1. Introduction
A heat exchanger is a device that can exchange heat between two fluids at different temperatures without mixing [
1,
2]. In industry, the heat exchanger plays a critical role especially in heat-based power such as nuclear power. Practically, shell-and-tube heat exchanger is the most popular in industry. However, the printed circuit heat exchanger (PCHE) is now widely developed due to several promising aspects, such as a large area density and good pressure and temperature capabilities [
3,
4,
5]. The development of highly efficient PCHE is important, which is strongly related to economy and safety aspects. In many cases, PCHE may be working at a high temperature and pressure [
6]. This means that safety is an important feature of PCHE because some critical issues may occur under high temperature and pressure conditions. For example, Rakesh and Anand found thermal stress to be more dominant than pressure cycle stress due to the higher temperature gradient [
7].
Many studies have been conducted to investigate thermal–hydraulic performance of PCHE. Mylavarapu et al. studied the thermal–hydraulic performance of PCHE which contains helium as the fluid [
8]. The thermal hydraulic performance of a PCHE which has a longitudinal corrugation flow channel was studied by Kim et al. [
9]. Sung and Lee conducted a study about the tangled channel heat PCHE for thermoelectric power generation [
10]. These studies show that the development of a cross-section shape may be able to enhance the thermal–hydraulic performance.
Besides the thermal–hydraulic performance study, mechanical integrity study is also important in PCHE development. Lee and Lee [
11] conducted a study about the structural assessment of a sodium and SCO2 zigzag channel by calculating the temperature and stress value. They found that the maximum stresses occurred at the channel tips which are the sharp corner of the semi-circular flow cross-section shape. Song et al. also conducted a study about the structural integrity evaluation of a lab-scale intermediate PCHE of very-high temperature reactor (VHTR). Under the test condition, the maximum Tresca stress was far below the allowable stress limit [
12]. Armanto and Lee conducted a study about the mechanical integrity analysis of a PCHE with channel misalignment. This study also shows high-stress intensity at the tip edge of PCHE channels [
13]. The phenomenon where the stress is shown high at the tip has also been observed at the nanoscale. Winter et al. [
14] conducted a study which shows that the different pore shape and pattern will cause stress accumulation inside the structure and may lead to failure. Vo et al. [
15] investigated the impact of nanopores and porosity on the mechanical properties of amorphous silica (a-SiO
2). Simulation results shows that high stress concentration occurs at the top and bottom of the pore.
A double-faced heat exchanger comes with a promising ability. Unlike the conventional plate heat exchanger where the channel geometries are semi-circle and etched at one side of the stacked plate, this double-faced PCHE has two faces on one plate. During the fabrication process, the metal stacked layer will be etched on two faces and after that, they will be stacked together through the diffusion bonding process. The shape of two-etched sides can be different or like each other. Usually, in double-faced PCHE, one side is the main channel while another face can be an additional upper channel. One of the reasons for double-faced application is to enhance the heat transfer by enlarging the fluid flow cross-section area. By considering an additional upper channel by etching two sides of one stacking plate, the flow cross-section area can be larger. Another reason is that the double-faced PCHE can reduce the friction as mentioned by Lee et al. [
16].
There are several studies conducted about double-etched circular channel PCHE. Ma et al. [
17] considered a double-etched PCHE at the high temperature of 900 °C and a high pressure above 7 MPa. One side of the stacked plate is considered as a semi-circle flow channel while another side is as an elliptical additional upper channel. A thermo-hydraulic performance of the proposed PCHE channel design was studied numerically. Based on the study, it was found that the additional elliptical upper channel can improve the heat transfer of PCHE and increase the pressure drop simultaneously. It was found that the Nusselt number was increased by 7−17% with a 0.234 mm additional upper channel, while the fanning factor increased by 3−5%. Lee and Kim [
18] investigated the performance of a zigzag printed circuit heat exchanger with various channel shapes. Four shapes of channel cross-section were investigated such as semi-circle, rectangle, trapezoid, and circle. The investigation aims to see the global Nusselt number, Colburn j-factor, effectiveness, and friction factor. This study showed that a rectangular channel provides the best thermal performance while the circular channel has the worst thermal performance.
Lee and Kim [
19] conducted a study about the thermal performance of a double-faced PCHE with thin plates. This study considered 2 mm thin plates inserted between the hot and cold channel. A thin plate is used to increase the overlapped area between the cold and hot channels which can improve the thermal performance of PCHE. This proposed geometry was studied under Reynold’s number in cold channels ranging from 67,000 to 280,000. The result was compared to a reference PCHE design channel which has only one etched side. It was claimed that the new PCHE design can maximize the heat transfer by minimizing the distance of heat conduction and maximizing the overlapping area between the hot and cold channels. Hence, the proposed design shows a remarkably higher thermal performance than the reference design.
The present study examined the capability of double-faced PCHE design from a mechanical integrity point of view since all double-faced PCHE previous studies claimed that the proposed design can enhance the thermal–hydraulic performance. However, considering PCHE for nuclear power plant applications should include a mechanical integrity assessment which is related to the safety concern. This study examined the additional elliptical upper channel effect in PCHE design and compared it to the design specification by considering the simplified design by rule assessment. Since the experiment was almost impractical to be conducted due to the tiny scale of geometry, the finite element method study was chosen to be conducted. The design condition used for the assessment was the PHCE design condition of sodium fast-cooled reactor (SFR) which has a 20 MPa and 0.5 MPa pressure of the cold and hot channel, respectively as shown in
Table 1 [
20]. The system will work under 525 °C maximum working environment. Two-dimensional finite element method (FEM) simulation was conducted to observe the stress distribution, the weakest area based on deformation analysis and construction code compliance including primary stress, primary and secondary stress, and yield stress assessment. Even though this model of geometry is not usual and still needs many supporting technology developments, especially for the assembly and etching processes, this study is important and innovative to prepare the more advanced PCHE design and manufacturing process in the future.
In this study, the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code was used. The obtained stress distributions were compared with the design criteria as stated in the construction code. ASME boiler and pressure vessel code Section III is the rule for the construction of nuclear facility components [
21]. It consists of Division 1, Division 2, Division 3, and Division 5. These four divisions are broken down into several subsections and several subsections will be broken down into several subparts. Since the design condition used in this study is the sodium-fast cooled reactor of which the maximum temperature reached 538 °C, ASME Section III Division 5 Subsection HB, Subpart B, was chosen as the criteria. ASME Section III Division 5 Subsection HB Subpart B contains rules for the construction of nuclear facility components of high temperature reactors specified for class A metallic pressure boundary components under elevated temperature service.
4. Conclusions
Finite element analysis simulation has been conducted to observe the mechanical integrity of double-etched printed circuit heat exchanger design. Even this design still needs more efforts to be applied in the future, but the design of double-etched design shows a promising and safer design in terms of a mechanical integrity point of view after some previous study mentioned double-faced PCHE from a thermal–hydraulic point of view. In this case, a sodium fast-cooled reactor steam generator heat exchanger is taken as the model for the proposed PCHE design. By considering the ASME Section III construction rule, the proposed design can comply with the design criteria where the primary membrane stress (Pm) and combined with primary bending stress (Pm + Pb) are still below maximum requirement criteria. The application of an additional ellipse upper channel helps the stress intensity decrease in the proposed PCHE channel. Five different cases were conducted for 0 < r1/r < 0.5 where r1 is the additional elliptical short radius and r is the semi-circular channel radius. The simulation shows that the stress intensity was reduced by up to 24%. Apart from that, the stress concentration factor also reduces with the increase in additional elliptical channel radius.
Besides that, the offset channel arrangement is also one of the possible arrangements that can be used in this type of PCHE. This offset arrangement can be done by shifting one plate to another during the construction process. This offset arrangement comes with the promising stress intensity decrease. Simulation results show that the 2.5 mm offset configuration can decrease 9% of the maximum stress intensity compared to the non-offset configuration. This work proposed an additional elliptical upper channel with a 2.5 mm offset configuration is an optimum design that can be applied in PCHE design.