OPTIMIZATION OF IMMOVABLE MATERIAL LAYER AT DRYING. Volodymyr Didukh, Ruslan Kirchuk

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1 TEKA Kom Mot Energ Roln OL PAN, 2007, 7, OPTIMIZATION OF IMMOVABLE MATERIAL LAYER AT DRYING Lutsk State Technical University, Lvivska Str 75, Lutsk, 43018, Ukraine, Summary The article reresents a mathematical model of drying of immovable layer of lant material, that enables otimization of the height of a layer loaded into the drier Key words: immovable thick layer, elementary thin layer, drying agent, drying coefficient, steby-ste method of drying calculation INTRODUCTION The roblem of convection drying of agricultural material in an immovable thick layer lies in the choice of its rational height that assures maximum utilization of a drying agent Insufficient height results in irreversible energy loss, and its increase leads to humidification of the uer layers having a negative effect [Selenko 1998] Another reason for negative effect (over-drying of material in some zones) is its non-uniform distribution in the dyer and non-uniformity of material [Ostachuk et al 1988] That is why majority of investigations on cost reduction of agricultural material drying is connected with rearation of material before loading into the dryer The rearation includes: elimination of imurities from main material, change of shae and sizes of material that can significantly imrove a number of efficient arameters of technological rocess INVESTIGATION ANALYSIS The theoretical descrition of agricultural material convection drying is done through heat and mass exchange euations Such method is comlicated and laborious Besides, it is hard to aly the obtained results in engineering calculation of drier units and imrovement of drying methods [Selenko 1998]

2 82 As shown by investigation results, moisture is changing according to comlicated laws: W = f ( W, τ,t) That is why the regression euations are used in engineering ractices n To analyze ractical tasks, the general characteristics of drying, seed and temerature curves are erformed After analysis of the curves, the euation of kinetics drying is obtained [Lykov 1968]: dw = K( W W k ), (1) d τ dw drying seed; dτ K drying coefficient, deending on roerties of agricultural materials and drying mode, min 1 ; W k finale material moister, % In its turn, drying coefficient K is directly roortional to drying seed and recirocally roortional to initial material moisture W n It is determined by the relative drying coefficient χ, like line sloe ratio K = χn 1,8 χ = (2) W n Purose of investigations To investigate theoretically and roose a method for defining the otimal size of immovable material layer at drying taking into account technological factors of the rocess INVESTIGATION RESULTS It is roblematic to obtain an analytical solution of differential euations, describing heat and mass exchange in a material layer, under condition of non-steady drying rocess In order to solve such alications, it is worth using a simlified mechanism for analysis of heat and mass exchange between the material for drying and the drying agent [Okun et al 1984] Analytically, the method can be reresented by a system of differential euations Euation (3) reresents energy conservation law in drying, euation (4) material conservation law, (5), (6) heat and mass exchange law between material and drying agent γ С V x γ С θ γ r ε γ С ε 1, (3)

3 OPTIMIZATION OF IMMOVABLE 83 γ ε d d V, (4) γ x α γ V ( t θ ), (5) x γ С ε K W ( ) W, (6) t drying agent temerature, o C ; d moisture ratio of drying agent, g/kg; W material moisture, %; θ material temerature, o C ; V drying agent seed, m/s; C, C heat caacity of material and drying agent, kilojoules/kg; ε material layer orosity; r heat of water evaoration, kilojoules/kg; α heat emission coefficient, kilocalorie/kg h; γ material bulk weight, kg/m 3 ; γ air secific gravity (drying agent), kg/m 3 ; K drying coefficient; W material moisture euilibrium, %; x satial value, m; τ time, hours The ste-by-ste method of immovable material drying is based on the following assumtions: moisture in the material has a liuid state, heat and mass is exchanged only between the drying agent and material being dried, thermal gradient in the material is not significant, heat between the drying agent and material is exchanged convectively Main oint of the ste-by-ste calculation in a thick layer is successive calculation of thin layer drying rocess, the changes of moisture and temerature of which can be ignored Thin layer drying during the eriod τ, when the drying seed does not significantly change, can be described by a system of algebraic euations [Okun et al 1984] γ С δ θ γ δ r t, (7) 3600 V γ С τ 3600 V γ С τ 10 γ δ d, (8) 3600 V γ τ

4 84 α γ δ t 3600 V γ С ( θ t), (9) δ thickness of thin layer, m ( W K W, (10) Precision of thick layer drying calculations by means of ste-by-ste method deends, first of all, on data validity of thin layer drying according to euations (7), (8), (9), (10) In its turn, it is deendant on correct choice of eriod τ, size of elementary thin layer δ and a number of thermal characteristics, used in euations Caability of modern comuter machinery and rational calculation algorithms enable to reduce magnitude δ to the seed thickness (for calculation of seed material) and τ 1s, increasing recision of drying rocess calculation Material and drying agent temerature are connected with correlation: t t i 1, i temerature of the drying agent at the entry to i ; i layer and at exit, o C t + t i 1 i θ, (11) 2 The biggest imact on calculation of lant material drying rocess comes from drying coefficient K and drying seed N The coefficient is a function of a number of arameters That is why, normally, it is the observed value, deending on the material being dried, drying agent arameters and drying conditions However, for the materials of gel tyes, including orous colloid materials, according to [Ostachuk et al 1988], the following euation can be used: NρRv α ( t θ ) =, (12) N drying seed, %/hour; ρ dry material thickness, kg/m 3 ; R ratio of drying material body to its surface v Thus, the defined relations and initial conditions, namely drying agent arameters t, d and materialw, θ at initial time τ = 0 enable formulating of a calculation model of drying rocess of the lant material layer For i thin layer within ( j 1 j τ eriod, the drying agent arameters are defined as: ( A) t + A θ B K( W W t = i,j i 1,j i,j 1 i, j 1 1, (13) d K 102 = d + i, j i 1, j i, j 1 ( W W ), (14)

5 OPTIMIZATION OF IMMOVABLE 85 and material arameters at temoral value j τ : W = Wi, j K W i, j i,j 1 C A = 102 С τ + 0, 5С ( W 1, (15) t i 1,j + ti, j θ, (16) i,j r, B = 102С τ + 0, 5 С Moisture euilibrium of seed and lant material for relevant arameters of the drying agent can be defined according to the Henderson formula: ln1 ϕ W = 6 5, ϕ drying agent moisture, % ( d ) ( t + 273) 0, d ϕ = 0, , 5 t + t , (17) The reresented model enables calculating drying rocess both in a thin and thick material layer Besides, the calculation data obtained characterize drying rocess enabling otimization of layer height under condition of maximally efficient utilization of the drying agent otential CONCLUSIONS Reresented mathematical model of drying rocess of immovable thick layer enables otimizing height of material being loaded into the drier Such a method for calculation of the drying rocess enables maximal efficient utilization of drying agent otential and reduces the cost of agricultural material rocessing oerations REFERENCES Lykov AV 1968: Teoria sushki Energia 472 Okun GS, Viercman II, Yesakov YuV 1984: Raschiet rodoldjitielnosti i enerhoyemkosti rocesa sushki zierna v sloye s omoshchyu EVM Sbornik nauchnykh trudov VNII mekhanisacyi sielskokho khosyaystva,, Ostachuk NV, Shashkin AB, Kaminskiy VD 1988: Povysheniye efektivnosti sushki zierna Urodjay 136 Selenko VI 1998: Konviektivnaya sushka sielskokhosyaistviennykh matryalov v lotnom sloye Osnovy teorii Tvierskoye oblastnoye knidjnoho-djurnalnoye isdatielstvo 96