表面效应对微管道中气体流动特性的影响
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摘要
随着微电子机械系统（MEMS）技术的迅猛发展，微流动特性的研究已成为当前流体力学研究热点。因此对微管道内流动特性的研究有着重要的理论价值和实际意义。本文通过实验研究、理论分析和数值模拟相结合的方法，就微管道内气体流动的若干问题进行了较为深入、细致的研究。主要工作如下：
（1）提出了一种便于工程应用的，适合于深宽比较大的，部分考虑压缩性的，微管道内质量流量的近似理论模型，给出了该近似理论模型和常用近似理论模型的适用范围。
（2）指出关于微管道内已有的一维可压缩等温流动的平均阻力系数确定方法的不足之处，并提出了一种便于实用的可压缩流动平均阻力系数的确定方法。该方法适用于可压缩流动，在实验数据的基础上可以方便地得到平均阻力系数和壁面平均切应力。
（3）将微管道表面粗糙度的影响等效为粗糙度粘性系数，提出适合于可压缩流动的二维和三维粗糙度粘性系数模型。应用该模型得到的数值模拟结果与实验结果符合的较为一致。
（4）对等直－收缩－扩张－等直微管道中气体流动的实验研究发现两个特异现象：其一为微管道内最早出现声速点的位置不一定在喉部附近，其二为微管道中的临界压比与常规值有很大差别。并采用数值实验的手段研究了微管道表面积与体积之比值对上述两个特异现象的影响。
（5）对等截面长微直管道中气体流动特性的实验研究发现：在保持进口压力不变的条件下，降低出口压力，质量流量随进出口压比增大而增加，但当进出口压比达到某一临界值以后，质量流量将保持基本不变。本文将这一现象定义为亚堵塞现象，并将对应的压比定义为亚堵塞临界压比。并研究了微管道表面积与体积之比值对亚堵塞临界压比的影响。
（6）采用BGK 方法对微管道内流动进行了数值模拟，得到微管道内连续流和滑移流并存流动的数值模拟结果，其沿程压力分布，质量流量与实验结果吻合。
With the rapid development of micoelectromechanical systems (MEMS), the study of the flow characteristics in microchannels has become a hot subject in the fluid mechanics. So it is very significant to investigate the flow characteristics in microchannels on both theoretical researches and applications. Based on large quantities of experimental data, theoretical analysis and numerical simulations，the gas flow characteristics were investigated. The main work is stated as follows.
(1) An approximate theoretical model was proposed with partial consideration of compressibility. It is used to compute the mass flow and is suitable for the microchannels with a large ratio of depth to width. The applicability of the new model and the model usually used is provided.
(2) The flaws on the one-dimension (1-D) compressible isothermal average-friction-factor were indicated. A friction factor computation method was proposed, which is not only suitable for compressible flow but also easy to achieve the average wall shear stress. Moreover, the applicability of the incompressible friction factor is discussed.
(3) The effects of surface roughness in microchannels were taken into account in terms of a roughness-viscosity function. The compressible two-dimension (2-D) and three-dimension (3-D) models were proposed to interpret the experimental results. Better agreements between computation results and experimental data were found using the models.
(4) Two phenomena in straight-convergent-divergent-straight microchannels were identified, which are different from the macroflow through experimental studies. One is that the first appearing sonic point position in microchannels is not near throat cross-section. The other is that the critical pressure ratio in microchannels is different from that in macroflow greatly. Numerical simulations were carried out to investigate the effects of the ratio of surface to volume on the two phenomena.
(5) Experimental investigations for the long-constant-area microchannel indicate that the mass flow rate through the microchannel changes considerably small as the pressure ratio of inlet to outlet arrived at some critical pressure ratio. The phenomenon is defined as sub-choking and the corresponding pressure ratio is defined as the sub-choking-critical-pressure-ratio. Moreover, the effects of the ratio of surface to volume on the critical pressure ratio are studied.
(6) Numerical simulations were conducted by using the Bhatnagar-Gross-Krook (BGK) method. Better agreements between computation results and experimental data were found about the pressure distribution and mass flow rate.
（1）提出了一种便于工程应用的，适合于深宽比较大的，部分考虑压缩性的，微管道内质量流量的近似理论模型，给出了该近似理论模型和常用近似理论模型的适用范围。
（2）指出关于微管道内已有的一维可压缩等温流动的平均阻力系数确定方法的不足之处，并提出了一种便于实用的可压缩流动平均阻力系数的确定方法。该方法适用于可压缩流动，在实验数据的基础上可以方便地得到平均阻力系数和壁面平均切应力。
（3）将微管道表面粗糙度的影响等效为粗糙度粘性系数，提出适合于可压缩流动的二维和三维粗糙度粘性系数模型。应用该模型得到的数值模拟结果与实验结果符合的较为一致。
（4）对等直－收缩－扩张－等直微管道中气体流动的实验研究发现两个特异现象：其一为微管道内最早出现声速点的位置不一定在喉部附近，其二为微管道中的临界压比与常规值有很大差别。并采用数值实验的手段研究了微管道表面积与体积之比值对上述两个特异现象的影响。
（5）对等截面长微直管道中气体流动特性的实验研究发现：在保持进口压力不变的条件下，降低出口压力，质量流量随进出口压比增大而增加，但当进出口压比达到某一临界值以后，质量流量将保持基本不变。本文将这一现象定义为亚堵塞现象，并将对应的压比定义为亚堵塞临界压比。并研究了微管道表面积与体积之比值对亚堵塞临界压比的影响。
（6）采用BGK 方法对微管道内流动进行了数值模拟，得到微管道内连续流和滑移流并存流动的数值模拟结果，其沿程压力分布，质量流量与实验结果吻合。
With the rapid development of micoelectromechanical systems (MEMS), the study of the flow characteristics in microchannels has become a hot subject in the fluid mechanics. So it is very significant to investigate the flow characteristics in microchannels on both theoretical researches and applications. Based on large quantities of experimental data, theoretical analysis and numerical simulations，the gas flow characteristics were investigated. The main work is stated as follows.
(1) An approximate theoretical model was proposed with partial consideration of compressibility. It is used to compute the mass flow and is suitable for the microchannels with a large ratio of depth to width. The applicability of the new model and the model usually used is provided.
(2) The flaws on the one-dimension (1-D) compressible isothermal average-friction-factor were indicated. A friction factor computation method was proposed, which is not only suitable for compressible flow but also easy to achieve the average wall shear stress. Moreover, the applicability of the incompressible friction factor is discussed.
(3) The effects of surface roughness in microchannels were taken into account in terms of a roughness-viscosity function. The compressible two-dimension (2-D) and three-dimension (3-D) models were proposed to interpret the experimental results. Better agreements between computation results and experimental data were found using the models.
(4) Two phenomena in straight-convergent-divergent-straight microchannels were identified, which are different from the macroflow through experimental studies. One is that the first appearing sonic point position in microchannels is not near throat cross-section. The other is that the critical pressure ratio in microchannels is different from that in macroflow greatly. Numerical simulations were carried out to investigate the effects of the ratio of surface to volume on the two phenomena.
(5) Experimental investigations for the long-constant-area microchannel indicate that the mass flow rate through the microchannel changes considerably small as the pressure ratio of inlet to outlet arrived at some critical pressure ratio. The phenomenon is defined as sub-choking and the corresponding pressure ratio is defined as the sub-choking-critical-pressure-ratio. Moreover, the effects of the ratio of surface to volume on the critical pressure ratio are studied.
(6) Numerical simulations were conducted by using the Bhatnagar-Gross-Krook (BGK) method. Better agreements between computation results and experimental data were found about the pressure distribution and mass flow rate.
引文
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[2] 梅涛,孔德义,张培强等.微电子机械系统的力学特性与尺度效应. 机械强度.2001, 23(4):373~379.
[3] Peter G, Jens B, Ole SJ. Microfluidics-a review. Journal of Micromechanics Microengineering. 1993, 3: 168~182.
[4] Ho CM, Tai YC. Review: MEMS and its applications for flow control. Journal of Fluids Engineering. 1996, 118:437~447.
[5] Muhammad MR. Measurements of heat transfer in microchannel heat sinks. Int. Comm. Heat Mass Transfer. 2000,27(4): 495~506.
[6] Jiang XN, Zhou ZY, Huang XY et al. Laminar flow through microchannels used for microscale cooling systems. IEEE/CPMT Electronic Packaging Technology Conference. 1997:119~122.
[7] Torsten G. Microdiffusers as dynamic passive valves for micropump applications. Sensors and Actuators A 1998,69:181~191.
[8] Nelsimar V, Donald W, Margo V. Development of a MEMS microvalve array for fluid flow control. Journal of MEMS.1998, 7(4): 395~402.
[9] Bayt R. Analysis, fabrication and testing of a MEMS-based micropropulsion system. PhD thesis. Massachusetts Institute of Technology. 1999.
[10] 崔大付.基于BioMEMS 技术的DNA芯片研究.机械强度.2001,23(4):471~475.
[11] Theo SJ, Lammerink, et al, Micro-liquid flow sensor, Sensors and Actuators A, 1993,37-38:45~50.
[12] Kohl F, Jachimowicz A, Steurer J, et al. A micromachined flow sensor for liquid and gaseous fluids. Sensors and Actuators A, 1994,41-42: 293~299.
[13] Mohamed Gad-el-Hak. The fluid mechanics of microdevices-the Freeman Scholar Lecture. Journal of Fluids Engineering. 1999,121:5~30.
[14] Wu PY and Little WA. Measurement of the heat transfer characteristics of gas flow in fine channel heat exchangers used for microminiature refrigerators. Cryogenics. 1984:415~420
[15] Stemme E, Stemme G. A novel piezoelectric valve-less fluid pump. Transducers. 1993:110.
[16] Lee W Y, Lee SYK, WM, et al. Microchannels in series with gradual contraction/expansion. MEMS, ASME 2000,2: 467~472.
[17] Olsson A, Enoksson P, Stemme G et al. Micromachined flat-walled valveless diffuser pumps. Journal of MEMS. 1997,6(2):161~166.
[18] Olsson A, Enoksson P, Stemme G et al. A valve-less planar pump is otropically etched in silicon. Journal of Micromechanics Microengineering. 1996,6:87~91.
[19] Ye XY, Tang F, Ding HQ et al. Study of a vaporizing water micro-thruster. Sensors and Actuators A. 2001,89:159~165.
[20] Timo V and Marek T. Compact damping models for laterally moving microstructures with gas-rarefaction effects. IEEE Journal of MEMS. 2001,10(2): 263~273.
[21] Farooqui MM, Evans AGR. Microfabrication of submicron nozzles in silicon nitride. Journal of MEMS. IEEE. 1992, 1(2): 86~88.
[22] Janson SW, Helvajian H and Breuer K. MEMS, Microengineering and Aerospace Systems. AIAA paper 99-3802.
[23] 谢中生.MEMS阔步迈入新世纪.电子工业专用设备.1999,28(4):22~24.
[24] 崔尔杰. MEMS与智能化流体力学. 空气动力学学报. 2000, 18(增刊):52~59.
[25] Kavehpour HP, Mohammad F, Asako Y. Effects of compressibility and rarefaction on gaseous flows in microchannels. Numerical Heat Transfer, Part A. 1997,32:677~696.
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