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Heat transfer deterioration (HTD) is one of the important issues in the study of supercritical fluid (SCF) heat transfer. However, when the SCF crosses the pseudo-critical point, the none-quilibrium process occurs in liquid, so SCF is very complicated. Recently, the existence of SCF pseudo-boiling on a macro scale has sparked controversy. There is still no unified understanding of the mechanism of gas-like and liquid-like transition affecting heat transfer. In this work, it is assumed that SCF has a macroscopic phenomenon similar to subcritical flow boiling. By analogy with subcritical boiling heat transfer, a boiling critical point model is proposed to describe the HTD in supercritical CO 2. Our study reveals that the HTD caused by pseudo-boiling only occurs under large temperature gradient, which makes the superheated liquid-like layer cover the wall, and the gas-like and liquid-like may present different distribution forms, thus changing the heat transfer characteristics. When the wall temperature is higher than the pseudo-critical temperature and the enthalpy of the fluid layer covering the wall exceeds a certain value, the HTD may occur. The proposed theoretical model can explain the experimental results well, and the prediction accuracy of heat transfer correlation considering pseudo-boiling is greatly improved. In this work, the connection between supercritical heat transfer and subcritical heat transfer is established theoretically, which provides a new idea for studying the deterioration of SCF heat transfer, thus enriching the theory of supercritical heat transfer.
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Keywords:
- supercritical fluid/
- expansion/
- pseudo-boiling/
- heat transfer deterioration/
- theoretical model
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Ref. Correlation Operatings parameters [25] $N{u_{\text{b}}} = 0.023 Re_{\text{b}}^{1.03}Pr_{\text{b}}^{0.5}{F_1}{F_2} \qquad\qquad \qquad \qquad \qquad \qquad \qquad \qquad $ CO2/H2O/R134a ${F_1} = \left\{ {\begin{aligned} &0.98, & &{\text{ for }}{{\textit{π}} _{\text{A}}} < 1.75 \times {{10}^{ - 4}}, \\ &0.85 + 0.056{{\left( {{{10}^4}{{\textit{π}} _{\text{A}}}} \right)}^{1.5}}, & &{\text{ for }}1.75 \times {{10}^{ - 4}} \leqslant {{\textit{π}} _{\text{A}}} < 3.75 \times {{10}^{ - 4}}, \\ &13.1/4.5 + {{\left( {104{{\textit{π}} _{\text{A}}}} \right)}^{1.35}}, & &{\text{ for }}3.75 \times {{10}^{ - 4}} < {{\textit{π}} _{\text{A}}} ,\end{aligned}} \right.$ $ {F_2} = \left\{ {\begin{aligned} & 0.93 Pr_{\text{b}}^{0.265}, & &{\text{ for }}P{r_{\text{b}}} \leqslant 2.5, \\ &1.61 Pr_{\text{b}}^{ - 0.333}, & &{\text{ for }}P{r_{\text{b}}} > 2.5, \end{aligned}} \right. \qquad {{\textit{π}} _{\text{A}}} = \dfrac{{{q_{\text{w}}}{\beta _{\text{b}}}}}{{G{c_{{\text{p}}, {\text{b}}}}}} \qquad\qquad \qquad\qquad $ [26] $N u_{\mathrm{w}}=0.0033 R e_{\mathrm{w}}^{0.94} \overline{Pr}_{\mathrm{w}}^{0.76}\left( {\rho_{\mathrm{w}}}/{\rho_{\mathrm{b}}}\right)^{0.16}\left( {\mu_{\mathrm{w}}}/{\mu_{\mathrm{b}}}\right)^{0.4} $ — [27] $N u_{\mathrm{b}}=0.0061 R e_{\mathrm{b}}^{0.904} P r_{\mathrm{b}, \mathrm{ave}}^{0.684}\left({\rho_{\mathrm{w}}}/{\rho_{\mathrm{b}}}\right)^{0.564}$ H2O
P= 24 MPa;di= 10.0 mm
G= 200—1500 kg/(m2·s)
qw= 0—1250 kW/m2$P{r_{{\mathrm{b, ave}}}} = \dfrac{{{\mu _{\text{b}}}}}{{{\lambda _{{\mathrm{b}}} }}}\dfrac{{{i_{{\mathrm{w}}} } - {i_{{\mathrm{b}}} }}}{{{T_{{\mathrm{w}}} } - {T_{{\mathrm{b}}} }}}$ [28] $ N{u_{\mathrm{b}}} = 0.226 Re_{\mathrm{b}}^{1.174}Pr_{{{\mathrm{b}}} , {\mathrm{ave}}}^{1.057}{\left( {\dfrac{{{\rho _{\mathrm{w}}}}}{{{\rho _{{\mathrm{b}}} }}}} \right)^{0.571}}{\left( {\dfrac{{{{\overline c }_{{{\mathrm{p, b}}}}}}}{{{c_{{{\mathrm{p} , b}}}}}}} \right)^{1.023}}A{c^{0.489}}B{u^{0.0021}} $ CO2
P= 7.46—10.26 MPa
di= 4.5 mm
G= 208–847 kg/(m2·s)
qw= 38—234 kW/m2$Ac = \dfrac{{{q_{{\mathrm{w}}} }{\beta _{{\mathrm{b}}} }}}{{G{c_{{{\mathrm{p}}} , {\mathrm{b}}}}Re_{{\mathrm{b}}} ^{0.625}}}\left( {\dfrac{{{\mu _{{\mathrm{w}}} }}}{{{\mu _{{\mathrm{b}}} }}}} \right){\left( {\dfrac{{{\rho _{{\mathrm{b}}} }}}{{{\rho _{{\mathrm{w}}} }}}} \right)^{0.5}}$, $Gr{=}\dfrac{{{g} {\beta _{{\mathrm{b}}} }d_{\mathrm{i}}^4{q_{{\mathrm{w}}} }}}{{v_{\mathrm{b}}^2{\lambda _{{\mathrm{b}}} }}}$ $ Bu = \dfrac{{Gr}}{{Re_{{\mathrm{b}}} ^{3.425}P{r^{0.8}}}}\left( {\dfrac{{{\mu _{{\mathrm{w}}} }}}{{{\mu _{{\mathrm{b}}} }}}} \right){\left( {\dfrac{{{\rho _{{\mathrm{b}}} }}}{{{\rho _{{\mathrm{w}}} }}}} \right)^{0.5}}$, ${\overline c _{{{\mathrm{p, b}}}}} = \dfrac{{{i_{{\mathrm{w}}} } - {i_{{\mathrm{b}}} }}}{{{T_{{\mathrm{w}}} } - {T_{{\mathrm{b}}} }}}$ [29] $ N u_{\mathrm{b}}=\dfrac{(\xi / 8) R e_{\mathrm{b}} \overline{{Pr}}_{\mathrm{b}}}{1+900 / R e_{\mathrm{b}}+12.7 \sqrt{\xi / 8}\left(\overline{P r}_{\mathrm{b}}^{2 / 3}-1\right)}$ — $\xi=\left[1.82 \log _{10}\left(R e_{\mathrm{b}}\right)-1.64\right]^{-2}\left( {\rho_{\mathrm{w}}}/{\rho_{\mathrm{b}}}\right)^{0.4}\left({\mu_{\mathrm{w}}}/{\mu_{\mathrm{b}}}\right)^{0.2}$ 
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