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 水利水运工程学报   2018 Issue (6): 70-76.  DOI: 10.16198/j.cnki.1009-640X.2018.06.009 0

### 引用本文 [复制中英文]

[复制中文]
WU You, CAO Bin, XIA Jianxin. Transport resistance characteristics of coal-water slurry considering effects of wall slip[J]. Hydro-science and Engineering, 2018(6): 70-76. (in Chinese) DOI: 10.16198/j.cnki.1009-640X.2018.06.009.
[复制英文]

### 文章历史

1 广义雷诺数和管道沿程阻力系数的确定方法 1.1 广义雷诺数

 $\text{d}u/\text{d}r=f\left( \tau \right)$ (1)

 $u=\int\limits_{r}^{R}{f\left( \tau \right)\text{d}r}$ (2)

 $\tau =\Delta \mathit{Pr}/\left( 2L \right)$ (3)

 $Q=2\text{ }\!\!\pi\!\!\text{ }\int\limits_{r}^{R}{ru\text{d}r}=2\text{ }\!\!\pi\!\!\text{ }\int\limits_{r}^{R}{r\left[ \int_{r}^{R}{f\left( \tau \right)\text{d}r} \right]\text{d}r}=\text{ }\!\!\pi\!\!\text{ }\int\limits_{r}^{R}{{{r}^{2}}f\left( \tau \right)\text{d}r}$ (4)
 $\text{d}r=\left( R/{{\tau }_{\omega }} \right)\text{d}\tau$ (5)

$Q = \frac{{{\rm{ \mathsf{ π} }}{R^3}}}{{\tau _\omega ^3}}\int\limits_0^{{\tau _\omega }} {{\tau ^2}f\left( \tau \right){\rm{d}}\tau }$变形得：

 $\frac{Q\tau _{\omega }^{3}}{\text{ }\!\!\pi\!\!\text{ }{{R}^{3}}}=\int\limits_{0}^{{{\tau }_{\omega }}}{{{\tau }^{2}}f\left( \tau \right)\text{d}\tau }$ (6)

τω微分，

 $\frac{3Q\tau _{\omega }^{2}}{\text{ }\!\!\pi\!\!\text{ }{{R}^{3}}}+\tau _{\omega }^{3}\text{d}\left( \frac{Q}{\text{ }\!\!\pi\!\!\text{ }{{R}^{3}}} \right)/\text{d}{{\tau }_{\omega }}=\tau _{\omega }^{2}f\left( {{\tau }_{\omega }} \right)$ (7)
 $f\left( {{\tau }_{\omega }} \right)={{\left( \frac{\text{d}u}{\text{d}r} \right)}_{\omega }}=\frac{3}{4}\frac{4Q}{\text{ }\!\!\pi\!\!\text{ }{{R}^{3}}}+\frac{{{\tau }_{\omega }}}{4}\frac{\text{d}\left( \frac{4Q}{\text{ }\!\!\pi\!\!\text{ }{{R}^{3}}} \right)}{\text{d}{{\tau }_{\omega }}}=\frac{8u}{D}\left[ \frac{3}{4}+\frac{1}{4}\frac{\text{dln}\left( \frac{8u}{D} \right)}{\text{dln}{{\tau }_{\omega }}} \right]$ (8)
 $n=\text{dln}\left( \frac{8u}{D} \right)/\text{dln}{{\tau }_{\omega }}$ (9)
 ${{\gamma }_{\omega }}=\frac{8u}{D}\left( \frac{1+3n}{4n} \right)$ (10)

 ${{\tau }_{\omega }}=\frac{\Delta \mathit{Pr}}{2L}={k}'\left( \frac{8u}{D} \right){n}'$ (11)

 $\mathit{Re}=D{{\rho }_{\text{m}}}u/\mu$ (12)

 $\mathit{R}{{\mathit{e}}_\text{g}}={{\rho }_{\text{m}}}uD/{{\mu }_{\text{e}}}$ (13)

 ${{\mu }_{\text{e}}}={{\tau }_{\omega }}/\left( 8\mu /D \right)$ (14)

 $\mathit{R}{{\mathit{e}}_\text{g}}=\frac{{{\rho }_{\text{m}}}uD}{{{\mu }_{\text{e}}}}=\frac{{{\rho }_{\text{m}}}uD}{{{\tau }_{\omega }}/\left( \frac{8u}{D} \right)}=\frac{{{\rho }_{\text{m}}}uD}{{k}'{{\left( \frac{8u}{D} \right)}^{n' - 1}}}=\frac{Dn'{{\rho }_{\text{m}}}{{u}^{2-{n}'}}}{{k}'{{8}^{{n}'-1}}}$ (15)

 $Q={{Q}_{\text{s}}}+{{Q}_{\text{c}}}$ (16)
 $u={{u}_{\text{s}}}+{{u}_{\text{c}}}$ (17)

 $\frac{8u}{D}=\frac{8{{u}_{\text{s}}}{{\tau }_{\omega }}}{D}+\frac{4}{\tau _{\omega }^{3}}\int\limits_{0}^{{{\tau }_{\omega }}}{{{\tau }^{2}}f\left( \tau \right)\text{d}\tau }$ (18)

 ${{\mu }_{\text{e}}}=\frac{{{\tau }_{\omega }}}{\frac{8{{u}_{\text{c}}}}{D}}\frac{{{\tau }_{\omega }}}{\frac{8\left( u-{{u}_{\text{s}}} \right)}{D}}=\frac{D{{\tau }_{\omega }}}{8\left( u-{{u}_{\text{s}}} \right)}\frac{u-{{u}_{\text{s}}}}{u}={{\mu }_{\text{e}}}\left( 1-\frac{{{u}_{\text{s}}}}{u} \right)=\frac{\tau _{\omega }^{4}}{4\int{{{\tau }_{{{\omega }_{0}}}}{{\tau }^{2}}f\left( \tau \right)\text{d}\tau }}$ (19)

1.2 管道沿程阻力系数

 $i=\lambda \frac{{{u}^{2}}}{2gD}\frac{{{\rho }_{\text{m}}}}{{{\rho }_{\text{l}}}}$ (20)

 $\lambda =8{{\tau }_{\omega }}/\left( {{\rho }_{\text{m}}}{{u}^{2}} \right)$ (21)

 $\lambda =64/\mathit{R}{{\mathit{e}}_{\text{g}}}$ (22)
2 试验装置及方法

 图 1 试验系统 Figure 1 Schematic diagram of experimental system

 图 2 颗粒粒径分布曲线 Figure 2 Particle size distribution of coal particles
3 结果与分析 3.1 流变特性

 图 3 不同浓度水煤浆滑移修正前后流变特性比较 Figure 3 Comparison of rheological properties before and after correction

3.2 阻力特性

 图 4 水煤浆沿程阻力系数与雷诺数的关系 Figure 4 Relationships between λ and Reg
 图 5 浓度为53%时不同阻力计算公式结果比较 Figure 5 Comparison between different formulas at 53% solid content
4 阻力计算结果比较

5 结语

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Transport resistance characteristics of coal-water slurry considering effects of wall slip
WU You, CAO Bin, XIA Jianxin
College of Life and Environmental of sciences, Minzu University of China, Beijing 100081, China
Abstract: With the development of coal chemical industry, efficient and clean transportation of the coal has become a real research subject. Using pipelines to convey high concentration coal-water slurry has obvious advantages, such as less investment, energy saving and environmental protection. Research on the resistance characteristics of the coal-water slurry is of great significance to the conveying experiment design. Because small-diameter pipe experiment is more convenient to operate and save more materials, the small-diameter pipe is often used for simulation in the laboratory. The flow characteristics of high concentration coal-water slurry with the mass concentrations of 53% and 58% in the pipes with a diameter of 50, 47, 32, and 29 mm were tested in this study. The formula of rheological parameters for different flow regimes under the slip condition is derived, and the resistance coefficients of the coal-water slurry are obtained based on the analysis of the slip efficiency. The resistance of high concentration coal-water slurry is calculated using the calculation formula of homogeneous flow resistance. Compared with other formulas, the homogeneous flow formula is most consistent with the experimental results. The calculated results show that the rheological model of CWS conforms to the Herschel-Bulkey model. Under the conditions of the sliding effects, the relationship between the resistance coefficients of the high concentration coal-water slurry and the generalized Reynolds number can be expressed as a formula, and the resistance can be calculated by the homogeneous flow formula.
Key words: resistance coefficient    Reynolds number    coal-water slurry    resistance characteristics    pipe flow