Application of the k–ε turbulence model to the high Reynolds number skimming flow field of an urban street canyon

A two-dimensional, steady, k–ε turbulence model was used to investigate the high Reynolds number skimming flow field of an urban street canyon. We describe the critical canyon width-to-height ratios that distinguish a cascade of vortex patterns that form in an urban street canyon. Details of the flow field are reported that includes the structure of the mean flow field, turbulent kinetic energy, turbulent length scale, turbulent eddy viscosity, and Reynolds stress for three typical different aspect ratios, W/H, of a street canyon. The consequences of vortex layering on vertical transport are explored.     

Turbulence effects on chemical reactions in smog chamber flows

Turbulent mixing effects on the reaction rate of a non-premixed flow are presented for a moderately slow second-order irreversible chemical reaction. The turbulent mixing process leads to inhomogeneities in the concentration of the reactants. Chemical reactions are normally highly non-linear and large errors can result from using average concentrations in the computation of mean reaction rates. A brief review of the literature on this problem and its application areas is made with particular emphasis placed on near isothermal flows where the fluctuation in the reaction rate constant can be neglected. The reaction between mixing air jets containing dilute nitric oxide, NO, and ozone, O₃, is studied in a large Turbulent Smog Chamber (TSC) under conditions of high Reynolds number, three-dimensional flow. The measured reactant concentrations, obtained with good time and space resolution, are used to investigate the effects of the reactant species concentration fluctuations on the mean reactant species concentration field through their contribution to the mean reaction rate. Two flow geometries have been studied: two opposed jets issuing into a large chamber and a plume-like source issuing into a turbulent background flow. A three-dimensional finite-difference computation has been carried out for the flow in the chamber using the k-ε-g model of turbulence and mixing. The reacting species concentration field is calculated by considering the transport of a ‘perturbation variable’ equal to the mean of the difference between the species concentration and its corresponding fast chemistry value. A closure for the mean chemical reaction rate based on this quantity is presented and its experimental validation discussed.     

Turbulent Schmidt numbers for CFD analysis with various types of flowfield

The application of CFD (computational fluid dynamics) using RANS (Reynolds-averaged Navier–Stokes equations) model to turbulent flows with mass transfer generally estimates the turbulent scalar flux assuming the gradient diffusion hypothesis, which requires definition of the turbulent Schmidt number, Sc_t However, no universal value of Sc_t has been established and empirical values have been used in different studies. In this paper, previous research related to the application of optimum values of Sc_t for engineering flowfields relevant to atmospheric dispersion is reviewed. The optimum values for Sc_t are widely distributed in the range of 0.2–1.3 and the specific value selected has a significant effect on the prediction results. On the basis of the present study results and since the optimum values of Sc_t largely depend on the local flow characteristics, it is recommended that Sc_t should be determined by considering the dominant flow structure in each case.     

Numerical simulation of dispersion around an isolated cubic building: Comparison of various types of k–ɛ models

Prediction accuracy of flow and dispersion around a cubic building with a flush vent located on its roof was examined using various k–? models, and numerical results were compared with wind-tunnel data. Four types of turbulence models, i.e., the standard k–? model, the RNG k–? model, the k–? model with Launder and Kato modification and the Realizable k–? model were compared in this study. The standard k–? model provided inadequate results for the concentration field, because it could not reproduce the basic flow structure, such as the reverse flow on the roof. However, revised k–? models provided concentrations in better agreement with the experimental data. The effect of an oblique wind angle and vent locations on the prediction accuracy was also investigated. It was confirmed that the prediction accuracy of the velocity field strongly affected that of the concentration field. The RNG model showed general agreement with the experiment, and was the best of the turbulence models tested. However, it becomes clear that the results for all CFD models show poor prediction accuracy of concentration distribution at the side and leeward surfaces of the building since they all underestimate the concentration diffusion on these regions. The concentrations predicted by all CFD models were less diffusive than those of the experiment.     

Experimental and numerical study of wind flow behind windbreaks

The shelter effect of a windbreak protects aggregate piles and provides a reduction of particle emissions in harbours. RANS (Reynolds-averaged Navier–Stokes equations) simulations using three variants of k–ε (standard k–ε, RNG k–ε and realizable k–ε) turbulence closure models have been performed to analyse wind flow characteristics behind an isolated fence located on a flat surface without roughness elements. The performance of the three turbulence models has been assessed by wind tunnel experiments. Cases of fences with different porosities (φ) have been evaluated using wind tunnel experiments as well as numerical simulations. The aim is to determine an optimum porosity for sheltering effect of an isolated windbreak. A value of 0.35 was found as the optimum value among the studied porosities (φ=0, 0.1, 0.24, 0.35, 0.4, 0.5).     

Strategic guidelines for street canyon geometry to achieve sustainable street air quality

This paper is concerned with the motion of air within the urban street canyon and is directed towards a deeper understanding of pollutant dispersion with respect to various simple canyon geometries and source positions. Taking into account the present days typical urban configurations, three principal flow regimes “isolated roughness flow”, “skimming flow” and “wake interference flow” (Boundary Layer Climates, 2nd edition, Methuen, London) and their corresponding pollutant dispersion characteristics are studied for various canopies aspect ratios, namely relative height (h₂/h₁), canyon height to width ratio (h/w) and canyon length to height ratio (l/h). A field-size canyon has been analyzed through numerical simulations using the standard k-ε turbulence closure model. It is found that the pollutant transport and diffusion is strongly dependent upon the type of flow regime inside the canyon and exchange between canyon and the above roof air. Some rules of thumbs have been established to get urban canyon geometries for efficient dispersion of pollutants.     

Strategic guidelines for street canyon geometry to achieve sustainable street air quality

This paper is concerned with the motion of air within the urban street canyon and is directed towards a deeper understanding of pollutant dispersion with respect to various simple canyon geometries and source positions. Taking into account the present days typical urban configurations, three principal flow regimes “isolated roughness flow”, “skimming flow” and “wake interference flow” (Boundary Layer Climates, 2nd edition, Methuen, London) and their corresponding pollutant dispersion characteristics are studied for various canopies aspect ratios, namely relative height (h₂/h₁), canyon height to width ratio (h/w) and canyon length to height ratio (l/h). A field-size canyon has been analyzed through numerical simulations using the standard k-ε turbulence closure model. It is found that the pollutant transport and diffusion is strongly dependent upon the type of flow regime inside the canyon and exchange between canyon and the above roof air. Some rules of thumbs have been established to get urban canyon geometries for efficient dispersion of pollutants.     

Influence of wall roughness on the dispersion of a passive scalar in a turbulent boundary layer

Many towns and cities consist of similarly sized buildings in relatively regular arrangements with smaller scale roughness elements such as roofs, chimneys and balconies. The objective of this study is to investigate how small scale roughness elements modify the influence of the large scale organized roughness on the dispersion of a passive scalar in a turbulent boundary layer. Wind tunnel experiments were performed using a passive tracer released from a line source and concentration profiles were measured with a Flame Ionisation Detector. The measurements are compared with numerical solutions of the advection–diffusion equation.The results show that decreasing the cavity aspect ratio increases the turbulent vertical mass fluxes, and that the small scale roughness enhances these fluxes, but only in the skimming flow regime. Numerical simulations showed that outside the roughness sub-layer (RSL) the changes in surface roughness could be accounted for by a simple variation of the friction velocity, but inside the RSL the spatial variability of the flow imposed by the roughness elements has much more influence. A simple model for a spatially averaged dispersion coefficient in the RSL has been developed and is shown to agree satisfactorily with the concentrations measured in these experiments.     

Modeling reactive pollutant dispersion in an urban street canyon

Reactive pollutant dispersion in an urban street canyon with a street aspect ratio of one is numerically investigated using a computational fluid dynamics (CFD) model. The CFD model developed is a Reynolds-averaged Navier–Stokes equations (RANS) model with the renormalization group (RNG) k–ε turbulence model and includes transport equations for NO, NO₂, and O₃ with simple photochemistry. An area emission source of NO and NO₂ is considered in the presence of background O₃ and street bottom heating (ΔT=5 °C) with an ambient wind perpendicular to the along-canyon direction. A primary vortex is formed in the street canyon and the line connecting the centers of cross-sectional vortices meanders over time and in the canyon space. The cross-canyon-averaged temperature and reactive pollutant concentrations oscillate with a period of about 15 min. The averaged temperature is found to be in phase with NO and NO₂ concentrations but out of phase with O₃ concentration. The photostationary state defect is small in the street canyon except for near the roof level and the upper downwind region of the canyon and its local minimum is observed near the center of the primary vortex. The budget analysis of NO (NO₂) concentration shows that the magnitude of the advection or turbulent diffusion term is much larger (larger) than that of the chemical reaction term and that the advection term is largely balanced by the turbulent diffusion term. On the other hand, the budget analysis of O₃ concentration shows that the magnitude of the chemical reaction term is comparable to that of the advection or turbulent diffusion term. The inhomogeneous temperature distribution itself affects O₃ concentration to some extent due to the temperature-dependent photolysis rate and reaction rate constant.     

Unsteady absorption of sulfur dioxide by an atmospheric water droplet with internal circulation

Unsteady absorption characteristics of sulfur dioxide by an atmospheric water droplet in motion are predicted numerically and analyzed theoretically to recognize the physical mass transport processes inside an aerosol droplet, which is frequently encountered in the atmosphere. Considering the absorption of sulfur dioxide by a droplet in cloud or fog with various velocities, three different Reynolds numbers, viz., Re_g=0.643, 1.287, and 12.87 are studied and compared with each other. The results indicate that for the Reynolds number of 0.643, sulfur dioxide always penetrates toward the droplet centerline throughout the entire absorption period. This is due to the mass transfer dominated by diffusion along the radial direction. In contrast, when the Reynolds number is 12.87, the strength of the vortex motion inside the droplet is strong enough. It results in that, most of the time the concentration contours parallel the streamlines and the lowest SO₂ concentration is located at the vortex center. As a consequence, the diffusion distance is reduced by a factor of three and the absorption time for the droplet reaching the saturated state is shortened in a significant way. With regard to an intermediate Reynolds number such as 1.287, a two-stage mass transfer process can be clearly identified. In the first stage, it is dominated by one-dimensional diffusion, in which over 50% sulfur dioxide is absorbed before the saturated state is reached. In the second stage, the vortex motion mainly controls the mass transfer. However, the contour core is inconsistent with the vortex center. This is because the characteristic time of mass diffusion is in a comparable state with that of droplet internal circulation. The present study elucidates that the strength of a droplet's internal motion plays a vital role in determining SO₂ absorption process.     

The effect of humidity and state of water surfaces on deposition of aerosol particles onto a water surface

Deposition processes of particles with dry diameter larger than about 10 μm are dominated by gravitational settling, while molecular diffusion and Brownian motion predominate the deposition processes of particles smaller than 0.1 μm in dry diameter. Many air pollution derived elements exhibit characteristics common to sub-micron particles. The objective of the present study is to examine the effects of meteorological conditions within the turbulent transfer layer on the deposition velocity of particles with dry diameter between 0.1 and 1 μm. It is for these sub-micron particles that particle growth by condensation in the deposition layer, the broken water surface effect and the enhanced transfer process due to atmospheric turbulence in the turbulent transfer layer play important roles in controlling the particle deposition velocity. Results of the present study show that the `dry air’ assumption of Williams’ model is unrealistic. Effects of ambient air relative humidity and water surface temperature cannot be ignored in determining the deposition velocity over a water surface. Neglecting effects of ambient air relative humidity and water surface temperature will result in defining atmospheric stability incorrectly. It is found that the largest effect of air relative humidity on deposition velocity occurs at an air–water temperature difference corresponding to the point of `displaced neutral stability'. For a given wind speed of U=5 m s⁻¹ the additive effects of water surface temperature, T_w, changes from 5 to 25°C and ambient air relative humidity variations from 85 to 60%, respectively, lead to a maximum difference in v_d of about 20%. For a higher wind speed of 10 m s⁻¹, however, the corresponding change in v_d reduces to less than 5%. This is further confirmation that wind speed is one of the strongest variables that governs the magnitude of v_d. The present study also found that the broken surface transfer coefficient, k_bs, given as a multiple of the smooth surface transfer coefficient, k_ss, is physically more meaningful than assigning it a constant value independent of particle size. The method used in this study requires only a single level of atmospheric data coupled with the surface temperature measurement. The present method is applicable for determining deposition velocity not only at the conventional measurement height of 10 m but also at any other heights that are different from the measurement height.     

CFD modelling of small particle dispersion: The influence of the turbulence kinetic energy in the atmospheric boundary layer

When considering the modelling of small particle dispersion in the lower part of the Atmospheric Boundary Layer (ABL) using Reynolds Averaged Navier Stokes simulations, the particle paths depend on the velocity profile and on the turbulence kinetic energy, from which the fluctuating velocity components are derived to predict turbulent dispersion. It is therefore important to correctly reproduce the ABL, both for the velocity profile and the turbulence kinetic energy profile.For RANS simulations with the standard k–ε model, Richards and Hoxey (1993. Appropriate boundary conditions for computational wind engineering models using the k–ε turbulence model. Journal of Wind Engineering and Industrial Aerodynamics 46–47, 145–153.) proposed a set of boundary conditions which result in horizontally homogeneous profiles. The drawback of this method is that it assumes a constant profile of turbulence kinetic energy, which is not always consistent with field or wind tunnel measurements. Therefore, a method was developed which allows the modelling of a horizontally homogeneous turbulence kinetic energy profile that is varying with height.By comparing simulations performed with the proposed method to simulations performed with the boundary conditions described by Richards and Hoxey (1993. Appropriate boundary conditions for computational wind engineering models using the k–ε turbulence model. Journal of Wind Engineering and Industrial Aerodynamics 46–47, 145–153.), the influence of the turbulence kinetic energy on the dispersion of small particles over flat terrain is quantified.     

A numerical study of interacting buoyant cooling-tower plumes

The compact design of mechanical cooling towers necessitates that the plumes are issued into the cross-wind in close proximity. An improved understanding of the interaction of adjacent plumes is therefore required for better design of such cooling towers, which may lead to a reduction in their environmental impact. This paper presents the results of a numerical investigation into the interaction of two adjacent plumes in a cross-flow. The numerical model simulates small-scale wind tunnel experiments of a cooling tower arrangement. The computations are performed for three-dimensional, turbulent, buoyant and interacting plumes, and for a single plume for comparison. Two double-source arrangements, namely, tandem and side-by-side, with respect to the oncoming atmospheric boundary layer are considered. A low Reynolds number k–ε turbulence model is used with two discretisation schemes, hybrid and QUICK, and the results are compared. Comparisons are also made with the experimental results. The results show that the interaction of side-by-side plumes is dominated by the interaction of the rotating vortex pairs within the plumes. A tandem source arrangement leads to early merging and efficient rise enhancement. Comparisons of the predicted results with experimental data show good agreement for the plume rise.     

Flamelet modeling of NO formation in laminar and turbulent diffusion flames

The applicability of the laminar flamelet concept for the formation and destruction of nitric oxides in laminar and turbulent diffusion flames has been studied. In a first step, temperatures and species concentrations in an axisymmetric laminar diffusion flame have been calculated (i) by solving the detailed conservation equations and (ii) by applying the laminar flamelet concept. The main purpose of this step was the identification of differences between results from both approaches. It turned out that for highly temperature sensitive or relatively slow chemical processes, the inclusion of the full range of the prevailing scalar dissipation rates plays a major role for the calculated species concentrations. This behavior is obvious from the concept of the laminar flamelet model, where the scalar dissipation rate can be discussed in terms of the reciprocal of a residence time for attaining chemical equilibrium. In a second step, flamelet modeling of NOx formation was extended to a turbulent hydrogen diffusion flame. In both the steps, the flow fields of the flames were calculated by solving the Navier-Stokes equations in axisymmetric formulation using the SIMPLER algorithm. For the turbulent flow, Favre-averaged equations have been used and turbulence was modeled with the standard k-epsilon model including a correction term for axisymmetric systems. The averaging of the species concentrations was accomplished with presumed shape probability density functions (pdfs). The pdf of the mixture fraction was described with a beta-function whereas that of the scalar dissipation rate was assumed to be log-normal. Buoyancy effects have been taken into account. The calculated temperatures and concentrations were compared with data from different experiments.     

On the correlation of air and pollutant exchange for street canyons in combined wind-buoyancy-driven flow

The ventilation and pollutant transport in a two-dimensional (2D) street canyon of building-height-to-street-width (aspect) ratio h/b = 1 under different unstable stratifications were examined. To characterize the combined wind-buoyancy-driven flow and pollutant transport at different Richardson number Ri, a computational fluid dynamics (CFD) model based on the Reynolds-averaged Navier–Stokes (RANS) equations with the Renormalization Group (RNG) k ? ε turbulence model was adopted. Unlike the isothermal condition, a secondary recirculation is initiated at the ground-level windward corner of the street canyon once the unstable stratification is switched on (Ri < 0). It traps the ground-level pollutant leading to elevated pollutant concentration there. As Ri further decreases, the enlarging secondary recirculation enables direct pollutant removal from its core to the shear layer that offsets the ground-level pollutant accumulation. The ventilation and pollutant removal performance under different unstable stratifications are compared by the air (ACH) and pollutant (PCH) exchange rates, and pollutant retention time (τ). Both the mean and turbulent components of ACH are found to increase with decreasing Ri, suggesting that unstable stratification promotes ventilation in street canyons. Moreover, the CFD results agree well with our theoretical model that ACH² varies linearly with Ri. Turbulent transport originally dominates the pollutant removal under isothermal condition. However, progressive domination of pollutant removal by mean wind can be observed with decreasing stability (decreasing Ri from 0 to ?10.6). The critical value is estimated to be Ri = ?8, below which mean wind is the major pollutant removal carrier. Reduction in τ is also observed with decreasing Ri. Hence, in unstable stratification, pollutant resides shorter time in the street canyon compared with its isothermal counterpart, and the ventilation and pollutant removal are more favorable.     

Wind tunnel investigation on the retention of air pollutants in three-dimensional recirculation zones in urban areas

The article discusses an experimental investigation of turbulent dispersion processes in a typical three-dimensional urban geometry, in reduced scale, in neutrally stable conditions. Wind tunnel experiments were carried out for characterizing the flow and the dispersion of a pollutant around a scaled model (1:400) of a group of eight 10-floor buildings surrounding a square. The situation corresponded to the dispersion of fine inertialess particles released from a line source positioned upstream of the urban geometry. After the sudden interruption of the source generation, the particles persisted in the recirculation cavity between the buildings, with the concentration decaying exponentially with time. This is in accordance with previous works on the dispersion process around bluff bodies of different shapes [e.g., Humphries and Vincent, 1976. An experimental investigation of the detention of airborne smoke in the wake bubble behind a disk. Journal of Fluid Mechanics 73, 453–464; Vincent, 1977. Model experiments on the nature of air pollution transport near buildings. Atmospheric Environment 11, 765–774; Fackrell, 1984. Parameters characterizing dispersion in the near wake of buildings. Journal of Wind Engineering and Industrial Aerodynamics 16, 97–118]. The main parameter in the investigation was the characteristic time constant for the concentration decay. The measurements of the variation in the concentration of the fine particles were performed by means of a photo-detection technique based on the attenuation of light. The velocity fields were evaluated with the particle image velocimetry (PIV) technique. The dimensionless residence time H for the particles (H=τU/L, where τ is the time constant for the concentration decay, U the free-stream velocity, and L is a characteristic dimension for the urban geometry, as defined by Humphries and Vincent [1976. An experimental investigation of the detention of airborne smoke in the wake bubble behind a disk. Journal of Fluid Mechanics 73, 453–464] was determined for various locations in the scaled model, in the range of Reynolds numbers (Re) between 8000 and 64,000. H was found to be 6.5±1.0.     

Flow and dispersion in an urban cubical cavity

Flow and dispersion in an urban cubical cavity are numerically investigated using a Reynolds-averaged Navier–Stokes equations (RANS) model with the renormalization group (RNG) k–? turbulence closure model. The urban cubical cavity is surrounded by flank walls that are parallel to the streamwise direction, called end-walls, as well as upstream and downstream walls. A primary vortex and secondary vortices including end-wall vortices are formed in the cavity. Because of the end-wall drag effect, the averaged mean-flow kinetic energy in the cavity is smaller than that in an urban street canyon that is open in the along-canyon direction. A trajectory analysis shows that the end-wall vortices cause fluid particles to move in the spanwise direction, indicating that flow in the cavity is essentially three-dimensional. The iso-surfaces of the Okubo–Weiss criterion capture cavity vortices well. The pollutant concentration is high near the bottom of the upstream side in the case of continuous pollutant emission, whereas it is high near the center of the primary vortex in the case of instantaneous pollutant emission. To get some insight into the degree of pollutant escape from the cavity according to various meteorological factors, extensive numerical experiments with different ambient wind speeds and directions, inflow turbulence intensities, and cavity-bottom heating intensities are performed. For each experiment, we calculate the time constant, which is defined as the time taken for the pollutant concentration to decrease to e^?1 of its initial value. The time constant decreases substantially with increasing ambient wind speed, and tends to decrease with increasing inflow turbulence intensity and cavity-bottom heating intensity. The time constant increases as the ambient wind direction becomes oblique. High ambient wind speed is found to be the most crucial factor for ventilating the cavity, thus improving air quality in an urban cubical cavity.     

Prediction of gas diffusion in complicated terrain by a potential flow model

A numerical model was developed to simulate gaseous diffusion in complicated terrain. This model calculates the air flow as a potential flow by the Boundary Element Method, and gaseous diffusion by an analytical Gaussian equation in the potential flow. Plume spreads σ_y and σ_z are modified by multiregression equations derived from wind tunnel experiments, and the terrain height is elongated depending on the atmospheric stability.First, tracer data from Cinder Cone Butte in the U.S. measured by the U.S.-EPA were predicted by the model in order to examine the prediction accuracy under stable conditions. The averaged ratio of the observed concentration to predicted concentration for 12 runs was better than a factor of 10. Next, tracer data from the Geysers area in the U.S. measured by the U.S.-DOE were used to examine the prediction accuracy under neutral conditions. The ratio of the observed concentration to predicted concentration for two runs under neutral conditions was better than factor of two at most locations, but prediction capability is poor in blocked or separated flow conditions.     

Kinetic study of the OH reaction with some hydrochloroethers under simulated atmospheric conditions

Using the relative rate technique, rate constants for the gas-phase reactions of hydroxyl radicals with 2-chloroethyl methyl ether (k₁), 2-chloroethyl ethyl ether (k₂) and bis(2-chloroethyl) ether (k₃) have been measured. Experiments were carried out at (298 ± 2) K and atmospheric pressure using synthetic air as bath gas. Using n-pentane and n-heptane as reference compounds, the following rate constants were derived: k₁ = (5.2 ± 1.2) × 10^?12, k₂ = (8.3 ± 1.9) × 10^?12 and k₃ = (7.6 ± 1.9) × 10^?12, in units of cm³ molecule^?1 s^?1. This is the first experimental determination of k₂ and k₃ under atmospheric pressure. The rate constants obtained are compared with previous literature data and the observed trends in the relative rates of reaction of hydroxyl radicals with the ethers studied are discussed. The atmospheric implications of the results are considered in terms of lifetimes and fates of the hydrochloroethers studied.     

Urban street-canyon flows with bottom heating

Urban street-canyon flows in the presence of street-bottom heating are investigated using a two-dimensional numerical model with a k–ε turbulence closure scheme. The street aspect ratio (H/D, where H and D are the building height and the width between two buildings, respectively) varies from 0.6 to 3.6 (in 0.2 interval) and the initial potential temperature difference between the street-canyon bottom and the air (ΔΘ) ranges from 0 to 16 K (in 2 K interval). Five flow regimes are identified. Regime I is observed when the aspect ratio is very small but the bottom heating is very strong (H/D=0.6 and ΔΘ⩾10 K). In regime I, as the heating intensity increases, the thermally induced vortex expands but the mechanically induced vortex contracts. Regime II is mainly observed when the aspect ratio is relatively small or the bottom heating is weak. In regime II, the vortex intensity increases with increasing heating intensity. Regime III is observed when the bottom heating is relatively significant (ΔΘ⩾4 K) and the aspect ratio lies in the range of 1.2–2. This regime differs from regime II in that the vortex induced by temperature gradient on the upwind side of the upper layer has meaningful intensity and size and the maximum horizontal velocity decreases with increasing heating intensity. When the bottom heating is relatively significant, regime IV is most commonly observed. This consists of two corotating vortices in the vertical within combined streamlines. Regime V exhibits two counterrotating vortices induced on both sides of the maximum temperature axis in the lower layer. The upper vortex is little influenced by the bottom heating. The numerical model result is shown to be reasonably in good agreement with the wind-tunnel data.