Analysis of Drying Kiln Aerodynamics Based on a Full Three-Dimensional Turbulent Numerical Computation

This paper introduces a numerical methodology based on a 3D turbulent fl ow computation developed to assess the aerodynamic performances of lumber drying kilns. The numerical results are validated against experimental data obtained by applying fi ve different fan speeds and reversible airfl ow. The distributions of the energy loss coeffi cient and of the non-uniformity fl ow coeffi cient were plotted along the fl ow path in both normal and reverse directions and the regions with larger air loss values were identifi ed. The numerical computation revealed that three quarters of the airfl ow delivered by the fans bypasses the wood stacks through different gaps, consequently leading to a low aerodynamic effi ciency (of 24-25 %) of the kiln.


INTRODUCTION
1. UVOD Despite having been in use for over a century, conventional heat-and-vent drying kilns (Figure 1) are still in need of innovative solutions in order to improve their aerodynamic performances, which lead to better product quality and energy savings.
Most drying kilns allow for reversible airfl ow, in order to reduce moisture variation along fl ow path.Furthermore, the air inside the kiln is regulated to fl ow for a set time in one direction (further called, normal direction) and then for the same time in the opposite direction (further called, reverse direction).The normal direction (marked in Figure 1b by continuous arrows) fl ows through the fan's outlet boundary → fan house → plenum chamber → stacks → plenum chamber → heating coils → fan house → fan's inlet boundary.The reverse direction (marked in Figure 1b by dotted arrows) fl ows through the fan's outlet boundary → fan house → heating coils → plenum chamber → stacks → plenum → fan house → fan's inlet boundary.
The lumber boards are sticker-stacked to enhance kiln-drying by generating air channels between the boards.These channels are called sticker spaces or fi llet spaces.When the stacks are placed inside the kiln, there are two large lateral spaces (plenum chambers) between the front door and the stacks and between the back wall and the stacks.Their function is to distribute the airfl ow evenly through the sticker spaces.Additionally, several further gaps (CPS, CPL, CPV and CPO) are generated around the stacks (Figure 1a).
Since these gaps have a lower aerodynamic resistance than the stacks, a part of the volumetric fl ow rate generated by the fans will bypass the lumber stacks.A bypass of 10-25 % normally occurs when a good kiln loading strategy is chosen (Langrish and Keey, 1996).
The airfl ow in lumber drying kilns has been studied since the 1930s by means of classical devices such as vane anemometers, hot-wire anemometers or pressure probes, but also by means of modern techniques like the Laser-Doppler anemometer (Ledig et al., 2007).In addition, numerical methods such as CFD (Computational Fluid Dynamics) are used to better understand and design drying equipment at lower costs than needed for experimental tests (Jamaleddine and Ray, 2010).
CFD has been used by several researchers to study the aerodynamics of lumber drying kilns or parts of it (Arnaud et al., 1991;Langrish and Keey, 1996 ).As a result, various solutions or recommendations have been formulated.Extensive reviews on different solutions and methodologies to improve the aerodynamic performances of lumber dryers have been published by Keey et al. (2000) and by Ledig et al. (2007).
Most of previous studies, that have analyzed the aerodynamics of drying kilns, have focused on the airfl ow either in front or inside the stacks, but not along the entire loop (i.e.fan's outlet boundary → fan house → plenum chamber → stacks → plenum chamber → heating coils → fan house → fan's inlet boundary).One possible reason is that the simultaneous interaction of all loop components upon the airfl ow behavior is very complex (Arnaud et al., 1991).In addition, there is a lack of numerical models in literature that are able to take into account all sources of airfl ow perturbations within the kiln (Ledig et al., 2001) such as: position of the fans, end-wall effects, separation zones, infl uence of the gaps around the stacks on the airfl ow bypass, etc.This work introduces a novel methodology based on the fl uid fl ow computation in 3D geometries, i.e. a lumber drying kiln.To demonstrate the applicability of the proposed methodology, the aerodynamics of a heatand-vent drying kiln (semi-scale model) was investigated in both normal and reverse airfl ow directions.In addition, the trapezoidal shape of the fan house (see Figure 1b) was taken into account.The methodology proposed in this paper paves the way towards a better analysis of the aerodynamics phenomena in order to improve the perfomances of lumber drying kilns.

Description of the drying kiln Opis sušionice
The experiments were performed in a 4 m 3 heatand-vent laboratory kiln, schematically presented in Figure 1.The kiln is equipped with two reversible overhead fans, a heating coil, two vents and two spray pipes, one on each side of the kiln.The fan speed can be adjusted from 0 to 1450 min -1 using an inverter and the power absorbed by each fan can be modifi ed within the range of 0…3000 W. Consequently, the volumetric fl ow rate can be modifi ed within the range of 0…8.33 m 3 •s -1 .The fan hub radius is r = 0.109 m.The outer fan radius is R = 0.405 m.This radius (R) is further considered as the reference size; all other linear dimensions are related to it in order to obtain dimensionless sizes.Similarly, the annular section delimited by the two radii  (R 2 -r 2 ) will be considered as a reference for the transformation of areas into dimensionless sizes.

Material and kiln setup 2.2. Materijal i postavke sušionice
Four stacks were placed inside the kiln as a 2 x 2 matrix (Figure 1).Each stack contained eighty-eight sticker-stacked spruce (Picea abies) boards.Three stickers were placed in a row, at the ends and at half the length of the boards.Based on these input data, twenty 1200 x 676 x 24 mm sticker spaces arranged as a 2 x 10 matrix were generated in each stack.Three bolsters were placed below each stack (Figure 1a).

Numerical setup 2.3. Numeričke postavke
The 3D computational domain (Figure 2b) was created by dividing the small-scale experimental kiln by a symmetry plane at mid length (Figure 2a).The governing equations (momentum and continuity) for the incompressible, steady and viscous fl ows are written as follows: and (1) Where, ν is the velocity (m•s -1 ), p is the pressure (Pa), ρis the air density (kg•m -3 ), μ is the dynamic air viscosity (Pa•s), and g is the gravitational acceleration (m•s -2 ).
The inlet boundary of the 3D computational domain is the annular section between the outer fan diameter and the fan hub diameter.A uniform normal velocity corresponding to each volumetric fl ow rate value is imposed as the infl ow condition, together with the turbulent quantities.A constant pressure on the annular outlet surface is imposed as the outfl ow boundary condition.The symmetry condition is imposed on the symmetry plane and the non-slip condition is imposed on all wall boundaries.
The Reynolds number corresponding to the airfl ow in the drying kiln ranges between 1.2x10 5 and 8.7x10 5 .The Reynolds number is computed using the bulk velocity on the annular surface of the fan, the outer fan diameter and the kinematic air viscosity at 20 C.
Turbulent fl ows with a high Reynolds number are diffi cult to model.Turbulence fl ows are greatly infl uenced by wall boundaries (Hinze, 1975), especially when dealing with fl ows through relatively narrow channels.The viscosity affects the near-wall region, where the variables of the numerical solution change most rapidly.The non-equilibrium wall function approach is used to model this region.The wall function approach substantially saves computational resources for high Reynolds number fl ows, since it is economical, robust and reasonably accurate for the near-wall treatments (Craft et al., 2004).The near-wall treatment employs the non-equilibrium wall function for the turbulence model, with the potential benefi t of better accounting for the adverse pressure gradients (Kim and Choudhury, 1995) in comparison to the standard wall functions.
Reynolds stress model (RSM) accounts for the effects of the streamline curvature, rotation, and rapid changes of the strain rate in a more rigorous manner than one-equation and two-equation models, and it is strongly recommended for highly anisotropic fl ows (Perot and Natu, 2004).In other words, the RSM accurately predicts complex fl ows.However, the fi delity of the RSM predictions is still limited by the closure assumptions employed to model various terms in the exact transport equations for the Reynolds stresses.The modeling of the pressure-strain and dissipationrate terms is particularly challenging, and is often considered responsible for compromising the accuracy of RSM predictions.The effects of strong turbulence anisotropy can only be rigorously modeled by applying the second-moment closure adopted in the RSM.The RSM closes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate.The RSM involves the calculation of individual Reynolds stresses using differential transport equations.The individual Reynolds stresses are then used to obtain closure of the Reynolds-averaged momentum equation.Therefore, the RSM yields results that are clearly superior to the simpler models.This means that seven additional transport equations are solved in 3D fl ows.However, additional computational resources are required.
On the inlet section, one must specify the individual Reynolds stresses and the turbulence dissipation rate ε.The turbulent kinetic energy k = /2 is ascertained by taking the trace of the Reynolds stress tensor.However, the turbulence intensity T u (%) expresses the "strength" of the turbulence motion being defi ned as the ratio of the root-mean-square of the velocity fl uctuations ν′ (m•s -1 ), to the mean fl ow velocity V (m•s -1 ), according to Eq. (2): . ( Turbulence intensities of 7 % and approximately 3 % were measured by Fernandez Oro et al. (2008) in the rotor wakes of the axial fan and in the main stream, respectively.Therefore, an average value of 5 % was selected on the annular inlet section of the drying kiln.
The second turbulent quantity corresponds to the characteristic length of the turbulence that has to be imposed on this section.This turbulent quantity char-acterizes the spatial dimension of the largest eddy of the turbulent structure.In our case, this length value was considered as l = 0.81 m; equal to the outer diameter of the axial fan.
Three grids with hexahedral cells were generated using Gambit (Fluent Inc., 2006a) in order to assess the numerical solution with respect to the mesh refi nement.As a result, the following structured meshes were considered in our procedure: a coarse grid (of approximately 1.2 M cells), a medium grid (of approximately 2.1 M cells) and a fi ne one (of approximately 2.6 M cells).
The 3D turbulent steady computation was carried out using Fluent (Fluent Inc., 2006b) running in parallel.The incompressible fl ow equations were discretized using a fi nite volume method (FVM).The semiimplicit pressure linked equations (SIMPLE) algorithm for pressure-velocity coupling was selected for the numerical investigation.The convection terms are discretized using a 2 nd order upwind scheme in both momentum and turbulence equations and a PRESTO scheme for pressure.The parallelization was obtained by a domain decomposition procedure.The communication time was minimized by employing the METIS graph partitioning procedure (Karypis and Kumar, 1998).

Experimental method 2.4. Eksperimentalna metoda
It was necessary to disassemble the heating coils in order to capture the fl ow features, particularly since this study focused on the aerodynamics of a drying kiln.The same strategy was applied by several researchers (Arnaud et al.,1991;Bian, 2001;Hua et al., 2001) in order to numerically investigate the airfl ow inside a lumber drying kiln.In particular, the pressure drop on the heating coils and other kiln elements (bends, baffl es) is less than that of the lumber stacks (Perre and Keey, 2006).
The static pressure and air velocity were measured at two different positions (P1 and P2, see Figure 1b), in both air stream directions (normal and reverse).The measurements were done for fi ve fan speeds, namely 1450, 1250, 1000, 750 and 500 min -1 .The fan speed was strictly controlled by a frequency inverter.The measurements were performed both in descending (1450…500 min -1 ) and ascending order (500...1450 min -1 ) to determine the experimental error.The kiln doors and vents were closed during the measurements.
At each point of interest, the static pressure and air velocity were recorded for 10 minutes, for each investigated fan speed; as a result, around 400 data were recorded for both static pressure and air velocity during this time.The static pressure was measured using a differential pressure sensor FD A602 -S1K with an accuracy of ±0.5 %, provided by Ahlborn.The static pressure probes with a diameter of 0.006 m were connected to the pressure sensor by means of two silicone hoses.The air velocity was measured using a rotating vane air velocity sensor FVA915S220, which was also delivered by Ahlborn, with an 11 mm measuring head diameter and an accuracy of ±3 %.Both sensors were connected to a data-logger Almemo 2590 -4S.The data were simultaneously recorded through different input channels.The AMR Control Software V.5.15 was used to acquire and transfer the data from the data-logger to a laptop computer.

Model validation 2.5. Provjera valjanosti modela
The numerical results are validated against the experimental data obtained in both directions of airfl ow.First, the measuring positions P1 and P2 located in the fan house are considered, see Figure 1.Figures 3  and 4 plot the pressure drop against the air velocity in both fl ow directions at these two points.A reasonable agreement between the numerical results (marked with stars) and the experimental data in the normal direction of the airfl ow was obtained (Figure 3).However, better agreement can be observed in the reverse direction of airfl ow (Figure 4).When comparing the results obtained in these two measuring locations (P1 and P2), a better validation of the numerical results against the experimental data is revealed at location P2, positioned near the false ceiling.

Numerical methodology for aerodynamic
analysis of the drying kiln 2.6.Numerička metodologija za aerodinamičku analizu sušionice When experimentally investigating the fl ow in a drying kiln, usually the average pressure is measured at the fan inlet and outlet.In addition, the loss coeffi cient is defi ned using the average air velocity, computed as the volumetric fl ow rate divided by the corresponding cross-section area.However, this rather simple approach, inspired from basic aerodynamics, does not provide meaningful results, especially when the fl ow is highly non-uniform, with large recirculation regions.
On the other hand, when a full 3D fl ow computation is performed on the drying kiln, both velocity and pressure fi elds are assessable in several sections, and a more rigorous approach can be employed to assess the fl ow within the control volume bounded by the closed surface consisting of the inlet section, outlet section and kiln walls, as shown in Figure 2b.When computing incompressible fl ows, the static pressure is defi ned up to an arbitrary constant.As a result, only pressure difference representations make sense.On the other hand, the dynamic pressure is relevant as an absolute value, since the lack of dynamic pressure clearly corresponds to fl ow stagnation.
Therefore, integral quantities are defi ned in order to compute the relevant parameters associated to the drying kiln aerodynamics.In order to analyze the energy transformation process, as well as its effi ciency, the following integral quantities on a generic cross section S were introduced (Susan-Resiga et al., 2010): ( Where, Π is the fl ux of the potential energy (W), K is the fl ux of the kinetic energy (W) and W is the fl ux of the mechanical energy (W) and v n is the normal component of the velocity on the surface S.
In numerical computations, the static pressure is actually the piezometric pressure p p = p + ρgz.For a control volume of the drying kiln, bounded by the closed surface previously described, the net fl ux of the specifi c mechanical energy is For viscous fl ows, the viscous friction converts part of the mechanical energy into heat yield (W > 0).This energy fl ux imbalance is associated with the aerodynamic losses.As a result, W(S) decreases monotonically from the inlet to the outlet of the drying kiln.In the present analysis, the authors considered only steady fl ows.Therefore, it is correct to consider the specifi c energy fl ux as defi ned by Eq. ( 6).
The total aerodynamic power, that has dissipated up to section S, is W(S) -W out > 0, where W out = Π out + K out with W out = W(S out ), Π out = Π(S out ) and K out = K(S out ), corresponding to the integral quantities on the annular outlet section.
The energy loss coeffi cient is usually defi ned as (7) The fi rst term in Eq. ( 7) corresponds to what is called the potential energy coeffi cient (8) while the second term in Eq. ( 7) corresponds to the so-called kinetic energy coeffi cient (9) The variance in kinetic energy within the drying kiln should also be considered.The fl ux of specifi c kinetic energy is computed according to Eq. ( 4).On the other hand, for an ideal fl ow with constant average volumetric fl ow rate (normal) velocity on each crosssection, the fl ux of specifi c kinetic energy would be K ideal (S) , defi ned by the following equation: (10) This is the reference baseline, and K(S) will always have higher values.Consequently, the airfl ow non-uniformity can be quantifi ed through the coefficient (11) Besides the non-uniformity coeffi cient ξ(S), the kinetic energy excess is also relevant for the analysis of the drying kiln aerodynamics.
In practice, the pressure drop is usually examined instead of the aerodynamic power loss.The corresponding pressure loss for the kiln control volume is defi ned by the equation: Where, Δp is the total pressure drop in the kiln (Pa) and Q is the volumetric fl ow rate (m 3 •s -1 ) computed according to the following equation: (13) Where, v n (m•s -1 ) is the normal component of the velocity on the surface S.
The following fl ow-related quantities associated with kiln drying are written in dimensionless form: Where, w is the dimensionless aerodynamic power loss, k is the dimensionless pressure loss, q is the dimensionless volumetric fl ow rate, A ref is the reference area (m 2 ) associated to the annular inlet section and v ref is the reference velocity (m•s -1 ) corresponding to the bulk velocity through the reference section.
Since the tested kiln had gaps around the stacks, the volumetric fl ow rate generated by the fan (Q) can be conveniently divided into two parts: one part goes through the stacks (Q 1 ) and the other goes around the stacks (Q 2 ) via the gaps.The bypass coeffi cient (b) in Eq. ( 21) is defi ned, according to Nijdam and Keey (1996), as a ratio between the two fl ow rates: (17) The aerodynamic effi ciency of the kiln can be defi ned either as a ratio between the volumetric fl ow rate through the stacks (Q 1 ) and the total volumetric fl ow rate delivered by the fan (Q) or by means of the bypass coeffi cient, according to Eq. ( 18): (18) 3 RESULTS AND DISCUSION 3. REZULTATI I RASPRAVA

Aerodynamic analysis of drying kiln 3.1. Aerodinamična analiza sušionice
The numerical simulations for turbulent fl ow in the drying kiln were performed in both airfl ow directions, for fi ve fan speeds, as detailed in the experimental approach.
The cross-sections S of the kiln geometry, defi ned for the numerical analysis, are marked with grey shadows in Figure 5a.The thick black line represents the mid-line, which connects the successive centers (bold black bullets) of these cross-sections.
From the geometrical point of view, the airfl ow in the drying kiln is suddenly modifi ed when the fl ow direction and/or the shape of the cross section changes along the kiln's mid-line, as shown in Figure 5b.
The cross-section area is expressed as a dimensionless size by relating it to the annular fan section, while the mid-line length is expressed as a dimensionless size by relating it to the outer fan radius.In our case, it can be observed that the mid-line length of the drying kiln is about fourteen times longer than the reference radius.It is important to mention that the lumber stacks are located approximately at mid length of the kiln's mid-line.Figure 5b shows a region with constant area distribution associated to the stacks and several sudden expansions/contractions of the cross-section area along the aerodynamic passage.
However, only one distribution is associated to each airfl ow direction using the dimensionless sizes.As a result, the distribution of the potential energy coeffi cient c  defi ned according to Eq. ( 8) is plotted against the dimensionless length of the kiln's mid-line, as illustrated in Figure 6a.The overall potential energy drop is the same in both airfl ow directions (normal and reverse).The potential energy drop from the annular inlet section to the stack is smaller than the value determined from the stack up to the outlet section in both airfl ow directions.The most signifi cant variation of the potential energy coeffi cient is observed in the fan house located in front of the outlet section.
The kinetic energy coeffi cient c K , expressed according to Eq. ( 9), is plotted versus the dimensionless length of the kiln's mid-line in Figure 6b.The overall kinetic energy difference, defi ned between the inlet and outlet sections of the drying kiln, is the same in both airfl ow directions (normal and reverse).In spite of this, the c K distribution along the kiln's mid-line signifi cantly differs between the normal and reverse direction of the airfl ow.A greater decrease is obtained up to the cross-section defi ned at the stack inlet in the normal fl ow direction compared to the reverse direction.This discrepancy includes the cross-section area variation from the annular fan inlet section to the stack inlet sec- tion in both directions.A signifi cant difference in the variation and values of the c K in both directions is also revealed in the stacks.This difference is clearly generated by the aerodynamic conditions, because the crosssectional area of the stack is considered constant from the point of the air inlet until the air outlet.In the last fan house, the kinetic energy increases again, due to the signifi cant decrease of the cross-sectional area.
The energy loss coeffi cient  determined along the kiln's mid-line, as defi ned according to Eq. ( 7), is represented in Figure 7a.The overall energy loss coeffi cient between the inlet and outlet sections of the drying kiln is about 2.0 in both airfl ow directions.However, the energy loss coeffi cient distribution along the kiln's mid-line is different to that in the opposite airfl ow direction.The value of the energy loss coeffi cient is practically the same for the stack inlet cross-section A monotonic decrease of the energy loss coefficient from the inlet to the outlet is revealed in both airfl ow directions.In the normal direction, the energy loss coeffi cient decreases up to the stack inlet cross-section, then it becomes negligible along the stacks and it decreases again, but considerably less, in the plenum and in the fan house.A signifi cant difference observed in the reverse direction is contributable to the stacks region, where the energy loss coeffi cient is no longer constant, but instead decreases by approximately 10 % and is due to the distribution of the kinetic energy component, as depicted in Figure 6b.
The non-uniformity coeffi cient ξ defi ned according to Eq. ( 11) is illustrated along the kiln's mid-line in The unit value of this coeffi cient indicates a uniform distribution of the fl ow over the cross section.In contrast, larger values suggest a non-uniform fl ow compared to the ideal case.The non-uniformity coeffi cient distributions in both airfl ow directions reveal larger values.Thus, a greater degree of non-uniformity is observed in the fan house located in front of the inlet section.Naturally, the air jet delivered by the fan in the house leads to greater non-uniformity of the fl ow, which is in agreement with the numerical results.Moreover, the value in the normal fl ow direction is larger than the value in the reverse direction, due to the differences in the fan house geometry.Figure 1 shows that the fan house geometry is divergent in the normal fl ow direction, inducing thus large recirculation regions.However, the recirculation regions are smaller in the reverse fl ow direction due to the convergent fan house geometry.
The values of the non-uniformity coeffi cient ξ on the stack inlet and outlet cross-sections are 2 to 4 times larger in the reverse airfl ow direction than in the normal direction.
The overall dimensionless quantities associated with this confi guration of the drying kiln, analyzed in both normal and reverse airfl ow directions, are given in Table 1.These overall values concerning aerodynamic parameters are useful in the design of axial fans for lumber drying kilns.

Bypass analysis 3.2. Analiza zaobilaženja
Considering the volumetric fl ow rate generated by the fan (Q), only 24 % in the normal direction and 25 % in the reverse direction pass through the sticker spaces (Q 1 ).The other part (Q 2 ) bypasses the stacks.This small percentage of volumetric fl ow rate that goes through the sticker spaces is due to the fact that the area of gaps around the stacks is about 1.15 times larger than that of the sticker spaces and, also, due to the fact that their aerodynamic resistance is smaller than that opposed by the stacks.
The bypass coeffi cient computed using Eq. ( 17) reveals that the volumetric fl ow rate that bypasses the stacks (Q 2 ), also called "air leakage", is about three times larger than the air quantity that goes through the sticker spaces (Q 1 ) in both air directions: the bypass coeffi cient is 3.15 for the normal airfl ow direction and 3.04 in the reverse direction.Therefore, the aerody- namic effi ciency values of the tested kiln are, according to Eq. ( 18), 0.24 and 0.25, respectively, in the normal and reverse directions.These are very low values and they apply when the kiln is loaded at full capacity.When the kiln is partially loaded, the aerodynamic effi ciency value is further reduced.This happens due to the increasing ratio between the aerodynamic resistance associated to the stack region and the aerodynamic resistance of the gaps around the stacks.Therefore, the drying kiln has to be equipped with baffl es in order to overcome both negative effects of the air bypass upon the drying time and the drying uniformity (Riley, 2006;Bedelean and Sova, 2012).
The infl uence of the airfl ow direction upon the air losses recorded in each gap around the stacks at the inlet section (S3 / S3b) is illustrated in Figure 8.The graph shows that the air leakage through the top gap (CPS) is 15 % higher in the reverse direction than in the normal direction.As a result, the reverse fl ow direction favors the drying of the fi rst row of boards located in the upper stack.On the other hand, the air loss in the side gap (CPL) is approximately 13 % higher in the normal direction.The air loss in the vertical gap (CPV), however, is not as strongly infl uenced by the airfl ow direction, being only slightly (by 2 %) higher in the normal direction (Figure 8).
The air leakage balance between the inlet and outlet section is analyzed in Figure 9 in each airfl ow A moderate air leakage balance (within a 7 % limit) is obtained in the normal fl ow direction between the inlet (S3) and outlet section (S4).In this case, air leakage through the top gap (CPS) of the outlet surface is redistributed towards the side gap (CPL) by 5 % and the vertical gap (CPV) by 2 %.
In the reverse direction, a signifi cant redistribution of the air leakage between the inlet (S3b) and outlet sections (S4b) takes place.The air leakage through the top gap (CPS) ranges between 40 % (at the inlet) and 16 % (at the outlet), which means a difference of 24 % (Figure 9b).This value is 3.5 times greater than the air leakage in the normal fl ow direction.Correspondingly, 14 % and 10 % of the air leakage through the top gap (CPS) on the outlet surface is redistributed towards the side gap (CPL) and the vertical gap (CPV), respectively.The redistribution of the air losses along the fl ow path from the inlet towards the outlet section of the stacks is due to the pressure distribution in the outlet plenum of the drying kiln.
The convergent study is performed in order to assess the numerical solution accuracy.The bypass coeffi cient (b) and the aerodynamic effi ciency (η) are computed on different grids.As a result, the relative error (e) is computed using Eq. ( 19) for both quantities (b and η) with respect to the corresponding value obtained on the fi nest grid (2.6M cells).The symbol  corresponds to the value obtained on the medium grid (2.1M cells) or coarse grid (1.2M cells), respectively. [%] The relative error (e) values for both quantities (b and η) and both grids (medium and coarse) are included in Table 2.The relative error values associated to the aerodynamic effi ciency computed on both grids (coarse and medium) are less than 5 %.Therefore, the numerical results selected for validation against experimental data belong to the medium grid.

ZAKLJUČAK
The paper introduces a methodology developed to assess the aerodynamic performances of lumber drying kilns.The 3D computational domain corresponds to half of the drying kiln (by dividing the kiln along a symmetry plane at mid length) including a fan, two wood stacks and the airfl ow loop.The 3D turbulent computations are performed for fi ve fan speeds considering air fl ow in both normal and reverse directions.A fi nite volume method (FVM) was used to solve the incompressible fl ow equations.The Reynolds stress model (RSM) was selected in order to capture the features of the turbulent fl ow associated with a drying kiln.
The experiment was carried out in a 4 m 3 heatand-vent kiln loaded at maximum capacity, and fi ve different fan speeds under reversible airfl ow conditions were tested.The numerical results obtained were validated against the experimental data that were measured in the drying kiln.A reasonable agreement was obtained between the numerical results and the experimental data in both airfl ow directions.the methodology core was embedded in the integral quantities defi ned in the paper.This approach was taken in order to assess the aerodynamic performances of the drying kiln, by expressing the energy loss coeffi cient and the non-uniformity coeffi cient.The energy loss coeffi cient was determined based on the computed potential and kinetic energy coeffi cients.The value of the overall energy loss coeffi cient between the inlet and outlet section of the drying kiln in both airfl ow directions was determined to be about 2. However, the energy loss coeffi cient distribution along the drying kiln differed from one airfl ow direction to the other.A signifi cant difference was observed in the reverse direction, which contains the stacks region; here the energy loss coeffi cient was no longer constant, but it decreased by approximately 10 % due to the distribution of the kinetic energy component.
The non-uniformity coeffi cient is considered a good indicator for quantifying the fl ow distribution with respect to the ideal one.Larger values suggest greater fl ow non-uniformity.The non-uniformity coeffi cient distributions in both airfl ow directions reveal larger values in the fan house located in front of the inlet section.This is in good agreement with the numerical results.
Finally, the bypass coeffi cient and the aerodynamic effi ciency were computed, in order to assess the aerodynamic performances of the drying kiln.The bypass coeffi cient revealed that the quantity of air that goes around the stacks is three times greater than the quantity of air that passes through the sticker spaces for the given confi guration.As a result, very low aerodynamic efficiency values were yielded: 24 % in the normal fl ow direction and 25 % in the reverse direction, even with a full-loaded kiln.A detailed analysis of air leakage through each gap around the stacks revealed changes in the percentage of air loss through the top gap (from inlet to outlet section), namely, 7 % and 24 % in the normal and reverse airfl ow directions, respectively.In order to overcome the negative effects of the air bypass upon the drying time, energy consumption and drying uniformity, the drying kiln has to be equipped with baffl es.
The methodology developed and validated in this paper can be further applied to assess the aerodynamic performance of lumber drying kilns with different confi gurations.Also, various solutions (e.g.baffl es) to improve the airfl ow in lumber drying kilns could be simulated based on the quantities defi ned in this paper (e.g.energy loss coeffi cient, non-uniformity coeffi cient and bypass coeffi cient).