Experimental study on pressure and temperature distribution characteristics of subcritical and supercritical water in vertical flow channel

A

Outside-wall heating area, m²

G

Mass flow rate, g min⁻¹

H

Specific enthalpy, kJ kg⁻¹

L

Distance to inlet, m

q

Heat flux density, W m⁻²

T

Temperature, K

ΔH

Enthalpy difference, kJ kg⁻¹

Δp

Pressure drop, MPa

δT

Horizontal temperature difference, K

ρ

Density, kg m⁻³

Subscripts

ave

Average of inlet and outlet

n

Measure point number

Supercritical water gasification (SCWG) has attracted significant attention from researchers as an efficient clean energy utilization technology to address global energy shortages and environmental degradation.^1–4 Due to its high solubility and reactivity with organic materials,⁵ SCWG can convert coal and biomass into hydrogen-rich fuels, enhancing combustion efficiency and recycling pollutants, making it a promising solution for future energy needs.

SCWG reactors are generally categorized into two types: batch reactors^6,7 and continuous reactors.^8,9 Compared to batch reactors, continuous reactors offer advantages such as easier temperature and pressure control, as well as higher efficiency, making them particularly suited for short-term reactions.¹⁰ However, in supercritical continuous reactors, maintaining uniform pressure and temperature is challenging due to several factors, including strong buoyancy-driven flow, mixing of hot and cold fluids, and external wall heating. Temperature variations inside the reactor can lead to different chemical reactions, such as pyrolysis, oxidation, and gasification, which may affect the reaction process and product outcomes. Therefore, understanding pressure and temperature distribution in continuous reactors is crucial for improving reaction efficiency and optimizing reactor design.

The flow in a supercritical continuous reactor can be simplified transcritical and supercritical water flow in vertically placed tubes or flow channels. However, the nonlinear variations in the physical properties of the transcritical state present challenges for studying flow and temperature distribution in these conditions. Some physical properties of water near the pseudocritical point under 22.5 MPa, calculated using IAPWS-IF97 equations,¹¹ are shown in Fig. 1. The pseudocritical point is defined as the point where specific heat capacity reaches its peak at pressures above the critical pressure (22.064 MPa). These unique physical properties significantly influence flow and heat transfer characteristics in the flow channel, as reported in numerous studies. Generally, heat transfer in supercritical water can be classified into three modes: normal heat transfer, heat transfer enhancement, and heat transfer deterioration.¹² Of these, heat transfer deterioration must be avoided in engineering applications because it usually leads to a low heat transfer coefficient and high wall temperatures. Early experiments on supercritical flow in circular tubes demonstrated that heat transfer deterioration occurs at low mass flow rates or high heat flux densities, particularly near the experimental section’s inlet and at locations with pseudocritical temperatures.^13–16 Similar phenomena have been observed in studies involving tubes,^14,15 annulus,^16,17 and rod bundles.¹⁸ Further experimental studies^19–21 have indicated that buoyancy and thermal acceleration effects, caused by drastic variation in physical properties near the pseudocritical point, are the main reasons for heat transfer deterioration. When the wall temperature reaches the pseudocritical temperature, the fluid density in the boundary layer decreases rapidly, causing buoyancy-driven upward flow thereby that reduces the velocity gradient and heat transfer efficiency. This suggests that buoyancy effects may also affect temperature distribution within the supercritical continuous reactor.

On the other hand, numerical simulations of flow and heat transfer in supercritical fluids are limited compared to those of conventional fluids. It has been observed that wall functions are not valid when buoyancy effects and variable thermodynamic properties exist, making them unsuitable for predicting heat transfer deterioration.^22,23 Jaromin and Anglart²⁴ and Mao et al.²⁵ recommended the SST k-ω turbulent model for simulating supercritical water flow and heat transfer, although Lei et al.²⁶ argued that this model does not perform very well for horizontal tubes with secondary flow. Wen and Gu²⁷ stated that low Re models can predict buoyancy effects on heat transfer to some extent. In summary, there has been extensive research on the flow and heat transfer characteristics of supercritical fluids in flow channels of various applications. The uniqueness of supercritical fluids compared to conventional fluids has been confirmed. However, it remains difficult to establish unified laws and mechanisms to fully explain the flow and temperature distribution in supercritical water continuous reactors. Therefore, further research is needed to expand our understanding.

In this work, an experimental system was designed to study the flow of subcritical and supercritical water in a channel, serving as a simplified model of a continuous reactor. The main objective was to investigate the characteristics of pressure drop and temperature distribution under different operating conditions. Finally, the influencing factors and mechanisms were analyzed and demonstrated based on the experimental data obtained.

The schematic diagram of the experimental system is shown in Fig. 1. Preheated subcritical water enters from the inlet at the bottom of the flow channel. It is reheated by heaters on two opposite sidewalls, bringing the water to a supercritical state. The system is designed for a maximum temperature of 723 K and a maximum pressure of 24 MPa. The flow channel has a rectangular cross-section with dimensions of 10 × 5 mm², and a total length of 900 mm, 300 mm of which constitutes the test section. An insulation layer surrounds the flow channel to minimize heat loss. The system’s flow rate and pressure are regulated by a constant flow pump and a backpressure valve. A heat exchanger located downstream of the flow channel ensures that the water discharged is at a safe temperature for the backpressure valve.

The layout of the measurement points is shown in Fig. 2. Pressure sensors, numbered #1 and #9, are located at both ends of the test section to measure pressure drop. Calibrated thermocouples are numbered from #2 to #8, arranged from the bottom to the top of the test section. Thermocouples #2 and #8 measure the inlet and outlet temperatures of the test section, respectively, while thermocouples #3, #5, and #7 consist of three thermocouples arranged in parallel at the same height. The distance between adjacent measurement points along the flow direction is 50 mm, and the parallel thermocouples are spaced 2.5 mm apart. In total, there are 13 thermocouples in the test section (numbered #2, #3-1, #3-2, #3-3, #4, #5-1, #5-2, #5-3, #6, #7-1, #7-2, #7-3, and #8), allowing for temperature measurements along and perpendicular to the flow direction.

To verify the accuracy of the experimental system, a series of validation tests were conducted. First, the relative deviation between thermocouples was checked. The test was performed at room temperature, as it is difficult to maintain a completely uniform temperature distribution inside the flow channel during heating. The results, shown in Table I, indicate that the range of measured temperatures for all thermocouples is 291.70 ± 0.07 K, with a difference of only 0.13 K between the maximum and minimum values, confirming that the relative deviations among the measurement points are minimal.

Next, repeatability tests were conducted under transcritical conditions. Parameters such as pressure drop, inlet and outlet temperatures, enthalpy difference across the test section, and the temperatures of the three parallel thermocouples (using #7 as an example) were used for comparison. The results, shown in Table II, demonstrate that the measured temperatures were relatively stable across three repeated experiments, with a maximum temperature difference of 0.63 K across all parameters. The pressure variation was 0.02 MPa, which is 12% of the average pressure drop. These results indicate that the measured data have acceptable repeatability. Additionally, the tests show that the temperature difference perpendicular to the flow direction, measured by the three thermocouples at #7, is not random, and this will be discussed in subsequent sections.

Generally, the pressure drop along the flow direction consists of both fluid friction and gravitational pressure drop, typically leading to a positive pressure drop at lower enthalpy levels. Since the mass flow rate remains constant, the negative pressure drop can be explained by increased volume expansion and decreasing fluid density as specific enthalpy rises. This volume expansion leads to a local pressure increase that overcomes the losses from friction and gravity. Figure 4 shows the relationship between water density and specific enthalpy, which follows a similar trend to the pressure drop seen in Fig. 3, even in the transcritical region, providing further support for this explanation. Thus, the change in water density during the transcritical process cannot be ignored.

Under subcritical conditions, the measured specific enthalpy distribution is nearly linear, with measured enthalpy and temperature values slightly higher than the calculated ones. This deviation is likely due to increased heat dissipation as the temperature rises along the flow direction during the experiment. In contrast, for supercritical conditions, there is a larger deviation between the measured and calculated enthalpy distributions near the pseudocritical point, which can be attributed to the effects of heat transfer deterioration. However, the temperature distribution remains relatively consistent due to the high heat capacity of transcritical water. Based on these results, the temperature and specific enthalpy (excluding the transcritical region) along the flow direction can be predicted to some extent and are mainly controlled by forced flow and heating conditions, as described by Eq. (2).

To analyze the temperature distribution perpendicular to the flow direction, thermocouples #3, #5, and #7 (as shown in Fig. 2 and Sec. II) were used. It is worth noting that the temperatures referred to for #3, #5, and #7 correspond to the middle thermocouples of the three parallel sensors (#3-2, #5-2, and #7-2). Figure 6 shows the measured temperatures at different points in both subcritical and supercritical conditions (as listed in Table III). The temperature readings from the three thermocouples differed slightly, forming a pattern with the highest temperature in the middle and lower temperatures on both sides. The maximum difference between the three thermocouples at each measurement point, referred to as the horizontal temperature difference, can be used to quantify temperature non-uniformity. In subcritical conditions, the horizontal temperature differences at measurement points #3, #5, and #7 were 2.40, 1.81, and 0.97 K, respectively. For supercritical conditions, these differences were 2.44, 0.30, and 3.84 K, respectively. It is important to note that, in supercritical conditions, the measurement points #3, #5, and #7 fall within the subcritical, transcritical, and supercritical regions, respectively.

These results suggest that the temperature distribution perpendicular to the flow direction becomes more uniform in the subcritical region as the fluid temperature approaches the pseudocritical point. On the other hand, horizontal temperature differences are minimal near the pseudocritical point due to the high heat capacity but increase significantly in the supercritical region. Although the results from subcritical and supercritical cases are not directly comparable due to different heating conditions, it can be inferred that the increased flow fluctuations in the supercritical state lead to larger horizontal temperature variations. The causes of these fluctuations may include near-wall natural convection due to wall heating, turbulent forced flow, and fluid volume expansion. However, the data available in this section are insufficient for a detailed analysis, and further investigation will be conducted in Sec. III B with additional test data.

The enthalpy difference between the outlet and inlet is solely determined by wall heating. In fact, the enthalpy difference is a more appropriate metric than wall heat flux density for representing the heat absorbed by the water, due to unavoidable heat dissipation along the flow direction. In other words, the enthalpy difference acts as the net wall heat flux density. Similar to Sec. III C, subcritical and supercritical cases are tested and discussed separately. By adjusting the preheating power, the temperatures at measurement point #7 are maintained constant within each experimental group as the enthalpy difference changes. This ensures that the bulk fluid temperature does not affect the horizontal temperature distribution. Additionally, the mass flow rate is kept constant within each group. Measurement point #7 is chosen for comparison because it is more likely to reach a supercritical state within the experimental system’s design parameters.

Figure 7 shows the variation of the horizontal temperature difference at measurement point #7 with enthalpy difference in both the subcritical and supercritical cases. The data in Fig. 7 indicates that the horizontal temperature difference increases linearly with enthalpy difference in the subcritical case but remains nearly constant in the supercritical case. Moreover, the horizontal temperature differences in supercritical cases are significantly higher than those in subcritical cases, consistent with the results presented in Sec. III B.

Similarly, when investigating the effect of mass flow rate, the enthalpy difference between the outlet and inlet and the temperature at measurement point #7 are held constant. Figure 8 shows the variation of the horizontal temperature difference at measurement point #7 with mass flow rate under both subcritical and supercritical conditions. The effect of mass flow rate on horizontal temperature difference is found to be similar to that of the enthalpy difference. In subcritical cases, the influence of mass flow rate diminishes as the rate increases. Essentially, increases in both enthalpy difference and mass flow rate correspond to the enhancement of near-wall natural convection (due to wall heating) and turbulent forced flow, respectively. Therefore, it can be concluded that horizontal temperature uniformity in the subcritical region is influenced by these two factors, as proposed in Sec. III B. In supercritical cases, the fluid’s volume expansion fluctuations are greatly amplified, leading to much higher horizontal temperature differences, which overshadow the effects of enthalpy difference and mass flow rate. To confirm this, further investigation is needed into how the bulk fluid temperature at measurement point #7 behaves in supercritical cases.

In this section, fluid temperature variation in the supercritical region is achieved by adjusting preheating and sidewall heating conditions while maintaining the same mass flow rate. As demonstrated in Sec. III C 1, enthalpy differences have little effect on horizontal temperature differences in supercritical cases. Thus, the obtained data remain valid even when enthalpy differences between different heating conditions are not completely consistent (ranging from 800 to 1100 kJ kg⁻¹). Figure 9 shows the variation of the horizontal temperature difference at measurement point #7 with fluid temperature in supercritical cases. The horizontal temperature difference is lower when the bulk fluid temperature is either near or far from the pseudocritical point, leading to a peak of 4.29 K at about 664 K in horizontal axis. Near the pseudocritical point, the low horizontal temperature difference can be explained by the fluid’s high heat capacity. As the fluid temperature rises, the rapid decrease in the fluid’s volume expansion coefficient (see Fig. 1) reduces fluctuations caused by fluid expansion, leading to a decrease in horizontal temperature difference, which corresponds with the inference in Sec. III C 2. In summary, among the three factors mentioned in Sec. III B, near-wall natural convection and turbulent forced flow fluctuations mainly affect horizontal temperature differences in the subcritical region, whereas the effects of fluid volume expansion are more pronounced when the fluid temperature is slightly higher than the pseudocritical point.

In this work, an experimental system was developed to investigate the pressure drop and temperature distribution in a vertically placed flow channel. Subcritical and supercritical conditions were achieved by adjusting preheating and wall heating settings. The characteristics of pressure drop and temperature distribution along and perpendicular to the flow direction were studied, and the factors affecting horizontal temperature differences were analyzed. Based on the experimental data, the main results and conclusions are as follows:

1. The pressure drop decreases from 0.091 to −0.177 MPa as the average enthalpy of the inlet and outlet increases from 600 to 2300 kJ kg⁻¹, showing a negative linear correlation. Fluid volume expansion along the flow direction is speculated as the main reason of this relationship and the negative pressure drop at high average enthalpy.

2. The temperature and specific enthalpy along the flow direction can be predicted by theoretical calculations, but the specific enthalpy near the pseudocritical point deviates from the calculated values.

3. In subcritical cases, the horizontal temperature difference is positively correlated with the enthalpy difference and mass flow rate, while it remains nearly unchanged in supercritical cases.

4. The horizontal temperature difference first increases and then decreases as the fluid temperature rises from the pseudocritical point, leading to a peak of 4.29 K at a fluid temperature of 664 K.

Based on these results, it can be concluded that near-wall natural convection and turbulent forced flow fluctuations mainly affect the horizontal temperature difference in subcritical regions, whereas fluid volume expansion becomes the dominant factor when the fluid temperature is slightly higher than the pseudocritical point.

This work is financially supported by the National Key R&D Program of China (Grant No. 2020YFA0714400).

The authors have no conflicts to disclose.

Hui Jin: Funding acquisition (equal); Methodology (equal); Supervision (equal). Huibo Wang: Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). Yi Li: Investigation (equal); Writing – original draft (equal). Petr A. Nikrityuk: Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.