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Published in Soil Sci. Soc. Am. J. 67:1352-1360 (2003).
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

DIVISION S-1—SOIL PHYSICS

Estimating Ammonia Volatilization from Swine-Effluent Droplets in Sprinkle Irrigation

J. Wu, D. L. Nofziger*, J. Warren and J. Hattey

Dep. of Plant and Soil Sciences, Oklahoma State Univ., Stillwater, OK 74078

* Corresponding author (dln{at}okstate.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENTS
 MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Irrigation of swine effluent is one of the most economical ways to dispose of swine manure. The determination of appropriate application rates requires the quantification of volatilization losses of ammoniacal N. In this research, a mechanistic model was developed to estimate droplet volatilization loss (excluding drift losses) of ammoniacal N from swine effluent in sprinkler irrigation. Field experiments were conducted to validate the model. The model combined energy balance, mass balances of ammoniacal N, and water to predict equilibrium temperature of a droplet, and losses of ammoniacal N and water from a droplet. Trajectory analysis was employed in the model to estimate a droplet's exposure time in air. Mass and heat transfer coefficients developed in boundary layer theory were incorporated in the mass and energy balance equations to predict fluxes of heat, ammoniacal N, and water. Equilibrium constants of transformation reactions were used in the model to establish relationships among component species of ammoniacal N. Field experiments measured concentrations of ammoniacal N in swine-effluent samples collected at the nozzles and ground surface to determine the loss of ammoniacal N caused by droplet volatilization. The measured concentration decreases were combined with water loss percentages to estimate percentage losses of ammoniacal N. Results from both field experiment and mathematical modeling indicated that loss of ammoniacal N from droplet volatilization was only a few percentages which was considered insignificant compared with common soil surface volatilization loss of 20 to 50% at the end of 1 wk after application.

Abbreviations: LDN, low drift nozzle


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MODEL DEVELOPMENT
 FIELD EXPERIMENTS
 MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
MANAGEMENT OF ANIMAL WASTES from animal confinement facilities is a very important issue in swine and poultry farming. If inadequately handled, animal manure poses a significant threat to the quality of air and water nearby the storage and disposal areas. When properly managed, animal manure is a valuable source of fertilizer for crop production. Swine-effluent irrigation is considered one of the most economic ways of swine-manure disposal (Zhang and Hamilton, 2000). One of the key issues in swine-effluent irrigation is the determination of a proper application rate because applying lagoon effluent at a rate exceeding the limit of the growing crop's N need may cause nitrate leaching to ground water. The amount of ammoniacal N added to a soil system from a swine-effluent-irrigation event is dependent on the initial amount of ammoniacal N in the effluent applied and the losses of ammoniacal N during the irrigation event. Zupancic et al. (1999) and Warren (2001) conducted field experiments at the Oklahoma State University Research Station in Goodwell, OK to measure volatilization losses of ammoniacal N from swine-effluent applied to the land surface by flood irrigation. Wu et al. (2003) developed a mechanistic model to predict N transport in a soil profile and ammonia volatilization from liquid and soil surfaces. The simulated ammonia-volatilization rate and cumulative volatilization from the model agreed well with the measured data from the flood irrigation experiments. A major purpose of the mechanistic model is to predict ammonia volatilization under the condition of sprinkler irrigation using parameters from field experiments with flood irrigation. In sprinkler irrigation losses from droplet volatilization, wind drift, and canopy interception are in addition to soil-surface volatilization loss with flood irrigation. Losses from wind drift and canopy interception represent the portion of volatilization losses from droplets falling outside the targeted area while the losses from droplet volatilization and soil-surface volatilization represent the portion of losses from droplets falling on the irrigated area. Droplet volatilization and soil-surface volatilization occur before and after the on-target droplets hit the ground. Losses from wind drift and canopy interception can be evaluated directly from estimations of water losses. They are the amount of water losses multiplied by the initial concentration of ammoniacal N in the effluent. Methods for estimating the amount of water losses from wind drift and canopy interception were developed by irrigation scientists and hydrologists (Brooks et al., 1991; Keller and Bliesner, 1990; van Dijk and Bruijnzeel, 2001a, b).

Pote et al. (1980) developed a numerical model to estimate ammonia volatilization from a droplet during its exposure time (i.e., the interval from the time a droplet leaves a sprinkler nozzle to the time it hits the ground). However, the model ignored the temperature dependence of the equilibrium constant, Ka, in the NH3 (aq) {leftrightarrow} NH+4 (aq) reaction, and therefore, may not be applicable for temperatures significantly different from 25°C. In this research, we developed an analytical model to predict droplet concentration of ammoniacal N at different times and to evaluate the volatilization loss of ammonia from a droplet. The model was derived from mass balance of ammoniacal N in a droplet and incorporated temperature dependence of the transport and reaction parameters. Energy balance and mass balance of water were also incorporated into the model to predicted equilibrium temperature of a droplet and evaporation loss of water, which were needed for evaluating volatilization loss of ammonia. Mass and heat transfer coefficients developed from boundary layer theory (Incropera and DeWitt, 1990) were used in the mass and energy balance models to predict fluxes of heat, ammoniacal N, and water. Equilibrium constant of the NH+4 (aq) - NH3 (aq) reaction and Henry's constant of the NH3 (aq) - NH3 (g) reaction were used in the models to establish relationships among component species of ammoniacal N. Trajectory analysis was employed to estimate a droplet's exposure time (Green, 1952a,b).

The droplet volatilization model developed in this research was used to estimate losses of ammoniacal N from low-drift nozzles (LDN) and impact sprinklers. The modeling results revealed that the loss of ammoniacal N from droplet volatilization was only a few percent. However, Safley et al. (1992) and Sharpe and Harper (1997) reported a range from 13 to 37.3% for ammonia-N losses during sprinkler irrigation. The reported losses included other components, such as wind drift losses, and the losses attributed to changes in droplet concentration accounted for only a small portion of the total losses (Safley et al., 1992). In this research, we conducted field experiments using a center-pivot irrigation system to measure droplet volatilization losses and to test the model.

The main objective of this paper is to describe the components of the droplet volatilization model and the results of the field experiments. The field experiments focused on the determination of percentage loss of ammoniacal N from droplet volatilization during a droplet's exposure time. Results of the model were compared with observed field data.


   MODEL DEVELOPMENT
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
FIELD EXPERIMENTS
 MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Ammonia Volatilization from a Droplet
Variation in Total Concentration
Assuming a uniform distribution of ammoniacal N concentration within a swine effluent droplet from sprinkler irrigation, the total ammoniacal N in a droplet, mt (g), can be expressed as

[1]
where V is the volume of the droplet (m3); and Ct is the total concentration of the ammoniacal N of all the component species (g m-3):

[2]
where CNH+4 is the concentration of ammoniacal N in the form of ammonium ions (g m-3); and CNH3 is the concentration of ammoniacal N in the form of dissolved ammonia (g m-3).

Ignoring the concentration of ammoniacal N in the surrounding air, the volatilization rate, J (g s-1), from a droplet can be estimated by

[3]
where hm in m s-1 is the mass transfer coefficient of ammonia across a concentration boundary layer around a droplet (Incropera and DeWitt, 1990; Munson et al., 1994); A is the surface area of the droplet (m2); CNH3 is the ammoniacal N concentration in the form of gas-phase ammonia at the droplet-air interface (g m-3). At equilibrium, CNH+4 and CNH3 are related to each other by

[4]
where CH3O+ is the hydronium ion concentration in the droplet (mol L-1), which is related to the pH of the liquid in the droplet

[5]

Ka is the equilibrium constant of the following acid-base reaction

[6]
where H2O(l) represents liquid water.

Under equilibrium conditions, the ammoniacal N concentrations in the forms of liquid-phase and gas-phase ammonia at the surface of a swine-effluent droplet are related to each other by

[7]
where KH is a dimensionless Henry's constant. Combining Eq. [2], [4], [5], and [7], we obtain

[8]
where ß is a dimensionless coefficient given by

The mass balance of ammoniacal N in a droplet can be expressed by

[9]
where t is time (s). The minus sign in Eq. [9] indicates a decrease of ammoniacal N with time due to volatilization loss.

Combining Eq. [1], [3], [8], and [9], we obtain

[10]

Solving Eq. [10] gives

[11]

In Eq. [11], Ct(t), V(t), A(t), hm(t), and ß(t) are used in the places of Ct, V, A, hm, and ß to emphasize their variation with time. In fact, all the equilibrium, transport, and geometric parameters in this paper vary with time. The time-dependence of the equilibrium and transport parameters, such as Henry's constant and mass transfer coefficient originates from their dependence on temperature and the variation of temperature with time. The time-dependence of the geometric parameters, such as the diameter of a droplet, is caused by the evaporation of water from the droplet's surface. Variation of droplet size with time is needed to compute droplet concentration at different times using Eq. [11].

The mass transfer coefficient of ammonia for freely falling liquid drops can be estimated by (Incropera and DeWitt, 1990)

[12]
where DNH3,air is the binary diffusion coefficient of ammonia in air (m2 s-1), d is the diameter of a sphere droplet (m), Re is the Reynolds number of air flow around a droplet

[13]
where Vwind is wind speed (m s-1), {nu} is the kinematic viscosity of the air (m2 s-1). Sc,m in Eq. [12] is the dimensionless Schmidt number for the transport of ammonia in the air

[14]

Substituting Eq. [13] and [14] into Eq. [12] yields

[15]

For spherical droplets,

[16]
where d0 is the initial diameter of a droplet (m). Substituting Eq. [15] and [16] into Eq. [11] yields

[17]

By introducing a time factor, {tau} {equiv} (s-1), we obtain

[18]

Loss
Both Eq. [11] and [18] can be used to calculate the total concentration of ammoniacal N in a swine-effluent droplet at time, t, given the initial concentration and size and the variation of droplet size with time up to time t. Equation [18] applies to spherical droplets only while Eq. [11] is applicable to spheroid droplets. In the case of droplet volatilization of ammonia from sprinkler irrigation with swine effluent, droplets were approximated as spheres. We are interested in the volatilization loss during the so called exposure time which is defined as an interval between the time a droplet leaves the nozzle and the time it hits the ground. The relative loss of ammoniacal N from a spherical droplet, {Delta}Nr, was defined as the ratio of decrease in the amount of ammoniacal N in the droplet to the initial amount and can be expressed as

[19]
where te is the exposure time (s) and de is the droplet diameter at the time it hits the ground (m). The relative decrease in concentration of ammoniacal N in a droplet, {Delta}Cr, was defined as the ratio of the decrease in total concentration of ammoniacal N in a droplet to the initial droplet concentration and can be expressed as

[20]

Exposure time te and variation of droplet diameter during the exposure time are needed to calculate the percentage loss of ammoniacal N from a sphere droplet using Eq. [19]. Estimation of the exposure time and the droplet diameters at different times is discussed in the following sections.

Variation in Droplet Diameter
Evaporation Rate
Variation in droplet diameter is caused by evaporation of water from a droplet's surface. Rate of droplet evaporation is dependent on the evaporative demand of the climate and the energy balance of the droplet. Equilibrium condition of energy balance is established in a droplet if all the energy absorbed by the droplet is consumed in the vaporizing process. The droplet temperature stays at a constant under equilibrium conditions. The constant temperature is called equilibrium temperature. Applying the boundary-layer theory to vapor transport from a spherical droplet into the surrounding air, the evaporation rate at equilibrium temperature can be expressed as (Guyot, 1998; Incropera and DeWitt, 1990; Munson et al., 1994)

[21]
where E is the evaporation rate from a droplet (kg s-1), Mw is the molar mass of water vapor (0.018 kg mol-1), R is the universal gas constant (8.314 x 10-6 m3 MPa mol-1 K-1), Tdrop is the equilibrium temperature of a droplet (K), hw is the mass transfer coefficient of water vapor in air (m s-1), es(Tdrop) is the saturation vapor pressure at the equilibrium temperature (MPa), and ea is the actual vapor pressure in the surrounding air (MPa).

The Magnus equation (Gordon et al., 1998) can be used to represent temperature-dependence of saturation vapor pressure

[22]

For freely falling droplets the mass transfer coefficient of water vapor can be expressed as

[23]
where DH2O,air is the binary diffusion coefficient of water vapor in the air (m2 s-1), Sc,w is the dimensionless Schmidt number for the transport of water vapor in the air

[24]

Given an equilibrium droplet temperature, Eq. [21] can be used to calculate the evaporation rate of water from a droplet.

Equilibrium Temperature
The equilibrium temperature can be determined from the energy balance of a droplet. Neglecting the longwave heat loss from a droplet, the energy balance of a droplet under equilibrium conditions can be expressed as

[25]
where Jcon is the sensible heat flow rate into the droplet across the surrounding temperature boundary layer (kJ s-1), Jsolar is the heat flow rate into the droplet from solar radiation (kJ s-1), {lambda} is the latent heat of vaporization of water (kJ kg-1).

The inflow rate of sensible heat across the temperature boundary layer surrounding a sphere droplet can be expressed as (Incropera and DeWitt, 1990)

[26]
where h is the heat transfer coefficient (kJ m-2 s-1 K-1), Tair is the temperature of the air surrounding the droplet (K), {pi}d2 is the surface area of a sphere. For freely falling sphere liquid droplets, the heat transfer coefficient can be estimated by

[27]
where Kh is the thermal conductivity of the air (kW m-1 K-1), Pr is the dimensionless Prandtl number defined as (Incropera and DeWitt, 1990)

[28]
where Dh is the thermal diffusivity of the air (m2 s-1).

Heat flow into a droplet from solar radiation is calculated from the incoming shortwave radiation by

[29]
where {alpha}refl ({equiv} 0.23) is the reflection coefficient of an effluent droplet (Allen et al., 1998; Brutsaert, 1982, pg. 136.), Rs is the measured solar radiation (kJ m-2 s-1); is the projective area of a sphere droplet on a plane normal to the incident solar radiation.

Combining Eq. [21], [22], [25], [26], and [29], we obtain

[30]

Solving Eq. [30] for Tdrop yields the droplet equilibrium temperature. Equation [30] is a transcendental algebraic equation. It can be solved numerically employing an iterative method. Weather data of air temperature, wind speed, solar radiation, and actual vapor pressure are needed to evaluate the algebraic coefficients in Eq. [30]. Since most of the algebraic coefficients in Eq. [30] are time-dependent and droplet diameter is needed for calculating the heat and mass transfer coefficients, h and hw, the equilibrium temperature varies with time as well, and computation of Tdrop needs to be coupled with calculation of droplet diameter.

Droplet Diameter
Variation of droplet diameter due to evaporation of water can be determined from water balance of a droplet. Water balance of a sphere droplet can be expressed as

[31]
where {rho}w is the density of liquid water (kg m-3). The diameter of a droplet at a given time is needed to solve the differential Eq. [31] for diameters at different times during a droplet's exposure time. In sprinkler irrigation, droplet-sizes are usually measured near the ground surface (Chen and Lin, 1992; Keller and Bliesner, 1990). The measured droplet diameters approximately correspond to those at the end of exposure time, te.

Integrating Eq. [31] from any time t, to the end of a droplet's exposure time, te, and solving the integrated equation for droplet diameter d at time t, we obtain

[32]

Again, d(t) and E(t) are used in the places of d and E in Eq. [32] to emphasize their variation with time, de is defined in Eq. [19]. The evaporation rate E(t) in Eq. [32] is calculated using Eq. [21] with the equilibrium droplet temperature, Tdrop, determined in Eq. [30]. Coupled with Eq. [21] and [30], Eq. [32] can be solved numerically employing a backward stepwise scheme for droplet diameters at different times. The computation starts at the end of exposure time, te, proceeds backward at pre-determined time steps, and ends at the beginning of the exposure time.

Exposure Time of a Droplet
Velocities of water drops from irrigation sprinklers can be expressed as (Green, 1952a; Green1952b; Tipler, 1982)

[33]
where v is the magnitude of the initial velocity of a droplet (m s-1), {phi} is the trajectory angle of a droplet leaving a nozzle, k is an air resistance coefficient (kg s-1), m is the mass of a droplet (kg), t is time (s), g is the acceleration of gravity (9.81 m s-2), vx and vy are the velocity components in a Cartesian coordinate system (m s-1). vy is defined positive downward. Trajectory angle was defined as the angle above a horizontal plane. The exposure time of a droplet is determined by vy. At large times, vy approaches a constant

[34]
where vt is called a terminal velocity (Green, 1952a). Terminal velocity varies with droplet size and values of terminal velocities at different droplet diameters can be obtained through linear interpolation using base points given by Keller and Bliesner (1990).

Substituting Eq. [34] into Eq. [33] yields

[35]

At time t, the position of a droplet can be represented by the height above ground, Ly (m), and the horizontal distance from a nozzle, Lx (m)

[36]
where H0 is the installation height of a nozzle (m). Since Ly becomes 0 as a droplet hits the ground, we have

[37]

The horizontal distance from a nozzle at time te, Lxe (m), is given by

[38]

Combining Eq. [37] and [38] to eliminate the initial velocity, v, yields

[39]

Equation [39] is derived in no wind conditions where {phi} is determined by nozzle installation and Lxe is, indeed, a droplet's radius of throw. Horizontal wind can affect both {phi} and Lxe of an individual droplet. But the exposure time of a droplet is independent of horizontal wind. Therefore, Eq. [39] is applicable to all horizontal wind conditions as long as Lxe is determined in no wind conditions.

An implicit assumption employed in the derivation of Eq. [39] is that a droplet's diameter does not change along its trajectory path. In sprinkler irrigation, droplet diameters decrease due to evaporation of water. Since the exposure time predicted by Eq. [39] decreases with the increase of droplet diameter, plugging d0 or de into Eq. [39] is expected to yield an under- or overestimation of the actual exposure time. Previous investigations by irrigation engineers (Edling, 1985; Kincaid and Longley, 1989; Kohl et al., 1987) revealed that water loss from droplet evaporation in sprinkler irrigation is <3%. At such a percentage of water loss, the difference between the exposure times predicted from d0 and de is <1%. Hence, the effect of variation of droplet diameter on predicted exposure time is considered negligible, and droplet diameter at ground surface, de, can be used to estimate exposure time te.

Temperature Dependence of Transformation and Transport Parameters
The equilibrium constant Ka, Henry's constant KH, diffusion coefficients DNH3,air and DH2O,air, viscosity {nu}, thermal conductivity Kh, thermal diffusivity Dh, and the latent heat of vaporization {lambda} vary with temperature. The temperature dependences of Ka, KH, DNH3,air and DH2O,air are described by the following empirical equations (Beutier and Renon, 1978; Genermont and Cellier, 1997)

[40]
where T(K) is the temperature of the fluids in which the acid-base reaction, liquid-gas transformation, and gaseous binary diffusion occur, R is the universal gas constant (0.008315 kJ mol-1 K-1). DRefNH3,air and DRefH2O,air (m2 s-1) are the diffusion coefficients at a reference temperature, TRef (K). At 25°C, the diffusion coefficients of ammonia and water vapor in air were taken as 2.8 x 10-5 and 2.6 x 10-5 m2 s-1 (Incropera and DeWitt, 1990), respectively. Values of {nu}, Kh, Dh, and {lambda} at different fluid temperatures were obtained through linear interpolation using the base points given by Incropera and DeWitt (1990).


   FIELD EXPERIMENTS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENTS
MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Field experiments measuring ammonia volatilization loss from swine effluent applied to a field through a center-pivot irrigation system were conducted in September 2000, at Oklahoma State University Panhandle Research Station located in Goodwell, OK. Three LDN sprinklers manufactured by Senninger Inc. (Orlando, FL) were used in the experiments. The nozzles selected for the experiments represented the low, medium, and high outlet-flow-rate nozzles. Characteristics of the nozzles used in the experiments are listed in Table 1. The sprinkler system was set up on a fallow field at the research station. Swine effluent from a lagoon of a Seaboard nursery swine farm was transported to the experiment site with a 17 000-L tanker. The effluent was delivered to the sprinkler nozzles by a pump on the tanker. The average pH of the effluent was 7.97 and the average concentration of total ammoniacal N in the effluent was 732 g m-3. Wind speed and air temperature readings at the experiment site were taken from a hand-held Rick anemometer manufactured by TSI Inc. (Shoreview, MN). Average wind speeds during Exp. I (high flow-rate nozzle), II (medium flow-rate nozzle), and III (low flow-rate nozzle) were 4.2, 4.5, and 3.3 m s-1 respectively. Average air temperatures were 36.0, 36.0, and 37.5°C during the experiments.


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  		Table 1. Characteristics of the low drift nozzles used in the sprinkler irrigation experiments.

 
The experiments focused on droplet volatilization loss between the time the effluent left the nozzle to the time it hit the ground. Swine effluent samples from a sprinkler nozzle were collected into cylindrical glass jars (75-mm i.d., 160 mm in height) distributed on the ground surface. The jars contained glass beads coated with oxalic acid to prevent further volatilization loss from collected samples. Unlike the traditional impact sprinklers, which shoot out water in only one direction at a time, LDN sprinklers spray water in all directions at the same time. They are designed to wet a narrow circular ring under no wind conditions. The radius of a wetted ring is defined as the radius of throw, which is dependent on the nozzle installation height and the working base pressure. The radius of throw at different installation heights and working pressures were available at Senninger Irrigation Inc.'s web site, www.senninger.com. In our experiments, sprinkler nozzles were installed at a height 0.56 m above ground surface. Single flat-pad LDN nozzles were used in the experiments. The average radius of throw was 2.67 m for Exp. I, 2.20 m for Exp. II, and 1.75 m for Exp. III.

In each experiment, 16 collection jars were placed on the wetted ring to collect swine effluent samples at the ground surface. Nine swine effluent samples (three in each experiment) were collected at the sprinkler nozzles to determine concentration of ammoniacal N in the effluent before droplet volatilization loss. Swine effluent samples collected in the glass jars were transferred to 40-mL borosilicate glass vials for storage and transportation. The samples were brought back to the soil-testing laboratory of Oklahoma State University at Stillwater, OK. The Lachat method 12-107-06-1-B (Bloxham, 1993) was used to determine ammonium concentration in the swine effluent samples. Means and standard errors of the concentrations of ammonium N in swine effluent samples collected at the ground surface and the nozzles of the sprinkler irrigation experiments are summarized in Table 2. The following equation was used to compute the relative decrease in droplet concentration of ammoniacal N in Table 2.


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  		Table 2. Average concentrations of ammonium N in swine effluent samples collected at the ground surface and the nozzles of the sprinkler irrigation experiments.

 

[41]
where {Delta}Cr is the relative decrease in concentration of ammoniacal N in a droplet; Ct0 is the initial concentration, which is the concentration at the time a droplet leaves a nozzle (g m-3); Cte is the concentration at the time a droplet hits the ground (g m-3).

Loss of ammoniacal N from a droplet in sprinkler irrigation can be calculated from the decrease in concentration of ammoniacal N in the droplet and the evaporation loss of water from the droplet. Mathematically, the relative loss of ammoniacal N from a droplet, {Delta}Nr, can be expressed as

[42]
where V0 is the initial volume of a droplet (m3), Ve is the volume of a droplet at the time it hits the ground (m3). The droplet-volume ratio, , is related to the relative loss of water from droplet evaporation, {Delta}Wr, by

[43]

Combining Eq. [41], [42], and [43] yields

[44]

The relative volatilization losses of ammoniacal N in Table 2 were estimated with a relative water loss of 0.025 (Edling, 1985; Kincaid and Longley, 1989; Kohl et al., 1987). In Exp. I, the observed difference in average concentration of ammoniacal N between samples collected at the nozzle and samples collected at the ground surface was 4.5 g m-3, while the standard error in measured concentration of ammoniacal N was 10.3 g m-3 for the samples collected at the nozzle and 5.8 g m-3 for the samples collected at the ground surface. The observed difference was much less than the sum of the standard errors in concentration measurements. The same was true for Exp. II. Hence, the measured average concentration of ammoniacal N of the samples collected at the nozzles was considered not statistically different from that of the samples collected at the ground surface. In Exp. III, the measured average concentration of samples collected at the ground surface was significantly higher than that of the samples collected at the nozzle. The following two processes could cause the concentration increase: one was the evaporation of water from the acidified solution in the collection jars; and the other was the so-called distillation process in the droplets. The distillation process was defined as the process in which water was leaving the droplets at a rate greater than that of ammonia. The distillation effect was predicted by the mechanistic model at pH values <7.85. Both the evaporation from collection jars and the distillation in the falling droplets might have been enhanced in Exp.III by the relatively low outlet flow rate, and consequently smaller droplet size, longer collection time, and smaller volume of the collected solution. The outlet flow rate in Exp. III was about a tenth of the rate in Exp. I and about a quarter of the rate in Exp. II. The collection time in Exp. III was about two times longer than those in Exp. I and II. The amount of solution collected at the ground in Exp. III was about a quarter of those in Exp. I and II.


   MODEL APPLICATION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENTS
 MODEL APPLICATION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
Low Drift Nozzle Sprinklers
The droplet volatilization model developed in this research can be used to estimate ammonia volatilization from droplets of LDN and impact sprinklers. Since a LDN sprinkler delivers water in all directions at the same time and throws all the droplets to about the same distance from its nozzle, droplet diameters from a LDN sprinkler can be considered a constant. Equation [19] can be used directly to estimate the average relative loss of ammoniacal N from a LDN sprinkler system. Figure 1 shows the simulated relative loss of ammoniacal N from droplet volatilization at different swine-effluent pHs. The dotted line in the figure is the relative loss of ammoniacal N. The solid line in the figure is the relative decrease in concentration of ammoniacal N. The horizontal line in the figure represents the simulated relative loss of water from droplet evaporation. The two vertical lines indicate the minimum and maximum pH values encountered in a long-term pH monitoring of swine lagoons (Mr. Turner, a Sr. Research Specialist at the Department of Plant and Soil Sciences, Oklahoma State University, personal communication, 2000). Weather data measured in field Exp. I was used in the computation. The installation height, H0, radius of throw, Lxe, and trajectory angle, {phi}, were also taken from the experimental setup. Since no measured droplet diameter was available for the LDN sprinklers used in the experiments, 0.5 mm, a lower limit of the reported range of average droplet diameter in sprinkler irrigation (Keller and Bliesner, 1990), was used for de in the simulation. Since the relative volatilization loss increases with the decrease in droplet diameter, the simulated losses using the diameter of 0.5 mm were considered overestimations of the actual losses. It is interesting to notice that, within the reported range of pH in swine lagoons, the simulated change in concentration of ammoniacal N in a droplet is quite small in magnitude (<1%). The relative loss of ammoniacal N is quite close to that of water (0.01–0.03 g g-1). The simulation result is consistent with the experimental observation that the measured average concentration of ammoniacal N of the samples collected at the nozzles is not statistically different from that of the samples collected at the ground surface. Table 3 shows the predicted relative losses of ammoniacal N and water from droplet volatilization and evaporation and the measured and predicted relative decreases in concentration of ammoniacal N for the three experiments. Again, droplet diameter at ground surface, de, was set at 0.5 mm in the simulations. Both the predicted and measured decreases in concentration of ammoniacal N were <1% of the concentrations at the nozzle for Experiment runs I, and II.



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  		Fig. 1. Simulated relative volatilization loss of ammoniacal N from swine-effluent droplets at different pHs.

 

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  		Table 3. Measured and predicted relative changes in concentration of ammoniacal N due to droplet volatilization.

 
Impact Sprinklers
Because of high variability in droplet diameter and radius of throw in an impact sprinkler system, computation of average droplet-volatilization loss of ammoniacal N from the system is more complicated. The computation can be divided into two steps. The first step is to determine the distribution of relative loss along a radius of a wetted circle of an individual sprinkler based on the relationship between average droplet diameter and radial distance from a sprinkler. At a given radial distance, Lxe, a mean droplet diameter (presumably measured at ground surface), de, can be obtained from distribution of droplet diameter over radial distance. Evaluating terminal velocity, vt, at the droplet diameter, de, through linear interpolation, plugging vt and Lxe into Eq. [39], and solving the equation with given installation height and trajectory angle yield the exposure time, te, at the radial distance, Lxe. With the exposure time, te, Eq. [19] can be used to calculate relative loss at the radial distance, Lxe. Evaluating relative loss at different radial distances produces the radial distribution of relative loss. The second step is to calculate average relative loss of an individual sprinkler using the radial distribution of relative loss determined in the first step and the radial distribution of water applied by the sprinkler system. Mathematically, the average relative loss, , can be expressed as

[45]
where Rw is the radius of a circular area wetted by a sprinkler (m), P(r) and {Delta}Nr(r) are the depth of water applied (mm) and relative droplet-volatilization loss at a radial distance r (m).

Using measured radial distributions of droplet diameter and precipitation depth for a standard 4-mm impact nozzle sprinkler operating at 138 kPa under low-wind conditions (Keller and Bliesner, 1990) and setting the installation height and trajectory angle at 2 m and 15° respectively, we obtained an average volatilization loss of 1% for the sprinkler system. The swine-effluent pH of 7.97 obtained in the field experiments described in the previous section was used in the computation.


   SUMMARY AND CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENTS
 MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
A mechanistic model was developed to predict ammonia volatilization from swine-effluent droplets in sprinkler irrigation. Field experiments were conducted to validate the model. Both the measured and simulated droplet volatilization losses were considered insignificant compared with surface volatilization losses. The simulation and experiment results also revealed that within the reported range of pH in swine lagoons, change in ammoniacal-N concentration caused by droplet volatilization is negligibly small, and the percentage loss from droplet volatilization can be approximated by that of droplet evaporation loss.


APPENDIX:

Symbols

Symbol
 Description
 Unit
A surface area of a droplet m2
CH3O+ hydronium concentration in a droplet mol L-1
CNH3 concentration of ammoniacal N in the form of dissolved ammonia g m-3
CNH3 ammoniacal N concentration in the form of gas-phase ammonia g m-3
CNH+4 concentration of ammoniacal N in the form of ammonium ions g m-3
Ct total concentration of ammoniacal N of all component species g m-3
Ct0 initial total concentration of ammoniacal N g m-3
Cte total concentration of ammoniacal N at the time a droplet hits the ground g m-3
d diameter of a sphere droplet m
d0 droplet diameter at the time it leaves a nozzle m
de droplet diameter at the time it hits the ground m
Dh thermal diffusivity of the air m2 s-1
DH2O,air the binary diffusion coefficient of water vapor in the air m2 s-1
DRefH2O,air the water-vapor diffusion coefficient at a reference temperature m2 s-1
DNH3,air the binary diffusion coefficient of ammonia in the air m2 s-1
DRefNH3,air the ammonia diffusion coefficient at a reference temperature m2 s-1
E evaporation rate from a droplet kg s-1
ea actual vapor pressure in the surrounding air MPa
es(Tdrop) saturation vapor pressure at temperature Tdrop MPa
g acceleration of gravity m s-2
h heat transfer coefficient across a temperature boundary layer around a droplet kJ m-2 s-1 K-1
H0 installation height of nozzle m
hm mass transfer coefficient of ammonia across a concentration boundary layer around a droplet m s-1
hw mass transfer coefficient of water vapor across a concentration boundary layer around a droplet m s-1
J rate of ammonia volatilization from a droplet g s-1
Jcon sensible heat flow rate into a droplet across the surrounding temperature boundary layer kJ s-1
Jsolar heat flow rate into a droplet from solar radiation kJ s-1
k air resistance coefficient kg s-1
Ka equilibrium constant of the NH3(aq) {leftrightarrow} NH+4 reaction mol L-1
Kh thermal conductivity of the air kW m-1 K-1
KH Henry's law constant dimensionless
Lx horizontal distance from a nozzle m
Lxe horizontal distance from a nozzle at the time a droplet hits the ground m
Ly height above ground m
m mass of a droplet kg
mt total mass of ammoniacal N in a droplet g
Mw molar mass of water kg mol-1
pH pH of the liquid in a droplet log10(mol L-1)
P(r) precipitation depth at a radial distance r from a sprinkler nozzle mm
Pr Prandtl number dimensionless
r radial distance from a sprinkler nozzle m
R the universal gas constant KJ mol-1 K-1
Re Reynolds number dimensionless
Rs measured solar radiation KJ m-2 s-1
Rw radius of a circular area wetted by a sprinkler m
Sc,m Schmidt number for the transport of ammonia dimensionless
Sc,w Schmidt number for the transport of water vapor dimensionless
t time s
T temperature of the fluids in which the acid-base reaction, liquid-gas transformation, and gaseous binary
  diffusion occur		 K
Tair temperature of the air surrounding the droplet K
Tdrop equilibrium temperature of a droplet K
te exposure time s
TRef reference temperature K
v magnitude of the initial velocity of a droplet m s-1
V volume of a droplet m3
V0 initial volume of a droplet m3
Ve the volume of a droplet at the time it hits the ground m3
vt terminal velocity of a droplet m s-1
Vwind wind speed m s-1
vx droplet velocity in horizontal direction m s-1
vy droplet velocity in vertical direction m s-1
{alpha}refl reflection coefficient of solar radiation dimensionless
ß a dimensionless coefficient to convert gas-phase concentration of ammonia at the liquid-air interface to total
  concentration of ammoniacal N in a droplet		 dimensionless
{Delta}Cr relative decrease in concentration of ammoniacal N in a droplet g m-3 g-1 m3
{Delta}Nr relative loss of ammoniacal N from a droplet g g-1
average relative loss of ammoniacal N over the wetted area of an impact sprinkler nozzle g g-1
{Delta}Wr relative loss of water from droplet evaporation g g-1
{phi} trajectory angle of a droplet leaving a nozzle, which was defined as the angle above a horizontal plane radian
{lambda} latent heat of vaporization of water kJ kg-1
{rho}w density of liquid water kg m-1
{nu} kinematic viscosity of the air m2 s-1
{tau}
 time factor
 s-1


   ACKNOWLEDGMENTS
 
The authors thank Clemn Turner for his help in the field experiments of this research and in the preparation of this manuscript.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENTS
 MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
This research was supported in part by funds from the Oklahoma Agricultural Experiment Station and from CSREES Project Number OKL02445.

Received for publication August 19, 2002.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENTS
 MODEL APPLICATION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 





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