Investigation of Shell Side Overall Performance of a Novel Shell-and-Double-Concentric –tube Heat Exchanger with Simple and Perforated Helical Baffles

In this study, the overall performance of a heat exchanger shell-and-double-concentric-tube with simple and perforated helical baffles is investigated in the shell side of the heat exchanger using ANSYS FLUENT 19.2. A comparison between the shell-side with simple helical baffles of the heat exchanger (SHB-SDCTHEX) and the one with perforated helical baffles (PHB-SDCTHEX) using numerous mass flow rates is carried out. For the perforated helical baffles heat transfer rate 𝑄 , thermo-hydraulic performance 𝑄/∆𝑃 and effectiveness 𝜀 are around 26.7%, 55.5% and 26.6% higher than the same parameters for the simple helical baffles of the heat exchanger, respectively. It is also observed that the flow and temperature distribution for the perforated helical baffles are more uniform with higher flow turbulence than the simple helical


INTRODUCTION
HEs are one of the principal supplies utilized extensively in chemical industry, steam production, and oil refineries.Among all groups of heat exchangers (HE), the shell and tube (S&T) one has had many applications in heat transfer technology [1][2][3][4] and is the most appropriate for higher pressure operations.Many investigations have been engaged to improve S&T HE efficiency and numerous approaches have been adopted for this purpose.One of the most important concerns of the industry has always been increasing heat transfer for various uses, and efforts have been made in this field.For example, the use of porous materials, Induced vibrations, nano-fluids, and nanoparticles in fluid have always been investigated to increase heat transfer in heat exchangers and energy storage systems [5][6][7][8][9][10][11][12][13][14].One of these practical approaches is using various baffles on shell-side to change the flow direction and mix the fluid.So far, researchers have investigated several baffles with diverse formations such as segmental and double segmental baffles [15,16], ring supports [17], helical baffles [18][19][20][21][22][23][24][25][26][27] and rod baffles [28][29][30] using empirical, numerical and analytical approaches.Hosseinzade et al. [31] investigated the effect of two different fins (longitudinaltree like) on energy storage using the phase changer method.Using the analytical method can reveal the possible defects in S&T design, but it cannot identify where these faults are [15].CFD (numerical approach) can conceive the distribution of temperature and fluid flow particularly on the shell-side, which can facilitate estimating the weak points, and so denoting the possible rectifications to be applied for efficiency improvement [15].In addition, economic efficiency, flow field observation, and time expenditure are some privileges of the numerical approach concerning to the empirical approach [32].As a result, several numerical investigations have been accomplished on S&T HE.Bougriou and Baadache [33] researched on SDCTHEX.Difference between the SDCTHEX and classical S&T HE is that the S&T HE tube has been replaced by the double concentric tube.As a result of adding the inner tube, the SDCTHEX has a larger heat transfer area than the S&T HE.Subsequently, increasing the area of heat transfer would make the HE more compact for a specific amount of heat transfer.This causes reducing the cost of manufacturing and the dimensions of the device.Shahril et al. [15] studied the SDCTHEX and S&T HE with segmental baffle and made a comprehensive comparison of both types of the HE.They revealed that a SDCTHEX is equivalent to a S&T HE if the S&T HE is used with two tube passes and one shell, where hot oil flows in the inner tube and shell.In contrast, water flows in the annulus they found that the average of /∆ parameter for SDCTHEX is around 343% higher than that of the S&T HE.They realized that apart from their advantages, using the segmental baffles has also some disadvantages as follows: (1) higher pressure drop in shell-side because of abrupt constriction and distension of flow and severity of flow contact with shell wall and baffles, (2) creation of dead spots in the junction of the segmental baffle and the shell resulting in low heat transfer coefficient, (3) They found that the average of /∆ parameter for SDCTHEX is around 343% higher than that of the S&T HE.In recent years, to crack these weaknesses, rod baffles, deflecting baffles, and disk-anddoughnut baffles have been evolved [1].But, none of these baffles could eliminate the defects listed above.Instead, baffles with helical shapes could be a suitable option to substitute segmental baffles by avoiding the cons cited above [34].
Finding a suitable design in heat exchangers to increase thermal efficiency along with reducing pressure drop has always been the focus of the industry.Therefore, a lot of research has been done on the types of fins and even their arrangement and this research has always continued.Helical fins are one of the types of fins used in shell-tube heat exchangers in order to increase heat transfer.Nevertheless, helical baffles cannot thoroughly flow the fluid uniformly across the shell-side as this issue can cause a low heat transfer coefficient in some spots of the shell-side.In this study, the perforated helical baffle is provided to resolve this issue.It is made by creating orifices on the simple helical baffle to allow the flow to cross through these orifices.This new type of fin, by affecting the amount of fluid flow turbulence, makes the thermal efficiency and performance of perforated fins much higher than its simple state, and the pressure drop of the fluid flow is also lower.This issue can be very important for the construction of shell and tube heat exchangers.Due to the fact that higher efficiency and smaller dimensions with lower pressure drop will be the result of using this type of fin.

DESCRIPTION OF THE SYSTEM
The perspective views of the SHB-SDCTHEX and the PHB-SDCTHEX are depicted in Figure 1.The length of the HE for the shell and tubes is 1270 mm and 1286 mm, respectively.The internal shell diameter is 337 mm with 55 concentric tubes placed inside the shell in a staggered arrangement.For the inner tubes of SHB-SDCTHEX and PHB-SDCTHEX the internal and external diameters are 8 mm and 12 mm, and 20 mm and 24 mm for the outer tubes, respectively.Also, the diameter of the orifices in the perforated helical baffle is 8 mm.The AISI 1042annealed steel is adopted as the material for the baffles and tubes, by density = 7840 kg m 3  ⁄ , specific heat   = 460 J kg.K ⁄ and thermal conductivity  = 50 w m.K ⁄  [20].The thickness and the section angle for both baffles are 5 mm and 20°, respectively.Also, the working fluids are engine oil and water.Engine oil flows inside the shell and the inner tube as the hot fluid, while water flows inside the annulus as the cold fluid.The properties of the working fluids are described in ANSYS FLUENT 19.2 using the piecewise-linear function of temperature and also can be obtained from literature [35].

1. Model Development
The equations of the momentum, continuity, energy, k and ɛ are shown as below.The steady state, incompressible and turbulent flow assumptions are engaged [15]: Continuity equation: Momentum equation: Energy equation: Turbulent kinetic energy k equation:

2. Boundary Conditions and Numerical Approach
Numerical analysis is accomplished by applying CFD software ANSYS FLUENT 19.2.The working fluids for both samples of the HE SHB-SDCTHEX and PHB-SDCTHEX are engine oil and water.The engine oil flows in the shell and the inner tubes with the same   , and water is allocated as working fluid in the annulus.The boundary conditions are explained for the SHB-SDCTHEX and the PHB-SDCTHEX as follows: (1) The shell-side inlet:   = 20 (kg/s),  , = 393 (°k),  , = 68.26(m/). (2) The inner tube side inlet:   = 20 (kg/s),  , = 393 (°k). (3) The annulus side inlet:   = 10.14 (kg/s),  , = 293 (°k).(4) The outlet boundary condition: pressure outlet.(5) Wall boundary conditions: non-slip boundary, the coupled thermal boundary is applied for the wall of the tubes and baffles.Also, adiabatic condition is used for thermal boundary of the shell wall.Pressure-based and double-precision solver is used here.For the near wall zone, the realizable k − ɛ and scalable wall function is employed for all simulations.The SIMPLE and the second-order-upwind difference scheme are set in the simulations.Simulations are carried out under the following assumptions: (1) The fluid properties of the working are constant.(2) The gravity effect is ignored.
Thermal radiation is negligible.Data reduction: Heat transfer balance for the shell and the inner tube is gained: where: The mean heat transfer rate (  ) is defined by: Where  , =   +   Due to the counter flow of the water in the annulus side, the logarithmic average temperature difference between the shell and the annulus is obtained by: The total heat transfer coefficient from the shell side to the annulus side is obtained by: The convection heat transfer coefficient of the shell side is obtained from:

Validation
3D geometry configurations of the HE were constructed using the Solid Works software.As shown in Figure 2, the computational mesh, by the workbench in ANSYS FLUENT, is generated with an unstructured grid.For grid study of the SHB-SDCTHEX model, five various meshes (M1: 6954315, M2: 11753218, M3: 12853619, M4: 13998340, and M5: 15697562 elements) were considered.In order to choose the best mesh that is favorable for the problem in terms of economy and accuracy of the results, by comparing the pressure drop and the heat transfer coefficient obtained for the meshes.The M4 was considered for further calculations (it should be noted that the residual squared errors for the flow field and pressure is considered 10 -5 for convergence).Comparing the results obtained in this research with the results of the Bell-Delaware approach described by Shahril et al. [15] is used for the heat transfer coefficient of shell side and the shell side pressure drop for the SHB-SDCTHEX and PHB-SDCTHEX in Figures 3 and 4  between the shell side heat transfer coefficient in this study and the Bell-Delaware approach is around 8.6%, and, this difference is about 2.8% for the shell side pressure drop.Similarly, in Figure 4, the maximum deviation for the (PHB-SDCTHEX) is approximately 8.9% and 2.5% for shell side heat transfer coefficient and the shell side pressure drop.With this comparison, it can be said that the results have acceptable accuracy.

1. Velocity and Pressure Distributions
Velocity profiles of the shell side of the SHB-SDCTHEX and the PHB-SDCTHEX are illustrated in Figures 5 and  6.Also, the so called active zones (A) and dead zones (D) are determined for both HE.Active zones have higher turbulent flow and velocity magnitude than the dead zones.Figure 5 shows that the helical flow has a higher velocity magnitude in the central zones of the shell side.This is due to the helical baffle and its section angle and dead zones, which are created far from central zones with low velocity magnitude and creates less turbulence and non-uniform flow across the shell in the SHB-SDCTHEX.

2. Temperature Distributions
For the SHB-SDCTHEX and the PHB-SDCTHEX in the shell temperature distributions are depicted in Figures 8 and 9 in four various zones.Due to a simple helical baffle, with the same   , the outlet and inlet temperature difference on the shell side is 9.9 K and 13 K for the SHB-SDCTHEX and the PHB-SDCTHEX, respectively.As the contours illustrate, active zones (A) have a higher heat transfer coefficient than dead zones (D).The results also reveal that the local temperature in the dead zones (D) is higher than that for the active zones (A).As can be seen, the temperature distributions of the PHB-SDCTHEX are more uniform with compare to the SHB-SDCTHEX, and temperature drop happens ahead for the PHB-SDCTHEX with respect to the SHB-SDCTHEX.

3. Overall Performance Comparison
To make a comparison between the performance of the SHB-SDCTHEX and the PHB-SDCTHEX, for various   parameters of the heat transfer rate (), pressure drop (∆), and thermo-hydraulic efficiency (/∆) are used.Figure 8 shows that the heat transfer rate is enhanced for both models with an increasing mass flow rate (  ).Increasing the value of   increases the amount of the convective heat transfer coefficient (ℎ).Also, the heat transfer rate for PHB-SDCTHEX has increased by about 14.9% compared to SHB-SDCTHEX.In PHB-SDCTHEX the trend of increase of the heat transfer rate is more than that for the SHB-SDCTHEX.This is due to eliminating the dead zones by perforating the simple  9. Notably, the pressure drop is an essential parameter from the cost point of view when modeling a S&T HE.The reason is that less pressure drop results in less pumping power and operating costs.Figure 9 indicates that pressure drop for the PHB-SDCTHEX is reduced by around 38.4% compared with the SHB-SDCTHEX.Also, increasing the   increases the pressure drop.
According to Figure 9, the growth of pressure drop for the PHB-SDCTHEX is less than that for the SHB-SDCTHEX.For evaluating the efficiency of a HE, the heat transfer rate and the pressure drop cannot be employed independently.Variations of The thermohydraulic performance (/∆) for both models are demonstrated in Figure 10.
It can be noticed from this figure that the (/∆) for the PHB-SDCTHEX is around 74% more than that of the SHB-SDCTHEX for the same   (  = 20 kg/s).Likewise, the (/∆) decreases with the increasing   .The effectiveness (ɛ) of a HE is expressed as follows [15]: In Figure 11, the pressure drop in both HEs are compared for different mass flow rates.It can be clearly seen that the pressure drop in both types of HEs increases with an increase in mass flow rate.In all flow rates, the pressure drop in SHB-SDCTHEX is always higher than PHB-SDCTHEX, and with an increase in flow rate, this difference also increases.The thermo-hydraulic performance for different values of mass flow for both HEs is shown in Figure 12.It can be seen that the maximum performance is at lower flow rates, and this parameter will decrease with an increase in flow rate of mass.Also, considering mass flow rates, the thermo-hydraulic performance of PHB-SDCTHEX is always higher than SHB-SDCTHEX, for the same flow rate.Figure 13 shows variation of the effectiveness as a function of   .Increasing   increases the effectiveness.For the PHB-SDCTHEX the effectiveness is around 25% more than that of the SHB-SDCTHEX.Therefore, based on the evaluation of the above parameters, the PHB-SDCTHEX is considered a convenient alternative to the SHB-SDCTHEX.

CONCLUSION
In this research, a shell-and-double-concentric-tube HE with a perforated helical baffle PHB-SDCTHEX is compared with a shell-and-double-concentric-tube HE with a simple helical baffle SHB-SDCTHEX using CFD.
The pressure drop of the fluid flow in the shell part of this type of heat exchanger will be reduced by using the new fin used, and the heat transfer in this exchanger will significantly increase.This can be considered for the design of new converters with smaller dimensions and higher efficiency.In the following, we can point out the advantages of the serious fin compared to the simple helical fin in this type of converter as follows: (1) Using perforated helical baffles makes the flow distribution further uniform and turbulent.Consequently, dead zones are eliminated across the shell side due to the orifices created on the simple helical baffle.It noted that the existence of the dead zones leads to a higher temperature than other zones on the shell side and less  happens within the dead zones due to higher temperature.(2)  raises for the PHB-SDCTHEX around 14.9% compared with the SHB-SDCTHEX in the same conditions.It is noted that the  increases with the increasing   .Also, the trend of growth of  for the PHB-SDCTHEX is higher than that for the SHB-SDCTHEX. (3) ∆ for the PHB-SDCTHEX decreases by about 38.4% compared with the SHB-SDCTHEX for the same   (  = 20 kg/s).Also, ∆ increases by increasing the   .Notably, the trend of growth of ∆ for the PHB-SDCTHEX is lower than that of the SHB-SDCTHEX.(4) For comprehensive efficiency, the thermohydraulic performance (/∆) and the effectiveness (ɛ) of the PHB-SDCTHEX are raised by about 74% and 25%, respectively; compared with the SHB-SDCTHEX for the same   .Likewise, (/∆) is reduced by increasing the   .On the other hand, the effectiveness increases by increasing   .It should, however, be noted that most deviation of the (/∆) and the (ɛ) in both models occurs at the minimum and maximum   , respectively.

Figure 1 .
Perspective views of the SHB-SDCTHEX and PHB-SDCTHEX k − ɛ turbulence model practical constants are:  2 = 1.2,   = 1.0,   = 1.2.Also,   has a constant value for a high Reynolds number.However,   was considered a function of the strain and rotation rate[36].

2 .
. The maximum difference (a) front view (b) side view Figure Local Views of the grid system for SHB-SDCTHEX and PHB-SDCTHEX.

Figure 3 .Figure 4 .
Figure 3.Comparison between the numerical calculations and the Bell-Delaware approach for the shell side of the SHB-SDCTHEX

Figure 8 .Figure 3 .
Temperature distribution across the shell side for the (SHB-SDCTHEX) with   = 20 (kg/s) in various zones Temperature distribution across the shell side for the (PHB-SDCTHEX) with   = 20 (/) in various zones helical baffle.Variations of the pressure drop are depicted in Figure , − , )