**1. Introduction**

A printed circuit heat exchanger (PCHE) is a type of compact heat exchanger with high efficiency, high application pressure, and high application temperature. It was invented in Australia in 1980 and promoted for commercial application by Heatric. It has broad application prospects in the fields of ultra-high-temperature gas-cooled reactors, floating liquefied natural gas storage units, and other industrial energy [1]. PCHE typically employs diffusion-bonded arrays of plates where microchannels are formed by chemical etching [2]. The typical cross section shape is semicircular and the hydraulic diameter in a PCHE passage is between 700 μm and 1.5 mm [3]. The flow channel geometries can be designed as straight, zigzag, S-shape, and airfoil-finned channels [4]. However, the zigzag-type channel is more widely used in industrial applications. CO2 is a nontoxic and inexpensive gas. It has excellent thermophysical properties (high specific heat, high thermal conductivity, and low viscosity) near the pseudocritical point, as shown in Figure 1, which can considerably enhance the heat transfer without sacrificing the hydraulic performance [5]. Consequently, the application of CO2 in PCHE has become the focus of researchers.

Heat transfer and hydraulic characteristics are the basis of PCHE thermal design. Various experimental and numerical investigations have been performed to optimize the channel structures, fluid mediums, and operation conditions. Nikitin and his team first published the experimental results of the flow and heat transfer characteristics of sCO2 in zigzag PCHE in 2016 and developed the correlations of *Nu* and *f*, while the correlations

**Citation:** Tu, Y.; Zeng, Y. Numerical Study on Flow and Heat Transfer Characteristics of Supercritical CO2 in Zigzag Microchannels. *Energies* **2022**, *15*, 2099. https://doi.org/ 10.3390/en15062099

Academic Editors: Abderrahmane Baïri, Angel A. Juan and Marcin Kami ´nski

Received: 10 February 2022 Accepted: 11 March 2022 Published: 13 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

are only applicable to channels of the specific geometric parameters and Reynolds number range of those used in the experimental study [6]. Kruizenga et al. investigated the thermal–hydraulic performance of sCO2 in a straight channel with semicircular cross section using both experimental and numerical methods, the analysis results showed that the commercial computational fluid dynamics (CFD) software can well predict the internal heat transfer characteristics of the PCHE channel [7]. Saeed and Kim also conducted the numerical analysis of an sCO2 PCHE using ANSYS-CFX and validated the simulation results using published experimental data [8]. Tu and Zeng studied the flow and heat transfer performance in semicircular straight channels of sCO2 fluid for both cooling and heating process using CFD method. A modified model based on Douglas A. Olson [9] correlation was proposed to predict the heat transfer performance of sCO2 in semicircular channels for both heating and cooling conditions [10]. These literature conclusions fully confirm the feasibility of the numerical method.

**Figure 1.** Thermophysical properties of supercritical CO2 at different pressure: (**a**) specific heat; (**b**) density; (**c**) dynamic viscosity; (**d**) thermal conductivity.

Subsequently, a large number of studies focused on finding better channel types. Kim et al. compared the heat transfer and hydraulic performance of sCO2 in PCHE with zigzag and airfoil-shaped fins. It was found that the thermal performance of the airfoil fin was close to that of zigzag, but the airfoil fin had lower pressure loss [11]. Mohammed et al. investigated the effect of channel shapes (zigzag, curve, and step) on the thermal and hydraulic performance of PCHE and found that the zigzag channels have the highest value of heat transfer coefficient and pressure drop [12]. Matsuo et al. conducted numerical simulations of three different channel types (zigzag, chamfered zigzag, airfoil) to study the geometrical effects on the local heat transfer coefficient and pressure drop for supercritical CO2 in PCHE and developed new correlations for *Nu* of the zigzag channels [13]. In the research of [14–16], the PCHE with zigzag channel and discontinuous S-shaped fins were

numerically and experimentally investigated, and it was found that the S-shaped channel can significantly improve the hydraulic performance while keeping almost equal heat transfer performance compared to the zigzag channels.

There are also studies focusing on thermal hydraulic characteristics of the other fluid media in PCHE channels. Dai et al. studied the flow and heat transfer performance of water in the semicircular zigzag passage experimentally [17]. Minghui Chen et al. investigated the thermal–hydraulic performance of a zigzag channel PCHE using helium as fluid media [18].

Most of the studies on the flow and heat transfer characteristics of PCHE channels use a specific geometric parameter channel or straight channel, or the comparison between zigzag channel and other types of channels such as S-type and discontinuous airfoil fin type. The experimental data and empirical correlations given in these studies are also limited to a certain type of channel, and the operating pressure, fluid bulk temperature, and Reynolds number are limited to a certain range. However, there are few studies on the effect of geometric parameters on the flow and heat transfer performance of a zigzag channel. This paper aims at modeling the forced convection heat transfer of CO2 within the zigzag channels, which are the main channel type of PCHE, and studies the effects of its main geometric parameters (hydraulic diameter, pitch length, and bending angle) on its internal flow and heat transfer parameters, especially near the pseudocritical point. The numerical method and analysis results of this study can be used as a reference for PCHE industrial design and channel performance investigation.

#### **2. Numerical Modeling**

A numerical method for analyzing the steady-state flow and heat transfer properties of a zigzag channel is defined. In this method, ANSYS Fluent 2019 is used to solve the governing equations of the steady turbulent flow of sCO2 in the zigzag channels. The NIST real gas model with REFPROP V9.1 database was used to evaluate the thermodynamics and transport of approximately of CO2. Yoon et al. [19] and Ren et al. [20] conducted comparative studies using STD k–e, realizable k–e, and SST (shear stress transport) k–ω turbulence models to simulate the thermal–hydraulic performance of sCO2 intube-flowing and found that the SST k–ω turbulence model gives the best quantitative prediction. The same conclusion was likewise reached in [21–24]. Therefore, the SST k–ω model is adopted for further analysis in this study. The pressure-based coupled algorithm was used to establish the coupling of velocity and pressure. The numerical simulation is considered convergent as all iterative residuals of the governing equations are less than 10−5, and area-weighted average outlet temperature and area-weighted average inlet pressure are stable.
