Dev. Chem. Eng. Mineral Process. 12(3/4),pp. 249-261, 2004. Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns T.A.G. Langrish"' and R.B. Keey2 Department of Chemical Engineering, University of Sydney, New South Wales 2006, Australia Wood Technology Research Centre, University of Canterbury, Private Bag 4800, Christchurch, 8004, New Zealand ' Progress in modelling air flow patterns in timber kilns using computational fluid dynamics (CFD) is reviewed in this work. These simulations are intended to predict the distribution of the flow in the fillet spaces between boards in a hydraulic model of a timber kiln. Here, the flow regime between the boards is transitional between laminar and turbulent flaw, with Reynolds numbers of the order of 5000. Running the simulation as a transient calculation has shown few problems with convergence issues, reaching a mass residual of 0.2% of the total inflow afler 40 to 100 iterations per time step for time steps of 0.OI s. Grid sensitivity studies have shown that nonuniform grids are necessary because of the sudden changes in flow cross section, and the flow simulations are insensitive to grid refinement for non-uniform grids with more than 300,000 cells. The best agreement between the experimentally-measured flow distributions between fillet spaces and those predicted by the simulation have been achieved for (effective) bulk viscosities between the laminar viscosity for water and ten times that value. This change in viscosity is not vely large (less than an order of magnitude), given that effective turbulent viscosities are typically several orders of magnitude greater than laminar ones. This result is consistent with the transitional flows here. The effect of weights above the stack can reduce the degree of nonuniformity in air velocities through the stack, especially when thick weights are used, because the stack may then be separated from the eddy at the top of the plenum chamber. * Author for correspondence (timl@chem.eng.usyd.edu.au). 249 T.A. G. Langrish and R.R.Keey Introduction Plantation-grown softwood timber (mainly Pinus rudiuta) is processed in Australia and New Zealand in considerable quantities. Annual production of softwood timber in Australia [ l ] is in the region of 1 million m3, while in New Zealand 3.3 million m3 is processed as board timber, of which one-thud was exported in 1998. This processing involves a drylng step that is significant in terms of both its energy usage and its importance in determining the final quality of the product. Softwood sawnboards are often seasoned in kilns at temperatures above 100°C. Reduction of the drytng time is the principal benefit of this technique, known as high-temperature drying of timber. Under these conditions, external convection is relatively more important in determining the drying time than at the lower temperatures traditionally used in kiln seasoning. In addition, appearance-grade timbers are kiln-dried under so-called "accelerated" conventional schedules with relatively long drying times (although short compared with hardwoods). It is desired to improve kiln techniques so that more timber can be dried at higher temperatures without loss of quality. High-temperature drying of timber is normally carried out with air velocities of the order of 7 m s" (or more) between the boards. A typical kiln layout involves rows of boards separated by spacer sticks or stickers. The separation between these rows is the board-row spacing (typically between 15 and 25 mm). There are also gaps between board edges, referred to here as board-edge gaps, which are an inevitable result of both imperfect sawing and shrinkage, and are usually of the order of 1 mm. These gaps lead to enhancements in the mass-transfer coefficients, both at the leading edges of the boards and over the entire board. These enhancements have been measured experimentally by Kho et al. [2], and have been numerically simulated most recently by Sun [3] and Hua et al. [4] using the k-E turbulence model whch assumes well-developed turbulence in the free stream. There is general agreement amongst all this previous work that the temperature variations in the kiln do not have a dominant influence on the air flow patterns in such highly forced-convection flows. The amount of water vapour lost in drying is negligible compared with the air flow rate through the stack, so the influence of drying on the air flow patterns is normally neglected in this type of study. The flow patterns influence both heat and mass transfer rates. 250 Progress in the Modelling of Air Flow Patterns in S o fio o d Timber Kilns The distribution of the flow in the fillet spaces between boards in a hydraulic model of a timber kiln has been measured by Nijdam and Keey [ 5 ] , with more details being given in Nijdam and Keey [ 6 ] . The simulations reported in this work are intended to predict these measurements, in which the flow regime between the boards is transitional between laminar and turbulent flow, with Reynolds numbers of the order of 5000. The purpose of low Reynolds number turbulence models is to allow direct integration through the boundary layer towards the wall, allowing fine detail to be resolved in these regions. However, they do not affect the assumption of welldeveloped turbulence in the bulk flow [7]. As such, they are not valid approaches for simulating flow situations that are transitional throughout the flow domain. In other words, at present there are no true developed models for transitional flows. The low Reynolds number turbulence models available are actually h g h Reynolds number models that allow integration of the turbulence equations to the wall. The constants in the hgh Reynolds number turbulence models have been fitted to data where the Reynolds numbers are generally above 20,000. The approach here is to simulate the flows assuming, firstly laminar flow only, then to implement a wall damping fimction to interpolate between the laminar viscosity at the wall and the effective (bulk) viscosity. The effective viscosity is fitted to experimental data. Theoretical Methods, Geometry and Operating Conditions CFX4 [S] is a general purpose CFD code that solves the conservation equations governing fluid flow via a fmite volume method. In this work, equations are solved for the conservation of mass and momentum for the isothermal, incompressible flow of water in a hydraulic model of a hgh-temperature kiln. Details of the kiln geometry and operating conditions are given in Nijdam and Keey [ 5 ] . For example, the temperature of the water was 2OoC, and the hydraulic model was scaled to retain both geometrical and dynamic similarity (same Reynolds number) as a full-scale kiln with air flowing though it. 251 T.A.G. Langrish and R.B. Keey The treatment of turbulence in transitional flows remains problematic, and welldeveloped turbulence cannot be assumed in the bulk of the flow for these cases. Hence, turbulence models, such as the k-e turbulence model, that make this assumption of well-developed turbulence are questionable under these conditions. Regardless of what the turbulence is in the main flow, it is necessary to account for the damping of turbulence near the wall. Here, a van Driest wall damping fbnction, as described in Wilcox [7], has been used to interpolate between the laminar viscosity at the wall (p,)and a fitted effective (bulk) viscosity (p,) in the main body of the flow: Here y+ is the dimensionless distance from the wall ( y G / p i ), p is the gas density, ‘I is the local shear stress and y is the actual distance fiom the nearest wall. Results and Discussion (i) Convergence Running the simulation as a transient calculation has shown few problems with convergence issues, reaching a mass residual of 0.2% of the total inflow after 40-100 iterations per time step for time steps of 0.01 s. Such low mass residuals at each time step are accepted as being evidence of reasonable convergence [9], so time steps of 0.01 s have been used in all the simulations reported here. (ii) Grid Sensitivity When starting the simulation, the maximum time derivatives are initially hgh, as would be expected when starting a real piece of experimental equipment. The maximum time derivatives do not disappear entirely, as they would be expected to do if the situation was eventually completely steady, and the time derivatives continue to oscillate indefinitely after an induction period. However, the impact of the unsteadiness on the flow distribution between fillet spaces appears to be minimal, 252 Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns 7 Figure 1. The effect of grid density on the predicted flow distribution (average and maximum predicted velocities in the hydraulic kiln) for the non-uniformgrids. Grids have been produced with grid lines concentrated in the regions of highest pressure gradients ("non-uniform" grids), as described earlier. In the case of the coarsest non-uniform grid, there are between 10 and 22 grid lines in the fillet spaces (with a total of 323,608 cells), with the highest number being concentrated at the top of the plenum chamber where the pressure gradients are greatest. In a second nonuniform grid, there are between 12 and 30 grid lines in the fillet spaces and a total of 475,872 cells. The predicted flow distributions at long times from the start are shown in Figure 1 for both grids, showing no significant grid density effect. This absence of grid sensitivity suggests that the coarse, non-uniform grid with 323,608 cells is adequate for hrther studies. This grid is shown in Figure 2 for the area in the top fillet spaces. 253 T.A. G. Langrish and R.B. Keey (iii) Flow Distributions The previous (laminar flow) estimates shown in Figure 1 have used the dynamic viscosity of water in the hydraulic model of the kiln used here, 9 x kg m-’ s-’ throughout the flow field. By definition, the hydraulic model is a water model of a real kiln that is scaled to have the same Reynolds number as a full-scale kiln with air flowing through it. Figure 3 shows the impact on the flow distribution between boards of effective viscosities of 9 x kg m-’ s-’ (the base case), 9 x l o 3 kg m‘’ s-I, and 9 x lo-’ kg m-l s-’. The flow fields for effective viscosities of 9 x 9x kg m-’ s-’ and kg m-’ s-’ near the top of the stack are shown in Figures 4 and 5 . Higher effective viscosities smooth out the flow distribution more and reduce the size of the recirculation zone near the top of the stack. Compared with the experimental distribution, an effective viscosity of 9 x kg m-’ s” shows too much variation in velocity with changing board number, while an effective viscosity of 9 x 1O 3 kg m-’ s-’ shows closer agreement. T h s change in viscosity is not very large (less than an order of magnitude), given that effective turbulent viscosities are typically several orders of magnitude greater than laminar ones. This result is consistent with the transitional flows here. A finer variation of effective viscosity has been carried out for the results shown in Figure 6 , which shows the impact on the flow distribution between boards of effective viscosities of 2 x kg m-‘ s-I, 4 x l o 3 kg m-’ s-I, and 6 x 10” kg m-’ s-I. The flow field near the top of the stack, for viscosity of 6 x 10” kg rn-’s-I, is shown in Figure 7. The changes in the flow field in this region are not large for the small variation in viscosity over the range from 2 to 6 x 10” kg m-’s-’. While the variation of velocity with board number is reasonable in terms of the range between maximum and minimum velocities, the predicted position of the peak velocity (board 3) is different to that observed (board 4). It is important to note that these are predicted water velocities for the hydraulic kiln. The difference may reflect the variation in the effective turbulent viscosity throughout the flow field, although this variation cannot be accurately modelled given the transitional flow regime for these experiments. 254 Progress in the Modelling of Air Flow Patterns in Sofmood Timber Kilns Figure 2. Fine non-uniform grid in the vicinity of the top fillet spacings of the hydraulic kiln. ~ ~~ ~~ .. ~~~~ ~~~~ - - 0 - 9 00E-03 9.00E-02 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 Board Number Figure 3. The effect of total viscosity on the predictedflow distribution (maximum predicted velocities in the hydraulic kiln) for a viscosity range of 9 x I kg m-’ s-’ to 9 x I 0-2kg m-’ s-’. 255 T.A.G. Langrish and R.B. Keey Figure 4. The predictedflow pattern in the upper part of the plenum chamber for the hydraulic kiln (predicted velocity magnitudes shown in legend) for a total viscosity of 9 x l o 4 kg m-' s-'. Figure 5. The predictedflow pattern in the upper part of the plenum chamber f o r the hydraulic kiln (predicted velocity magnitudes shown in legend) for a total viscosity of 9 x 10.' kg rn-' s-'. 2.56 Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns The agreement between prediction and experiment for the flow distribution with an effective viscosity of 6 x kg m-’ s-’ is reasonable, in the sense that the maximum velocity is predicted to be in the third fillet space, whereas the actual maximum velocity is in the fourth fillet space. Ths slight disagreement in the prediction of the point of maximum velocity also corresponds to a predicted vortex zone in Figure 7 that is more elongated than the actual vortex, which was more circular. Nevertheless, the predicted visualization in Figure 7 is quite close in appearance to the experimental one [ 5 ] . The observed vortex zone is about three boards high and just under half the plenum chamber wide, while the predicted one is also three boards high although slightly narrower. Nevertheless, the best fitted effective viscosity of 6 x 10” kg my’s-’ is not very far above the molecular viscosity of water (1 x 10” kg m-’ s-I) (less than an order of magnitude), given that effective turbulent viscosities are typically several orders of magnitude greater than laminar ones. This result is consistent with the transitional flows here. This fitted effective viscosity is meaningful for assessing the effects of different stack geometries for this system. 0.80 ....................... 0 10 -~ . .._.._.,.I .. ....... .... ........ ~ - * 6 00E-03 -+experiment t Figure 6. The effect of total viscosity on the predicted jlow distribution (maximum predicted velocities in the hydraulic kiln) for a viscosity range of 2 x kg m-’ s-’to 6 x IO” kg rr-’ s-’. 25 7 lhc significance ul‘ the predicted vortex and eddying at the top nf the chanihelr IS that this region currcsponds to rclatively tow velociries (even back fIo\.t) in the iilIet spaces at the top ufthe stack Eflecrlve contouring ofthe Fin region in the roof and ul‘ the plenum chamber is likely to be rrecessary to reduce tht:, prt3blem which i s linked to the mornenturn of the flow ernergrng from the roof region and tile sharp change flow direction that is required at the ctirmnce to the plenum chamhcr in area [6]. Figure 8 shows the efkct of blocking the gaps at the top af the stack, simulating the situatrair where there are weights hetween the top of the stack and below the faris (iivcn that a large eddy is predicted (see Figure 9) in the plenum chamber, covertrig the first thrce brads, the reduced range of alltximurn velocities caused by blocking these iirst three board gaps is possibly not roo surprising. For no blockage (the hast: case, see Iiigurc !it, thc range of velocities is from 0,31 to 0.52 m s progressively more gaps reduces the amount of varrstwn bloiked. 0.39 to 0.54 m s in ’ Blocking tile velocitj (one gap ’.two paps k1oclt.d. 0 40 to 0.5X rn s I: ttixre gaps blockcd: 0 . 5 8 to 0.64 ni s ’ 1 Even w i t h thrtc: gaps covered, the eddy is not prcdrcted to move significantly, so the cfkct o f weights tvlth suf’ficienr thickness above the stack 1s llkely to reduce ttte degree of rrcln-untf~~rrmty f ~ 31r i velocities thmttgh the stack. Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns i 0.70 0 f 0.30 1 0.20 0.10- 0.00 -+-onegap blocked --*-.twogaps blocked three gaps blocked - ~ Figure 8. The effect of blocking the gaps at the top of the stack, simulating the situation where there are weights between the top of the stack and below the fans. Figure 9. The predictedflow distribution where three gaps are blocked at the top of the stack, where the blockage covers the size of the main eddy. 259 Conclusions i'ur 11mtransitional f10w ctmulatrrco, c o I w q w c e ha$ reached catasfactory tdcrances 1% ttcn tlic c t ~ l i ~ i B ~ ~Etas i i t r ihecn rim in trart5tcnr la&, ftlecfirng J n of the total inthiu 'xtter 30 to 100 iteriitictns per ttnie stcp firr t m e steps o f 0 0 1 s. tirid scnsiaiviry studies have showi tl-rat ~ion-umiformgrid\ are rreccs,siq hccause of tile w&ic.n clianges 1n flow cross ~ ~ t i o r and i . the flow 'rirniildfiotis drc' imensitwe to grid refnrmcnt fur non-unifonri grids with rnore than 300,000 c e k The hest agrcrment bstw*ceii the cxpcrinienlally-m~rtsurcd Row distributions betwen fillet spaces and tfiusc predicttd by the sintilation haw been achieved fur total I rffectiw) tiux>sitics betwecn thc imiinat tiscostty fctr water and ten tines that ralue T h i s ctwnge LII v~m)siry1s nut very large (less than an order of mgnttude), given that effcctsve rurbuicnt viscosities ones. This rcsult 15 ilIC typically wvcral orders of mgnitudc greeter than laminar consistent w t t i thc transitional flows here '1 he effect of weights with sufficient thickness above the stack i s likely to rc*ducc the degree of ntrn- uniformity in air vctocitics through the stack, hecauw the stack may then be \eparatcd from the eddy at the top of rhe plenum chamber Acknowledgements l'hanks are dtie to the Kcw Zcaland Fuunciatton for Research Science and "I'echiiolog) t Publrc Gooti Scicucc f:untl) under sub-contract PXOO for financial support. assistance of. Dr J J h'iltfsm and Associate Professor D.F, Fletcher in ilhc tlic Department of Chemical Engineering ar the 1 3uversity of Sydney. Austrrtfta, is also acknoalrdged fir helphtl cnmmcnts, iriiiial wntk. advice regarding turbulence modelling in C'FL3 and fcecibacli. Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns 4. 5. 6. 7. 8. 9. Hua, L., Bibeau, E., He, P., Gartshore, I., Salcudean, M., Bian, Z., and Chow, S. 2001. Modelling of Airflow in Wood Kilns, Forest Products Journal, 5 1(6), 74-8 1. Nijdam, J.J., and Keey, R.B. 1999. Airflow Behaviour in Timber (Lumber) Kilns, Drying Technology - An International Journal, 17(7&8), 15 11-1 522. Nijdam, J.J., and Keey, R.B. 2002. An Experimental Study of Airflow in Lumber Kilns, Wood Science and Technology, 36, 19-26. Wilcox, D.C. 1996. Turbulence Modelling for CFD, DCW Industries, Inc., California. CFDS-CFX4.2: User Manual. 1999. Computational Fluid Dynamics Service, AEA Technology PLC, Hanvell Laboratory, Didcot, Oxfordshire, UK. Fletcher, D.F., Haynes, B.S.,Chen, J., and Joseph, S.D. 1998. Computational Fluid Dynamics Modelling of an Entrained Flow Gasifier, Appl. Math. Modelling, 22(10), 747-757. 261

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