Modeling the Airflow and Particle Dispersion in Street Canyons under Unsteady Thermal Environment with Sinusoidal Variation

Unstable temperature stratification conditions have a considerable influence on pollutant diffusion inside street canyons. In this study, we tried to model the air flow and particle dispersion in street canyons under unsteady thermal environment. The sinusoidal variation was used to model the atmosphere temperature on the basis of the solar radiation cycle that occurs over a day. The two-dimensional model of step-up building layouts was applied as the research object and an RNG turbulence model was applied to study the dynamic characteristics of instantaneous airflow, the dimensionless air exchange rate (ACH) and turbulent kinetic energy (TKE) in the different canyons. A series of numerical simulations were performed for different Richardson numbers (Ri). The results demonstrated that the stream function within the street canyons exhibited a periodic shift over a day, and the flow morphology gradually evolved from paralleled bilateral vortexes into a row of vortexes, particularly when the ground temperature increased. Moreover, the local PM concentrations at different times were obtained, and they were affected by the flow field patterns. The total PM mass in the street canyon decreased as the air velocity increased. Furthermore, the dimensionless ACH and TKE exhibit a noticeable fluctuation with time at higher Ri and stronger buoyancy. As the Ri decreases, the enhanced forced convection causes the ACH and TKE to remain constant over time. From these results, inhabitants should be advised to adopt preventative measures aimed at the PM pollution according to the time and location where they live.


INTRODUCTION
A street canyon is basic geometric units of residential urban structures.It generally refers to a relatively narrow street between buildings that is also bounded by the ground surface at the bottom and the roof level at the top.The stream flow in the street canyons is the source of fresh air for building ventilation.The increasing trend towards urbanization has resulted in higher anthropogenic emissions that have exacerbated urban environmental problems worldwide (Shui et al., 2016).The most essential features of street-canyon microclimates are thermal and wind-induced flow patterns such as the air recirculation inside the street canyons.Thus, these unique micro-scale meteorological processes affect not only the local air quality but also the comfort and health of urban inhabitants.
In the past decade, micro-scale Computational Fluid Dynamics (CFD) simulation of pollutant dispersion around buildings has been widely used rather than wind tunnel testing, to analyze pollutant concentration fields and flow patterns.Some researchers modeled and predicted the pollutant diffusion in actual urban three-dimensional areas such as London (Xie and Castro, 2009), Montreal (Gousseau et al., 2011), Macao (Liu et al., 2011b).In order to clarify the effect of the street structure, weather conditions and other flow boundary conditions on the diffusion of pollutants, it was necessary to simplify the real street arrangement to ensure the general applicability of the research results.A two-dimensional (2D) street canyon is a simplification of an actual urban geometry.Numerous studies have focused on the impact of building characteristics (such as building heights, the shape roof of building, and the density of the building group) on the diffusion of pollutants in idealized and modeling urban street canyons (Li et al., 2008;Huang et al., 2009;Li et al., 2010;Buccolieri et al., 2011;Scargiali et al., 2011;Hang et al., 2012;Addepalli and Pardyjak, 2013;Scungio, 2013;Huang et al., 2015).Scungio et al. (2015a) have used the detached eddy simulation to study the turbulent flow in isolated street canyons of different aspect ratios.Hong and Lin (2015) have investigated the effects of building layout patterns on the outdoor wind environment by using Simulation Platform for Outdoor Thermal Environment.
Most of these studies considered the ambient temperature as constant in the domain of interest, which was neutral thermal condition.In fact, besides the building characteristics, the variation of temperature would alter the flow patterns in the street canyon.During the field measurements carried out by Niachou et al. (2008), unstable thermal variation in the atmospheric boundary layer occupied 85% of cases in the daytime; and this value remained at 64% during the night.Some studies have also indicated that the non-neutral conditions induced by solar radiation have a considerable influence on pollutant diffusion within street canyons and the capability of air flows to transport and exchange pollutants (Tsai et al., 2005;Tominaga and Stathopoulos, 2013;Tan et al., 2015).Li et al. (2010Li et al. ( , 2014) ) have investigated the flow field and pollutant dispersion characteristics inside urban street canyons with ground heating at different Richardson (Ri) numbers.Increasing ground temperature substantially enhanced the mean flow, turbulence, and pollutant flux inside the street canyons, but weakened the shear at the roof level.In addition to ground heating, Cheng and Liu (2011) have examined the characteristics of flows and pollutant dispersion in 2D urban street canyons with ground cooling conditions at different bulk Richardson numbers.The observed results have shown the stable stratification (ground cooling) slowed primary recirculation in the unique geometry of the 2D street canyons.Uehara et al. (2000) has used a stratified wind tunnel to study the airflow within street canyons and examined how it was affected by atmospheric stability.Although a fairly large body of research on thermal stratification inside street canyons exists, most of the literatures assumed a steady temperature distribution per canyon facet.Tan et al. (2015) has performed four steady temperature distributions along ground, leeward walls and windward walls representing four time scenarios (Morning, Afternoon, Noon and Night).The simulation results demonstrated that air flow patterns and pollutant dispersion are greatly influenced by diurnal variation of surface temperature under unstable stratification.
However, there are some drawbacks if the unsteady temperature variation in a day is divided into several parts which are assumed steady simulations.Firstly, the calculation cost will increase due to multiple calculations for different cases.Secondly, the steady numerical cases can not show the dynamic characteristic of air flow and pollutant transport.Therefore, the transient flow characteristic and pollutant dispersion variation in street canyons should be reflected under time-varied temperature condition and obtained from unsteady simulations.This is our study focus, which is still lacking from other researches.
As we know, under real meteorological conditions, the ambient temperature is periodic variation with the sunrise and the sunset due to solar radiation angles.To reveal the effects of temporal variation of ambient temperature on street canyon flows, CFD simulations adopt a temporal sine function as boundary conditions to express the air temperature diurnal variation.Combined with a constant pollutant emission source, this simulation provided detailed temporal variations of street canyon flow fields, PM dispersion, air exchange rate and turbulence energy under unsteady stratification conditions.

Expression of Diurnal Variation of Ambient Temperature
The meteorological data from the Sep, 25 th , 2016 to the Sep, 28 th , 2016 were reported from the China meteorological data web (http://data.cma.cn/user/toLogin.html).The dimensionless temperatures for these days were depicted in Fig. 1.(The dimensionless temperature T was defined as T = (t -(t max + t min )/2)/((t max -t min )/2), where t is monitoring temperature of Wuhan from the China meteorological data web, t max and t min were the maximum and minimum temperature of the 24 hours in a day.From Fig. 1, the curves of ambient temperature varied with 24 hours have periodic wave with peaks and valleys, which is cold in the morning and evening and warm in the midday.Because the variation of temperature is related to the solar altitude, when the solar altitude is 90°, the solar radiation and air temperature reaches the maximum value; when the solar altitude less or more than 90°, the solar radiation intensity decreases.The trigonometric function can be used to express the periodic diurnal variation of the air temperature.For example, in the Fig. 1, the function of θ = sin π/12(x -1.2) is adopted to match the temperature curves, where x is the hour of a day, θ is the fitting temperature.Some researchers have used the sine function to express the temperature varied with time in calculation heat transfer of the two-dimensional cavity (Kwak et al., 1998;Liu et al., 2008).However, when simulating the atmospheric environment, the sine variation has seldom been used to match the instantaneous temperature.

Physical Model and Computational Domain of Numerical Simulation
There were various profiles of street canyons in the city, which were decided by the appearances and layouts of buildings.Generally, due to the height of buildings, the shapes of street canyons include step-up, step-down and uniform arrangements along the stream wise direction.The step-up arrangement is usually selected for urban residences which are adjacent to lake and in villa districts.By studying the effects of buildings arrangements in the cities on the particle dispersion, the particle concentration in the step-up street canyon was the most than that of other building arrangements (Mei et al., 2016).So the step-up building model is used as object model to study the particle temporal distribution.
A step-up 2D hypothetical street canyon was established in Fig. 2. The computational domain is of 200 m (H) × 1000 m (L), and comprised four identical street canyons under a free surface layer.The first building height (h) and street canyon width (w) were both set as 20 m, and the heights of the final four buildings were 2 h, 3 h, 4 h, and 5 h respectively.The aspect ratios (AR) of the street canyons in the step-up building groups were 2, 3, 4, and 5, sequentially.The extended length behind the final building was set to Le = 720 m to ensure fully developed turbulence at the outlet.To illustrate the air flow and variation in PM concentration in the different street canyons, the four street canyons were numbered in sequence along the x direction, as shown in Fig. 2.

Mathematical Model
The governing equations for fluid flow and temperature are shown in Eqs. ( 1)-( 3) in tensor form, where the Boussinesq approximation was adopted to account for buoyant force.
where u is the fluid velocity tensor, p is the pressure, T is the fluid temperature , α is the thermal diffusivity, ρ and µ are the fluid density and the dynamic viscosity.It was demonstrated that the RNG k-ε turbulence model has a relative good predicting for both velocity contour and the surface pressure of buildings by wind tunnel experiments (Li et al., 2015).Thus, we adopted the RNG k-ε turbulence model to solve the turbulent kinetic energy (TKE, k) and turbulent dissipation rate (ε).The turbulent dynamic viscosity (µ t ) is defined as where additional detailed model parameters are available in Cheng et al. (2009) For microparticles (d p ≥ 1 µm), a Lagrange frame of reference can be used to analyze the trajectory of particles in the atmosphere.The discrete phase model was used to simulate the particle dispersion.The particle motion governing equation is written as follows: where F D (u i -u p ) is the drag force per unit particle mass.
2 18 24 , in which Re p is particle Reynolds number, u p is the particle velocity, ρ p and u p are the density and diameter of the particle, C D is drag coefficient.

Boundary Conditions
Velocity Boundary Conditions.The prevailing ambient wind was introduced along the x direction.The inflow wind velocities were set as u 0 = 1, 2, and 4 m s -1 ; an intermediate turbulence intensity value (I = 0.005) was imposed at the inlet.A pressure outlet boundary was applied at the downstream outflow.The height of the computational domain was sufficient for the development of a free-stream wind layer with a constant inflow wind speed.The top side plane of the computational domain was set as free-slip boundary condition.No slip boundary condition was applied to any of the street canyon facets.
Thermal Boundary Conditions.The sinusoidal functions are used to model the time-varying temperature boundary.The temperatures at the inlet, outlet and ground surface were set as follows: T = 294 -6sin(0.26t+ 1.05) at inlet and outlet (6) T = 313 -13sin(0.26t+ 0.523) at ground surface (7) Because of the heat storage capacity of buildings and the ground, we considered the time of the peak of the ground temperature lagged behind that of the atmospheric temperature (Yang and Li, 2013).And due to solar radiation and urban heat island effects, the urban ground temperature is higher than the atmospheric temperature in suburban areas (Wen and Lian, 2009;Toparlar et al., 2015).Constant surface temperature was set as 300 K for the buildings and the heat transfer coefficients of the building walls were fixed at 2.05 W m -2 K -1 .
Pollutant Boundary Conditions.Particle matters from industrial emissions are important sources of atmospheric haze, which transport trajectories are different from internal ones such as automobile exhausts.Numerous researchers have focused on internal source in the urban street (Albriet et al., 2010;Chan et al., 2010;Liu et al., 2011a).However, considerable numbers of people live in industrial areas and are exposed to industrial PM pollutants for prolonged periods.If inhaled industrial PM emissions exceed safety standards, long-term inhabitants in such areas are at a high healthy risk (Scungio et al., 2015;Johnson, 2016;Scungio et al., 2016).Therefore, we discuss that particle matters (PM) from factory chimneys transport within the building groups.A source with a constant particle emission rate (Q = 0.002 kg s -1 ) and particle size of 2.5 × 10 -6 m was placed at the inlet of the domain.All the street canyon facets were set as trap boundaries.

Governing Parameter and Air Exchange Rate
The purpose of this simulation was to study the effect of different stream-wise velocities and air temperatures on the flow field and PM transportation; therefore, the governing parameter Ri is defined as follows: where h is the height of building, T max = 326 K and T min = 288 K are the highest and lowest air temperatures inside the street canyon according to Eqs. ( 5)-( 6), respectively.The air exchange rate (ACH) represents the rate of air removal from a street canyon (Cheng et al., 2008).ACH (m 3 s -1 ) can be used to illustrate the fresh air quality and as a value for optimizing the street structures.It is defined as where w is the velocity component in the y direction, Γ roof is the roof area of the street canyon (in the step-up building model the location of roof is shown in Fig. 2).λ is the average time period and x is the coordinate in the streamwise direction.The subscript + signifies that only the upward velocity component w > 0 is taken into account.
ACH is normalized by Ω/Λ where Ω is the volume of the center street canyon and Λ = H/u 0 is the characteristic time scale.

Numerical Analysis
This study generated a hex mesh by using commercial ICEM software (Ansys Inc., 2016).The number of mesh elements was set as 118126 for discretizing the computational domain.The mesh sensitivity analysis is presented in appendix A. All the governing equations were solved using the commercial CFD code ANASYS-Fluent (Ansys Inc., 2016).
An additional examination was conducted for a time-step independence test for u 0 = 1 m s -1 .Five different time steps of Δτ = 1/288 (h), 1/144 (h), 1/96 (h), 1/72 (h), and 1/48 (h) were assessed for a specific temperature period in the day.With respect to the accuracy and computational time, a time step of Δτ = 1/144 (h) was selected in this study.

Model Validation
Because of the absence of comprehensive experimental studies recording on both street canyon thermal environment data and airflow pattern results, this study implemented two simulation validation tasks to adequately validate the numerical accuracy.First, air vertical velocity profiles were validated against water channel experiments (Baik and Kim, 2002) and simulations (Baik and Kim, 2002;Cheng et al., 2008).The inside temperature along the vertical centerline of the street canyon was then compared with the wind tunnel measurements obtained by Uehara et al. (2000) and Tan et al. (2015).As demonstrated in the preceding model validation exercise, the numerical model used in this study is capable of simulating airflow patterns and temperature profiles in street canyons with temperature-varied thermal environments.The detailed validation was explained in appendix B.

RSSULTS AND DISCUSSION
This section discusses the results calculated at different Ri.The dimensionless parameter Ri = 26.3(u 0 = 1 m s -1 ), 6.575 (u 0 = 2 m s -1 ), 1.644 (u 0 = 4 m s -1 ) represents the magnitude of the buoyancy relative to the inertial force in the domain.Airflow patterns and pollutant dispersion were analyzed at different times.In this section, the temporal variations of airflow and PM concentration are described in detail.

Temporal Variations of Air Flow Structure with Varied Ri
The stream functions of the street canyon at different Ri number were represented at five typical time (local standard time) events-namely late night (02:00), morning (08:00), afternoon (14:00), and evening (20:00).
Fig. 3 shows the streamline and velocity contours of air flow in the region at 500 < x < 780 m, 0 < y < 120 m and Ri = 26.3,6.575, and 1.644, respectively.From 02:00 to 8:00, as the inlet air temperature gradually increased, two parallel eddies manifested in the street canyon near the windward and leeward walls.When the inlet temperature peaked at 14:00, a row of the vortexes appeared from the top to the bottom of the canyon, which was quite different from those observed in the morning.As the buoyancy increased due to the rising ground temperature, the flow pattern of the vortexes in the street canyon fluctuated from the afternoon 14:00 to the evening 20:00.The number of vortexes in the canyon increased as the aspect ratios ranging from H/W = 2 to 5 when time was 20:00.Because particles dispersed with air flow, the vortexes accumulating on the left and right sides in the canyon caused the particle concentration different at the windward and leeward sides.Because of the vertical arrangement of the vortexes, the PM concentration distribution at different street canyon also differed (a detailed analysis is provided subsequently).
When the Ri number decreased, the velocity of the air flow increased, and the vertical airflow velocity from the top of the canyon was enhanced.When the Ri was 1.644, the inlet temperature was lowest at 02:00, and the cells began to exhibit a vertical arrangement.During 02:00-8:00, the intensity of the side-by-side vortexes increased gradually.At 20:00, the temperature at the bottom of the street reached its maximum value; buoyancy caused a vortex to form at the lower zone of the street canyon.

Temporal-spatial Variations of PM Concentration with Varied Ri
To clarify the temporal and spatial changes, Fig. 4 present the dimensionless concentration in each street canyon at 02:00, 08:00, 14:00 and 20:00 separately.When the Ri number was 26.300, at 2:00, the PM concentration in the canyon I was the maximum of the street canyons.At 8:00 and 14:00, the PM concentration in the canyon III were heavier than other canyons.At 20:00, the PM concentration in the canyon II reached the maximum of all the canyons.So by the effect of unsteady temperature, the PM concentration in the different street canyon had remarkable distinction with time.When the Ri number decreased to 1.644, the PM concentration in every street canyon was reduced substantially.The pattern of flow field altered the distribution of PM concentrations.In contrast to Fig. 3, there were big cells throughout the first street canyon from the roof to the ground at 2:00.The same patterns of airflow occurred in the third street canyon at 8:00, and the second street canyon at 20:00.Therefore, the PM were entrained by the cells into the deep canyon, so that the PM concentration at the specific time was increasing.Nevertheless when Ri = 1.644, there were some small swirls filling in the deep canyon of H/W = 5.The swirls were stratified with the height of canyons.The particles from the roof of the street canyon would stay in the top swirls, and they were seldom taken to the second or the third layer swirls.So in this case, the PM concentration was lower than other cases.The preceding analysis demonstrates that the PM mass concentration in the canyon decreased and varied slightly with time with Ri number decreasing.
Fig. 5 presents the total PM masses in the street canyons at each time for different Ri.It reveals that the total PM mass in the street canyon decreased and the fluctuation trends were more gentle over time as Ri number increasing.When the Ri number was 26.300, the total PM mass reached peaked values at 06:00, 11:00, 15:00, and 20:00; in other words, a peak occurred nearly every 5 h.Relatively small peaks occurred before each large one at the same 5-h intervals.However, when the Ri number was 6.575, the total PM mass reached peak values at 05:00, 10:00, 14:00, and 20:00; thus, the schedule moved ahead 1 h compared with that observed when the Ri number was 26.300.When the Ri number was 1.644, the time interval of the large and small peaks appeared to be reduced, as was the difference between the values.This illustrates that the variation of the total PM mass with time was more uniform with the drop of the Ri number.On the basis of the temporal distribution of total PM masses in street canyons, necessary preventative measures should be provided for people's health in advance of PM peaks.

Temporal Variations of ACH and TKE with Varied Ri
Fig. 6 presented a plot of the dimensionless ACH of each street canyon roof versus time when the Ri were 26.3, 6.575, and 1.644.Because the step-up street model inherently engendered substantial increases in the aspect ratio of street canyons from 2 to 5, the depth of the canyons also increased.As the Ri number decreased, the dimensionless ACH of the street canyons among the building groups did not vary with time, but diverged at different heights.So the ACH of the street canyon V was the maximum and that of the street canyon I was the smallest one.The ACH in the second canyon closely resembled that in the third canyon.This demonstrated that when the inlet flow speed increased, the inertia force was dominant in the area, and the buoyancy lift which was introduced by the unsteady air temperature was wakened.As shown in Fig. 6(a), when the Ri number was 26.300, the effect of the buoyancy lift was dominant, and the four curves of the dimensionless ACH exhibited a notable variation with time.They first decreased and then increased over time, peaking at 13:00, 12:00, and 11:00 respectively; the dimensionless ACH of the bottom zone reached the maximum first.Comparing the stream function in Fig. 3, it revealed that when the ACH reached its minimum value, two side-by-side balanced vortexes occurred inside the canyons, causing the inflow and outflow velocity at the top of the canyon in the y direction to cancel out.When the airflow inside the canyon formed a series of cells exhibiting a vertical arrangement, the ACH reached its maximum value at this time, because of an independent vortex formed at the top of the canyon.Fig. 7 showed that the dimensionless TKE of the four street canyons varied with time under different Ri. 2 0 u was used as the characteristic scale to normalize the TKE.As turbulence was transported from the shear layer into the canyon region, the in-canyon turbulence characteristics varied as a function of upwind velocity and stability (Klein and Jose, 2014).In the Fig. 7(a), the right Y axis represented the air temperature at the inlet and the ground surface.It indicated that when the Ri number was 26.3, the dimensionless TKE variation with time almost resembled a sinusoidal function due to the ground temperature variation.However, it lagged by 3 h compared with the phase of the ground temperature.In this case, the thermal instability introduced the TKE to vary with time.With Ri number increased, the dimensionless TKE of each street canyon decreased and did not vary with time, as shown in Fig. 7(c).Moreover, the dimensionless TKE of different canyons had little disparity.Turbulence kinetic energy in the shear-layer region at roof layer varied depending on upwind fetch and stability.
In summary, when the Ri number was higher, the buoyancy effect was strong and the dimensionless ACH and TKE in the canyons presented periodic fluctuation with time.When the Ri number decreased, the forced convection was enhanced.When the Ri number was 1.644, the constant flow velocity ceased the dimensionless ACH and TKE in the canyons change with time.In addition, the dimensionless TKE decreased with the Ri number.

CONCLUSIONS
Unstable temperature stratification conditions have a considerable influence on pollutant diffusion inside street canyons.In this study, we tried to model the flow characteristics and particle dispersion in street canyons under unsteady thermal environment.We used sinusoidal function to model the atmosphere and ground temperature, which varied over time periodically.Our case study has shown that the monitoring temperatures of 72 hours in Wuhan were accorded with the sine function curve.The numerical simulation using a sine variation of temperature with time as the boundary condition can reveal the effect of temporal variation of ambient temperature on street canyon flows.Furthermore, a 2D model of step-up building layouts was applied as the research object and an RNG turbulence model was applied to study the dynamic characteristics of instantaneous flow patterns, ACH and TKE at different positions and Ri numbers.In addition, a discrete phase model was used to study the spatial and temporal distribution characteristics of PM concentration in street canyons.The conclusions are summarized as follows: On the basis of variations in the temperature of the atmosphere and the urban ground, the stream function appears as a periodic shift over a 24-h period.With increasing ground temperature, the flow pattern in the canyon gradually evolves from parallel bilateral vortexes into a row of vortexes.As the Ri number decreases, which enhances forced convection, the higher vertical velocity restrains the double-sided cells formed in the canyons.
The instantaneous airflow pattern altered the PM concentration in the street canyons.When there are big cells throughout the street canyon from the roof to the ground, the PM concentration of this canyon is heavier than others.When there are some stratified small swirls filling in the deep canyon, the PM concentration of this canyon is lower than other cases.Because the particles stay in the top swirls, and they are seldom taken to the second or the third layer swirls in this case.Moreover the CFD results indicate that the total PM mass in the street canyon shows different characteristics on the varying Ri number and unsteady thermal stratification conditions.The total PM mass is reduced and more uniform with the drop of the Ri number.
In addition, the dimensionless ACH and TKE exhibit a noticeable fluctuation with time at higher Ri and stronger buoyancy.The ACH first decreased and then increased over time, and curves of the TKE seem sine fluctuations approximately when Ri = 16.300.As the Ri decreases, the enhanced forced convection causes the ACH and TKE to remain constant over time.
Despite some limitations of the research, the sine variation boundary temperature with time proposed by this study can benefit other researchers using the same conditions for transient simulations to obtain the spatial-temporal flow patterns.According to the spatial-temporal distribution of PM concentration in street canyons, some necessary preventative measures in advance of pollution peaks can be provided for residents' health.

Fig. 2 .
Fig. 2. Geometrical model of urban street canyons for computational simulation.

Fig. 5 .
Fig. 5. Profiles of the total PM mass in the street canyon with time.