Modeling and Identification of Agricultural Driers

(:opvrighl © 1L\C 111h Triennial \\'orld Congress, Tallinn, Eslonia , l'SSR, 19'H)

MODELING AND IDENTIFICATION OF AGRICULTURAL DRIERS I. Farkas Institut~

fur l\;fatliematics alld Compllter Science, L'lIi" frs itl of Ag'1l'1i1tllm/ Sril'llcr.I, CiJi/allB, H-2103 , HUlIgan'

Ab stract. A block-oriented simulation system ( BOSS) ha s been developed for t ~ e modeling and identification of different types of agricultural driers. Tl;e basic system consists of a meteorological data generator, a ma ss flow rate setting, a moi sture generator, a heater, a mi x er, a drier and some supplementarj blocks. Experimental and analytical mo deling tecrJ'liques of drjing processes were reviewed especially for grain and hay. A fixed-bed, a simple crossflow and a recycled crossflow drying arrangements ~ere studied creating t h eir block-oriented sch eme. Keywords. Agriculture; comp uter simulation; drying ; functio n generators; identification; mo deli ng . nm.lSNCLATURE 2 3 a, m /m specific s urface of comp onent 2 cross-sectional area of drier A, m biological heat vol ume b, :J/m 3 specific h eat c, J/kgK enthalpy i, J/kg rh, kg/s mass flow rate of air 1.: , kg/s ma ss flow rate of material r,lP , % - mo isture ratio 2 N, kg/sm - drying rate r, J/kg - latent h eat drj matter to air ratio R, kg/kg t, CO temperature of air CO T, temp erature of material air humidity x, kg/kg y ." , kg/kg - material moist ure cont ent dept h z, m

n:T: ~ODijCTION

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There are a lot of differen t types of driers in operation in the agriculture. Und er Hungarian co n di tions mainly grai n and hay are dried artifiC ial ly, wh ich are big energy consumers. !e t the same time the quality of dried material i s also an important factor for the evaluation of drying process. So , t h e optimiz ation of operation of driers with the minimi za t ion of energy consumption and the development of new energy effic i ent driers came into the focus of ,int erest. ~ rthematical model ing and comput er si~ula ti o n have become a part of this i nvestigation s. ~ith a good model the Derformen ce of a drier ca n be predicted,"and the phys i cal behaviour also be satisfactorily calcule t ed. How0ver, mo deling is faster, easier a nd cheaper comparing to the invest igatio ns do n e only by experiments.

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!:ATHSllATICAL r.:ODELIl'G OF DP.YIlTG PROCESSES

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number of models have been proposed to calculate the combined heat and mass transfer during the drying process. To select the proper technique t he contribution of t h e modeling ,~a s to be taken i nto account.

le

Greek letters: 2 heat trans fer coefficien t I., '.7/m K mass trans fer c oefficient ~, m/s 3 3 porosity ~, m /m 3 kg/m density S' t, s time relative hurnidi ty 'f, etp

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In our case consideratio n is given to two models which describe the low temperature grain and hay drying, as well.

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Subscripts: o a abs d e f i m out w -

Grain drying In Hungary, the existing grain driers are mainly crossflow type. The purpose of these modeling is to study the energy calculations and control aspects of these driers. Therefore it was appropriate to apply an empirical approach . Basically, a second order exponential drying equation proposed by Thompson and oth ers (1968 ) was used for the moisture calculation in the t h in-layer of crop:

initial air absolute dry basis equilibrilli~

fi na l input material output ambient, water, wet basis

291

't

=

A In(!.~) + B [In (I.:R)] 2

where, the moisture ratio is: UR = (X-Xe)/( Xo- Xe ) .

(1 )

partial differential equation seems to be advisiable as it was proposed by Imre and others (1983a, 1963b). The deep bed model of a batch drier consi sts of the following h eat and mas s balance equations:

(2)

The parameters A and B in the Eq . (1) depend on the dryin~ air temperature, that is A=A(t) and B=B(t) , respectively. Nevertheless, the equation is valid for a wide (60-150 CC) temperature range. Beside this, for lower and higher temperatures the equations suggested by Flood and others (1969) and Troeger and Huki l (1970), as well were considered in the model. However, these empirical equations can be handled quite easily, but an equation for the equilibri um ~ oisture content (X e ) should ~lso be added representing the sorption and desorption isotherms of t he crop to be dried. Fo r cereal grai ns an empirical equation could be used as Henders on ( 1 95 2 ) suggested in his earlier Vlork:


- a k Nk ,

dT

cl.

k

rr Clx k

~

ot

k

3Z

ak

(tk-T k )

ck~k

ak

m.k a

N

(7 )

k -

k

~

ak r N , - ck~k k

ga~k OXk

_lD= J

(8)

(9)

m;- n'

( Nkcw+lk)(Tk-tk) -

( 1- Sk ) bk ~8Sk ot k .-m,- + Jl ffi k ~ '( k ca

(3) exp (- c t a b s Xn) e To calculate t he simul taneous h eat and mass transfer process t he elementary heat balance equation of the t hin layer should also be written : Fo r eq u ili bri ~~ temperat u re of drying air: 1

a't'

(10)

wh ere, t h e drying ra te : (ll )

To solve the equation set of (7-11) an i mplic it finite difference scheme, based on t he time and place discretization, h ave be en used succesfully. Th e necessary isoth ermes of material components were determined by laboratory experiments (Imre and oth ers, 198 3a). The approximation equations for the leaf and stem eouili bri um moisture con tent Xek = i ek(~,t ) could be explicitly derived ( Farkas, 1985) and us ed i n the model.

cmTabs o = 1. 005 tabse+ x o ( 2467 .4+1. 884 tabsJ+cmtabse l and for final air and grain temperatures: 1. 005 tabse+xo(2467.4.+1.884 tabse> +

BLOCK OTIIEI:T3D APPROACH TO TI-I3 SnilULATION

cmT abse+ Li x (T a bs e -2 73 .1 6) = 1. 005 tabsf+xf(2467.4+1. 884 t absf )+

Reviewing t h e mat h ematical models applied for de t erminatio n of t he beilaviour of drJing process, it seems, a l ot of additio nal effcr t is n eeded to fit them to different material an d especially to differe n t stru c ture of drJers, as well. Therefore, a bloc k- or i ent ed approach s hould be advised for simulatio n of drying layout s including t he h eAters, mixers, meteo rolo gi cal date genera to r, etc. Let u s consider now t he main blocks required for a g eneral dryi ng arrangement.

(5 )

The specific heat of corn was calculated by a linear c m=c m (ZVI ), though the latent heat of water in corn was calculated by a combined lin ear a.nd exponen tial function r=r(t,Xd ) · The moisture change duri ng a time interval can be written, as t he following:

~ eteorological

(6 )

data generator

(~rG)

The me teoro lo gical dat6 of ambient air u sed fo r drJi ng is n ecessary to take i n to ac c ount . In tb..e case of dryi ng , however, two pa ra~ e t ers of ambient air are enough , f or instanse, t h e temperature (t ) and the absolute humidity (x,) of a i I<. There are t~o ways for data gen eration , we directly measure t h ese values or we use approximation equations ( ? arkas, 1988) In both cases, the bloc k dravm in Fig . l. could represent a meteorol og ical data in the simulation mo del.

The mo deling of a batch-type drier means a layer by layer calculation . Th e exhausting air from a given layer ent ers to the n ext on e, etc. In the case of crossflow drier the air is mo ving perpendicularly to the mat erial movement , so layer by layer calculation should be applied in both directions. Hay drying Principally, it is possible to use the same empirical approach as was applied for grain drying. Nowadays, in Hungary the alfalfa (lucerne) is main ly dried artificially in batch driers. The alfalfa plant h~ two main parts (leaf an d stem) drying in very different way, so a two- component model described by a set of 292

m.In

~IW

(14)

Even though, the Eq. (13) and Eq. (14) ape e"lde11t it is advl:sOlble to include them in the block due to the uniformity between the Dlocks to be 1ntrodueed later on.

~'W

Fig. 1. 310ck of meteorological data generator

l.1ixer (M) A mixer unit serves to make a combination of two different stages of air. Usually one is ambient, the other is exhausting air. The scheme is drawn in Fig. 5.

;:ass flow rate To set ma3S flow rate of air and/or material to a value of ~ and/or t a single step-function generator and A coefficient adjusting are required as it can be seen in Fig. 2.

MIXER

Fig. 2. Bl ocks of mass flow rate setting Tnlet material moist ure The inlet moisture content of material to t h e drier is changing stoch psticelly in time. To measure it con tinously is a little bit comolicated due t o t h e lack of precise moisture sensors. Therefore, in the simulation system, 'lie assume a constant value for it or a given distribution function is applied. The scheme of block is s h own in Fig. 3.

Fig. 5. Block of mixer The relating equations can be written in the following way:

(15) where: (16 )

(17) (18) (19)

Fig·. 3. Block of inlet moisture generator Heater (H) For preheating the ambient air with a mass flow rate of i by e given heating capacity (p) in oil or gas burner is needed to be solved, even in the most elementary drying set-up. The scheme of the block is given in Fig. 4.

~

Keeping in our mind the equations summarized in previous chapter for the modeling of drying processes it is easy to state that the block of the dryer is most complicated. Beside th7 inlet and out~et air and material functlons we should Involve the Pi' i=1,2, ••••• ,m parameters relating to the physical and geometrical feature of the material to be dried Bnd the given type of dryer. Eolding the unifornity concept, the drier block is defined as it CBn be seen in Fig. 6.

Fig. 4. Block of heater The equations relating to the block of heater should be formed, as follows: P/(c a m.In )+t.In

(12) (13 )

293

Simple crossflow drier (SCD) In the case of a simple crossflow drier the material is moving perpendicularly to the air flow. I t is assumed t h at the material temperature in the i nlet layer is equivalent to the am bient air temperature. The final aim is that moisture content of exhausting material fells bellow a desired value. Th e sch eme of a SCD is presented in Fig. 8.

... i.U•. · ...

DRYER TYPE N

,

Fig . 6. Bl ock of dryer

SCD

TO THE LDENTIFICAT I ON OF DIFFERENT TYPE OF DRIERS The sLmulation program developed on the basis of block-oriented modeling technique is a good tool to solve several tasks in conjuction with the optiffisl operation of agricultural driers. The 2 ain purposes are as follows: - studying the theory of drying processes - evaluation of different drying model~ - investigation of different drying arrangements, and solving its control through parameter sensitivity analysis and parameter identification.

Eig. 8.

'.~ odel

of simple crossflow dryer

Recycled crossflow dryer (RCD ) To use up t h e drying capacity of exhausting air it can be recycled after mixing with 5Mbient air afid it . Oan be taken to anot her zone of drier. The multi-stage operation could yield more efficien t energy consumption, so t h is set-up is commonly used. I n the Fig. 9. a two-stage (drying and cooling) drier model is shown, h owever, a more complicated arrangement could be carried out in t h e same mann er.

The block-oriented system simulation (BOSS) was applied first, for the problems listed above in the case of a fixed-bed, a simple crossflow and a recycled crossflow type of dryer.

,

Fixed-bed dryer ( FED) The main feature of a fixed-bed dryer is that a constant volume of preheated air is forced through a static material bed, so the material mass flow rate M=O. It has been assumed that the initial temperature and moisture distribution are uniformly constant in every layer of bed (Toand Xo ). Here the output temperature and moisture content (Tout, Xout ) mean the values at the top layer, where the drying air is exhausting. The purpose is to reach a desired final moisture in each layer of bed. The block-oriented model of a FBD is shown in Fig. 7.

RCD COOL~G

p

ZONE

Pi

Tout

Xout L -_ _---Jr-1I4

H Fig. 9. :.!odel of recycled crossflow drier

FBM .... 0

Fig. 7. I,10del of fixed-bed dryer

294

CONCLUSIONS A block-oriented simulation system (BOSS) intended for a special application area that is for the agricultural driers can be succesfully applied. The introduced basic system can be easily extended with new blocks for extra necessities. Nevertheless, the blocks required for the process control could also be linked. The recent set-up is good for developing the scheme of most important types of drier which is needed to identify their operational parameters and to evaluate the selected drying diffusion models, too. The BOSS can be installed in microcomputers and the modeling of a system by simply linking the blocks makes it user's friendly both in research as well as in education. REFERENCES Farkas, I. (1985). Control and computer simulation of a complex solar drying system. Ph. D. Thesis, Budapest. Farkas, I. (1988). On the estimation possibilities of solar radiation and ambient temperature used for solar system. Technical-Agricultural Academy Bydgoszcz, Poland, Agriculture 27, No.158. 5-1 0. Farkas, I. (1989). Computer aided off-line grain dryer operation. Problems of A ricultural and Forest En lneering, n a lona Clen l ence, Warsaw, 221-224. Flood, C.A., M.A. Sabbah and R.M. Peart (1969). Simulation of natural air corn drying system. Transaction of ASAE, 15/1, 156. Henderson, S.M. (1952). A basic concept of equilibrium moisture. Agricultural Engeneerin~, 33/1, 29. Imre, t., K.Mo nar, S. Szentgyorgyi (1983a) Drying characteristics of lucerne. In A.S. Mujumdar (Ed.), DRYING. 83. Imre, L., K.Molmir and 1. Farkas (1983p). Some aspects of the intermittent solar drying oi: lucerile~ Int. ·!.leeting on Solar Dryin~ and Rural Development, Bordeaux, 9 -103. Thompson t T.L. R.M. Peart and G.H. Foster (1968). Mathematical simulation of corn drying - A new model, Transaction of ASAE, 582-586. Troeger, J.M., W.V. Hukil (1970). Mathematical description of the drying rate of fully exposed corn. ASAE Paper No. 70-324. --

295