CO₂-SASS: A Modular Test Rig for the Scientific Assessment of Heat Transfer of Carbon Dioxide in the Supercritical State

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this work, a modular test rig to study heat transfer with supercritical carbon dioxide has been developed and validated. The topic is interesting and design is novel. This work can be published after addressing the following issues.

1. The manuscript lacks a detailed discussion on the repeatability of experimental measurements for the CO2-SASS rig. It is recommended to add experimental data on the repeatability of key parameters (e.g., local heat transfer coefficient, pressure drop) under identical operating conditions, which is critical to verify the reliability and stability of the test rig for long-term experiments.
2. In Section 6 (System calibration and measurement uncertainty), the uncertainty analysis of the pipe roughness is only briefly mentioned (1.15 µm) but not integrated into the overall uncertainty propagation of the heat transfer coefficient. Please supplement the quantitative analysis of how pipe roughness affects the friction factor and further impacts the calculated heat transfer coefficient and pressure drop results.

Author Response

We sincerely thank the reviewer for the assessment of our work and for the constructive comments provided. We appreciate the recognition of the novelty of the test rig design. The manuscript has been revised accordingly, and the requested clarifications and additional analyses have been incorporated. A detailed point-by-point response is provided below.

Comments 1: The manuscript lacks a detailed discussion on the repeatability of experimental measurements for the CO2-SASS rig. It is recommended to add experimental data on the repeatability of key parameters (e.g., local heat transfer coefficient, pressure drop) under identical operating conditions, which is critical to verify the reliability and stability of the test rig for long-term experiments.

Thank you for pointing this out, as it is an important characteristic of a reliable data acquisition facility. We have included a paragraph discussing this issue.

To assess repeatability, selected operating points were repeated on different days, with the facility fully shut down and restarted between runs. The relative difference in the local heat transfer coefficient between repeated measurements was typically below 5% in the liquid-like region (away from the pseudo-critical regime), with most data points showing deviations of only a few percent, demonstrating good experimental stability. Under such conditions, the relative difference in pressure drop measurements remained below 1%.

Comments 2: In Section 6 (System calibration and measurement uncertainty), the uncertainty analysis of the pipe roughness is only briefly mentioned (1.15 µm) but not integrated into the overall uncertainty propagation of the heat transfer coefficient. Please supplement the quantitative analysis of how pipe roughness affects the friction factor and further impacts the calculated heat transfer coefficient and pressure drop results.

Thank you for this valuable suggestion. We agree that the influence of pipe roughness should be quantitatively assessed. The manuscript has been revised in Section 6 (System calibration and measurement uncertainty) to include an explicit analysis of how roughness affects the friction factor, pressure drop, and ultimately the heat transfer coefficient.

In the turbulent regime relevant to the present experiments (Re ≈ 10⁴–10⁵), the dependence of the Darcy friction factor on relative roughness (ε/D) is weak. Using the Swamee–Jain explicit form of the Colebrook relation, the roughness contribution to the friction factor uncertainty was estimated via a local sensitivity analysis. For D ≈ 1 mm and ε = 1.15 ± 0.05 μm (corresponding to ε/D ≈ 1.1×10⁻³ and a relative roughness uncertainty of approximately 4.3%), and taking a representative Reynolds number of 10⁵, the resulting relative uncertainty in the friction factor is approximately 0.7%.

Since the frictional pressure drop is proportional to the friction factor (Darcy–Weisbach relation), the same relative contribution applies to the pressure drop. Assuming conservatively a total frictional pressure drop of about 1 bar over the heated length, the roughness-induced uncertainty corresponds to approximately 0.007 bar. This value is small compared to the absolute pressure uncertainty of approximately 0.2 bar.

The resulting pressure-drop uncertainty propagates to the enthalpy-rise term through (∂h/∂P)_T·u_{ΔP,ε}. Its magnitude is negligible compared to the dominant contributions arising from temperature and mass flow uncertainties. Therefore, the contribution of roughness uncertainty to the overall relative uncertainty of the heat transfer coefficient is negligible.

 

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents CO2-SASS, a well-designed and carefully instrumented high-pressure test rig for localized heat transfer and pressure drop measurements of supercritical CO₂ in small-diameter channels. The work addresses a clear gap in experimental capabilities for micro-scale cooling applications and is strongly motivated by the needs of modern microelectronics thermal management. The experimental design is rigorous, with independent control of key operating parameters and high-quality local measurements.

A major strength is the authors’ strong focus on temperature measurement accuracy, including detailed calibration procedures and cold-junction correction, supported by a thorough and transparent uncertainty analysis. The discussion clearly demonstrates an excellent understanding of the challenges associated with measurements near the pseudo-critical region. Overall, the manuscript is technically sound, clearly written, and provides a valuable experimental contribution that will benefit future research in supercritical CO₂ heat transfer. I recommend publication.

Author Response

We sincerely thank the reviewer for the positive assessment of our work and for the constructive evaluation of the experimental design and uncertainty analysis. We greatly appreciate the recognition of the rigor of the temperature calibration procedure and the relevance of the setup for supercritical CO₂ heat transfer research.

We are grateful for the recommendation for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a well-designed and validated test rig for supercritical CO₂ heat transfer with high measurement accuracy; however, revisions are needed to improve clarity and presentation.

What novel scientific insights does CO₂-SASS offer over existing sCO₂ test rigs, especially for heat transfer in small-diameter channels.

Justify assuming uniform axial heat flux despite strong property gradients near the pseudo-critical region.

Figure 2(a) and Figure 2(b) should be clearly labelled, with the key components and features clearly labelled.

Based on the uncertainty analysis, provide practical operating guidelines to maintain the relative uncertainty of the heat-transfer coefficient within acceptable limits.

Could the authors provide the LabVIEW source and project files in a LabVIEW 2018–compatible format?

Author Response

We sincerely thank the reviewer for the careful evaluation of our manuscript and for the constructive comments provided. We appreciate the positive assessment of the design and validation of the CO₂-SASS test rig and its measurement accuracy. The suggested revisions have helped us improve the clarity and overall presentation of the manuscript.

Comments 1: What novel scientific insights does CO₂-SASS offer over existing sCO₂ test rigs, especially for heat transfer in small-diameter channels.

CO₂-SASS enables systematic measurement of local heat transfer coefficients in small-diameter channels under supercritical conditions. While numerous studies report averaged heat transfer coefficients in macro-scale tubes, experimental data in channels below 2 mm diameter remain extremely scarce. Further, only one study reports local heat transfer data in a 1 mm pipe.

Therefore, the novelty of CO₂-SASS lies in:

• The use of a 1 mm inner diameter channel representative of detector cooling applications.
• The ability to measure local wall temperatures and derive local heat transfer coefficients.
• The operation across the pseudo-critical region under controlled pressure and mass flux conditions.
• A detailed and traceable calibration procedure with a rigorous uncertainty quantification.

This combination allows a structured, high-accuracy dataset suitable for correlation assessment and future model development in small diameters.

Comments 2: Justify assuming uniform axial heat flux despite strong property gradients near the pseudo-critical region.

The assumption of uniform axial heat flux originates from the imposed boundary condition rather than from thermophysical property behavior. The electrical heating elements are designed to provide a spatially uniform power input per unit length along the test section. As a result, the imposed wall heat flux is uniform by construction.

While thermophysical properties of CO₂ vary strongly near the pseudo-critical region, these gradients influence the local temperature response and heat transfer coefficient, not the externally imposed heat flux distribution. The local convective heat transfer coefficient may vary significantly; however, the axial heat input remains controlled by the electrical power supplied to the heater.

From an energy balance perspective, the enthalpy increase of the fluid must correspond to the integrated heat input. If the applied heat flux is uniform along the heated length, the axial increase in bulk enthalpy follows directly from conservation of energy, independent of local property gradients.

Comments 3: Figure 2(a) and Figure 2(b) should be clearly labelled, with the key components and features clearly labelled.

Thank you for this comment. Labels have been added to the revised manuscript.

Comments 4: Based on the uncertainty analysis, provide practical operating guidelines to maintain the relative uncertainty of the heat-transfer coefficient within acceptable limits.

Thank you for this valuable suggestion, as it adds completeness to the manuscript. Based on the uncertainty analysis presented in Section 8, practical operating guidelines have been added to the revised manuscript to help maintain the relative uncertainty of the heat transfer coefficient within acceptable limits.

Certain practical considerations can be identified to maintain a controlled relative uncertainty in the heat transfer coefficient. A primary factor is the thermodynamic proximity of the inlet and outlet states to the pseudo-critical region. When either endpoint lies close to the pseudo-critical temperature at a given pressure—particularly at pressures near the critical value—the strong gradients in thermophysical properties significantly increase the propagated uncertainty of the enthalpy rise. Consequently, operating points in this region inherently carry higher relative uncertainty and require careful thermodynamic evaluation. Furthermore, sufficient thermal input is required to ensure a measurable enthalpy rise. For a given absolute measurement accuracy, a small enthalpy increase leads to a larger relative uncertainty in $\Delta h$, directly affecting the derived heat transfer coefficient.

In addition, small wall–bulk temperature differences amplify the contribution of temperature measurement uncertainty, as demonstrated in the preceding derivation. These effects do not prevent operation in such regimes, but rather highlight that low driving temperature differences demand proportionally higher measurement accuracy and careful uncertainty propagation.

Indeed, the reliability of the heat transfer coefficient determination depends critically on the individual calibration and characterization of all temperature and pressure sensors involved. Detailed and transparent reporting of calibration procedures is therefore essential for meaningful comparison of results across different experimental facilities.

Comments 5: Could the authors provide the LabVIEW source and project files in a LabVIEW 2018–compatible format?

Thank you for this suggestion. The LabVIEW source and project files are provided in the version currently used for operation of the CO₂-SASS facility. Due to compatibility limitations between LabVIEW versions, reliable backward conversion to LabVIEW 2018 cannot be guaranteed without potential loss of functionality. We therefore provide the files in the current supported format and recommend the use of an updated LabVIEW environment for replication and further development.

 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

None