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Analysis of Heat Transfer and Pressure Drop Characteristics of Two-Phase Flow in Shell-and-Tube Cooler

Abstract: A shell-and-tube cooler at the outlet of a compressor is studied in this paper. Through theoretical analysis and considering the effect of phase change of the thermal fluid in the shell side, the calcu-lation expressions for the outlet temperature and pressure drop of the shell side are given. The numerical results are compared and verified with the existing measured data, and the influence of structural parameters on the outlet temperature and pressure drop of the shell side is studied. The calculation results show that the outlet temperature of the shell side of the cooler increases with the increase of the medium density of the tube side, and at the same time, it decreases with the increase of the outer diameter of the heat exchange tube. The heat exchange tube, the baffle spacing and the height of baffle notch have a significant effect on the pressure drop of the shell side. The pressure drop in the shell side decreases with the increase of the heat exchange tube’s transverse and longitudinal tube spacing, baffle spacing and notch height, and increases with the increase of the shell side fluid flow, showing a non-linear change.

1. 引言

2. 几何模型及其数学描述

2.1. 几何模型

Figure 1. Outline structure diagram of the shell-and-tube cooler

Figure 2. Tube bundle layout diagram

Figure 3. 3D schematic diagram of internal local structure

Table 1. Structural geometric parameters of the shell-and-tube cooler

2.2. 数学模型

2.2.1. 传热过程

${Q}_{H}=kA\Delta {t}_{m}$ (1)

${Q}_{H}={q}_{m1}{c}_{1}\left({t}_{h}^{1}-{t}_{h}^{2}\right)={q}_{m2}{c}_{2}\left({t}_{c}^{2}-{t}_{c}^{1}\right)$ (2)

${\epsilon }_{H}=\frac{{q}_{H}}{{q}_{H\mathrm{max}}}$ (3)

${C}^{\ast }=\frac{{C}_{\mathrm{min}}}{{C}_{\mathrm{max}}}=\left\{\begin{array}{l}\frac{{t}_{c}^{2}-{t}_{c}^{1}}{{t}_{h}^{2}-{t}_{h}^{1}},{C}_{h}={C}_{\mathrm{min}}\\ \frac{{t}_{h}^{1}-{t}_{h}^{2}}{{t}_{c}^{1}-{t}_{c}^{2}},{C}_{c}={C}_{\mathrm{min}}\end{array}$ (4)

$NTU=\frac{{K}_{1}\cdot {F}_{1}}{{C}_{\mathrm{min}}}$ (5)

${C}_{\mathrm{min}}=\left\{\begin{array}{l}{C}_{k},{C}_{k}<{C}_{g}\\ {C}_{g},{C}_{g}<{C}_{k}\end{array}$ (6)

$\begin{array}{l}若{C}_{\mathrm{min}}={C}_{k},{t}_{kout}={t}_{kin}-{\epsilon }_{{}_{H}}\left({t}_{kin}-{t}_{gin}\right);\\ 若{C}_{\mathrm{min}}={C}_{g},{t}_{gout}={t}_{gin}+{\epsilon }_{H}\left({t}_{kin}-{t}_{gin}\right),{t}_{kout}={t}_{kin}-{Q}_{H}/{C}_{k};\end{array}$ (7)

$\begin{array}{l}{\alpha }_{1}=0.725{n}_{m}{B}_{m}{r}_{s}^{\frac{1}{4}}\Delta {t}_{0}^{-\frac{1}{4}}{d}_{0}^{-\frac{1}{4}}\\ {B}_{m}=\left(9.81\rho {\lambda }^{3}\right)/{\nu }_{m}^{\frac{1}{4}}\end{array}$ (8)

${{Q}^{\prime }}_{H}={h}_{con}A\left({T}_{sat}-{T}_{w}\right)$ (9)

${{t}^{″}}_{kout}={t}_{\text{kin}}-{{Q}^{\prime }}_{h}/{q}_{m1}{c}_{1}$ (10)

2.2.2. 压降分析

$\Delta {P}_{b,id}=\frac{4{f}_{id}{G}_{c}^{2}}{2{g}_{c}{\rho }_{s}}{N}_{r,cc}{\left(\frac{{\mu }_{w}}{{\mu }_{m}}\right)}^{0.25}$ (11)

$\Delta {P}_{w,id}=\left\{\begin{array}{l}\left(2+0.6{N}_{r,cw}\right)\frac{{G}_{w}^{2}}{2{g}_{c}{\rho }_{s}},Re\ge 100\\ \frac{26{G}_{w}{\mu }_{s}}{{g}_{c}{\rho }_{s}}\left(\frac{{N}_{r,cw}}{{P}_{t}-{d}_{0}}+\frac{{L}_{b}}{{D}_{h,w}^{2}}\right)+\frac{{G}_{w}^{2}}{{g}_{c}{\rho }_{s}},Re<100\end{array}$ (12)

$\Delta {P}_{i-o}=2\Delta {P}_{b,id}\left(1+\frac{{N}_{r,cw}}{{N}_{r,cc}}\right){\xi }_{b}{\xi }_{s}$ (13)

$\begin{array}{c}\Delta {P}_{s}=\Delta {P}_{cr}+\Delta {P}_{w}+\Delta {P}_{i-o}\\ =\left[\left({N}_{b}-1\right)\Delta {P}_{b,id}{\xi }_{b}+{N}_{b}\Delta {P}_{w,id}\right]{\xi }_{l}+2\Delta {P}_{b,id}\left(1+\frac{{N}_{r,cw}}{{N}_{r,cc}}\right){\xi }_{b}{\xi }_{s}\end{array}$ (14)

2.3. 理论计算具体表达式

$\alpha =\frac{1863.9×{\left(0.5980+1.373×{10}^{-3}-5.333×{10}^{-6}{P}_{kin}^{2}\right)}^{3}}{{\left(1.006{\epsilon }_{H}\left({t}_{kin}-{t}_{kout}\right)\right)}^{0.25}×{10}^{\left(\frac{230.298}{{P}_{kin}+126.203}-4.5668\right)}}$ (15)

${t}_{kout}=0.13\left({t}_{kin}-\frac{1.006{C}_{k}{\epsilon }_{H}\left({t}_{kin}-{t}_{gin}\right)}{2460.7\alpha }\right)$ (16)

${C}_{k}=\frac{2400{W}_{y}{A}_{k}}{4018\left({t}_{yin}+273.15\right)×\left({\left({P}_{kin}/{P}_{yin}\right)}^{\frac{1}{4}}-1\right)}$ (17)

${A}_{k}=1004.18+0.0171{P}_{kin}+\left(0.260175+0.000057142{P}_{kin}\right){t}_{kin}+0.364286×{10}^{-3}{t}_{kin}^{2}$ (18)

εH可表示为：

${\epsilon }_{H}=\frac{2}{\left(1+{C}^{*}\right)+\sqrt{1+{C}^{*}{}^{2}}\left(1+{\text{e}}^{-\frac{2460.7k}{{C}_{k}}×\sqrt{\left(1+{C}^{*}{}^{2}\right)}}\right)/\left(1-{\text{e}}^{-\frac{2460.7k}{{C}_{k}}×\sqrt{1+{C}^{*}{}^{2}}}\right)}$ (19)

${C}^{*}={C}_{k}/\left(4.005{P}_{gin}^{0.8}×\left(4184.4-0.6964{t}_{gin}+1.036×{10}^{-2}{t}_{gin}^{2}\right)\right)$ (20)

$k=\frac{1}{4.56×{10}^{-4}+1.281×{10}^{-8}{\left({t}_{kin}+273\right)}^{0.823}}$ (21)

Pgin为管程入口压力。

$\Delta {P}_{s}=\frac{167.134}{307.46{A}_{t}^{0.476}+22473.997{A}_{t}^{0.996}}+\frac{0.444}{{A}_{k2}}$ (22)

${A}_{t}=\frac{{t}_{kin}+273}{{t}_{kin}+395}$ (23)

${A}_{k2}=\frac{{P}_{kin}}{273.15+{t}_{kin}}$ (24)

3. 计算结果与分析

Figure 4. Program flow chart

3.1. 计算结果与实验结果的对比分析

Figure 5. Shell side inlet temperature curve

Figure 6. Shell side outlet temperature curve

Figure 7. Shell side inlet pressure curve

Figure 8. Shell side outlet pressure curve

Figure 9. Shell side pressure drop curve

Table 2. Partial calculation results and measured data of the shell-and-tube cooler

3.2. 各参数对冷却器性能的影响分析

3.2.1. 各参数对壳程出口温度的影响

Figure 10. Effect of tube medium density on shell side outlet temperature

Figure 11. Effect of outer diameter of heat exchanger tube on outlet temperature of shell side

3.2.2. 各参数对壳程压降的影响

Figure 12. Effect of transverse tube spacing on pressure drop

Figure 13. Effect of longitudinal tube spacing on pressure drop

Figure 14. Effect of baffle spacing on pressure drop

4. 结论

Figure 15. Influence of baffle notch height on pressure drop

Figure 16. Effect of fluid flow on pressure drop

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