The effects on the positions of rib vortex generators (RVGs) for periodic laminar flow behavior are presented numerically in threedimensional. The RVGs with constant blockage ratio (b/H, BR = 0.15), the pitch ratio (P/H, PR = 1), and flow attack angle (
Due to the relationship between flow configuration and heat transfer, the study for enhancing heat transfer in heat exchanger system leads to the investigation on flow configuration. The use of vortex generators or turbulator, such as rib, baffle, and winglet, is a main aim to change the flow field and also to create the flow separation, secondary flow, and impinging jet flow for heat transfer augmentation. The investigations on flow structure and heat transfer are separated into two methods, experimental and numerical. Owing to the limitation of experimental measurement, high cost materials and more time for study, therefore, the numerical method is advantages for study flow configurations and heat transfer characteristics. However, the investigation with the numerical method needs the high accuracy of mathematical model and condition for calculation.
As the requirements above, the periodic concept on flow configuration is extensively applied in the numerical model to approximate the large heat transfer system that leads to the low cost and saves more time for the simulation. Many investigations use periodic concept to study the flow configuration, heat transfer enhancement, and thermal performance. For example, Sripattanapipat and Promvonge [
The literature reviews for numerical investigation with using periodic concept.
Authors  Studied cases 


TEF 

Jedsadaratanachai et al. [ 
30° inclined baffle 
1.00–9.20  1.00–21.50  3.78 


Kwankaomeng and Promvonge [ 
30° inclined baffle 
1.00–9.23  1.09–45.31  3.10 


Promvonge et al. [ 
30° inclined baffle 
1.20–11.00  2.00–54.00  4.00 


Promvonge and Kwankaomeng, [ 
45° Vbaffle 
1.00–11.00  2.00–90.00  2.75 


Promvonge et al. [ 
45° inclined baffle 
1.50–8.50  2.00–70.00  2.60 


Promvonge et al. [ 
45° Vbaffle 
1.00–21.00  1.10–225.00  3.80 


Boonloi [ 
20° Vbaffle 
1.00–13.00  1.00–52.00  4.20 


Boonloi and Jedsadaratanachai [ 
30° Vbaffle 
1.00–14.49  2.18–313.24  2.44 


Jedsadaratanachai and Boonloi [ 
45° discreteVbaffle 
1.40–8.10  2.50–36.00  2.50 


Jedsadaratanachai and Boonloi [ 
Single twisted tape 
1.00–10.00  3.00–44.00  3.51 
Except from the use of periodic concept to study heat transfer and flow structure, the descriptions of behavior for the periodic flow structure and periodic heat transfer behavior were reported. Jedsadaratanachai et al. [
As the literature above, most investigations studied the effect of blockage ratio, pitch ratio, and Reynolds number on the developing periodic flow and heat transfer behavior. Therefore, the study of the influence on the position of the vortex generators for developing the periodic flow concept has rarely been reported. In this present work, the investigation on the effect of positioning on vortex generators for the periodic flow concept is presented numerically in three dimensional. The different gap ratios,
All of the methodologies for numerical investigation are following [
(a) Square channel with RVG, (b) details of square channel with RVG, (c) computational domain.
The mathematical foundations for the present work are referred from [
steady threedimensional fluid flow,
the flow is laminar and incompressible,
constant air properties,
body forces and viscous dissipation are ignored.
Based on the above assumptions, the relevant equation is the NavierStokes equation. The equations in the tensor notation form are as follows.
Continuity equation:
Momentum equation:
The governing equations were discretized by the power law scheme, decoupling with the SIMPLE algorithm, and solved using a finite volume approach [
The calculations of the two parameters including the Reynolds number, Re, and friction factor,
The friction factor,
The boundary conditions are following [
The validation of the smooth square channel with no RVG for this current investigation is tested by comparing the present prediction with the correlation of the friction factor values at various Reynolds numbers as shown in Figure
Validation of friction factor for smooth square channel.
Figure
The variations of friction factor with Re at various
The flow profiles for RVG at various
Streamlines in transverse planes at various
The periodic flow descriptions are presented in the forms of the streamlines in transverse planes at similar position of each module and the variations of
Streamlines in transverse planes for
For
The streamlines in transverse planes for
Streamlines in transverse planes for
The streamlines in transverse planes for
Streamlines in transverse planes for
Streamlines in transverse planes for
Streamlines in transverse planes for
The two main counterrotating vortex flows that are similar as
In addition, the presentations on this part may be described roughly as flow configuration in the RVG tested channel but cannot identify for the equivalent value of the velocity on the
The variations of
The variations of
The variations of
The variations of
The variations of
The periodic flow profiles appear around the 2nd module (
The similar results as
As seen in Figure
In Figure
The RVG arrangements in
The flow area descriptions.
Case  Upper flow area  Lower flow area  Middle flow area 


0  0  0.70 

0.05  0.05  0.60 

0.10  0.10  0.50 

0.15  0.15  0.40 

0.20  0.20  0.30 

0.25  0.25  0.20 

0.30  0.30  0.10 

0.35  0.35  0 
The flow area descriptions at various
The variations of
The variations of
The variations of
The variations of
The variations of
The numerical investigations on the effects of RVG positions on the periodic flow concept are presented in three dimensional. The 30° RVG insert in the square channel with inline arrangement on both the upper and lower parts. The constants BR = 0.15 and PR = 1.0 with various
The friction factor tends to decrease with the rise of Reynolds number for all cases. In range
The difference of
The visualizations of flow structure in the form of streamlines in transverse planes can describe the flow pattern as two groups: developing flow and periodic flow. The developing flow profiles appear earlier in the tested section when the periodic flow profiles, similar to flow structures, are found after the flow passes around the 6th module.
The numerical results in terms of variations of
In the range studied, the periodic flow profiles appear around the 2nd module and the fully developed periodic flow profiles show around the 6th–9th modules. Close to the RVG regimes and decreasing continuous flow area, the flow profiles perform the speedup of fully developed periodic flow profiles.
The author declares that there is no conflict of interests regarding the publication of this paper.
This research was funded by King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand. The author would like to thank Associate Professor Dr. Pongjet Promvonge and Mr. Jaray Wongpueng for suggestions.