Technical Sharing: Calculation and Optimization of Flow Resistance in Plate Heat Exchangers

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Plate heat exchangers are widely used in industrial production and civilian applications due to their advantages such as high efficiency, compactness, and flexibility. However, the narrow flow channels in the heat exchanger and high flow velocities result in flow resistance that cannot be ignored. This paper analyzes the types of flow resistance in plate heat exchangers and their influencing factors, and focuses on introducing several calculation methods for the resistance of typical plate heat exchangers. https://www.cidrg.com/wp-content/uploads/2024/07/2024070208390054.png (Schematic diagram; it does not correspond to any specific information in the text) 1 Introduction Plate heat exchangers are new types of efficient heat exchange devices that are created by stacking and sealing a series of metal plates together. Compared with traditional shell-and-tube heat exchangers, plate heat exchangers have a high heat transfer coefficient, a compact structure, and are easy to disassemble and maintain; therefore, they are being increasingly adopted and used. However, due to limitations in plate strength and sealing requirements, the width of the flow channels between the plates is small, typically only 2–5 mm. As the fluid flows through narrow corrugated channels, frictional and local resistance are significant, resulting in substantial pressure losses. Especially under conditions of high viscosity and high flow rates, the pump power consumption resulting from flow resistance cannot be ignored. Therefore, it is crucial for the industrial application of plate heat exchangers to understand the characteristics and calculation methods of flow resistance in such exchangers, to take effective measures to reduce this resistance, and to lower operating costs while maintaining satisfactory heat transfer performance. 2 Types and Influencing Factors of Flow Resistance 2.1 Types of Flow Resistance The flow resistance in plate heat exchangers can be divided into three categories: (1) Frictional resistance, which is the pressure loss resulting from friction between the fluid and the plate walls as it flows through the channels between the plates; (2) Local resistance, which mainly includes the pressure losses at the inlets, outlets, and connection pipes, and is caused by sudden changes in the cross-section of the flow channels; (3) Gravitational resistance, which is the energy consumed by the fluid to overcome its own gravity, and is related to factors such as the inclination angle of the plates and the height of the equipment. In engineering calculations, the first two terms play a dominant role, while gravitational drag can generally be ignored. 2.2 Influencing factors There are many factors that affect the flow resistance of plate heat exchangers, including both the physical properties of the fluid itself and the structural characteristics of the heat exchanger. Specifically including: (1) fluid viscosity. The greater the fluid viscosity, the greater the frictional resistance; (2) fluid density. The greater the density, the greater the inertial force and the greater the local resistance; (3) Flow velocity. Flow velocity is the main factor affecting resistance; the higher the flow velocity, the greater the resistance, and this relationship is quadratic in nature; (4) equivalent diameter of the flow channel. The narrower the flow channel, the better the heat transfer enhancement effect, but as the flow velocity increases, the frictional resistance also rises; (5) Wave angle. The ripple angle affects the turbulence intensity of the fluid, which in turn influences the local drag coefficient; (6) inlet and outlet diameters. The ratio of the inlet and outlet diameters to the equivalent flow channel diameter affects the contraction and expansion resistance. Therefore, when analyzing the resistance of plate heat exchangers, the effects of fluid properties and geometric structure must be systematically considered. 3 Methods for calculating flow resistance 3.1 Plate-fin heat exchangers Plate-fin heat exchangers are a type of common plate heat exchanger, and they are highly favored due to their high compactness and high heat transfer coefficients. Due to the narrow flow channels in plate-fin heat exchangers, the frictional loss along the flow path plays a dominant role. The classical Kays-London method is based on a large amount of experimental data. For different fin types, it provides a correlation between the drag coefficient f and the Reynolds number Re: f = a·Re^b, where a and b are empirical coefficients related to the fin shape and arrangement. This method is simple and practical, but the values of coefficients a and b require consulting numerous charts, which makes it difficult to implement in programming. Considering the high non-uniformity of compact heat exchangers, some scholars have proposed modified correlations. Based on a summary of previous research, Shah proposed an f-Re correlation equation applicable to various types of fins: f = c1/Re^c2 + c3, where c1, c2, and c3 are correction coefficients that are related to parameters such as the equivalent diameter of the flow channel and the properties of the fluid. This method features high calculation accuracy and a wide range of applicability, and has been widely adopted in engineering design. 3.2 Spiral plate heat exchangers The flow channels in spiral plate heat exchangers are spiral in shape; the fluid flows both radially and axially, resulting in more complex flow behavior. The spiral flow channel can be simplified as a series of concentric annular flow channels, with radial leakage existing between each annular flow channel. Based on this, Minton derived the formula for calculating the friction factor along the length of a spiral plate heat exchanger: f = 24/Re3.3. Removable plate heat exchangers use rubber gaskets for sealing, which facilitates disassembly and cleaning. The flow channels between the plates are in a herringbone pattern, which enhances fluid turbulence; thus, the local resistance cannot be ignored. Kumar provided a formula for calculating the drag coefficient taking into account the pressure losses at the inlet and outlet: f = (2ΔP·De)/(ρv^2·L) + Kp·v^2/(2Dh), where ΔP is the total pressure drop between the plates, Kp is the local drag coefficient, L is the flow length, and Dh is the equivalent diameter of the flow channel. Focke et al. experimentally studied the effect of the corrugation angle β on the local resistance coefficient. They derived a relationship between the local resistance coefficient Kp and β: Kp = 986.2β^(-2.611). This formula takes into account both frictional resistance along the flow path and local resistance, and is applicable to chevron-corrugated plate heat exchangers. For other ripple forms, such as trapezoidal and rectangular, further corrections are needed. 3.4 Numerical simulation methods Traditional drag calculations largely rely on experimental correlations; however, the applicability of these correlations is limited, and they fail to enable a thorough analysis of the distribution characteristics of the velocity and pressure fields. In recent years, computational fluid dynamics (CFD) methods have been introduced into the study of the flow characteristics of plate heat exchangers. By solving the N-S equations, detailed flow field information within the channel can be obtained, and the drag coefficient can be further calculated. Li Xuesong et al. used the CFD method to simulate the three-dimensional flow and heat transfer process in spiral plate heat exchangers, obtaining the flow resistance coefficients at different Reynolds numbers, which matched well with the experimental values. Zhang Ruipu et al. conducted numerical simulations of the flow in herringbone plate heat exchangers using the fluid volume method, revealing the influence of boundary layer separation and reattachment on flow resistance. The CFD method visualizes the fine structure of the flow field between plates, which aids in conducting targeted optimization design. 4 Methods to reduce flow resistance: While ensuring an adequate heat transfer rate, reducing flow resistance can achieve twice the result with half the effort. Based on existing research findings, the following optimization measures are proposed: (1) Optimize the corrugation angle and depth. The ripple angle β is a key parameter affecting flow resistance. If β is too high, turbulence intensity increases and local resistance rises; if β is too low, the effect of enhancing turbulence is poor and heat transfer deteriorates. A balance should be struck between heat transfer and resistance to find the optimal compromise. There is also an optimal value for the plate corrugation depth; generally, 1/8 to 1/4 of the wavelength is a suitable range. (2) A multi-channel design is adopted. Traditional single-channel flow has high resistance, resulting in high pump power consumption. Using multi-channel parallel connection can significantly reduce the flow velocity, thereby reducing the frictional loss along the flow path. Wang Jingjing et al. designed a three-channel plate heat exchanger; at a constant total flow rate, the flow resistance coefficient of this three-channel heat exchanger was reduced by more than 50% compared to that of a single-channel heat exchanger. (3) Reasonably mix media with high and low viscosities. When a high-viscosity medium exchanges heat with a low-viscosity medium, the low-viscosity medium can be placed on the side of the narrow flow channel to reduce flow resistance. Studies by Yao Jia and others have shown that by appropriately mixing in 10% of low-viscosity water, the pressure drop of high-viscosity crude oil in plate heat exchangers can be reduced by about 30%. (4) Optimize the import and export speed distribution. An uneven distribution of import and export speeds can lead to increased local resistance. Zhang Yong et al. used numerical simulation methods to optimize the velocity distribution in the inlet flow channel of the plate heat exchanger, reducing the pressure drop in the inlet section by 15%. Zheng Nan and others improved the velocity distribution in the outlet section by properly arranging guide vanes, thereby reducing the local drag coefficient by 20%. (5) Match the flow rate to the channel size. When designing heat exchangers, the flow rate and channel dimensions should be properly matched. Excessively high flow rates, while enhancing heat transfer, also cause significant flow resistance. On the basis of meeting process requirements, the flow rate should be appropriately reduced and the channel dimensions enlarged. Yao Jun and colleagues reduced the pressure drop by 30% while maintaining the heat transfer capacity, by optimizing the flow rate and channel width of the spiral plate heat exchanger.