Mathematical Models of Throttle Elements of Gas-hydrodynamic Measuring Transducers

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dc.citation.epage107
dc.citation.issue2
dc.citation.spage94
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorПістун, Євген
dc.contributor.authorМатіко, Галина
dc.contributor.authorКрих, Ганна
dc.contributor.authorPistun, Yevhen
dc.contributor.authorMatiko, Halyna
dc.contributor.authorKrykh, Hanna
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2020-02-18T11:53:10Z
dc.date.available2020-02-18T11:53:10Z
dc.date.created2019-02-26
dc.date.issued2019-02-26
dc.description.abstractУ статті наведено витратні характеристики дросельних елементів, які застосовують у вимірювальних схемах перетворювачів параметрів плинних середовищ. Огляд охоплює широке коло досліджень характеристик нестискуваних та стискуваних, ньютонівських та неньютонівських середовищ в умовах ламінарного, перехідного та турбулентного режиму руху в каналах різного поперечного перерізу. Розглянуто рівняння, що застосовуються для макроскопічних потоків. Наведено теоретичні рівняння для розрахунку перепаду тиску під час руху середовищ у мікроканалах та зазначено умови та діапазон їхнього застосування. Розглянуто експериментальні результати дослідження коефіцієнтів тертя для стискуваних і нестискуваних середовищ в мікроканалах різних розмірів та форми, з гладкими і шорсткими поверхнями. Отримані результати можна застосовувати для комп’ютерного дослідження статичних і метрологічних характеристик газогідродинамічних вимірювальних перетворювачів конкретних фізико-механічних параметрів.
dc.description.abstractThis is a review article and it presents the flowrate characteristics of throttle elements used for measuring diagrams of transducers of fluids parameters. The review includes a wide range of research on the characteristics of incompressible and compressible fluids, Newtonian and Non-Newtonian fluids at the conditions of laminar, transient and turbulent flow through the channels of different cross-sections. The article considers equations for macroscopic flows. The theoretical equations for calculating the pressure drop for fluid flow in microchannels are presented. The conditions and the range of their application are presented for these equations. The results of experimental research of friction factor for compressible and incompressible fluids in microchannels of various sizes and shapes with smooth and rough surfaces are considered. The obtained results can be used for computer research of static and metrological characteristics of gas-hydrodynamic measuring transducers of specific physical and mechanical parameters of fluids.
dc.format.extent94-107
dc.format.pages14
dc.identifier.citationPistun Y. Mathematical Models of Throttle Elements of Gas-hydrodynamic Measuring Transducers / Yevhen Pistun, Halyna Matiko, Hanna Krykh // Energy Engineering and Control Systems. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 5. — No 2. — P. 94–107.
dc.identifier.citationenPistun Y. Mathematical Models of Throttle Elements of Gas-hydrodynamic Measuring Transducers / Yevhen Pistun, Halyna Matiko, Hanna Krykh // Energy Engineering and Control Systems. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 5. — No 2. — P. 94–107.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/45667
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofEnergy Engineering and Control Systems, 2 (5), 2019
dc.relation.references1. Profos, P., Pfeifer, T. (1994) Handbuch der Industriellen Meßtechnik. Wissenschaftsverlag, Oldenbourg.
dc.relation.references2. Webster, J., Eren, H. (2014) Measurement, Instrumentation, and Sensors Handbook: Spatial, Mechanical, Thermal, and Radiation Measurement, Second Edition, CRC Press Reference.
dc.relation.references3. Pistun, Ye. (1985) Theoretical Foundations for Constructing and Calculating Gas-Hydrodynamic Throttle Measuring Transducers. Abstracts of the XV All-Union Conference “Pnevmoavtomatika”, P.1, Lvov, 104–105. (in Russian)
dc.relation.references4. Pistun, Ye., Leskiv, H. (2002) Gas-hydrodynamic Measuring Transducers Built on Complex Throttle Elements. Proc. of Lviv Polytechnic National University: Heat Power Engineering. Environmental Engineering. Automation, 460, 81–88. (in Ukrainian)
dc.relation.references5. Pistun, Ye., Krykh, H., Leskiv, H. (2003) Modeling of Gas-hydrodynamic Measuring Transducers Built on Bridge Throttle Schemes with Constant Flowrate. Scientific and technical journal “Methods and instruments of quality control”, 10, 87–89. (in Ukrainian)
dc.relation.references6. Pistun, Ye., Matiko, H., Krykh, H., Matiko, F. (2018) Structural Modeling of Throttle Diagrams for Measuring Fluid Parameters. Metrology аnd Measurement Systems. 25(4), 659–673. DOI: 10.24425/mms.2018.124884
dc.relation.references7. Pistun E. P., Stasiuk I. D., Tepliukh Z. M. (1985) Investigation of Flowrate Curves of Capillary Elements of Measurement Instruments // Control and Measurement Instrumentation. 38, 44–46. (in Russian)
dc.relation.references8. Pistun, Ye., Matiko, H., Krykh, H. (2016) Modelling of Measuring Transducers Schemes Using Set Theory. Metrology and instruments, 3, 53–61. (in Ukrainian)
dc.relation.references9. Pistun, Ye., Matiko, H., Krykh, H., Matiko, F. (2017) Synthesizing the Schemes of Multifunctional Measuring Transducers of the Fluid Parameters. Eastern-European Journal of Enterprise Technologies, 6, 5(90), 13–22. https://doi.org/10.15587/1729-4061.2017.114110
dc.relation.references10. Poling, B., Prausnitz, J., O' Connell, J. (2000) The Properties of Gases and Liquids. McGraw-Hill Education.
dc.relation.references11. Zalmanzon, L. (1973) Aero-Hydrodynamic Methods for Measuring the Input Parameters of Automatic Systems. Science, Moscow. (in Russian)
dc.relation.references12. Ibragimov, I., Farzane, N., Ilyasov, L. (1985) Elements and Systems of Pneumatic Automation. Higher school, Moscow. (in Russian)
dc.relation.references13. Nagornyi, V. (2014) Means of Automation of Hydraulic and Pneumatic Systems. Tutorial. Publishing house “Lan”. (in Russian)
dc.relation.references14. Kremlevskyi, P. (2002) Flowmeters and Meters of Substances. Publishing House “Polytechnic”. (in Russian)
dc.relation.references15. Kabza, Z. (1981) Mathematical Modeling of Flowmeters with Constricting Devices. Mechanical Engineering, Leningrad. (in Russian)
dc.relation.references16. ISO 5167-1:2003. Measurement of Fluid Flow by Means of Pressure Differential Devices Inserted in Circular Cross-Section Conduits Running Full – Part 1: General Principles and Requirements.
dc.relation.references17. Pistun, Ye., Lesovoi, L. (2006) Standardization of Pressure Differential Flowmeters. CJSC “Institute of Energy Audit and Energy Resources”, Lviv. (in Ukrainian)
dc.relation.references18. Pistun, Ye., Tepliukh, Z., Stasiuk, I. (1986) Flow Characteristics of Gas-Dynamic Throttle Elements. In Book: Pneumatic and Hydraulic Devices and Control Systems. X International Conference “Jablonna”, Energoatomizdat, 31–34. (in Russian)
dc.relation.references19. Stasiuk, I. (2015) Gas Dynamical Capillary Flowmeters of Small and Micro Flowrates of Gases, Energy Engineering and Control Systems, 1 (2), 117–126
dc.relation.references20. Tepliukh, Z., Pistun, Ye. (1978) Using Various Functional Dependencies to Describe Flow Characteristics of Turbulent Throttles, Measurement Techniques, 2, 231–234. (Translated from Izmeritel'naya Tekhnika, No. 2, pp. 48–50 by Plenum Publishing Corporation, February, 1977.)
dc.relation.references21. Gornstein, B. (1979) Determining of Gas Flow Through a Capillary, Metrology, 1, 66–74. (in Russian)
dc.relation.references22. Walicka, A. (2018) Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Capillary Fissures and Tubes. Int. J. of Applied Mechanics and Engineering, 23 (1), 187–211. https://doi.org/10.1515/ijame-2018-0011
dc.relation.references23. Steffе, J. (1996) Rheological Methods in Food Process Engineering, USA, Freeman Press.
dc.relation.references24. Krykh, H. (2008) Mathematical Models of Throttle Elements of Hydrodynamic Measuring Transducers of Non-Newtonian Liquid Parameters. Proc. of Lviv Polytechnic National University: Heat Power Engineering. Environmental Engineering. Automation, 617, 122–129. (in Ukrainian)
dc.relation.references25. Venerus, D. (2006) Laminar Capillary Flow of Compressible Viscous Fluids. Journal Fluid Mechanics, 555, 59–80. https://doi.org/10.1017/S0022112006008755
dc.relation.references26. Malkin, A., Isayev, A. (2017) Rheology: Concepts, Methods and Applications. Chemical Technology Publishing House.
dc.relation.references27. Drevetskyi, V. (2012) Mathematical Models of Throttle Transducers for Hydrodynamic Measuring Devices of Viscosity and Density of Liquids. Methods and Instruments of Quality Control, 29, 38–46. (in Ukrainian)
dc.relation.references28. Karniadakis, G., Beskok, A., Aluru, N. (2002) Microflows. Fundamentals and Simulation.
dc.relation.references29. Sharp, K., Adrian, R., Santiago, J., Molho, J. (2005) MEMS: Background and Fundamentals. Chapter 10: Liquid Flows in Microchannels, 10-1–10-45.
dc.relation.references30. Cao, B., Chen, G., Li, Y., Yuan, Q. (2006) Numerical Analysis of Isothermal Gaseous Flows in Microchannel. Chemical Engineering Technology, 29 (1), 66–71. https://doi.org/10.1002/ceat.200407079
dc.relation.references31. Hetsroni, G., Mosyak, A., Pogrebnyak, E., Yarin, L. (2005) Fluid Flow in Micro-Channels International. Journal of Heat and Mass Transfer, 48, 1982–1998. DOI: 10.1016/j.ijheatmasstransfer.2004.12.019
dc.relation.references32. Guangwen, Y., Yuan , Ch. (2014) Effect of Viscosity on the Hydrodynamics of Liquid Processes in Microchannels. Chemical Engineering Technology, 37 (3), 427–434. https://doi.org/10.1002/ceat.201300468
dc.relation.references33. Bucci, A., Celata, G., Cumo, M., Serra, E., Zummo, G. (2003) Water Single-Phase Fluid Flow and Heat Transfer in Capillary Tubes. Conference ASME 2003, 1st International Conference on Microchannels and Minichannels, 319–326. doi:10.1115/ICMM2003-1037
dc.relation.references34. Kim, M., Araki T., Inaoka, K., Suzuki, K. (2000) Gas Flow Characteristics in Microtubes. JSME International Journal Series B, 43 (4),634–639. https://doi.org/10.1299/jsmeb.43.634
dc.relation.references35. Tang, G., Li, Zh., He, Y., Tao, W. (2007) Experimental Study of Compressibility, Roughness and Rarefaction Influences on Microchannel Flow. International Journal of Heat and Mass Transfer, 50, 2282–2295. DOI: 10.1016/j.ijheatmasstransfer.2006.10.034
dc.relation.references36. Taliadoroua, E., Georgioua, G., Moulitsas, I. (2009) Weakly Compressible Poiseuille Flows of a Herschel–Bulkley Fluid. Journal NonNewtonian Fluid Mechanics, 158, 162–169. DOI: 10.1016/j.jnnfm.2008.11.010
dc.relation.references37. Liu, D., Garimella, S. (2004) Investigation of Liquid Flow in Microchannels. AIAA Journal of Thermophysics and Heat Transfer. 18 (1), 65–72. https://doi.org/10.2514/1.9124
dc.relation.references38. Obot, N. (2000) Toward a Better Understanding of Friction and Heat/Mass Transfer in Microchannels – A Literature Review. United Engineering Foundation Conference, Heat Transfer and Transport Phenomena in Microsystems, Oct. 15-20, 2000, Banff, Alberta, 1–8.
dc.relation.references39. Harley, J., Huang, Y., Bau, H., Zemel, J. (1994) Gas Flow in Micro-Channels. Journal of Fluid Mechanics, 284, 257–274. http://dx.doi.org/10.1017/S0022112095000358
dc.relation.references40. Cai, Ch., Sun, Q., Boyd, I. (2007) Gas Flows in Microchannels and Microtubes. Fluid Mechanics, 589, 305–314. https://doi.org/10.1017/S0022112007008178
dc.relation.references41. Taliadoroua, E., Neophytou, M., Georgiou, G. (2009) Perturbation Solutions of Poiseuille Flows of Weakly Compressible Newtonian Liquids, Journal of Non-Newtonian Fluid Mechanics, 163, 1-3, 25–34. https://doi.org/10.1016/j.jnnfm.2009.06.003
dc.relation.references42. Teng, J., Chu, J., Yu, X., Dang, Th., Lee, M. et al. Fluid Dynamics, Computational Modeling and Applications. Chapter – Fluid Dynamics in Microchannels, 403–436.
dc.relation.references43. Zhang, X., Zhu, W., Cai, Q., Shi, Y. Wu, X. Jin, T. Yang, L., Song, H. (2018) Compressible Liquid Flow in Nano– or Micro-Sized Circular Tubes Considering Wall–Liquid Lifshitz–Van Der Waals Interaction. Physics of Fluids, 30, 062002. https://doi.org/10.1063/1.5023291
dc.relation.references44. Bahrami, M., Yovanovich, M. and Culham, J. (2005) Pressure Drop of Fully Developed, Laminar Flow in Rough Microtubes. Journal of Fluids Engineering, 128 (3), 632–637. doi:10.1115/1.2175171
dc.relation.references45. Silva, G., Leal, N. Semião, V. (2008) Effect of Wall Roughness on Fluid Flow Inside a Microchannel. 14th Int Symp on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 07–10 July, 2008, 1–12.
dc.relation.references46. Celata, G., Cumo, M., McPhail, S., Tesfagabir, L., Zummo, G. (2007) Experimental Study on Compressible Flow in Microtubes. International Journal of Heat and Fluid Flow, 28, 28–36. https://doi.org/10.1016/j.ijheatfluidflow.2006.04.009
dc.relation.references47. Mortensen, N., Okkels, F., Bruus, H. (2005) Reexamination of Hagen–Poiseuille flow: Shape Dependence of the Hydraulic Resistance in Microchannels. Physical Review, E. Statistical Nonlinear and Soft Matter Physics, 71(5), 057301, 1–5. doi:10.1103/PhysRevE.71.057301
dc.relation.references48. Bulhakov, B., Kubrak, A. (1977) Pneumatic Automation, Tehnika, Kyjiv. (in Russian)
dc.relation.references49. RD 50-411-83. (1984) Methodical Instructions. Flowrate of Liquids and Gases. Technique for Measuring Using Special Constricting Devices. Publishing House of Standards, Moscow. (in Russian)
dc.relation.references50. Pistun, Ye., Teplykh, Z., Stasyuk, I. (1984) Watch Jewels in Gas Microflow Measurement, Measurement Techniques, 11, 929–931 (Translated from Izmeritel'naya Tekhniya, No. 11, pp. 36–38 by Plenum Publishing Corporation, November, 1983).
dc.relation.referencesen1. Profos, P., Pfeifer, T. (1994) Handbuch der Industriellen Meßtechnik. Wissenschaftsverlag, Oldenbourg.
dc.relation.referencesen2. Webster, J., Eren, H. (2014) Measurement, Instrumentation, and Sensors Handbook: Spatial, Mechanical, Thermal, and Radiation Measurement, Second Edition, CRC Press Reference.
dc.relation.referencesen3. Pistun, Ye. (1985) Theoretical Foundations for Constructing and Calculating Gas-Hydrodynamic Throttle Measuring Transducers. Abstracts of the XV All-Union Conference "Pnevmoavtomatika", P.1, Lvov, 104–105. (in Russian)
dc.relation.referencesen4. Pistun, Ye., Leskiv, H. (2002) Gas-hydrodynamic Measuring Transducers Built on Complex Throttle Elements. Proc. of Lviv Polytechnic National University: Heat Power Engineering. Environmental Engineering. Automation, 460, 81–88. (in Ukrainian)
dc.relation.referencesen5. Pistun, Ye., Krykh, H., Leskiv, H. (2003) Modeling of Gas-hydrodynamic Measuring Transducers Built on Bridge Throttle Schemes with Constant Flowrate. Scientific and technical journal "Methods and instruments of quality control", 10, 87–89. (in Ukrainian)
dc.relation.referencesen6. Pistun, Ye., Matiko, H., Krykh, H., Matiko, F. (2018) Structural Modeling of Throttle Diagrams for Measuring Fluid Parameters. Metrology and Measurement Systems. 25(4), 659–673. DOI: 10.24425/mms.2018.124884
dc.relation.referencesen7. Pistun E. P., Stasiuk I. D., Tepliukh Z. M. (1985) Investigation of Flowrate Curves of Capillary Elements of Measurement Instruments, Control and Measurement Instrumentation. 38, 44–46. (in Russian)
dc.relation.referencesen8. Pistun, Ye., Matiko, H., Krykh, H. (2016) Modelling of Measuring Transducers Schemes Using Set Theory. Metrology and instruments, 3, 53–61. (in Ukrainian)
dc.relation.referencesen9. Pistun, Ye., Matiko, H., Krykh, H., Matiko, F. (2017) Synthesizing the Schemes of Multifunctional Measuring Transducers of the Fluid Parameters. Eastern-European Journal of Enterprise Technologies, 6, 5(90), 13–22. https://doi.org/10.15587/1729-4061.2017.114110
dc.relation.referencesen10. Poling, B., Prausnitz, J., O' Connell, J. (2000) The Properties of Gases and Liquids. McGraw-Hill Education.
dc.relation.referencesen11. Zalmanzon, L. (1973) Aero-Hydrodynamic Methods for Measuring the Input Parameters of Automatic Systems. Science, Moscow. (in Russian)
dc.relation.referencesen12. Ibragimov, I., Farzane, N., Ilyasov, L. (1985) Elements and Systems of Pneumatic Automation. Higher school, Moscow. (in Russian)
dc.relation.referencesen13. Nagornyi, V. (2014) Means of Automation of Hydraulic and Pneumatic Systems. Tutorial. Publishing house "Lan". (in Russian)
dc.relation.referencesen14. Kremlevskyi, P. (2002) Flowmeters and Meters of Substances. Publishing House "Polytechnic". (in Russian)
dc.relation.referencesen15. Kabza, Z. (1981) Mathematical Modeling of Flowmeters with Constricting Devices. Mechanical Engineering, Leningrad. (in Russian)
dc.relation.referencesen16. ISO 5167-1:2003. Measurement of Fluid Flow by Means of Pressure Differential Devices Inserted in Circular Cross-Section Conduits Running Full – Part 1: General Principles and Requirements.
dc.relation.referencesen17. Pistun, Ye., Lesovoi, L. (2006) Standardization of Pressure Differential Flowmeters. CJSC "Institute of Energy Audit and Energy Resources", Lviv. (in Ukrainian)
dc.relation.referencesen18. Pistun, Ye., Tepliukh, Z., Stasiuk, I. (1986) Flow Characteristics of Gas-Dynamic Throttle Elements. In Book: Pneumatic and Hydraulic Devices and Control Systems. X International Conference "Jablonna", Energoatomizdat, 31–34. (in Russian)
dc.relation.referencesen19. Stasiuk, I. (2015) Gas Dynamical Capillary Flowmeters of Small and Micro Flowrates of Gases, Energy Engineering and Control Systems, 1 (2), 117–126
dc.relation.referencesen20. Tepliukh, Z., Pistun, Ye. (1978) Using Various Functional Dependencies to Describe Flow Characteristics of Turbulent Throttles, Measurement Techniques, 2, 231–234. (Translated from Izmeritel'naya Tekhnika, No. 2, pp. 48–50 by Plenum Publishing Corporation, February, 1977.)
dc.relation.referencesen21. Gornstein, B. (1979) Determining of Gas Flow Through a Capillary, Metrology, 1, 66–74. (in Russian)
dc.relation.referencesen22. Walicka, A. (2018) Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Capillary Fissures and Tubes. Int. J. of Applied Mechanics and Engineering, 23 (1), 187–211. https://doi.org/10.1515/ijame-2018-0011
dc.relation.referencesen23. Steffe, J. (1996) Rheological Methods in Food Process Engineering, USA, Freeman Press.
dc.relation.referencesen24. Krykh, H. (2008) Mathematical Models of Throttle Elements of Hydrodynamic Measuring Transducers of Non-Newtonian Liquid Parameters. Proc. of Lviv Polytechnic National University: Heat Power Engineering. Environmental Engineering. Automation, 617, 122–129. (in Ukrainian)
dc.relation.referencesen25. Venerus, D. (2006) Laminar Capillary Flow of Compressible Viscous Fluids. Journal Fluid Mechanics, 555, 59–80. https://doi.org/10.1017/S0022112006008755
dc.relation.referencesen26. Malkin, A., Isayev, A. (2017) Rheology: Concepts, Methods and Applications. Chemical Technology Publishing House.
dc.relation.referencesen27. Drevetskyi, V. (2012) Mathematical Models of Throttle Transducers for Hydrodynamic Measuring Devices of Viscosity and Density of Liquids. Methods and Instruments of Quality Control, 29, 38–46. (in Ukrainian)
dc.relation.referencesen28. Karniadakis, G., Beskok, A., Aluru, N. (2002) Microflows. Fundamentals and Simulation.
dc.relation.referencesen29. Sharp, K., Adrian, R., Santiago, J., Molho, J. (2005) MEMS: Background and Fundamentals. Chapter 10: Liquid Flows in Microchannels, 10-1–10-45.
dc.relation.referencesen30. Cao, B., Chen, G., Li, Y., Yuan, Q. (2006) Numerical Analysis of Isothermal Gaseous Flows in Microchannel. Chemical Engineering Technology, 29 (1), 66–71. https://doi.org/10.1002/ceat.200407079
dc.relation.referencesen31. Hetsroni, G., Mosyak, A., Pogrebnyak, E., Yarin, L. (2005) Fluid Flow in Micro-Channels International. Journal of Heat and Mass Transfer, 48, 1982–1998. DOI: 10.1016/j.ijheatmasstransfer.2004.12.019
dc.relation.referencesen32. Guangwen, Y., Yuan , Ch. (2014) Effect of Viscosity on the Hydrodynamics of Liquid Processes in Microchannels. Chemical Engineering Technology, 37 (3), 427–434. https://doi.org/10.1002/ceat.201300468
dc.relation.referencesen33. Bucci, A., Celata, G., Cumo, M., Serra, E., Zummo, G. (2003) Water Single-Phase Fluid Flow and Heat Transfer in Capillary Tubes. Conference ASME 2003, 1st International Conference on Microchannels and Minichannels, 319–326. doi:10.1115/ICMM2003-1037
dc.relation.referencesen34. Kim, M., Araki T., Inaoka, K., Suzuki, K. (2000) Gas Flow Characteristics in Microtubes. JSME International Journal Series B, 43 (4),634–639. https://doi.org/10.1299/jsmeb.43.634
dc.relation.referencesen35. Tang, G., Li, Zh., He, Y., Tao, W. (2007) Experimental Study of Compressibility, Roughness and Rarefaction Influences on Microchannel Flow. International Journal of Heat and Mass Transfer, 50, 2282–2295. DOI: 10.1016/j.ijheatmasstransfer.2006.10.034
dc.relation.referencesen36. Taliadoroua, E., Georgioua, G., Moulitsas, I. (2009) Weakly Compressible Poiseuille Flows of a Herschel–Bulkley Fluid. Journal NonNewtonian Fluid Mechanics, 158, 162–169. DOI: 10.1016/j.jnnfm.2008.11.010
dc.relation.referencesen37. Liu, D., Garimella, S. (2004) Investigation of Liquid Flow in Microchannels. AIAA Journal of Thermophysics and Heat Transfer. 18 (1), 65–72. https://doi.org/10.2514/1.9124
dc.relation.referencesen38. Obot, N. (2000) Toward a Better Understanding of Friction and Heat/Mass Transfer in Microchannels – A Literature Review. United Engineering Foundation Conference, Heat Transfer and Transport Phenomena in Microsystems, Oct. 15-20, 2000, Banff, Alberta, 1–8.
dc.relation.referencesen39. Harley, J., Huang, Y., Bau, H., Zemel, J. (1994) Gas Flow in Micro-Channels. Journal of Fluid Mechanics, 284, 257–274. http://dx.doi.org/10.1017/S0022112095000358
dc.relation.referencesen40. Cai, Ch., Sun, Q., Boyd, I. (2007) Gas Flows in Microchannels and Microtubes. Fluid Mechanics, 589, 305–314. https://doi.org/10.1017/S0022112007008178
dc.relation.referencesen41. Taliadoroua, E., Neophytou, M., Georgiou, G. (2009) Perturbation Solutions of Poiseuille Flows of Weakly Compressible Newtonian Liquids, Journal of Non-Newtonian Fluid Mechanics, 163, 1-3, 25–34. https://doi.org/10.1016/j.jnnfm.2009.06.003
dc.relation.referencesen42. Teng, J., Chu, J., Yu, X., Dang, Th., Lee, M. et al. Fluid Dynamics, Computational Modeling and Applications. Chapter – Fluid Dynamics in Microchannels, 403–436.
dc.relation.referencesen43. Zhang, X., Zhu, W., Cai, Q., Shi, Y. Wu, X. Jin, T. Yang, L., Song, H. (2018) Compressible Liquid Flow in Nano– or Micro-Sized Circular Tubes Considering Wall–Liquid Lifshitz–Van Der Waals Interaction. Physics of Fluids, 30, 062002. https://doi.org/10.1063/1.5023291
dc.relation.referencesen44. Bahrami, M., Yovanovich, M. and Culham, J. (2005) Pressure Drop of Fully Developed, Laminar Flow in Rough Microtubes. Journal of Fluids Engineering, 128 (3), 632–637. doi:10.1115/1.2175171
dc.relation.referencesen45. Silva, G., Leal, N. Semião, V. (2008) Effect of Wall Roughness on Fluid Flow Inside a Microchannel. 14th Int Symp on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 07–10 July, 2008, 1–12.
dc.relation.referencesen46. Celata, G., Cumo, M., McPhail, S., Tesfagabir, L., Zummo, G. (2007) Experimental Study on Compressible Flow in Microtubes. International Journal of Heat and Fluid Flow, 28, 28–36. https://doi.org/10.1016/j.ijheatfluidflow.2006.04.009
dc.relation.referencesen47. Mortensen, N., Okkels, F., Bruus, H. (2005) Reexamination of Hagen–Poiseuille flow: Shape Dependence of the Hydraulic Resistance in Microchannels. Physical Review, E. Statistical Nonlinear and Soft Matter Physics, 71(5), 057301, 1–5. doi:10.1103/PhysRevE.71.057301
dc.relation.referencesen48. Bulhakov, B., Kubrak, A. (1977) Pneumatic Automation, Tehnika, Kyjiv. (in Russian)
dc.relation.referencesen49. RD 50-411-83. (1984) Methodical Instructions. Flowrate of Liquids and Gases. Technique for Measuring Using Special Constricting Devices. Publishing House of Standards, Moscow. (in Russian)
dc.relation.referencesen50. Pistun, Ye., Teplykh, Z., Stasyuk, I. (1984) Watch Jewels in Gas Microflow Measurement, Measurement Techniques, 11, 929–931 (Translated from Izmeritel'naya Tekhniya, No. 11, pp. 36–38 by Plenum Publishing Corporation, November, 1983).
dc.relation.urihttps://doi.org/10.15587/1729-4061.2017.114110
dc.relation.urihttps://doi.org/10.1515/ijame-2018-0011
dc.relation.urihttps://doi.org/10.1017/S0022112006008755
dc.relation.urihttps://doi.org/10.1002/ceat.200407079
dc.relation.urihttps://doi.org/10.1002/ceat.201300468
dc.relation.urihttps://doi.org/10.1299/jsmeb.43.634
dc.relation.urihttps://doi.org/10.2514/1.9124
dc.relation.urihttp://dx.doi.org/10.1017/S0022112095000358
dc.relation.urihttps://doi.org/10.1017/S0022112007008178
dc.relation.urihttps://doi.org/10.1016/j.jnnfm.2009.06.003
dc.relation.urihttps://doi.org/10.1063/1.5023291
dc.relation.urihttps://doi.org/10.1016/j.ijheatfluidflow.2006.04.009
dc.rights.holder© Національний університет “Львівська політехніка”, 2019
dc.subjectвитратна характеристика
dc.subjectкапілярна трубка
dc.subjectпристрій звуження
dc.subjectмікроканал
dc.subjectвимірювальний перетворювач
dc.subjectфізико-механічні параметри
dc.subjectflowrate characteristic
dc.subjectcapillary tube
dc.subjectconstricting device
dc.subjectmicrochannel
dc.subjectmeasuring transducer
dc.subjectphysical and mechanical parameters
dc.titleMathematical Models of Throttle Elements of Gas-hydrodynamic Measuring Transducers
dc.title.alternativeМатематичні моделі дросельних елементів газогідродинамічних вимірювальних перетворювачів
dc.typeArticle

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Energy Engineering and Control Systems. – 2019. – Vol. 5, No. 2