BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

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120 Petru Cârlescu et al hs p dT dr = + h r dp dT v sat 1 . (Hunter, 1987) provides the following empirical relationship between the saturation vapour pressure of water and temperature 25 6 ⋅10 ⎛ 6800 ⎞ psat = exp . 5 ⎜ − ⎟ (6) ( T + 273.15) ⎝ T + 273.15 ⎠ The relative humidity, r, of the intergranular air is defined as in Eq. (7), where p is the vapour pressure of water and p sat is the saturation vapour pressure of free water. p r = . p (7) sat where: p – vapour pressure of water vapour may be expressed in terms of the humidity, w, of the intergranular air by wpatm p = . 0.622 + w (8) where: p atm is atmospheric pressure. Differentiation and inversion of Eq. (6) results in dT ⎛T + 273.15 ⎞ ⎛ 6800 ⎞ =⎜ ⎟ 5 . dpsat p ⎜ − sat T + 273.15 ⎟ (9) ⎝ ⎠ ⎝ ⎠ and dr Ar = exp( −BWe ). dT (10) T + C ( ) 2 where: A, B and C – are empirical constants widely used to sorption isoterm proposed by (Chung & Pfost, 1967) and for this case assume the values of (921.69 º C, 18.077 and 112.35 º C). sat 2.2. Momentum Transfer A bed of malt constitutes a porous medium and FLUENT accounts for the resistance to air flow by adding a source term, S i , to the standard momentum transport equation. S i as the pressure gradient along a bed of grain uniformly aerated in the i-th direction with air with a velocity v i . It takes the form ⎛ 3 3 ρ ⎞ a S =− ⎜ D μv + C v vj⎟ ∑ ∑ , i = 1, 2, 3 (11) i ij j ij j= 1 j= 1 2 ⎝ ⎠ where: μ is the viscosity of the intergranular air, v j represent the components of the velocity in all three dimensions, ρ a is the density of air, v is the superficial or Darcian velocity of the air as opposed to the average velocity of the air flowing between the malt kernels, D ij is tensor component what represent the Darcian or viscous resistance, C ij is tensor component what represent inertial (5)
Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 121 resistence. The empirical coefficients D ij , C ij can be related to those in the FLUENT - CFD programme Eq. (12). The components of the resistance in these two directions and resistance terms in the horizontal direction can be designated as R h and S ho , and those in the vertical direction R v and S v . Two orthogonal horizontal directions are designated by the indices 1 and 2, and the vertical direction has the index 3. This is implemented in FLUENT by introducing temperature of 30 º C the viscosity and density of air are, respectively (18.37·10 6 Pa·s and 1.191 kg/m 3 ). Using these values we find that D 11 =D 22 =1.833·10 8 , D 33 =2.037·10 8 and C 11 =C 22 =18371, C 33 =26767. ⎧Rh μ; i= j = 1,2, ⎪ D Rv ; i j 3, ij = ⎨ μ = = ⎪ ⎩0; i≠ j, i= 1,2,3, j = 1,2,3. (12) ⎧2 ⋅ Sh0 ρa; i= j = 1,2, ⎪ Cij = ⎨2 ⋅ Sv ρa; i= j = 3, ⎪ ⎩0; i≠ j, i= 1,2,3, j = 1,2,3. 3. Simulation The aim of this paper is to illustrate how a standard CFD package may be modified so it can be used to simulate heat and moisture processes that occur during malt drying process. The features that apply specifically to bulk dry malt are accommodated by User-Defined Functions (UDF-s) written in a high-level computer language such as C and introduce in the computer package FLUENT. A possible further outcome of the work is that it demonstrates how standard CFD codes can be modified to account for the behaviour of other drying systems such as those used for horticultural and other agricultural products. Pre-processing as a first step in CFD simulation is achieved by creating the drying zone geometry and meshes it with the GAMBIT software. Drying area is composed of three regions shown in Fig. 1, hot air input with a low moisture content, malt box region and exhaust air region with high humidity. The geometry is discretization with structured mesh and 1200000 elements. Table 1 Geometric dimensions Areas Length, m Width, m Height, m Thickness malt bed, m input 0.380 0.370 0.5 - malt bed 0.380 0.370 0.05 0.007 output 0.380 0.370 0.3 -
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BULETINUL INSTITUTULUI POLITEHNIC D
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