ReviewCounterflow heat exchanger with core and plenums at both ends
Graphical abstract
Introduction
Heat exchangers are a central topic in thermal science and engineering because of their essential role across the landscape of technology, from geothermal and fossil power generation to refrigeration, desalination, and air conditioning [1], [2], [3], [4]. The literature on heat exchangers is voluminous and continues to be active today (e.g., Refs. [5], [6], [7], [8], [9], [10]). The field covers two main aspects of this class of flow systems: fluid flow and heat transfer performance, and ways (criteria) of evaluating performance [11], [12], [13], [14], [15]. The general trend in the field is to develop heat exchangers that offer better performance. This trend is universal in evolution [16], and unites heat exchangers with other evolutionary flow systems, bio, non bio, and manmade.
The starting point for the present paper is the observation that all performance criteria change, and hopefully improve, when one changes and chooses a better flowing architecture. This, the free evolution of the flow architecture is captured by the law of physics of evolution [17]: it is the essence of constructal design [18], and serves as unifying method for all evolutionary design phenomena. Here, we illustrate this approach by analyzing a morphing two-stream counterflow heat exchanger with one plenum at each end. The key architectural feature to be discovered is how much of the total volume is allocated to the counterflow core and the plenums.
Section snippets
Model
Two streams flow in counterflow through parallel tubes of diameter D, in a core situated between two plenums. As shown in Fig. 1, each stream arrives into a plenum (xL) by flowing across tubes that carry the second stream. At the other end, the second stream arrives into a plenum by flowing across tubes that carry the first stream.
The elemental volume of the heat exchanger has the longitudinal length L (one plenum + the flow length of one stream) and the width H = nD, shown in the
Pressure drop
The overall pressure drop experienced by one stream is due to contributions from the plenum (p) and the core flow (c), through tubes of diameter D and length (1 − x) L,
The plenum has the flow cross section xLD, flow length H (vertical in Fig. 1), and average fluid velocity . The drag force experienced by each tube of length xL (or frontal area xLD) inside the plenum is , where we regard CD as of order 1, based on the assumption that the Reynolds number
Thermal conductance
The thermal contact between the two streams in Fig. 1 is proportional to the overall thermal conductancewhere hp,tot and hc,tot are the overall heat transfer coefficients including htc on both sides of the tubes and conduction through the tube. Ap and Ac are the contact surfaces in the plenum and the core,or using H ∼ nD:where n is the number of tubes in cross flow in each plenum, and hp and hc are the respective scales (orders of
Numerical method
The pressure drop experienced by one stream in the counterflow parallel tubes solved analytically in the previous section can be solved numerically using the software COMSOL [23]. Consider a fixed element volume of one stream in the heat exchanger with a longitudinal length L = 1 m (one plenum + core), width H = 1 m and depth W = 0.1 m, as shown in Fig. 4. The number of parallel counterflow tubes in the element volume is n = 8. Each tube has the diameter D = 0.7 W. The fluid is water and the flow is
Effectiveness
In order to find the effectiveness of the heat exchanger, consider a fixed element volume of two streams and in a heat exchanger with a longitudinal length L = 2 m, transversal dimension H = 0.4 m and depth W = 0.1 m. As shown in Fig. 6, the hot stream enters the volume at one end with temperature Th,in = 330 K, and the cold stream enters the volume at the other end with temperature Tc,in = 295 K. Each stream flows through a tube before exiting the volume. The tube diameter remains D = 0.7 W. The flow is
Conclusions
Correlations for laminar and turbulent flows were used to assess performance of a heat exchanger that consists of a core sandwiched between two plenums. The length of the core with respect to the length of the plenums is sought based on two objectives: low flow resistance and low thermal resistance. The analysis showed that both the pressure drop and thermal resistance monotonically decrease with decreasing the core length.
In order to verify the use of correlations to evaluate the pressure
Acknowledgements
This work was performed for the project “Freeform Heat Exchangers for Binary Geothermal Power Plants” sponsored by the Geothermal Technologies Program, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy under contract DE-AC05-00OR22725, Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC. Mr. Alalaimi’s work was supported by Kuwait University, Kuwait.
Notice: This submission was sponsored by a contractor of the United States Government under contract
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