Exploring the Effects of Wind Direction on De-Icing Salt Aerosol from Moving Vehicles

Abstract

Aerosol sprayed from the wheels of vehicles driving on wet roads is a significant source of pollution in the vicinity of roads. If it contains residues of chemical de-icing agents, it can contribute to the faster degradation of objects and structures within its reach. The aim of this research was to determine how the direction of the wind and the intensity of traffic affect the dispersion of the aerosol particles. Using a numerical model of turbulent flow incorporating discrete phase modeling, seven variants of wind direction and two traffic intensities represented by the passing of one or two vehicles were simulated. The results showed that when the wind blew from the location where the particle amount was measured, particle deposition was highly concentrated near the road—peaking at 6.5% of the injected amount at a distance of 5 m—followed by a steep decline to negligible levels at 9 m. Conversely, in the opposite wind direction, deposition was lower (<1%) but exhibited a flat profile, maintaining stable particle concentrations even at the most distant sampling plane (13 m). The passage of two vehicles led to a higher number of particles being detected (reaching up to 8.1%) and induced a vertical dispersion plume reaching up to 13 m above the road surface, compared to a maximum of approximately 7 m observed for a single vehicle. A comparison of the simulated data with long-term in situ experimental measurements confirmed a decrease in aerosol particle deposition with distance from the road. The simulations revealed that the aerosol dispersion is influenced not only by the wind or traffic intensity, but also by specific flow conditions resulting from the terrain configuration. In conclusion, the study shows that while increased traffic intensity mainly extends the vertical reach of the aerosol, wind direction determines its spatial distribution. Since the particle cloud is uneven, measuring devices in a single line perpendicular to the road axis may not accurately capture the highest concentrations. Therefore, to reliably capture aerosol dispersion, it is recommended to also place measuring devices in a direction that is parallel to the road, with a spacing of approximately 9 m.

1. Introduction

Road transport is a significant source of various pollutants that adversely affect the environment and accelerate the degradation of structures located near the road, such as bridges, underpasses, noise barriers, and other steel or reinforced concrete structures. From the point of view of sustainability, it is important to consider the negative effects of aggressive substances during the design of structures and to predict their service life. Microclimate monitoring is carried out near roads, which involves examining the dispersion of pollutant droplets from moving vehicles in terms of their size, quantity, density, and spatial distribution at different distances from the road. All these quantities can be examined by many different parameters. It is necessary to find ways to minimize the spread of pollutants in the surrounding environment. It is possible to measure aerosol dispersion or other pollutants in the vicinity of roads by using experimental measurements or numerical simulations.

Computer simulations of transport, dispersion, and deposition of pollutant particles near the bridge were carried out in article [1], where k-ε model of Fluent software was used to simulate the mean airflow conditions. A Lagrangian particle tracking model was used and the dispersion and deposition of particulate emissions from a motor vehicle exhaust on the bridge was analyzed. The corresponding deposition rates on different surfaces were studied and the importance of wind turbulence and gravity on particle deposition was evaluated. In article [2], particular attention was paid to the evaluation of particle concentration at different sites. Several computer simulations of the transport and deposition of particles near the Peace Bridge were performed.

In Ref. [3], simplified models are used to investigate the numerical simulation method of wheel spray, as well as the simulation result based on the finite-volume method. The motion of the droplets emanated from the wheelhouse, depending on the flow structure, and the influence of the vortex on the motion of the particles was solved there. The injection of particles was distributed in lines on the wheel. The particles were generated on the surface and have an initial velocity that is tangential to the surface of the wheel and equal to the surface velocity. In paper [4], a method combining a computational fluid dynamics model and a statistical procedure is proposed for the efficient estimation of the area-wide distributions of the cumulative amount of sea salt in the air, taking into account the local topography. The results confirmed that the predicted amount of sea salt in the air decreases with increasing distance from the coast and varies with topography and onshore winds. Study [5] highlights new phenomena associated with droplets on porous media that could have implications for environmental aerosol formation research. In this paper, aerosols were experimentally investigated because of their significant impact on the environment. The authors of the paper investigated aerosol formation from droplets impinging on wettable porous surfaces, including various soil classifications, and they confirmed the importance of research on aerosol dispersion to soil around roads. Prevention of steel bridge degradation due to salt particle deposition and comparisons between the numerical and observed results are made in the article [6]. The numerical simulations of the adhesion behavior of salt particles were carried out using a two-phase Lagrangian flow analysis. The article demonstrates the importance of research on the dispersion of aerosol particles around roads, including the impact on the beams of bridge structures. In study [7], the authors engaged in numerical simulations, where they solved the location of the spray from the vehicle. They simplified their numerical model of tire spray to consider only the spray released from behind the contact patch between the wheel and the ground. In the literature, articles can be found that provide quantitative information about the physical characteristics of aerosols produced by trucks and lorries. In Ref. [8], there are solved droplet size distributions and time-resolved data regarding averaged and maximum droplet sizes and number density and mass concentration are presented from the trucks rolling on wet asphalt, obtained by optical methods. The data presented in the paper contribute to understanding the effects caused by aerosols produced by heavy vehicles rolling on wet asphalt.

The physical principles of particle dispersion, transport and deposition by the CFD-based approach were adopted by the authors of [9], who investigated the migration behavior of dust particles and the effectiveness of spray-based dust suppression in a fully mechanized mining environment. Their model simulated the interaction between water droplets and airborne dust particles to analyze the dispersion and settling mechanisms under varying airflow conditions, and the numerical predictions were validated through in situ measurements of dust concentration. The obtained data showed that the appropriate position and angle of the nozzles significantly affect the flow of dust particles and the effectiveness of their suppression.

One of the sources of pollution in the vicinity of roads is aerosol generated from the de-icing salts applied during winter maintenance [10,11]. These road salts have a negative impact on the environment, causing problems such as soil contamination, water pollution, adverse effects on flora and fauna, degradation of road surfaces and traffic structures, and corrosion of vehicles [12]. Some of the factors that increase the degradation of these building surfaces are carbonization, the deposition of chloride ions, and other pollutants.

Study [13] utilizes numerical simulations to specifically address the effect of the wind direction on droplet dispersion from de-icing salt, and there is an analysis of the transport of truck-generated salt spray near bridges. This report documents work using the k-ε turbulence model in CFD (computational fluid dynamics) analysis to study the conditions and mechanisms that lead to salt-water droplets, originating from truck tires, reaching bridge girders.

From an experimental point of view, the topic is addressed in [14,15]. The authors of these studies have been conducting long-term experimental research on measuring the amount of salt in the roadway environment and evaluating the average corrosion loss and the average SO₂ concentration. In Ref. [14], experimental measurements of chloride deposition around a motorway in the Czech Republic using the dry plate method, the wet candle method and the corrosion coupon method are discussed and statistical correlation and regression analysis are performed on the measurement results. In another study [15], the Bresle method was used to measure vertical surface salinity and the results for four winter months were evaluated from three different measurement sites. A related experimental study by [16] examined the transport of sea-salt aerosols, in which the authors analyzed how chloride ions settle at different altitudes and distances from the coast. The research combines measurements of chloride concentrations using the kite-hanging wet candle method and a three-dimensional analysis of the spatial distribution of deposition, with the conclusion that the intensity of chloride sedimentation strongly depends on the distance from the source, altitude, wind direction and velocity and terrain topography.

While standard experimental methods, such as the wet candle and dry plate method, provide reliable data on cumulative deposition, they are typically limited to single-point measurements and cannot isolate specific transport mechanisms. Currently, there is a lack of detailed understanding of how the combined interaction of variable wind direction and traffic intensity shapes the dispersion plume in the immediate vicinity of the road. Driven by the need to better predict structural durability, this study aims to bridge this gap by using numerical modeling to determine the spatial distribution of particle impacts. Even with a simplified model, this approach allows us to visualize specific “impact zones” on sampling planes, revealing how these combined factors shift the pollution load vertically and horizontally: insight that static field sensors cannot provide.

This paper focuses on computational modeling of aerosol droplet transport generated by vehicles driving on wet roads, specifically examining how the droplets disperse in the immediate vicinity of the roadway. The numerical simulations are inspired by the experimental conditions described in the previously cited studies [14,15]. The primary aim of this modeling is to qualitatively assess how wind direction and the number of vehicles influence the spread of aerosol droplets in the environment that is adjacent to the roadway. Wind blowing toward the sampling planes is expected to increase particle transport and capture. In terms of vehicle numbers, two vehicles can generally be expected to produce higher numbers of captured particles than one vehicle. The secondary intent is to verify whether and to what extent computational modeling can provide data on particle dispersion, which could be helpful in designing the placement of measuring stands and possibly supplement the data from the experiment.

2. Methodology

The de-icing salt applied to the roads contributes significantly to the formation of aerosols. A simple classification [17] distinguishes coarse droplets (tens of micrometers or larger) and fine particles (a few micrometers or less). Coarse aerosol particles settle rapidly and are deposited close to the road. They primarily contribute to localized pollution in the immediate vicinity of roads and are the subject of this study. In contrast, fine aerosol particles remain suspended in the air and can be transported over distances of several hundred meters.

The results of numerical calculations are analyzed from two perspectives. The first evaluation investigates how the direction of the wind and the number of passing vehicles influence the dispersion of particles across the entire monitored area. Numerical simulations are conducted for seven wind scenarios, representing different wind directions, including a no-wind case. Two traffic configurations are considered for one and two vehicles.

The second evaluation focuses on the comparison of the simulation results with the experimental data. For this purpose, the modeled domain is aligned with the site map indicating the locations of the measuring devices [15]. For each traffic configuration, the frequency of winds from different directions is subsequently analyzed.

2.1. Numerical Model

The computational model is based on the terrain near the I/11 expressway between Ostrava and Opava, Czech Republic (Figure 1), which is one of the locations where long-term measurements were carried out in [14,15]. The shape of the computational domain is assumed to have a dominant influence on the flow characteristics, while the influences of barriers, traffic signs, measuring stands or solitary trees are considered negligible for the problem and are therefore neglected. Consequently, the cross-sectional profile of the domain is represented in a simplified form, as shown in Figure 2.

The computing domain is 300 m long, 60 m wide, and 15.85 m high, and it is divided into 3 zones (Figure 3 and Figure 4): the preparation zone (150 m long), the analytic zone (90 m long), and the exit zone (60 m long). The length of the preparation zone is chosen to allow for sufficient vortex development in the wake behind the vehicle, whereas the exit zone allows for the vehicle to exit the analytical zone without negatively affecting the movement of particles and air in the analytical zone.

The dispersion of coarse aerosol droplets generated by vehicles is investigated for two traffic configurations: a single passing truck and two trucks traveling 66 m apart. In the task with one vehicle, the vehicle is placed in a separate subdomain consisting of a 603 m long prism. The task with two vehicles is modeled in the same way, but the subdomain with the vehicles was 669 m long. Placing the vehicle(s) in a separate subdomain allowed for the vehicle motion to be simulated by using a sliding mesh technique.

The domain mesh with one vehicle has 740 thousand polyhedral cells and the mesh with 2 vehicles had 860 thousand polyhedral cells. Cells in close proximity to vehicles have diameters within the range of 0.05 and 0.2 m, and the maximum size of all other cells is 0.5 m.

The vehicle is modeled with simplified geometry based on [19]. It represents a general, most commonly used, truck with a length of 16 m, a width of 2.7 m and a height of 4 m.

Our preliminary calculations have shown that detailed modeling of the splash of droplets from rotating wheels entering the liquid layer is inefficient and has unacceptably high computing requirements because of the scale of the task. Therefore, a simplified model was considered, where particles are injected from the sidewalls of tires. Although this simplified boundary condition does not capture in detail the physics of water ejection from the tread grooves, it provides a consistent source term in all simulated cases. This consistency ensures that the observed differences in dispersion are caused solely by aerodynamic factors (wind and traffic) and not by source variability, allowing for a valid comparative analysis. This numerical study addresses the dispersion of aerosols consisting of larger droplets with a diameter of 25 µm. These are constant diameter inert particles with a total flow rate of 4.5 kg·s⁻¹, because according to findings published in [13], particles of this size reached the distance at which they were counted in the highest numbers. The material of particles was simplified to liquid water with a density of 1000 kg·m⁻³.

The calculation was carried out in 4 steps. For both the one-vehicle and the two-vehicle tasks, all steps are the same in principle, with only minor differences in steps 3 and 4.

Step 1: Air flows through the entire domain (that is, preparation, analytical and exit zone) at 20 m·s⁻¹ and the vehicle (or the first of two vehicles) is located 3 m in front of the preparation zone. This step lasts 45 s of flow-time, until the domain velocity could be considered steady.

Step 2: The vehicle (or the first of two vehicles) enters the preparation zone at a constant speed of 25 m·s⁻¹ until it reaches the “start position” at a distance of 120 m from the analytic zone boundary. This step lasts 1.32 s of flow time.

Step 3: The vehicle continues to move through the preparation zone at a constant speed of 25 m·s⁻¹ and droplets of water begin to spray from its wheels. In the case of two vehicles, the second vehicle will also start spraying water droplets when it reaches 120 m from the analytic zone boundary. This step lasts 4.8 s of flow time for both cases.

Step 4: The vehicle enters the analytic zone at a constant speed of 25 m·s⁻¹ and water droplets are still spraying from its wheels. It moves through the entire zone, and after 8.64 s of moving, when the vehicle (second vehicle for two-vehicle task) is in the exit zone for its entire length, the calculation ends. In the case of the two-vehicle problem, the second vehicle enters the analytic zone after 2.64 s and, like the first vehicle, water droplets spray from its wheels. The single vehicle or the first of the two vehicles has the same driving time of 8.64 s for an easier comparison of the two tasks, during which they inject the same amount of aerosol into the domain. The distance they travel is 216 m. The second vehicle in the two-vehicle task travels only 150 m, which is a sufficient distance for it to leave the analytic zone entirely.

All transient simulations were performed with a fixed time step of Δt = 0.01 s.

The calculation was carried out for six variants of wind direction, which are shown in Figure 5. The seventh variant is “no wind” (that is, wind velocity 0 m·s⁻¹). The wind direction vector lies in the horizontal plane XZ, in which its angle to the X-axis is also measured. If the direction of the wind is relative to the direction of travel of the vehicle(s), then the symbol −X corresponds to the wind in the direction of travel and +X to the wind acting against the direction of travel of the vehicle. Wind blowing from the right side of a moving vehicle is indicated by +Z (that is, wind blowing from sampling planes), and wind blowing from the left side is indicated by −Z (that is, wind blowing on sampling planes).

The calculations are performed on the Karolina high-performance computing cluster, which is equipped with 128 core processors.

2.1.1. Boundary Conditions

The bottom faces of the domain and the walls of the truck have a wall boundary condition. The top face of the domain is the free-slip wall. The front, back, left and right sides of the domain are velocity inlets or pressure outlets, depending on the direction of the wind flow, according to Figure 5. There are also interfaces between the moving subdomain and the surrounding domain, allowing for smooth fluid and particle transport.

As mentioned above, the inlet wind (air) speed is 20 m·s⁻¹. Vehicle/vehicles move at a constant speed of 25 m·s⁻¹.

2.1.2. Mathematical Model

The simulation of the problem includes two different phases: the continuous phase consists of air and the discrete phase contains water droplet particles. Considering the high velocity of the water mist after release from the wheels and considering the velocity of the surrounding air due to wind and vehicle motion, a k-ε turbulence model is used to account for the effects of turbulence. This model was selected based on its proven capability to predict vehicle-induced turbulence and near-road dispersion trends in similar computational domains [20].

The standard two-equation k-ε model is based on model transport equations for the turbulence kinetic energy, k, and its dissipation rate, ε. The turbulence kinetic energy, k, and its rate of dissipation, ε, are obtained from transport Equations (1) and (2)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho k{\overline{u}}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}){\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(1)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho \epsilon {\overline{u}}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }\mathsf{\rho }{\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }$$

(2)

where $G_k$ [kg·m⁻¹s⁻³] represents the generation of turbulence kinetic energy due to the mean velocity gradients calculated, $G_b$ [kg·m⁻¹s⁻³] is the generation of turbulence kinetic energy due to buoyancy and $Y_M$ [kg·m⁻¹s⁻³] represents the contribution of fluctuating dilatation in compressible turbulence to the overall dissipation rate. $C_{1\epsilon }$, $C_{2\epsilon }$ and $C_{3\epsilon }$ are constants. ${\sigma }_k$ and ${\sigma }_{\epsilon }$ are the turbulent Prandtl numbers for k and ε, respectively. $S_k$ [kg·m⁻¹s⁻³] and $S_{\epsilon }$ [kg·m⁻¹s⁻⁴] are user-defined source terms.

The turbulent viscosity, ${\mu }_t$, is computed according to Equation (3), where $C_{\mu }$ is constant.

$${\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}$$

(3)

Model constants have the following values [21]:

$$C_{1\epsilon }=1.44,C_{2\epsilon }=1.92,C_{\mu }=0.09,{\sigma }_k=1,{\sigma }_{\epsilon }=1.3$$

(4)

In Equations (1)–(3), u [m·s⁻¹] represents the velocity, ρ [kg·m⁻³] is the density of the flowing medium, t [s] is time, $\overline{{u^{\prime }}_{𝚤}{u^{\prime }}_{𝚥}}$ [m²s⁻²] is the mean value of the product of velocity fluctuations, k [m²s⁻²] is the turbulent kinetic energy and μ_t [Pa·s] is the turbulent dynamic viscosity.

The discrete phase model (DPM) is based on the Euler–Lagrange approach. The fluid phase is treated as a continuum by solving the Navier–Stokes equations, while the dispersed phase is solved by tracking a large number of droplets through the calculated flow field. The droplet trajectories are individually computed at specified intervals during the fluid phase calculation.

Ansys Fluent predicts the trajectory of a discrete phase particle by integrating the force balance on the particle, which is written in a Lagrangian reference frame. This force balance equates the particle inertia with the forces acting on the particle and can be written as

$$m_p{\displaystyle \frac{d{\overline{u}}_p}{dt}}=m_p{\displaystyle \frac{\overline{u}-{\overline{u}}_p}{{\tau }_r}}+m_p{\displaystyle \frac{\overline{g}\left({\rho }_p-\rho \right)}{{\rho }_p}}+\overline{F}$$

(5)

where $m_p$ [kg] is the particle mass, $\overline{u}$ [m·s⁻¹] is the fluid phase velocity, ${\overline{u}}_p$ [m·s⁻¹] is the particle velocity, $\rho$ [kg·m⁻³] is the fluid density, ${\rho }_p$ [kg·m⁻³] is the density of the particle, $\overline{F}$ [kg·m·s⁻²] is an additional force, $m_p{\displaystyle \frac{\overline{u}-{\overline{u}}_p}{{\tau }_r}}$ is the drag force [kg·m·s⁻²] and ${\tau }_r$ [s] is the particle relaxation time, calculated by the following:

$${\tau }_r={\displaystyle \frac{{\rho }_p{d}_p^2}{18\mu }}{\displaystyle \frac{24}{C_{d}Re}}$$

(6)

where $\mu$ [kg·m⁻¹·s⁻¹] is the molecular viscosity of the fluid and $d_p$ [m] is the particle diameter.

Re [-] is the relative Reynolds number, which is defined as

$$\mathrm{Re}\equiv {\displaystyle \frac{\rho d_p\left|{\overline{u}}_p-\overline{u}\right|}{\mu }}$$

(7)

Tracking the movement of a large number of particles in a simulation is computationally intensive. To reduce the computational complexity, Ansys Fluent does not track particles directly but, rather, their clusters called parcels, which are groups of particles with identical properties (i.e., diameter, velocity, position, material) [21]. Each parcel corresponds to a fraction of the total mass flow rate, with the number of particles per parcel determined by the injection setup and meshing conditions. For the simulations in this article, the number of particles in the parcels is calculated as

$$NP={\dot{m}}_s{\displaystyle \frac{∆t}{m_p}}$$

(8)

where $NP$ is the number of particles in parcel, $m_p$ [kg] is the particle mass, ${\dot{m}}_s$ [kg·s⁻¹] is the mass flow rate of the particle stream and $∆t$ is the time step size [s]. The dispersed phase was introduced via surface injection from the sidewalls of wheels, generating one parcel per mesh face per time step. The particle trajectory integration utilized an adaptive time-stepping scheme with a maximum tracking error tolerance set to 10⁻⁵.

2.1.3. Sampling Planes

To monitor the number of particles that reach the locations of the monitoring stands during vehicle’s/vehicles’ passage, 3 sampling planes were defined in the analytical zone at distances corresponding to the experiment (Figure 2 and Figure 5). These planes were located on the right side, from the point of view of the direction of travel of the vehicle at distances of 5, 9 and 13 m from the edge of the road. If any of the particle parcels hit the sampling plane, data about this hit were recorded, but the further movement of this particle parcel was not limited by the hit and may have possibly hit some of the other sampling planes.

Although the height of the monitoring stand was approximately 1.5 m [15], previous calculations have shown [22] that a height of 1.5 m may be limiting in regard to monitoring particle passage for a given task. Therefore, sampling planes were considered at the full height defined by the domain thickness, because capturing particles on small target areas (corresponding to experimental sensors) during a short-term simulation would result in insufficient data capture.

Table 1. Dimensional characteristics of the sampling planes.

	Height [m]	Y Coordinate of Bottom Edge [m]	Y Coordinate of Top Edge [m]
Sampling plane 5	13.47	2.38	15.85
Sampling plane 9	11.57	4.28	15.85
Sampling plane 13	9.67	6.18	15.85

shows the total heights and y-coordinates of the bottom and top edges of each sampling plane. The different values of the y-coordinates of the lower edge of each sampling plane result from the geometry of the sloping terrain upon which the measuring stands are located (Figure 2).

To obtain a better idea of which part of the sampling planes is most frequently hit by particles, all sampling planes were divided into 10 equal subzones of 9 m width (Figure 6). Subzones are indicated by x-coordinates, where x = 0 is the entry point of the vehicle into the analytical zone.

2.1.4. Model Simplifications

The interpretation of the results requires taking several simplifications that are inherent to the numerical model into account. First, regarding the discrete phase, the aerosol droplets are modeled as inert spheres of a single uniform diameter. The simulation neglects the variety of droplet sizes found in a real spray, as well as physical phenomena such as droplet evaporation, breakup, and coalescence, meaning that potential changes in particle size and mass during flight are not considered. Second, concerning the continuous phase, the turbulence is resolved using the standard k-ε model. This approach provides a time-averaged description of the turbulent flow field. While effective for capturing general dispersion trends that are suitable for this study, it implies that instantaneous turbulent fluctuations are resolved in an averaged sense, rather than explicitly simulating the transient eddy structures in the vehicle wake. Third, the geometry and boundary conditions represent an idealized scenario. The vehicle is modeled with a simplified shape, and the domain corresponds to a specific terrain shape, generating airflow patterns that may differ from open-road conditions. Finally, the traffic is simulated as isolated passages to capture the primary wake effects, rather than representing a complex continuous traffic flow.

3. Results

Table 2. Extended summary of discrete phase modeling.

	Wind direction
	+X +Z 60	+Z 90	−X +Z 60	+X −Z 60	−Z 90	−X −Z 60	No wind
One-vehicle task
Aborted particle parcels	124	834	117	9	18	35	22
Escaped particle parcels	29,142	167,301	241,661	251,305	120,944	491,293	7360
Injected particle parcels $N_{inj,1}$	1,998,528	1,998,528	1,998,528	1,998,528	1,998,528	1,998,528	1,998,528
Aborted/Injected ratio	0.0062%	0.0417%	0.0059%	0.0005%	0.0009%	0.0018%	0.0011%
Escaped/Injected ratio	1.5%	8.4%	12.1%	12.6%	6.1%	24.6%	0.4%
Two-vehicles task
Aborted particle parcels	777	557	315	204	47	28	58
Escaped particle parcels	53,679	94,612	281,440	271,284	189,866	517,535	9927
Injected particle parcels $N_{inj,2}$	3,213,000	3,213,000	3,213,000	3,213,000	3,213,000	3,213,000	3,213,000
Aborted/Injected ratio	0.0242%	0.0173%	0.0098%	0.0063%	0.0015%	0.0009%	0.0018%
Escaped/Injected ratio	1.7%	2.9%	8.8%	8.4%	5.9%	16.1%	0.3%

gives a summary of all calculations performed in terms of injection and tracking of particle parcels. For the one-vehicle task, the total number of injected parcels is 1,998,528, and for the two-vehicle task, it is 3,213,000, and both values are the same for all considered wind directions. The difference between them is caused by the different number of vehicles in both tasks. In the two-vehicle task, the second vehicle travels a shorter distance, during which it generates droplets than the first vehicle. From the perspective of numerical uncertainty, the ratio between aborted and injected parcels is negligible. For all tasks, it is less than 0.042%, which means that the tracking of the vast majority of particles captured virtually their entire trajectory, ensuring the statistical robustness of the dispersion results. The ratio of escaped to injected particles shows in which wind directions there is a greater or lesser escape of particles from the domain through the outlet zone and in which directions the particles tend to remain in the domain.

3.1. Influence of Wind Direction and Number of Vehicles

The amount of aerosol particles that reached the sampling planes in different wind directions and in calm conditions for both traffic configurations is shown in

Table 3. Number of particle parcels recorded on sampling planes. Left: One-vehicle task. Right: Two-vehicle task.

	One-vehicle task			Two-vehicles task
	Sampling plane			Sampling plane
Wind direction	Plane 5	Plane 9	Plane 13	Plane 5	Plane 9	Plane 13
+X +Z 60	58,761	1467	0	163,842	15,378	0
+Z 90	130,150	4183	0	259,998	57,077	0
−X +Z 60	35,515	8436	0	220,629	23,720	0
+X −Z 60	7314	10,323	10,623	28,380	18,820	15,712
−Z 90	0	0	0	0	0	0
−X −Z 60	8359	612	2579	46,519	5153	3996
No wind	37,138	69	0	65,094	0	0
Avg. of +Z directions	74,809	4695	0	214,823	32,058	0
Avg. of −Z directions	5224	3645	4401	24,966	7991	6569
Avg. of all incl. No wind	39,605	3584	1886	112,066	17,164	2815

. The table also shows the arithmetic means of the number of particles recorded on individual planes when the wind was only blowing in the +Z or −Z axis direction, i.e., when the wind was blowing away from or toward the sampling planes. The total arithmetic means of the number of records from all directions, including no wind, are also given.

To compare the results of both traffic configurations, it is useful to disregard the absolute number of records on sampling planes, as this is necessarily higher for the two-vehicle task than for the one-vehicle task, due to the higher number of injected particle parcels. By relating these values to the total number of injected particle parcels in the relevant task, $N_{inj,i}$ (Table 2), it is possible to express for each wind direction the percentage of recorded particle parcels on the sampling planes that is relative to their total amount in a given task (Figure 7 and Figure 8). Figure 8 shows the changes in the recorded particle parcels between planes in detail.

$$N_{rel,i}={\displaystyle \frac{N_{rec,i}}{N_{inj,i}}}$$

(9)

where $N_{rel,i}$ [%] is the percentage of recorded particle parcels on one sampling plane, $N_{rec,i}$ is the number of recorded particle parcels on one sampling plane and $N_{inj,i}$ is the number of injected particle parcels in the task; index $i\in \left\{1,2\right\}$ indicates a task with one or two vehicles.

Table 3 and Figure 7 and Figure 8 show how the wind direction and the number of vehicles affect the hitting of particles on the individual sampling planes. The most significant difference in the particles’ hitting trend occurs when comparing the +Z and −Z directions: see the averages in Table 3. For both modeled cases of one or two vehicles, no particles reached Plane 13 in either of the modeled cases in any traffic configuration when the wind was blowing from the +Z direction. For winds from the −Z direction, the opposite trend is evident, as particles reached the furthest plane, Plane 13, in both traffic configurations. The highest percentage of particles reached Plane 13 when the wind direction was +X−Z 60 in both traffic variants.

The calculated averages also show a significant difference in the number of particles recorded on the nearest plane, Plane 5, which is closest to the road in both variants. When the wind direction is +Z, many times more particles reach Plane 5 than when the wind blows from the opposite direction, −Z.

Figure 7 shows that for all wind directions, the number of particles recorded on the sampling planes decreases with the increasing distance, with exceptions in cases with one vehicle in the +X−Z 60 and −X−Z 60 directions. In these two cases, less than 1% of the particles were recorded on all planes.

For the no-wind variant, particles were recorded on the closest plane, Plane 5, in both traffic configurations, and on Plane 9 only in the one-vehicle task.

The recorded values for wind direction −Z90 are zero.

The difference, $R_{2,1}$, between the two traffic configurations, expressed as the percentage of particle parcels recorded on a given sampling plane, $N_{rel,i}$ [%], is determined according to Equation (10):

$$R_{2,1} =N_{rel,2}-N_{rel,1}$$

(10)

where $N_{rel,2}$ [%] is the relative ratio of recorded particle parcels on one sampling plane in the two-vehicle task and $N_{rel,1}$ [%] is the relative ratio of recorded parcels on the same sampling plane in the one-vehicle task. $N_{rel,2}$ and $N_{rel,1}$ are calculated according to Equation (9). Figure 9 shows these differences for all wind directions, including no wind. The graph shows that doubling the number of vehicles usually results in at least a small increase in the percentage of records on the sampling planes. A slight decrease in the percentage of records for two vehicles occurs only on Plane 13, in the −Z directions and in no-wind conditions. The observed differences are caused by the fact that the second vehicle travels in the wake of the first vehicle. This modified airflow influences the dispersion of particles generated by the second vehicle.

3.2. Distribution of Captured Droplets and Relative Density of Droplets in Subzones

The number of particle parcels, as well as the distribution and relative density of captured droplets in 10 individual 9 m subzones, according to Figure 6, can be seen in the graphs and figures in Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21. The results are shown for six wind directions and for both traffic configurations, and they serve to illustrate the distribution of droplets on individual sampling planes. The upper limit of the vertical axis in the graphs in Figure 11, Figure 13, Figure 15, Figure 17, Figure 19, and Figure 21 is determined automatically, according to the highest y-coordinate of the droplets, provided that any particles are recorded in the given sampling plane. If no particles are recorded, then the limits on the y-axis are given by the values in Table 1. There is no graph for wind direction −Z90, because the recorded values are zero.

In all directions of wind, and in no-wind conditions, the most numerous records were on Plane 5. In the case of winds from the +Z direction (Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15), they were distributed along the entire length of the sampling plane, with at least a small number of droplets recorded in each subzone. On Plane 9, droplets occurred only in some subzones, which differed according to the specific wind direction. They did not reach Plane 13. In terms of the height reached by the droplets, the records are similar, with their upper limit generally being 6 to 7 m.

In the case of winds from the -Z direction (Figure 16, Figure 17, Figure 18 and Figure 19), significantly fewer droplets were recorded than in the case of winds from the +Z direction, but they reached higher heights, up to 12 m in the two-vehicle task, and in both cases they reached Plane 13. However, their distribution along the length is not uniform on either sampling plane. There are zero records in some subzones of the sampling planes and their position varies depending on the direction of the wind and distance from the road. Therefore, it is clear that particles do not decrease with increasing distance from the road, but are carried further by turbulent flow.

In calm conditions (Figure 20 and Figure 21), droplets were recorded only on the nearest plane, Plane 5, and only locally on two to four short sections. Only 69 particle parcels were recorded on Plane 9, which is almost zero percent in relation to the number of particles injected. The highest altitude at which the particles hit the sampling planes ranges from 6.5 to 7 m. Unlike other wind directions, the particles reached a higher altitude during the one-vehicle task.

3.3. Wind Influence in the Modeled Area

According to the available long-term measurement data from the Czech Hydrometeorological Institute (CHMI), southwest winds prevail in the wider region, which also includes the section of road we are modeling. The measured wind direction frequencies in

Table 4. Windrose data.

Wind Directions								No Wind	Sum
N	NE	E	SE	S	SW	W	NW
10.58	9.38	8.54	5.07	10.51	42.88	5.37	7.56	0.13	100

for the last year, 2024, were taken from the nearest meteorological station [23] and converted into a windrose diagram (Figure 22).

Figure 23 shows the computational domain from Figure 5, overlaid on a map and rotated to correspond to the actual modeled situation. The figure shows the orientation of the vehicle’s/vehicles’ direction of travel, the wind directions considered in the numerical simulations, and the location of the sensors (or sampling planes). The positive direction of the x-axis (see Figure 5) points northwest in Figure 23. The prevailing southwest wind corresponds to the modeled direction +Z90.

Using the frequencies of wind directions from different cardinal directions according to CHMI (Table 4), weights for the directions used in the simulation (

Table 5. Weights of simulated wind directions, taking into account windrose data.

direction symbol	d1	d2	d3	d4	d5	d6	d7
direction name	+X +Z 60	+Z 90	−X +Z 60	+X −Z 60	−Z 90	−X −Z 60	No wind
weight symbol	w1	w2	w3	w4	w5	w6	w7
weight value	21.30	42.88	17.87	8.82	9.38	10.18	0.13

) were calculated using relations (11). Linear weighting was applied to reflect the smooth variation in dispersion and to avoid artificial discontinuities at sector boundaries. The following consideration was used as a basis: according to Figure 23, the directions +Z 90 and −Z 90 (i.e., $d_2$ and $d_5$ in Table 5) are oriented identically to the SW and NE directions, and therefore the values from Table 4 are entered in full into the calculation of weights $w_2$ and $w_5$, according to relations (11). The same applies to weight $w_7$ for no wind. The other directions are rotated by angles of 15 and 30 degrees, relative to the directions determined by the windrose diagram; therefore, their contribution of $1/3$ or $2/3$ of the corresponding value from Table 4 is taken into account in relations (11) for $w_1$, $w_3$, $w_4$ and $w_6$.

Using Equation (12), in which d_i is the number of particles recorded for a specific wind direction, according to Table 3 and Table 5, and w_i is the weight of this direction, the weighted average, $\overline{d}$, was calculated for both traffic configurations. The resulting values are shown in

Table 6. Number of particle parcels recorded on sampling planes—weighted arithmetic mean.

	Sampling planes
	Plane 5	Plane 9	Plane 13
One-vehicle task	68,935	4149	1085
Two-vehicles task	174,690	30,909	1621

.

$$\begin{array}{c}{w}_1={\displaystyle \frac{1}{3}}SW+{\displaystyle \frac{2}{3}}S{w}_2=SW{w}_3={\displaystyle \frac{1}{3}}SW+{\displaystyle \frac{2}{3}}W{w}_4={\displaystyle \frac{1}{3}}NE+{\displaystyle \frac{2}{3}}E\hfill \\ w_5=NE{w}_6={\displaystyle \frac{1}{3}}NE+{\displaystyle \frac{2}{3}}N{w}_7=No wind \hfill \end{array}$$

(11)

$$\overline{d}={\displaystyle \frac{{\sum }_{i=1}^7{d}_i{w}_i}{{\sum }_{i=1}^7{w}_i}}={\displaystyle \frac{d_1{w}_1+d_2{w}_2+\cdots +d_7{w}_7}{w_1+w_2+\cdots +w_7}}$$

(12)

Figure 24 presents the number of records on individual sampling planes when taking into account the influence of the windrose diagram, according to Table 6, and without the influence of the windrose diagram. For values without the influence of the windrose diagram, the arithmetic mean of the values of all directions, including no wind, was taken from Table 3.

Figure 24 shows that when the windrose diagram is taken into account, the number of records on the first two sampling planes is significantly higher. As the distance between the sampling planes and the road increases, the differences between the values that take the windrose diagram into account and those that do not decrease.

The effects of taking the windrose diagram into account on the ratio of recorded values between individual sampling planes are shown in the graph in Figure 25. The graph is based on the arithmetic mean values in the last row of Table 3 and the values in Table 6.

3.4. Comparison with the Experiment

As discussed in the Introduction, the authors of the article [15] recorded experimental measurements of chloride ion concentrations on a specific road near Ostrava during the winter period. Their measuring stands, V2-C to V4-C, were located in a road cut at distances of 5 m, 9 m and 13 m from the roadside, which corresponds to the location of sampling planes 5, 9 and 13 in the computational model. The measured values of cumulative surface salinity for the measuring points and periods corresponding to the numerical analysis of the cited article are shown in Figure 26. For an indicative comparison of trends in changes in values between measuring stations and sampling planes, the same graph also shows values from Table 6, which are results from numerical simulations that have been recalculated according to the windrose diagram of prevailing wind directions.

Although this is a comparison of results in different units and of a different nature, Figure 26 nevertheless shows a clear trend, which is evident in half of the measured data series and in both simulated traffic configurations, where the value decreases with the increasing distance of the measuring stand or sampling plane from the source of particles: that is, from the road. A small exception is the measurements from February and March 2024, where higher surface salinity was measured at the more distant V3-C stand than at the closer V2-C stand.

It is important to note that this study only simulated the short passage of one or two vehicles. Therefore, the results primarily show the immediate response of droplets to wind conditions, not their long-term behavior.

4. Discussion

4.1. Influence of Terrain and Wind Direction

The dispersion and range of particles in the modeled tasks are not only influenced by the wind direction but are also significantly affected by the shape of the terrain. The road is located in a 7.85 m deep cut, which means that the wind in the specified directions only directly affects the upper half of the calculation domain (i.e., approximately the upper 8 m). At lower levels, the direction of particle movement is determined by the turbulence caused by traffic and the shape of the terrain. This fact is key to interpreting the findings below.

The observed differences in the recorded quantities and distances reached by the particles show that the wind direction has an influence on their dispersion (Table 3, Figure 7 and Figure 8).

In the case of winds blowing from the +Z direction, which is the direction of flow from the sampling planes towards the vehicle, the largest number of particles was recorded on the sampling planes (reaching a peak capture ratio of approx. 6.5%). However, the vast majority of the particles only reached Plane 5. Only a negligible fraction of the amount from Plane 5 reached the following plane, Plane 9. Plane 13 was not affected by particles from this direction of wind. The intense decrease in records between the individual sampling planes clearly shows the restrictive effect of the wind on particle movement. We see the cause of the significant accumulation of records on the nearest plane, Plane 5, in the aforementioned shape of the road profile and the surrounding terrain, which is a basin-shaped depression. The shape of the basin naturally promotes a circulating air flow, which significantly aids in the transport of particles to the sampling planes. The influence of gravity and the slope of the hill are factors that limit the particles from reaching the more distant Planes 9 and 13.

When winds blew from the -Z direction, which is the direction of flow from the vehicle to the sampling planes, several times fewer particles (generally < 1%) were recorded on the planes than when the winds blew from the +Z direction, but a stable non-zero number of particles was recorded on all three planes, up to the distance of 13 m. The decrease in the number of records between individual planes is not as intense as with wind from the +Z direction; in the single-vehicle task, it can even be considered to be negligible.

In the no-wind conditions, particles were recorded on the nearest plane, Plane 5, in both traffic configurations and also on Plane 9 in the single-vehicle task.

4.2. Influence of the Number of Vehicles

Numerical calculations for all wind directions, including no wind, and for both variants of the number of vehicles confirm that a higher percentage of particles was recorded after the passage of two cars, increasing the maximum recorded capture ratio to 8.1% (Figure 7).

Figure 9 shows that in all cases, more particles were recorded on Plane 5 after the passage of two vehicles. In contrast, more particles were recorded only on the most distant sampling plane after the passage of one vehicle for both −Z wind directions and in the case of no wind. In these cases, however, the difference between the two traffic configurations is very small, approaching zero.

The results shown in Figure 11, Figure 13, Figure 15, Figure 17, Figure 19 and Figure 21 confirm that the presence of two vehicles changes the dispersion of particles in space. These figures, showing the relative density of droplets, clearly show a higher density of particles recorded for the two-vehicle variant in most of the tasks that were solved. For both traffic variants, the particles reached a similar height on all sampling planes, except for the +X−Z60 direction. In this case, when two vehicles passed, the particles were recorded at approximately twice the height on all surfaces than when one vehicle passed, reaching up to 13 m above the road compared to the maximum of approximately 7 m observed for the single-vehicle task.

4.3. Comparison with Long-Term Measurements

From the variability of the records of the experimental research in Figure 26 [15], it is clear that the climatic conditions and the related winter road maintenance and amount of road salt are significant factors influencing the measured values.

Although this is a comparison of results in different units and of a different nature, a similar trend can be seen in part of the measured data and in both simulated traffic configurations, where the value decreases with the increasing distance of the measuring stand or sampling plane from the particles’ source. A detailed comparison (Figure 26) shows that the decrease in the simulated values is significantly higher than in the experimental data, which can be attributed to the simplified nature of the model and the particle size considered (25 µm), which fall mainly at a relatively short distance from the road.

From the perspective of the practical application of the simulation results, it can be observed in the relative density graphs (Figure 11, Figure 13, Figure 15, Figure 17, Figure 19 and Figure 21) that the location of areas with the highest particle density varies, depending on the wind direction and traffic intensity. The simulations indicate that particle concentrations exhibit significant spatial variations within a range of 10–15 m.

The use of a device with a relatively small sampling area in one location may mean that a significant part of the aerosol will miss it during measurement. Therefore, when planning experimental measurements, we recommend placing measurement equipment not only in a direction that is perpendicular to the axis of the road, but also in a direction that is parallel to it, with a spacing of approximately 9 m. This configuration is needed to capture the spatial gradients and to empirically verify the longitudinal homogeneity during long-term monitoring.

Both numerical simulations and experimental measurements have limitations. Experimental data capture the accumulation of chloride ions over several months, while numerical simulations describe short-term processes that last only a few seconds and reflect the immediate response of sprayed droplets to the current wind direction. Although the measurements correspond to real traffic involving different types of vehicles and variable conditions, the numerical analysis is based on an idealized scenario of one or two vehicles passing through. Furthermore, treating droplets as inert mass without evaporation provides a conservative estimate of the maximum dispersion range, as aerodynamic transport dominates within the short simulation timeframe.

To reduce these limitations, future work should combine simulations of various wind scenarios with local weather data. Additionally, including droplet evaporation would better reflect the real deposition range. Furthermore, based on the obtained results, it is suggested that future research could focus on increasing traffic intensity in numerical models, including finer particle fractions, extending simulation times and monitoring particle reach on both sides of the road.

5. Conclusions

Based on the numerical simulations of de-icing salt aerosol dispersion and their comparison with experimental data, the following conclusions can be drawn:

• Influence of terrain and wind: The location of the road in a deep cut (7.85 m) significantly shapes the airflow. While the wind direction influences dispersion, the terrain profile creates local turbulence. Wind blowing from the sampling planes towards the vehicle (+Z) causes high particle accumulation near the road due to recirculation (within 5 m) but limits long-distance transport. Conversely, wind blowing away from the vehicle to the sampling planes (−Z) transports particles to greater distances (exceeding 13 m), but with several times fewer particles recorded.
• Effect of traffic intensity: The passage of two vehicles resulted in a higher number of recorded particles compared to a single vehicle. The simulations confirm that an increased traffic intensity alters the spatial dispersion of the aerosol. While the vertical reach was generally similar for both traffic variants, specific wind conditions caused particles to reach significantly higher levels during the passage of two vehicles, extending the plume height from approx. 7 m up to 13 m.
• Practical implications for measurement: The simulations reveal significant spatial variations in particle concentration within a range of 10–15 m. Using a single measurement device may lead to missing the main aerosol cloud. Therefore, for future field experiments, we recommend placing measurement equipment not only perpendicular to the road axis but also parallel to it, with a longitudinal spacing of approximately 9 m, to capture the spatial gradients effectively.

Future research should focus on simulations with higher traffic intensity, finer particle fractions (<25 µm) and extended simulation times to better reflect complex real-world conditions.