Determination Of Turbulence Model

Results of analyses, which were performed under indicated conditions with Standard, k- RNG, k- Realizable, k- Standard and Spallart-Almaras turbulence models can be seen in Table 4.13.

Table 4.13. Results obtained from experiment and analyses with different turbulence

Results of the analyses were compared with the experimental results and it was tried to determine the suitable turbulence model. In order to see the similarity between the experimental and analysis results, comparison graphics were drawn and showed in the following Figures.

Exit Velocities Experiment vs k-Epsion STD

13,00 experimental and analysis with k- Standard turbulence model

Exit Velocities Experiment vs k-Epsion RNG experimental and analysis with k- RNG turbulence model

Exit Velocities Experiment vs k-Epsion Realizable

13,00 experimental and analysis with k- Realizable turbulence model

Exit Velocities Experiment vs Spallart-Almaras experimental and analysis with Spallart-Almaras turbulence model

Exit Velocities Experiment vs k-Omega

13,00 experimental and analysis with k-Ω turbulence model

When the graphics were investigated, it was seen that while k-ε RNG, Realizable and k-Ω turbulence models are not suitable, k-ε Standard and Spallart-Almaras Turbulence models seem suitable for this application. In order to clearly

determine the suitable turbulence model, correlation between experimental and numerical results was investigated my means of Pearson correlation coefficient.

Correlation graphics with calculated correlation coefficients (R²) are shown in Figure 4.18.

As can be seen form the graphics on Figure 4.18, results of all turbulence models are very close to each other, however k-ε Standard Turbulence model with a correlation coefficient of 0,948 seems the most suitable model for this application.

Figure 4.18. Correlation graphics with calculated correlation coefficients (R²)

Also a standard deviation value was calculated for each of the turbulence model with experimental value by taking square root of the average of square of differences of each exit velocity results obtained from experimentally and numerically. The formula employed can be seen as follows;

n

i XNUMERICAL XEXPERIMENTAL

n 1

)2

1 (

Deviations calculated by using the above formula was tabulated in Table 4.14.

Table 4.14. Standard deviations of Turbulence models

Turbulence obtained from Spallart-Almaras turbulence also seems suitable. In order to clarify this situation, a new experimental and numerical study was conducted by dismounting 2 fans, which supply air to 1,2,5 and 6 numbered inlets. In this situation, only 1 fan supplies air to 3 and 4 numbered inlets, was run and the other inlets were closed. And with this new setup exit velocity measurements and inlet velocity calculations were again performed as described previously. Fan configuration can be seen in Figure 4.19.

Figure 4.19. Single fan configuration

Experimental test results for single fan application can be seen in Table 4.15.

Table 4.15. Experimental test results for single fan application

Exit Number Single Fan Measurement 1

A volume flow rate and inlet velocity calculation procedure, which is similar to performed for 3-fan application previously, was conducted for single fan application and inlet velocity boundary condition for this application was determined as 8,2 m/s.

Numerical analyses were performed with a manner previously conducted for 3-fan application. Only cancelled inlet surfaces were defined as “wall” instead of

“Velocity Inlet” boundary condition. And the analyses were again conducted with under same conditions.

Results of analyses, which were performed under indicated conditions with standard, k- RNG, k- Realizable, k- Standard and Spallart-Almaras turbulence models with single fan application can be seen in Table 4.16.

Table 4.16. Results obtained from experiment and analyses with single fan application

Exit Velocity

(m/s) Experiment k-ε STD k-ε RNG k-ε Real Spallart-Almaras k-Ω STD

Exit 1 9,20 9,36 9,51 9,19 9,30 7,69

Exit 2 8,85 9,02 9,39 8,99 9,15 9,04

Exit 3 8,53 8,78 8,95 8,83 8,89 9,68

Exit 4 8,26 8,47 8,90 8,83 8,65 9,90

Exit 5 7,91 8,22 8,06 8,31 7,91 5,24

Exit 6 7,45 7,51 7,77 7,34 7,56 5,77

Exit 7 6,25 6,44 7,31 6,86 6,85 4,80

Exit 8 7,85 7,52 7,41 7,59 6,94 8,64

Exit 9 7,75 7,45 8,04 7,63 7,58 8,82

Exit 10 8,15 7,75 7,84 7,92 7,89 9,02

Exit 11 8,31 8,10 8,40 8,15 8,24 9,10

Exit 12 8,71 8,37 8,52 8,24 8,56 9,65

Exit 13 8,72 8,59 8,71 8,52 8,72 9,90

Exit 14 8,90 8,73 9,07 8,75 8,87 10,16

Results of the analyses were compared with the experimental results and it was tried to determine the suitable turbulence model. In order to see the similarity between the experimental and analysis results, comparison graphics were again drawn and showed in the following Figures.

Exit Velocities Experiment vs k-Epsion STD

Exit Velocities Experim ent vs k-Epsilon RNG

6,00 single fan experimental and analysis with k- RNG turbulence model

Exit Velocities Experiment vs k-Epsilon Realizable single fan experimental and analysis with k- Realizable turbulence model

Exit Velocities Experim ent vs Spallart-Alm aras

6,00 single fan experimental and analysis with Spallart-Almaras turbulence model

Exit Velocities Experiment vs k-Omega STD single fan experimental and analysis with k-Ω Standard turbulence model

As the results and graphics showed above were investigated, it is clearly seen that k-ε Standard turbulence model is the most suitable turbulence model for this application. However, in order to represent this decision on a numerical basis, again correlation coefficients and standard deviations were calculated and presented in the following Figures and Table.

Figure 4.25. Correlation graphics with calculated correlation coefficients (R²)

Table 4.17. Standard deviations of Turbulence models

Turbulence Model Standard Deviation

k-Eps. STD 0,25

k-Eps. RNG 0,44

k-Eps. Real 0,32

Spallart-Almaras 0,35

k-Omega STD 1,35

Since results of k-ε turbulence model provide highest correlation coefficient, lowest standard deviation, most similar flow characteristics and very close exit velocity values to the experimental results, it is proved that, k-ε Standard turbulence model is the most suitable turbulence model for this application.

One of the most widely used turbulence models is the two-equation model of kinetic energy, k, and its dissipation rate ε .This model has been applied by most investigators who studied the numerical solution of airflow in rooms (Awbi and Setrak, 1986, Patankar, 1980).

Consequently, as a result of studies conducted until now, it is decided that numerical analyses can be conducted with a grid having approximately 14 millions of elements and k-ε Standard turbulence model until residuals converges up to 10^-5 level.

4.3. Channel Design Studies

Design of the channel will be conducted with 3 different sections.

In the first section, in order to investigate the effect of main and exit channel diameters on the exit velocity fluctuations, 4 configurations of channels having 2 different main and 2 different exit channel diameters will be investigated.

In the second section, instead of employing a single part main channel, a main channel, separated 2 zones from different points will be used to see the effect of zoning.

In the third section, a new design strategy based on keeping the main channel diameter constant and employing exit channels having different diameters on a single main channel will be discussed.

4.3.1. Effect Of Main And Exit Channels’ Diameters on Exit Velocity