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A numerical modelling approach for biomass field drying

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Research Paper
A numerical modelling approach for biomass ﬁeld drying
T. Bartzanas
a,b
, D.D. Bochtis
a,
*, C.G. Sørensen
a
, A.A. Sapounas
c
, O. Green
a
a
University of Aarhus, Faculty of Agricultural Sciences, Department of Agricultural Engineering, Blichers Alle´ 20, 8830 Tjele, Denmark
b
Center for Research and Technology of Thessaly, Institute of Technology and Management of Agricultural Ecosystems, Technology Park of Thessaly, 1st Industrial Area, 38500 Volos, Greece
c
Wageningen UR Greenhouse Horticulture, P.O. Box 16, 6700 AA Wageningen, The Netherlands
a r t i c l e i n f o
Article history:
Received 24 November 2009Received in revised form18 May 2010Accepted 19 May 2010Published online 23 June 2010In grass conservation systems, the ﬁeld drying process of cut grass is an important functionsince it determines subsequent losses and possible hazardous effects of during silage. Thedrying process of harvested grass was evaluated using two different numerical approaches.Firstly, an existing experimentally-veriﬁed analytical model was used. Several parameterswere improved from previous studies such as the evaluation of stomata conductance fromoutside climate variables. Secondly, a CFD modelling approach was applied to open ﬁelddrying process of the biomass. The cut biomass in the ﬁeld was simulated using theequivalent macro-porous medium approach. Experimental values were used to obtainrealistic and accurate boundary conditions. The developed CFD model was validated using the existing analytical model that is based on evaporations as estimated from the Penmanequation. An acceptable agreement between simulated and measured values of watercontent was obtained. The mean difference in the estimated outputs from the two modelswas 8%. Condensation occurred during the night and was correctly simulated by both typesof models. In general, a good correspondence was found between the two approaches. Theuse of the CFD model reveals the climate heterogeneity in the grass area and also, createsthe possibility of applying the model as a decision support model for an enhanced treat-ment of the grass after cutting.
ª
2010 IAgrE. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The production and handling of a biomass feedstock, such asgrasses should be viewed as an integral part of an overallbiomasssupplychain.Biomassfrommanysourcesandcanbeconverted into many different end products ranging fromfeeds to feedstock for bioenergy (e.g., Bekkering, Broekhuis, &van Gemert, 2010). In terms of the planning and optimisationof the supply chain, it is vital that interactions betweenquantity and quality parameters such as moisture content,dry matter losses in storage, and biomass bulk densities, arerecognised as signiﬁcantly affecting the overall viability of thesupply chain (McKendry, 2002; Mitchell, 2000). Most types of biomass contain moisture to varying degrees which affectsthe energy content and quality of the material. In this regard,the monitoring, measuring, and prediction of moisturecontent is critical as a prerequisite for biomass assessmentand the planning and control of supply chain operations.Biomass assessment is especially important in the case of optimised storage and for conservation purposes.
*
Corresponding author
. University of Aarhus, Faculty of Agricultural Sciences, Department of Agricultural Engineering, Blichers Alle´ 20,8830 Tjele, Denmark. Tel.:
þ
45 89991931.E-mail address: Dionysis.Bochtis@agrsci.dk (D.D. Bochtis).
Available at www.sciencedirect.comjournal homepage: www.elsevier.com/locate/issn/15375110
biosystems engineering 106 (2010) 458
e
469
1537-5110/$
e
see front matter
ª
2010 IAgrE. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.biosystemseng.2010.05.010
The principal objective of any grass conservation system istominimiselosses,andspeciallyinthecaseoffeedinguses,toprevent the hazardous effects of silage efﬂuent. Since silageefﬂuent poses a serious pollution risk to water recipients, it isimportanttodeveloppracticalandeconomicwaysofreducing this risk. Removal of excess moisture from in-ﬁeld grass caneliminate the problems associated with silage efﬂuentcontainment and disposal. It is generally recognised that ﬁelddrying of grass and its decrease to a typical condition in therange of 5.7 kg kg
1
to 2.3 kg kg
1
dry basis moisture contentprevents efﬂuent production in the silo (Haigh, 1997). In thelast decade, improved crop conditioning equipment has beenintroducedwith the potential to increase yield drying rates upto 25% (Klinner & Hale, 1984). In recent years, dispersing andtedding machines have been developed for northern Euro-pean conditions with heavy yielding wet grass crops to facil-itate the comprehensive practice of mowing, conditioning,dispersing, tedding, and windrowing.Field drying is a complex biophysical process involving water retaining properties of the grass, energy absorption andutilisation, and the removal of vapour from the swath (Bosma& Gabriels, 1992). To develop detailed recommendations forcutting and wilting of grass silage crops based on forecasts of meteorological conditions over a period of several days,accurate drying models are required. A drying model canestimate the moisture content of grass as a function of timefor given weather and yield conditions. For this reason,several empirical approaches have developed based ondiffusion equations, or energy balance approaches consid-ering mass and energy ﬂows ( Jenkins, Ebeling, & Rumsey,1984). Energy balance models often include the Pen-man
e
Monteith equation (Monteith, 1965) to estimate evapo-transpiration and incorporate the effects of net radiation,vapour pressure deﬁcit (VPD) and wind speed. (i.e., Atzema,1992; Smith, Duncan, McGechan, & Haughey, 1988). Atzema(1992) divided the moisture content into bounded and freewater, whereas, Nilsson and Karlsson (1995) combined thisassumptionwithdiffusionmodelsinordertoshowtheimpactof equilibrium moisture content on drying characteristics.Although much of the research into grass drying rates hasinvolved experimental work carried out in the ﬁeld, speciﬁcstudies involved wind tunnels or drying chambers as ways of collection relevant grass drying data. For example, Lamondand Graham (1993) estimated the equilibrium moisturecontent of grass with the air and Lamond, Spencer, Graham,and Moore (1989) examined the dependence of swath drying rates on variables relating to the swath lay-out, using thedrying rate of thin layers of grass under controlled conditionswith air supplied from drying equipment ﬁrst described byClark (1966).Even so, there is a lack of information concerning thedistribution of moisture either along the height of the grass orin the whole multi-hectare ﬁeld. Existing models are able toestimate single-point moisture content, or in some cases intwo different vertical layers. Nevertheless, these modelscannot predict the variability of the moisture content in thewholeﬁeld.Ontheotherhand,asinthecaseofwindtunnelorchampers, modelling measurements may not always berepresentative of the full-scale phenomena, e.g., because of the poor application of scaling. Numerical modelling tech-niques such as computational ﬂuid dynamics (CFD) can offeran effective way of accurately quantifying the moisturecontent and other environment parameters of interest undervarious design and weather conditions within a virtual envi-ronment. Thus, the amount of physical experimentation canbe reduced considerably, although, to date, it cannot beeliminated.CFD is a simulation method that can efﬁciently estimateboth spatial and temporal ﬁeld ﬂuid pressure, as well astemperature and velocity. The CFD method has proven itseffectiveness in system design and optimisation within thechemical, aerospace, and hydrodynamic industries (e.g.,Zhang,Liu,Zhu,&Zhao,2006).Theubiquitousnatureofﬂuidsand their inﬂuence on system performance has caused
Nomenclature
C
D
drag coefﬁcient
Cp
, J kg
1
K
1
speciﬁc heat of air
d
, m zero plane displacement
D
i
, Pa water vapour pressure deﬁcit of air
E
, kg m
2
h
1
rate of potential evapotranspiration
g
a
, m s
1
crop aerodynamic resistance
g
c
, m s
1
crop resistance
G,
W m
2
soil heat ﬂux
k
von Karman’s constant (
k
¼
0.41)
L
, m
2
m
3
leaf area density
q
i
, kg m
2
the internal water
q
eq
, kg m
2
quantity of water at equilibrium
Q
lat
, W m
2
latent heat exchange
Q
sen
, W m
2
sensible heat exchange
RH
i
,decimal air relative humidity
R
g
, W m
2
global solar radiation
R
n
, W m
2
net radiation
T
c
, K grass temperature
T
i
,
K air temperature
u,
m s
1
air velocity
u(z)
, m s
1
wind speed in at height
zU, V, W
components of air velocity
z
0
, m roughness parameter
S
F
source term
t
, h time
Y
non
e
linear momentum loss coefﬁcient
Greek letters
a
, m
2
permeability
g
, Pa K
1
psychrometric constant
G
diffusion coefﬁcient
D
, Pa K
1
slope of saturation vapour pressure versus thetemperature curve
l
, J kg
1
latent heat of vaporisation
m
, Pa s dynamic viscosity
m
t
Pa s turbulent viscosity
r
, kg m
3
air density
u
c
, kg kg
1
water content of the grass
u
i
, kg kg
1
water content of air
biosystems engineering 106 (2010) 458
e
469
459
a widespread take-up of CFD by many other disciplines. Asa developing technique, CFD has received extensive attentionthroughout the international community since the advent of the digital computer. As a result, CFD has become an integralpart of the engineering design and analysis environment of many companies because of its ability to predict the perfor-mance of new designs or processes prior to manufacturing orimplementation (Schaldach, Berger, Razilov, & Berndt, 2000).Typical applications of the CFD in the agri-food industryincludes food storage, drying and sterilisation (Chourasia &Goswami, 2007; Le Page, Chevarin, Kondjoyan, Daudin, &Mirade, 2009; van Mourik, Zwart, & Keesman, 2009), speciﬁcagricultural applications, such as the estimation of losses of pesticide drift from ﬁeld crop sprayers (Nuyttens, DeSchampheleire, Verboven, & Sonck, 2010), and environ-mental control of agriculture buildings (Bartzanas, Boulard, &Kittas, 2002; Bartzanas, Kittas, & Boulard, 2004; Bartzanas,Kittas, Sapounas, & Nikita-Martzopoulou, 2007; Fatnassi,Boulard, Poncet, & Chave, 2006; Gebremedhin & Wu, 2005;Lee et al., 2005; Molina-Aiz, Valera, Pen ˜ a, Gil, & Lo´pez, 2009;Sun, Stowell, Keener, Elwell, & Michel, 2002).The complexity and importance of agricultural operationsmanagementhasincreasedasagriculturehasadaptedcapital-intensive production systems, thereby stimulating the devel-opment of more formal planning techniques (Sørensen &Bochtis, 2010). Regarding grass handling operations, a signiﬁ-cant cost reductions can be achieved by using dedicated deci-sion support systems predicting when to cut, ted, and collectthe grass (Bochtis, Sørensen, Green, Bartzanas, & Fountas,2010). However, these used models assume complete homo-geneityonthedistributionofclimatevariablesinthegrassandconsequentlyhomogeneousdryingconditions. Climatologicalvariables are inhomogeneous in ﬁeld-grown grass sincenumerous exchanges occur on the surface of the grass, in thesoil and in the surrounding air which are governed by a localmicroclimate. Knowledge of the distribution of climatologicalvariables inside cut grass is therefore necessary in order tofurther improve the optimisation of the whole process. Thisknowledge can be provided by advanced numericalapproaches such as the CFD codes. One of the advantages of CFDmodellingisthecapabilitytoinvestigatethedevelopmentof the drying process and the details from which this processwasinﬂuenced.Throughthisapproach,informationabouttheair movement inside the grass, and the distribution of airtemperature and relative humidity could be obtained.In this paper, a CFD modelling approach applied to theopen ﬁeld drying process of the biomass is presented. The cutbiomass in the ﬁeld was simulated using the equivalentmacro-porous medium approach. The model developed isvalidated using an existing analytical model that is based onevaporation as estimated from the Penman equation.
2. Materials and methods
2.1. Analytical model
Whenbiomassiscut,transpirationquicklyceasesbecausetheconnection between the stem and the root is broken. Thestomata close some time after cutting, and the rate of thedrying process then depends on, e.g., the resistance of theepidermis and the microclimate in the surrounding environ-ment (Atzema, 1992). The driving force for the drying processis the difference in partial vapour pressure between the plantandthesurroundingair.Whentheinternalvapourpressureisin equilibrium with the vapour pressure of the environment,the material has reached its equilibrium moisture content(Brooker, Bakker-Arkema, & Hall, 1992). The moisture contentof the materialincreases if precipitation (rain) occurs or watercondensed from the air (dew) is absorbed.A number of researchers have agreed that solar radiationis the main source of energy for evaporating moisture froma drying crop. For example, Savoie and Beauregard (1991)showed that the forage drying rate was closely related tothe amount of solar radiation, but they also suggested thatair temperature was a signiﬁcant variable, while Hill, Ross,and Barﬁeld (1977) and Parke, Dumont, and Boyce (1978)developed models based upon the vapour pressure deﬁcit(VPD). Savoie and Mailhot (1986) showed that the drying ratewas highly and positively correlated with both solar radia-tion and VPD. Convincing evidence exists on the effect of wind speed on drying. Although Monteith and Unsworth(1990) reported that the rate of evaporation from wetsurfaces always increases with an increase in wind speed,both Thompson (1981) and Atzema (1993) noted that
increasing wind speed slowed grass drying. Smith et al.(1988) postulated that the adverse effect of increasing windspeed on grass drying only occurred when the grass wasrelatively dry.Following Nilsson and Karlsson (1995), the changes of theinternal quantity of water in the cut grass in relation to timecan be modelled using the equation:
q
i
;
2
¼
q
eq
þ
q
i
;
1
q
eq
e
aE
ð
t
2
t
1
Þ
(1)where:
q
i
,2
is the internal water at time
t
2
in kg m
2
;
q
eq
is thequantity of water at equilibrium in kg m
2
;
a
is an empiricalconstant;
E
is the rate of potential evapotranspiration inkg m
2
h
1
;
q
i,1
is the internal water in time
t
1
in kg m
2
and
t
2
t
1
is the time interval for the change of internal watercontent in
h
.The quantity of water at equilibrium
q
eq
was determinedfrom the modiﬁed Halsey equation (Iglesias & Chirife, 1976;Nilsson, Svennerstedt, & Wretfors, 2005):
q
eq
=
q
dm
¼
e
A
þ
B
ð
T
i
273
Þ
ln
RH
i
1
=
C
(2)where:
T
i
is the air temperature in K;
RH
i
is the relativehumidity (decimal); and A, B and C are empirical constants.For ﬂax straw, Nilsson et al. (2005) used the values of 5.11,
0.00846 and 2.26 for the constants
A
,
B
and
C
, respectively,and the same values were adopted in this study. It should benoted that the equilibrium moisture content is uncertain athigh values of relative humidity (Nevander & Elmarsson,1994), and a maximum value for
q
eq
¼
q
dm
of 0.30 was usedin the model, according to the study by Nilsson et al. (2005).Water evaporation
E
in kg m
2
h
1
and condensation wasexpressed according to the well known Penman
e
Monteithequation (Monteith & Unsworth, 1990):
biosystems engineering 106 (2010) 458
e
469
460
l
E
¼
3600
D
ð
R
n
G
Þ þ
r
C
p
D
i
g
a
D
þ
g
1
þ
g
a
g
c
(3)where
l
isthelatentheatofvaporisationinJ kg
1
;
R
n
isthenetradiation in W m
2
;
G
is the soil heat ﬂux in W m
2
;
D
is theslope of saturation vapour pressure versus the temperaturecurve in Pa K
1
;
r
is the density of air in kg m
3
;
C
p
is thespeciﬁc heat at constant pressure in J kg
1
K
1
;
D
i
is the watervapourpressuredeﬁcitoftheinteriorairin Pa calculated fromthe difference of saturation vapour pressure minus the actualvapour pressure; g
a
is the crop aerodynamic resistance inm s
1
;
g
is the psychrometric constant in Pa K
1
;
g
c
is the cropresistance in m s
1
; and the time conversion factor 3600 is thenumber of seconds per hour. If
E
>
0 there is evaporation,while
E
<
0 there is condensation. Where evaporation takesplace from a constantly wet surface,
g
c
can be set to zero.The aerodynamic conductance,
g
a
, was calculated using the method proposed by (Monteith & Unsworth, 1990):
g
a
¼
k
2
u
ð
z
Þ
ln
ð
z
d
Þ
2
z
0
(4)where
u(z)
is the wind speed in m s
1
at height
z
;
d
is thezero plane displacement in m;
z
0
is the roughness parameterin m; and
k
is von Karman’s constant (
k
¼
0.41). The zeroplane displacement
d
and the roughness parameter
z
0
werecalculated according to the method presented by Abtew,Gregory, and Borelli (1989), which resulted in values for
d
of 0.096 m and
z
0
of 0.007 m, with a height of cut ﬂax at0.15 m.Watervapourreleasefromtheplanttissueduringdryingisassumed to follow different patterns. In the earlier stages of the drying process, stomata are open and they constitute theeasiest pathway for vapour loss, so that leaf tissue conduc-tance is equal to the stomatal conductance. The latter isassumed to vary with shortwave irradiation
Rg
(W m
2
)attenuateduponpassagethroughthecanopyinthesamewayas net radiation. In the model, the following relationwas usedfor the stomata conductance:
g
s
¼
60
1
þ
1exp
0
:
005
R
g
50
1
(5)where
R
g
is the global radiation in W m
2
.
2.2. Numerical model
The commercially available CFD code Fluent
was used forthis study. Fluent
code uses a ﬁnite volume numericalscheme to solve the equations of conservation for thedifferent transported quantities of ﬂow (mass, momentum,energy, water vapour concentration). The code ﬁrstlyperforms the coupled resolution of the pressure and velocityﬁelds and then continues with the others parameters, such astemperature or water vapour concentration. Special itemssuch as the mechanical or climatic behaviour of cut grasswere simulated using a customisation,
i.e.
a routine includedin a user-deﬁned ﬁle (UDF) and built for the determination of the parameters exclusively relevant to the grass. The domainof interest was generated and then meshed using the inte-grated pre-processor software of Fluent
, Gambit.
2.2.1. Governing equations
The CFD technique numerically solved the Navier
e
Stokesequations and the mass and energy conservation equations.The three dimensional conservation equations describing thetransport phenomena for steady ﬂows in free convection areof the general form:
v
ð
U
F
Þ
v
x
þ
v
ð
V
F
Þ
v
y
þ
v
ð
W
F
Þ
v
z
¼
G
V
2
F
þ
S
F
(6)In Eq. (6),
F
stands for the transport quantity in a dimension-less form, while
U
,
V
and
W
are the components of velocityvector;
G
is the diffusion coefﬁcient; and
S
F
is the source term.The present ﬂow and transport phenomena are describedby the Navier
e
Stokes equations. The time-averagedNavier
e
Stokes equations for the continuity, momentum aregiven as follow:Continuity equation :
v
U
i
v
x
i
¼
0 (7)Momentum conservation :
r
U
j
v
U
i
v
x
j
¼
v
P
v
x
i
þ
vv
x
j
ð
m
þ
m
i
Þ
v
U
i
v
x
j
þ
f
b
þ
S
i
(8)
2.2.2. Turbulence modelling
As shown by the measurements of turbulent airﬂows andmicroclimate patterns in open ﬁeld conditions, the airﬂowsare highly turbulent (Monteith & Unsworth, 1990). Conse-quently,turbulentmodelsmustbeintroducedintheReynoldsequations written to separate the mean ﬂow from its ﬂuctu-ating components. Several considerations inﬂuence thechoice of turbulence model. The most important ones, whichguidedourselectionaretheaccuracyandthe simplicityoftheturbulence model.The standard k
e
3
model (Launder & Spalding, 1974)assuming isotropic turbulence was adopted to describeturbulent transport. The k
e
3
turbulence model is an eddy
e
viscosity model in which the Reynolds stresses are assumedto be proportional to the mean velocity gradients, with theconstantofproportionalitybeingtheturbulenteddyviscosity.The complete set of equations for the k
e
3
model can be foundin Mohammadi and Pironneau (1994).The effect of turbulence on the ﬂow was implemented viathe high
Re
k
e
3
model (standard) model (Launder & Spalding,1974):
r
v
k
v
t
þ
r
U
j
v
k
v
x
j
¼
vv
x
j
m
þ
m
t
s
k
v
k
v
x
j
þ
s
ij
v
U
i
v
x
j
r3
(9)
r
v
3
v
t
þ
r
U
j
v
3
v
x
j
¼
vv
x
j
m
þ
m
t
s
3
v
3
v
x
j
r
C
3
2
3
2
k
þ
C
3
1
3
kP
k
(10)where, the turbulent viscosity is:
m
t
¼
r
C
m
k
2
3
(11)and
P
k
¼
s
ij
v
U
i
v
x
j
(12)
biosystems engineering 106 (2010) 458
e
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461
and
C
m
¼
0.09,
s
k
¼
1,
C
3
1
¼
1.44,
C
3
2
¼
1.96, and
s
3
¼
1.3 aremodel constants.
2.2.3. Porous media treatment
The cut grass in the ﬁeld was simulated using the equivalentmacro-porous medium approach, which refers to the combi-nationoftheporousmediumapproach(tomodelthedynamiceffect of the crop cover to the ﬂow) with a macro-model of heat and mass transfer between the grass and thesurrounding air.Thesinkofmomentumduetothedrageffectofthecrop,issymbolised by the sourceterm
S
F
of the Navier
e
StokesEq. (6).This drag force may be expressed by unit volume of the coverby the commonly used formula. The drag force per unitvolume of the crop can be expressed as (Wilson, 1985):
S
F
¼
LC
D
u
2
(13)where
u
is the air velocity,
L
the leaf area density in m
2
m
3
and
C
D
the drag coefﬁcient. For the speciﬁc case the value of 0.25 for the grass was adopted as it was proposed by Tuzet,Perrier, and Oulid Aissa (1993). The source term,
S
F
, iscomposed of two parts, a viscous loss term (Darcy), and aninertia lose term. In the case of a simple homogenous porousmedia the source term was described as:
S
F
¼
m
au
þ
Y
12
r
j
u
j
u
(14)where
a
isthepermeabilityoftheporousmedium(crop)inm
2
,
Y
the non
e
linear momentum loss coefﬁcient, and
m
thedynamic viscosity in N s m
2
. For simplicity, in the case of thegrass crop, it is assumed that pressure forces contributed tothe major portion of the total canopy drag (Thom, 1971).The exchange of heat and water vapour between the grassand the air was considered through the heat and massbalance. The sensible heat, Q
sen
(W m
2
) from the crop wascalculated using the following equation:
Q
sen
¼
r
C
p
ð
T
c
T
i
Þ
g
a
(15)where
T
c
is the grass temperature. It must be noted that theperforming of the heat and water vapour balances for grassleaves require the introduction of a new phenomenologicalvariable
T
c
.Thelatentheatexchangebetweencropandair,
Q
lat
(Wm
2
)was calculated using the following equation:
Q
lat
¼
rl
ð
u
c
u
i
Þ
g
a
þ
g
s
(16)where
u
c
and
u
i
are the water content of the grass and air inkg kg
1
also in the same mesh.Withineachmeshofthegrass,thesensibleandlatentheatexchange depends on the values of the aerodynamic
g
a
andstomatal
g
s
conductance between the virtual solid matrixrepresenting the grass and is characterised by its surface (
T
c
)and air (
T
i
) temperatures. As
g
a
and
g
s
depend on the localcomputed air speed (
u, v, w
) and the climatic conditions (
T, q
),aclosecouplingisrealisedbetweenthegrassandairﬂow.Thenumerical model was customised in C
þþ
in order to performthe balance described above, based on the local computed airspeedandclimaticconditionswithineachmeshoftheporousmedium.
2.2.4. Boundary conditions
The precision of the numerical solution depends strongly onthe accuracy of the boundary conditions and on the way thatthese conditions are integrated within the numerical model.For the simulation needs, a complete three dimensional (3D)modelwasdeveloped.Forthegeometry,acontrolvolumewasselected representing a large domain including the ﬁeld withthe cut grass. An area of 1000 m
2
of cut grass (100 m in widthand 100 m in length) was simulated with height 0.25 m. Thegrid structurewas a structured meshwith quadraticelementsand higher density in critical portions of the ﬂow subject tostrong gradients (i.e., in the limits of the cut grass). Afterseveral attempts at simulations with different densities, thecalculations were based on a 10 m (in
x
-direction) by 250 m (in
y
-direction) by 200 m (in
z
-direction) grid. The leading edge of the stackof cutgrasswas located50m downwind thevelocityinlet. This result from an empirical compromise betweena dense grid associated with a long computational time, anda less dense grid, associated with a marked deterioration of the simulated results. The ﬁnal grid has 324,000 cells and 8face zones.The grid was subjected to grid independence tests in orderto ensure the solution independency from numerical errorsdue to spatial discretisation. In addition, mesh properties like
0123456789100 0,25 0,5 0,75 1 1,25 1,5
H e i g h t f r o m g r o u n d , m
Wind speed, ms
-1
Fig. 1
e
Logarithmic wind speed proﬁle.
biosystems engineering 106 (2010) 458
e
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462

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