A computational study of particulate emissions from Old Moor Quarry, UK

Abstract This paper presents an evaluation of a buoyancy-modified k − e dust dispersion model for predicting fugitive dust deposition from a surface quarry. The dust clouds are modelled as volumetric emissions and their dispersion simulated by coupling the flow-field with stochastic tracking of the particulates. The coefficients of the turbulence model are modified and source terms are added to the turbulence equations to permit simulation of both adiabatic and diabatic atmospheric stability conditions. These modifications ensure compatibility with Monin-Obukhuv similarity scaling of the atmospheric surface layer. Also, mesoscale wind direction variability is included. The Monin-Obukhuv scaling parameters have been derived from routine meteorological data recorded during a month-long monitoring campaign conducted at the quarry. Dust deposition measurements from a network of Frisbee deposition gauges are used to validate the predictions of the CFD model. A number of statistical performance metrics have been applied to evaluate the degree of uncertainty in the predictions. The dust deposition predictions of the CFD model are compared to those of the UK-ADMS, to demonstrate how the treatment of the terrain in the CFD model improves the accuracy of the deposition predictions.

(1 − a)K + + c 1 T 6 a − σT 4 a + c 2 N 1 + c 3 , and surface sensible heat flux, where c 1 is an empirical constant determined by Swinbank (1963) The surface sensible heat flux can subsequently be determined from, benches and slopes. However, since we are including the quarry geometry ex-230 plicitly here, a roughness length corresponding to the surrounding terrain has 231 been adopted. The quarry is predominantly surrounded by grasslands and low 232 vegetation, thus, a surface roughness length of z 0 = 0.1 m has been assumed.

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The first iteration is carried out for neutral atmospheric conditions, such 234 that the Businger-Dyer non-dimensional wind shear has the value of unity, and u * is computed from substitution of the reference  processes under these strongly advective conditions. In Figure 2, the frequency 255 conditions. Therefore, they are preferred for estimating continuous releases over Moor Quarry.

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In Table 2, the Easting and Northing coordinates of the centres of the blasts  The source regions are illustrated in Figure 3(a) and it can be seen that 305 some are very close to each other. Therefore, for expediency, the blasts clouds 306 in these clusters are represented by "average" blasts as shown in Figure 3(b).

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The bounding vertices and average emission rates of these average blasts are 308 listed in Table 3.        The run time for each simulation ranged from 8 to 10 hours.
399 Figure 5 shows the surface mesh including the prismatic boundary layer.

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The region inside the rectangle is magnified in Figure 6 to better illustrate the 401 prismatic boundary layer applied near the ground.
and for L > 0, where u * is the friction velocity and the temperature scale, T * , is given by whereq w is the surface heat flux, c p is the specific heat capacity of air, g is and where ψ is the solution to a Poisson equation where u and v are the x and y-components of velocity, θ is the wind direction 473 and u 10 is the wind speed at a reference height of 10 m above the ground. Note 474 that North is aligned with the y-axis.

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In Figure 9 the wind approaches the quarry from the NW and passes over

Performance Metrics for Dispersion Model Evaluation
The geometric mean bias, MG, evaluates the mean error, but on a logarithmic subsequently the random component of the total NMSE, can be obtained from, where the subscripts s and r refer to systematic and random respectively.

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In dispersion studies which attempt to analyse the degree of correlation

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Therefore the exposure duration was taken as the meteorological averaging time.  Table 6 contains observed deposition as well as dust deposition predicted by 587 UK-ADMS and the k − ε model. The k − ε predictions consist of two datasets: 588 one for a single simulation at the wind direction stated in Table 5; and one 589 which incorporates a wind direction variability correction.
which specify a constant value of σ θ for winds above 5 ms −1 . UK-ADMS imposes 606 a limit of ±π/6 to wind direction variability to restrict wind direction variability 607 to realistic values in low wind conditions, thus the component of wind variability 608 due to motions which exceed the turbulence scale is given by: for −π/6 ≤ σ θ ≤ π/6, where σ θ represents the wind direction variability in 610 radians, T A is the averaging time in hours and U 10 is the wind velocity in ms −1 611 at a reference height of 10 m above the ground (Moore, 1976).

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The process of weighting the contribution of each of the directional variations 613 including the mean wind to the resultant plume was automated in MATLAB 614 according to the following equation: whereĀ is the weighted average accretion rate, i is an integer corresponding to the simulation number, n is the total number of simulations and p is the to σ θ /2, thus determining the probability of occurrence of each wind direction 624 variation from the following expression, where φ is the integration variable.

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The wind variability post-processing methodology has been applied to ob-627 tain weighted summations for the five blast events which contributed most to 628 dust deposition at the gauge locations. Table 5 gives the wind speed, u h , the 629 prevailing wind direction,θ and the standard deviation of the wind direction 630 variability, σ θ , for each of these blast events.

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The observed dust deposition is equivalent to the mass of dust accumulated 632 on the filtration medium. For each of these datasets, a reduction of the emission 633 factor has been considered resulting in two sub-datasets, EF 1.0 and EF 0.5 which 634 correspond to 100% and 50% of the emission factor respectivel (Table 6). Also, 635 the occurrence of zero values in the CFD dataset without wind variability is 636 likely to be due to the use of a finite number of particles injected into the model,

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since accretion rates at a specific location on the wall boundary are dependent 638 on particles colliding with the wall at that location.

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The k − ε model predictions of cumulative dust deposition over the mea- the data by either the mean observed or mean predicted deposition is recommended in order to offset systematic errors. In addition, 1:2, 2:1 and 1:1 corre-647 lation lines have been superimposed on the plots to permit assessment of F AC2 648 in accordance with the model performance evaluation procedure prescribed by From Figure 13(a), it appears that UK-ADMS has a tendency to over predict    (Table 7). An hence re-ordering of the data pairs is likely to change the random scatter.

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The results indicate that all the models over-predicted deposition when 100% of the emission factor was considered. At 50% of the emission factor, the k − ε   The error bars on Figure 17 show that approximately 83% of the k − ε model