane, with larger values in the regions characterized by stronger currents. The water renewal within the port is quantified for particular sub-domain regions, showing that the complexity of the harbour is such that certain in-harbour basins have a water renewal of over five days, including the yacht marina area. The LES solution compares favourably with available current-meter data. The LES solution is also compared with a RANS solution obtained in literature for the same site under the same forcing conditions, the comparison demonstrating a large sensitivity of properties to model resolution and frictional parametrization.     

Comparison of atmospheric modelling systems simulating the flow,turbulence and dispersion at the microscale within obstacles

Three different modelling techniques to simulate the pollutant dispersion in the atmosphere at the microscale and in presence of obstacles are evaluated and compared. The Eulerian and Lagrangian approaches are discussed, using RAMS6.0 and MicroSpray models respectively. Both prognostic and diagnostic modelling systems are considered for the meteorology as input to the Lagrangian model, their differences and performances are investigated. An experiment from the Mock Urban Setting Test field campaign observed dataset, measured within an idealized urban roughness, is used as reference for the comparison. A case in neutral conditions was chosen among the available ones. The predicted mean flow, turbulence and concentration fields are analysed on the basis of the observed data. The performances of the different modelling approaches are compared and their specific characteristics are addressed. Given the same flow and turbulence input fields, the quality of the Lagrangian particle model is found to be overall comparable to the full-Eulerian approach. The diagnostic approach for the meteorology shows a worse agreement with observations than the prognostic approach but still providing, in a much shorter simulation time, fields that are suitable and reliable for driving the dispersion model.     

Performance analysis of WRF and LES in describing the evolution and structure of the planetary boundary layer

We implemented the Weather Research and Forecast (WRF) model and WRF Large-Eddy Simulation (WRF–LES), focusing on calculations for the planetary boundary layer (PBL), and compared the results against a data set of a well-documented campaign, in the Houston–Galveston area, Texas, in summer 2006. A methodology using WRF in a mesoscale and LES was implemented to assess the performance of the model in simulating the evolution and structure of the PBL over Houston during the Vertical Mixing Experiment. Also, the WRF model in a real case mode was examined to explore potential differences between the results of each simulation approach. We analyzed both WRF results for key meteorological parameters like wind speed, wind direction and potential temperature, and compared the model results against the observations. The reasonably good agreement of LES results forced with observed surface fluxes provides confidence that LES describes turbulence quantities such as turbulent kinetic energy correctly and warrants further turbulence structure analysis. The LES results indicate a weak but noticeable nighttime turbulent kinetic energy which was produced by wind shear in Houston’s planetary boundary layer and which may likely be related to intermittent turbulence. This is supported by observations made at the University of Houston Moody Tower air quality station when intermittent peaks of carbon monoxide occurred in the evening, although the variability in wind conditions was very little.     

Evaluation of SWAT sub-daily runoff estimation at small agricultural watershed in Korea

A study was undertaken for the prediction of runoff flow from 0.8 ha field-sized agricultural watershed in South Korea using Soil and Water Assessment Tool (SWAT) sub-daily. The SWAT model with sub-daily configuration predicted flow from the watershed within the range of acceptable accuracy. The SWAT sub-daily simulations were carried out for a total of 18 rainfall events, 9 each for calibration and validation. Overall trend and extent of matching simulated flow for the rainfall events in 2007-2008 with measured data during the calibration process were coefficient of determination (R²) value of 0.88 and Nash and Sutcliffe Efficiency (E_NS) value of 0.88. For validation, R² and E_NS values were 0.9 and 0.84, respectively. Whereas R² and E_NS values for simulation results using daily rainfall data were 0.79 and -0.01, respectively, that were observed to be out of acceptable limits for the model simulation. The importance of higher time resolution (hourly) precipitation records for flow simulation were evaluated by comparing R² and E_NS with 15 min, 2 h, 6 h and 12 h precipitation data, which resulted in lower statistics with increases in time resolution of precipitation data. The SWAT sub-daily sensitivity analysis was performed with the consideration of hydraulic parameter and was found as in the rank order of CN2 (curve number), ESCO (soil evaporation compensation factor), GW_DELAY (ground water delay time), ALPHA_BF ( base flow alpha factor), GWQMN ( a threshold minimum depth of water in the shallow aquifer required for return flow to occur) , REVAPMN (minimum depth of water in shallow aquifer for re-evaporation to occur) , LAT_TIME (lateral flow travel time) respectively. These sensitive parameters were evaluated at 10% higher and lower values of the parameters, corresponding to 70.5% higher and 23.2% lower in simulated flow out from the SWAT model. From the results obtained in this study, hourly precipitation record for SWAT sub-daily with Green-Ampt infiltration method was proven to be efficient for runoff estimation at field sized watershed with higher accuracies that could be efficiently used to develop site-specific Best Management Practices (BMPs) considering rainfall intensity, rather than simply using daily rainfall data.     

Alternating skimming flow over a stepped spillway

The study of stepped spillways in laboratory scales has been essentially focused on two separated sub-regimes within skimming flow. In this paper we investigate the appearance of an unclassified alternating skimming flow regime in a 0.5 m wide stepped spillway which does not fit on these earlier definitions, and which does not occur in a 0.3 m wide spillway. Our aim is to explain the genesis of this unclassified flow which is visualised in the physical stepped spillway, by using 3D numerical modelling. Flow depths and velocities are measured using an ultrasonic sensor and Bubble Image Velocimetry in the wider flume (0.5 m). The numerical model is validated with the experimental data from the 0.5 m wide spillway. After validation, the channel width of the same numerical model is reduced to 0.3 m wide spillway in order to characterise (compare) the case without (with) alternating skimming flow. Both cases are solved using Reynolds-Averaged Navier–Stokes equations together with the Volume-of-Fluid technique and SST k-\(\omega\) turbulence model. The experimental results reveal that the alternating skimming flow regime is characterised by an evident seesaw pattern of flow properties over consecutive steps. In turn, the numerical modelling clarified that this seesaw pattern is due to the presence of a complex system of cross waves along the spillway. These cross waves are also responsible for a mass and momentum exchange in the transversal direction and for the formation of the alternating skimming flow in the spillway.     

Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways

We present and discuss the results of a comprehensive study addressing the non-aerated region of the skimming flow in steep stepped spillways. Although flows in stepped spillways are usually characterized by high air concentrations concomitant with high rates of energy dissipation, the non-aerated region becomes important in small dams and/or spillways with high specific discharges. A relatively large physical model of such spillway was used to acquire data on flow velocities and water levels and, then, well-resolved numerical simulations were performed with a commercial code to reproduce those experimental conditions. The numerical runs benefited from the ability of using multi-block grids in a Cartesian coordinate system, from capturing the free surface with the TruVOF method embedded in the code, and from the use of two turbulence models: the k-e{k{-}\varepsilon} and the RNGk-e{k{-}\varepsilon} models. Numerical results are in good agreement with the experimental data corresponding to three volumetric flow rates in terms of the time-averaged velocities measured at diverse steps in the spillway, and they are in very satisfactory agreement for water levels along the spillway. In addition, the numerical results provide information on the turbulence statistics of the flow. This work also discusses important aspects of the flow, such as the values of the exponents of the power-law velocity profiles, and the characteristics of the development of the boundary layer in the spillway.     

Large eddy simulation of flow and scalar transport in a vegetated channel

Predicting flow and mass transport in vegetated regions has a broad range of applications in ecology and engineering practice. This paper presents large eddy simulation (LES) of turbulent flow and scalar transport within a fully developed open-channel with submerged vegetation. To properly represent the scalar transport, an additional diffusivity was introduced within the canopy to account for the contribution of stem wakes, which were not resolved by the LES, to turbulent diffusion. The LES produced good agreement with the velocity and concentration fields measured in a flume experiment. The simulation revealed a secondary flow distributed symmetrically about the channel centerline, which differed significantly from the circulation in a bare channel. The secondary circulation accelerated the vertical spread of the plume both within and above the canopy layer. Quadrant analysis was used to identify the form and shape of canopy-scale turbulent structures within and above the vegetation canopy. Within the canopy, sweep events contributed more to momentum transfer than ejection events, whereas the opposite occurred above the canopy. The coherent structures were similar to those observed in terrestrial canopies, but smaller in scale due to the constraint of the water surface.     

A stochastic Lagrangian micromixing model for the dispersion of reactive scalars in turbulent flows: role of concentration fluctuations and improvements to the conserved scalar theory under non-homogeneous conditions

Several reaction schemes, based on the conserved scalar theory, are implemented within a stochastic Lagrangian micromixing model to simulate the dispersion of reactive scalars in turbulent flows. In particular, the formulation of the reaction-dominated limit (RDL) reaction scheme is here extended to improve the model performance under non-homogeneous conditions (NHRDL scheme). The validation of the stochastic model is obtained by comparison with the available measurements of reactive pollutant concentrations in a grid-generated turbulent flow. This test case describes the dispersion of two atmospheric reactant species (NO and O₃) and their reaction product (NO₂) in an unbounded turbulent flow. Model inter-comparisons are also assessed, by considering the results of state-of-the-art models for pollutant dispersion. The present validation shows that RDL reaction scheme provides a systematic overestimation (relative error of ca. 85% around the centreline) in computing the local reactant consumption/production rate, whereas the NHRDL scheme drastically reduces this gap (relative error lower than 5% around the centreline). In terms of NO₂ production (or reactant consumption), neglecting concentration fluctuations determines overestimations of the product mean of around 100% and a NO₂ local production of one order of magnitude higher than the reference simulation. In terms of standard deviations, the concentration fluctuations of both the passive and reactive scalars are generally of the same order of magnitude or up to 1 or 2 orders of magnitudes higher than the corresponding ensemble mean values, except for the background reactant close to the plume edges. The study highlights the importance of modelling pollutant reactions depending on the instantaneous instead of the mean concentrations of the reactants, thus quantifying the role of the turbulent fluctuations of concentration, in terms of scalar statistics (mean, standard deviation, intensity of fluctuations, skewness and kurtosis of concentration, segregation coefficient, simulated reaction rate). This stochastic particle method represents an efficient numerical technique to solve the convection–diffusion equation for reactive scalars and involves several application fields: micro-scale air quality (urban and street-canyon scales), accidental releases, impact of odours, water quality and fluid flow industrial processes (e.g. combustion).     

Mass exchange in a shallow channel flow with a series of groynes: LES study and comparison with laboratory and field experiments

The exchange of dissolved matter between a straight open channel and a series of shallow embayments present at one of its sides is investigated using large eddy simulation (LES). The direct link between the mechanism of mass exchange and the dynamics of coherent structures is demonstrated. It is shown that for the geometrical configuration considered in the present study, the mass exchange process is very non-uniform over the depth in the vicinity of the channel–embayment interface. Most of the contaminant is ejected from the embayments close to the free surface. The amount of contaminant re-entrained into the embayments situated downstream of the one in which contaminant was introduced is quantified. The mass exchange coefficient predicted by LES does not vary significantly with the embayment rank and is in very good agreement with the one predicted by the model proposed by Weitbrecht et al. (J Hydraul Eng 134(2):173–183, 2008) based on the value of a dimensionless morphometric groyne-field parameter. Field experiments were purposely performed in a natural stream with embayments whose length over width ratios were close to the ratio in the LES study. The concentration fields predicted by LES are compared with video-records of colored dye used to visualize the mass exchange in the field experiment. It is shown that, for both LES and the field experiment, the dominant passage frequency of the eddies inside the interfacial mixing layer is well predicted by the analytical model of Sukhodolov and Sukhodolova (in: Cowen et al (eds) Hydraulic measurements & experimental methods. Proceedings of international conference, Lake Placid, USA, pp 172–177, 2007). The model is then used to scale the time in the LES animations and field video-records showing the temporal evolution of the concentration field. The results of the comparison indicate several similarities in the mixing process, despite the differences in the bathymetry and the large difference in the Reynolds number between LES and the field experiment. This proves the usefulness of performing detailed LES and laboratory studies in well-controlled environments to understand mass-exchange processes around river groyne fields.     

Hierarchical modeling of the dilute transport of suspended sediment in open channels

We propose, discuss and validate a theoretical and numerical framework for sediment-laden, open-channel flows which is based on the two-fluid-model (TFM) equations of motion. The framework models involve mass and momentum equations for both phases (sediment and water) including the interactive forces of drag, lift, virtual mass and turbulent dispersion. The developed framework is composed by the complete two-fluid model (CTFM), a partial two-fluid model (PTFM), and a standard sediment-transport model (SSTM). Within the umbrella of the Reynolds-Averaged Navier-Stokes (RANS) equations, we apply K–ε type closures (standard and extended) to account for the turbulence in the carrier phase (water). We present the results of numerical computations undertaken by integrating the differential equations over control volumes. We address several issues of the theoretical models, especially those related to coupling between the two phases, interaction forces, turbulence closure and turbulent diffusivities. We compare simulation results with various recent experimental datasets for mean flow variables of the carrier as well as, for the first time, mean flow of the disperse phase and turbulence statistics. We show that most models analyzed in this paper predict the velocity of the carrier phase and that of the disperse phase within 10% of error. We also show that the PTFM provides better predictions of the distribution of sediment in the wall-normal direction as opposed to the standard Rousean profile, and that the CTFM is by no means superior to the PTFM for dilute mixtures. We additionally report and discuss the values of the Schmidt number found to improve the agreement between predictions of the distribution of suspended sediment and the experimental data.     

Study on the concentration distribution in a trapezoidal open-channel flow with a side discharge

The number and distribution of pollutant concentration in a trapezoidal open channel flow with a side discharge is calculated and effects of the bank gradient are investigated in this paper. A sigma-coordinate water quality numerical model is used to simulate the process of both water and pollutant transportation in the trapezoidal channel open flow. The diffusion coefficient used in the prediction is determined by two methods including constant coefficient and the depth-averaged k-epsilon turbulence closure model. The change of the concentration with the bank gradient is acquired based on the simulation of cases with different bank gradients. An analytical formula is derived by using the mirror image method and related diffusion theories, ignoring the discharge momentum and the influence of the opposite bank. The formula can predict the number and distribution of pollutant concentration with some acceptable errors. The results demonstrate that the bank gradient has great influence on the concentration distribution which will decrease with the increase of the bank gradient approximately following a hyperbolic law.     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

Modeling the buoyant flow of heated water discharged from surface and submerged side outfalls in shallow and deep water with a cross flow

In this study, a three-dimensional model was used to numerically study the buoyant flow, along with its mixing characteristics, of heated water discharged from the surface and submerged side outfalls in shallow and deep water with a cross flow. Hydraulic experimental data were used to evaluate the applicability of the model. The simulation results agree well with the experimental results, particularly, the jet trajectories, the dimensions of the recirculating zone, and the distribution of the dimensionless excess temperature. The level of accuracy of the simulation results of the present study is nearly identical to that of the results conducted by McGuirk and Rodi (1978). If the heated water is discharged into shallow water where the momentum flux ratio and the discharge densimetric Froude number are high, the submerged discharge method is better than the surface discharge method in terms of the scale of the recirculating zone and the minimum dilution. In deep water, where the momentum flux ratio and discharge densimetric Froude number are low, however, the submerged discharge method had few advantages. In shallow water, the discharge jet is deflected by the ambient cross flow, while forcing the ambient flow to bend towards the far bank for the full depth. For a submerged discharge in shallow water, the recirculating zone is the largest in the lowest layer but becomes smaller in the upper layer. As the water depth increases, the ambient flow goes over the jet and diminishes the blocking effect, thereby decreasing the bending of the jet.