Numerical Study on Flow and Heat Transfer Mechanisms in the Heat Exchanger Channel with V-Orifice at Various Blockage Ratios , Gap Spacing Ratios , and Flow Directions

Numerical assessments in the square channel heat exchanger installed with various parameters of V-orifices are presented. ,e V-orifice is installed in the heat exchanger channel with gap spacing between the upper-lower edges of the orifice and the channel wall. ,e purposes of the design are to reduce the pressure loss, increase the vortex strength, and increase the turbulent mixing of the flow. ,e influence of the blockage ratio and V-orifice arrangement is investigated. ,e blockage ratio, b/H, of the V-orifice is varied in the range 0.05–0.30. ,e V-tip of the V-orifice pointing downstream (V-downstream) is compared with the V-tip pointing upstream (V-upstream) by both flow and heat transfer. ,e numerical results are reported in terms of flow visualization and heat transfer pattern in the test section.,e thermal performance assessments in terms of Nusselt number, friction factor, and thermal enhancement factor are also concluded. ,e numerical results reveal that the maximum heat transfer enhancement is found to be around 26.13 times higher than the smooth channel, while the optimum TEF is around 3.2.,e suggested gap spacing for the present configuration of the V-orifice channel is around 5–10%.


Introduction
e development method for the various types of the heat exchanger has been widely reported by many researchers.
e development method for the heat exchanger can be separated into two ways: (1) passive method and (2) active method.e active method is to add the external power such as vibration, to increase the heat transfer rate and efficiency.erefore, the use of the active method must consider on both the additional power cost and the benefit of the system.e passive method is to generate the vortex flow or swirling flow and to disturb the thermal boundary layer by installed with vortex generator or turbulators such as baffle, rib, winglet, wing, etc., in the heating system.e improvement of the thermal performance for the heat exchanger with passive method is widely selected because this method does not consider the additional power cost of the system.e investigations of the thermal performance augmentation in the heat exchanger are divided into two methods: (1) numerical method and (2) experimental method.
e experimental method gives high reliability result, but the operation cost is more expensive than the numerical study.e numerical investigation can help to describe the mechanisms in the system that is an important knowledge to design and improve the thermal performance of the heating system.However, the researchers must sure that the computational model has more reliability to predict the flow and heat transfer in the channel when studied with numerical method.
e selection of the vortex generator type depends on the application of the heat exchanger.e baffle and rib always select to enhance heat transfer rate and performance in the channel or tube heat exchanger [1][2][3][4][5].e baffle and rib give high heat transfer rate and thermal efficiency when compared with the other types of the generators, especially, V-shaped rib/baffle [6][7][8][9][10][11][12][13][14][15].However, it is found that the installation of the V-rib is quite difficult.e V-rib in the heat section had been modified to help to support the installation and maintenance, while the benefit of the V-rib nearly remains the general type.e structure of the V-rib is developed like as orifice plate when considered at the projected view [16].e researchers found that the modified V-rib can enhance the heat transfer rate nearly as the V-rib, but the pressure loss of the system is extremely found.
In the present work, the orifice is modified like V-baffle (called "V-orifice") and inserted in the square channel heat exchanger.e purpose for the insertion of the V-orifice is to generate the vortex flow through the test section.e vortex flow will disturb the thermal boundary layer on the heat transfer surface causing heat transfer rate and thermal performance enhancements.e installation of the V-orifice in the channel is designed with gap spacing between edges of the orifice and the channel walls.e optimum gap spacing may increase the turbulent mixing, help to distribute the fluid temperature, and also reduce the pressure loss in the tested channel.e numerical investigation is selected to solve the current problem.
e numerical study helps to describe the mechanisms in the heating channel that is an important knowledge to develop the thermal performance of the heat exchanger.e flow visualization and heat transfer behavior in the test channel are shown.e thermal analysis for the present problem is also concluded.

Physical Domain of the Square
Channel with V-Orifice e V-orifices are inserted in the square channel heat exchanger as shown in Figure 1. e square channel height, H, is set around 0.05 m. e orifice height (projected view) is represented with "b." e ratio between orifice height and the channel height, b/H, is called blockage ratio.e blockage ratio is varied in the range around 0.05-0.30.e gap spacing between the edges of the orifice and the channel walls is represented with "g." e ratio between gap spacing and channel height, g/H, is known as the gap spacing ratio.
e gap spacing ratio is varied in the range around 0-0.35.e laminar flow regime (inlet condition) with the Reynolds number around 100-2000 is considered for the present investigation."P" is the distance between the V-orifice.e P/H or pitch spacing ratio is fixed at 1. e flow attack angle for the V-orifice is set around 30 °for all examples.e V-tip arrangement of the V-orifice is divided into two directions: V-tip pointing downstream (V-downstream) and V-tip pointing upstream (V-upstream).e investigated cases and code are concluded as Table 1.

Assumption
e numerical model of the heat exchanger square channel inserted with V-orifice is developed with the following assumptions: (1) e test fluid is air with 300 K (Pr � 0.707) (2) e flow and heat transfer is steady in three dimensions (3) e flow is incompressible (4) Laminar flow regime is measured (5) e convective heat transfer is considered for the present work, while natural convection and radiation heat transfer are ignored (6) e body force and viscous dissipation are disregarded (7) e properties of the air assume to be constant at the average bulk mean temperature (8) No slip wall condition is applied for all surfaces (9) e uniform temperature of the channel walls is maintained around 310 K (10) e V-orifice plate assumes to be an insulator

Boundary Condition and Initial Condition
e boundary condition and initial condition for the numerical model of the square channel inserted with the V-orifice are given in Table 2.

Mathematical Foundation and Numerical Method
e numerical problem is answered by the finite volume method (SIMPLE algorithm).e tested channel is governed by the continuity, the Navier-Stokes equations, and the energy equation as equations ( 1)-(3), respectively.Continuity equation: Momentum equation: Energy equation: where Γ is the thermal diffusivity and is written as e continuity and momentum equations are discretized by the power law scheme, while the energy equation is discretized by QUICK scheme.e solutions are determined 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.
e velocity of the flow is presented in terms of the Reynolds number as equation (5).e pressure loss of the tested section is shown with the friction factor (equation ( 6)), while the heat transfer rate is concluded with the local Nusselt number and average Nusselt number (equations ( 7) Modelling and Simulation in Engineering and ( 8)). e thermal performance of the heating system is summarized with the thermal enhancement factor as follows: Re where D h is hydraulic diameter of the square channel heat exchanger.
e thermal enhancement factor (TEF) is de ned as the ratio of the heat transfer coe cient of an augmented surface, h, to that of a smooth surface, h 0 , at similar pumping power.
Nu 0 and f 0 are the Nusselt number and friction factor for the smooth square channel, respectively.

Validation of the Computational Domain
e numerical validation is an important part for the numerical simulation.e validation result can con rm the reliability of the numerical result.e validation of the numerical model for the square channel inserted with V-ori ce can be divided into two parts: (1) grid independence and (2) veri cations with the smooth channel for the Nusselt number and friction factor.
b15g15 of the numerical model is selected to check the grid independence.e hexahedral mesh with nonuniformity is applied for all investigated cases.e di erent numbers of grid, 120000, 240000, 360000, 440000, and 600000, are applied for the numerical model.It is found that the increment of cells from 240000 to 360000 has no e ect for both Nusselt number and friction loss.e deviations for both values are found to be around ±0.2%.erefore, the grid cell around 240000 is created for all investigated cases when considered by both time for investigation and accuracy result.e veri cations of the smooth channel with no ori ce for heat transfer and pressure loss are plotted as Figure 2. e results from the present prediction are compared with the results from the correlations [17].e heat transfer rate is presented with the Nusselt number, Nu 0 , while the pressure loss is o ered in term of friction factor, f 0 .As the gure, the deviations of the Nusselt number and friction factor are around ±2.4% and ±3.0%, respectively.
As the results above, it can be concluded that the creation domain has enough reliability to predict ow and heat transfer mechanisms in the heat exchanger square channel inserted with V-ori ce.

In uence of Blockage Ratio and Gap Spacing Ratio.
e ow con gurations in the heat exchanger channel tted with various parameters of the V-ori ce are presented by streamline in transverse planes and longitudinal vortex ow through the test section.e streamline in transverse planes at x/D 0.5 in the square channel with V-ori ce is depicted as Figure 3 for V-downstream arrangement.It is found that the V-ori ce can generate the vortex ow in all investigated cases.In general, the four main vortex ows are detected.
e symmetry ow for left-right parts and upper-lower parts is found due to the symmetry con guration of the V-ori ce.
e small vortices at four corners of the channel are also detected in all cases.e vortex core has change depended on the position in the test section, blockage ratio, and gap spacing ratio.e vortex ow in the test section helps to improve the uid mixing and the distribution of the uid temperature between core of the channel and near the channel walls.
e vortex ow also disturbs the thermal boundary layer on the heat transfer surface.ese behaviors are causes for heat transfer and thermal performance augmentations.e strength of the vortex ow directly a ects the enhancement of the heat transfer rate and thermal performance.
Figures 4(a) and 4(b) report the longitudinal vortex ow of the square channel heat exchanger tted with V-ori ce at Re 600 and V-downstream arrangement for b15g0 (no gap) and b15g15 (with gap), respectively.e longitudinal vortex ow is found through the test section on both cases.e ow con guration is found to be in nearly pattern.Some parts of the air ow pass the gap between the ori ce and the  local Nusselt number on the heat transfer surface.Figure 5 illustrates the temperature distributions in transverse planes for the square duct inserted with V-ori ce at various ow blockage ratios and gap spacing ratios.In general, the low temperature of the uid (blue layer) is detected at core of the square channel, while the high uid temperature (red layer) is found near the channel walls for the smooth channel with no ori ce. e insertion of the V-ori ce in the channel changes the heat transfer behavior.e thermal boundary layer near the channel walls is disturbed by the vortex ow, which is generated by the V-ori ce in all cases.e red layer near the channel walls is found to be thinner, while the blue layer distributes from the center of the channel.
e local Nusselt number for the heat exchanger square channel placed with V-ori ce at various cases is plotted as Figure 6 for V-downstream arrangement.e increment of the ow blockage ratio of the V-ori ce performs higher heat transfer rate in all gap spacing ratios.e worst heat transfer area is clearly found at behind the V-ori ce when g/H 0 (no gap).
e gap spacing ratio helps to increase heat transfer rate, especially, at behind the V-ori ce, but the strength of the vortex ow seems to be decrease at high gap spacing ratio.

In uence of Flow Direction.
e in uences of the V-tip arrangement for the V-ori ce in the heat exchanger channel are presented by both ow con guration and heat transfer characteristic.
e streamline in transverse plane in the square channel placed with V-ori ce at various blockage ratios, gap spacing ratios, and arrangement is shown in Figure 7. e four to eight main vortex ows is detected in all cases.e augmentation on the number of the vortex core helps to distribute the temperature of the uid ow in the test section, but the strength of the vortex ow may decrease.e di erent arrangement of the V-ori ce directly a ects the rotational direction of the vortex ow. e V-downstream arrangement gives the opposite rotation of the vortex ow when compared with the V-upstream arrangement.
Figures 8(a) and 8(b) report the longitudinal vortex ow of the square channel inserted with V-ori ce for V-downstream and V-upstream arrangements, respectively.e longitudinal vortex ow is found through the test section on both examples.Some parts of the air ows pass the gap between the channel wall and the edges of the V-ori ce. is behavior may help to enhance the turbulent mixing of the air ow and also reduce the pressure drop across the test section.
e heat transfer behaviors in the heat exchanger channel tted with the V-ori ce are plotted in forms of the temperature distribution in transverse planes and the local Nusselt number distribution on the heat transfer surface as depicted in Figures 9 and 10 installation of the V-orifice in the heat exchanger channel has an effect for the change of the temperature distribution and thermal boundary layer.e better mixing of the fluid flow is found, while the thermal boundary layer is disturbed.e perturbation of the thermal boundary layer on each side of the heat transfer surface is not similar when the arrangement of the V-orifice is changed.e severe disturbance of the thermal boundary is found at the upper-lower sides of the channel for the V-downstream arrangement, while it is detected at the left-right sidewalls of the channel in the case of the V-upstream arrangement.erefore, the peak of heat transfer rate is found at the upper-lower walls of the channel for the V-Downstream arrangement, while it is detected at the left-right sidewalls of the channel for the V-upstream arrangement (Figure 10).

Performance Analysis.
e performance assessments in the heat exchanger square channel placed with the V-orifice are shown in terms of the Nusselt number ratio (Nu/Nu 0 ), friction factor ratio (f/f 0 ), and thermal enhancement factor (TEF).
e relations of the Nu/Nu 0 with the Reynolds number for the square channel heat exchanger inserted with the V-orifice are depicted in Figures 11(a)-11(f ), respectively, for b5, b10, b15, b20, b25, and b30 at V-downstream arrangement.In general, the heat transfer coefficient increases when enhancing the Reynolds number for all examples.
Figure 12 presents the relations of Nu/Nu 0 with the Reynolds number for the heat exchanger channel inserted with the V-orifice at V-tip pointing upstream.e similar trend as the V-downstream arrangement is detected; the heat transfer rate increases when increasing the Reynolds number.At b05, the peak of heat transfer rate is found at g/H around 15-20%.
e pressure loss in the heat exchanger channel is presented with the friction factor values. e variation of the friction factor ratio for the channel fitted with various parameters of the V-downstream orifice is illustrated in

Modelling and Simulation in Engineering
Re 2000 and 100, respectively.e presence of the V-ori ce in the heat exchanger channel not only increases in heat transfer rate but also increases in the pressure loss.e friction loss of the channel with V-ori ce is higher than the smooth channel in all studied cases (f/f 0 > 1).e peak of friction loss is found at g20 and g10 for b05 and b10, respectively, while found at g0 when b/H > 0.1.f/f 0 is around 1.00-9.12,1.90-19.65,3.64-51.41,6.28-153.22,9.93-444.14, and 18.68-1309.53,respectively, for b05, b10, b15, b20, b25, and b30.e similar trend of f/f 0 is found in the case of V-upstream arrangement as depicted in Figure 14.g15 and g5 of b05 and b10, respectively, perform the maximum heat transfer rate when compared at similar blockage ratio.When b/H > 10%, g/H 0 brings the uppermost friction loss at similar  Because the installation of the V-ori ce in the heat exchanger channel increases both heat transfer rate and friction loss, the thermal enhancement factor is measured for the present investigation to check the advantage of the V-ori ce in the heat exchanger channel.Figures 15(a)-15(f ) show the relation of the TEF with the Reynolds number at various cases of V-downstream ori ce at b05, b10, b15, b20, b25, and b30, respectively.Almost in all cases, the insertion of the V-ori ce in the heat exchanger channel can improve the thermal performance higher than the smooth channel (TEF > 1).
e TEF tends to increase when raising the     e nearly pattern of the TEF is found in the case of V-upstream arrangement as illustrated in Figure 16.At Re 2000 and similar blockage ratio, g35, g05, g0, g20, g15, and g05 lead to the highest TEF at b05, b10, b15, b20, b25, and b30, respectively, around 2.60, 3.00, 2.85, 2.55, 2.45, and 2.60.Modelling and Simulation in Engineering

Conclusion
Convective heat transfer, ow visualization, and thermal performance assessment in the square channel heat exchanger installed with various parameters of the V-ori ce are performed.e in uences of the blockage ratio, gap spacing ratio and ow direction on heat transfer, and ow structure are considered for the laminar regime, Re 100-2000.
e numerical method is selected to solve the numerical problem.
e major outcomes from the present investigation can be concluded as follows.
e V-ori ce can generate the vortex ow through the test section in all examples.e vortex ow is a key to enhance heat transfer rate and thermal performance.e vortex ow helps to improve the uid mixing between core of the channel and near the channel walls.e vortex ow also disturbs the thermal boundary layer on the heat transfer surface.
e vortex strength increases when enhancing the blockage ratio.
e gap spacing between the edges of the ori ce and the channel walls can help to reduce the pressure loss in the test section and also augments the turbulent mixing.
e arrangement of the V-ori ce a ects the variation of heat transfer regime.e V-downstream arrangement provided the peak of heat transfer regime at the upper-lower parts of the channel, while the V-upstream arrangement gives the highest heat transfer region at the left-right sidewalls.
e suggestion of the optimum gap spacing ratio is around 5-10%, which generates the best thermal performance, while the vortex strength lightly decreases when compared with no gap (g 0).

Figure 1 :
Figure 1: (a) Computational domain of the square channel heat exchanger installed with V-ori ce.Numerical model in transverse plane (b) and with mesh (c).

Figure 2 :Figure 3 :
Figure 2: Validation of the smooth channel on Nusselt number and friction factor.

Figure 4 :Figure 5 :
Figure 4: Longitudinal vortex ow for the square channel heat exchanger installed with V-ori ce at (a) b15g0 and (b) b15g10 for Re 800 and V-downstream arrangement.

Figure 6 :Figure 7 :Figure 8
Figure6: Local Nusselt number distribution on the channel walls for the square channel heat exchanger installed with V-orifice at various blockage ratios and gap spacing ratios for Re � 800 and Vdownstream arrangement.

Figure 8 : 15 b 15 Figure 9 :Figure 10 :b 10 g 0 b 10 g 05 b 10 g 10 b 10 g 15 b 10 g 20 b 10 g 25 b 10 Figure 11 :
Figure 8: Longitudinal vortex ow for the square channel heat exchanger installed with V-ori ce at (a) V-downstream and (b) V-upstream for b15g15 and Re 600.

Table 2 :
Boundary condition and initial condition.