Analysis of heat and mass transfer characteristics of supercritical CO 2 in vertical U-tube

. The heat and mass exchange of CO 2 in a vertical U-tube under supercritical pressure was simulated. The effects of the geometry of the bend area, The center arc radius of the bend area and the different bend orientations on the flow heat transfer of supercritical CO 2 in the U-tube were analyzed. The results show that in the bend area, the flow is affected by the combined action of centrifugal force and gravity, as well as the pipe structure, so the flow mixing is intense, and the heat transfer capacity is significantly enhanced. When the direction of the bend changes, the interaction between centrifugal force and gravity will affect the heat transfer at pipe bending. When the central arc radius r of the bend area increases from 0.5D to 3D, the heat transfer at the bend can be strengthened, but will weaken the heat transfer at the bend outlet area.


Introduction
As a new and efficient refrigerant, supercritical fluid has been widely used in chemical engineering, power engineering, aerospace technology and other fields.Due to the drastic change of the thermal properties of supercritical fluid in the pseudo-critical zone, the study of its flow heat transfer in various pipelines has received more and more attention.The use of supercritical fluid as refrigerant is a promising new refrigeration method.However, due to the complex change of thermal properties of supercritical fluid, numerous constraints of supercritical heat transfer experiment, and various heat transfer situations in pipelines, supercritical heat transfer still needs to be studied in depth.At present, the research of supercritical fluid working medium at home and abroad mainly focuses on water, CO2, helium and nitrogen [1].The research on supercritical fluid flow pipeline at home and abroad mainly focuses on straight passage, U-shaped passage, serpentine passage and spiral passage.U-shaped channel is a kind of structure widely used in heat exchange equipment.Because the flow of ordinary fluid will turn when flowing through the U-shaped bend area, the flow will be separated to form a secondary flow, so that the local pressure drop [2] can not be ignored.For supercritical CO2, the conditions will be more complicated, because it is subject to the combined action of buoyancy, gravity and centrifugal force.The complex flow and heat transfer characteristics of supercritical CO 2 in the U-tube will determine the overall performance of supercritical CO 2 heat exchangers.Therefore, this paper intends to study the flow heat transfer of supercritical CO 2 in the U-tube, and analyze the influence of the number of bends and the geometry of the bends on the flow and heat transfer characteristics of supercritical CO 2 , which provides a partial reference for the design of efficient supercritical CO 2 heat exchanger.Zhang Lina et [3] al., Wang Junhui et[4] al., studied the heat transfer characteristics of horizontal circular tubes, and analyzed the influence of heat flux, wall temperature, mass flow rate and pressure on the convective heat transfer of CO 2 .Jiang et [5] al. conducted experiments and numerical simulations on convective heat transfer of supercritical CO 2 in a vertical circular tube, and the results showed that flow direction and velocity had little influence on heat transfer, and no heat transfer deterioration occurred.Wei et [6] al., Ma Xu et [7] al studied supercritical flow heat transfer in a rotating Utube, and analyzed the influences of rotational speed, rotational radius and pipe diameter on heat transfer characteristics.Xu et [8] al. conducted an experimental study on the characteristics of carbon dioxide heat transfer in the spiral tube, and found that the fluid turbulence was increased when flowing in the spiral tube, and the influence of floating lift and gravity on the fluid heat transfer factor was intensified, so the heat transfer efficiency of the fluid in the spiral tube was higher than that in the straight tube.Nemati et [9] al. found that, compared with ideal gas heat transfer, the additional term in the average flow control equation has a significant effect on the energy balance.The Reynolds mean Navier-Stokes equation (RANS) is an economical and easy way to model turbulence.Pecnik et [10] al. point out that multiple revisions to turbulence models often negatively affect the accuracy of the model's turbulent kinetic energy.He et [11,12] al. carried out numerical studies using the two-path turbulence model and found that the turbulence model significantly overestimated the flow stratification, which led to the deterioration of heat transfer.
Based on the continuity equation, momentum conservation equation and energy conservation equation of compressible fluid, and considering the thermophysical parameters of supercritical CO 2 as well as the compressibility effect and floating lift effect of the flow, this paper studies and analyzes the heat and mass transfer characteristics of supercritical CO 2 when it flows in a Utube uniformly heated on the outer wall by numerical simulation.And through the distribution characteristics of the flow field velocity, temperature, turbulent kinetic energy and heat transfer coefficient inside the tube to further analyze the heat and mass transfer characteristics of supercritical CO 2 flowing in the U-tube.And the special phenomena of fluid passing through U-tube and the influence of the change of center arc radius in bend area on the heat and mass transfer ability of fluid flowing in tube are analyzed.

Governing equation and physical model 2.1 Governing Equations
The governing equation [13] for fluid flow heat transfer in a U-tube heated with uniform heat flux is as follows: Continuous equation: Momentum equation: Energy equation: Where 2 2 2 2 3 In the above formula, x is the Cartesian coordinate,m; i is the general spatial index; g is acceleration of gravity, m/s 2 ; r is the radius of curvature of the bend, m; u, w are radial and axial velocity respectively, m/s; p is fluid pressure, Pa; T is the fluid temperature, K; cp is the specific heat capacity of the fluid, J/(kgꞏK); ρ is fluid density, m/s 2 ; μ is hydrodynamic viscosity, Paꞏs; λ is the fluid thermal conductivity, W/(mꞏK); β is the coefficient of volume expansion, K -1 ; k is the turbulent kinetic energy, m 2 /s 2 .

Physical model and boundary conditions
In this paper, the flow and heat transfer characteristics of supercritical CO 2 in U-tube are numerically simulated.The physical model is shown in Fig. 1.
The flow area of supercritical CO 2 adopts a doublebend U-tube model.The pipe is vertically arranged as shown in the figure.Supercritical CO 2 with an inlet temperature of 25℃ Tin enters from the bottom of the flow inlet and flows vertically upward into a straight pipe section with inner diameter D of 9mm.When flowing in this section of pipe and subsequent pipes, the fluid is uniformly heated by a heat flux q of 16 kw/m 2 outside the pipe.After passing through the 500mm straight pipe section, it enters the U-shaped bend, which is a bend with an arc upward, and the diameter of the pipe with three times the central arc radius of the bend section is 27mm, and then passes through the straight pipe with the same size and then enters a U-shaped bend with the arc downward, the size of the pipe is unchanged, and finally flows out through the straight pipe upward.The mass flow rate of supercritical CO 2 flowing in the pipe is 300kg/m 2 •s.The above physical model is divided into meshes.In order to make the simulation results closer to the experimental results, the U-tube is divided into meshes as shown in Fig. 1.Hexahedral structured meshes are adopted, uniform meshes are adopted along the fluid flow direction, nonuniform meshes are adopted in the radial direction, and the size of the meshes is smaller the closer it is to the wall.The O-shaped grid is used to divide the cross-section of the round pipe, which can solve the problem that the distortion rate of the grid in the center of the cylinder is too large, and the grid division at the bend of the pipe is shown in Fig. 1.

Result analysis and discussion
In this paper, ANSYS FLUENT is used for calculation, SST k-ω [14] model is used for turbulence model, and curvature correction is carried out, and SMPLIC algorithm is used for pressure velocity coupling.. Since the thermal properties of CO 2 change rapidly near the pseudo-critical temperature, the model adopts the variable properties.Based on the self-programming of REFPROP in NIST database, the supercritical CO 2 thermal properties journal file is established in advance.During calculation, the journal file is directly read in FLUENT to obtain the thermal physical property parameters such as ρ, cp, λ and μ.The operating pressure of the whole simulation experiment is P=8MPa, the operating temperature is T=25℃, and the acceleration of gravity in the z direction is gz=9.8N/kg.In this paper, the turbulence intensity is defined as the ratio of the root  1.

Model verification
In order to ensure the accuracy of the calculation model, according to the physical model and method described above, the heat and mass transfer in supercritical tubes was verified by using the experimental results of Dang and Hihara [15] in literature [15].The parameters of the verified model are inlet temperature Tin=25℃, inlet pressure Pin=8MPa, tube length L=475mm, tube inner diameter D=6mm, inlet mass flow rate G= 200,400 kg/(m 2 ꞏs), wall heat flux q=12.0kW/m2.The comparison between numerical calculation results and experimental data is shown in Fig. 2. It can be seen that the calculated results are basically consistent with the experimental results of the two mass flow rates.When the mass flow rate is G=200kg/(m 2 ꞏs), the numerical calculation results are consistent with the experimental data.When G=400kg/(m 2 ꞏs) and the average CO 2 temperature is 308-316℃, the numerical simulation average heat transfer is significantly higher.This may be due to the fact that the temperature of CO 2 is near quasi-critical when the tube is flowing.In order to verify the validity of the numerical method, the flow and heat transfer characteristics of supercritical CO 2 in horizontal tubes were simulated using the same grid scale and numerical method, and compared with the published experimental results.Before using the model for simulation calculation, it is necessary to verify the grid independence and select grid types with similar fit degree and relatively small number of grids.In this paper, three structured grids with different distribution types are created, which mainly change the grid distribution in the radial way and distribute the grid evenly in the axial way.Specific parameters are shown in Table 2. Fig. 3 shows the simulation results of the three types of grids under the conditions set above.There is a small difference in the calculation results of the three grids, among which Case 2 and Case 3 basically coincide, which indicates that Case 2 not only meets the need of independence, but also meets the calculation accuracy requirements.Therefore, the grid in Case 2 is selected in this paper for the subsequent numerical simulation analysis.

Influence of the geometry of the bend area on the flow and heat transfer characteristics
In this paper, the flow heat transfer characteristics of supercritical CO 2 in U-tube are studied.Fig. 4 and Fig. 5 show the distribution of temperature and flow velocity at different sections in the U-tube.It can be found that when supercritical CO 2 flows vertically upward in the straight pipe at the front end of the U-bend, its internal fluid temperature distribution is exactly the same, and due to the heating effect of the tube wall, the fluid temperature increases gradually from the entrance, forming a uniform high-temperature fluid zone around the wall, and the mainstream temperature is relatively low.When the conventional fluid enters the Ubend area, the mainstream fluid will shift to the outer wall due to the action of centrifugal force, and the flow of the fluid will no longer be one-way flow, forming a secondary vortex structure, called Dean vortex.However, since the density of supercritical CO 2 changes dramatically with temperature near the quasi-critical point, the gravity change dominates when supercritical CO 2 flows through the bend area.The mainstream of high-density fluid sinks towards the inner wall under the action of gravity, forming a secondary vortex structure opposite to the Dean vortex form, as shown in the cloud image of the bend area in Fig. 5.After flowing out of the bend area, the non-uniform temperature field and velocity field gradually dissipate and weaken with the mixing of the fluid.However, at this time, due to the influence of pressure gradient, the fluid will accelerate separation at the outlet of the bend area, forming a low-speed and high-temperature fluid area.Fig. 6 shows the distribution of turbulent kinetic energy at different sections of U-tube.Before entering the U-shaped bend area, the overall level of turbulent kinetic energy is low, and the floating lift near the wall is relatively large.When the fluid enters the U-bend area, the fluid with higher turbulent kinetic energy begins to sink and move to the inner wall under the action of gravity.Due to the separation of the fluid, the turbulent kinetic energy of the fluid after the bend is much greater than that before the bend.The increase of turbulent kinetic energy at the bend enhances the heat transfer performance of the fluid.Therefore, the study of the bend area plays an important role in improving the heat transfer performance of heat exchange equipment.There are two abrupt changes in the heat transfer coefficient in the curve, because the larger the central arc radius of the bend, the larger the centrifugal force, and the increase of the centrifugal force will lead to the increase of radial velocity, thus strengthening the secondary flow at the section and enhancing the heat transfer capacity.
However, as the central arc of the bend increases from 0.5D to 3D, the flow separation and flow mixing strength weaken, and the fluid with high turbulent kinetic energy moves from the inner wall to the outer wall, which gradually reduces the level of turbulent kinetic energy and weakens the heat transfer ability.Therefore, as shown in Fig. 7, when the radius of the central arc of the bend is changed, the overall heat transfer capacity does not change greatly, and there are certain differences in the average heat transfer coefficient in the bend area.It can be judged that there is only one optimal bend center arc radius for U-tubes with different pipe diameters.

Conclusion
In this paper, the heat and mass transfer characteristics of supercritical CO 2 in U-tube are studied by numerical simulation.The influence of different bending center arc radius and bending direction on supercritical temperature field is compared.The following conclusions are obtained: (1) After CO 2 absorbs heat in the pipe, its temperature increases gradually along the inlet to the outlet, most of the fluid pressure in the pipe exceeds the critical pressure, when the temperature reaches the critical temperature, the fluid will enter the supercritical state.When supercritical CO 2 is in the bend area, it is affected by gravity to form a secondary flow structure, which is opposite to the Dean vortex of conventional fluid.After the fluid flows out of the bend area, the flow separation and secondary flow lead to the sharp fluctuation of the pressure in the bend area.
(2) As the radius of the center arc of the bend increases from 0.5D to 3D, the centrifugal force increases during the bend.The increase of centrifugal force can strengthen the secondary flow of fluid flowing in the tube, and play a role in strengthening the heat transfer at the bend.After turning, the flow separation and fluid mixing weaken with the increase of the bend center arc radius, and the fluid will separate and form a low-speed and high-temperature fluid to move to the outer wall after flowing out of the bend, weakening the heat transfer of the fluid in the straight tube after the turn.
(3) When U-tube is used in supercritical CO2 heat exchanger, the heat transfer characteristics of U-tube can be optimized by changing the geometric parameters and layout of U-tube.There are many factors that can be optimized and improved in future experiments and studies to further enhance the heat exchange performance of supercritical heat exchangers.

Fig. 2 .
Fig. 2. The relationship between the average heat transfer coefficient and the mainstream temperature.(Source of experimental data [17])

Fig. 4
Fig. 4 Temperature distribution of U-tube section

Fig. 5
Fig. 5 Velocity distribution of U-tube section

Fig. 6
Fig. 6 Turbulent kinetic energy distribution of U-tube section

Fig. 7
Fig. 7 Average heat transfer coefficient distribution of U-tube with center arc radius of different bending sections

Table 1 .
Example boundary conditions

Table 2
describes the grid division status Fig. 3 Comparison of calculated values of mean temperature of cross section