Assessment of heat transfer enhancement technique in flow boiling conditions based on entropy generation analysis: twisted-tape tube

Abstract

Twisted-tape tubes are commonly used in practice to passively enhance heat transfer. A clear understanding of the effect of variations in geometrical parameters as well as flow conditions is necessary, most importantly when it comes to finding the conditions in which the application of twisted-tape tubes is justifiable. The entropy generation analysis is a suitable approach towards defining such criteria. Therefore, in this paper, the effects of tube diameter, twist pitch, mass velocity, vapor quality, and saturation temperature are discussed in detail through entropy generation analysis. The Irreversibility Distribution Ratio (IDR) and Bejan number (Be), which track the variations of the components of total entropy generation, are discussed in each of these conditions. Finally, favorable conditions for using twisted-tape tubes rather than plain straight tubes are distinguished by defining entropy generation number (N_s). The results showed that twisted-tape tubes with bigger diameters have higher entropy generations. Also, increasing twist pitch and, similarly, increasing saturation temperature result in lower entropy generation. In addition, higher qualities lead to higher entropy generations and, finally, by increasing mass flux, entropy generation initially shows a drop and later a growth. The results for N_s show that employing twisted-tape tubes in lower mass velocities (roughly G ≤ 80 kg/m²s) and lower qualities (roughly x ≤ 0.4) and, as well as higher saturation temperatures (roughly T_sat ≥  − 18 ° C) is advantageous compared to plain straight ones.

Appendices

Appendix 1: The heat transfer coefficient correlations for the twisted-tape and plain straight tubes

Akhavan-Behabadi et al. [12]. correlated their experimental data in heat transfer coefficient in a Twisted-tape tube as Eq. (25):

$$ \frac{h_s}{h_p}=0.0056{\mathit{\operatorname{Re}}}_{fo}^{2.214}{Bo}^{1.532}{Y}^{-0.5}+1.2156 $$

(25)

Where h_s is the two-phase heat transfer coefficient for Twisted-tape tube. Re_fo, Bo and Y are Reynolds number, Boiling number and twist ratio and are defined as Eqs. (26), (27) and (28) respectively.

$$ {\mathit{\operatorname{Re}}}_{fo}=\frac{\rho_fG{d}_i}{\mu_f} $$

(26)

$$ Bo=\frac{q}{G{i}_{fg}} $$

(27)

$$ Y=\frac{H}{d_i} $$

(28)

In Eq. (25), h_p is the two-phase heat transfer coefficient for plain straight tube. Akhavan-Behabadi et al. [12] used Gungor and Winterton’s [36] correlation to obtain h_p as Eq. (29):

$$ {h}_p={h}_f\left[1+3000{Bo}^{0.86}+1.12{\left(\frac{x}{1-x}\right)}^{0.75}{\left(\frac{\rho_f}{\rho_g}\right)}^{0.41}\right] $$

(29)

Where x is the vapor quality and the value of h_f is calculated by Eq. (30) as follows:

$$ {h}_f=0.023{\mathit{\operatorname{Re}}}_f^{0.8}{\mathit{\Pr}}_f^{0.4}\left(\frac{k_f}{d_i}\right) $$

(30)

Re_f in Eq. (30) is the liquid Reynolds number and is given as Eq. (31):

$$ {\mathit{\operatorname{Re}}}_f=\frac{G\left(1-x\right){d}_i}{\mu_f} $$

(31)

In this study, Eqs. (25) and (29) were used to compute the heat transfer contribution to entropy generation in twisted-tape and plain straight tubes, respectively.

Appendix 2: The frictional pressure drop correlations for twisted tape and plain straight tubes

Equation (32) is suggested by Akhavan-Behabadi et al. [13] to calculate pressure drop for the Twisted-tape tube.

$$ \frac{{\Delta P}_s}{{\left({\Delta P}_f\right)}_{Friedel}}=\frac{5.1}{Y^{0.28}} $$

(32)

Where ∆P_s and Y are frictional pressure drop for the Twisted-tape tube and twisted tape ratio respectively. (∆P_f)_Friedel is the frictional pressure drop for flow boiling in plain straight tube and obtained by the use of Friedel method.

In order to calculate the frictional pressure drop contribution to entropy generation in the twisted-tape and plain straight tubes, Eq. (32) and Friedel method were used respectively.