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B. Transport of NH3 in Animal Houses

B. Transport of NH3 in Animal Houses

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S. G. SOMMER ET AL.



280



Applying the analogy of the Ohm’s law, combining Eqs. (7) and (8), we

have

1

1

1

1





ỵỵ

ẳ r1 ỵ r2 þ Á Á Á þ rn

Kt K1 K2

Kn



ð9Þ



and the overall NH3 mass transfer coeYcient given in Eq. (3).

Kt ẳ



1

:

r1 ỵ r2 ỵ ỵ rn



10ị



Transport from the sources in the animal building to the outdoor atmosphere may be simplified as presented in Fig. 4. The four major sources for

NH3 emission considered in the model for a livestock building are: (i)

manure surface, (ii) sidewalls in slurry channels, (iii) surface of the slatted

floor, and (iv) surface of the solid floor. The air volumes in the room space

and in the headspace of a slurry channel are assumed to be fully mixed,

except in the boundary layers near the source surfaces. The locations of

animals in the building are not considered in the model.

An essential issue to consider when characterizing convection transfer is

to determine whether the air motion in the boundary layer is laminar or

turbulent. Surface friction and the convection transfer rates depend strongly

on which of those conditions exists (Incropera and DeWitt, 1990). In a

laminar boundary layer, air motion is highly ordered and it is possible to

identify airflow dynamics. In contrast, air motion in a turbulent boundary

layer is highly irregular and is characterized by velocity fluctuations. These

fluctuations enhance the transfer momentum, energy, and surface friction as

well as mass convection transfer rate.

In a slurry channel, the NH3 emission flux from manure surface may be

described as

Fsl;s ¼ DShsl;s ðNH3;G À NH3;sl;a Þ=lsl;s ¼ Ksl;s ðNH3;G À NH3;sl;a ị

1

NH3;G NH3;sl;a ị;



rsl;s



11ị



where rsl;s ẳ lsl;s D1 Sh1

sl;s is the resistance in the boundary layer over the

emission surface (m sÀ1); D, is the NH3 diVusion coeYcient in air (m2 sÀ1);

NH3,sl,s and NH3,sl,a are NH3 concentrations at the slurry surface and in the

headspace of the slurry channel, respectively. The diVusion coeYcient of

NH3 in air may be calculated by an empirical relation developed by Fuller

et al. (1966),



NH3 EMISSION LIVESTOCK HOUSES & MANURE STORES



281



107 273:15 ỵ Tị1:75 1=MNH3 ỵ 1=Ma ị1=2

12ị

P

P

pẵ NH3 vi ị1=3 ỵ a vi ị1=3 2

P

P

where diVusion volumes for molecules of air, a vi and NH3 NH3 vi have a

value of 20.1 and 14.9, respectively (Fuller et al., 1966). For laminar flow sh

may be calculated as follows,







Sh ¼ 0:644Re1=2 Sc1=3 :



ð13Þ



For turbulent flow the following algorithm may be used.

Sh ẳ 0:037Re4=5 Sc1=3 :



14ị



The transport of NH3 from the surface of the slurry to the slats may be a

combination of laminar flow in a boundary layer just above the slurry

surface and turbulent flow between this boundary layer and the slats above

the slurry channel.

The emission rate from the slatted floor of the slurry channels is related to

the air exchange rate between the headspace in the channel and the room

airspace. The air exchange is driven by the pressure variation at the openings

of the slatted floor. The exchange rate depends on the ventilation rate, the

airflow pattern in the room, turbulence level above the slatted floor, and

opening area in the slatted floor. If we consider the mass transfer between the

air in the headspace of the slurry channel and the air in the room space as

independent of the convection transfer process from the slatted floor, and

the air exchange rate in the slurry channel is Vsl, the NH3 mass flux through

the slat openings may be expressed as,

Fsl;o ẳ



Vsl

1

NH3;sl;a NH3;a;r ị ẳ

NH3;sl;a NH3;a;r Þ

rsl;o

Asl;o



ð15Þ



where Asl,o is opening area of slatted floor (m2); rsl;o ¼ Asl;o =Vsl , is the

resistance of the slatted floor to emission from the slurry channels, s mÀ1;

NH3,sl,a and NH3,a,r are NH3 concentrations in air in the headspace in

the slurry channels and in the room space, respectively. Here, the NH3

concentration in the boundary layer at the surface of slats is assumed to be

the same everywhere, the airflow rate into the headspace is equal to the

airflow out.



S. G. SOMMER ET AL.



282



The sidewalls in the slurry channel are also contaminant sources for NH3

emissions. We may describe the emission in the same forms as in Eq. (11):

Fsl;w;s ẳ DShsl;w;s NH3;sl;w;s NH3;sl;a ị=lsl;w;s

ẳ Ksl;w;s NH3;sl;w;s NH3;sl;a ị

1

NH3;sl;w;s NH3;sl;a ị:



rsl;w;s



16ị



Similar to Eq. (11), the NH3 emission fluxes from the surfaces of slatted

and solid floor may be estimated by

Fof;s ¼



DShof ðNH3;of;s À NH3;a;r Þ

¼ Kof;s ðNH3;of;s À NH3;a;r Þ

lof

1

ðNH3;of;s À NH3;a;r Þ

¼

rof;s



ð17Þ



DShsf ðNH3;sf;s NH3;a;r ị

ẳ Ksf;s NH3;sf;s NH3;a;r ị

lsf

1



NH3;sf;s NH3;a;r Þ

rsf;s



ð18Þ



and

Fsf;s ¼



respectively.

À1

À1

The emission resistances rof;s ¼ lof;s DÀ1 ShÀ1

of;s and rsf;s ¼ lsf;s D Shsf;s are

dependent on the characteristics of the airflow in the surface boundary layers

above the slatted and solid floor. The maximum thickness of the boundary

layers may be estimated by the following equation for laminar flow,

dc ¼ 5lReÀ1=2 Sc1=3



19ị



and the following equation for turbulent flow,

dc ẳ 0:37lRe1=5 :



20ị



The NH3 mass flux through the exhaust openings of building ventilation

may be described as:



NH3 EMISSION LIVESTOCK HOUSES & MANURE STORES



Frv ¼



Vrv

1

ðNH3;a;r NH3;a ị ẳ

NH3;a;r NH3;a ị

rrv;o

Arv;o



283



21ị



where, Vrv is room ventilation rates (m3 sÀ1); Arv,o is the outlet opening area

(m2); rrv;o ¼ Arv;o =Vrv , is resistance of the ventilation outlet to NH3 mass flux

from the room airspace to the atmosphere, s mÀ1. The rrv,o value has eVects

on the emissions from all the NH3 sources in the building envelope.

Summarizing the above analysis and with continuity of the mass flux

transfer, we have the following equations to estimate NH3 mass transfer

coeYcients from slurry channels, slatted and solid floors through the exhaust

openings of the room to atmosphere:

Ksl ẳ



1



22ị



rsl;s ỵ rsl;o ỵ rrv;o



Ksl;w ẳ



1

rsl;w;s ỵ rsl;o ỵ rrv;o



23ị



Kof ẳ



1

rof;s ỵ rrv;o



24ị



Ksf ẳ



1

:

rsf;s ỵ rrv;o



25ị



Therefore, the total NH3 emission from a livestock building may be

estimated by

FNH3 ẳ Fsl Asl ỵ Fsl;w Asl;w ỵ Fof Aof ỵ Fsf Asf



26ị



where

Fsl ẳ Ksl NH3;sl;s NH3;a ị ẳ



1

NH3;sl;s NH3;a ị;

rsl



Fsl;w ẳ Ksl;w NH3;sl;s NH3;a ị ẳ



Fof ¼ Kof ðNH3;of;s À NH3;a Þ ¼



1

ðNH3;sl;s À NH3;a Þ;

rsl;w



1

ðNH3;of;s NH3;a ị;

rof



27ị



28ị



29ị



S. G. SOMMER ET AL.



284



and

Fsf ẳ Ksf NH3;sf;s NH3;a ị ẳ



1

NH3;sf;s NH3;a ị

rsf



30ị



In this approach, the most important issue is to determine the resistance

parameters. The basic factors that aVect the resistances are ventilation rate,

outlet area, the airflow characteristics above the floors, air exchange rate in

the slurry channel, and the airflow characteristics in the slurry channel. The

ventilation rate may be estimated based on the CO2 production model of the

animals. The method may be applied to both mechanically and naturally

ventilated buildings (Pedersen et al., 1998; Zhang et al., 2004). A major

challenge for a naturally ventilated building is to accurately estimate the

outlet area in windy conditions. For a mechanical ventilation system the

ventilation rate may be achieved directly by measurement. Airflow characteristics above the floor and the factors that aVect them can be found in the

literature (Heber et al., 1996; Strøm et al., 2002; Zhang et al., 1999). In many

cases, the flow characteristics vary according to the ventilation systems,

partition of pens, and density of the animals in the room. Temperature

gradients between emission source and air space above the source may also

aVect the airflow due to the buoyancy eVect (Zhang et al., 2002). In an

investigation of the mass transfer coeYcient of ammonia in liquid pig

manure and aqueous solution by Arogo et al. (1999), the turbulence caused

by thermal buoyancy was reported. A high turbulence level may result in a

reduced resistance to mass flow from the emitting surfaces by reducing the

boundary layer thickness. To estimate the flow characteristics in the headspace of the slurry channel and the air exchange rate in the headspace,

further research is needed.



C. TRANSPORT FROM UNCONFINED SOURCES

For NH3 emission from unconfined slurry stores, beef feedlots, and

hardstandings, a three‐layer model (Hutchings et al., 1996; Olesen and

Sommer, 1993) can be applied. The layers are a surface layer aVected by

surface condition, a laminar airflow layer above the surface layer, and a

layer where airflow is fully turbulent. Kt [see Eq. (3)] is defined as:



Kt ẳ



1

ra ỵ rb ỵ rc



31ị



NH3 EMISSION LIVESTOCK HOUSES & MANURE STORES



285



where ra is the resistance in the turbulent layer above the slurry, rb is the

resistance in the laminary boundary layer (i.e., between the gas–liquid interface and the turbulent layer), and rc is the resistance of the manure surface

cover.

The resistance ra in the turbulent layer is calculated as [according to van

der Molen et al. (1990a); Padro et al. (1994)]:

ra ẳ



Inl=z0 ị

:

Ku



32ị



The wind velocity profile above the slurry is described by the standard

equation under neutral conditions (Monteith and Unsworth, 1990):

uz ẳ



u

z

In

k z0



33ị



where uz is the wind velocity at height z above the slurry surface, uà is the

friction velocity, z0 is the roughness length, and k is von Karman’s constant.

The roughness length varies with surface characteristics and wind velocity.

The typical roughness length of z0 ¼ 1 mm used for bare soils (van der

Molen et al., 1990b) is chosen because the physical structure of typical slurry

surfaces resembles that of bare soils. z is a correction for the atmospheric

stability, which depends on the Richardson number Ri (Padro et al., 1994):



zẳ



Ri ẳ



1 Riị2

1 16Riị0:75



gzTa À Tm Þ

u2z Ta



À0:1 Ri

Ri < À0:1



ð34Þ



ð35Þ



where g is the gravitational acceleration, and Ta and Tm are air and manure

surface temperatures, respectively. The correction factor (l ) is calculated as

shown by Monteith and Unsworth (1990). l is the height of the internal

boundary layer, that is, the distance from the slurry or soil surface to the

point where the atmospheric NH3 concentration equals the background

concentration. The following approximate equation for l is used (van der

Molen et al., 1990a):



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