低温气液两相弹状流流动特性和流场结构的实验及数值研究
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摘要
低温气液两相流是低温工程中经常遇到的现象，例如低温管路中的火箭推进剂和液化天然气输送，以及高热流密度的芯片冷却。低温输送管路内不可避免的漏热将形成小气泡，小气泡相互碰撞合并进而生成Taylor气泡。这些Taylor气泡导致管路堵塞并将低温液体挤出管路形成喷发。回流的低温流体还会导致管路和阀门的结构损坏，并造成火箭发动机的气蚀。因此低温流体中Taylor气泡的形成、发展和合并是低温工程中的重要问题。
在一定漏热条件下，管路内尚未发生间歇泉时，就会出现弹状流动，这已经对火箭发动机的安全运行造成极大隐患。因此，准确判断低温管路中Taylor气泡的形成位置非常重要。Taylor气泡周围的流场，尤其是尾迹区流场是Taylor气泡合并过程的关键因素，两个连续的Taylor气泡之间的相互作用过程取决于领先气泡的尾迹区流型。首先，不同的尾迹区流型（层流、过渡流或湍流）导致不同的合并速率，一些尾迹区流型甚至会阻止两个Taylor气泡的合并。因此，尾迹区的流型决定了弹单元中的Taylor气泡长度份额，进而影响低温气液两相弹状流的压降参数和空泡份额。其次，Taylor气泡尾迹区内的湍流强度决定了液弹中弥散气泡和液体的速度分布，也会影响两相流动的空泡份额。同时Taylor气泡头部区域的流场对Taylor气泡的上升速度有重要影响。综上所述，Taylor气泡周围流场的研究是低温气液两相弹状流中的重要课题，对低温系统的工作效率和安全运行都具有重要的科学意义和实用价值。
在低温管路中，由漏热产生弥散气泡到Taylor气泡的形成，以及间歇泉的产生，这是一个整体的连续过程，其中对Taylor气泡的形成过程还缺乏统一的判据，而且该过程的研究尚未涉及管路内的流动结构对Taylor气泡形成的影响。对于低温气液两相弹状流研究，大多数研究限于宏观流动特征，如压降测量和图像研究。由于低温气液两相流中流场测量的难度较大，关于低温气液两相流中Taylor气泡周围流场的研究国内外未见报道，且尚没有建立针对低温气液两相流中Taylor气泡尾迹区流型的判据。低温流体的研究已经远落后于常温流体。
本文以液氮为工质，对低温管路中由漏热产生的Taylor气泡的形成、运动和合并过程进行了实验和数值模拟研究。对漏热形成的低温气液两相流动中Taylor气泡的形成位置、长度和速度分布进行了可视化研究。使用PIV流场测量方法对低温液体中Taylor气泡周围流场进行了定量测量，使用POD数据分析方法对PIV测量结果进行了进一步分析，探讨了流场的湍流大尺度结构对Taylor气泡之间相互作用的影响、管路内湍流强度对Taylor气泡形成的影响，最后对对理想状态下，静止低温流体中单个Taylor气泡的运动特征和周围流场结构进行了数值模拟研究。具体如下：
（1）建立了适用于低温气液两相流动的PIV测速和可视化测量相结合的实验平台。针对圆形截面管路中的图像畸变问题，建立了一种通用的可用于多层管壁情况下的直接校正方法。使用方形规则化网格进行验证，最大相对误差不超过3%。使用Fortran语言编制了通用校正程序。
（2）利用上述实验台结合高速相机在多种倾角下，对多种管路内液氮沸腾形成的气液两相流动中Taylor气泡宏观特征进行了可视化研究。分析了多种倾角下Taylor气泡的合并过程，建立了跟随气泡和领先气泡速度与气泡间距的关系。已有的由常温流体得到的速度关系式不适用于液氮流体，普遍高估了本文实验结果，新建立的关系式和实验结果吻合较好。得到了Taylor气泡的形成位置、速度和长度份额分布与管路内径、倾角的关系。
（3）使用所建实验台结合PIV实验手段得到了Taylor气泡周围流场结构。结果分析表明，常温流体中Taylor气泡尾迹区流型判定方法不再适用于液氮流体，传统理论认为当无量纲流体逆粘度数Nf>1500时，Taylor气泡尾迹区为湍流。在液氮流体中，当Nf数远大于这一临界值时，液氮流体中的Taylor气泡尾迹区仍然为过渡流和层流。
（4）使用POD方法对PIV实验结果进行了进一步的分析，得到了尾迹区流场中湍流大尺度结构，解释了可视化实验中不同倾角下Taylor气泡合并过程，得到了改变Taylor气泡尾迹区的湍流大尺度结构可抑制Taylor气泡的合并的结论。
（5）在PIV实验和可视化实验的基础上，考察了流场湍流强度、热流密度、管路内径和管路倾角等对Taylor气泡形成的影响，提出了无量纲气相速度vq。在此基础上，建立了液氮管路中由漏热形成的Taylor气泡的生成位置预测公式，公式预测结果与本文和文献中的实验结果相比最大误差在±20%以内。
（6）使用VOF方法对静止液氮中，单个Taylor气泡运动的理想过程进行了数值模拟，得到了尾迹区流型转变过程、上升速度、尾缘几何特征等。与文献数据对比表明本文模型可信。得到了Taylor气泡尾迹区内层流、过渡流和湍流的流型转变过程，建立了适用于液氮流体中Taylor气泡尾迹区流型转变的判据，该结果也表明常温流体尾迹区流型判据不适用于液氮流体。
Cryogenic gas-liquid two-phase flow is usually encountered in cryogenicengineering such as pipe transportation of cryogenic liquid and high heat-fluxelectronic chip cooling. Due to the inevitable heat leak along the pipe, smallbubbles form from the boiling cryogenic liquid and coalesce to bullet shapedlarge bubbles (also named Taylor bubble) with almost the same diameter ofthe pipe. These Taylor bubbles cause pipe line blockage and extrude thecryogenic liquid from the pipe line, and could lead to the destruction of pipeand valve, and also cavitation erosion of rocket engine. Thus the Taylorbubble formation and evolution in the pipe line are the importantcharacteristics in cryogenic engineering.
Cryogenic gas-liquid slug flow has already formed under some thermalconditions when there is no geysering phenomenon in the tube. This is hiddendanger for the safty operation of crogenic tubes. Thus the prediction forTaylor bubble formation is very important for the safe operation of cryogenictransportation tube.
The flow field around Taylor bubble, especially the flow field in bubblewake has great influence on the flow parameters of cryogenic two-phase slugflow, and then affects the interaction of two consectutive Taylor bubbles.Firstly, the flow pattern in the leading Taylor bubble’s wake determines theinteraction between two adjacent Taylor bubbles. Different flow patterns(laminar, transition or turbulent) result in different bubble coalescence speedand rate, and some will prohibit the coalescence. Then the flow field inbubble wake affects the length fraction of gas slug in a slug unit. Finally itinfluences the pressure drop and void fraction in cryogenic two-phase flow.And the turbulence intensity in Taylor bubble wake defines the velocity ofdispersed bubbles in a liquid slug, the velocity of liquid phase and the distribution of void fraction. Meanwhile, the velocity field ahead of Taylorbubble is highly important for Taylor bubble velocity. Thus the present studyis meaningful for studying on these important parameters in cryogenicengineering.
In cryogenic tube, the coalescence of dispersed vapor bubbles leads tothe formation of Taylor bubbles. And the continuous coalescence of Taylorbubbles leads to the geysering phenomenon. In this continuous process, thereis a lack of the criterion of Taylor bubble formation in cryogenic tube causedby heat leak. And the research about this process has not included the effect offlow structure on the formation of Taylor bubbles. For the cryogenictwo-phase slug flow, most studies are limited to the macroscopic properties,e.g. the pressure measurement or photographic study. However, moredeveloped investigation on the flow field in cryogenic two-phase slug flow isscarce. And little literature can be found to define the wake pattern of a Taylorbubble in cryogenic fluid. The critierion for defining the wake pattern ofcryogenic Taylor bubble has not been developed. In this particular field, theresearch in cryogenic engineering has fallen behind that focusing on ordinaryfluid.
The purpose of the present study is to experimently and numericallyinvestigate the formation, motion and coalescence process of Taylor bubblecaused by heak leak in cryogenic tubes. The formation position, length andvelocity distribution of Taylor bubble are studied by vasulization technique.The flow field around Taylor bubble was obtained by PIV technique. Basedon PIV results, snapshot POD was introduced to reveal the effect of flowstructure on the interaction of Taylor bubbles, and the effect of turbulence onthe formation of Taylor bubble. At last, the motion of a single Taylor bubblein stagnant liquid nitrogen and the flow structure aound it were numericallyinvestigated. The main conclusions are summarized as follows:
(1) An experimental system was built to investage the characteristics andthe flow field of cryogenic gas-liquid slug flow. A correction algorithm wasdeveloped for reconstructing the flow field based on ray tracing method,which showed the maximum error was3%by the uniform grid validation. Acorrection program was built using Fortran language.
(2) The characteristics of Taylor bubble in cryogenic slug flow were studied, including the length, velocity and length fraction. The coalescenceprocess of Taylor bubble was analysed under different inclination angles. Thevelocity ratio of trailing and leading bubble as a function of bubble distancewas built based on the experimental data. The existing correlations fromordinary two-phase flow are no longer suitable for liquid nitrogen, andoverestimate the present result. The present correlation agrees well with theexperimental data. Further more, the formation position, velocity and lengthdistribution in different tubes and inclination angles were obtained.
(3) The flow structure around Taylor bubble was obtained by PIVtechnique based on the present experimental system. The traditional criterionraised from water based fluid experiments is no longer applicable for liquidnitrogen. According to the traditional criterion, the occurrence of turbulentwake appears when the Nfnumber is larger than1500. However, in this study,both the transitional and laminar flow patterns are observed with the Nfnumbers much larger than1500.
(4) The PIV experimental results were further analyzed by POD method.The large-scale structure of Taylor bubble wake was calculated to explain thecoalescence between consecutive Taylor bubbles. The coalescence processcan be inhibited by changing the large-scale structure of Taylor bubble wake.
(5) Based on the PIV and visualization experiment, the effect ofturbulence intensity, heat flux, tube diameter and inclination angle on theformation of Taylor bubble was investigated. A new dimensionless gasvelocity vqwas introduced. On this basis, a correlation for predicting theformation position of Taylor bubble caused by heat leakage in liquid nitrogentube was developed. Compared with the experimental results of present studyand reference, the relative error is less than±20%.
(6) A detailed CFD research on the motion of a single Taylor bubble inliquid nitrogen was conducted using VOF method. The transition of flowpattern in Taylor bubble wake, bubble rising velocity and geometriccharacteristics of trailing edge were obtained. The comparison with theexsiting literature data showed that the present model is credible. Thetransiton of laminar, transitional and turbulent flow pattern was oobtained. Onthis basis, the transition criterion of the flow pattern in nitrogen Taylor bubblewake was built. The numerical result also shows the traditional criterion raised from water based fluid experiments is no longer applicable for liquidnitrogen.
在一定漏热条件下，管路内尚未发生间歇泉时，就会出现弹状流动，这已经对火箭发动机的安全运行造成极大隐患。因此，准确判断低温管路中Taylor气泡的形成位置非常重要。Taylor气泡周围的流场，尤其是尾迹区流场是Taylor气泡合并过程的关键因素，两个连续的Taylor气泡之间的相互作用过程取决于领先气泡的尾迹区流型。首先，不同的尾迹区流型（层流、过渡流或湍流）导致不同的合并速率，一些尾迹区流型甚至会阻止两个Taylor气泡的合并。因此，尾迹区的流型决定了弹单元中的Taylor气泡长度份额，进而影响低温气液两相弹状流的压降参数和空泡份额。其次，Taylor气泡尾迹区内的湍流强度决定了液弹中弥散气泡和液体的速度分布，也会影响两相流动的空泡份额。同时Taylor气泡头部区域的流场对Taylor气泡的上升速度有重要影响。综上所述，Taylor气泡周围流场的研究是低温气液两相弹状流中的重要课题，对低温系统的工作效率和安全运行都具有重要的科学意义和实用价值。
在低温管路中，由漏热产生弥散气泡到Taylor气泡的形成，以及间歇泉的产生，这是一个整体的连续过程，其中对Taylor气泡的形成过程还缺乏统一的判据，而且该过程的研究尚未涉及管路内的流动结构对Taylor气泡形成的影响。对于低温气液两相弹状流研究，大多数研究限于宏观流动特征，如压降测量和图像研究。由于低温气液两相流中流场测量的难度较大，关于低温气液两相流中Taylor气泡周围流场的研究国内外未见报道，且尚没有建立针对低温气液两相流中Taylor气泡尾迹区流型的判据。低温流体的研究已经远落后于常温流体。
本文以液氮为工质，对低温管路中由漏热产生的Taylor气泡的形成、运动和合并过程进行了实验和数值模拟研究。对漏热形成的低温气液两相流动中Taylor气泡的形成位置、长度和速度分布进行了可视化研究。使用PIV流场测量方法对低温液体中Taylor气泡周围流场进行了定量测量，使用POD数据分析方法对PIV测量结果进行了进一步分析，探讨了流场的湍流大尺度结构对Taylor气泡之间相互作用的影响、管路内湍流强度对Taylor气泡形成的影响，最后对对理想状态下，静止低温流体中单个Taylor气泡的运动特征和周围流场结构进行了数值模拟研究。具体如下：
（1）建立了适用于低温气液两相流动的PIV测速和可视化测量相结合的实验平台。针对圆形截面管路中的图像畸变问题，建立了一种通用的可用于多层管壁情况下的直接校正方法。使用方形规则化网格进行验证，最大相对误差不超过3%。使用Fortran语言编制了通用校正程序。
（2）利用上述实验台结合高速相机在多种倾角下，对多种管路内液氮沸腾形成的气液两相流动中Taylor气泡宏观特征进行了可视化研究。分析了多种倾角下Taylor气泡的合并过程，建立了跟随气泡和领先气泡速度与气泡间距的关系。已有的由常温流体得到的速度关系式不适用于液氮流体，普遍高估了本文实验结果，新建立的关系式和实验结果吻合较好。得到了Taylor气泡的形成位置、速度和长度份额分布与管路内径、倾角的关系。
（3）使用所建实验台结合PIV实验手段得到了Taylor气泡周围流场结构。结果分析表明，常温流体中Taylor气泡尾迹区流型判定方法不再适用于液氮流体，传统理论认为当无量纲流体逆粘度数Nf>1500时，Taylor气泡尾迹区为湍流。在液氮流体中，当Nf数远大于这一临界值时，液氮流体中的Taylor气泡尾迹区仍然为过渡流和层流。
（4）使用POD方法对PIV实验结果进行了进一步的分析，得到了尾迹区流场中湍流大尺度结构，解释了可视化实验中不同倾角下Taylor气泡合并过程，得到了改变Taylor气泡尾迹区的湍流大尺度结构可抑制Taylor气泡的合并的结论。
（5）在PIV实验和可视化实验的基础上，考察了流场湍流强度、热流密度、管路内径和管路倾角等对Taylor气泡形成的影响，提出了无量纲气相速度vq。在此基础上，建立了液氮管路中由漏热形成的Taylor气泡的生成位置预测公式，公式预测结果与本文和文献中的实验结果相比最大误差在±20%以内。
（6）使用VOF方法对静止液氮中，单个Taylor气泡运动的理想过程进行了数值模拟，得到了尾迹区流型转变过程、上升速度、尾缘几何特征等。与文献数据对比表明本文模型可信。得到了Taylor气泡尾迹区内层流、过渡流和湍流的流型转变过程，建立了适用于液氮流体中Taylor气泡尾迹区流型转变的判据，该结果也表明常温流体尾迹区流型判据不适用于液氮流体。
Cryogenic gas-liquid two-phase flow is usually encountered in cryogenicengineering such as pipe transportation of cryogenic liquid and high heat-fluxelectronic chip cooling. Due to the inevitable heat leak along the pipe, smallbubbles form from the boiling cryogenic liquid and coalesce to bullet shapedlarge bubbles (also named Taylor bubble) with almost the same diameter ofthe pipe. These Taylor bubbles cause pipe line blockage and extrude thecryogenic liquid from the pipe line, and could lead to the destruction of pipeand valve, and also cavitation erosion of rocket engine. Thus the Taylorbubble formation and evolution in the pipe line are the importantcharacteristics in cryogenic engineering.
Cryogenic gas-liquid slug flow has already formed under some thermalconditions when there is no geysering phenomenon in the tube. This is hiddendanger for the safty operation of crogenic tubes. Thus the prediction forTaylor bubble formation is very important for the safe operation of cryogenictransportation tube.
The flow field around Taylor bubble, especially the flow field in bubblewake has great influence on the flow parameters of cryogenic two-phase slugflow, and then affects the interaction of two consectutive Taylor bubbles.Firstly, the flow pattern in the leading Taylor bubble’s wake determines theinteraction between two adjacent Taylor bubbles. Different flow patterns(laminar, transition or turbulent) result in different bubble coalescence speedand rate, and some will prohibit the coalescence. Then the flow field inbubble wake affects the length fraction of gas slug in a slug unit. Finally itinfluences the pressure drop and void fraction in cryogenic two-phase flow.And the turbulence intensity in Taylor bubble wake defines the velocity ofdispersed bubbles in a liquid slug, the velocity of liquid phase and the distribution of void fraction. Meanwhile, the velocity field ahead of Taylorbubble is highly important for Taylor bubble velocity. Thus the present studyis meaningful for studying on these important parameters in cryogenicengineering.
In cryogenic tube, the coalescence of dispersed vapor bubbles leads tothe formation of Taylor bubbles. And the continuous coalescence of Taylorbubbles leads to the geysering phenomenon. In this continuous process, thereis a lack of the criterion of Taylor bubble formation in cryogenic tube causedby heat leak. And the research about this process has not included the effect offlow structure on the formation of Taylor bubbles. For the cryogenictwo-phase slug flow, most studies are limited to the macroscopic properties,e.g. the pressure measurement or photographic study. However, moredeveloped investigation on the flow field in cryogenic two-phase slug flow isscarce. And little literature can be found to define the wake pattern of a Taylorbubble in cryogenic fluid. The critierion for defining the wake pattern ofcryogenic Taylor bubble has not been developed. In this particular field, theresearch in cryogenic engineering has fallen behind that focusing on ordinaryfluid.
The purpose of the present study is to experimently and numericallyinvestigate the formation, motion and coalescence process of Taylor bubblecaused by heak leak in cryogenic tubes. The formation position, length andvelocity distribution of Taylor bubble are studied by vasulization technique.The flow field around Taylor bubble was obtained by PIV technique. Basedon PIV results, snapshot POD was introduced to reveal the effect of flowstructure on the interaction of Taylor bubbles, and the effect of turbulence onthe formation of Taylor bubble. At last, the motion of a single Taylor bubblein stagnant liquid nitrogen and the flow structure aound it were numericallyinvestigated. The main conclusions are summarized as follows:
(1) An experimental system was built to investage the characteristics andthe flow field of cryogenic gas-liquid slug flow. A correction algorithm wasdeveloped for reconstructing the flow field based on ray tracing method,which showed the maximum error was3%by the uniform grid validation. Acorrection program was built using Fortran language.
(2) The characteristics of Taylor bubble in cryogenic slug flow were studied, including the length, velocity and length fraction. The coalescenceprocess of Taylor bubble was analysed under different inclination angles. Thevelocity ratio of trailing and leading bubble as a function of bubble distancewas built based on the experimental data. The existing correlations fromordinary two-phase flow are no longer suitable for liquid nitrogen, andoverestimate the present result. The present correlation agrees well with theexperimental data. Further more, the formation position, velocity and lengthdistribution in different tubes and inclination angles were obtained.
(3) The flow structure around Taylor bubble was obtained by PIVtechnique based on the present experimental system. The traditional criterionraised from water based fluid experiments is no longer applicable for liquidnitrogen. According to the traditional criterion, the occurrence of turbulentwake appears when the Nfnumber is larger than1500. However, in this study,both the transitional and laminar flow patterns are observed with the Nfnumbers much larger than1500.
(4) The PIV experimental results were further analyzed by POD method.The large-scale structure of Taylor bubble wake was calculated to explain thecoalescence between consecutive Taylor bubbles. The coalescence processcan be inhibited by changing the large-scale structure of Taylor bubble wake.
(5) Based on the PIV and visualization experiment, the effect ofturbulence intensity, heat flux, tube diameter and inclination angle on theformation of Taylor bubble was investigated. A new dimensionless gasvelocity vqwas introduced. On this basis, a correlation for predicting theformation position of Taylor bubble caused by heat leakage in liquid nitrogentube was developed. Compared with the experimental results of present studyand reference, the relative error is less than±20%.
(6) A detailed CFD research on the motion of a single Taylor bubble inliquid nitrogen was conducted using VOF method. The transition of flowpattern in Taylor bubble wake, bubble rising velocity and geometriccharacteristics of trailing edge were obtained. The comparison with theexsiting literature data showed that the present model is credible. Thetransiton of laminar, transitional and turbulent flow pattern was oobtained. Onthis basis, the transition criterion of the flow pattern in nitrogen Taylor bubblewake was built. The numerical result also shows the traditional criterion raised from water based fluid experiments is no longer applicable for liquidnitrogen.
引文
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