1.1 The intended oven geometry and operation of the device
When the forced convection industrial ovens are examined, it is seen that the fans with radial geometry are mostly aligned along the direction of travel, perpendicular to the direction of travel. Fans can be blown directly over the belt or air can be sucked and redirected through a channel. In such a discrete channel structure, the position of the suction holes and the location of the blow holes in which the air is directed to different regions of the belt is of high importance for the air distribution in the oven and therefore for the optimization of the heat distribution. The heaters can be placed in parallel with the flow direction. The amount of heat needed will be reduced as a result of the optimization of the indoor air distribution.
In the general design stages of the belt oven, the systematic steps of conformity were followed. The design has been realized by taking into consideration the ease of installation and manufacturing, based on the use of modular, common parts. In the detail design phase, the assembly and manufacturing difficulties encountered during the prototype production were eliminated and visual improvements were made. The dimensions of the main cooking chamber are 1128mm in length, 295mm in width, and 337 mm in height with a porous belt surface located at the height of 100 mm. Fans sucked the air inside the chamber to a discrete channel structure and the air is blown back to the main cooking chamber with blowing holes located at a height of 63mm.
The distance between the suction fans (Lf) is parameterized, which changes between 170 mm to 240 mm with 35mm increments. Also, the vertical location of fans is parameterized, which is changed between 200mm to 250mm with 25 mm increments. The number of fans changed between 2 to 4. Fans are positioned symmetrically on both sides of the oven centerline. Pr Fans are positioned symmetrically on both sides of the oven centerline. Fans are positioned symmetrically on both sides of the oven centerline. Fans are positioned symmetrically on both sides of the oven centerline. Fans are positioned symmetrically on both sides of the oven centerline. oduct inlet and product outlet details are excluded from the design because of the complexity. Air circulating hole dimensions and locations were kept constant due to construction issues. A stainless-steel chain belt with a porosity of 0.5 volume fraction is used. Resistances are located under the top side of the oven. Each resistance has a power of 900W. Although the total power of the heaters used in the oven is 4.5kw, only a certain amount of this power will be used to maintain the temperature inside the oven after the set temperature is reached. In Fig. 1, the schematic drawing of the proposed oven is given. In Fig. 2, a schematic of the proposed air circulation is given.
All sides of the heating chamber were covered with 20 mm glass wool isolation material except the product inlet, the product outlet, and the ventilation openings. The heating chamber was isolated from the main chassis to prevent critical areas such as maintenance doors and electronics from overheating.
1.3 Numerical Simulations
To analyze a continuous and differential fluid flow, Navier-Stokes equations, which are derived from the laws of conservation of mass (continuity), conservation of energy (first law of thermodynamics), and conservation of momentum (Newton’s second law of motion), are used. Conservation of mass is the general law that states that the amount of mass change in a given fixed control volume is equal to the difference between the amount of mass entering and leaving. The law can be formulated for compressible flows in differential form as:
$$\frac{\partial \rho }{\partial t}+\nabla .\left(\rho V\right)=0$$
2
And for incompressible flows \(\left(\frac{\partial \rho }{\partial t}=0\right)\), law of continuity will be:
$$\nabla .\left(V\right)=0$$
3
Conservation of energy or the first law of thermodynamics simply states that energy can neither be created nor destroyed, it can only be converted from one form to another. In other words, for a fixed control volume, the rate of energy change is equal to the heat addition and work done, total energy remains constant. For the steady state, incompressible flow conservation of energy law will be:
$$\rho {c}_{v}\frac{dT}{dt}=k{\nabla }^{2}T+\theta$$
4
The Law of conservation of momentum or Newton’s second law of motion states that the rate of momentum change in a control volume is equal to the sum of the external forces. For the steady state, incompressible flow conservation of momentum law will be:
$$\rho \frac{dV}{dt}=\rho g-\nabla p+\mu {\nabla }^{2}V$$
5
For the above equations, V is the velocity field, p is the pressure, T is the temperature, k is the thermal conductivity, ρ is the density, g is the gravity, t is the time, µ is the viscosity, ϴ is the viscous dissipation function.
The Navier-Stokes equations have no analytical solutions except for very simple flows under ideal conditions. To find solutions in real flows, numerical methods using algebraic approaches must be used. For numerical modeling and solving the conservation equations, ANSYS CFX, a computational fluid dynamics program that uses the finite volume method, was used. ANSYS CFX uses an element-based finite volume method, which first involves discretizing the spatial domain using a mesh. The mesh is used to construct finite volumes, which are used to conserve relevant quantities such as mass, momentum, and energy (Inc A., 2011). The finite volume method is widely used in fluid dynamics and heat transfer problems (Norton & Da-WenSun, 2006).
All fans are modeled as rotating bodies that had transient rotor-stator interface model boundary conditions in a stationary fluid domain, based on the standard Φ150mm diameter oven fan (Fig. 4).
Angular velocities of all rotating fan bodies are equal to 2800rpm and constant. Possible rpm changes due to temperature are neglected. All walls have a thermal conductivity value of 0.04W/m.K.
The standard k-epsilon turbulence model is not recommended for flows impinging on surfaces because the turbulence energy may be over-predicted at the stagnation points (Durbin, 1996). SST (shear stress turbulence) method is validated by researchers(Kokolj, Škerget, & Ravnik, 2017) (Kokolj, Škerget, & Ravnik, 2017) and also used for this analysis. For the heat transfer mechanism Total Energy and for thermal radiation Monte Carlo approaches were used. For more accurate solutions, physical modeling errors and mesh quality must be considered. Ansys CFX uses scalable wall functions to solve the boundary layer profile near-wall regions in turbulent flow with an acceptable computational load. But there is a danger of overestimating the boundary layer so a non-dimensional parameter y+ (YPLUS) is used for quality check. y + is a non-dimensional variable representing the distance from the wall to the first node away from the wall. As the y + increase, the wall-type conditions will be imposed further from the wall by scalable wall functions. By definition, y + is dependent on the size of the mesh near wall regions (Inc., 2011). The upper limit of y + is a function of the Reynolds number and for large Reynolds numbers as Re = 109, y + can be around 1000 or more but for typical applications which have lower Reynolds numbers, entire boundary layers might only extend around y + = 300 for not overestimations, and not to underestimate the boundary layer, lower bound for y + will be y + = 30. (Inc A., 2011). As Ansys CFX uses scalable wall functions, no need to worry about the lower limit for y+. The growth rate of the elements was kept low to avoid poor quality cells but as a result of the low growth rate and complex oven geometry. Mesh size range changes due to geometric parameterization. In Table 3 summary of the settings used in the simulation is given.
Table 3
Summary of settings used in simulations
Governing equations
|
|
Total Energy for conduction and convection
|
|
Monte Carlo for thermal radiation
|
|
SST (shear stress turbulence) method for turbulence modeling
|
Material properties
|
|
All air properties temperature-dependent
|
|
Thermal conductivity of the wall insulation, 0.04 W/(mK)
|
|
Constant solid material properties
|
Boundary conditions
|
|
Product inlet, product outlet, and ventilation holes defined as openings
|
|
External walls, mixed convective and radiative heat flux
|
The mesh is a hybrid of tetrahedra and hexahedra elements. The maximum element skewness, aspect ratio, and orthogonal quality index values of the elements and their recommended values (Inc A., 2009) are given in Table 4. Air is defined as an incompressible ideal gas. The thermal conductivity, viscosity, density, and specific heat of air were considered temperature-dependent. All solid material properties were considered fixed. Product inlet, product outlet, and ventilation holes are defined as openings to the atmospheric pressure and ambient room temperature (25 ℃). The belt speed is not included in the simulations as it varies according to the product to be processed. The convergence criteria are given in Table 5.
All analyses were performed as transient with a full buoyancy model due to the extreme complexity of the flow and heat transfer mechanisms. The first-time step is 1 s with an adaptive timestep setting and the max number of the time steps is 80. The target max loop number is 5 and the target min loop number is 2. The Total Energy heat transfer model and Monte Carlo thermal radiation model with isotropic scattering model were used. Grid sensitivity analysis is done for Run1 with 2.5, 3, 3.5 and 4 million elements. And found that for above 3 million elements, belt surface temperatures deviations for intended point is below % 2. For timestep 80, temperature levels stabilized. From these results model concluded as grid independent.
For each model, it took approximately 8 hours to calculate the mesh structure and numerical simulations. All calculations were made on a workstation with a quad-core 3.80GHz Xeon processor and 32GB of ram.
Table 4
|
Model
|
Recommended
|
Elm.size range
|
~ 3,500.000
|
|
Max. Elm.skewness
|
0.9481
|
< 0.95
|
Max. Aspect ratio
|
34.186
|
< 35/1
|
Orthogonal quality
|
0.25
|
> 0.14
|
Table 5
Residuals of continuity
|
Residuals of momentum
|
Residuals of energy
|
1.0e-04
|
1.0e-04
|
1.0e-06
|
In the Taguchi method, the signal-to-noise ratio (S/N Ratio) is used to measure the variability between experimental data. Three types of S/N Ratios are defined in the Taguchi method: smaller is the best, nominal is the best, and larger is the best. In this study, the smaller is the best (Eq. (5)) approach was used since it is aimed to have the lowest deviations in the temperature and velocity distribution on the belt surface where the product is treated. CFD models were compared due to belt surface velocity and temperature deviations. Belt surface temperature and velocity deviations transformed into S/N ratios are given in Table 6. The aim of this study is to minimize the deviations so the S/N ratio is defined as:
$${SN}_{s}=-10\text{l}\text{o}\text{g}\left(\frac{1}{n}\sum _{i=1}^{n}{y}_{i}^{2}\right)$$
5
Table 6
S/N ratios for Taguchi DOE runs
Run
|
A
|
B
|
C
|
SNRA-Temp
|
SNRA-Vel
|
1
|
1
|
1
|
1
|
-32.856
|
-0.172
|
2
|
1
|
2
|
2
|
-34.762
|
0.468
|
3
|
1
|
3
|
3
|
-29.971
|
3.715
|
4
|
2
|
1
|
2
|
-33.174
|
-0.442
|
5
|
2
|
2
|
3
|
-32.690
|
0.250
|
6
|
2
|
3
|
1
|
-29.311
|
-0.649
|
7
|
3
|
1
|
3
|
-30.365
|
4.243
|
8
|
3
|
2
|
1
|
-32.826
|
-2.047
|
9
|
3
|
3
|
2
|
-31.716
|
0.543
|
Table 7
Response Table of means of SN Ratios for temperature deviations
Level
|
MeanA-Temp
|
MeanB-Temp
|
MeanC-Temp
|
1
|
-32.529
|
-96.395
|
-94.993
|
2
|
-31.725
|
-100.278
|
-99.651
|
3
|
-31.636
|
-90.998
|
-93.026
|
Delta
|
0.089
|
5.397
|
6.626
|
Rank
|
3
|
2
|
1
|
Table 8
Response Table of means of SN Ratios for velocity deviations
Level
|
MeanA-Vel
|
MeanB-Vel
|
MeanC-Vel
|
1
|
1.337
|
3.629
|
-2.868
|
2
|
-0.280
|
-1.329
|
0.569
|
3
|
0.913
|
3.608
|
8.207
|
Delta
|
0.424
|
-0.020
|
7.638
|
Rank
|
2
|
3
|
1
|
In Fig. 5 and Fig. 6 mean velocity change and mean temperature change are given in the X direction. To find the belt surface average temperature, 100 different point values were taken along the X-axis at the Y = 0.05m, Y = 0.15m, and Y = 0.25m positions. All values were taken 0.01 m above the belt.
For the factors examined, the average of the signal-to-noise ratios was calculated and the factors that most affected the deviations in the temperature (Table 7) and velocity distribution (Table 8) were determined. Regardless of which of the smaller is the best, nominal is the best, and larger is the best approaches are used to evaluate the experimental results, in calculating the S/N ratio, as the value of the calculated S/N ratio gets higher, its effect on the test result increases. For belt surface temperature deviation minimization, with the respect to the criteria smaller is the best, and the best combination of factors is A3B3C3. For belt surface velocity deviation minimization, with the respect to the criteria smaller is the best, and the best combination of factors is A1B1C3.
Variance analyzes of the parameters were performed using the S/N ratios obtained from the experimental results (Table 9, Table 10). In Table 9 and Table 10 Param. is for parameter, DOF is for degree of freedom, SS is for sum of squares, MS is for mean of squares and Cont. is for contribution.
The purpose of analysis of variance is to determine to what extent the examined variables affect the targeted values and how different levels cause variability, and at the same time to test the statistical reliability of the results obtained. The F values calculated in the analysis of variance were compared with the values taken from the F value table for \({F}_{\text{0.05,2},6}\) and it was seen that 95% confidence level was provided. A3B3C3 variance is chosen for product verification.
Table 9
Analysis of variance table for heat distribution
Param.
|
DOF
|
SS
|
MS
|
Cont. %
|
F
|
|
2
|
16348
|
8174
|
66%
|
1528
|
B
|
2
|
4217
|
2108
|
17%
|
394
|
C
|
2
|
4156
|
2078
|
17%
|
388
|
Err.
|
2
|
11
|
5
|
0%
|
|
Ttl.
|
8
|
24732
|
|
100%
|
|
Table 10
Analysis of variance table for vel. distribution
Param.
|
DOF
|
SS
|
MS
|
Cont. %
|
F
|
A
|
2
|
11.1
|
5.6
|
4%
|
10.2
|
B
|
2
|
50.7
|
25.3
|
20%
|
46.5
|
C
|
2
|
194.5
|
97.3
|
76%
|
178.6
|
Err.
|
2
|
1.1
|
0.5
|
0%
|
|
Ttl.
|
8
|
257,4
|
|
100%
|
|