Description of experimental windbreak sites with tree type. All locations are located within 50km of the Island of Montreal, Canada, in the south west region
Worldwide, population and economic growth has reduced the distance separating residential areas and odour sources. Annoyance can result from not only obnoxious odours but also prolonged pleasant odours such as produced by a chocolate or frying factory. Odours indirectly affect human health through stress (Evans & Cohens, 1987) and their impact is greater when humans are exposed to a continuous rather than an intermittent source. People with a problem coping style (seeking a solution to the odour problem) can become more annoyed by odours than those using comforting cognition (telling themselves that the situation will improve) or having an emotional oriented style (those looking for a diversion) because the solution is often out of hand (Cavalini et al., 1991). Although pleasant odours can become annoying when too concentrated or persistent, malodours are perceived as unpleasant under most if not all conditions. Malodours are also known to activate a different area of the brain, as compared to pleasant odours (Zald & Pardo, 2000). According to Jacob et al. (2003), the response of humans to malodours is quite consistent and it differs compared to that of pleasant odours which produce a wider range of response. Furthermore, Jacob et al. (2003) found that the detection of any odour increases with dose and duration, but that the change in response of humans is much more important for small increases of malodour concentrations when presented at a low level just above their detection threshold.
Accordingly, odour dispersion models must take into consideration the olfactory response of humans. Noxious odours are likely much easier to model because most humans will classify them as an annoyance, as opposed to pleasant odours where the response is more variable. Furthermore, the human olfactory sense will detect the presence of an odour at a low level and if noxious, will immediately classify it as a nuisance. As the air concentration of the odorous gas increases, the relative level of annoyance does not increase as quickly. Furthermore, at a specific odorous gas air concentration, the response becomes intolerable and increasing the concentration any further will not increase the level of annoyance. To be accurate, this type of response must be incorporated into an odour dispersion model.
The use of separation or setback distances for odour sources conveniently insures the dilution of malodours to acceptable levels in the vicinity of neighbours (Redwine & Lacey, 2000). Nevertheless, conventional separation distances rely on the generalized odour emission associated with a given operation regardless of management issues. Accordingly, separation distances do not provide satisfactory legislation against nuisance in many instances (Jacobston et al., 2005). Effective separation distances need to consider a greater number of factors pertaining to odour emission rate and character, and subsequent dispersion before reaching the neighbours. Furthermore, management practices can change the cleanliness of the operation, the frequency and intensity of odour emissions and the location of the source on the property (Li & Guo, 2008; Le et al., 2005; Lim et al. 2001). Physical and climatic factors constitute other factors, namely topography and buildings, and atmospheric stability, air temperature, and wind velocity and direction (Schauberger et al., 1999; Zhu et al. 2000; Lin et al., 2007c, 2009a,b).
To improve the calculation of separation distances, several industrial models were modified for agricultural applications. The first models where steady state and Gaussian based (Chen et al., 1998; Smith & Watts, 1994) with a normally distributed exponential function extrapolated to ground level. Examples of such models are the ISCST3 and AUSPLUME. Later, McPhail (1991) and Gassman (1993) suggested that odours should be modelled as a series of puffs, to produce cycles of strong followed by weaker odour concentrations. An example of such models is INPUFF2, which is Gaussian based and is capable of simulating the release of odours over short intermittent periods. Zhu et al. (2000) tested this model in the Canadian Prairie Provinces with swine operations and resident panellists trained to compare odour annoyance against the n-butanol scale (ASTM 1999). Whereas the accuracy was relatively high up to a distance of 300 m from the source, INPUFF2 performed poorly at distances exceeding 400 m, where simulation was critical in determining the annoyance limit of the odour plume. Furthermore, the odour source emission rate needed to be scaled up by a factor of 35 and 10, for odours from livestock shelters and manure storages, respectively. CALPUFF is another Gaussian dispersion model simulating the dispersion of odours released over short time intervals, but with the added advantage of a Lagrangian function simulating the effect of spatially variable wind conditions. Xing et al. (2006) evaluated CALPUFF along with three other models, using once more panellists trained to recognize odour intensity using the n-butanol scale. The agreement between measured field data and the four models ranged between 37 and 50 %.
Computational Fluid Dynamics models have successfully simulated gas dispersion in complex spaces (Riddle et al., 2004), such as ammonia distribution in barns (Sun et al., 2002) and spray droplet transport in fields (Ucar & Hall, 2001). Lin et al. (2007b, 2009a, b) produced a model based on Computational Fluid Dynamics (CFD) to simulate odour dispersion downwind from natural windbreaks. The model was calibrated with field odour observations using panellists trained to associate odour concentration with an odour annoyance scale of 0 to 10, where 10 is the maximum level of annoyance. The CFD model required as input, the exponential equation correlating odour annoyance and concentration, as perceived by the panellists in an olfactory laboratory, after each morning of field measurements. The R2 exceeded 0.75 when all the data beyond 150 m was considered, as these observation points corresponded to odour concentration below 117 OU m-3 and within the annoyance scale of 1 to 10. For odour concentrations exceeding 117 OU m-3, the panellists were assigning the maximum annoyance level of 10, irrespective of the odour concentration value. In contrast, the n-butanol scale uses an odour intensity scale of 1 for 25 OU m-3, of 2 for 72 OU m-3, and so on up to 1834 OU m-3 for a scale of 5 (Guo et al., 2001). Accordingly, the n-butanol scale is designed to measure high odour concentration levels whereas the method used by Lin et al. (2007b, 2009a, b) is designed to measure odour levels in the vicinity of the threshold values. In determining separation distances, the threshold values can be most useful.
Windbreaks were suggested in the late 1990’s as a possible odour dispersion technique. Based on Asian research demonstrating the successful reduction of odours, North American livestock producers have used natural and artificial windbreaks on the fan side of livestock shelters to reduce odours emissions. The effect of a porous wall was studied by means of smoke emitters and simulated using a Gaussian model (Bottcher et al., 2000; Bottcher et al., 2001). The porous wall was found to vertically divert the odours from the exhaust fans and promote mixing with the wind flowing over the building, but not to be as effective as tall stacks. In Asia, solid walls have been used around livestock barns to precipitate dust released by the ventilation system (Bottcher, 2000). Dust has been shown to carry odours (Das et al., 2004). Such application requires a windbreak with a high porosity capable of reducing wind velocity and turbulence. The same principle has been applied to control snow and sand accumulation, reduce pesticide drift, increase crop yield and reduce heat losses from animals and buildings (Plate, 1971; Heisler & Dewalle, 1988; Wang & Takle, 1997; Ucar & Hall, 2001; Guan et al., 2003; Vigiak et al., 2003; Wilson & Yee, 2003a). Accordingly, several North American cooperative extension services offer information on planting natural windbreaks or tree shelter belts, suggesting a high porosity in the absence of solid scientific testing.
The objective of the present chapter is therefore to present the development of a model simulating the dispersion of odours or the size of the odour plume formed downwind from a natural shelter belt or windbreak located at a specific distance from an odour source. The purpose of the model was to identify the best management practices for the implementation of natural windbreaks minimizing the size of the odour plume; best management practices pertain to the properties of the windbreak itself, its location with respect to the odour source and the general climatic environment for the given region. The model uses Computational Fluid Dynamics (CFD) to estimate the size and intensity of the odour plume to establish the necessary separation distance between the source and the neighbouring receptor susceptible to annoyance. The model development includes the selection of a computational method capable of handling conditions of high turbulence, the addition of an olfactory perception equation and finally the output validation.
In summary and with the windbreak dispersion model developed, this Chapter will examine the features of natural windbreaks which enhance atmospheric dispersion and maximize the reduction in odour plume length. Finally, this Chapter will examine the effect of various climatic conditions on the performance of windbreak and their effectiveness in shortening odour plumes.
2. Field acquisition of calibrating and validating data
Field odour dispersion data was required to calibrate and validate the model. As well, typical natural windbreak characteristics were required to establish equations for its physical description. The field work therefore consisted in producing an odour generator which could generate an odorous air stream from a single point. Then, 5 sites were used to measure odour plumes under different climatic conditions: 1 control site without a windbreak, and 4 sites where the windbreaks offered different combinations of tree type, dimension and porosity. The distance between the odour generator and the windbreak were also varied. In all, 39 different field tests were conducted to obtain data for the calibration and validation of the model.
2.1. The field instruments
A mobile odour generator was designed and built to be able to produce, in the field, a controllable level of odour emissions during the experiment (Lin et al., 2006). The odour generator consisted of a 500 L tank filled with swine manure (Fig. 1). A pump provided a consistent flow of manure over a vertical porous filter through which air was blown at a rate of 1.65 m3 s-1. The odour generator offered an air/liquid contact surfaced of 76.8 m2.
During all field tests, the released odorous air was sampled at regular 30 minute intervals using Alinfan® bags. A laboratory forced choice dynamic olfactometer was then used to establish the threshold dilution value of each air samples by the same 12 trained panellists who observed the field odour plume dispersion. Odour concentration (OC) was expressed as "odour units per cubic meter" (OU m-3) (CEN, 2001; Schauberger et al., 1999; Zhang et al., 2002). The rate of odour production, OU s-1, was computed using the air flow rate of the odour generator.
During each field test and installed on a 7.6 m high tower, a weather station was positioned 200 m upwind from the windbreak to avoid disturbance. At one minute intervals, a computer recorded the temperature, wind direction and wind speed. The wind direction was measured before hand to estimate the range of the field odour plume and to direct panellists into the odour plume zone. Air stability values were obtained from the weather station at the Pierre Elliott Trudeau Airport (Montreal, Canada) located 50 km north of the field sites. This weather station was the nearest measuring Pasquill-Gifford atmospheric stability conditions.
2.2. The experimental windbreaks
This experiment was conducted using 4 uniform single row natural windbreaks located at least 5 km away from any livestock operation to eliminate interferences (Table 1; Fig. 2). The porosity of each windbreak was optically evaluated by measuring the percentage of open surface visible through the windbreak (Heisler and Dewalle, 1988; Guan et al., 2003).
Each natural windbreak was different in terms of porosity, tree type and height (Lin et al., 2006). The optical porosity of the windbreaks on sites 1 and 3 was 0.55 compared to 0.35 for those on sites 2 and 4 (Table 1). The windbreaks on sites 1 and 2 were of deciduous trees as compared to conifers for those on sites 3 and 4. All sites were located on farm land with a relatively flat and consistent slope of 0.1 % and the vegetation did not exceed a height of 0.7 m. Tree height was the other parameter which varied among windbreaks, sites 1 and 4 offering windbreaks with a height exceeding 15 m compared to sites 2 and 3 offering windbreaks with a height under 10 m. A control site (site 5) without windbreak was selected to also observe odour dispersion. This site consisted of relatively flat (0.1 % uniform slope) land without trees or fences, where a cereal crop had been freshly harvested.
2.3. The panelists and the olfactomètre
For the field tests and the laboratory olfactory work, three groups of four panellists were trained by requiring them to detect n-butanol at concentrations of 20 to 80 ppb and to show consistency in their individual measurements (Choinière and Barrington, 1998; Edeogn et al., 2001). In the field, the panellists were trained to evaluate the hedonic tone (HT) of the ambient air using a scale of 0 to -10, where 0 to -2 is tolerable, -2 to -4 is unpleasant, -4 to -6 is very unpleasant, -6 to -8 is terrible and -8 to -10 is intolerable. For each day of field testing, HT evaluations were translated into OC (OU m-3) by asking the panellists in the laboratory, to evaluate the HT of various dilutions of the odorous air samples collected at the generator and at known OC strengths. The reading of each panellist forming a group of four was averaged to convert the field HT observations into OC.
The laboratory forced choice dynamic olfactometer used in this experiment was fully automated and capable of analyzing 4 contaminated air samples in 20 minutes, using 12 panellists. The olfactometer is unique because of its level of automation and speed suitable to evaluate air samples (Choinière and Barrington, 1998).
2.4. The field testing operation
Before each field test, the odour generator and weather station tower were checked and installed upwind from the windbreak. During the tests, the odour generator was positioned upwind from the windbreak, at a distance of 15, 30, 49 or 60 m. Each three groups of four panellists was assigned evaluation points organized in a zigzag pattern over part of a 25 ha area (500 m x 500 m downwind from the windbreak or odour generator) and given a GPS to keep track of their exact field position. Panellist paths were also designed to overlap each other.
After operating the odour generator for 15 minutes, the groups of panellists would start covering their specified overlapping zigzagged path and measure the odour plume. At each measurement point, the group would stop walking, removed their face masks and evaluate for one minute the hedonic tone (HT) of the ambient air using the scale of 0 to -10. An odour point was defined as a point in the field where at least 50 % (2 out of 4) of the panellists detected an odour. The HT of the ambient air at an odour reading point was averaged from the four panellist evaluations.
During each test day, the odour plume was observed in the morning by 12 trained panellists. Then, in the afternoon, the same 12 panellists evaluated the air samples collected at the odour generator using the laboratory olfactometer. This laboratory work served two purposes: measure the odour concentration (OC in OU m-3) of each odorous air sample, and; correlate the measured field hedonic tone (HT) observed by the panellists with odour concentration values. This correlation was then used to translate the HT plumes into OC plumes.
During 18 days between the end of August and the beginning of December 2003, 39 different tests were conducted on the 4 windbreak sites and the single control site (Lin et al., 2006). On the control site without a windbreak, 6 repeated tests were conducted on 4 different days. Then, 33 tests were conducted on the 4 windbreak sites. A total of 12, 11, 9 and 1 tests were conducted with the odour generator located 15, 30, 60 and 49 m upwind from the windbreak, respectively. Tests on site 4 were conducted in December 2003, because of delays in finding a suitable windbreak site.
During each test, the odour generator emitted a decreasing odour level and, from one test to other, the odour level varied. Each odour plume was therefore standardized for purposes of comparison. Thus, the odour concentration measured at every station by each group of panellists, at a given period in time, was divided by the odour concentration of the generator at that time, and multiplied by the average odour level of 471.6 OU m-3 calculated from all 39 tests.
|Tree type||poplar||mixed mature|
- length (m)
- height (m)
- depth (m)
- optical porosity (fraction)
- porosity at the base (fraction)
|Location||Sherrington||St Chrysostome||St Amable||St Charles|
2.5. The statistical analysis of panelist performance and windbreak dispersion
In the laboratory, the panellists HT as observed in the field needed to be translated into an odour concentration value (OC) using the forced choice dynamic olfactometer. During the 39 tests conducted over 18 days, the odorous air released by the odour generator was samples 78 times or once every 30 minutes. From these 78 samples, 56 were used to have the panellists produced sets of HT and corresponding OC readings. Based on these data sets, a regression equation was produced to correlate OC with HT using SAS (SAS Institute Inc., 2001).
Based on the field data, the effect of the windbreak on the size of the odour plume was tested statistically. A 2 OU m-3 contour for each measured odour plume was plotted and enclosed within a rectangle to define its length and width equal to the side of the rectangle parallel and perpendicular to the average wind direction, respectively. The statistical classification and covariance models were used to analyze the various factors affecting the size of the odour plume (length and width). The covariance model is the combination of the regression and classification models in the same analysis of variance model (SAS Institute Inc., 2001). The distance between the windbreak and the odour generator (DWO), atmospheric stability (AS), and windbreak porosity were fixed factors used for the classification, and wind speed, wind angle against the windbreak (90˚ being perpendicular), odour emission rate (OER) and temperature (T) were the continuous factors used for the regression analysis. Tree height and type were not considered in the analysis.
3. Model development
The Computational Fluid Dynamic used for this modelling was based on the SST k-ω model capable of considering a high level of turbulence (Fluent inc., 2005). The model development respected the following steps: 1) determining the governing equations; 2) meshing the computational domain; 3) selecting the solver capable of defining the fluid properties and its components such as the windbreak, and; 4) setting boundary conditions.
3.1. Governing equations
The air flow moving from one computational cell to the next must respect the governing equations of mass, momentum, energy and species conservation expressed as:
where ρ is fluid density; t is time; ui (i=1, 2, 3, indicating x, y, and z direction) is the mean velocity u in ith direction; ui ‘is the fluctuating component of the instantaneous velocity; µ is fluid viscosity; δij is the unit tensor; p is the static pressure; gi is the gravitational acceleration constant in the ith direction; α is the aerodynamic porosity or permeability of the windbreak; α-1 is the viscous resistance coefficient; Cir is the inertial resistance coefficient caused by the windbreak; umag is the magnitude of the velocity (Hinze, 1975; Saatdjian, 2000); E is the total energy; keff is the effective thermal conductivity; Sh represents all volumetric heat sources such as those of chemical reactions; T is temperature, and; (τij)eff is the effective deviatoric stress tensor.
The coefficients Yi, Ji and hi are the mass fraction, diffusion flux and the sensible enthalpy of the ith atmospheric species (Bird et al., 2002; Fox & McDonald, 1992). The term – ρ ui ‘uj ‘ is called the Reynolds stresses.
In Eq. (4), the diffusion flux Ji of the atmospheric species i, arises due to concentration gradients. The diffusion flux for turbulent flow is:
where Yi is mass fraction of the species i; Di,m is the diffusion coefficient for species i in the mixture; and DT,i is the thermal diffusion coefficient; Sct is the turbulent Schmidt number generally equal to 0.7, and; μt is the turbulent viscosity (Saatdjian, 2000; Bird et al., 2002).
3.2. Describing the windbreak
A windbreak is a porous medium resisting wind or air flow and therefore constituting a momentum sink. This resistance can be introduced in the momentum equation in terms of viscous and inertial resistance:
where Fi is the resistance to wind flow; µ is fluid viscosity; α is the aerodynamic porosity or permeability of the windbreak; α-1 is the viscous resistance coefficient; Cir is the inertial resistance coefficient caused by the windbreak; umag is the magnitude of the average velocity, and; ui (i=1, 2, 3, indicating x, y, and z direction) is the mean velocity u in ith direction.The term μ ui/ α in Eqn (6) is Darcy’s law for porous medium which calculates the resistance exerted by the windbreak due to fluid viscosity (Bird et al., 2002). The term (Cir ρ umag ui /2) in Eqn (6) computes the inertial loss of the fluid flowing through the windbreak, which varies over the height of the tree depending on its shape (Wang & Takle, 1995; Wilson, 2004; Wilson, 1985). Poplars offer dense foliage at their top compared to conifers which offer more foliage at their base. Accordingly, a valid simulation uses an inertial resistance coefficient which varies over tree height.
In this project, the simulated windbreak was designed as a cubic volume with a specific width, height, length and optical porosity, positioned at a specific distanced x downwind from the odour source. The optical porosity was used to compute the aerodynamic porosity representing the exact amount of air flowing through the foliage of the windbreak. The aerodynamic porosity, or permeability, is defined as the ratio of wind speed perpendicular to the windbreak, immediately downwind and averaged over the full height of the windbreak, to that upwind from the windbreak (Guan et al., 2003; Wang & Takle, 1995):
The relationship between optical and aerodynamic porosity is defined according to the wind tunnel measurements of Guan et al. (2003):
where α is the aerodynamic porosity and β is the optical porosity. Accordingly, an optical porosity of 0.35 results in an aerodynamic porosity of 0.66, implying that 66 % and 34 % of the air flows through and over the windbreak, respectively.
To calibrate and validate the model, the field work in this project observed the effect of tree types (poplar and deciduous, Fig. 3) and size forming the windbreaks using sites 1, 2 and 3 (Table 1). On site 1, the windbreak consisted of mature deciduous trees offering an averaged optical porosity of 0.35 but the optical porosity at its base was 0.30 while that over the rest of its profile was 0.40. Therefore, the inertial resistance Cir was defined as proportional to the density (1.0 minus its porosity) of the windbreak:
where z is the coordinate value in the vertical direction; H is the height of the windbreak; h1 is the height at which the porosity of the windbreak changes (0 < h1 < H), and; w1, w2, and w3 are three constants corresponding to the thickness of the real windbreak, set in the simulation to allow 66 % of the air to pass through.
For the windbreak on site 2, the averaged optical porosity was 0.35: the optical porosity at the base was 0.40; that between heights of 3 to 14 m was 0.3, and; above 14 m, the porosity was gradually increased from 0.3 to 1.0. Therefore Cir was:
where w1, w2, and w3 were set at 0.27, 0.39 and 0.05, and; h1, h2 and H were set at 3, 14 and 15 m, respectively. Again, such conditions allowed 66 % of the air to pass through the windbreak.
The windbreak on site 3 offered an average optical porosity of 0.55. Its porosity was assumed to be 0.7 at a height of 1.0 m, to linearly decrease to 0.47 at a height of 3 m, to remain constant between the height of 3 to 15 m, and; then, to increase to 1.0 at the tree top. These conditions produced an average air permeability of 0.79 and a Cir calculated as:
where w1 and w2 were set at 0.1 and 0.205, and; h1, h2, h3 and H were set at 1, 3, 15 and 18 m, respectively.
3.3. Computational domain
The computational domain was designed as a volume measuring 690 m in length (75 H, H being the height of the windbreak of 9.2 m), 184 m (20 H) in width and 73.6 m (8 H) in height (Fig. 4). The left and right faces of the space were the wind inlet and outlet, located 138 and 552 m from the origin, respectively. The front, back and top faces of the volume were set to have an open or undisturbed wind velocity and were positioned at 92, -92 and 73.6 m from the origin, respectively. The bottom face of the volume was the ground surface.
The odorous air was introduced into this computational volume by a single source opening measuring 1.5 m × 0.376 m × 1.75 m in x, y, z directions with the right face positioned at x = 0 m and the front face at y = -0.188 m. The centre of the odour emission surface was positioned at x = 0 m, y = 0 m and z = 1.562 m. Odours were blown from the right-up rectangular face (the red zone in Fig. 4) measuring 0.376 × 0.376 m. The windbreak (green zone in Fig. 4) was designed as a porous cubic volume.
For computational purposes, the computational volume was meshed into 228, 81, and 46 segments in the x, y and z coordinates, respectively, and the size of the rectangular cells gradually increased from the odour generator towards the outward faces of the system. For the odour inlet, 64 rectangles were meshed over an area of 0.376 × 0.376 m2 to effectively transfer the odour mass fraction to other cells.
3.4. Numerical solver
The Reynolds stresses in Eq. (8) can be computed using the Boussinesq Hypothesis based on the mean velocity gradients:
where μt is the turbulent viscosity, and; k is the turbulence kinetic energy.
Selected to perform the simulations, the SST k-ω model of the Fluent software uses two different transport equation to express the turbulence kinetic energy k and the specific dissipation rate ω. The SST k-ω accounts for the principal turbulent shear stress and uses a cross-diffusion term in the ω equation to blend both the k-ω and k-ε models and to ensure that the model equations behave appropriately in both the near-wall and far-field zones. Thus, the SST k-ω model offers a superior simulation performance as compared to the individual k-ω and k-ε models (Menter et al., 2003).
The Fluent 6.2 steady 3-dimension segregated solver was used to solve the SST k-ω model through second and quick orders of discretisation schemes converting the governing equations into algebraic equations solved numerically while increasing the calculation accuracy. The second order scheme was used to compute the pressure, the second order upwind scheme was used to compute odour dispersion and the quick scheme was used to compute momentum, turbulence kinetic energy, turbulence dissipation rate and energy. The SIMPLE method was applied to the velocity and pressure coupling (Fluent inc., 2005).
3.5. Fluid properties
Livestock manures emit over 168 odorous compounds and six of the ten compounds with the lowest detection thresholds contained sulphur (O’Neil & Phillips, 1992). Hydrogen sulphide (H2S) was selected as odour and presumed to flow along with clean dry air. Therefore, the modelled fluid was defined as clean air and H2S and its mass fraction at the odour source was:
where Y2 is the odour mass fraction (OMF) at the odour inlet, or the ratio of the odour mass to the total air and odour mass in 1.0 m3, dimensionless; Pa is the atmospheric pressure of 101325 Pa at sea level; T is temperature in K; M is the molecular weight of dry air or 0.028966 kg mol-1; R is the universal gas constant or 8.31432J mol-1 K-1 (ASHRAE, 2009); OCg is the odour source concentration, in OU m-3, and; mH2S is the mass of H2S required to produce one odour unit, expressed as kg OU-1 and mH2S = 7.0 × 10-9 kg OU-1 (Blackadar, 1997).
|Density||kg m-3||Impressible-ideal-gas law|
|Cp||J kg-1 K-1||Mixing law||1005.422||1005.333|
|Thermal conductivity||W m-1 K-1||Mass-weighted-mixing-law||0.0260411||0.0137023|
|Viscosity||kg m-1 s-1||Mass-weighted-mixing-law||1.458E-6 T1.5 / (T + 110.1)||-1.4839E-6|
+ 5.1E-8T -1.26E-11 T2
|Mass diffusivity||m2 s-1||-1.3497E-5 + 1.05772E-7T|
|Thermal diffusivity coefficient||kg m-1 s-1||Kinetic-theory|
|Molecular weight||kg kgmol-1||28.966||34.07994|
The modelled fluid was defined using the physical properties of clean dry air and H2S, including density, specific heat capacity, thermal conductivity, viscosity, mass and thermal diffusion coefficients for the mixture and individual species. The modelled fluid was considered incompressible and its density varied with temperature but not with pressure because of a Mach number under 10 %. The fluid's specific heat capacity, thermal conductivity and viscosity were calculated using the mass mixing-law and the thermal diffusion coefficient was calculated using the kinetic-theory (Table 2).
3.6. Boundary conditions
The boundary conditions define the faces of the computational volume and the velocity inlet of the clean air and odorous gas. The bottom face of the odour dispersion system (ODS) was assumed to be no slip requiring as input only temperature and roughness length. As air inlet velocity, the inputs included the vertical profile of the horizontal wind velocity, temperature, turbulence kinetic energy and specific dissipation rate.
The odour dispersion around the windbreak was assumed to occur in the homogeneous plat terrain of the surface layer of the atmosphere, and the approaching wind flow was assumed not to change the vertical direction of horizontal velocity and to satisfy the assumption of the Monin Obukhov similarity theory. Atmospheric stability was determined by the Monin Obukhov length LMO:
where u* is the friction velocity; ka is the von Karman constant ranging from 0.35 to 0.43 and usually equal to 0.4; T is the surface temperature; Cp is the specific heat of air; HF is the vertical heat flux; ρ the air density, and; g is the gravitational acceleration constant (Schnelle, 2000). When the convective heat flux is upward, LMO is negative and the air is unstable. When the earth absorbs heat energy, the heat flux is negative, LMO is positive and hence the air is stable. However, when the heat flux is zero, LMO is infinite and the air stability conditions are neutral.
The vertical profile of the horizontal mean wind velocity is calculated by:
where umag is the magnitude of the horizontal mean wind velocity at height z above the surface (z ≥ z0); z0 is the roughness length of the surface, hABL is the height of the atmospheric boundary layer, and LMO is the Monin Obukhov length (Panofsky & Dutton, 1984; Blackadar, 1997; Jacobson, 1999).
Assuming that the potential temperature is equal to the temperature at zs, the vertical temperature profile T(z) can be calculated as (Panofsky & Dutton, 1984):
where zs is a height of 1.35 m above ground; Ts is the temperature at height zs; g is the gravitational acceleration constant, and; Υd is the dry adiabatic lapse rate of 0.01 K m-1.
The vertical turbulence kinetic energy profile within the surface atmospheric layer can be defined as:
where k(z) is the turbulence kinetic energy (TKE), and; σu, σv and σw are turbulence components in the x, y, z coordinates.
For neutral conditions, hABL/LMO = 0, TKE linearly decreased with height, and at the top of the atmospheric boundary layer, equals 20 % of its value at the ground level (Carruthers & Dyster, 2006). The TKE for neutral condition is:
where as = 0.8.
For unstable conditions (hABL/LMO < 0), the TKE is:
where is the mixing layer velocity scale.
For stable conditions (hABL/LMO > 0), TKE is expressed as:
and as = 0.5 for roughness length z0 ≥ 0.1 m.
The vertical turbulence specific dissipation rate ω(z) is:
where l is the turbulence length scale set as twice the height of the ground surface roughness length (2z0) based on a calibration of the horizontal velocity recovery rate downwind from the windbreak (Schnelle, 2000; Menter, 2003).
The parameters defining the surface layer conditions in the SST model, namely z0, LMO, hABL, u* and Ts are determined according to the simulation conditions. Corresponding to the physical conditions of the ground surface, z0 was 0.13 m (Lin et al., 2007b). The coefficient LMO was estimated from the Pasquill atmospheric stability categories. When z0 was 0.13 m, the average LMO was -20 m for the Pasquill stability category B, and was 20 for the stability category F (Golder, 1972). The coefficient hABL was designated as the average rural mixing height for each stability category measured at the weather station. Once z0, LMO and hABL were determined, u* and Ts were calculated from the temperature and wind velocity measured at a height of 10 m and using Eqs. (15) and (18), respectively.
3.7. Simulating the effect of weather conditions
The effect on odour plume length of climatic factors was tested through 21 simulations (Table 3): simulations 1 to 9 for wind velocity; simulations 10 to 12 for air temperature; simulations 13 to 19 for wind direction, and; simulations 20 and 21 for atmospheric stability. Simulations 1 to 12, 20 and 21 respected an odour dispersion system (ODS) as shown in Fig. 4, and presumed a constant odour concentration at the source of 300 OU m-3. For simulations 13 to 19, the ODS measured 460 m × 414 m × 73.6 m, and the odour concentration at the source was 550 OU m-3. For all simulations, the surface roughness length was 0.13 m, the odour generator emitted odorous air at a rate of 1.6 m3 s-1 and the natural windbreak consisted of a single row of conifers, measuring 7.0 m in width and 9.2 m in height and offering an aerodynamic porosity of 0.4 with a coefficient Cir0 equal to 0.08706. The windbreak was located 30 m downwind from the odour source.
Simulations 1 to 9 tested the effect on odour dispersion of the wind velocity for unstable (category B), neutral (category D) and stable (category F) atmospheric conditions for their average T, LMO and hABL values. The wind velocity ranges were measured in September 2003 at PE Tudeau airport by Environment Canada for stability category B, D and F. For simulations 1, 2 and 3 under stability category B, the averaged values of T, LMO and hABL were 293 K, -20 m and 1390 m and the velocities were 1.0, 1.8 and 3.0 m s-1, respectively (Table 8.2). For simulations 4, 5 and 6 under stability category D, the averaged T, LMO and hABL were 291 K, infinity (∞) and 2090 m, and the velocities were 3.0, 5.4 and 6.4 m s-1, respectively. Finally, for simulations 7, 8 and 9 under stability category F, the averaged T, LMO and hABL were 287 K, 20 m and 1811 m, and the velocities were set at 1.0, 1.9 and 3.0 m s-1, respectively.
Temperature effects were tested under unstable, neutral and stable atmospheric stability categories, using simulations 10, 11 and 12 with average December 2003 temperatures of 269, 270 and 265 K, and simulations 2, 5 and 8 with average September temperature of 293, 291 and 287 K.
Simulations 13 to 19 tested the effect of the wind direction, measured from the positive x-axis and set at 0, -15, -30, -45, -60, -75 and -90˚, respectively. The weather atmospheric stability category D was assumed and T, LMO, hABL and wind velocity were 291 K, ∞, 2090 m and 5.4 m s-1, respectively.
The effect of the atmospheric stability was tested twice. Simulations 2, 5 and 8 compared average values of wind velocity, atmospheric boundary layer height and temperature. Simulations 4, 20 and 21 were also similar except for their respective stability categories B, D and F. For these three simulations, wind velocity, hABL and T were set at 3.0 m s-1, 2090 m and 291 K, respectively, which are mean values for the atmospheric stability categories B, D and F.
|Test||Weather condition||Computed results|
|umag at 10 m||T at 10 m||Wind||Atm. Stab.||LMO||hABL||Length 1||Length 2||Length 3||Width||Height|
3.8. Generating the simulated odour plumes
An odour plume is expressed by a series of odour concentration (OC) contours within a plane. In the field and at various locations, the trained panellists detected the odour hedonic tone (HT) which is the degree of pleasant or unpleasant smells, expressed using a scale 0 to -10, where 0 is neutral and -10 is extremely unpleasant (Lin et al., 2007b). In the laboratory, the panellists were then asked to detect the HT and OC of 56 odour samples, which produced the following correlation:
where OC is odour concentration in OU m-3, and; AHT is an absolute value of HT ranging from 0 to 10. From Eq. (27), the maximum AHT is 10 and the corresponding OC is 117 OU m-3. Hence, when OC exceeds 117 OU m-3, AHT is still defined as 10, because panellists still feel an extremely unpleasant odour.
To plot the odour plume reflecting HT, the computed dimensionless odour mass fraction (OMF) for all point of the ODS needs to be transformed into a simulated odour mass concentration (SOMC):
where SOMC is simulated odour (H2S) mass concentration in μg m-3; OMF is the odour (H2S) mass fraction computed by the model for a given point in space, dimensionless; Y2 and OCg are the odour mass fraction and odour concentration at the odour source as defined by Eq. (28), which are respectively dimensionless and in OU m-3, and; mH2S is the mass of H2S required to produce 1.0 OU m-3 in kg OU-1 as described by Eq. (28).
Secondly, the SOMC were transformed into SAHT by correlating the 5 field test AHT (absolute HT readings) with SOMC:
where SAHT is simulated absolute hedonic tone, and; SOMC is defined by Eq. (29). The field test correlation indicated a statistically significance (P < 0.01) relationship between AHT and SOMC (Lin et al., 2007b). In this procedure, the odour mass fraction of 506.5 μg m-3 results in AHT of 10 for an OC of 117 OU m-3.
4. Results and discussion
The following sections will start by characterizing the panellists, on which all results where based, and then providing a comparison for windbreak performance as observed from the field data. The modelling section will follow, starting with the model calibration using literature data, and then model application to identify the windbreak characteristics having the most influence on odour plume length, followed by the effect of climate. In all results presented, the length of the odour zone or plume is measured from the odour source. Furthermore, the strength of the odour was standardized using an average odour source emission of 471.6 OU m-3; this standardization compensated for the variability in odour generation between field tests.
4.1. Odour interpretation
The relationship between hedonic tone (HT) and odour concentration (OC) for the 56 samples measured during the field tests is presented in Figure 5. Collected in the morning during the odour plume observation, the field odour samples produced by the odour generator were evaluated for their threshold dilution and hedonic tone by the same 12 panellists in the afternoon using the olfactometer. There was a dual purpose to this exercise: evaluate the odour concentration (OC) of the sample collected at the odour generator, and; obtain a correlation between odour concentrations (OC) in OU m-3 and hedonic tones (HT) measured in the field while sizing the odour plume.
Several interesting aspects can be concluded from Fig. 5: correlation between the odour concentration (OC) and the hedonic tone (scale of 0 to -10) is quite variable although typical of panellist response (Edeogn et al., 2001); the present panellist response differs from that of Lim et al. (2001) and Nimmermark (2006), despite the n-butanol rating of all panellists before hand, according to standards (CEN, 2001; ASTM 1997a, b).This difference resulted from culture, tolerance, and previous historical exposure to odorous situations, and; above the observed OC of 117 OU m-3, the response in HT reached its peak value of -10, explaining the larger variability in reported OC value.
4.2. Field windbreak odour dispersion
The odour plumes observed in the field are far from being regular, as illustrated by Fig. 6, rather the odour plumes are formed of odour puffs resulting from the oscillating wind speed and direction. Nevertheless in terms of modelling, it will be assumed that the OC profile parallel to wind direction follows an average trend.
The control without a windbreak (field tests 37, 38 and 39 on site 5) is compared (Fig. 6a) to that of site 2 with a mature deciduous windbreak (field tests 5, 8, 12 and 16, on site 2) and the odour generator located 30 m upwind (Fig. 6b). The average air temperature was 26.4 and 22.6 C, respectively, for the control and windbreak sites. On site 2, the wind direction ranged between 20 to 90 with respect to the windbreak, 90 being perpendicular. Both odour plumes were observed in late August and early September under similar landscape and weather conditions.
Fig. 6 demonstrates that the plume developed without a windbreak reached a much longer distance downwind, compared to that developed with the windbreak. Measured furthest away, the windbreak created an odour zone of 2.0 OU m-3 ending at 500 m away from the source, compared to the same level of odour extending beyond 550 m for the control site. Without a windbreak, the control produced an odour plume with a maximum odour peak of 16 OU m-3 at a distance of 69 m while the windbreak produced a plume with a peak of 50 OU m-3 at a distance of 117 m. Accordingly, the windbreak is observed to concentrate or trap the odours on its leeward position before further dispersion.
The most significant parameter affecting the length of the odour plume was found to be the foliage porosity (Fig. 7). Despite the greater tree height on site 1, the more open foliage (optical porosity of 0.55) produce a longer odour plume covering 150 m in width by 600 m in length, compared to that of the windbreak on site 2 with a porosity of 0.35, generally covering a width of also 150 m but a shorter length of 300 m.
The furthest measured odour concentrations for the windbreak optical porosity of 0.55 and 0.35 had values of 3.2 and 4.0 OU m-3 at a respective distance of 601 and 281 m. However, the windbreak optical porosity of 0.55 produced a maximum odour peak of 22 OU m-3 at a distance of 138 m while that with an optical porosity of 0.35 produced a maximum odour peak of 50 OU m-3 at a distance of 117 m. Again, the smaller odour plume corresponded to a more intense odour trapping in the leeward position of the windbreak.
In summary and for the field observation, the more open windbreak produce an odour plume similar to that of the control without a windbreak, likely because a porous windbreak produces less turbulent energy and therefore less odour mixing and odour dilution, compared to a denser windbreak. The denser windbreak with a foliage porosity of 0.35 was able to reduce the length of the odour plume by 25 %, as compared to no windbreak, but the peak odour concentration was several times higher immediately downwind from the windbreak.
4.3. Calibrating the dispersion model
For the model to reproduce adequate wind velocities about windbreaks, the standard k-ε model was calibrated using field data measured at half height around a natural windbreak 2.2 m tall and offering an optical porosity of 0.55 (Eimern et al., 1964). The model parameter Cμ (a constant use to quantify the level of turbulent viscosity μt) and C2ε (a constant used to define the turbulent dissipation rate w) were adjusted from the default of 0.09 and 1.92, to 0.12 and 2.2, respectively. Also, the inertial resistance parameter of the windbreak was set at 10.3 m-1. Once calibrated, the differences between the simulated and measured wind speeds were (Fig. 8): from -10 to 0H, lower by 4.5 %; from 0 to 30H, slightly greater by 0 to 10 %, and; at 30 H, negligible. An R2 value of 0.97 was obtained between the measured and simulated velocity values from -10 to 30 H.
The model was also validated for odour concentration simulation (Fig. 9). The correlations between MAHT and SAHT for the 11 tests, as a function of distance from the source, were found to be statistically significant (P = 0.01), implying that the standard k-ε model can accurately predicts odour HT downwind from windbreaks. As illustrated in Figure 5 a, c, e, and g for tests 2, 5, 7, and 8, the simulated lines are found in the centre of the range of MAHT, which is a good indication that the model can reproduce the observations. Depending on the test, the R2 value ranged between 0.48 and 0.90. If all values within 150 m of the windbreak are excluded to remove the odour puff effect, then R2 exceeds 0.75 for all simulations.
4.4. Simulated effect of windbreak characteristics on odour dispersion
When establishing a natural windbreak to improve odour dispersion, the tree belt characteristics must be optimized in terms of porosity, height and distance from the source. The following sections will present results of simulations designed to identify the windbreak characteristics minimizing the size of the odour plume.
4.4.1. Windbreak porosity, tree type and height
The porosity is the main factor governing the amount of air flowing through the windbreak as determined by the inertial resistance coefficient Cir, for given H, h1, w1, w2, and w3 values (Eqn 9, 10 and 11).
The following values were used to simulate conditions establishing optimal windbreak porosity: H and h1 of 9.2 and 6.9 m; an aerodynamic porosity α of 0.2, 0.3 and 0.66 resulting in respective w1, w2, and w3 values of 4.508, 3.864 and 0.644 for α = 0.2, values of 1.204, 1.032 and 0.172 for α = 0.4, and values of 0.38, 0.2598 and 0.16 for α = 0.66, and; an odour source 30 m upwind from the windbreak.
The simulation indicated that aerodynamic porosity is the main factor governing odour trapping behind the windbreak, and accordingly, odour dispersion and odour plume shortening (Fig. 10). As compare to α of 0.2 dropping the odour concentration to 2 OU m-3 at a distance of 217 m, α of 0.4 required a distance of 292 m to drop the odour concentration to the same level. For α of 0.66, a distance of over 452 m was required to reach the same OC of 1 OU m-3. Furthermore and for aerodynamic porosities of 0.2, 0.4 and 0.6, the odour plume width measured 73, 37 and 30 m, respectively. Thus, lower aerodynamic porosities produced shorter but wider odour plumes, because of the trapping of more odours immediately downwind from the windbreak. Fig. 6 shows the effect of windbreak aerodynamic porosity on the profile of the odour dispersion plume. Again, the lower density windbreak produced a higher OC immediately downwind, confirming the enhanced trapping of odours before dispersion.
The tree type had a slight impact on odour plume length, for the same aerodynamic porosity. For example, a single row conifer produced an OC of 2 OU m-3 at 320 m, as compared to 310 m for the poplars. The velocity gradient created by the conifer windbreak gradually increased with height especially above 6.4 m as a result of the drop in horizontal tree section area, explaining its slightly poorer performance.
As for a tree height of 4.6 and 9.2 m, for a windbreak offering the same aerodynamic porosity of 0.4, an OC of 3 OU m-3 was reached at 225 and 407 m, respectively. The size of the low turbulence zone is thus directly related to the windbreak tree height.
4.4.2. Windbreak distance from the source
The simulations demonstrated that the shorter the distance between the source and the windbreak, the faster the odours are trapped to be concentrated and then dispersed. For the 15 m distance, the 2 OU m-3 contour occurred at a distance of 309 m from the source or 287 m from the windbreak, including its thickness. The 2 OU m-3 contour appeared for the 60 m distance, at a distance of 411 m from the source and 347 m from the windbreak. The 15 and 60 m distance between the source and windbreak resulted in simulated OC upwind from the windbreak of 228 and 73 OU m-3 respectively, at a height z = 1.5 m.
When the odour is released from a building ventilated naturally, the windbreak should be positioned at least 24 m away, a condition which does not necessarily optimise odour dispersion.
4.5. Simulated effect of climatic conditions on windbreak odour dispersion
Weather conditions certainly vary in time and affect the dispersion performance of a windbreak. Furthermore, atmospheric stability impacts the effect of climatic factors since it represents the degree of air convection or air movement in the vertical direction. It can compete against wind and it defines air temperature gradient with height. Accordingly and when simulating the effect of the main climatic factors of wind velocity and air temperature, atmospheric stability must be examined in parallel.
4.5.1. Effect of wind velocity and direction
For unstable atmospheric stability conditions (Category B), wind velocities of 1.0, 1.8 and 3.0 m s-1 produced simulated odour plume length of 321 m, 406 m and 268 m for a 2 OU contour (Fig. 11). Accordingly, low wind velocity (1.0 m s-1) could not counteract the air lifting effect of unstable conditions, as opposed to stronger winds carrying odours further. Similarly, the height of the odour plume decreased from 43 to 17 and 15 m with increasing wind velocities 1.0, 1.8 and 3.0 m s-1, respectively.
For neutral atmospheric stability conditions (Category D) with wind velocities of 3.0, 5.4 and 6.4 m s-1, the odour plume length decreased from 272 m to 121 and 102 m (Fig. 11) respectively, for a 2 OU m-3 contour.Wind velocities for neutral atmospheric conditions are normally higher than those associated with unstable conditions and produce a higher turbulence kinetic energy at the windbreak which enhances odour dispersion (Lin et al., 2007b). This is also reflected in terms of odour flux which is accelerated by the turbulence viscosity proportional to turbulent kinetic energy.
For stable atmospheric stability conditions (Category F) with typical wind velocities of 1.0, 1.9 to 3.0 m s-1, the odour plume length dropped from 552 to 350 and 253 m, respectively. Under stable atmospheric conditions with limited upward convection, as compared to unstable conditions, vertical forces are not as strong and less air is projected upwards at the windbreak, resulting in lower wind velocities, weaker turbulent kinetic energy at the windbreak and therefore a longer odour plume.
Wind direction affects the orientation and shape of the odour plume. On the horizontal plane z = 1.5 m and for wind directions varying from 0 to -90˚, the shape of the odour plume followed wind direction (Fig 12). The length of the odour plume decreased from 281 to 176 m for a wind direction changing from 0 to -45˚ and then increased from 176 to 321 m for a wind direction changing from -45 to -90˚, for a 2 OU contour. The odour plume developed a fin immediately downwind from the windbreak when the wind direction ranged between -15 and -75 . This fin was generated when sufficient air flowed parallel to the windbreak and when the windbreak could sufficiently reduce the x-component of the air flow. At a distance of 28 m downwind from the windbreak, the wind streamlines were observed to sharply change direction and become parallel to the windbreak. As a result, the fin reached its maximum length when the wind direction was -45˚.
4.5.2. Effect of atmospheric stability
Atmospheric stability condition had a major impact on odour plume length because it establishes wind velocity range and temperature gradient as well as the strength of the convective air forces. Assuming an average wind velocity, temperature and atmospheric boundary layer height, the odour plume length for an odour contour of 2 OU, measured 406, 170 and 350 m for unstable, neutral and stable atmospheric stability conditions (Categories B, D and F), respectively. Hence, OPL increased from Category D to B and then F, because Categories B and F generally exhibit lower wind speeds compared to Category D.
For the same atmospheric boundary layer height, and wind velocity and air temperature at a height of 10 m, but for Stability Categories B, D and F, odour plumes measured in length 267, 272 and 253 m, respectively because of a different typical profile for wind velocity, temperature and turbulence. The turbulent kinetic energy on the upwind side of the windbreak decreases from Stability Category B, to that of D and then F but then increases in the opposite order on the downwind side of the windbreak, thus shortening the odour plume (Lin et al., 2007b).
For Stability Categories B, D and F, the vertical wind velocity profile was different for 3 m s-1 at a 10 m height. Stability Category B produced a profile slightly smaller than that obtained with Category D, but for Categories B and D, the profile was much smaller than that for Category F.
For a temperature of 291 K at a 10 m height, the vertical temperature profile was quite different for Stability Categories D, B and F. For Stability Category D (neutral conditions), this profile decreased with height at a rate 0.01 K m-1, but for that of B (unstable conditions), it dropped much faster over a height of 0 to 10 m and then deceases at a slower rate but still faster than that obtained with Stability Category D. The temperature profile for Stability Category F (stable conditions) increased with height and produced the inverse of stable effects. Because Stability Category F produced larger profile differences for wind velocity and temperature, between heights of 0 and 73.6 m in the computational domain, compared to D and B, the resulting odour plume was shorter.
Generally, the odour plume length for neutral atmospheric conditions (Category D) was shorter than that for unstable (Category B) and stable conditions (Category F), because of the corresponding different wind velocity. However, when all the conditions were the same except for atmospheric stability conditions, Category F produced a slightly shorter odour plume compared to that under neutral and unstable conditions.
4.5.3. Effect of air temperature gradient
In general, the ground air temperature had limited effect on odour plume size, when associated with a specific atmospheric condition. On a horizontal plane with z = 1.5 m, same length odour plumes were obtained at temperatures of 293 and 269 K under unstable neutral and stable atmospheric conditions.
The phenomenon can be explained by the fact that the odour diffusion flux is proportional to (ΔT/T) or the rate of change of temperature T. For neutral atmospheric conditions, T dropped with height at 0.01 K m-1, but the rate of change of T over a 0 to 20 m height was similar in both cases at 0.069 % and 0.074 %, respectively. The differences for Simulations 2 and 10, and 8 and 12 of 0.006 % and 0.005 %, respectively, were too small to influence odour dispersion. Hence, the same odour plumes were observed for the different temperatures under the same atmospheric stability condition.
The objective of the project was to develop a model from the Computational Fluid Dynamics method based on SST k-ω computations (Fluent inc., 2005) to simulate odour dispersion around windbreaks and then to use this validated model to observe the effect on odour plume size of windbreak characteristics and climatic factors. The model was calibrated for odour dispersion using field data measured by panellists.
The simulations produced the following conclusions:
After calibration, the SST k-ω model simulated the velocity recovery rate observed downwind from a 2-dimensional windbreak with an R2 factor of 0.95 for distances of 0 to 30 H, where H is the height of the windbreak;
The SST k-ω model predicted odour concentration with an R2 value generally above 0.75 for values over 150 m away from the windbreak, which is considered quite acceptable for odour simulations.
A less porous or denser windbreak (aerodynamic porosity of 0.2 versus 0.4 and 0.66) produced a shorter, wider and more intense odour plume;
Assuming that the air flow resistance was proportional to the square of the tree diameter, the tree type had almost no effect on the size of the odour plume. As opposed to the conifer, the poplar windbreak created a slightly shorter odour plume for the same aerodynamic porosity;
A taller windbreak resulted in a shorter odour plume, by creating a taller low turbulence zone downwind from the windbreak, where more odours were trapped and retained for dispersion;
When close to odour source, the windbreak produces a shorter odour plume.
In terms of climatic factors, atmospheric stability was the governing element since it generally establishes wind speed and air temperature gradient; under low wind speeds weaker than convective forces, the odour plume was shorter but under low convective forces, higher wind speeds created more turbulences and shorter odour plumes.
AHT is absolute hedonic tone
AS is atmospheric stability
as is a factor involved in determining TKE
Cir is the inertial resistance coefficient
Cir0 is the constant
Cp is specific heat of air
D1 and D2 are the tree diameters
Di,m is the diffusion coefficient for species i in the gaseous mixture
DT,i is the thermal diffusion coefficient for species i in the gaseous mixture
DWO is the distance between the windbreak and the odour source
E is the total energy
Fi is the resistance to wind flow
g is acceleration of gravity
gi is the component of the gravitational vector in the ith direction
H is the total height of the windbreak
HF is the vertical heat flux
hi is the height at which the rate of the gradient of the tree diameter changed at the ith height
hABL is the height of the atmospheric boundary layer
Hi is the sensible enthalpy of ith species
HT is the odour hedonic tone
Ji is the diffusion flux of species i
ka is the van Karman constant ranging from 0.35 to 0.43, and n9ormally equal to 0.4
k is the turbulence kinetic energy
keff is the effective thermal conductivity
k(z) is the turbulence kinetic energy (TKE)
l is the turbulence length scaleis the Monin Obukhov length
M is the molecular weight of dry air (0.028966kg mol-1)
mH2S is the mass of hydrogen sulphide in one odour unit
OC is the odour concentration in OU m-3
OCg is the odour concentration at odour generator in OU m-3
ODS is the odour dispersion system used for simulations
OER is the odour emission rate
OMF is odour mass fraction, dimensionless
p is the static pressure
Pa is the atmospheric pressure at sea level
R is the universal gas constant (8.31432J mol-1 K-1)
SAHT is simulated absolute hedonic tone
Sct is the turbulent Schmidt number generally equal to 0.7
Sh is the heat of chemical reaction and other volumetric heat sources
SOC is simulated odour concentration in OU m-3
SOMC is odour mass concentration in μg m-3
T is temperature
TKE is turbulence kinetic energy
Ts is the temperature at the zs
T(z) is the vertical temperature profile
TWC is a factor to control the convective energy varied with height
TWN is a factor controlling the drop in TKE with height within the atmospheric boundary layer
t is time
u is instantaneous wind velocity
u and u’ are mean and fluctuating component of instantaneous velocity
u* is the friction velocity
ui (i=1, 2, 3) is scalar component of the mean velocity in ith direction, indicating in x, y, z direction in Cartesian coordinate system, respectively
ui ‘ (i=1, 2, 3) is the fluctuating component of the instantaneous velocity ith direction, indicating in x, y, z direction in Cartesian coordinate system, respectively
umag is magnitude of the mean velocity
u0 is the undisturbed wind velocityis the mixing layer velocity scale
w(z) is the vertical turbulence specific dissipation rate
w1, w2, w3 are constant describing the tree shape and resistance to wind flow
at a height h1, h2, h3 respectively
x is the coordinate for the axis perpendicular to the windbreak
y is the coordinate for the axis parallel to the windbreak
z is the coordinate for the vertical axis
z0 is roughness length
zs is a height of 1.35 m above surface
Yi is the mass fraction of the species i in a mixture of gases
Y2 is the odour mass fraction
z is a coordinate in the vertical direction
α is the aerodynamic porosity, or permeability
α-1 is the viscous resistance coefficient
β is the optical porosity
μ is viscosity of mixture of the air and odorous gases
μt is the turbulence kinetic viscosity
ρ is fluid density
ω is the specific dissipation rate
δij is the unit tensor
(τij)eff is the effective deviatoric stress tensor
σu, σv and σw are the turbulence components in x, y, z coordinates
Υd is dry adiabatic lapse rate of 0.01 K m-1
The authors wish to acknowledge the financial contribution of Consumaj inc., CDAQ, the Livestock Initiative Program, Agriculture and Agro-Food Canada and the Natural Sciences and Engineering Research Council of Canada.