⚡ electrical engineering

Improvement of Two-Phase Flow Simulation in a Thermosyphon Using a New Saturation Temperature Model

This study introduces and validates a new mean saturation temperature model within an OpenFOAM-based CFD solver that significantly improves the accuracy of transient two-phase flow simulations in thermosyphons by dynamically accounting for internal pressure and temperature variations, outperforming conventional constant-saturation approaches with errors below 6%.

Original authors: Quang-Hat Cao, Shehnaz Akhtar, Minseong Choi, Kyoungsik Chang, Sang-Wook Lee

Published 2026-11-04

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CC BY 4.0

Original authors: Quang-Hat Cao, Shehnaz Akhtar, Minseong Choi, Kyoungsik Chang, Sang-Wook Lee

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

Heat moves through the world in predictable ways, but when a liquid turns into a gas and back again inside a sealed tube, the physics become a complex dance of pressure, temperature, and gravity. These sealed tubes, known as thermosyphons, are simple yet powerful devices used to move heat from one place to another without any moving parts like pumps or fans. They work because a liquid at the bottom absorbs heat, boils into vapor, rises to the top, releases that heat, and turns back into a liquid to fall down again. This cycle is essential for cooling everything from spacecraft to solar energy systems. However, predicting exactly how these tubes behave, especially when they are just starting up, has been a stubborn challenge for engineers. For decades, computer models used to design these systems relied on a simplifying assumption: that the temperature at which the liquid boils stays the same throughout the entire process. While this made the math easier, it ignored the reality that the pressure and temperature inside the tube are constantly shifting as the system warms up from a cold start.

A team of researchers at the University of Ulsan in South Korea has developed a new way to simulate this behavior that captures those shifting conditions. Instead of assuming a fixed boiling point, their new computer model calculates the saturation temperature—the specific point where the liquid turns to gas—as a dynamic value that changes based on the average temperatures of the hot bottom section and the cool top section. They built this model into a free, open-source software tool called OpenFOAM, which allows scientists to visualize the invisible flow of fluids inside the tube. By tracking how the liquid and vapor mix and move, and by accounting for how heat travels through the metal walls of the tube itself, the researchers created a more realistic picture of what happens inside a thermosyphon. Their work suggests that by letting the boiling temperature change as the system operates, they can predict the tube's performance with much greater accuracy than previous methods.

The researchers tested their new approach by simulating the startup of a thermosyphon and comparing the results against real-world experiments and older computer models. In the past, standard simulations often struggled to predict the temperature of the tube's walls during the critical startup phase, sometimes missing the mark by a significant margin. The new model, however, showed a much tighter alignment with reality. When the team compared their predictions to experimental data, the error in the wall temperature readings dropped to less than six percent across all the scenarios they tested. This improvement is particularly important in the evaporator section, the bottom part of the tube where heat is first absorbed. Here, the old models tended to overestimate the temperature because they could not account for the rapid changes in the boiling point as the system heated up. The new model, by contrast, tracked these local changes, providing a clearer view of how the heat moves from the wall into the liquid.

Beyond just getting the numbers right, the simulations revealed how the amount of liquid inside the tube affects how quickly the system settles into a steady rhythm. The researchers found that the "filling ratio," or how much of the tube is filled with liquid, plays a major role in startup speed. When the tube was filled with only a small amount of liquid, it took much longer to reach a stable operating state. In these low-fill scenarios, the liquid struggled to form a continuous film along the walls, leading to patches of dry surface that had to be rewetted repeatedly before the flow stabilized. This instability delayed the system, taking up to 55 seconds to settle. As the team increased the amount of liquid, the system stabilized much faster. When the tube was filled to capacity, the steady state was reached in just 18 seconds. The extra liquid ensured a constant supply to the heated surface, preventing the dry patches and allowing the circulation to smooth out almost immediately.

The study also looked at how the tube handles different amounts of heat input. Whether the heat applied was moderate or high, the new model consistently outperformed the older, static approaches. It correctly predicted that as more heat is added, the overall resistance to heat flow decreases, meaning the tube becomes more efficient at moving energy. This happens because higher heat levels cause the liquid to boil more vigorously, creating more vapor that rises quickly and carries energy to the top. The researchers noted that while their model is a significant step forward, it still has limits. It assumes the flow is smooth and two-dimensional, and it does not yet account for non-condensable gases that might get trapped inside real-world tubes. Nevertheless, the work demonstrates that treating the boiling temperature as a variable rather than a constant is key to understanding these systems. By refining how we simulate the invisible dance of phase change, this new tool offers a reliable way for engineers to design better cooling systems for the future, ensuring that heat is managed efficiently in everything from electronics to space exploration.

Technical Summary: Improvement of Two-Phase Flow Simulation in a Thermosyphon Using a New Saturation Temperature Model

Problem Statement
Thermosyphons (wickless heat pipes) are critical for thermal management in aerospace, electronics, and solar applications. While Computational Fluid Dynamics (CFD) offers a cost-effective method to investigate their internal flow and heat transfer, existing numerical simulations often rely on a simplifying assumption: a constant saturation temperature ( $T_{sat}$ ). This paper identifies that such an assumption is inadequate for modeling transient operations, particularly during startup. During startup, the internal pressure and temperature of the thermosyphon evolve dynamically until a steady state is reached; a fixed $T_{sat}$ fails to capture this transient behavior, leading to inaccuracies in predicting wall temperatures and thermal resistance. Furthermore, the authors note that open-source CFD frameworks like OpenFOAM currently possess limited capabilities for simulating conjugate heat transfer involving phase change.

Methodology
To address these limitations, the authors developed a new solver based on the interFoam solver in OpenFOAM (version 8). The methodology integrates the following components:

Governing Equations: The solver employs the Volume of Fluid (VOF) method for interface tracking and assumes laminar, incompressible, two-dimensional flow. It solves the mixture continuity, momentum, and energy equations, including latent heat terms for phase change and conjugate heat transfer between the fluid and solid walls.
Phase Change Model: The Lee evaporation-condensation model is utilized to compute mass transfer rates.
New Saturation Temperature Model: The core innovation is a mean saturation temperature model derived from the equilibrium conditions of the Lee model. Instead of a constant value, $T_{sat}$ is calculated as a weighted function of the mean temperatures at the evaporator ( $\bar{T}_e$ ) and condenser ( $\bar{T}_c$ ) sections:
$T_{sat} = \frac{A\bar{T}_e + \bar{T}_c}{A + 1}$
where $A$ is a non-dimensional coefficient dependent on evaporation/condensation coefficients and phase densities.
Numerical Scheme: The PIMPLE algorithm handles pressure-velocity coupling, and the Multi-dimensional Universal Limiter for Explicit Solution (MULES) tracks the volume fraction. The simulations use an adaptive time step with a Courant number of 0.8.
Validation: The model was validated against published experimental data and prior numerical results across multiple heat flux conditions and geometries (Cases 1–4).

Key Contributions

Development of a Transient Saturation Model: The paper introduces a formulation where $T_{sat}$ evolves dynamically based on the thermal state of the evaporator and condenser, rather than remaining static.
OpenFOAM Implementation: The study provides a functional, open-source solver capable of handling conjugate heat transfer and phase change in thermosyphons, addressing a gap in current OpenFOAM capabilities.
Improved Accuracy: The new model specifically targets the improvement of wall temperature predictions in the evaporator section, which is identified as the most critical region for thermal design.

Results

Startup Behavior: In the validation case (Case 1), the model successfully captured the transient temperature evolution from startup to steady state (approx. 120 seconds). The predicted temperature profiles in the evaporator, adiabatic, and condenser sections showed close agreement with experimental data, with a maximum deviation of less than 2%.
Wall Temperature Accuracy: Compared to simulations using a constant saturation temperature, the proposed mean saturation model significantly reduced errors in evaporator wall temperature predictions. The errors were maintained below 6% across all tested cases. The constant model tended to overpredict wall temperatures in the evaporator due to its inability to capture local superheat driving nucleate boiling.
Thermal Resistance: The new model predicted thermal resistance with a maximum error of 34%, a notable improvement over the 54.7% error observed in previous constant-saturation simulations. Thermal resistance was observed to decrease as heating power increased, consistent with established literature.
Filling Ratio Effects: The study investigated the relationship between filling ratio and the time required to reach steady state. Results indicated that lower filling ratios (e.g., 25%) require significantly longer times to stabilize (55 s) due to intermittent dry-out and re-wetting cycles. As the filling ratio increased to 100%, the steady-state time decreased to 18 s, with the system achieving a more uniform, isothermal temperature profile.

Significance and Claims
The authors claim that the proposed OpenFOAM-based solver offers a "reliable and accessible tool" for simulating phase-change heat transfer in thermosyphon systems. The primary significance lies in the demonstrated ability of the new saturation temperature model to improve the accuracy of transient simulations, particularly during the critical startup phase and in the evaporator section. By moving away from the constant saturation assumption, the model provides a more physically representative description of the thermosyphon's internal dynamics.

The paper maintains a modest tone regarding its scope, acknowledging limitations such as the assumption of two-dimensional, laminar flow and the neglect of non-condensable gases, which may contribute to deviations in the condenser section. The authors suggest that future work will extend the model to three dimensions and refine the saturation temperature closure to include local phase-fraction weighting, but they do not propose specific new applications beyond the simulation of thermosyphon systems.

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