Fluid transients in complex systems with air entrainment

FLUID TRANSIENTS IN COMPLEX SYSTEMS WITH AIR ENTRAINMENT NGUYEN DINH TAM (B.Eng., HCMUT) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2009 ACKNOWLEDGEMENTS I am enormously grateful to my supervisors at National University of Singapore: Associate Professor Lee Thong See, and Associate Professor Low Hong Tong, for their personal support and encouragement as well their guidance in this study. Their advice and support played an important role in the success of this thesis. I wish to thank my former supervisors at Ho Chi Minh City University of Technology: Associate Professor Nguyen Thien Tong, and Associate Professor Le Thi Minh Nghia, for their encouragement. I wish to especially acknowledge Miss Koh Jie Ying, and Mr. Neo Wei Rong, Avan for their cooperation in the experiment study. I am very grateful acknowledges the financial support of the National University of Singapore. I would like to thank the Fluid mechanics group members and graduate students for their invaluable assistance and friendship during this study. I especially thank my flat-mates Nguyen Khang, The Cuong and Khoi Khoa for helping me overcome difficulties in my daily life during my PhD study. Gratitude is also extended to Associate Professor Loh Wai Lam for his help, and support. I wish to dedicate this thesis to my lovely wife Lien Minh and my son Huu Loc. I would also like to dedicate this work to my family, especially my mum and dad. I will always be thankful to them for their huge support, encouragement and love. i CONTENTS ACKNOWLEDGEMENTS .i CONTENTS .ii SUMMARY v LIST OF TABLES .vii LIST OF FIGURES .vii LIST OF SYMBOLS .ix LIST OF ABBREVIATIONS . xii CHAPTER INTRODUCTION 1.1. BACKGROUND 1.2. SCOPE AND OBJECTIVES .11 1.3. ORGANISATION OF THESIS .12 CHAPTER LITERATURE REVIEW 13 2.1. INTRODUCTION 13 2.2. WATER HAMMER THEORY AND PRACTICE .13 2.2.1. Numerical solutions for 1-D water hammer equations 17 2.2.2. Quasi-two-dimensional water hammer simulation 20 2.2.3. Practical and research needs in water hammer 22 2.3. FLUID TRANSIENT WITH AIR ENTRAINMENT .25 2.4. FLUID TRANSIENT WITH VAPOROUS CAVITATION AND COLUMN SEPARATION 31 2.4.1. Single vapor cavity numerical models .32 2.4.2. Discrete multiple cavity models .33 ii 2.4.3. Shallow water flow or separated flow models .37 2.4.4. Two phase or distributed vaporous cavitation models .38 2.4.5. Combined models / interface models .41 2.4.6. A comparison of models 42 2.4.7. State of the art - the recommended models 43 2.4.8. Fluid structure interaction (FSI) .46 2.5. SUMMARY .47 CHAPTER FLUID TRANSIENT ANALYSIS METHOD . 50 3.1. INTRODUCTION 50 3.2. GOVERNING EQUATIONS FOR TRANSIENT FLOW 50 3.3. VARIABLE WAVE SPEED MODEL 51 3.4. FRICTION FACTOR CALCULATION .57 3.5. NUMERICAL METHOD 60 3.6. BOUNDARY CONDITIONS .64 3.7. COMPUTATION OF PUMP RUN-DOWN CHARACTERISTICS .66 CHAPTER VALIDATION OF THE NUMERICAL MODEL . 71 4.1. INTRODUCTION 71 4.2. COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL RESULT 71 4.2.1. Test rig and instrumentation .71 4.2.2. Results and discussion .73 4.3. COMPARISON BETWEEN THE RESULTS FROM VARIABLE WAVE SPEED MODEL AND PUBLISHED RESULTS 77 4.4. SUMMARY .80 CHAPTER NUMERICAL MODELLING AND COMPUTATION OF FLUID TRANSIENT IN COMPEX SYSTEM WITH AIR ENTRAINMENT 82 5.1. INTRODUCTION 82 iii 5.2. GRID INDEPENDENCE TEST 83 5.3. WATER HAMMER WITH AIR ENTRAINMENT 87 5.4. FLUID TRANSIENT WITH GASEOUS CAVITATION 94 5.5. SUMMARY .101 CHAPTER EXPERIMENTAL STUDY OF CHECK VALVE PERPORMANCES IN FLUID TRANSIENT WITH AIR ENTRAINMENT 103 6.1. INTRODUCTION 103 6.2. TEST RIG, INSTRUMENTATION AND TEST METHOD .105 6.3. RESULTS AND DISCUSSION 110 6.3.1. Pressure surge analysis 110 6.3.2. Dynamic characteristics .117 6.3.3. Dimensionless dynamic characteristics .120 6.4. SUMMARY .118 CHAPTER CONCLUSIONS AND RECOMMENDATIONS . 124 7.1. CONCLUSIONS .124 7.2. RECOMMENDATIONS FOR FUTURE WORK .125 REFERENCES .128 PUBLICATIONS .145 APPENDICES 146 Appendix A: Experimental setup specifications 146 Appendix B: Chaudhry et al. (1990) experimental setup specifications. 147 Appendix C: Technical data for the simulation of pumping systems 148 iv SUMMARY Fluid transient analysis is commonly based on the assumption of no air in the liquid. In fact, air entrainment, trapped air pockets, free gas, and dissolved gases frequently present in the pipeline. The effects of entrapped or entrained air on pressure transient in pipeline systems can be either beneficial or detrimental; the outcome highly depends on the characteristics of the pipeline concerned and the nature and cause of the transient. This thesis presents a variable wave speed model which can improve the computational and modeling of fluid transients in pipelines with air entrainment. By using the variable wave speed model, wave speed is calculated depending on the local pressure and the local air void fraction at any local point along the pipeline. Therefore, wave speed was no longer constant as in the constant wave speed model, it varied along the pipeline and varied in time. Free gas in fluid and released/absorbed gas from gaseous cavitation is modeled. The variable wave speed model is validated by comparison the numerical results with experimental results and published results. The variable wave speed model was then applied to investigate the fluid transient with air entrainment in the pumping system. The numerical results showed that entrained, entrapped or released gases amplified the first pressure peak, increased surge damping and produced asymmetric pressure surges with respect to the static head. These results are consistent with the experimental and field data observed by other investigators. The findings show that even with a very small amount of air entrainment in the liquid; the pressure transients are considerably different from the case of pure liquid. v Hence the inclusion of the effects of air entrainment can improve the accuracy of fluid transient analysis. In addition, we also study the mechanisms of the effects of air entrainment on the pressure transient. To explain the increase in peak pressure, the study suggested that the higher pressure peak is caused by the lapping of the effects of two factors: the delay wave reflection at reservoir and the change of wave speed. We also study experimentally the check valve performances in fluid transients with air entrainment. The experimental study presents the comparison of the dynamic behaviour of difference types of check valve under pressure transient condition, and three useful methods to evaluate the pressure transient characteristics of check valves. In this thesis, the investigation of pressure transient was restricted to the complex system without the installation of pressure surge protection devices such as air vessels, air valves, surge tanks etc. In practical systems, these devices are used to protect the system under excessive pressure transient conditions. The ability of these hydraulic components in pressure surge suppressions should be affected by air entrainment. The variable wave speed model can be applied to carry out these further investigations. Keywords: Pressure transient, Air entrainment, Variable wave speed, Check valve vi LIST OF TABLES Table. 5.1. Grid independence test result .86 LIST OF FIGURES Fig. 3.1. Angle between horizontal direction and fluid velocity direction 51 Fig. 3.2. Computational grid .62 Fig. 3.3. Schematic diagram of typical pumping system 64 Fig. 3.4. Boundary condition at pump .65 Fig. 3.5. Boundary condition at reservoir .66 Fig. 4.1. Hydraulic schematic of the pumping system 73 Fig. 4.2. Transient pressure measured from the experiment at check valve 74 Fig. 4.3. Transient pressures predicted from present method at check valve 74 Fig. 4.4. Effects of air content on maximum and minimum pressure head 75 Fig. 4.5. Comparison between experimental resutls and numerical results .77 Fig. 4.6. Schematic of experiment by Chaudhry et al. (1990) 78 Fig. 4.7. Comparison of computed and experimental results at Station .79 Fig. 4.8. Comparison of computed and experimental results at Station .79 Fig. 5.1. Pumping station pipeline profile 84 Fig. 5.2. Pressure transient at check valve using different grid resolution .84 Fig. 5.3. The change of pressure value with grid resolution 85 Fig. 5.4. Pipeline contour for pumping station 86 Fig. 5.5. Pressure head downstream of pump 88 Fig. 5.6. Max. and min. pressure head along pipeline .89 Fig. 5.7. Wave speed with different initial air void fractions .90 Fig. 5.8. Air void fraction at check valve .91 Fig. 5.9. Pressure head with different initial air void fractions 91 Fig. 5.10. Max. and min. pressure head along pipeline .92 Fig. 5.11. Effects of air content on max. and min. transient pressure head .93 vii Fig. 5.12. Pressure head downstream of pump .97 Fig. 5.13. Pressure head with different initial air void fraction .97 Fig. 5.14. Pressure head of first pressure peak with initial air void fraction .98 Fig. 5.15. Variation of air void fraction with initial value ε0 = 0.001 98 Fig. 5.16. Variation of wave speed with initial air void fraction ε0 = 0.001 99 Fig. 5.17. Pressure transient without the effects of gas release (ε0 = 0.001) .100 Fig. 5.18. Pressure transient with the effects of gas release (ε0 = 0.001) .100 Fig. 5.19. Maximum and minimum pressure head long pipeline 101 Fig. 6.1. Hydraulic schematic of the pumping system .106 Fig. 6.2. Experimental sequence flowchart .107 Fig. 6.3. Check valves used in the test and test section 108 Fig. 6.4. Pressure transient in horizontal orientation of ball check valve 110 Fig. 6.5. Pressure transient in horizontal orientation of swing check valve 111 Fig. 6.6. Pressure transient in horizontal orientation of piston check valve 111 Fig. 6.7. Pressure transient in horizontal orientation of nozzle check valve112 Fig. 6.8. Pressure transient in horizontal orientation of double flap check valve 112 Fig. 6.9. Pressure transient in vertical orientation of ball check valve 113 Fig. 6.10. Pressure transient in vertical orientation of swing check valve .113 Fig. 6.11. Pressure transient in vertical orientation of piston check valve .114 Fig. 6.12. Pressure transient in vertical orientation of nozzle check valve 114 Fig. 6.13. Pressure transient in vertical orientation of double flap check valve .115 Fig. 6.14. Dynamic characteristics chart in horizontal orientation .117 Fig. 6.15. Dynamic characteristics chart in vertical orientation .118 Fig. 6.16. Dimensionless dynamic characteristics in horizontal orientation 120 Fig. 6.17. Dimensionless dynamic characteristics in vertical orientation .121 viii LIST OF SYMBOLS a wave speed A cross-sectional area of pipe A1, A2, A3 constants for pump H-Q curve B1, B2, B3 constants for pump T-Q curve cl parameter describing pipe constraint C1, C2, C3 constants for pump η-Q curve D Inner diameter of pipe E modulus of elasticity e local pipe wall thickness ƒ friction factor ƒl local equivalent loss factor g gravitational acceleration H gauge piezometric pressure head i node along the pipeline I pump set moment of inertia k time level K bulk modulus of elasticity Kloss total local loss factor Km local loss factor due to pipe features Kf local loss factor due to nature of flow Ka, Kr time delay factors L pipeline length n the polytropic index np number of pumps operating in parallel N total number of node points Nik pump speed in rpm Np number of transient periods P pressure inside the pipe ix Fanelli, M. (2000). 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(1968). Frequency-Dependent Friction in Transient Pipe Flow, ASME J. Basic Eng. 90(1), pp. 109–115. Zielke, W., Perko, H.-D., Keller, A. (1989). Gas release in transient pipe flow. Proceedings of the 6th International Conference on Pressure Surges, BHRA, Cambridge, UK, 3-13. 144 PUBLICATIONS 1. Lee, T. S., Low, H. T., and Nguyen, D. T. (2006). Effects of air entrainment on fluid transients in pumping systems. Proceedings of the Eleventh Asian Congress of Fluid Mechanics， Kuala Lumpur, Malaysia 22nd-25th May 2006 2. Lee, T. S., Low, H. T., and Nguyen, D. T. (2007). Effects of air entrainment on fluid transients in pumping systems. Journal of Applied Fluid Mechanics, Vol. 1, No. 1, pp55-61. 3. Lee, T. S., Nguyen, D. T., Low, H. T., and Koh, J. Y., (2008). Investigation of fluid transients in pipelines with air entrainment. Advanced and Applications in Fluid Mechanics, Vol. 4, Issue 2, pp. 117-133. 4. Lee, T. S., Low, H. T., Nguyen, D. T., and Neo, W. R. A., (2008). Experimental Study of Check Valves in Pumping System with Air Entrainment. International Journal of Fluid Machinery and Systems. Vol. 1, No. 1, pp. 140-147. 5. Lee, T. S., Low, H. T., and Nguyen, D. T., (2008). The Effects of air entrainment on the pressure damping in pipeline transient flows. Proceedings of the 12th Asian Congress of Fluid Mechanics， Daejeon, Korea 18-21 August 2008. 6. Lee, T. S., Low, H. T., Nguyen, D. T., and Neo, W. R. A., (2009). Experimental study of check valves performances in fluid transient. Proc. IMechE., Journal of Process Mechanical Engineering. Vol. 223, No. 2, pp. 61-69. 145 APPENDICES Appendix A: Experimental setup specifications Pipe Length 15.75 m Pipe Material Perspex, PVC Modulus Elasticity of Pipe, E 2.835 GN/m3 Poisson’s Ratio 0.38 Pipe External Diameter, De 89 mm Pipe Internal Diameter, Di 77 mm Pipe-wall Thickness, e mm Pump Specifications Speed, N 1450 rpm Total Head, H 5.12 m Capacity, Q 60 m3/h Motor HP 146 Appendix B: Chaudhry et at. (1990) experimental setup specifications Pipe Length, L 30.6 m Constant wave speed 715 m/s Constant upstream reservoir pressure 18.46 m Steady flow velocity 2.42 m/s Steady air mass flow rate 4.1 x 10-6 kg/s Pipe Diameter 0.026 m Downstream void ratio 0.0023 Steady flow friction factor 0.0205 147 Appendix C: Technical data for the simulation of pumping systems Pipeline longitudinal profile As given in Fig. 5.1 Sump Level 92.8 m As given in Fig. 5.4 92.8 m Delivery Exit Level 112.5 m 112.5 m Distance from pumping station to delivery exit Pipe Material 4725 m 1550 m Steel Steel Modulus Elasticity of Pipe, E 205 x 109 N/m2 205 x 109 N/m2 Poisson’s Ratio 0.28 0.28 Estimated Factor of Friction f 0.0088 0.0088 Pipe External Diameter 1.05 m 1.05 m Pipe Internal Diameter 0.985 m 0.985 m Wall Thickness (mm) 20 mm 20 mm Pump Nos. Speed, N 730 RPM 730 RPM Moment of Inertial of Pumpset 33.30 kg.m2 33.30 kg.m2 Diameter of Impeller (mm) 655 mm 655 mm Pump Specifications 148 [...]... presented in the flow The pressure transient damping with air entrainment is faster than the damping with no air entrainment Computational and modeling of fluid transient with air entrainment has been carried out by many researchers together with practical experiments and field measurements Most fluid transient studies based on single fluid models use the method of characteristics to solve the resulting finite... very challenging In this thesis, we focus on study fluid transient in complex systems with air entrainment and released gas The objectives of this study are: i To develop a variable wave speed model for analyzing the fluid transient in complex systems with air entrainment The proposed model includes the effects of free gas in the liquid and released gas on the pressure transient in the pipeline This model... the model In Chapter 5, analysis of fluid transient in typical pumping systems with air entrainment is presented In Chapter 6, experiment study of the check valve performances in fluid transient with air entrainment is provided Finally, in Chapter 7, some conclusions from this study, together with some suggestions for future works are drawn 12 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION Fluid transient... of fluid transients with and without air entrainment In general, the first pressure peak with entrained air is found to be higher than that predicted by models with no air The pressure periods are longer when air entrainment is considered The pressure surges are asymmetric with respect to the static head, while the pressure surges are symmetric with respect to the static head for 8 models with no air. .. towards the operating pump Air may also be admitted through packing, valves, air vessel, etc under vacuum conditions In short, air always presents in a pressurized pipeline The pockets of air accumulating at a high point can result in a line restriction which increases head loss, extends pumping cycles and increases energy consumption As the air pockets grow, the fluid velocity will be 7 increased and... 1.1 BACKGROUND During the operations of complex fluid systems, such as pumping installation, oil-gas pipeline system, and nuclear power plant, unsteady and transient flow conditions will be inevitably encountered Pressure transients in pipeline systems are caused by fluid flow interruption from operational changes such as starting/stopping of pumps, changes to valve setting, changes in power demand,... the present study is outlined In Chapter 3, a variable wave speed model for computational and modelling fluid transient in complex systems with air entrainment and released gas is introduced The numerical scheme adopted for the developing variable wave speed model is also presented in this chapter In Chapter 4, numerical result from the variable wave speed model is compared with experimental and published... leading to permanent deformation or rupture of the pipeline and components; damage to joints, seals and anchor blocks; leakage out of the pipeline, causing wastage, environment contamination and fire hazard • Pressures too low – may cause collapse of the pipeline; leakage into the line at joints and seals under sub-atmospheric conditions; contamination of the fluid being pumped; fire hazard with some fluids... numerically by using the method of characteristics ii To validate the proposed variable wave speed model by experimental and published results 11 iii To evaluation of the effects of free entrained air and released gas in the fluid transient in typical pumping systems due to pump trip using the variable wave speed model iv To study check valve performances in fluid transient with air entrainment by experiments... start-up, pipeline is full of air As the line fills, much of this air will be removed through hydrants, faucets, etc However, a large amount of air will still be trapped at high points since air is lighter than water This air will continuously be added due to the progressive upward migration of pockets of air as the system operation continues The second source of air is free gas, dissolved gases in the flow . MODELLING AND COMPUTATION OF FLUID TRANSIENT IN COMPEX SYSTEM WITH AIR ENTRAINMENT 82 5.1. INTRODUCTION 82 iv 5.2. GRID INDEPENDENCE TEST 83 5.3. WATER HAMMER WITH AIR ENTRAINMENT 87 5.4. FLUID. of the pipeline; leakage into the line at joints and seals under sub-atmospheric conditions; contamination of the fluid being pumped; fire hazard with some fluids if air is sucked in. • Reverse. simulation of pumping systems 148 v SUMMARY Fluid transient analysis is commonly based on the assumption of no air in the liquid. In fact, air entrainment, trapped air pockets, free