||Investigation of Micronozzles Flow
||Department of Mechanical and Electro-Mechanical Engineering
Pressure loss coefficient
Ratio of pressure loss coefficient
在微文氏管的研究部分，首先利用微機電製程技術製造出兩種不同尺寸的微文氏管，寬度分別為150及200微米，開口角度各為45°，總長則為10 mm，再以空氣作為工作流體，利用不同質量流率來量測微文氏管進出口的壓力差並配合FLUENT軟體分析觀察其流場分佈的情況。結果顯示，當流量小時，此兩種不同外型的喉部出口處都會因回流的關係產生相對稱的分離渦流，但隨著流量增大，分離區會持續擴大導致渦流相互影響，此時渦流之間的吸引力造成分離區不再對稱進而使流場的分佈偏向於一邊。而在速度分佈部分，當流量為5.338 mg/min時，寬度為150微米的喉部區流速已經高於聲速，隨後因速度不斷增加，空氣黏滯力影響了速度分佈而產生了速度衝擊現象。
||This study presents the investigating of microchannels flow. It is divided into two parts, the flow characteristics of micro venturi and the performance of straight-walled and curved-walled micro nozzle/diffuser respectively. The experimental results are also compared with the simulation results whereby we can observe the flow field in micro venturi and discuss the bounder effect of micro nozzle/diffuser.
First, we adopt MEMS technology to fabricate micro venturis with different widths of 150 and 200 um respectively and utilize FLUENT software to analyze the flow fields. Air was set as the working fluid and the air mass flow rate of inlet is changed to obtain the pressure drop between inlet and outlet.
When a flow passes through the throat, the backflow results in the symmetric separations occur and grow with the increase of mass flow rate. As the separation is large enough, the suction between both separations will be larger than the resistance of flow, the larger separation will appear on one side and leads the flow to slant to the other side. The result also shows the complicated shock wave flow structure was generated by the effect of viscosity.
The second part of this paper presents a CFD-simulation of the performance of straight-walled and curved-walled micro nozzle/diffuser by FLUENT software. Such nozzle/diffusers are mainly used in micro venturi and also applied to valveless micropumps.
The results show that the pressure loss coefficient for the micro nozzle/diffuser decreases with the Reynolds number whereas the ratio of the pressure loss coefficient increases with the Reynolds number. At the same Reynolds number, the pressure loss coefficient of micro nozzle is higher than that of the micro diffuser.
The model is also compared with different previously experimental measurements and shows a good agreement. For a fixed volumetric flow rate, the results show the curved profile bounder (a = 5/3) micro nozzle/diffuser has higher pressure loss coefficient and higher ratio of the pressure loss coefficient than that of the straight profile bounder. The theoretical analysis and design basis can then be formulated as a reference and applied to the fabrication of micro nozzle/diffuser from this study.
||List of Contents
List of Contents VI
List of Figures IX
List of Tables XVI
Chapter 1 Introduction 1
1-1 Background 1
1-2 Motivation and Goals 2
1-3 Literature Review 3
Chapter 2 Theoretical Analysis 10
2-1 Microchannel Flow 10
2-2 Governing equations 11
2-3 Restriction Flow Meters for Internal Flows 12
2-4 Compressible Fluids 13
2-5 Incompressible Flow in Micro Nozzle/Diffuser 16
Chapter 3 The Investigation of Micro Venturi 19
3-1 Introduction 19
3-2 Fabrication of Silicon Micro Venturi 20
3-3 Experiment of Micro Venturi 22
3-3-1 Error Correction of Experimental Equipment 23
3-3-2 Procedure of Experiment 23
3-4 Numerical Analysis 24
3-4-1 Introduction to FLUENT 24
3-4-2 Basic Theory of FLUENT 25
3-5 Numerical Study of Micro Venturi 27
3-5-1 Graphics Design and Mesh Generation 27
3-5-2 Boundary Condition 28
3-6 Results and Discussion 28
3-6-1 Experimental Results 28
3-6-2 Numerical Simulation Results 29
3-6-3 Comparison of Experiment and Simulation 31
3-7 Conclusions 32
Chapter 4 The Analysis of Curved-walled Micro Nozzle/diffuser 34
4-1 Introduction 34
4-2 Numerical Study of Curved-walled micro nozzle/diffuser 35
4-2-1 Model Construction 35
4-2-2 Boundary Condition 36
4-3 Result and Discussion 37
4-3-1 Results of Numerical Simulation 37
4-3-2 Analysis of Theoretical, Experimental and Simulation Results 39
4-3-3 Effects of Reynolds Numbers, Open Angle and Coefficient “a” 40
4-4 Conclusions 41
Chapter 5 Conclusions 43
List of Figures
Figure 1-1 The fabricated micronozzle with 19 mm width of throat 51
Figure 1-2 Trust efficiency results for both the fluid and experimental testing for two different nozzles, (a) 34 mm throat and a 7.1:1 expansion ratio (b) 37.5 mm throat and a 16.9:1 expansion ratio 51
Figure 1-3 Streamline for low-Re Model 52
Figure 1-4 Comparison of DSMC results with NS prediction and experimental data 52
Figure 1-5 Illustration of fluid flow through an orifice 53
Figure 1-6 Discharge coefficient for compressible flow through microorifices 53
Figure 1-7 Manufactured meso and micro nozzles 53
Figure 1-8 Distribution of centerline Mach number in micro nozzles with different scales 54
Figure 1-9 Contours of Mach number at different outlet pressures, (a) 65 kPa; (b) 55 kPa; (c) 30 kPa 54
Figure 1-10 The comparison of DSMC, NC, and experimental data for mass flux vs pressure difference 55
Figure 1-11 The flow field at Re = 15 55
Figure 1-12 The flow field at Re = 45 56
Figure 1-13 The streamline of the flow field and the Mach number contours 56
Figure 1-14 The contours of nozzle discharge coefficient and the jet diameter 57
Figure 1-15 The valveless pump 57
Figure 1-16 Turbulent flux throughout a diffuser, (a) positive flow direction, (b) negative flow direction 58
Figure 1-17 The diagrams of diffuser efficiency ratio and volume flow rate with pump pressure 58
Figure 1-18 Nozzle/diffuser flow at small Re 59
Figure 1-19 Nozzle/diffuser flow at large Re 59
Figure 1-20 Influence of the Reynolds number on the pressure loss coefficient 60
Figure 1-21 Influence of the opening angle on the pressure loss coefficient 60
Figure 1-22 The variation of pressure loss coefficient in a conical diffuser, (a) fully development; (b) thin inlet boundary layer 61
Figure 1-23 The variation of pressure loss coefficient in a planar diffuser, (a) fully development; (b) thin inlet boundary layer 62
Figure 2-1 Gas flow regime with different Knudsen number 63
Figure 2-2 The main models with different Knudsen number 63
Figure 2-3 Internal flow through a generalized nozzle 64
Figure 2-4 Definitions of the different regions in the nozzle/diffuser element 64
Figure 2-5 The loss coefficient K and pressure loss coefficient ξ in different types of nozzle/diffuser 65
Figure 2-6 Compressible flow in an infinitesimal stream tube 65
Figure 3-1 The Herschel standard Venturi 66
Figure 3-2 The illustration of micro orifice plate 66
Figure 3-3 The illustration of micro venture tube 66
Figure 3-4 Fabrication processes of micro venture 67
Figure 3-5 The illustrations of two different micro venture 68
Figure 3-6 The arc corner of micro venturi after RIE etching 68
Figure 3-7 The diagram of micro venturi after dry etching 69
Figure 3-8 The roughness of fabricated micro venturi 69
Figure 3-9 The setup of experimental equipment 70
Figure 3-10 The sketch of micro venturi 70
Figure 3-11 The entity photo of micro venturi 71
Figure 3-12 The pressure gauge, Drunk DPI 705 71
Figure 3-13 The processes of FLUENT solving the program 72
Figure 3-14 The simulation domains of micro venturi by GAMBIT 73
Figure 3-15 The grid contour of micro venture 74
Figure 3-16 Overview of the coupled solution method 74
Figure 3-17 The experimental and simulation results in two different types of micro venturi 75
Figure 3-18 The illustration of Type I with Qm=0.767 mg/min, (a) velocity contour, (b) streamline of velocity 76
Figure 3-19 The flow distribution of Type I with different mass flow rate 77
Figure 3-20 The cross-cutting line on Y-axis of velocity in Type I 78
Figure 3-21 Velocity magnitude profile along the cross-cutting line with different mass flow rate 78
Figure 3-22 The velocity contour of Type I when mass flow rate is 5.338 mg/min 79
Figure 3-23 The diagram shows the shock occurs when mass flow rate is 8.52 mg/min 79
Figure 3-24 Contours of Mach number when mass flow rate is 16.472 mg/min 80
Figure 3-25 The asymmetry separations of Type II when mass flow rate is 8.275 mg/min 80
Figure 3-26 The flow distribution of Type II with different mass flow rate 81
Figure 3-27 The length of separation with different mass flow rate 82
Figure 3-28 The comparison diagram of the experimental and simulation results in Type I 83
Figure 3-29 The comparison diagram of the experimental and simulation results in Type II 83
Figure 4-1 The operation of the parallel arrangement of a double-chamber diffuser pump 84
Figure 4-2 Operation of the diffuser-based pump: (a) Supply mode; (b) Pump mode 84
Figure 4-3 The illustrations of straight-walled micro nozzle/diffuser with different open angles (a) 5°, (b) 10°, (c) 15°, (d) 20° and (e) comparison sketch 85
Figure 4-4 The illustrations of curved-walled (I) micro nozzle/diffuser with different mid-point width (a) 431.2, (b) 564.5, (c) 701.9, (d) 864 m and (e) comparison sketch 86
Figure 4-5 The illustrations of curved-walled (II) micro nozzle/diffuser with different parameter, a, (a) 1/1780, (b) 1/884, (c) 1/582, (d) 1/428 and (e) comparison sketch 87
Figure 4-6 The mesh density of straight-walled micro nozzle/diffuser 88
Figure 4-7 The mesh density of curved-walled (I) micro nozzle/ diffuser 88
Figure 4-8 The mesh density of curved-walled (II) micro nozzle/ diffuser 89
Figure 4-9 The sketch of straight-walled and curved-walled (I) micro nozzle/diffuser ( = 20°) 89
Figure 4-10 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (5° and 5° SIO) 90
Figure 4-11 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (10° and 10° SIO) 90
Figure 4-12 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (15° and 15° SIO) 91
Figure 4-13 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (20° and 20° SIO) 91
Figure 4-14 The relationship between pressure loss coefficient and open angle of Model 1 when Reynolds number is 70 92
Figure 4-15 The relationship between pressure loss coefficient and open angle of Model 2 when Reynolds number is 70 92
Figure 4-16 The sketch of straight-walled and curved-walled (II) micro nozzle/diffuser ( = 20°) 93
Figure 4-17 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (5° and a = 1/1780) 93
Figure 4-18 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (10° and a = 1/884)
Figure 4-19 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (15° and a = 1/582) 94
Figure 4-20 The distribution of pressure loss coefficient and its ratio at different Reynolds numbers (20° and a = 1/428) 95
Figure 4-21 The relationship between pressure loss coefficient and open angle of Model 3 when Reynolds number is 70 95
Figure 4-22 The relationship between pressure loss coefficient and Reynolds numbers with different results at = 10° and 20° (Mode 1, diffuser) 96
Figure 4-23 The relationship between pressure loss coefficient and Reynolds numbers with different results at = 10° and 20° (Mode 1, nozzle) 96
Figure 4-24 The relationship between pressure loss coefficient and Reynolds numbers with different results at = 10° and 20° (Mode 2, SIO diffuser) 97
Figure 4-25 The relationship between pressure loss coefficient and Reynolds numbers with different results at = 10° and 20° (Mode 2, SIO nozzle) 97
Figure 4-26 The relationship between pressure loss coefficient and open angle when Reynolds number from 300 to 1500 98
Figure 4-27 The relationship between pressure loss coefficient and coefficient a when Reynolds number from 300 to 1500 98
Figure 4-28 The diagram of the “backflow” when the open angle is 20 and Reynolds number is 1500 99
Figure 4-29 The diagram of the “backflow” when the coefficient a is 1/428 and Reynolds number is 1500 99
List of Tables
Table 2-1 The mean free path of the air with different pressure 100
Table 3-1 The size chart of micro venturi 100
Table 4-1 The description of the size of micro nozzle/diffuser 101
Table 4-2 The pressure loss coefficient of micro nozzle/diffuser when Re = 70 102
Table 4-3 The results of theoretical, experimental and simulation when Re = 70 103
|| R. L. Bayt and K. S. Breuer, “Viscous Effects in Supersonic MEMS-Fabricated Micronozzle”, American Society of Mechanical Engineers, DSC, Vol. 66, pp. 117-123 (1998).
 I. D. Boyd, D. B. VanGilder and E. J. Beiting, “Computational and Experimental Investigations of Rarefied Flows in Small Nozzles”, AIAA Journal, Vol. 34, pp. 2320-2326 (1996).
 Y. T. Yang, and C. F. Hou, “Numerical Calculation of Turbulent Flow in Symmetric Two-Dimensional Diffusers”, Acta Mechanica, Vol. 137, pp. 43-54 (1999).
 G. N. Markelov and M. S. Ivanov, “Numerical Study of 2D/3D Micronozzle Flows”, AIP Conf. Proc., Vol. 585, pp. 539-546 (2001).
 R. D. D. Menzies, B. E. Richards, K. J. Badcock, L. Loseken and M. Kahl, “Computational Investigation of Three-Dimensional Flow Effects on Micronozzles”, J. Spacecraft, Vol. 39, pp. 642-644 (2002).
 A. A. Alexeenko, and D. A. Levin, “Numerical Modeling of Axisymmetric and Three-Dimensional Flows in Microelectromechanical Systems Nozzles”, AIAA J., Vol. 40, pp. 897-904 (2002).
 H. V. Tafreshi, and B. Pourdeyhimi, “The Effects of Nozzle Geometry on Waterjet Breakup at High Reynolds Numbers”, Experiments in Fluids, Vol. 35, pp. 364-371 (2003).
 A. Begenir, H. V. Tafreshi and B. Pourdeyhimi, “Effect of Nozzle Geometry on Hydroentangling Water Jets: Experimental Observations”, Textile Research Journal, Vol. 74, pp. 178-184 (2004).
 H. V. Tafreshi, and B. Pourdeyhimi, “Simulating Cavitation and Hydraulic Flip Inside Hydroentangling Nozzles”, Textile Research Journal, Vol. 74, pp. 359-364 (2004).
 E. Ghassemieh, H. K. Versteeg and M. Acar, “Effect of Nozzle Geometry on the Flow Characteristics of Hydroentangling Jets”, Textile Research Journal, Vol. 73, pp. 444-450 (2003).
 M. B. D. Dietz, K. Aslam and V. V. Subramaniam, “Simulation of Compressible Gas Flow in a Micronozzle - Effect of Walls on Shock Structure”, AIAA Thermophysics Conference, 35th, Anaheim, CA, June 11-14 (2001).
 C. Mishra and Y. Peles, “Incompressible and Compressible Flows through Rectangular Microorifices Entrenched in Silicon Microchannels”, Journal of Microelectromechanical Systems, Vol. 14, pp. 1000-1012 (2005).
 S. S. Hsieh, H. H. Tsai, C. Y. Lin, C. F. Huang and C. M. Chien, “Gas Flow in a Long Microchannel”, International Journal of Heat and Mass Transfer, Vol. 47, pp. 3877-3887 (2004).
 G. Hetsroni, A. Mosyak, E. Pogrebnyak and L. P. Yarin, “Fluid Flow in Micro-Channels”, International Journal of Heat and Mass Transfer, Vol. 48, pp. 1982-1998 (2005).
 K. Chen, M. Winter and R. F. Huang, “Supersonic Flow in Miniature Nozzles of Planar Configuration”, J. Micromech. Microeng., Vol.15, pp. 1736-1744 (2005).
 P. F. Hao, Y. T. Ding, Z. H. Yao, F. He and K. Q. Zhu, “Size Effect on Gas Flow in Micro Nozzles”, J. Micromech. Microeng., Vol.15, pp. 2069-2073 (2005).
 Z. Yang and Y. H. Wei, “Gas Flow Simulation in a Micro Nozzle”, Aircraft Engineering and Aerospace Technology: An International Journal, Vol. 48, pp. 387-390 (2006).
 C. Xie, “Characteristics of Micronozzle Gas Flow”, Physics of Fluids, Vol. 19, 037102 (2007).
 C. L. Sun and K. H. Huang, “Numerical Characterization of the Flow Rectification of dynamic Microdiffusers”, J. Micromech. Microeng., Vol.16, pp. 1331-1339 (2006).
 J. L. Xu and C. G. Zhao, “Two-Dimensional Numerical Simulations of Shock Waves in Micro Convergent-Divergent Nozzles”, International Journal of Heat and Mass Transfer, Vol. 50, pp. 2434-2438 (2007).
 N. Anantharamaiah, H. Vahedi Tafreshi and B. Pourdeyhimi, “A Simple Expression for Predicting the Inlet Roundness of Micro-Nozzles”, J. Micromech. Microeng., Vol.17, N31-N39 (2007).
 F. C. M. Van De Pol, A Pump Based on Micro-Engineering Techniques, Thesis, University of Twente, Netherlands (1989).
 T. Gerlach, H. Wurmus, “Working Principle and Performance of the Dynamic Micropump”, Sensors and Actuator A, Vol. 50, pp. 135-140 (1995).
 A. Olsson, G. Stemme, E. Stemme, “Diffuser-Element Design Investigation for Valve-less Pumps”, Sensors and Actuator A, Vol. 57, pp. 137-143 (1996).
 A. Olssen, G. Stemme and E. Stemme, “A Numerical Design Study of the Valveless Diffuser Pump using a Lumper-mass Model”, Journal of Micromechanical and Microengineering, Vol. 9, pp. 34-44 (1999).
 A. Olssen, G. Stemme and E. Stemme, “Numerical and Experimental Studies of Flat-walled Diffuser Elements for Valve-less Micropumps”, Sensor and Actuator A, Vol. 84, pp. 165–175 (2000).
 X. N. Jiang, Z. Y. Zhou, Y. Li, Y. Yang, X. Y. Huang, C. Y. Liu, “Micronozzle/diffuser Flow and Its Application in Micro Valveless Pumps”, Sensor and Actuator A, Vol. 70, pp. 81-87 (1998).
 K. S. Yang, I. Y. Chen, B. Y. Shew, C. C. Wang, “Investigation of the Flow Characteristics within a Micronozzle∕diffuser”, Journal of Micromechanical and Microengineering, Vol. 14, pp. 26-31 (2004).
 K. S. Yang, I. Y. Chen and C. C. Wang, “Performance of Nozzle/Diffuser Micro-Pumps Subject to Parallel and Series Combinations”, Chem. Eng. Technol., Vol. 29, No. 6, pp.703-710 (2006).
 V. Singhal, S. V. Garimella and J. Y. Murthy, “Low Reynolds Number Flow through Nozzle-Diffuser Elements in Valveless Micropumps”, Sensors and Actuator A, Vol. 113, pp. 226-235 (2004).
 S. G. Kandlikar, S. Garimella, D. Li, S. Colin and M. R. King, Heat Transfer and Fluid Flow in Minichannels and Microchannels, ELSEVIER (2006).
 R. W. Fox, A. T. McDonald and P. J. Pritchard, Introduction to Fluid Mechanics, John Wiley & Sons, Inc., 6th ed. (2004).
 F. M. White, Fluid Mechanics, McGraw-Hill, New York (1986).
 J. Q. Liu, Y. C. Tai, K. C. Pong and C. M. Ho, “Micro-machined Channel/ Pressure Sensor Systems for Micro Flow Studies”, Transducer’93, pp. 995-997 (1993).
 X. X. Li, W. Y. Lee, M. Wong and Y. Zohar, “Gas Flow in Contriction Microdevices”, Sensors and Acctuators A, Vol. 83, pp. 277-283 (2000).
 F. Durst, A. Melling, and J. H. Whitelaw, “Low Reynolds Number Flow over a Plane Symmetric Sudden Expansions”, Journal of Fluid Mechanics, Vol. 64, pp. 111-128 (1974).
 W. Cherdron, F. Durst, and J. H. Whitelaw, “Asymmetric Flow and Instabilities in Symmetric Ducts with Sudden Expansions”, Journal of Fluid Mechanics, Vol. 84, pp. 13-31 (1978).
 Y. Y. Tsui and C. K. Wang, “Calculation if Laminar Separated Flow in Symmetric Two-dimentional Diffuser”, Journal of Fluid Mechanics, Vol. 117, pp. 612-616 (1995).
 E. Stemme and G. Stemme, “A Valveless Diffuser/Nozzle-based Fluid Pump”, Sensors and Actuators A, Vol. 39, pp. 159-167 (1993).
 A. Olsson, G. Stemme and E. Stemme, “A Vlave-less Planar Fluid Pump with Two Pump Chambers”, Sensors and Actuators A, Vol. 47, pp. 549-556 (1995).
 Y. T. Chen, S. W. Kang, L. C. Wu and S. H. Lee, “Fabrication and Investigation of PDMS Micro-diffuser/nozzle”, Journal of Materials Processing Technology, Vol, 198, pp. 479-484 (2008).