臺灣博碩士論文加值系統

本論文探討在靜止流體中圓柱管噴流之特性, 本實驗雷諾數範圍為層
流到近紊流。實驗分為固定壓力和馬達驅動之兩種噴流實驗。在固定壓力噴
流的實驗中所取雷諾數為Red = 500, 670和835, 在馬達驅動噴流的實驗
中所取雷諾數為Red = 450 1350, 藉由流場可視化及質點影像速度儀
(P.I.V.) 觀察流場結構和速度。
在固定壓力噴流實驗中雷諾數Red = 500和670屬於全層流噴流, 而
雷諾數Red = 835為近紊流。在馬達驅動噴流中雷諾數Red = 450, 600和
750為全層流層流噴流, 雷諾數Red = 1050和1350為近紊流。
固定壓力下之噴流在層流中的速度分布曲線相當接近於理論值, 距離
噴流出口下游1d的速度分布曲線接近於拋物線。雷諾數Red = 500和670
的速度分布曲線在距離噴流出口之無因次數位置xc = 0.018後和Schlichting
的解析結果相符。雷諾數ReD = 835時, 渦流環(vortex ring) 結構產
生, 其明顯地改變流場形成紊流。相較於層流區域, 紊流區域之軸向中心線
速度衰減與噴流之r1/2 (half radius) 皆具有顯著的變化。層流與紊流在橫
截面上也有不同的平均軸向速度分布變化。軸向與徑向上不同的紊流強度
大小顯示流體之非等向性。
馬達驅動噴流的雷諾數範圍較大。在層流區域中, 速度曲線呈現輕微的
傾斜。Red = 450, 600和750時, 速度曲線距離噴流出口1d處接近拋物線模
型(parabolic model)。速度曲線在層流範圍中Red = 750, xc = 0.016開
· i ·
始與Schlichting 模型吻合。Red = 450及600之實驗結果與Schlichting
模型比較後, 噴流流體有較明顯的散布情形。
本研究主要討論由馬達驅動噴流實驗之紊流定量分析。完全紊流之噴
流區域之r1/2分布及速度縮減率與先前的研究相互比較, 紊流區域的軸向速
度與理論高斯分布曲線接近。紊流區域中Red = 1,050和1,350的捲增係數,
, 為0.0655及0.053。

This research studies the characteristics of laminar and semi-turbulent round jet flows in a stationary environment. The experiments are categorized as constant pressure head driven jet flows and pump driven jet flows. The constant pressure head driven jet flows with Reynolds numbers of 500, 670 and 835, and pump driven jet flows with Reynolds numbers ranging from 450 to 1,350, are investigated. Particle tracer flow visualization technique is used to observe the flow patterns qualitatively and flow velocity measurements are performed by Particle Image Velocimetry (PIV).
Flow visualization results show that the constant pressure head driven jet flows with Reynolds numbers as 500 and 670 are fully laminar, and the jet flow becomes semi-turbulent with Reynolds number as 835. The pump driven jet flow
results show that the flows are fully laminar for Reynolds numbers as 450, 600 and 750, and semi-turbulent flows for Reynolds numbers as 1,050 and 1,350.
The velocity profiles of the constant pressure head driven jet flows in the laminar regime fit well to the theoretical models. At a distance of 1d downstream from the pipe exit, the velocity profiles fit close to the parabolic model. The velocity profiles fit reasonably to the Schlichting model starting from a non-dimensional distance, xc = 0.018, and beyond at Reynolds numbers as 500 and 670 in the laminar regime. The vortex rings formation changes the flow characteristics quite significantly. The flow becomes turbulent after the vortex rings formation, when Reynolds number becomes 835. The mean center velocity decays faster and the jet flow half radius increases more dramatically in the axial direction than those in the laminar regime. The cross-sectional distribution of mean axial velocity changes from the laminar distribution to the turbulent distribution. The different magnitudes of cross-sectional turbulence intensities on the axial and radial velocities show the anisotropy of the flows.
The pump driven jet flows have the wider range of Reynolds numbers. In the laminar regime, the velocity profiles show a slight tilt. The velocity profiles are close to the parabolic model at a distance of 1d from the pipe exit for Reynolds numbers as 450, 600 and 750. The velocity profiles fit close to the Schlichting’s model starting from xc = 0.016 and beyond for Reynolds number as 750 in the laminar regime. For Reynolds numbers as 450 and 600, the experimental results show a greater scatter in the outer region of the jet flow, compared with the parabolic and Schlichting’s models.
Most of the quantitative analysis for the turbulent regime in this thesis are done for pump driven jet flows. The half radius spreading rate and velocity decay rate of the turbulent regime are compared with the values presented in previous research on fully turbulent jet flows. The mean axial velocity in the turbulent flow regime becomes self-similar and is well approximated by the Gaussian profile. The entrainment coefficient, α, of the turbulent flow regime at Reynolds number of 1,350 and 1,050 is 0.053 and 0.0655 respectively.

Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introduction 1
1.1 Background and Purpose for this Study . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Schlichting’s Similarity Solution for the Laminar Round Jet Flow . 6
1.4 Flow Regions of a Submerged Laminar Round Jet Flow . . . . . . . 11
1.5 The Turbulent Round Jet Flow . . . . . . . . . . . . . . . . . . . . 13
1.6 The Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 16
2 Experiments 19
2.1 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1 Water Tunnel Facility . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 Jet Flow Facility . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Experimental Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Constant Pressure Head Driven Jet Flows . . . . . . . . . . 22
2.2.2 Pump Driven Jet Flows . . . . . . . . . . . . . . . . . . . . 22
2.3 Optical Measurement Techniques . . . . . . . . . . . . . . . . . . . 23
2.3.1 Particle Tracer Flow Visualization . . . . . . . . . . . . . . . 23
2.3.2 Particle Image Velocimetry (PIV) . . . . . . . . . . . . . . . 24
2.4 Instruments and Components for Optical Measurement . . . . . . . 26
2.4.1 Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Characteristics of Tracer Particles . . . . . . . . . . . . . . . 26
3 Experimental Results on Constant Pressure Head 29
3.1 Particle tracer flow visualization . . . . . . . . . . . . . . . . . . . . 30
3.2 Mean velocity contour and vector plots . . . . . . . . . . . . . . . . 30
3.3 Entrance lengths in pipe flow and jet flow virtual origins for laminar
flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Mean center velocity decay . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 Jet flow half radius growth . . . . . . . . . . . . . . . . . . . . . . . 36
3.7 Turbulence intensity on the axial and radial velocities . . . . . . . . 37
3.8 Volume flow rate growth . . . . . . . . . . . . . . . . . . . . . . . . 38
3.9 Jet flow momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 Experimental Results on Pump Driven 41
4.1 Particle tracer flow visualization . . . . . . . . . . . . . . . . . . . . 41
4.2 Mean velocity contour and vector plots . . . . . . . . . . . . . . . . 42
4.3 Entrance lengths in pipe flow and jet flow virtual origins for laminar
flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5 Mean center velocity decay . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Jet flow half radius growth . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Turbulence intensity on the axial and radial velocities . . . . . . . . 48
4.8 Radial distribution of velocity components . . . . . . . . . . . . . . 48
4.9 Jet flow Gaussian radius in the turbulent region . . . . . . . . . . . 50
4.10 Entrainment coefficient . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.11 Volume flow rate growth . . . . . . . . . . . . . . . . . . . . . . . . 50
4.12 Jet flow momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Conclusions and Suggestions 55
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References 59
Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

References
[1] Andrade, E. N., Tsien, L. C., 1937. The velocity distribution in a liquid-intoliquid
jet. Proc. Phys. Soc. Lond. 29, 381-391.
[2] Abramovich, S., Solan, A., 1973. The initial development of a submerged
laminar round jet. J. Fluid Mech. 59, 791-801.
[3] Rankin, G. W., Sridhar, K., 1981. Developing region of laminar jets with
parabolic exit velocity profiles. ASME 103, 322-327.
[4] Rankin, G. W., 1980. Developing Region of Laminar Jets. Ph.D. thesis, University
of Windsor, Ontario, Canada.
[5] Wygnanski, I., Fielder, H., 1969. Some measurements in the self-preserving
jet. J. Fluid Mech. 38, 577-612.
[6] Papanicolaou, P. N., List, E. J., 1988. Investigations in round vertical turbulent
buoyant jets. J. Fluid Mech. 195, 341-391.
[7] Panchapakesan, N. R., Lumley J. L., 1993. Turbulence measurements in axisymmetric
jets of air and helium. Part 1. Air jet, J. Fluid Mech. 246, 197-223.
[8] McNaughton, K. J., Sinclair, C. G., 1966. Submerged jets in short cylindrical
flow vessels. J. Fluid Mech. 25, 367-375.
[9] Schlichting, H., 1979. Boundary Layer Theory. 7th edition, McGraw-Hill Publishers,
ISBN 0-07-055334-3.
[10] Rankin, G. W., Sridhar, K., Arulraja, M., Kumar, K. R., 1983. An experimental
investigation of laminar axisymmetric submerged jets. J. Fluid Mech.
133, 217-231.
[11] Lee, D. S., Kihm, K. D., Chung, S. H., 1997. Analytical solutions for the
developing jet from a fully developed laminar tube flow. ASME 119, 716-
718.[12] Symons, E. P., Labus, T. L., 1971. Experimental investigation of an axisymmetric
fully developed laminar free jet. NASA TN D-6304.
[13] Kwon, S. J., Seo, W., 2005. Reynolds number effects on the behavior of a
non-buoyant round jet. Exp. Fluids 38, 801-812.
[14] Vouros, A. P., Panadis, T., 2013. Turbulent properties of a low Reynolds
number, axisymmetric, pipe jet. Exp. Thermal and Fluid Sci. 44, 42-50.
[15] Fellouah, H., Ball, C. G., Pollard, A., 2009. Reynolds number effects within
the developing region of a turbulent round free jet. Int. J. of Heat and Mass
Transfer 52, 3943-3954.
[16] Milanovic, M. I, Khaled, J. H., 2010. PIV study of the near-field region
of a turbulent round jet. Proc. of the ASME 2010. 3rd Joint US-European
FEDSM-ICNMM2010-31139, Montreal, Canada.
[17] Zaouali, Y., Ammar, S., Kechiche, N., Jay, J., Aissia, H. B., 2010. Experimental
and quantitative investigation of a free round jet. Eur. Phys. J. Appl.
Phys. 52, 11302-P1 - 11302-P11.
[18] Ball, C. G., Fellough, H., Pollard, A., 2012. The flow field in turbulent round
free jets. Prog. Aero. Sci. 50, 1-26.
[19] Lipari, G., Stansby, K. P., 2011. Review of experimental data on incompressible
turbulent round jets. Flow Turbulence Combust. 87, 79-114.
[20] White, F. M., 2006. Viscous Fluid Flow. 3rd edition, McGraw-Hill, New York,
USA. ISBN 007-124493-X.
[21] Lee, J. H. W, Chu, V. H., 2003. Turbulent Jets and Plumes. Kluwer Academic
Publishers, ISBN 1-4020-7520-0.
[22] Albertson, M. L., Dai, Y. B., Jenson, R. A., Rouse, H., 1950. Diffusion of
submerged jets. Trans. ASCE 115, 639-644.
[23] Adrian, R. J., 2005. Twenty years of particle image velocimetry. Exp. Fluids
39, 159-169.
[24] Tian, J., 2010. Free Surface Confinement Effects on a Round Jet. Master
thesis, University of Windsor, Ontario, Canada.[25] Tsai, B. -C., 2012. An Experimental Study of a Round Tube Jet in a Stationary
Environment and a Cross-flow Environment. Master thesis, NTUST, Taipei,
Taiwan.
[26] Raffel, M., Willert, C., Kompenhans, J., 1998. Particle Image Velocimetry-A
Practical Guide. Springer, Berlin Heldelberg New York. ISBN 3-540-63683-8.
[27] Adrian, R. J., Westerweel, J., 2011. Particle Image Velocimetry. Cambridge
University Press, New York, USA. ISBN 978-0-521-44008-0.
[28] Westerweel, J., 1997. Fundamentals of digital particle image velocimetry.
Meas. Sci. Tech. 8, 1379-1392.
[29] Merzkirch, W., 1974. Flow Visualization. Academic press, New York.
[30] Munson, B. R., Young, D. F., Okiishi, T. H., Huebsch, W. W., 2010. Fundamentals
of Fluid Mechanics. John Wiley and Sons. ISBN 978-0-470-39881-4.
[31] Cengel, Y. A., Cimbala, J. M., 2006. Fluid Mechanics Fundamentals and
Applications. McGraw-Hill, New York.
[32] Sato, H., Sakao, F., 1964. An experimental investigation of the instability of
a two-dimensional jet at low Reynolds numbers. J. Fluid Mech. 20, 337-352.
[33] Sato, H., 1960. The stability and transition of a two-dimensional jet. J. Fluid
Mech. 7, 53-80.
[34] Labus, T. L., Symons, E. P., 1972. Experimental investigation of an axisymmetric
free jet with an initially uniform velocity profile. NASA TN D-6783.
[35] Hussein, H. J., Capp, S. P., George, W. K., 1994. Velocity measurements in a
high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet.
J. Fluid Mech. 258, 31-75.
[36] Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., Brooks, N. H., 1979.
Mixing in Inland and Coastal Waters. Academic Press, San Diego, California.
[37] Ricou, F. P., Spalding, D. B., 1961. Measurements of entrainment by axisymmetrical
turbulent jets. J. Fluid Mech. 11, 21-32.