Dispersion of Particulate Matter in Urban Area Modelling

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  1. Introduction
  2. Air Quality Modelling
  3. Literature Review
  4. Overview of Dispersion Models
  5. CFD Models
  6. Turbulent Gas-Particle Flows
  7. Reference List

Introduction

The release of harmful substances in the atmosphere is a major concern among both the science community and policymakers. Evaluating the quality of the air and understanding the long-term effects of pollutants on the environment and human health is crucial to developing adequate planning and response to mitigate toxic effects. Dispersion modeling has emerged as a reliable methodology to assess the consequences of the discharge of gases, aerosols, and particles from industrial plants, vehicular transportation, and unpredictable events, such as terroristic attacks or involuntary chemicals releases. These analytic models are complex simulations aimed at estimating the long-term, annual or seasonal impacts of noxious substances in limited and ideal situations.

Particularly, the adverse impact of particulate matter discharges from traffic vehicles in polluted urban environments has urged the competent authorities to strengthen research. Research (Pey et al., 2009) shows that the emissions caused by transports alone, powered either by gasoline or diesel engines, constitute 90% of global particle number (ToN) concentrations. Other common emissions sources include power plants (Li et al., 2009), dismantling of old buildings (Hansen et al., 2008), airports (Hu et al., 2009), the release of rubber and asphalt particles due to traffic (Dahl et al., 2006), atmospheric formation depending on precursor compounds (Holmes, 2007), pollutants from biofuel residues (Kumar, Robins and ApSimon, 2010), as well as emerging manufacturing processes, such as the production of nanomaterials (Kumar, Fennell and Robins, 2010). From the perspective of this research, the locution urban environment refers to a specific setting characterized by a dense network of roads and the presence of various obstacles, which favor high concentrations of pollutants.

Compared to unobstructed locations, the level of noxious substances within an urban environment can be several times higher. It depends on several factors, including the geographical location, shapes and size of building defining the street, flow of discharges from neighbouring streets, turbulence caused by airflows, characteristics and volume of the vehicular traffic and meteorological conditions (Kumar, Fennell and Britter, 2008; Kumar et al., 2009). It is essential to highlight how real-time estimations that cover a significant part of the urban environment are almost impossible. Due to the nature of the typical city texture, practical and technical limitations hinder consistent measurements (Kumar et al., under review). Hence, understanding and developing relevant dispersion modellings emerge as an useful tool for the development of effective mitigation strategies, both in short- and long-term perspectives.

In urban environments, the presence of buildings and other obstacles plays a major role in the dynamics of the formation and dispersion of nanoparticles due to transportation pollution. Fig. 1 shows how the atmospheric flow is hindered by the urban texture, particularly at the urban canopy layer, where the traffic emissions are more impacting (COST732, 2010). The height and shape of the buildings influence how pollutants distribute. Different urban settings lead to various flow and dispersion characteristics (Britter and Hanna, 2003), affecting the dilution of harmful emissions. Dilution is a core process in defining nanoparticles and their dynamics to design appropriate dispersion modellings. Moreover, dilution entails a series of transformation processes, including evaporation, condensation, coagulation, nucleation and deposition (Ketzel et al., 2007). The transformation phenomena occurring after the emissions from the exhaust systems of vehicles represent a challenge to outline a coherent dispersion modelling.

Transformation processes affect the size and distribution of nanoparticles continuously, making the dispersion modelling distinct from gaseous air pollutants. Moreover, the available evidence on how transformation processes affect nanoparticle dispersion modelling is limited and partially contradictory. This paper provides an overview of dispersion modelling, focusing on relevant techniques, experimental and theoretical studies and available software to evaluate air quality in the urban environment. Specific aspects related to vehicles pollution and the relations among transformation processes and dispersion patterns will be deepened.

Air Quality Modelling

Urban environments represent critical areas from the air pollution perspective. The impact of noxious emissions on urban environments has become a major research topic (Georgii, 1969; Oke, 1988; Bitan, 1992) and modelling approaches have been proposed since the early 1970s when several studies addressed the influence of various types of urban structures on the dynamics of dispersion, dissipation and accumulation of pollutants within urban canyons (Johnson et al., 1973; Dabberdt et al., 1973; Hotchkiss and Harlow; 1973; Nicholson, 1975). Today, dispersion modelling is a consolidated practise, commonly used to evaluate the air quality through assessment and projections of the pollution levels and their spatial and temporal variations (Sharma and Khare, 2001). Dispersion models constitute priceless tools to obtain information about the chemical and physical dynamics involved in the dispersion and transformation processes of harmful particles in the atmosphere.

Literature Review

Key Flow and Mixing Features in Urban Areas

The structural complexity of urban settings and the numerous factors affecting the dispersion of pollutants within the atmosphere hinder a clear and definitive description of how noxious substances blend in the wind flow. These factors include the articulate network of buildings and streets, the various nature of sources of pollution, surface heating and synoptic-scale winds (Belcher, 2005). Several studies have highlighted that the inclusion of mixing behaviours in turbulent conditions can improve the projections of the pollution levels near roadways and their spatial distribution. The prediction model results improved when contributions from vehicles, geometry of the street and atmospheric boundary layer (ABL)(Wang and Zhang, 2009; Heist, Perry and Brixy, 2009). “Britter and Hanna (2003) (cited in Kumar et al., 2011, p. 583) proposed a simple approach to describe urban scales; length scales such as street (Ls, less than #100–200 m), neighbourhood (LN, upto1or2km), city (LC, up to 10 or 20 km) and regional (LR, up to 100 or 200 km) scales.” The smallest length scale relates to vehicles wake (Lv), where mixing and diluting are the fastest and most impacting (Baker, 2001; Carpentieri, Kumar and Robins, 2010). Thorough understanding of flow and mixing patterns at the different scales is crucial to designing credible and effective dispersion modellings of nanoparticles. An inside-out advection approach is useful to shed light on the mixing processes at various scale lengths.

Street Canyons

Once the exhaust emissions are discharged via the tailpipe, the nanoparticles disperse into the environment in the wake of the vehicle. Depending on the characteristics of the flow, the mixing patterns and the actual composition of the background, they undergo certain transformations and are further spread into the environment, specifically in the street canyon. At this scale, the measurement is relevant as it affects the air quality of densely crowded areas and monitoring stations are mandatory. Numerous factors intervene to influence the direction of the flow within a canyon:

  • geometry and aspect ratio are used to define the typology of the canyon, classified in regular, avenue, deep, symmetric and asymmetric (Vardoulakis et al., 2003). Aspect ratio refers to the proportion between the average building height and width.
  • the presence of elements, such as trees, monuments and balconies, among others, which contribute to roughness of the street (Gayev and Savoury, 1999)
  • the orientation and relative position of the streets (Hoydysh and Dabberdt, 1998; Vardoulakis et al., 2003)
  • above-roof wind characteristics (Britter and Hanna, 2003)

The above-roof wind characteristics, or synoptic wind conditions, are particularly relevant to classify the flow. Above-roof wind velocity and blowing direction are the main parameters used. The flow can be neutral (Ur<1.5 ms-1), perpendicular or near-perpendicular (Ur>1.5 ms-1 and blowing inclination greater than 30°) and parallel or near-parallel (Ur>1.5 ms-1 and coming with all other inclinations) (Vardoulakis et al., 2003). For example, Britter and Hanna (2003) shows that in regular street canyons, where the aspect ratio is approximately equal to 1, the typical recirculating speeds vary from 0.33 to 0.50 Ur and the turbulence level is approximately equal to 0.10 Ur.

Several factors contribute to influencing how the nanoparticles blend with the atmosphere within a street canyon. They include the airflow within the canyon (Barlow, Harman and Belcher, 2004; Caton et al., 2003), eventual “turbulence generated by the wind (De Paul and Sheih, 1986), atmospheric instability (Xie et al., 2005) (cited in Kumar et al., 2011, p. 584)” and amount of traffic (Solazzo, Vardoulakis and Cai, 2007a, 2007b; Solazzo, Cai and Vardoulakis, 2008). Other thermic effects, including atmospheric stability and differential temperature of walls and road surface, might influence the wind vortices (Kim and Baik, 2001; Sini, Anquetin and Mestayer, 1996). At the street canyon scale, the main mixing patterns are the turbulences generated by wind (wind-produced turbulences, WPT) and traffic (traffic-produced turbulences, TPT), each prevailing during specific atmospheric conditions. WPT will prevail in the presence of strong winds, while TPT will be the main cause of mixing during weak breezes and atmospheric stability (De Paul and Sheih, 1986; Di Sabatino et al., 2003; Kastner-Klein et al., 2003; Solazzo, Vardoulakis and Cai, 2007a, 2007b). Overall, high-speed winds and large presence of rugged urban elements increase the significance of the mechanical mixing, while free convective forces caused by solar radiation hitting the building are almost unnoticeable (Kim and Baik, 2001; Kovar-Panskus et al., 2002; Louka et al., 2002).

Neighbourhood Scale

As the urban scale increases, the number of factors affecting the flow grows, as several street canyons and related buildings interact, making the mixing patterns and the turbulences more difficult to evaluate. Table 1 provides a hint on the neighbourhood scale, characterized by an Ln of 1-2 km and turbulences generated by adjacent canyons (Belcher, 2005). At the neighbourhood scale, the flow presents two major assumed traits. While it features the status of quasi-equilibrium over a range of surfaces considered uniform, it is the sum of the changes occurred moving across different regions (Smits and Wood, 1985). Summing up, the mixing dynamics are the result of various street scale flows from numerous systems of streets and buildings. Comprehensive literature (Belcher, 2005; Britter et al., 2002; Britter and Hanna, 2003; Coceal and Belcher, 2005; Grimmond and Oke, 1999; Louka, Belcher and Harrison, 2000) is available to deepen the flow patterns at the neighbourhood scale.

City Scale

From the street and the neighbourhood, pollutants are spread at a larger scale across the city, as shown in Table 1. City scale refers to an urban agglomeration that consists of many neighbourhoods and carries specific characteristics: the presence of large buildings and obstacles, consistent population density and related activities that produce heat and moisture, the ability of concrete buildings and asphalt surfaces to store heat. Also, the varying design and location patterns of buildings affect the atmospheric boundary layer (ABL), creating roughness above the average building height (H). The ABL is composed of three main sublayers, whose dynamics, together, contribute to forming a logarithmic wind profile within the ABL (Raupach, Thom and Edwards, 1980; Rotach, 1993a, 1993b). In the urban canopy sublayer, the flow is influenced by the presence of various obstacles. The second roughness sublayer is characterised by a flow still negotiating the hindrances caused by the urban obstacles. The third inertial sublayer, the flow has reached a relatively stable condition, yet still affected by the dynamics of the urban flow (Britter and Hanna, 2003). Usually, it is considered that the advection of a nanoparticle can reach about 2H, which is, broadly, the height of the roughness sublayer. Hence, the assessment of pollution concerns the whole ABL, being the data related to specific buildings irrelevant (Di Sabatino, 2005). Also, the mixing patterns are affected by the surface roughness and the traffic-produced turbulences.

Overview of Dispersion Models

Today, there is a large availability of dispersion modellings that research the pollutants mixing dynamics at various scales. Through the years, different studies have addressed gaseous dispersion models and nanoparticle predictions, proposing basic box models, Lagrangian or Eulerian approaches, Gaussian representations and computational fluid dynamics (CFD) models. For convenience, this overview classifies the research according to the length scale addressed. Also, it offers a summary of each model, highlighting strengths, weaknesses and challenges, as well as recommendations for further research, whereas relevant.

Seigneur (2009) offered an exhaustive review of research addressing the chemical and physical composition of ultra fine particles of vehicle emissions and highlights various measurement techniques. Carpentieri, Kumar and Robins (2010) synthesized diverse techniques to evaluate the dispersion patterns in the vehicle wake. “Sharma and Khare (2001) (cited in Kumar et al., 2011, p. 586) reviewed commonly used analytical models for the dispersion of vehicle exhaust emissions near roadways, intersections and in street canyons.” Sharma, Chaudhry and Rao (2004) examined and evaluated the efficiency of several models used in the highway environment. “Gokhale and Khare (2004) (cited in Kumar et al., 2011, p. 586) reviewed various deterministic, stochastic and hybrid (the combination of the former two) vehicular exhaust emission models for traffic intersections and urban roadways.” Dispersion patterns in street canyons have been thoroughly studied by Vardoulakis et al. (2003), who also analysed the precision and margins of error of street scale modellings (Vardoulakis et al., 2002). Li et al. (2006) focused on CFD approaches in street canyons.

From a more general perspective, Milionis and Davies (1994) reviewed and assessed theory, benefits and downsides of regression and stochastic techniques related to research in atmospheric contamination. Holmes and Morawska (2006) examined various types of dispersion models to approach several urban scale problematics. The US EPA funded National Research Councils Committee on Regulatory Environmental Models performed thorough research about computational techniques (Holmes et al., 2009), while the Model Documentation System of the European Topic Centre on Air and Climate Change (MDS, 2010) provides an exhaustive casuistry of different modelling approaches. Finally, model assessment case studies can be found in some COST Action publications (COST732, 2005–2009, 2010).

While there is a large availability of dispersion models, only a bunch of them (see Table 2) include particle dynamics in the projection of distribution and concentration of the nanoparticles. In most cases, whenever these dynamics are taken into consideration (Holmes and Morawska, 2006), the outcomes are mass-based and do not provide numeric results. The non-linear relation between chemical and physical transformations involving atmospheric parcels and their sizes constitutes a serious hindrance to predicting reliable numeric outcomes at the various urban scales. However, while the large number of unstable variables affecting the flow and the complex mixing patterns pose severe challenges to such predictions (Britter and Hanna, 2003), the models should be implemented by a description of the particle dynamics. Such an approach would ensure coherent performances with any mitigation strategy developed on a number basis.

Relevance of Particle Dynamics in Dispersion Modelling

Understanding how transformation processes affect the concentration and distribution of the particle from a numeric perspective is paramount to obtain reliable and unambiguous data from the dispersion modellings. These processes have been dissected in many studies that provided thorough insight into the mathematical details (Jacobson, 2005; Seinfeld and Pandis, 2006; Hinds, 1999). Table 3 highlights how they influence the number and volume of nanoparticle concentration at the various urban scales.

Key Concepts Affecting Transformation and Removal Processes

Emissions. Pollutants distributions of discharges from vehicular traffic can be classified into three main types, each carrying peculiar traits and susceptible to temporal and spatial changes as the effect of processes as the dilution. Distribution modalities include nucleation, accumulation mode, Aitken and coarse mode particles, (Kumar et al., 2010). Dilution. Understanding dilution is essential as it triggers other reactions that, ultimately, change number and size distribution of the nanoparticles. Both emission and dilution require detailed descriptions to ensure effective inclusion of particle dynamics al all urban levels (Gidhagen et al., 2004a; Jacobson and Seinfeld, 2004; Ketzel and Berkowicz, 2004).

Homogeneous nucleation refers to the process of gas-to-particle occurring in the presence of fast dilution as soon that the gases are released (Kulmala et al., 2004; Wehner and Wiedensohler, 2003). The phenomenon is limited to a given area; near the exhaust tailpipe, non-volatile organic elements and sulphuric acid nucleation and condensation generate new particles continuously as soon as dilution occurs (Kittelson, 1998; Shi, Khan and Harrison, 1999). Depending on the urban scale, the nucleation has various characteristics, hence, calling for tailored modelling. A spread approach considers nucleation as an integral part of the discharges, which are, therefore, called ‘effective’ emissions. Olivares et al. (2007) highlighted how ‘effective’ emissions increase at low temperatures, while Wåhlin (2009) noticed that their percentage grows with high sulphur ratios within the fuel. Other research (Arnold et al., 2006; Sakurai et al., 2003; Rönkko et al., 2007) studied the concentration of nucleation under various running situations. These investigations highlighted the direct relation between sulphuric acid percentage and number of nucleation mode particles. Moreover, they discovered that the process involved substances with non-volatile cores, such as oxidised metals and hydrocarbons.

During the process of coagulation, collisions among nanoparticles generate larger particles. Clashes are caused by the Brownian motion of the particles and are influenced by viscosity, intermolecular forces, known as Van der Waals forces, and fractal characteristics of aggregates. As temporary dipoles form in uncharged molecules, intermolecular forces are generated, increasing the percentage of coagulation (Seinfeld and Pandis, 2006; Jacobson and Seinfeld, 2004). The fractal geometry of aggregates contributes to expanding the size of the coagulation core. The process of coagulation is significant when small particles impact larger molecules. At large, it lessens the count of nanoparticle while keeping the same mass ratio, yet changing distribution and concentration of differently sized particles and blending compounds from different sources (Jacobson, 2002). To prevent the overestimation of nanoparticles concentrations, effective modelling needs to recognise coagulation as a major variable. When the phenomenon refers to solid components, the process is known as agglomeration (Hinds, 1999).

Besides coagulation, condensable gas species are subjected to the process of condensation, which involves small amounts of mass transfer between the gas and the particle phases, and depends on the differential in the vapour pressure among the particles. In most cases, condensation and coagulation compete (Jacobson, 2002; Pirjola et al., 2004; Kulmala et al., 2004). Particularly, a large concentration of pre-existing particles favour condensation and discourage coagulation (Kerminen et al., 2004), while a small number of pre-existing particle induces coagulation (Kulmala et al., 2004). The phenomenon opposite to condensation, known as evaporation, entails a decrement of the volume of the particles. The process happens when the differential of the pressure between the particles and the air favours particle surface changes causing the particles to disperse in the atmosphere (Jacobson, 2005). The smaller the particles, the faster the evaporation because of the Kelvin effect (Hinds, 1999; Fushimi et al., 2008). Also, small particles are volatile, boosting the loss of volume (Kittelson, Watts and Johnson, 2004). In the case of the semi-volatile substances that accumulate near the exhaust pipe, the evaporation occurs almost instantaneously (Jacobson et al., 2005). These organics generate through nucleation and condensation caused by sudden cooling after the initial dilution and include, besides particles of unburned fuel, unburned oil and sulphate. Moreover, the organic compounds are extremely volatile (Sakurai et al., 2003), while the dilution of volatile gases trigger evaporation in nanoparticles, especially in the smallest ones (Zhang et al., 2004). Some studies (Kuhn et al., 2005) focused on the volatility of particles both in indoor and outdoor situations, highlighting how the diminution of the volume concentration is not significant until a certain temperature (60° C) yet rocketing to half of the initial value at higher temperatures (130° C). Jacobson et al. (2005) noticed that, in the case of partial evaporation, coagulation occurrences increase. Summing up, evaporation is weightier in conditions of high temperature, high dilution rate and new emissions; from the urban perspective, hence, the process is more significant in the wake area and at the roadside level.

Dry deposition refers to the air–surface removal of particles from the atmosphere (Seinfeld and Pandis, 2006). The process is triggered by two main factors, Brownian diffusion and inertial impaction. The former affects particles generated through nucleation, characterized by a conspicuous diffusion coefficient. The latter involves bigger particles, with diameter larger than 100 nm, when the flow has relevant characteristics of turbulence (Lee and Gieseke, 1994). Dry deposition impacts particle dispersion remarkably, and proper understanding of dry deposition schemes of differently sized particles is crucial to create efficient dispersion modellings (Petroff and Zhang, 2010).

Wet deposition is a precipitation phenomenon that eliminates particles through incorporation processes (Laakso et al., 2003). When the incorporation occurs below-cloud during precipitation, the phenomenon is known as washout. When the inclusion of pollutant particles relates to nucleation scavenging of precipitation that already contains contaminated particles, the process is called rainout (Jacobson, 2003). Also, Jacobson (2003) highlighted that the total amount of aerosols is largely affected by the washout process. On the contrary, rainout is an occasional phenomenon that impacts coarse particles yet with scarce relevance on the removal of ultra fine particles (<100 nm). From this perspective, most nanoparticles generated through nucleation within ABL have dimensions inferior to 100 nm; moreover, the growth rate of nucleation mode particles is relatively slow, and it takes about two/days to reach the size of cloud droplets (Kulmala et al., 2004). Hence, they are not affected by the scavenging process, if not minimally (Andronache, 2005).

Street Canyons

Removal processes are incorporated in dispersion modelling following different approaches. At the street canyon level, both dilution and dry deposition play a major role, as highlighted by most scholars (Gidhagen et al., 2004; Ketzel et al., 2007). Particularly, dilution is by far the major process as highlighted by the inactivity of nitrogen oxides (Jacobson and Seinfeld, 2004; Ketzel et al., 2007). Another crucial factor affecting deposition is the traffic movement, responsible for decreasing the global amount of concentration by 10-20% (Gidhagen et al., 2004; Ketzel et al., 2007). On the contrary, the inclusion of nucleation, coagulation and condensation is the subject of lively debate particularly concerning the street scale (Kumar et al., 2011). While some studies highlight the positive aspects of both the approaches (Gidhagen et al., 2004; Ketzel and Berkowicz, 2004), it is essential to reiterate the notion that removal processes are more or less significant, depending on the concentration of vehicle discharges, the amount of the pre-existing particles and the meteorological conditions (Charron and Harrison, 2003; Wehner et al., 2002). Further, the various processes might result in contrasting outcomes, where each phenomenon neutralizes the other; hence, they do not influence the particle concentrations significantly (Kumar et al., 2008; Kumar et al. 2009). A relevant study by Vignati et al. (1999) showed how the typical coagulation time of small particles discharged by a diesel engine is not comparable with the average residence span of noxious substances in a street canyon. The quick dilution of particles ranging from 0.002–10 mm makes the percentage of coagulation insignificant. Moreover, water vapour condensation does not affect the particle size distribution as the induced transformations are negligible.

Time scale analysis provides a valid technique to asses the weight of transformation and removal processes. Applying time scales to dilution, coagulation and deposition to the different spatial lengths provides useful data on the relations among concentration levels, transformational processes and urban lengths (see Fig. 3). Overall, processes characterized by small time scales are fast and relevant at every spatial scale, and dilution is the most significant phenomenon of all (Ketzel and Berkowicz, 2004). The differences are substantial. For example, at the street scale level, dilution is 10 times faster than the deposition. The only exception is within a road tunnel, where time scales of dilution, coagulation and deposition are comparable. Also, Kumar et al. (2008) demonstrated that dilution hinders other processes at the road surface level, with the exclusion of dry deposition. At the road surface length, time scales for dilution and dry deposition were is 40 s and 30-130 s for dilution and dry deposition respectively. All other values are not comparable; for example, the time scales for condensation and coagulation ranging from 104 to 105 s (Kumar et al., 2008).

Other investigations confirm the hypothesis that particle dynamics are negligible at street scale and the ToN remains unaffected. Moreover, the decision to exclude some parameters, namely Van der Waals forces, fractal geometry of the aggregates and small particles (diameter < 10 nm) confirms the result. Also, when the particles are analysed at the roadside level of a street, the transformation processes have already happened in large part as shown by Kumar et al. (2009) through the analysis of time scales as soon as they they are released by the exhaust tailpipe of a rolling vehicle (1 s) and in the lapse of time required to hit the kerbside (45 s). Also, almost simultaneous observations of particle number and size distributions at diverse elevations (1, 2.25, 4.62 and 7.37 m, respectively) performed in a regular street canyon (Fig. 4) provided consistent results: number and size distributions were comparable, shifting from 13.3 to 86.6 nm at different heights, while the variation of their average diameters was irrelevant (Kumar et al., 2008). The outcomes show that variations in the vertical concentration cooperate with dilution to transform the particles at the street length. Gidhagen et al. (2004), Pohjola et al. (2003, 2007) and Ketzel and Berkowicz (2004), produced comparable outcomes in the description of the inclusion of street-level particles in dispersion modelling.

Neighbourhood and City Scales

The effects of coagulation at the neighbourhood and city scales under normal traffic and meteorological conditions are not fully understood, and various studies showed contradictory outcomes. While some researches (Gidhagen et al., 2005; Zhang and Wexler, 2002) hold that the phenomenon occurs too slowly to change the particle size distributions, others found a relevant increase of the particles (Wehner et al., 2002). In other cases (Gidhagen et al., 2003), the increase occurred sporadically under specific ambient conditions. From a city-scale modelling perspective, coagulation seems to have a certain degree of influence on ToN concentrations (Ketzel and Berkowicz, 2005). On the contrary, ToN concentrations are not affected by changes in the status of the particle, which impact size and type of distributions. Notably, new particles are generated through several nucleation processes that involve, besides water, sulphuric acid and ammonia. In some cases, nucleation phenomena occur through ion inclusion or irradiation of supersaturated particles that enhance attraction among molecules (Kulmala et al., 2004).

Typically, the growth pace for urban environments ranges from 1 to 10 nm–1, and the formation of new particles (about 100# cm–3 s–1) impacts the ToN concentrations quite heavily (Kulmala et al., 2004). Indeed, these results are weighty, and several urban scale models, including MAT and MATCH, among others, include them in their calculations (see Table 2). Ketzel and Berkowicz (2005) utilized MAT to develop a model where they showed the influence of the removal processes on the ToN concentrations: while coagulation can eliminate a small percentage of the total (10% ca.), dry deposition weights for a larger removal percentage. The initial calculation hypotheses influence the latter percentage, which ranges from 50 to 70%. Gidhagen et al. (2005) developed a MATCH model, recording removal of 25% of the total under typical conditions compared with inert treatment, with a marked increase (50%) in the case of moderate winds and stationary conditions. Whereas removal phenomena are included in city-scale modelling, they can arguably produce decrease rate in ToN concentrations ranging from 13% to 23% (Ketzel and Berkowicz, 2005).

Uncertainties in Dispersion Modelling of Nanoparticles

As dispersion models are ideal simplifications of complex phenomena, they are blurred by a certain degree of uncertainty. Moreover, while some margins of error are typical of gaseous dispersion models, others are peculiar to the particle dynamics. More specifically, two categories of uncertainties, structural and parametric, decrease the reliability of the models. Besides, the stochastic fluctuations within the atmosphere contribute to increasing uncertainty (Holmes et al., 2009; Vardoulakis et al., 2002). Stochastic processes refer to all those events, such as turbulence, which affect the scattering of nanoparticles, causing dilution and, therefore, impacting the ToN and size distributions. The problem is that stochastic phenomena can hardly be included in models coherently, and are simplified in semi-empirical and CFD models.

Structural Uncertainty

Structural uncertainties refer to the margins of error intrinsic to the description of both chemical and physical processes in the designing of the model. A valid procedure to assess structural uncertainties is to compare the model outcomes with the observation (COST Action732, 2005–2009). The same method is also efficient in particle dispersion models. In this case, the testing parameters to be included are: “(i) FB (fractional bias), (ii) FAC2 (fractions of predictions within a factor of 2), (iii) NMSE (normalised mean square error), (iv) MG (Geometric mean) and (v) VG (geometric variance)” (Kumar et al., 2011, p. 595). When nanoparticles dynamics are included, improper approaches to evaluating transformation processes at various spatial lengths lead to further structural uncertainties. The significance of the removal and transformation processes at each urban scale affects the weight of uncertainty. Vardoulakis et al. (2002) suggest the implementation of adequate parameters and algorithms to improve the description realistically and efficiently from a computational perspective. Finally, uncertainty characterises also other model approaches, including several numerical techniques and semi-numerical methods used to describe particle size distributions.

Parametric Uncertainty

The uncertainty of some of the factors required to define a coherent dispersion model is the main responsible for parametric uncertainty. The unpredictability of “wind speed and direction, traffic volume” (Kumar et al., 2011, p. 595) and amount and distribution of the vehicle discharges are the main causes of hindering precision in model calculations. The reasons are inadequate knowledge of the main parameters, uncertainties due to measurement or calibration issues and scarce significance of the available data. Lohmeyer, Mueller and Baechlin (2002) stated that the accuracy of data input is paramount for reliable predictions; from this perspective, they showed discrepancies up to a factor of four in the projections of gaseous substances under identical conditions.

Albeit the unquestionable relevance for implementing mitigation strategies, currently, there is no availability of consistent comparative studies for nanoparticles dispersion models. The direct correlation between PNEFs (particle number emission factors) and projected particle number concentrations implies that approximate evaluation of PNEFs will inevitably lead to inadequate outcomes of the dispersion model (Holmes and Morawska, 2006). Hence, PNEFs are the main responsible for parametric uncertainty in dispersion models. Overall, once the vehicle discharges are expelled from the tailpipe, they undergo quick changeling due to dilution. At this scale, as underlined by Wehner et al. (2009), the formation of secondary particles prevents the stability of the particle number concentrations, contrarily to what happens in the case of gaseous pollutants, where the concentration rate is conserved.

CFD Models

CFD (computational fluid dynamics) modelling refers to a branch of fluid mechanics specialised in the analysis of systems where fluid flows, heat transfer and associated processes are involved through the use of software-based numerical approaches. Unlike other Eulerian approaches, CFD models are characterised by the capability to handle complex boundary conditions, including elaborated architectural structures and aerodynamic shapes, such as vehicles and aircraft, through flexible grids. Also, they introduce turbulence schemes in their calculations. Largely used in many industrial applications, CFD modelling has emerged as a coherent technique in biomedical and environmental purposes (Gosman, 1999). The ability to include turbulences in the final predictions, make CFD models especially effective for nanoparticle dispersion modelling.

The core of CFD models consists of elaborate numerical algorithms able to deal with fluid flow challenges through advanced interfaces. The key components of a typical CFD model are the pre-processor, the solver and the post-processor. The pre-processor allows users to enter the input data, including fluid properties, physical and chemical processes object of the analysis, identification of the boundary conditions and definition of the grid for the specific computational domain. The solver implements an approximate numerical evaluation of the flow variables, applies adequate discretization techniques to the governing equations, and eventually resolves the discretized equations. The post-processor provides a thorough insight into the simulation outcomes through various graphic techniques. In environmental applications, the outputs include, among others, the wind velocity and pollutant distribution and concentrations. Some advanced models can eve deliver dynamic display through animation renderings.

Turbulent Gas-Particle Flows

Computational fluid dynamics (CFD) modelling is an invaluable tool for research, optimal design and malfunction diagnose in many engineering problems. The advancement in computational technologies and the availability of efficient commercial modelling software has made the CFD approach a favourite technique to analyze turbulent gas-particle flow problems. The CFD modelling is especially effective whereas thorough understanding and in-depth knowledge of gas behaviours and particle phases are necessary.

Turbulent gas-particle flow problems characterize a vast array of engineering situations, including indoor airflow and contaminant particle transport in buildings (Fogarty and Nelson, 2003), flue gas and flue ash flow in pulverized coal-fired boilers (Tu, 1997) and medicine particles delivered in inhalers (Tang, Xue and Abu-Hijleh, 2004). The CFD methodology offers both macroscopic and microscopic approaches; hence, it is time-saving and cost-effective and, in many cases, more desirable than the physical model testing approach. Macroscopic or global data include all the parameters affecting the system as a whole, such as gas and particle velocity, turbulence intensity and total mass flow rate. Microscopic or local information focus on specific parameters, such as peak value of gas and particle velocity, specific particle trajectories and concentrations and particle-wall collision dynamics. Moreover, CFD models display graphical outputs of the results, easing the understanding of the essential parameters (flow geometry, velocity, pressure and particle concentration fields) and deepening the knowledge of gas-particle behaviours.

Eulerian-Eulerian and Eulerian-Lagrangian models are the core CFD approaches to analyze and predict the gas-particle flows. The first method assumes that gas and particle flows have the characteristics of continuous flows and the ability to interact with each other; hence, it eases the implementation of CFD codes. Advanced solvers can manage the computational time of the average parameters of particle flow smoothly and effectively. The efficiency of the Eulerian-Eulerian approach, however, should be reconsidered as some intrinsic weaknesses hinder perfect modelling of the turbulent gas-particle flows. Particularly, the method does not allow a coherent description of the aerodynamics drag force affecting the particle phase in the proximity of solid walls. Moreover, the continuum hypothesis is limiting as the description refers to average parameters instead of specific trajectories. The reason is that particles equilibrate with neither local fluid nor other particles when moving through the flow domain (Shirolkar, Coimbra and McQuay, 1996). Moreover, the approach does not consider other phenomena, including crossing trajectories (Slater and Young, 2001) and loss of particle properties, even though they can be relevant in evaluating the reaction rate of particles (Shirolkar, Coimbra and McQuay, 1996).

The Eulerian-Lagrangian method offers a more comprehensive approach. Within this approach, the Eulerian equations of the gas phases are complemented by the Lagrangian equations of particle motion, which allow tracing single particles in their movements through the flow field. A large amount of tracked particles results in conspicuous statistic data and reliable particle flows prediction. Until recent times, this aspect led to increased computational expenses and long processing times. However, advancement in technology has decreased both the computational time and the costs, making the Eulerian-Lagrangian method affordable and efficient.

However, some ambiguities in the approximation of turbulence models for gas phases should be addressed and optimized, as they are relevant to the correct prediction of gas and particle dynamics. The standard k-ε turbulence model, used in many simulations, is ineffective in many cases. A typical example is the prediction of indoor flows under conditions of low-Reynolds-number (LRN) turbulence. Inaccurate evaluation of LRN flow and turbulence leads to an approximate prediction of indoor airflows and pollutant particle concentrations, the latter being largely influenced by the air phase velocity and turbulent fluctuations. Several implementations of the standard k-ε model, including Renormalization Group (RNG) k-ε model and Realizable k-ε model, aim at increasing accuracy and reliability. Also, as the computational performance increase, old mathematical models for turbulence as the large eddy simulation (LES) are gaining new momentum. However, optimized assessment and accreditation for turbulence models for gas-particle flows are yet to come, at least for some specific cases. For instance, in the LES model literature, there is evident lacking of prediction of indoor pollutant particle transport.

The description of particle-wall collision dynamics represents another flawless in Eulerian-Lagrangian models. The study of these dynamic processes is particularly challenging and complex and successful and consistent outcomes are lacking despite broad research. The uncertainty increases when the particles are large. Various physical parameters intervene in defining particle-wall collision dynamics, including the angular velocity of particles at the initial stage, incident angle, characteristics of the particles (shape and size) and their composition. The stochastic nature of the particle-wall collision dynamics, as well as the characteristics of the roughness of the wall, should also be included in the model: several empirical studies (Grant and Tabakoff, 1975; Govan, Hewitt and Terry, 1989; Sommerfeld, 1992) reported that the particle restitution coefficient is affected by the wall asperities and non-spherically shaped particles. Hence, further research is recommended, as proper understanding and description of these dynamics are crucial to developing precise gas-particle flow model predictions.

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