Numerical Simulation of Thermo-hydraulic Behaviour of Shell and Tube Heat Exchanger Equipped with Segmental Baffle and Helical Baffle

The baffle type and structure are critical to enhancing the comprehensive thermo-hydraulic behavior of shell-and-tube heat exchangers (STHX). In the study, Solidworks software was used to establish three-dimensional mesh models of STHX equipped with the segmental baffle and the continuous helical baffle, respectively. ANSYS software was adopted to study the effects of the baffle type and the baffle geometric parameters on the thermo-hydraulic characteristic of STHXs using the pressure drop of the shell side, the coefficient of heat transfer and isobaric JFP factor as the evaluation characteristics. For segmental baffles, better thermo-hydraulic performance could be obtained with a baffle spacing of 200 mm and a gap height of 0.4 D. For helical baffles, an optimized thermo-hydraulic performance could be obtained with a baffle pitch of 150 mm. By comparing the comprehensive thermo-hydraulic performances of STHXs equipped with two different baffles, it could be concluded that the isobaric JFP factor of STHX equipped with the helical baffle was 1.18 times that of STHX equipped with the segmental baffle under the different suitable flow rate.


Introduction
As a common chemical unit equipment, STHXs are commonly used in various chemical engineering processes.The baffle is often arranged on the STHX shell side, which not only plays an important role in supporting the exchange tube bundle but also improves the heat transfer characteristics.Therefore, many scholars have devoted themselves to strengthening the heat transfer performance and reducing the pressure loss of the shell side in STHXs, hoping to achieve the purpose of high efficiency and energy saving by employing the proper baffle or optimizing the structure size of the existing baffle.
At present, the baffles of STHXs mainly involve segmental baffles, circular integral baffles and helical baffles, and so on [1][2][3] .Segmental baffles are commonly used in STHX to support the exchange tubes and change the direction of the fluid flow process.The fluid medium flow in STHX equipped with the segmental baffle exhibits a tortuous flow direction across the shell side exchange tube bundle in STHX to improve the heat transfer property.The circular integral baffle is a complete circular plate or a complete circular plate opened with round holes, rectangular holes, trefoil holes and various specialshaped holes.The fluid in STHX equipped with circular integral baffle flows in the longitudinal direction through the gap between the orifice edges and the exchange tube walls, which can provide a better thermo-hydraulic performance, eliminate recirculation zones and avoid the vibration induced by the flow.Because a certain angle between the baffle and the tube bundle is from 10 to 40 º, the helical baffle can change the flow direction in a continuous spiral shape on the shell side.Due to the spiral flow state, the fluid flow turns more smoothly on the STHX shell side, which can improve the ratio of the heat transfer rates to the pressure drop of the shell side and reduce the underscouring of the exchange tube bundle caused by the fluid medium, thereby increasing the equipment service life.As mentioned so far, the shape of the baffle and its structure size plays an important role in the fluid flow state in the shell side of STHX and the heat transfer property of STHX.
Much of the research is usually done numerically and in the laboratory [4,5] .In the current work, Solidworks software was used to establish a three-dimensional mesh model of STHXs equipped with the segmental baffle and the helical baffle, respectively.The evaluation of STHX with the abovementioned baffles was carried out via numerical simulation with ANSYS software for the sake of providing the base theory for the optimal design of baffles.

Establishment of the geometric model
The physical geometric parameters of STHX equipped with the segmental baffle in the laboratory are displayed in Table 1.According to the geometric size, the physical models of STHXs equipped with the segmental baffle and the helical baffle were established by using Solidworks software, exhibited in Figure 1.The following aspects need to be considered during the establishment of the physical model: (1) the gap between the baffle and the heat exchanger tube bundle is ignored; (2) the slit between the segmental baffle (continuous helical baffle) and the wall of the heat exchange shell is ignored; (3) the heat transfer effect on spacer tube, tie rod, and various holes and instrument interfaces are ignored; (4) the inner wall of the shell side is assumed to be smooth everywhere.

Meshing generation and independency analysis
The software HyperMesh was adopted to divide STHX in Table 1 into unstructured tetrahedral meshes, and the volume meshes were smoothed by the adaptive function to obtain high-quality meshes.
Considering the accuracy of the simulation result, the verification of grid independency was carried and analyzed by taking STHX equipped with a segmental baffle under the condition of water as the shell side fluid medium with a fluid flow velocity of 2.0 kg/s.Figure 2 shows the coefficient of heat transfer α, and the pressure drop P of the shell side as a function of grids number obtained by the simulation results using six grid division methods.In Figure 2, the pressure drop P of the shell side as well as the coefficient of heat transfer α both show a trend of decreasing first and then tending to be stable along with the increasing of grids number.Among NO.4,NO.5, and NO.6 grid division methods, it can be found the differences in the pressure drop P of the shell side and the coefficient of heat transfer α are both less than 1%.As a result, the NO. 5 grid division method was used in this study.Figure 3 displays the cross-sectional mesh obtained by NO. 5 method.

Simulation setting and boundary condition setting
In this study, tapwater was adopted as the flowing fluid medium in the shell side of STHX with a flow velocity of 0.5 -2.5 kg/s at the inlet of STHX.Furthermore, the inlet temperature of the tapwater was 293 K and the exchange tube wall temperature was 335 K.In addition, the fluid-solid interface between the STHX shell wall and the baffle in STHX was a smooth and non-slip adiabatic wall surface.In the setting of simulation conditions, the velocity inlet and the pressure outlet were set as the inlet boundary and the outlet boundary of STHXs equipped with two different baffles, respectively.The fluid flow and heat transfer properties were numerically simulated by ANSYS software.The stability of the calculation convergence was guaranteed via Segregated implicit.The momentum, turbulent kinetic energy and turbulent dissipation rate were dealt with the second order upwind method.The coupling of the continuity equation and N-S equations adopted the SIMPLE algorithm.The numerical simulation model used the RNG k-ε model [6] .Due to the influence of the boundary layer, the wall function was also introduced.In addition, the convergence criterion was less than 10 -7 .

Model correctness and rationality verification
In the same STHX equipped with a segmental baffle, a comparison was done between the numerical result and the experimental research result to check the correctness and rationality of the numerical simulation model.Under the fluid flow mass velocity in the shell side of STHX between 0.5 and 2.5 kg/s, Figure 4 shows the performances of the pressure drop ΔP of the shell side and the coefficient of heat transfer α as a function of the fluid medium flow rate of the shell side acquired with the numerical simulation and the experiment research.The maximum deviation between the experiment research result and the simulated value is 4.64% for the coefficient of heat transfer α and 4.69% for the pressure drop P of the shell side, respectively.As a result, the established ANSYS model in this study has good consistency with the experiment research result.

Evaluation methods of thermo-hydraulic performance
Heat transfer characteristics and resistance characteristics are two key factors that determine the comprehensive thermo-hydraulic characteristic of STHX.Therefore, the pressure drop P of the shell side and the coefficient of heat transfer α were adopted as the single evaluation index in this work, respectively.The isobaric JF p was employed for the evaluation of the comprehensive thermo-hydraulic performance [7] , listed in Equation (1).JF p is a dimensionless numerical value, which means that the larger the JF p value is, the better comprehensive thermo-hydraulic performance will be. .

Effect of the segmental baffle on thermo-hydraulic performance
The structure parameters of the segmental baffle are the spacing of baffle l and the gap height of baffle h.The numerical simulation was carried out when the shell side fluid medium flow rate was 1.0 kg/s, the spacing of baffle l was from 100 to 500 mm and the gap height of baffle h was from 0.2 D to 0.5 D.

3.1.1.
Effect of the segmental baffle on pressure drop of shell side.It is well known that a lower pressure drop of the shell side can result in lower operating costs, therefore, the pressure drop P of the shell side is one of the key factors in the equipment design of STHX. Figure 5 represents the pressure drop P of the shell side for each of the computed STHXs equipped with different sizes of segmental baffles.From Figure 5, the pressure drop ΔP of the shell side decreases gradually with the increase of the gap height h at a constant baffle spacing l, and the shell side pressure drop ΔP decreases with the increase of the baffle spacing l at a constant gap height h.In particular, when the baffle spacing l increases from 100 mm to 200 mm, the pressure drop ΔP of the shell side decreases most obviously.It is well known that a smaller baffle spacing l means a lots number of baffles, as a result, the shell side fluid medium in STHX equipped with the segmental baffle is blocked easily during the flowing process.Hence, under the same mass flow rate, it can be deduced that when both the spacing of baffle l and the gap height of baffle h are smaller, the flow velocity change of the shell side fluid flow becomes more obvious, resulting in a greater pressure drop ΔP of the shell side in STHX.

Influence of segmental baffle on heat transfer property.
The coefficient of heat transfer α for each of the computed STHX configurations is displayed in Figure 6.From Figure 6, the coefficient of heat transfer α decreases with the increases of the gap height of baffle h at a constant baffle spacing l, at the same time, the coefficient of heat transfer α decreases along with the increase of baffle spacing l at the same baffle gap height h.The reason is that the coefficient of heat transfer α is determined by the degree of turbulence in the shell side of STHX.The greater turbulence degree of the shell side fluid can be achieved under both the baffle spacing l and the gap height of baffle h are in the small value, thus, resulting in an obvious thermal enhancement effect.

Influence of segmental baffle on comprehensive thermo-hydraulic analysis.
Since the pressure drop P of the shell side and the coefficient of heat transfer α are highly dependent on each other, the isobaric JF p factor is used for the assessment of the comprehensive thermo-hydraulic behavior of STHX equipped with a segmental baffle.Figure 7 shows the effect of segmental baffle structure parameters on isobaric JF p factors.When the baffle spacing l is less than 300 mm, the isobaric JF p value first increases and then decreases slightly along with the increase of the gap height of baffle h, and reaches a maximum value when the gap height of baffle h is 0.4D.When the baffle spacing l is 400 mm, the isobaric JF p factor increases with the increases of the baffle gap height h, and a maximum isobaric JF p value can be obtained when gap height h is 0.5D.When the baffle spacing l is 500 mm, the isobaric JF p factor decreases slowly with the increases of the gap height h.As a result, it can be suggested that there is an equilibrium point of the design between the baffle spacing l and the gap height of baffle h.In other words, a better comprehensive thermo-hydraulic performance of STHX can be obtained from the segmental baffle with a smaller baffle spacing l and a larger gap height h, or the segmental baffle with a larger baffle spacing l and a smaller gap height h.Under the simulation conditions adopted in this paper, a better comprehensive performance could be obtained when baffle spacing l of 200 mm and the baffle gap height h of 0.4 D.

Effect of the helical baffle on thermo-hydraulic behavior
Because of the continuous helical baffle with an approximately 40° inclined helix angle from the perpendicular to the STHX axis, it can effectively guide the shell side fluid to fit with the arc surface of the baffle.As a result, helical baffles can provide a more uniform flow velocity distribution and can reduce bypass effects [8][9][10] .As for STHX equipped with a continuous helical baffle, the main structure parameter is the baffle pitch p.The numerical simulation was performed when the fluid medium flow rate in the STHX shell side was 2.0 kg/s, the baffle pitch p was from 100 mm to 250 mm (Δp=50 mm).

Effect of the continuous helical baffle on pressure drop of shell side and coefficient of heat transfer.
Figure 8 reveals the influences of the pressure drop ΔP of the shell side and the coefficient of heat transfer α of STHX equipped with the different baffle pitch p.The pressure drop ΔP of the shell side and the coefficient of heat transfer α both decrease with the increases of the baffle pitch p.The relationship between the heat transfer coefficient α and the baffle pitch p exhibits a nearly linear trend, while the pressure drop ΔP of the shell side displays a larger decline when the baffle pitch p increases from 100 mm to 150 mm.Furthermore, for the coefficient of heat transfer α, the difference between the maximum value and the minimum value is 1.66 times, and for the pressure drop of the shell side, the difference between the maximum and the minimum is 2.02 times.Then, it can be concluded that baffle pitch p has a greater impact on the pressure drop ΔP of the shell side than that on the coefficient of heat transfer α.

Comprehensive thermo-hydraulic analysis.
The influence of isobaric JF p factor on STHX with different baffle pitch p is shown in Figure 9.It can be observed that isobaric JF p factor increases as the baffle pitch p increases initially and decreases afterward.For STHX with a certain diameter, if the baffle pitch p is too large, the fluid flow of the shell side in STHX tends to parallel to the exchange tube bundle of STHX, which results in a lower turbulence degree.On the contrary, if the baffle pitch p is too small, the fluid medium flow of the shell side in STHX tends to be transverse to the exchange tube bundle of STHX, which can result in the flow obstruction and the pressure drop ΔP of the shell side increment.Then, when the pitch of baffle p was 150 mm, a better comprehensive thermo-hydraulic performance could be obtained in our study.

Comparison of thermo-hydraulic of different baffles
The numerical simulation was carried out when the fluid medium flow rate was 0.5 to 2.5 kg/s under the optimal structure of STHXs equipped with two different baffles.Figure 11 depicts the comparison of the coefficient of heat transfer α for two STHXs.The coefficient of heat transfer α increases along with the increase of the fluid mass flow rate.The maximum α for STHX equipped with a segmental baffle is 1.42 times more than that for STHX equipped with a helical baffle.The reason may be that the turbulence effect produced by the helical baffle was not as obvious as that of the segmental baffle.

Comprehensive thermo-hydraulic analysis.
Figure 12 shows the variations in the comparison of the isobaric JF p factor for two heat exchangers.No matter what kind of baffle in STHX, it can be seen that the isobaric JF p factor first increases and then decreases with the increases of the fluid medium mass flow rate.The maximum isobaric JF p can be achieved under the fluid flow rate of 1.0 kg/s in STHX with segmental baffle, and the fluid flow rate of 2.0 kg/s in STHX with continuous helical baffle, respectively.At this point, it can be concluded that there is an optimal shell side fluid flow rate for each baffle to obtain a better comprehensive thermohydraulic behavior.Furthermore, under the optimal fluid flow rate, a better comprehensive thermohydraulic characteristic can be obtained from STHX with continuous helical baffle, which is increased by 17.66% compared with STHX with a segmental baffle.

Conclusions
In the current work, the fluent module in ANSYS software was used to estimate the thermo-hydraulic behaviors of STHXs equipped with the segmental baffle and the continuous helical baffle, respectively.It can be obtained that the established physical model and the numerical calculation model were correctness and rationality from the comparison of the experiment research result and the numerical simulation result by using the same segmental baffle STHX.During the geometric parameter optimization simulation process, a better thermo-hydraulic performance was achieved in segmental baffle STHX with an optimal baffle spacing l of 200 mm and the baffle gap height ratio h/D of 0.4, and helical baffle STHX with a pitch p of 150 mm, respectively.Compared to the segmental baffle, the continuous helical baffle could provide a better balance between the heat transfer characteristic and the pressure drop of the shell side in STHX, which not only improved the efficiency of heat exchanging by 17.66% but also increased the fluid flow velocity by 2 times.

Figure 2 .
Figure 2.  and P under different meshing generation methods.

Figure 4 .
Figure 4. Comparison of experimental data and numerical simulation result.

Figure 5 .
Figure 5. Influence of baffle structure size on P.

Figure 6 .
Figure 6.Influence of baffle structure size on .

Figure 7 .
Figure 7. Influence of baffle structure size on isobaric JF p .

Figure 8 .
Figure 8. Influence of baffle pitch p on α and ΔP.

Figure 9 .
Figure 9. Influence of baffle pitch p on isobaric JF p factor.

3. 3 . 1 .
Pressure drop ΔP of shell side and coefficient of heat transfer α.Figure10exhibits the variation of the pressure drop ΔP of the shell side versus the fluid flow rate for STHXs equipped with two different baffles.The pressure drop ΔP of the shell side increases nearly proportional to the fluid flow rate.STHX equipped with a segmental baffle produces a higher pressure drop ΔP, which is higher by 235% than STHX equipped with a helical baffle.This is because the segmental baffle can cause the fluid flow distribution to be zigzag, which causes an abrupt change in momentum and the pressure drop ΔP of the shell side at the edge of the baffle, whereas, the mainstream fluid flow direction of continuous helical baffle does not modify significantly.

Figure 12 .
Figure 12.Comparison of isobaric JF p of STHXs with different baffles.

Table 1 .
Structure parameters of STHX in the laboratory