Review of advancements in heat transfer

1. 1
NAGPUR
Recent Advancement in the field of Heat Transfer
Amritansh Manthapurwar
V-A-09, MECHANICAL DEPT.

2. 2
Experimental investigation on natural
circulation heat transfer of supercritical CO2
in a closed loop
YuanluLi, Gongming Xin, Baoqiang Yuan, Shuangxing Zhang, Wenjing Du
School of Energy and Power Engineering, Shandong University,
Jinan 250061, China

3. 3
Highlights
● The flow and heat transfer of supercritical CO2 natural circulation in
closed loop were studied.
● Normal heat transfer and heat transfer deterioration were also observed.
● A heat transfer deterioration criterion for natural circulation was
obtained.
● A heat transfer correlation applicable to supercritical CO2 natural
circulation is developed.

4. 4
● The natural circulation system based on supercritical CO2 has attracted attention due to its
simple structure and safety compared with the forced circulation system. This work
presented an experimental investigation of the heat transfer characteristics of CO2 based on
natural circulation.
● Two heat transfer modes can also be observed in supercritical CO2 natural circulation,
normal heat transfer and heat transfer deterioration. The development of heat transfer
deterioration criterion and heat transfer correlation is significant for the application of
supercritical CO2 natural circulation, but there are few related studies.
● Direct adoption of the supercritical CO2 forced convective criteria and heat transfer
correlations to natural circulation introduces large deviations. By analyzing the existing
research results of forced convection in supercritical CO2 and introducing new
dimensionless parameters SBO and K, a deterioration criterion and a heat transfer
correlation suitable for natural circulation of supercritical CO2 are developed based on
experimental data.
● The new criterion can well distinguish the two heat transfer modes, and the new correlation
improves markedly. The results can benefit engineering applications in advanced power
cycles.
Abstract

5. 5
Discussion
● Supercritical fluids have been widely used in various industrial applications, such as
chemical extraction, nuclear reactors, refrigeration systems, heat pumps and geothermal
energy. Especially in the field of nuclear energy supercritical fluids are widely used and play
an important role in the development of nuclear energy, and are considered to be the ideal
working medium for GEN 4 nuclear reactors. Supercritical CO2 (sCO2) has received more
and more attention due to its special thermodynamic properties. Carbon dioxide is
inexpensive, environmentally friendly, abundant in reserves, and its critical pressure and
temperature are 7.38 MPa and 31.1°C, respectively, making it easier to supercritical.
● The sCO2 has promising applications. However, in the pseudo-critical region, the physical
properties of CO2 vary drastically with temperature, as shown in Fig. 1, resulting in complex
heat transfer characteristics. Therefore, many scholars have conducted in-depth studies on
sCO2 in recent years. However, due to the complexity of its heat transfer behavior, there are
still doubts in some aspects.

6. 6
● It is undeniable that there are two modes of heat transfer in the forced convection of
sCO2 in a tube: normal heat transfer (NHT) and heat transfer deterioration (HTD).
The normal heat transfer is consistent with the conventional single-phase heat
transfer, where the wall temperature profile varies monotonically with the direction of
flow, and we can use the Dittus-Boelter equation to predict the heat transfer.
● When the heat transfer deteriorates, a local high temperature will be generated in the
heating section, and the temperature will increase abnormally and then fall back
along the flow direction. This poses challenges to the safety of equipment. In order to
deeply explore the application value of sCO2, many scholars were committed to the
study of heat transfer deterioration prediction and heat transfer correlation of
supercritical fluid.

7. 7
Fig. 1. Thermal-physical properties of supercritical CO2 at pressure of 7.5 MPa.

8. 8
● Although research on supercritical fluid has been around since the 1930s, most of these
studies were limited to the heat transfer characteristics of sCO2 under forced convection,
while few studies on sCO2 natural circulation have been conducted. In a natural circulation
loop (also called NCL or thermosyphon), the fluid is driven by buoyancy force resulting from
the density difference between the hot and cold fluid.
● With the elimination of driving components, such as pumps, natural circulation systems are
simple and reliable, thus outperforming forced circulation systems in terms of cost and
system safety. Natural circulation loop based on supercritical fluid has been applied to
nuclear cooling and in other energy systems, such as solar energy conversion, geothermal
energy utilization.
● Liu et al. experimentally investigated the heat transfer characteristics of sCO2 in a
rectangular circulation loop, in which significant heat transfer enhancement and heat
transfer deterioration were observed. The effects of heat flux, pressure, buoyancy force on
heat transfer of sCO2 were carefully discussed. They concluded that steep gradient of physical
property over the tube cross-section is the key reason for heat transfer deterioration.

9. 9
● Liu et al. then conducted a theoretical and experimental study of the steady-state
characteristics of the sCO2 natural circulation. The effects of system pressure, inlet
temperature and enthalpy difference on the steady-state characteristics were discussed in
detail. And a new theoretical model was further validated. Deng et al. investigated the
flow and heat transfer characteristics of the sCO2 natural circulation system both
numerically and experimentally. The flow changes during the heat flux input variation
were investigated, and it was found that the supercritical natural circulation flow is very
sensitive to the heat flow variation.
● It is worth noting that prediction of heat transfer is important for sCO2 natural
circulation applications due to the fact that heat transfer deterioration also occurs in
natural circulation, but there is a lack of research on heat transfer prediction in sCO2
natural circulation. Fortunately, there is a lot of in-depth research on predicting heat
transfer deterioration in forced convection, which provides a foundation for the study of
heat transfer deterioration in natural circulation.

10. 10
● As heat transfer deterioration can pose a challenge to the safety of equipment, many scholars
have proposed various deterioration criteria based on forced convection of sCO2 in order to
accurately predict the heat transfer deterioration. Table 1 summarizes several existing
deterioration criteria. However, due to the complex heat transfer characteristics of sCO2,
there is no unified conclusion on the heat transfer deterioration criterion. In the earliest
study of forced convection of sCO2, it was found that heat transfer deterioration was related
to heat flux qw and mass flux G, and a basic heat transfer deterioration criterion was
proposed, which contained only qw and G parameters.
● The heat transfer deterioration and normal heat transfer can be distinguished by drawing
qw∼G graphs, such as qw,CHF = 0.0002G2 proposed by Kim et al. [28], qw,CHF = 0.00316G1.49
proposed by Zhang et al. [29] and qw,CHF = 0.116G proposed by Shiralkar et al. [30], which
all belong to this type of criterion. However, these criteria were found to be flawed in
subsequent studies and only suitable for the scholar's own range of experimental
parameters, which are difficult to extend.

11. 11
● More results show that using two parameters, qw and G, to predict deterioration is not
sufficient and that heat transfer deterioration is not only related to these two
parameters.
● Therefore, more and more complex criteria based on qw and G were proposed, Cheng
et al. took pressure P into account, Kline et al. took pipe diameter d into account, and
Ma et al. criterion was more complex, and the fluid inlet temperature Tin, diameter d
and pressure P were considered.

12. 12

13. 13
● The development process through the deterioration criteria shows that new parameters are
constantly introduced, which does not solve the problem fundamentally. In the recent
years of sCO2 research, Zhu et al. provided a new theory. They analogized the heat transfer
behavior under supercritical pressure with the growth and detachment of bubbles under
subcritical pressure. Under the subcritical pressure two-phase flow, the force on the
expansion of the bubble tends to attach the bubble to the wall, which is called the
evaporation induced momentum force FM'v. On the other hand, the mass flux G exerts an
inertial force FI’ on the bubbles, making the bubbles tend to detach the wall.
● The relative magnitude of the two forces is called the K number, Eq. (1), which reflects the
competition between evaporation induced momentum force and inertia force. Where the
term qw/(G·ifg) is the Bo (boiling number). A large K number indicates the vapor expansion
to attach the bubble on the wall. Coalescence of various bubbles forms a vapor blanket to
trigger the wall temperature overshoot. Alternatively, a small K number represents large
inertia force to detach the bubble from the wall.

14. 14
● Thus, the tube wall can be rewetted by liquid to keep better heat transfer performance. They
compared supercritical heat transfer with boiling under subcritical pressure and proposed
new dimensionless numbers supercritical K and SBO (supercritical boiling number). The
basis of this theory lies in the fact that supercritical fluids are not homogeneous fluids, and
their physical properties change drastically at a certain temperature and pressure, called the
pseudo-critical point, which can divide supercritical fluid into two different regions, the
liquid-like and gas-like regions, as shown in Fig. 2. K = (qw/G·ipc)2ρb/ρw, supercritical K
reflects the competitive relationship between the two forces, momentum force and inertia
force of gas-like layer evaporation, and reflects the influence of gas-like layer on heat
transfer.
● Zhu et al. defined qw/G·ipc in K as SBO (supercritical boiling number), SBO = qw/G·ipc. The
SBO was used to successfully predict the heat transfer deterioration of sCO2 forced
convective. The proposed new parameters K and SBO provide a new method for
supercritical fluid study.

15. 15
Fig. 2. Phase diagram of CO2.

16. 16
● At the same time, fitting the heat transfer correlation is also critical to accurately predict Nu,
which is essential for the application of sCO2 natural circulation. Due to the complexity of
supercritical fluid heat transfer, it is difficult to obtain analytical solutions, most of which are
empirical correlations. Table 2 lists four typical heat transfer correlations with different
structures and different ranges of applicable parameters. Jackson et al. and Gupta et al.
correlations are two widely used sCO2 forced convective heat transfer correlations. Liu et al.
proposed a heat transfer correlation in the study of sCO2 natural circulation, and the
buoyancy Bu was introduced into the correlation.
● However, due to the lack of relevant research on the development of sCO2 natural circulation
heat transfer correlation, there is no widely accepted heat transfer correlation. Locally, the
sCO2 flow is caused by the pressure difference between the inlet and outlet, which is
consistent with the forced convection. However, on the whole, the driving force of the system
is caused by the change of the physical properties of sCO2, which is different from the forced
convection.

17. ● The flow and heat transfer behaviors of natural circulation require further discussion
compared to forced convection. The applicability of forced convection correlations is also
discussed further, and a correlation suitable for natural circulation needs to be developed
on the basis of forced convection.
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● In this study, an experimental system for natural circulation of CO2 in a closed loop was
established. The general trends and heat transfer characteristics of natural circulation were
analyzed.
● The effects of operating parameters on flow and heat transfer were discussed in detail, such
as heat flux, mass flux, pressure and filling mass. Subsequently, the sCO2 forced convection
deterioration criteria and correlations were analyzed and compared, and a deterioration
criterion and heat transfer correlation with higher prediction accuracy were developed for
the natural circulation of sCO2 based on experimental data. The results of the study can
provide theoretical guidance for the design and optimization of the sCO2 power cycle.

18. 18

19. CONCLUSION
The experiment investigates the flow and heat transfer characteristics of supercritical CO2 in a closed
natural circulation loop. The following conclusions are obtained:
1. A closed loop natural circulation system is built. The general trend and heat transfer characteristics
of sCO2 natural circulation are analyzed. There are also two heat transfer modes in the natural
circulation, normal heat transfer (NHT) and heat transfer deterioration (HTD).
2. The transition of heat transfer mode is analyzed and the existing HTD criteria of sCO2 are evaluated.
A new dimensionless parameter, SBO, is introduced to develop a heat transfer deterioration criterion
for the natural circulation of sCO2, qw,CHF = 3.05 × 10−4G·ipc.
3. The existing sCO2 forced convection heat transfer correlation is not applicable to natural circulation.
By comparing and analyzing several typical sCO2 heat transfer correlations and introducing the
dimensionless parameter K number into the sCO2 natural circulation heat transfer correlation, a heat
transfer correlation applicable to sCO2 natural circulation is developed. The new correlation
improves markedly, which captures 96.31% of the data with an accuracy of ±30%.
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20. References
● https://www.sciencedirect.com/science/article/pii/S0017931022009723
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21. THANK YOU
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