Heat Transfer from Supercritical Carbon Dioxide in Tube Flow: A Critical Review

Characteristics of evaporative heat transfer and pressure drop of carbon dioxide and correlation development

Buoyancy effects on turbulent heat transfer of supercritical CO2 in a vertical mini-tube based on continuous wall temperature measurements

This work is devoted to investigating the difference in flow and heat transfer characteristics between vertical upward flow and horizontal flow of supercritical carbon dioxide (<inline-formula><tex-math id="Z-20240119215215">\begin{document}$\rm sCO_2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215215.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215215.png"/></alternatives></inline-formula>) based on the pseudo-boiling theory and the experimental parameters: mass flux <i>G</i> = 496–1100 kg/m<sup>2</sup>s, heat flux <i>q</i><sub>w</sub> = 54.4–300.2 kW/m<sup>2,</sup> and pressure <i>P</i> = 7.531–20.513 MPa. The differences in flow and heat transfer characteristics between horizontal upward tube and vertical upward tube are compared at different mass fluxes, heat fluxes and pressures fully. Finally, unlike the classical treatment of flow and heat transfer for supercritical fluid, single-phase fluid assumption is abandoned, instead, the pseudo-boiling theory is introduced to deal with the flow transfer and heat transfer of <inline-formula><tex-math id="Z-20240119215113">\begin{document}$\rm sCO_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215113.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215113.png"/></alternatives></inline-formula> in the two tubes. Supercritical fluid is regarded as a multiphase structure in this work, including a vapor-like layer near the wall and a liquid-like fluid in tube core. The results are indicated below. 1) In terms of heat transfer, the inner-wall temperature of the vertical upward tube and the bottom generatrix of horizontal tube are basically the same under normal heat transfer mode. When the heat transfer deterioration occurs in the vertical upward tube, larger supercritical boiling number (<i>SBO</i>) will cause the wall temperature peak of the vertical upward tube to be much higher than the wall temperature at top generatrix of the horizontal tube at the corresponding enthalpy. The <i>SBO</i> (<i>SBO</i> = 5.126×10<sup>–4</sup>) distinguishes between normal heat transfer deterioration and heat transfer deterioration in the vertical upward tube. In the horizontal tubes, <i>SBO</i> dominates the maximum wall temperature difference between the top generatrix and the bottom generatrix. Comparing with vertical upward tubes, higher <i>q</i><sub>w</sub>/<i>G</i> is required for the heat transfer deterioration of supercritical fluid in the horizontal tubes under the same pressure. 2) In terms of flow, the increase in slope of pressure drop in the vertical upward tube is due to the orifice contraction effect. The mechanism that dominates the variation of pressure drop in the horizontal tube is the flow stratification effect, and we show that Froude number <i>Fr</i><sub>ave</sub> can be the similarity criterion number to connect the temperature difference between the top and bottom generatrix of horizontal tube and the pressure drop. The analysis suggests that mechanisms governing horizontal flow and vertical flow of <inline-formula><tex-math id="Z-20240119215057">\begin{document}$\rm sCO_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215057.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215057.png"/></alternatives></inline-formula> are different in heat transfer deterioration mode. For the vertical flow, the <i>SBO</i> plays a leading role, while for the horizontal flow, the <i>Fr</i> plays an indispensable role.

Supercritical carbon dioxide (CO 2 ) has special thermal properties with better heat transfer and flow characteristics. Due to this reason, supercritical CO 2 is being used recently in air-condition and refrigeration systems to replace non environmental friendly refrigerants. Even though many researches have been done, there are not many literatures for heat transfer and flow characteristics of supercritical CO 2 . Therefore, the main purpose of this study is to develop flow and heat transfer CFD models on two different phases; vapour and supercritical of CO 2 to investigate the heat transfer characteristics and pressure drop in micro-channels. CO 2 is considered to be in different phases with different flow pressures but at same temperature. For the simulation, the CO 2 flow was assumed to be turbulent, nonisothermal and Newtonian. The numerical results for both phases are compared. From the numerical analysis, for both vapour and supercritical phases, the heat energy from CO 2 gas transferred to water to attain thermal equilibrium. The temperature of CO 2 at vapour phase decreased 1.78% compared to supercritical phase, which decreased for 0.56% from the inlet temperature. There was a drastic increase of 72% for average Nu when the phase changed from vapour to supercritical. The average Nu decreased rapidly about 41% after total pressure of 9.0 MPa. Pressure drop (Δ P ) increased together with Reynolds number ( Re ) for vapour and supercritical phases. When the phase changed from vapour to supercritical, Δ P was increased about 26%. The results obtained from this study can provide information for further investigations on supercritical CO 2 .

Numerical study on characteristics of heat transfer and friction factor in a circular tube with central slant rods

A review of heat transfer deterioration mechanisms and mitigation strategies of supercritical CO2 heat transfer

Experimental studies on the evaporative heat transfer and pressure drop of CO 2 in smooth and micro-fin tubes of the diameters of 5 and 9.52 mm

Modeling convective heat transfer of supercritical carbon dioxide using an artificial neural network

A comprehensive review on heat transfer and pressure drop characteristics and correlations with supercritical CO2 under heating and cooling applications

Supercritical carbon dioxide Taylor–Couette–Poiseuille flow heat transfer

The increasing importance of improving efficiency and reducing capital costs has lead to significant work studying advanced Brayton cycles for high temperature energy conversion. Using compact, highly efficient, diffusion-bonded heat exchangers for the recuperators, has been a noteworthy improvement in the design of advanced carbon dioxide Brayton Cycles. These heat exchangers will operate near the pseudocritical point of carbon dioxide, making use of the drastic variation of the thermo-physical properties. This paper focuses on the experimental measurements of heat transfer under cooling conditions, as well as pressure drop characteristics within a prototypic printed circuit heat exchanger. Studies utilize type-316 stainless steel, nine channel, semi-circular test section, and supercritical carbon dioxide serves as the working fluid throughout all experiments. The test section channels have a hydraulic diameter of 1.16mm and a length of 0.5m. The mini-channels are fabricated using current chemical etching technology, emulating techniques used in current diffusion bonded printed circuit heat exchanger manufacturing. Local heat transfer values were determined using measured wall temperatures and heat fluxes over a large set of experimental parameters that varied system pressure, inlet temperature, and mass flux. Experimentally determined heat transfer coefficients and pressure drop data are compared to correlations and earlier data available in literature. Modeling predictions using the CFD package FLUENT are included to supplement experimental data. All nine channels were modeled using known inlet conditions and measured wall temperatures as boundary conditions. The FLUENT results show excellent agreement in total power removal for the near pseudocritical region, as well as regions where carbon dioxide is a high or low density fluid.

The increasing importance of improving efficiency and reducing capital costs has led to significant work studying advanced Brayton cycles for high temperature energy conversion. Using compact, highly efficient, diffusion-bonded heat exchangers for the recuperators has been a noteworthy improvement in the design of advanced carbon dioxide Brayton cycles. These heat exchangers will operate near the pseudocritical point of carbon dioxide, making use of the drastic variation of the thermophysical properties. This paper focuses on the experimental measurements of heat transfer under cooling conditions, as well as pressure drop characteristics within a prototypic printed circuit heat exchanger. Studies utilize type-316 stainless steel, nine channel, semi-circular test section, and supercritical carbon dioxide serves as the working fluid throughout all experiments. The test section channels have a hydraulic diameter of 1.16 mm and a length of 0.5 m. The mini-channels are fabricated using current chemical etching technology, emulating techniques used in current diffusion-bonded printed circuit heat exchanger manufacturing. Local heat transfer values were determined using measured wall temperatures and heat fluxes over a large set of experimental parameters that varied system pressure, inlet temperature, and mass flux. Experimentally determined heat transfer coefficients and pressure drop data are compared to correlations and earlier data available in literature. Modeling predictions using the computational fluid dynamics (CFD) package FLUENT are included to supplement experimental data. All nine channels were modeled using known inlet conditions and measured wall temperatures as boundary conditions. The CFD results show excellent agreement in total heat removal for the near pseudocritical region, as well as regions where carbon dioxide is a high or low density fluid.

The supercritical carbon dioxide (S-CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) power generation system has the characteristics of compact structure and high efficiency, and can be applied to the waste heat recovery of ships. The hybrid heat exchanger with printed circuit heat exchanger (PCHE) and formed plate heat exchanger (FPHE) can meet the heat exchange requirements of S-CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and flue gas. In order to study the fin micro channels performance of hybrid heat exchangers, a simulation model of the fin micro channels of the hybrid heat exchanger was established. The effects of fin thickness, inlet temperatures and inlet mass flow rates on heat transfer and pressure drop characteristics were studied. The results show that the fin thicknesses of 0.2 mm 0.3 mm and 0.4 mm have little effect on heat transfer and pressure drop characteristics. When the inlet temperature increases from 663K to 723K, the total heat transfer rate increases, and the heat transfer coefficient and pressure drop remain substantially unchanged. When the mass flow rate of the inlet increases from 0.0007 kg/s to 0.0013 kg/s, the total heat exchange rate, total heat transfer coefficient and pressure drop increase. The research work in this paper can provide theoretical guidance for the design of the fin micro channels of the hybrid microchannel heat exchanger.

The heat transfer performance of the pulsating flow in the convergent-divergent tube is analyzed. The influence of pulsation amplitude, pulsation frequency and divergent segment-convergent segment ratio on heat transfer and resistance of the tube was simulated by numerical simulation. The results show that the heat transfer performance of the pulsating flow in the convergent-divergent tube is better than the fluid steady flow in the tube. The heat transfer is enhanced by about 11.4% compared with the fluid flow in the tube was steady. The pulsating flow in the tube strengthens the heat transfer, but also increases the resistance. Through the analysis of enhanced heat transfer comprehensive index, the heat transfer performance of the tube under pulsating flow conditions is significantly enhanced.

Supercritical CO&lt;sub&gt;2&lt;/sub&gt; can be used as a heat transfer fluid in a solar receiver, especially for a concentrating solar thermal power tower system. Such applications require better understanding of the heat transfer characteristics of supercritical CO&lt;sub&gt;2&lt;/sub&gt; in the solar receiver tube in a high temperature region. However, most of the existing experimental and numerical studies of the heat transfer characteristics of supercritical CO&lt;sub&gt;2&lt;/sub&gt; in tubes near the critical temperature region, and the corresponding heat transfer characteristics in the high temperature region are conducted. In this paper, a three-dimensional steady-state numerical simulation with the standard &lt;i&gt;k&lt;/i&gt;-&lt;i&gt;ε&lt;/i&gt; turbulent model is established by using ANSYS FLUENT for the flow and heat transfer of supercritical CO&lt;sub&gt;2&lt;/sub&gt; in a heated circular tube with an inner diameter of 6 mm and a length of 500 mm in the high temperature region. The effects of the fluid temperature (823–1023 K), the flow direction (horizontal, downward and upward), the pressure (7.5–9 MPa), the mass flux (200–500 kg·m&lt;sup&gt;–2&lt;/sup&gt;·s&lt;sup&gt;–1&lt;/sup&gt;) and the heat flux (100–800 kW·m&lt;sup&gt;–2&lt;/sup&gt;) on the convection heat transfer coefficient and Nusselt number are discussed. The results show that the convection heat transfer coefficient increases while Nusselt number decreases nearly linearly with fluid temperature increasing. Both fluid direction and pressure have negligible effects on the convection heat transfer coefficient and Nusselt number. Moreover, the convective heat transfer coefficient and Nusselt number are enhanced greatly with the increasing of mass flux and the decreasing of heat flux, which is more obvious at a higher heat flux. The influences of buoyancy and flow acceleration on the heat transfer characteristics are also investigated. The buoyancy effect can be ignored within the present parameter range. However, the flow acceleration induced by the high heat flux significantly deteriorates the heat transfer preformation. Moreover, eight heat transfer correlations of supercritical fluid in tubes are evaluated and compared with the present numerical data. The comparison indicates that the correlations based on the thermal property modification show better performance in the heat transfer prediction in the high temperature region than those based on the dimensionless number modification. And Nusselt number predicted by the best correlation has a mean absolute relative deviation of 8.1% compared with the present numerical results, with all predicted data points located in the deviation bandwidth of ±20%. The present work can provide a theoretical guidance for the optimal design and safe operation of concentrating solar receivers where supercritical CO&lt;sub&gt;2&lt;/sub&gt; is used as a heat transfer fluid.