The general supercritical heat transfer correlation for vertical up-flow tubes: K number correlation

The objective of this paper is to present a general supercritical heat transfer (SHT) correlation for advanced power cycles. In textbooks, supercritical fluid is considered to have single-phase structure. However, various SHT correlations incorporating buoyancy/acceleration effects fail to predict heat transfer coefficients. Here, pseud-boiling assumption is introduced to deal with SHT. Supercritical fluid is treated to have a heterogeneous structure consisting of vapor-like fluid and liquid-like fluid. Similarity analysis between subcritical boiling and SHT creates a new dimensionless parameter, the K number, representing evaporation induced momentum force relative to inertia force to govern the growth of wall attached vapor-like fluid layer thickness, which is key to dominate SHT. Thus, SHT is correlated in a simple form as Nu = (CRebPrb,aveKn3)-Pr-n1-K-n2, where Nu, Re-b, Pr-b,Pr-ave are Nusselt number, Reynolds number and Prandtl number, respectively. Totally, 5560 data points, including our newly obtained 2028 data points for S-CO 2 with pressures up to 21 MPa, and other 3532 data points cited from 18 articles for carbon dioxide, water and R134a, are used to determine the coefficients C and nl-n3, yielding the expression ofNu = 0.0012Re(b)(0.)(9484)pr(b.ave)(0.718)K(-0.0313). The negative exponent -0.0313 for the K number explains the improved heat transfer by increasing pressures. By comparing with experiment database, the general correlation has better prediction accuracy than the widely cited correlations in the literature. The correlation is also compared with R22 data. Even though such data are not involved in the development of the SHT correlation, the correlation excellently matched the experimental data. This work paves a new road to understand SHT. The correlation ensures heat exchangers operating at supercritical pressures to be designed more accurately and safely. (C) 2019 Elsevier Ltd. All rights reserved.