⚡ electrical engineering

Experimental Investigation and Correlation Development of the Overall Heat Transfer Coefficient for a Multi-channel Evaporator Heated by Subcritical CO₂

This study experimentally investigates the overall heat transfer coefficient of a multi-channel evaporator heated by subcritical CO₂, demonstrating that the coefficient increases with higher mass flow rates and Reynolds numbers, and subsequently develops a highly accurate empirical correlation to guide the design and performance evaluation of such systems.

Original authors: Hongbo Wang, Cong Liu, Qimin Wang, Xiaohui Zhang

Published 2026-07-29

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CC BY 4.0

Original authors: Hongbo Wang, Cong Liu, Qimin Wang, Xiaohui Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to warm up a cold room, but instead of using a standard electric heater, you have a giant, invisible river of hot air rushing through your walls. This is the world of thermal energy storage, where scientists are looking for the best "heat couriers" to carry energy from a storage tank to a place where it's needed, like a factory or a power plant. For a long time, we've used air or water, but there's a new contender: carbon dioxide (CO₂). You might know CO₂ as the gas in your soda or the one plants breathe in, but when it's squeezed tight and heated up, it becomes a super-efficient heat carrier. The big question scientists are asking is: "How well does this hot CO₂ river actually dump its heat into water to turn it into steam?" It's a bit like trying to figure out exactly how fast a hot cup of coffee cools down when you pour it into a cold mug, but on a massive, industrial scale. If we can't predict this heat transfer perfectly, our energy systems might be inefficient, wasting precious fuel or failing to generate enough steam to spin turbines.

This paper is like a detective story where the authors set up a giant, high-tech playground to watch this heat exchange happen in real life. They built a special "multi-channel evaporator," which is essentially a bundle of 63 parallel pipes, like a dense forest of straws. They pumped hot, subcritical CO₂ (meaning it's hot but not quite at the super-critical, super-dense state) through these pipes while cold water flowed on the outside, trying to boil into steam. The team wanted to see how the speed of the CO₂ river changed the rate at which heat jumped from the gas to the water. They found that when they cranked up the CO₂ flow, making it rush faster through the pipes, the heat transfer got significantly better. Specifically, as they increased the "Reynolds number" (a fancy way of describing how turbulent and energetic the flow is) from about 120,000 to 205,000, the overall heat transfer coefficient jumped from 132.52 to 151.49 W/(m²·K). Think of it like stirring a pot of soup: the faster you stir, the more evenly and quickly the heat spreads.

But the real magic of this paper isn't just watching the heat move; it's about creating a "recipe" or a mathematical formula to predict exactly how well this will work in the future. The authors tested three different formulas to see which one could guess the heat transfer rate most accurately. They found that a simple formula based only on flow speed wasn't quite good enough. However, a more complex recipe that mixed the flow speed with the ratio of how much CO₂ was flowing versus how much water was flowing worked like a charm. Their best-performing formula was incredibly precise, with a maximum error of just 2.71%—which is tiny, especially considering the messy reality of hot gases and boiling water. They even checked their work by making sure the heat lost by the CO₂ matched the heat gained by the water, and they found they were about 92.2% in sync, which is a solid confirmation that their data was trustworthy.

So, what's the takeaway for anyone building these energy systems? The authors have handed engineers a new, reliable tool. They've proven that for this specific type of multi-channel pipe setup, you can predict exactly how much steam you'll get based on how fast you pump the CO₂. It's not a magic wand that solves every energy problem in the world, and the authors are careful to say this recipe works best for the specific pipe sizes and pressures they tested. But for anyone designing a system that uses hot CO₂ to make steam, this paper provides a clear, tested map to navigate the heat, ensuring that the energy stored in the CO₂ is delivered efficiently to the water waiting to turn into steam.

Technical Summary: Experimental Investigation and Correlation Development for a Multi-channel CO₂ Evaporator

Problem Statement
Subcritical carbon dioxide (CO₂) is increasingly recognized as a viable heat-release medium for high-temperature thermal energy storage and steam generation systems. While its thermodynamic adaptability in closed-loop cycles is well-documented, the specific heat-release behavior of gaseous subcritical CO₂ within evaporators remains insufficiently understood. Unlike conventional heat exchangers, these systems involve a unique coupling: single-phase forced convection on the CO₂ side transferring sensible heat to a water-steam side undergoing phase change. Existing literature largely focuses on refrigerant evaporation, falling-film processes, or porous media, leaving a gap in understanding the overall heat transfer performance of gaseous CO₂ releasing heat to generate steam. Furthermore, the applicability of standard heat transfer correlations to this specific multi-channel configuration has not been fully evaluated.

Methodology
The study employed an experimental approach using a dedicated multi-channel evaporator test rig. The system operated under steady-state conditions with CO₂ circulating in a closed loop, heated by a thermal storage medium before entering the evaporator.

Experimental Setup: The evaporator featured 63 parallel and staggered heat transfer channels. The CO₂ pressure was maintained at approximately 0.2 MPa (subcritical). The system was designed to generate steam at a rate of approximately 1.5 t/h.
Data Acquisition: Key parameters, including inlet/outlet temperatures, pressures, and flow rates for both the CO₂ and water-steam sides, were monitored using calibrated instruments (thermocouples, pressure transmitters, and flow meters).
Data Processing: The study utilized heat balance analysis to verify data reliability, calculating the heat released by CO₂ ( $Q_{CO_2}$ ) and the heat absorbed by the water-steam side ( $Q_w$ ). The overall heat transfer coefficient ( $U$ ) was derived using the logarithmic mean temperature difference ( $\Delta T_{lm}$ ).
Correlation Development: Based on the experimental dataset, three empirical correlations were developed to predict $U$ . These models ranged from a basic power-law function of the Reynolds number ($Re$) to more complex forms incorporating the Prandtl number ($Pr$) and the mass flow rate ratio between the CO₂ and steam sides ( $m_{CO_2}/m_s$ ).
Validation: The predictive accuracy of the correlations was assessed using statistical indicators: the coefficient of determination ( $R^2$ ), mean absolute percentage error (MAPE), root mean square error (RMSE), and maximum relative deviation ( $\delta_{max}$ ).

Key Results

Data Reliability: The heat balance ratio between the CO₂ side and the water-steam side ranged from 0.904 to 0.964, with an average of 0.922. This indicates that approximately 92.2% of the heat released by CO₂ was absorbed by the steam side, with the remainder attributed to heat loss and measurement uncertainty. The overall uncertainty of the heat transfer coefficient was calculated to be 5.62%.
Parametric Effects:
- Mass Flow Rate: The overall heat transfer coefficient ( $U$ ) increased with increasing CO₂ mass flow rate, rising from 132.52 to 151.49 W/(m²·K) as the flow rate increased. This is attributed to intensified forced convection and reduced thermal boundary layer thickness.
- Reynolds Number: A strong positive, non-linear correlation was observed between $U$ and $Re$. As $Re$ increased from approximately $1.20 \times 10^5$ to $2.05 \times 10^5$ , $U$ increased by approximately 14.3%.
Correlation Performance: Three correlations were compared. The recommended correlation, which incorporates the Reynolds number and the mass flow rate ratio (excluding the Prandtl number due to its narrow variation range), demonstrated the best balance of accuracy and simplicity:
$U = 0.044 \cdot Re^{0.774} \cdot \left(\frac{m_{CO_2}}{m_s}\right)^{0.891}$
This model achieved an $R^2$ of 0.9682, a MAPE of 0.5713%, an RMSE of 1.0354 W/(m²·K), and a maximum relative deviation of 2.7072%. Notably, the maximum deviation was lower than the experimental uncertainty of the coefficient itself.

Significance and Claims
The authors claim that this study provides essential experimental evidence for the heat-release behavior of subcritical CO₂ in steam-generating evaporators, a area previously lacking sufficient data. The primary contribution is the development of a validated empirical correlation that accurately predicts the overall heat transfer coefficient under specific operating conditions. The authors state that this correlation serves as a useful reference for the preliminary design, performance evaluation, and operating parameter optimization of evaporators in CO₂-based high-temperature heat-release systems.

The paper maintains a modest scope regarding its applicability, explicitly noting that the correlation is empirical and limited to the geometric structure and operating parameter ranges investigated (specifically the multi-channel evaporator design and subcritical pressure conditions). The authors suggest that future work is required to expand the database across different pressures, geometries, and water-steam-side conditions to improve the generality of the model.

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