NUMERICAL INVESTIGATIONS ON FLOW STRUCTURE AND HEAT TRANSFER IN A SQUARE DUCT EQUIPPED WITH DOUBLE V- ORIFICE

Numerical predictions on heat transfer characteristic, flow topology and thermal performance assessment in a square duct are presented. The passive technique, insertion of the vortex generator, is opted to develop the heat transfer rate in the square duct heat exchanger. The vortex generator of the present research is Double V-Orifice (DVO). The square duct equipped with DVO is tested with various parameters. The influences of DVO height, b, to the duct height, H, or b/H, gap spacing between the outer edge of the orifice and the duct wall, s, to the duct height or s/H and flow directions (tip-pointing-Downstream and tip-pointing-Upstream) on flow pattern and heat transfer profile are considered for laminar flow regime with similar pitch, P, to duct height or P/H of 1. The Reynolds number, Re, based on the hydraulic diameter, Dh, of the square duct around 100 – 2000 is discussed. The numerical model is solved with the commercial software (finite volume method). As the numerical result, the square duct inserted with the DVO offers greater Nusselt number, Nu, than the plain duct around 1.00 – 14.80 times. The maximum thermal enhancement factor, TEF, for the square duct inserted with the DVO is found to be about 3.60 depended on s/H, b/H and flow direction. The flow and heat transfer profiles in the square duct inserted with the DVO are also illustrated.


INTRODUCTION 1
The ability of heat transfer for heat exchanger devices or heat transfer system for many industries had been improved by many researchers. The researchers bring the passive technique to expand the efficiency and heat transfer rate of the heat exchanger systems. The passive method can remain the operation cost of the thermal process. The passive method has high potentiality to enhance heat transfer rate in the heat exchanger devices. The passive method is the insertion of the vortex generator in the thermal system to produce vortex flow or swirling flow. Various kinds of vortex generator or turbulator had been opted to develop the thermal process. The selection of the vortex generator depends on the application of the heat exchanger device and heat transfer process.
As the literature reviews, the advantages of the conical ring (Nakhchi and Esfahani (2019a), Nakhchi and Esfahani (2019b), Ibrahim et al. (2019), Mohammed (2019), Bahiraei et al. (2020c, d)) and baffle , , Wang et al. (2019), Liu et al. (2019), , Li et al. (2019), , Chai et al. (2018), Chai et al. (2019), Ahmed et al. (2019), Boonloi and Jedsadaratanachai (2019c)) or rib (Ameur and Menni (2019), Karami et al. (2019), Cao et al. (2019), Chen et al. (2019), Arani and Moradi (2019), Bahiraei et al. (2020a)) are focused. The prominent point of the conical ring is the convenience for the installation and maintenance, while the rib and baffle give high heat transfer rate, especially, V-shape and wavy configuration. The combination of the vortex generator between the conical ring and the baffle likes "orifice" (Boonloi and Jedsadaratanachai (2019a, b)) is opted to grow the heat transfer ability of the heat transfer process for the square duct heat exchanger. The * Corresponding author. Email: kjwithad@kmitl.ac.th Double V-shape is selected for the orifice due to the Double V-shaped configuration of the rib and baffle has high performance to improve heat transfer rate. The new kind of the vortex generator is called "Double V-orifice" or DVO. The DVO may enhance heat transfer rate and thermal performance nearly as the V-rib or V-baffle, while the structure of the DVO has more stable than the other types of the vortex generators. The installation method of the DVO in the duct is also convenient as the installation of the conical ring and twisted tape (Bahiraei et al. (2020a)).
The investigation methods for the heat exchanger improvement include numerical and experimental studies. The credibility of the experimental result is higher than the numerical result. However, the spending of the experimental test is also higher than the numerical study. The experimental examination also spends time and human resource higher than the numerical study. For the present research, the numerical investigation is opted to predict the mechanisms in the heat exchanger. For the pre-process, the numerical model is validated to increase the reliance of the numerical result. The numerical result can help to state the mechanisms of flow and heat transfer patterns in the test section. The knowledge of the heat transfer mechanism is significant factor to develop the heat transfer rate of the heat exchanger.

MATHEMATICAL FOUNDATION, BOUNDARY CONDITION, ASSUMPTION AND NUMERICAL METHOD
The forced convective heat transfer in the square duct inserted with the DVO is discussed. The unforced convection and radiation heat transfer in the square duct inserted with the DVO are disregarded. The air with the temperature around 300K and Prandtl number of 0.707 is opted as the tested fluid. The tested fluid is agreed as incompressible flow because of the low velocity. Due to the variation of the fluid temperature is not higher than 10 o C, the thermal properties of the fluid are approved as constant values. The body force and viscous dissipation are ignored. The no slip wall condition is applied for all surfaces of the square duct inserted with the DVO. The fluid flow and heat transfer in the square duct inserted with the DVO are counted to be steady in three dimensions. The Reynolds number based on the hydraulic diameter of the square duct in the range 100 -2000 is analyzed. The periodic condition (Patankar et al. (1977)) on flow and heat transfer is adopted for the entrance and exit regions of the computational domain. The constant temperature around 310K is applied for the duct walls. The constant heat flux around 0 W/m 2 is adopted for the DVO.
The numerical model of the square duct inserted with the DVO is simulated by the commercial software (FLUENT). The major equations for the simulation procedure of the square duct inserted with the DVO are continuity, Navier-Stokes and energy equations as Equations 1, 2 and 3, respectively. In the simulation process, the continuity and momentum equations are discretized by the power law scheme, while the energy equation is discretized with QUICK scheme. The numerical solutions are evaluated to be converged when the normalized residual values are less than 10 -5 for all variables, but less than 10 -9 only for the energy equation.
where,  is the thermal diffusivity and is written as follows: (4) The dimensionless variable of the fluid velocity in the square duct inserted with the DVO is Reynolds number. The Reynolds number is computed as Equation 5.
The pressure loss of the square duct inserted with the DVO is also concluded with the dimensionless variable, friction factor. The friction factor can be calculated from Equation 6.
The ability of heat transfer in the square duct inserted with the DVO is summarized by local Nusselt number and average Nusselt number (Promvonge et al. (2010)) as Equations 7 and 8, respectively.
The thermal enhancement factor or TEF (Promvonge et al. (2010)) of the square duct inserted with the DVO is considered at similar pumping power as Equation 9. The TEF is defined as the ratio between the heat transfer coefficient of the square duct inserted with the DVO, h, and the heat transfer coefficient of the plain duct, h0.
The subscript zero means the value of the plain duct.

NUMERICAL VALIDATION
The numerical validation is an important process for the numerical investigation. The model validation helps to increase the reliance of the numerical result. The validations of the computational domain for the square duct inserted with the DVO consist 1. Plain duct validation and 2. Grid independence. For the plain duct validation, the comparison between the numerical results with the results from the correlations (Cengel and Ghajar (2015)) is conducted. The deviations between the present results and the values from the correlations both Nusselt number and friction factor are not higher than ±10%. The plain duct validations of the present work are depicted as Fig. 3. The purpose for the grid check is to find appropriate number of grid cell. The suitable grid cell can help to conserve computational resource and time for simulation. For the smooth duct, the variation of grid cells in the range 80000 -310000 has no effect for both Nusselt number and friction factor for all Reynolds numbers. The models of the square duct inserted with the DVO with various grid cells; 100000, 160000, 210000, 260000 and 310000, are compared. The heat transfer and pressure loss in the square duct inserted with the DVO for the B20S0D are checked. The trends of the Nusselt number and friction factor for the square duct inserted with the DVO with grid cell around 160000 differs from the trends of the numerical model with grid cell higher than 160000 around ±3%, as Fig. 4. From the pre-result, the grid cell around 160000 is opted for all cases of the computational domain for the square duct inserted with the DVO.

Flow structure
The flow description in the square duct inserted with the DVO is stated in this section. The streamline plot in transverse planes is created to check the generation of the vortex flow in the square duct inserted with the DVO. The streamline plot in transverse planes of the square duct inserted with the DVO is reported as Figs. 5 and 6 for V-Downstream and V-Upstream arrangements, respectively. In all planes, the vortex flow, which is built by the DVO, is seen. The general configuration of the vortex flow includes four main vortex cores and small vortices at the corners of the square duct. The symmetry structure of the flow at the left-right parts and upper-lower parts is seen due to the symmetry shape of the DVO. Seeing at the lower pair of the vortex core, the V-Downstream direction produces the counter-rotating flow with common-flow-down, while the V-Upstream direction forms the counter-rotating flow with common-flow-up. The main flow pattern in the square duct inserted with the DVO slightly change when changing the s/H value. The vortex flow affects for the variation of the boundary layer in the square duct inserted with the DVO. The thermal boundary layer in the square duct inserted with the DVO is annoyed by the vortex flow. Moreover, the vortex flow in the square duct inserted with the DVO affects for the fluid temperature distribution. The turbulent fluid mixing always found when installed the vortex generator in the heat exchanger device. The temperature distribution and thermal boundary layer change in the square duct inserted with the DVO can be seen in the next part, heat transfer profile.
The vortex core of the square duct inserted with the DVO slightly differ when varied the b/H values. The size of the vortices at the corner of the square duct inserted with the DVO obviously increases when augmenting s/H values, especially, at s/H > 0.05.
The small vortices at the corner of the square duct inserted with the DVO have opposite rotation from the main flow. The improvement of the vortices size may affect for the reduction of the main vortex strength and the variation of the local heat transfer coefficient on the duct wall. The differentiation of the flow profile in the square duct inserted with the DVO influences for the increment or decrease of the heat transfer rate and pressure loss.

Heat transfer profile
The variations of fluid temperature, thermal boundary layer and local Nusselt number of the square duct inserted with the DVO are considered in this part. The fluid temperature distribution in y-z plane for the square duct inserted with the DVO is plotted as Figs. 8 and 9 for V-Downstream and V-Upstream cases, respectively, at Re = 600. The disruption of the thermal boundary layer in the square duct inserted with the DVO is detected along the heating duct for all examined cases. The disturbance layer can be considered by the thickness of the red contour. The high heat transfer rate is found in all walls of the square duct inserted with the DVO, while the four corners of the square duct are detected in reverse trend.

CONCLUSION
The flow and heat transfer mechanisms in the square duct inserted with the DVO with various s/H, b/H and Re values are numerically studied. The effect of s/H and b/H on flow and heat transfer for the square duct inserted with the DVO are analyzed for the Reynolds number around 100 -2000. The outcomes from the present investigation can conclude as follows; The DVO in the square duct heat exchanger can produce the vortex flow through the test section in all cases. The vortex flow disturbs the thermal boundary layer that the cause for heat transfer and performance developments. The vortex flow in the heat exchanger duct also helps a better fluid mixing.
The maximum heat transfer rate of the heat exchanger square duct inserted with the DVO is about 14.80 times above the plain duct, while the optimal thermal enhancement factor is found to be about 3.60.
For suggestion, the gap spacing between the outer edges of the DVO and the square duct should be around 0 -10% when considered the TEF value.
The installation, manufacturing and maintenance of the heat exchanger square duct inserted with the DVO are more stable and convenience than the rib or baffle type vortex generator. The heat exchanger square duct inserted the DVO gives closely value of thermal enhancement factor when compared with rib and baffle vortex generators (Jedsadaratanachai et al. (2015), Jedsadaratanachai and Boonloi (2014), Jedsadaratanachai et al. (2011), Promvonge et al. (2012, Promvonge et al. (2010)).