This paper presents a 3D numerical analysis of fully developed periodic laminar flow in a circular tube fitted with 45° inclined baffles with inline arrangement. The computations are based on a finite volume method, and the SIMPLE algorithm has been implemented. The characteristics of fluid flow are presented for Reynolds number, Re = 100–1000, based on the hydraulic diameter (

The studies of fluid flow structure and heat transfer behavior are among the most important in the design of heat exchangers in applied engineering works. Many works studied flow structure and heat transfer by using turbulators, ribs fins grooves, or baffles. It is a matter of concern that the enhancement of heat transfer rate depends on effect of turbulators that can change flow structure and behavior in the tested section.

Sripattanapipat and Promvonge [

Li and Braun [

The concept of periodically fully developed flow was widely used. However, most investigations studied only effects of turbulators and their parameters. Therefore, the study on developing of periodic flow structure concept has rarely been reported. In this present work, the numerical computations for three-dimensional laminar periodic channel flows over a 45° inclined baffle are conducted to examine the changes in the flow structure and a way to develop to fully developed periodic flow profile.

The system of interest is a horizontal circular tube with inclined baffles which are repeatedly inserted at the middle of the test tube as shown in Figure

(a) Circular tube geometry with 45° inclined baffle inserted (b) baffled tube details, and (c) computational domain.

For baffled circular tube, a uniform air velocity is introduced at the inlet while a pressure outlet condition is applied at the exit. The physical properties of the air have been assumed to be constant at mean bulk temperature. Impermeable boundary and no-slip wall conditions have been implemented over the tube walls as well as the baffle.

The numerical model for fluid flow in a circular tube was developed under the following assumptions.

Steady, three-dimensional, laminar, and incompressible fluid flows.

Constant fluid properties.

Ignoring body forces.

Based on the above assumptions, the tube flow is governed by the continuity and the Navier-Stokes equations. In the Cartesian tensor system, these equations can be written as follows.

Continuity equation:

Momentum equation:

Apart from the energy equation discretized by the QUICK scheme, the governing equations were discretized by the power law scheme, decoupling with the SIMPLE algorithm and solved using a finite volume approach [^{−5} for all variables.

The Reynolds number is defined as

The friction factor,

The variation in

The results of 45° inclined baffle with inline arrangement in circular tested tube are expressed in six parts, such as validation, fully developed periodic concept, effect of transverse plane position, flow structure, effect of Reynolds number, and effect of blockage ratio.

Verification for the friction factor of the smooth circular tube with no baffle is initially performed by a comparison with the values from previous correlations under a similar operating condition as shown in Figure

Verification of friction factor for smooth circular tube with no baffle.

Understanding of a fully developed periodic profile condition in the baffled tube is needed before discussing the results. The fully developed periodic flow conditions in the tube mounted repeatedly with inline 45° inclined baffles can be displayed by considering the axial _{0} distribution as depicted in Figures _{0} distributions of a baffled test tube are presented at different transverse plane positions as Figure

Velocity profile at

Velocity profile at

The profile of velocity is explained into 2 forms. First, the velocity profile that structures similarity to other modules but the values are not equal as shown in Figures

The effect of transverse plane position is expressed into 2 axes, such as

Figure _{0} profiles along the baffled tube with BR = 0.2 and Re = 600 at location _{0} profiles for all cases become periodic at the 2nd module and tend to increase to a fully developed periodic flow at about the 6th-7th module or at _{0} profile at the location

Figure _{
0} for _{0} profiles for different

Therefore, the concept of fully developed periodic flow profile can be applied efficiently to laminar tube flow through baffles if the test tube is sufficiently long (_{0} value is not much different for both the periodic regions. Further, with considering both convergent time and solution precision, only a fully developed periodic flow tube model is employed in the computation.

The flow structure in the tube repeatedly mounted with the inline 45° inclined baffles can be displayed by considering the streamline in transverse planes for Re = 600 and BR = 0.20 as shown in Figures

Streamline in transverse plane for BR = 0.20 at Re = 600.

Streamline in transverse planes m1 to m8 for BR = 0.20 at Re = 600.

Streamline in transverse plane for a module at BR = 0.20 at Re = 600.

Streamline in transverse planes A1 to A5 for a module at BR = 0.20 at Re = 600.

The concept of fully developed periodic flow profile is shown in Figures

The change of flow structure in fully developed periodic flow profile (Figure

The effect or Re is described by considering _{0} profile versus

Velocity profile at

The effect of BR can be displayed by considering the velocity profile, _{
i}/_{0}, as depicted in Figures

Velocity profile at

In Figure _{0} profile shows periodic profile at _{0} profile provides periodic profile at _{0} profile shows periodic profile and fully developed periodic flow profile at

In Figures _{0} profile presents periodic at _{0} and _{0} develop into fully developed periodic flow profile slightly faster than

3D laminar fully developed periodic flow characteristics in a circular test tube mounted repeatedly with inline 45° inclined baffles inserted in the middle of the test tube for 14 modules are numerically investigated.

The baffled tube flow shows periodic flow profile at

Thus, the fully developed periodic flow structure and behavior concept in tested tube at BR ≥ 0.15, PR = 1, and Re = 100–1000 are recommended for use instead of the full tube and all of systems in order to save more resources and time in numerical investigation. In case of BR ≤ 0.10, the fully developed periodic flow profile concept may be used for PR < 1 and the tested section is higher than 14 modules.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to gratefully thank the King Mongkut’s Institute of Technology Ladkrabang (KMITL) for the financial support of the research.