舰船科学技术  2022, Vol. 44 Issue (7): 47-50    DOI: 10.3404/j.issn.1672-7649.2022.07.009 PDF

Analysis of influence of temperature change on test pressure of pressure cabin
ZHANG Dong-jing, CONG Shu-guang, ZHANG Zhen, PAN Guang-shan, WU Guo-qing
State Key Laboratory of Deep-sea Manned Vehicles, China Ship Scientific Research Center, Wuxi 214082, China
Abstract: To provide a theoretical calculation method and basis for the pressure change of pressure chamber caused by temperature change. Firstly, combined with the basic knowledge of elasticity and hydraulics, the influence law of temperature change on the test pressure of pressure chamber is analyzed, and the relationship between temperature change and pressure drop is established. Then, the pressure drop caused by temperature change was quantitatively analyzed through specific examples. the data show that the theoretical calculation is basically consistent with the experimental results.
Key words: pressure cabin     Pressure test     temperature change     pressure drop
0 引　言

1 理论分析

 ${\rm{d}}{V_t}{\text{ + }}{\rm{d}}{V_P}{\text{ = }}{\rm{d}}{V_{st}} + {\rm{d}}{V_{sp}}。$ (1)

1.1 水受温度影响的体积变化计算

 ${\beta _{\text{t}}} = \frac{1}{V} \cdot \frac{{{\rm{d}}{V_{\text{t}}}}}{{{\rm{d}}t}}{{ = - }}\frac{1}{{{\rho _{\text{t}}}}} \cdot \frac{{{\rm{d}}{\rho _{\text{t}}}}}{{{\rm{d}}t}} ，$ (2)
 $即{\rm{d}}{V_{\text{t}}} = {\beta _{\text{t}}}V{\rm{d}}t = {{ - }}\frac{V}{{{\rho _{\text{t}}}}} \cdot {\rm{d}}{\rho _{\text{t}}} 。$ (3)

 ${\rho _{\text{t}}}{{ = - 0}}{{.003\;5}}{t^2} - 0.077\;5t + 1\;000.799\;5 ，$

 ${\rm{d}}{V}_{\text{t}}=\frac{V}{{\rho }_{\text{t}}}(0.007t+0.077\;5){\rm{d}}t 。$ (4)
 图 1 水的密度-温度曲线 Fig. 1 Overall effect diagram of a pressure test facility
1.2 水受压力影响的体积变化计算

 ${\beta _{\text{p}}} = {{ - }}\frac{1}{V} \cdot \frac{{{\rm{d}}{V_{\text{p}}}}}{{{\rm{d}}P}}{\text{ = }}\frac{1}{{{\rho _{\text{p}}}}} \cdot \frac{{{\rm{d}}{\rho _{\text{p}}}}}{{dP}} ，$ (5)
 $即 {\rm{d}}{V_{\text{P}}} = - {\beta _{\text{P}}}V{\rm{d}}P = {{ - }}\frac{V}{{{\rho _{\text{p}}}}} \cdot {\rm{d}}{\rho _{\text{p}}} 。$ (6)

 $\begin{split}& {\left(\frac{V-{\rm{d}}{V}_{p}}{V}\right)}_{0℃}=-0.000\;429p+0.999\;483 \text{，} \\&{\left(\frac{V-{\rm{d}}{V}_{p}}{V}\right)}_{10℃}=-0.000\;405p+0.999\;517 ，\end{split}$
 $\begin{split} &{\left(\frac{V-{\rm{d}}{V}_{p}}{V}\right)}_{20℃}=-0.000\;393p+1.001\;183 \text{，} \\&{\left(\frac{V-{\rm{d}}{V}_{p}}{V}\right)}_{40℃}=-0.000\;383p+1.007\;083 , \end{split}$
 $\begin{split} &{\left(\frac{V-{\rm{d}}{V}_{p}}{V}\right)}_{60℃}=-0.000\;384p+1.016\;6 \text{，}\\& {\left(\frac{V-{\rm{d}}{V}_{p}}{V}\right)}_{80℃}=-0.000\;398p+1.028\;233 。\end{split}$
 图 2 不同温度下水的可压缩性-压力曲线 Fig. 2 Compressibility pressure curve of water at different temperatures

1.3 压力舱受温度影响的体积变化计算

 ${\rm{d}}{V}_{st,1}=2\pi rL{\rm{d}}r+\pi {r}^{2}{\rm{d}}L=3\alpha \pi {r}^{2}L{{{\rm{d}}}}t ，$ (7)

 ${\rm{d}}{V_{st,2}} = 4\pi {r^2}{\rm{d}}r{\text{ = 4}}\alpha \pi {r^3}{{{\rm{d}}}}t ，$ (8)

 ${\rm{d}}{V}_{st}={\rm{d}}{V}_{st,1}\text+{\rm{d}}{V}_{st,2}\text=（3\alpha \pi {r}^{2}L+\text{4}\alpha \pi {r}^{3}）{{{\rm{d}}}}t 。$ (9)

1.4 压力舱受压力影响的体积变化计算

 ${\rm{d}}{V_{sp,1}}{\text{ = }}2\pi RLdR + \pi {R^2}{\rm{d}}L{\text{ = }}\frac{{1.9\pi {R^3}L}}{{{\xi _1}E}}{\rm{d}}P ，$ (10)

 ${\rm{d}}{V_{sp,2}}{\text{ = }}\frac{{4\pi {R^3} \times 0.7R{\rm{d}}P}}{{{\xi _2}E}}{\text{ = }}\frac{{2.8\pi {R^4}{\rm{d}}P}}{{{\xi _2}E}} ，$ (11)

 ${\rm{d}}{V_{sp}}{\text{ = }}{\rm{d}}{V_{sp,1}}{\text{ + }}{\rm{d}}{V_{sp,2}}{\text{ = }}\left( {\frac{{1.9\pi {R^3}L}}{{{\xi _1}E}}{\text{ + }}\frac{{2.8\pi {R^4}}}{{{\xi _2}E}}} \right){\rm{d}}P。$ (12)

1.5 压力舱压力变化-温度变化关系式确立

 ${\rm{d}}P{\text{ = }}\frac{{{\beta _t}V - {k_1}}}{{{k_2}{\text{ + }}{\beta _{\text{P}}}V}}{{{\rm{d}}}}t ，$ (13)
 $\text{或} {\rm{d}}P= \left(\frac{{{k_1}}}{{{k_2} + {\beta _{\text{p}}}V}}{\text{ + }}\frac{{V\left( {0.007t + 0.077\;5} \right)}}{{{\rho _{\text{t}}}({k_2} + {\beta _{\text{p}}}V)}}\right){{{\rm{d}}}}t ，$ (14)
 $\text{其中，}{k_1}{\text{ = }}3\alpha \pi {r^2}L + {\text{4}}\alpha \pi {r^3} ，{k_2}{\text{ = }}\frac{{1.9\pi {R^3}L}}{{{\xi _1}E}}{\text{ + }}\frac{{2.8\pi {R^4}}}{{{\xi _2}E}} 。$
2 实例分析 2.1 实例理论计算

 图 3 承压试验设施总体效果图 Fig. 3 Overall effect diagram of a pressure test facility

 图 4 舱内温降1℃时的压降-温降曲线 Fig. 4 Pressure drop temperature drop curve when the cabin temperature drops by 1 ℃
 ${\rm{d}}{P_1}{\text{ = }}0.004t + 1.001\;8 。$ (15)

 ${\rm{d}}{P_{\text{k}}} = k\left[ {0.004t + 1.001\;8 - \frac{{(k - 1)}}{2} \times 0.004} \right] (0 < k < t,k \in N )。$ (16)

2.2 实例现场试验

 图 5 现场试验舱内压力-温度曲线 Fig. 5 Pressure curve in field test chamber

3 结　语

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