工程科学与技术   2017, Vol. 49 Issue (2): 254-261

Numerical Simulation of Flow Field for High Pressure Dry Gas Seals
CHEN Zhi, GAO Yunhao, ZHAO Peng, JI Hua
College of Chemical Eng., Sichuan Univ., Chengdu 610065, China
Abstract: The dry gas seals have wide applications in the conditions of high temperature, high pressure and a variety of corrosive media, but it has been not enough to understand the effects of high pressure and high temperature on dry gas seals, especially the problems in the numerical simulation.Both pressure and temperature of end-face gas film field in dry gas seals change greatly, especially at the working condition of high pressure.The density and viscosity of sealing medium or nitrogen change with varying pressure and temperature.Especially, the effect of pressure on the former is greater.In usual numerical simulation for dry gas seals, the density of sealing medium is determined according to the given temperature and pressure, which does not take into account the influences of physical parameters of sealing medium on seal performance so that the results might have errors.A new way used for the simulation of flow field of high pressure dry gas seals was proposed with the consideration of the effects of the changes of flow field and temperature field on the density of sealing medium in order to decrease the errors.Firstly, ANSYS Workbench software was used to make a thermal analysis for sealing rings to obtain the temperature field.The temperature distribution in the gas film field was then estimated by CFD.Then, user defined functions (UDFs) were created to relate the density of nitrogen (sealing medium) to pressure and temperature.Fluent software was used to complete the simulation with UDF loaded.Pressure distribution of end-face gas field and the opening force of the seal were obtained after continuous iteration.The flow fields of high pressure dry gas seals were reflected more truly.The flow fields of a dry gas seal were simulated using Fluent soft ware by the methods of variable-density (to define the density as a function of pressure and temperature) and the given density (to take density as the given directly), respectively.The grid size independent verification was carried out.The comparison of simulation results showed that the variable-density method could make the results closer to the conditions of the actual situation.It is feasible to use UDFs of Fluent to describe the variable-density of gas film between the sealing faces of a dry gas seal, which provides a new method to more accurately simulate gap flow field between sealing faces.The effect of pressure on the density of sealing gas is great under high pressure.The flow fields of high pressure dry gas seals are reflected more truly by the methods of variable-density.Moreover, the influence of temperature change on the density of sealing gas should be taken into account.
Key words: dry gas seal    density    fluid field    spiral groove    numerical simulation

Muijderman[1]采用复变函数将螺旋槽模型转变成了平行直线槽模型，考虑了槽形端部的影响，首次提出了比较完整的关于螺旋槽轴承的理论。干气密封的端面流场计算是通过求解雷诺方程实现的，Faria[2]提出一种使用伽辽金加权余量法结合高阶函数来求解非线性雷诺方程，得到了螺旋槽干气密封端面气膜流场压力分布、开启力和泄漏量等，该方法与传统的有限元法解雷诺方程的方法比，在求解步骤与求解难度上有了一定的改善。宋鹏云[3]使用了端面气膜压力控制方程，给出了螺旋槽干气密封端面气膜力的一种近似解析计算方法。随着计算机技术的不断发展，越来越多的学者开始使用CFD软件来进行端面气膜流场的研究。Shahin等[4]建立了螺旋槽干气密封3维计算模型，采用k-ε湍流和层流运动方程分别对等深槽和锥度槽进行CFD模拟，得到了不同转速、气膜厚度下的开启力和泄漏量，提出了层流模型更加符合实验数据的论断，同时分析出槽的锥度对密封端面压力分布有较小影响，但锥度增大会使端面温度降低。Qiu等[5]使用商业CFD软件CFD-ACE对高速螺旋槽流体动压密封做了研究，计算了在不同转速、动压槽深、槽长坝长比以及槽台宽比的情况下动静环的温度分布和压力分布，与实验值进行对比，并得出温度分布对密封的性能指标有很大影响的结论。Fairuz等[6]的研究证明介质密度变化对密封性能参数 (应力分布、开启力和泄漏率) 有较大影响，而这种密度变化可以是同一种介质在不同操作温度下引起的变化。不同半径处的密度变化较大，甚至高达39%的变化。然而在通常情况下，利用CFD软件进行干气密封端面流场计算时，并不考虑温度的影响，只是给出流场在定性温度下的密度，如Gabriel[7]使用30 ℃的定性温度，研究了空气作为密封介质且4.58 MPa压力下的干气密封的密封性能，并将理论分析与试验结果就行了比较。艾俊峰等[8]模拟计算时也采用了300 K的定性温度来进行数值模拟。

1 模型及热分析 1.1 模型与工况条件

 图1 螺旋槽干气密封的结构 Fig. 1 Structure of spiral groove dry gas seals

1.2 密封环热分析及气膜温度分布

 图2 干气密封传热模型及边界条件 Fig. 2 Heat model and boundary condition of dry gas seals

Qv+QB+Qc=Q1+Q2+Q3

 $q = \tau \cdot\nu = \mu \frac{{{\rm{d}}\nu }}{{{\rm{d}}r}}\cdot\nu = \mu \cdot\frac{{r\omega }}{h}\nu = \mu \cdot\frac{{{r^2}{\omega ^2}}}{h}$ (1)

 ${Q_{\rm{v}}} = \int\limits_{{r_{\rm{i}}}}^{{r_{\rm{o}}}} q \cdot2{\rm{\pi }}r{\rm{d}}r = \frac{{{\rm{\pi }}\mu {\omega ^2}}}{{2h}}({r_{\rm{o}}}^4-{r_{\rm{i}}}^4)$ (2)

 ${h_{\rm{r}}} = 0.135k{[(0.5\;R{e_{\rm{c}}}^2 + R{e_{\rm{a}}}^2)Pr]^{0.33}}/D$ (3)
 ${h_{\rm{s}}} = 0.011{\rm{ }}5k\xi R{e^{0.8}}P{r^{0.4}}/s$ (4)
 $R{e_{\rm{c}}} = \omega {D^2}/\nu$ (5)
 $R{e_{\rm{a}}} = UD/\nu$ (6)
 $Re = 2Vs/\nu$ (7)

 图3 密封环温度分布 Fig. 3 Temperature distribution of sealing rings

 图4 动、静环端面温度随半径的分布曲线 Fig. 4 Temperature profiles of rotor and stator in radial direction

 图5 不同网格数下动环端面温度分布 Fig. 5 Temperature profile of rotor end-face in different cells

 图6 气膜温度随半径的分布曲线 Fig. 6 Temperature profile of gas film in radial direction

2 气膜流场的数值模拟 2.1 建模与网格

 图7 ICEM CFD网格划分结构 Fig. 7 Structure of mesh with ICEM CFD

2.2 UDF的使用

 图8 N2密度随压力和温度变化关系 Fig. 8 Change of nitrogen density with different pressure and temperature

ρ(T=88.45 ℃)=-0.022 2p2+9.390 4p-0.052 7,

ρ(T=80.60 ℃)=-0.021 1p2+9.605 6p-0.058 9。

 $a = \sqrt {\gamma \frac{p}{\rho }}$ (8)

2.3 计算结果与分析

 图9 网格无关性验证 Fig. 9 Verification of mesh irrelevant

 图10 气膜间隙为2.8 μm时端面压力云图 (变密度方法) Fig. 10 Pressure contour on end face for gas film thickness of 2.8 μm (variable density method)

 图11 气膜间隙为2.8 μm时端面压力云图 (定密度方法) Fig. 11 Pressure contour on end face for gas film thickness of 2.8 μm (constant density method)

 图12 气膜沿半径方向的压力分布曲线 Fig. 12 Pressure profile of gas film in radial direction

3 结论

1) 使用Fluent的UDF功能来描述干气密封端面间隙气体密度的变化是可行的。将温度分区，再在不同区域内加载密度对压力的函数，使用这种方法表达密度与压力和温度的函数，可以避免多变量拟合的问题，为更精确地模拟端面间隙流场提供了一种新方法。

2) 传统采用恒定密度的算法会造成较大的误差，特别是高压工况下模拟计算时尤其要注意。

3) 干气密封气膜剪切热主要是通过动环对流传热传到密封介质的，静环的对流传热及泄漏带走的热量相对较小。

4) 不论是动环还是静环，内径处温度较高，而外径处的温度相对较低。

5) 相比而言，压力变化对气体密度影响较大；在高压工况下，应考虑温度变化对气体密度的影响。

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