poster - International Conference of Agricultural Engineering
poster - International Conference of Agricultural Engineering poster - International Conference of Agricultural Engineering
model was introduced to estimate the air flow turbulence. Using the wind velocity predicted by this model, the vapor pressure and air temperature in the vicinity of the soil surface were estimated by the numerical model describing the air heat and vapor transfer in the microadvective condition. The energy budget on the soil surface was estimated using the wind velocity, vapor pressure, and air temperature simulated by these models. The soil water content and temperature were predicted using the simulation model describing the water and heat transfer in the soil. Using the energy budget, the accuracy of this model was verified by a wind tunnel. 2. Methodology 2.1. Analysis of airflow field around an isolated crop The governing equations describing the wind flow around an isolated crop can be written as follows: ∂u ∂v + = 0 ∂x ∂z ∂u ∂u ∂u 1 ∂p ∂ ⎛ + u + v = − + ⎜ K ∂t ∂x ∂z ρ ∂x ∂x ⎝ ∂v ∂v ∂v 1 ∂p ∂ ⎛ + u + v = − + ⎜ K ∂t ∂x ∂z ρ ∂z ∂x ⎝ a a ∂u ⎞ ∂ ⎛ ⎟ + ⎜ K ∂x ⎠ ∂z ⎝ ∂v ⎞ ∂ ⎛ ⎟ + ⎜ K ∂x ⎠ ∂z ⎝ a a ∂u ⎞ ⎟ − C ∂z ⎠ ∂v ⎞ ⎟ − C ∂z ⎠ where u and v are the wind velocity in horizontal and vertical directions (m·s -1 ), ρ is the air density (=1.293kg/m 3 ), p is the air pressure (g·m -1·s -2 ), K a is the eddy diffusion coefficient (m 2·s -1 ), C m is the resistance coefficient by crop canopy, S is the leaf area density(m 2·m -3 ) , t is the time, x is the fetch, and z is the height. Eddy coefficient described in eqs. (2) and (3) can be estimated as follows: K a 2 ∂u = λ m (4) ∂z The parameter λ m , inside and outside of the crop canopy can be represented as the following equations, respectively. 3 2κ λ m in = (5) C m S ( z − ) λ = κ (6) m out d 0 The parameter of inside of the crop canopy λ m in can be estimated as follows: ( z − d ) 0 m in : = κ ( z − ) κ > λ m in d 0 m m S S u u 2 2 + v + v λ (7) 2 2 v u (1) (2) (3) κ z > λ m in : λ = κz (8) m in 2.2. Heat and vapor transfer under micro-scale advection The equations that describe the air heat and vapor transfer in the advective condition can be written as follows:
∂e ∂e ∂e + u + v ∂t ∂x ∂z = ∂ ⎛ ∂e ⎞ ∂ ⎛ ∂e ⎞ ⎜ K a ⎟ + ⎜ K a ⎟ (9) ∂x ⎝ ∂x ⎠ ∂z ⎝ ∂z ⎠ ∂T a ∂t ∂Ta + u ∂x ∂Ta + v ∂z ∂ ⎛ = ⎜ K ∂x ⎝ a ∂Ta ∂x ⎞ ∂ ⎛ ⎟ + ⎜ K ⎠ ∂z ⎝ a ∂T ∂z where, T a is the air temperature(°C), and e is the vapor pressure(hPa). K a can be given using eq. (4). a ⎞ ⎟ ⎠ (10) 2.3. Soil moisture and heat transfer The moisture and heat transfer at the soil surface can be described as follows: ∂θ ∂ ∂θ ∂ ∂θ ∂ ∂T ∂ ∂T ∂K = ( Dw ) + ( Dw ) + ( DT ) + ( DT ) + ∂t ∂x ∂x ∂z ∂z ∂x ∂x ∂z ∂z ∂z C v ∂T ∂t (11) ∂ ∂T ∂ ∂T ⎧ ∂ ∂θ ∂ ∂θ ⎫ = ( λ ) + ( λ ) + Lρ w ⎨ ( Dwv ) + ( Dwv ) ⎬ (12) ∂x ∂x ∂z ∂z ⎩∂x ∂x ∂z ∂z ⎭ where C v is the volumetric heat capacity(J·m -3·ºC -1 ), D θ is the isothermal water diffusivity(m 2·s -1 ), D θv is the isothermal vapor diffusivity(m 2·s -1 ), D T is the thermal water diffusivity(m 2·s -1·ºC -1 ), K is the hydraulic conductivity(m·s -1 ), L is the latent heat of water vaporization(J·kg -1 ), T is the soil temperature(ºC), t is the time(s), λ is the thermal conductivity(W·m -1·ºC -1 ), ρ l is the water density(kg·m -3 ), and θ is the volumetric soil water content(m 3·m -3 ). 2.4. Model structure Figure 1 shows the schematic view of the numerical model used to simulate the air-flow field, vapor, and heat environment around an isolated crop and the moisture and heat transfer in soil. z Above soil surface ∂ ⎛ ⎜ K ∂z ⎝ ∂ ⎛ ⎜ K ∂z ⎝ a a ∂e ⎞ ⎟ = 0 ∂z ⎠ ∂Ta ⎞ ⎟ = 0 ∂z ⎠ 風 Wind e and T a are uniform. ∂Ta ∂Ta ∂Ta ∂ ⎛ ∂Ta ⎞ ∂ ⎛ + u + v = ⎜ K a ⎟ + ⎜ K ∂t ∂x ∂z ∂x ⎝ ∂x ⎠ ∂z ⎝ ∂e ∂e ∂e ∂ ⎛ ∂e ⎞ ∂ ⎛ ∂e ⎞ + u + v = ⎜ K a ⎟ + ⎜ K a ⎟ ∂t ∂x ∂z ∂x ⎝ ∂x ⎠ ∂z ⎝ ∂z ⎠ a ∂Ta ∂z ⎞ ⎟ ⎠ ⎛ ∂θ ∂T ⎞ E = Lρ w ⎜ − D w − D T − K ⎟ ⎝ ∂z ∂z ⎠ ∂T ∂θ G = −λ − Lρ w D wv ∂z ∂z x v u The values of e and T a are the same as the adjacent node. Subsurface ∂θ ∂ ∂θ ∂ ∂θ ∂ ∂T ∂ ∂T ∂K = ( D w ) + ( D w ) + ( DT ) + ( DT ) + ∂t ∂x ∂x ∂z ∂z ∂x ∂x ∂z ∂z ∂z ∂T ∂ ∂T ∂ ∂T ⎧ ∂ ∂θ ∂ ∂θ ⎫ C v = ( λ ) + ( λ ) + Lw ρ w ⎨ ( D wv ) + ( D wv ) ⎬ ∂t ∂x ∂x ∂z ∂z ⎩ ∂x ∂x ∂z ∂z ⎭ Dry Wet Dry θ,T are same value as the adjacent node. FIGURE 1: Schematic view of the numerical model used to simulate the air-flow field, vapor, and heat environment around an isolated crop and the moisture and heat transfer in soil.
- Page 291 and 292: References Choi, W.-J., Lee, S.-M.,
- Page 293 and 294: of faecal bacteria (Kummerer, 2004;
- Page 295 and 296: FIGURE 1 - Project tasks and links
- Page 297 and 298: Oliveira, A.B. & Henriques, M. (201
- Page 299 and 300: 1 Introduction To irrigate is to su
- Page 301 and 302: the inverter that provides a refere
- Page 303 and 304: OLIVEIRA FILHO, D. ; SAMPAIO, R. P.
- Page 305 and 306: 1.1 Description of the Study Area T
- Page 307 and 308: Refrences: Bruce J.P. (1994). Natur
- Page 309 and 310: RE because it has the advantages ov
- Page 311 and 312: with L 1 2 com obs J ( k ) = ∑{ f
- Page 313 and 314: Relative hydraulic conductivity r 1
- Page 315 and 316: surfaces requires information on th
- Page 317 and 318: climate. Therefore a special coeffi
- Page 319 and 320: FIGURE 2: The relation between K pa
- Page 321 and 322: Coagulation using Moringa oleifera
- Page 323 and 324: After the assembly of the experimen
- Page 325 and 326: For the positive control test, the
- Page 327 and 328: MULTIVARIATE STATISTICAL OF PRINCIP
- Page 329 and 330: The multiple regression equations w
- Page 331 and 332: Table 3 - Regression models that be
- Page 333 and 334: Is Imaging Analysis Quantifying the
- Page 335 and 336: of the computer. All additional ima
- Page 337 and 338: The final enhanced images were segm
- Page 339 and 340: image analysis is well suited and f
- Page 341: EVALUATION OF CROP CANOPY EFFECT ON
- Page 345 and 346: 4. Results and discussion 4.1. Spat
- Page 347 and 348: Benchmarking of Irrigated Agricultu
- Page 349 and 350: Indicators can be thought of as sta
- Page 351 and 352: total area is about 13,700 km2. The
∂e<br />
∂e<br />
∂e<br />
+ u + v<br />
∂t<br />
∂x<br />
∂z<br />
=<br />
∂ ⎛ ∂e<br />
⎞ ∂ ⎛ ∂e<br />
⎞<br />
⎜ K<br />
a ⎟ + ⎜ K<br />
a ⎟<br />
(9)<br />
∂x<br />
⎝ ∂x<br />
⎠ ∂z<br />
⎝ ∂z<br />
⎠<br />
∂T<br />
a<br />
∂t<br />
∂Ta<br />
+ u<br />
∂x<br />
∂Ta<br />
+ v<br />
∂z<br />
∂ ⎛<br />
= ⎜ K<br />
∂x<br />
⎝<br />
a<br />
∂Ta<br />
∂x<br />
⎞ ∂ ⎛<br />
⎟ + ⎜ K<br />
⎠ ∂z<br />
⎝<br />
a<br />
∂T<br />
∂z<br />
where, T a is the air temperature(°C), and e is the vapor pressure(hPa).<br />
K a can be given using eq. (4).<br />
a<br />
⎞<br />
⎟<br />
⎠<br />
(10)<br />
2.3. Soil moisture and heat transfer<br />
The moisture and heat transfer at the soil surface can be described as follows:<br />
∂θ<br />
∂ ∂θ<br />
∂ ∂θ<br />
∂ ∂T<br />
∂ ∂T<br />
∂K<br />
= ( Dw<br />
) + ( Dw<br />
) + ( DT<br />
) + ( DT<br />
) +<br />
∂t<br />
∂x<br />
∂x<br />
∂z<br />
∂z<br />
∂x<br />
∂x<br />
∂z<br />
∂z<br />
∂z<br />
C<br />
v<br />
∂T<br />
∂t<br />
(11)<br />
∂ ∂T<br />
∂ ∂T<br />
⎧ ∂ ∂θ<br />
∂ ∂θ<br />
⎫<br />
= ( λ ) + ( λ ) + Lρ<br />
w ⎨ ( Dwv<br />
) + ( Dwv<br />
) ⎬<br />
(12)<br />
∂x<br />
∂x<br />
∂z<br />
∂z<br />
⎩∂x<br />
∂x<br />
∂z<br />
∂z<br />
⎭<br />
where C v is the volumetric heat capacity(J·m -3·ºC -1 ), D θ is the isothermal water<br />
diffusivity(m 2·s -1 ), D θv is the isothermal vapor diffusivity(m 2·s -1 ), D T is the thermal water<br />
diffusivity(m 2·s -1·ºC -1 ), K is the hydraulic conductivity(m·s -1 ), L is the latent heat <strong>of</strong> water<br />
vaporization(J·kg -1 ), T is the soil temperature(ºC), t is the time(s), λ is the thermal<br />
conductivity(W·m -1·ºC -1 ), ρ l is the water density(kg·m -3 ), and θ is the volumetric soil water<br />
content(m 3·m -3 ).<br />
2.4. Model structure<br />
Figure 1 shows the schematic view <strong>of</strong> the numerical model used to simulate the air-flow field,<br />
vapor, and heat environment around an isolated crop and the moisture and heat transfer in<br />
soil.<br />
z<br />
Above soil<br />
surface<br />
∂ ⎛<br />
⎜ K<br />
∂z<br />
⎝<br />
∂ ⎛<br />
⎜ K<br />
∂z<br />
⎝<br />
a<br />
a<br />
∂e<br />
⎞<br />
⎟ = 0<br />
∂z<br />
⎠<br />
∂Ta<br />
⎞<br />
⎟ = 0<br />
∂z<br />
⎠<br />
風 Wind<br />
e and T a are uniform.<br />
∂Ta<br />
∂Ta<br />
∂Ta<br />
∂ ⎛ ∂Ta<br />
⎞ ∂ ⎛<br />
+ u + v = ⎜ K<br />
a ⎟ + ⎜ K<br />
∂t<br />
∂x<br />
∂z<br />
∂x<br />
⎝ ∂x<br />
⎠ ∂z<br />
⎝<br />
∂e<br />
∂e<br />
∂e<br />
∂ ⎛ ∂e<br />
⎞ ∂ ⎛ ∂e<br />
⎞<br />
+ u + v = ⎜ K<br />
a ⎟ + ⎜ K<br />
a ⎟<br />
∂t<br />
∂x<br />
∂z<br />
∂x<br />
⎝ ∂x<br />
⎠ ∂z<br />
⎝ ∂z<br />
⎠<br />
a<br />
∂Ta<br />
∂z<br />
⎞<br />
⎟<br />
⎠<br />
⎛ ∂θ<br />
∂T<br />
⎞<br />
E = Lρ<br />
w ⎜ − D<br />
w<br />
− D<br />
T<br />
− K ⎟<br />
⎝ ∂z<br />
∂z<br />
⎠<br />
∂T<br />
∂θ<br />
G = −λ<br />
− Lρ<br />
w<br />
D<br />
wv<br />
∂z<br />
∂z<br />
x<br />
v<br />
u<br />
The values <strong>of</strong> e and<br />
T a are the same as<br />
the adjacent node.<br />
Subsurface<br />
∂θ<br />
∂ ∂θ<br />
∂ ∂θ<br />
∂ ∂T<br />
∂ ∂T<br />
∂K<br />
= ( D<br />
w<br />
) + ( D<br />
w<br />
) + ( DT<br />
) + ( DT<br />
) +<br />
∂t<br />
∂x<br />
∂x<br />
∂z<br />
∂z<br />
∂x<br />
∂x<br />
∂z<br />
∂z<br />
∂z<br />
∂T<br />
∂ ∂T<br />
∂ ∂T<br />
⎧ ∂ ∂θ<br />
∂ ∂θ<br />
⎫<br />
C<br />
v<br />
= ( λ ) + ( λ ) + Lw<br />
ρ<br />
w ⎨ ( D<br />
wv<br />
) + ( D<br />
wv<br />
) ⎬<br />
∂t<br />
∂x<br />
∂x<br />
∂z<br />
∂z<br />
⎩ ∂x<br />
∂x<br />
∂z<br />
∂z<br />
⎭<br />
Dry<br />
Wet<br />
Dry<br />
θ,T are same value as<br />
the adjacent node.<br />
FIGURE 1: Schematic view <strong>of</strong> the numerical model used to simulate the air-flow field, vapor,<br />
and heat environment around an isolated crop and the moisture and heat transfer in soil.
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