USING MATHEMATICAL MODELS OF TURBULENCE TO DETERMINE GAS DYNAMIC CHARACTERISTICS IMPACT CENTRIFUGAL MILL

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024

UDC 621.926.88

 

Fedarovich Evgeniy Gennad’yevich – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: zhenya.fedorovich.1999@mail.ru

Levdanski Alexander Eduardovich – DSc (Engineering), Professor, Head of the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: alex_levdansky@mail.ru

Kovaleva Anastasiya Aleksandrovna – PhD student, the Department of Processes and Apparatus for Chemical Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: nastya.covaleva1969@mail.ru

Nurmukhamedov Habibulla Sagdullayevich – Professor, the Department of Technological Machines and Eguipment. Тashkent Institute of Chemical Technology (32, Navoi str., 100011, Tashkent, Republic of Uzbekistan). E-mail: has-bek@mail.ru

 

https://doi.org/10.52065/2519-402X-2023-264-01DOI: https://doi.org/ 10.52065/2520-2669-2024-283-7.

Key words: centrifugal impact mill, modeling, turbulence model, air flow, kinetic energy turbulence.

For citation: Fedarovich E. G., Levdanski A. E., Kovaleva A. A., Nurmukhamedov H. S. Using mathematical models of turbulence to determine gas dynamic characteristics impact centrifugal mill. Proceedings of BSTU, issue 2, Chemical Engineering, Biotechnologies, Genecology, 2024, no. 2 (283), pp. 50–58 (In Russian). DOI: 10.52065/2520-2669-2024-283-7.

Abstract

The article discusses the aerodynamics of an impact centrifugal mill. Using three-dimensional numerical modeling, theoretical studies were carried out on the use of mathematical models of turbulence to determine the gas-dynamic characteristics of an impact centrifugal mill. The work examined the currently most common turbulence models with two differential equations: the standard k-ε turbulence model, the Baseline model, and the Shear Stress Transport model. Three-dimensional numerical modeling included the construction of a three-dimensional geometric model of an impact centrifugal mill with the definition of a computational domain, the construction of a hexagonal computational mesh in the resulting computational domain, the definition of boundary conditions on the inlet and outlet pipes and carrying out calculations with subsequent processing of the obtained data. The aerodynamic characteristics of the air flow of an impact centrifugal mill are determined, such as mass air flow, degree of pressure increase, air temperature, average air flow speed in the inlet pipe, average air flow speed at the inner and outer edges of the accelerating blades. Graphic dependences of the influence of the speed of rotation of the mill working body on the speed of air flow in the working chamber of the mill, as well as on the values of the kinetic energy of turbulence, were constructed Based on the values of kinetic energy of turbulence, a characteristic is given of the structure of the air flow in the interblade region using the studied turbulence models. A comparison of theoretical and experimental data is presented for determining the mass air flow rate in the outlet pipe of an impact centrifugal mill at different rotor speeds. Based on the results of the theoretical studies, a conclusion was made about the suitability of the studied turbulence models for simulating aerodynamics in a centrifugal impact mill.

Download

References

  1. Bai Y., Appiah D., Tao Y. Computational turbulent flow characteristics in a centrifugal pump. AIP Advances, 2022, vol. 12, issue 7, 14 p. DOI: 10.1063/5.0100915.
  2. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data. Annul Review of Fluid Mechanics, 2019, vol. 51, pp. 357– 377. DOI: 10.1146/annurev-fluid-010518-040547.
  3. Turubaev R. R., Shvab A. V. Numerical study of swirling turbulent flow aerodynamics and classification of particles in a vortex chamber of a centrifugal machine. Vestnik Tomskogo gosudarstvennogo universiteta [Tomsk State University Journal], 2020, no. 65: Mathematics and Mechanics, pp. 137–147 (In Russian). DOI: 10.17223/19988621/65/11.
  4. Novitskiy B. B. Compfrison of turbulence models in simulation on flow in small-size centrifugal compressor. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2015, no. 6, pp. 67–82. DOI: 10.7463/0615.0778604.
  5. Karlov A. M., Kuftov A. F. Working off the methodology of numerical simulation of three-dimensional viscous flow in axially radial impeller os centrifugal compressor using ANSYS CFX. Nauka i obrazovanie (MGTU im. N. E. Baumana) [Science and education (Bauman MSTU)], 2012, no. 11, pp. 69–80. DOI: 10.7463/1112.0465832.
  6. Gamburger D. M. Chislennoye modelirovaniye techeniya vyazkogo gaza v centrobezhnoy kompressornoy stupeni: metodika i rezul’taty: avtoreferat dissertatsii kandidata tehnicheskih nauk [Numerical modeling of viscous gas flow in a centrifugal compressor stage: methodology and results: abstract of the dissertation PhD (Engineering)]. St. Petersburg, 2009. 16 p. (In Russian).
  7. Belov I. A., Isaev S. A. Modelirovaniye turbulentnykh techeniy: uchebnoe posobie [Modeling of turbulent flows: a tutorial]. St. Petersburg, Baltic State Technical University Publ., 2001. 108 p. (In Russian).
  8. Korkodinov I. A. The review of set of k-ε models for modeling turbulence. Vestnik Permskogo natsional’nogo politehnicheskogo universiteta [Bulletin of Perm National Polytechnic University], 2013, vol. 15, no. 2: Mechanical engineering, materials science, pp. 5–16 (In Russian).
  9. Wilcox D. C. Reassessment of the scale determining equation for advanced turbulence models. AIAA journal, 1988, vol. 26, no. 11, pp. 1299–1310. DOI: 10.2514/3.10041.
  10. Baranov P. A., Guvernyuk S. V., Zubin M. A., Isaev S. A., Usachov A. E. Application of various models of turbulence for calculation of incompressible internal flows. Uchenye zapiski TSAGI [TsAGI science journal], 2017, vol. 48, no. 1, pp. 26–36 (In Russian). DOI: 10.1615/TsAGISciJ.2017020750.
  11. Levdanskiy A. E., Levdanskiy E. I., Fedarovich E. G., Golubev V. G., Sarsenbekuly D., Zhumadullaev D. K. Vortex mill. Patent KZ 34889, 2021 (In Russian).
  12. Galerkin Yu. B., Hamburger D. M., Epifanov A. A. Analysis of flow in centrifugal compressor stages using computational fluid dynamics methods. Kompressornaya tekhnika i pnevmatika [Compressor technology and pneumatics], 2019, no. 3, pp. 22–32 (In Russian).
  13. Seleznev K. P., Galerkin Yu. B. Centrobezhnyye kompressory [Centrifugal compressors]. St. Petersburg, Mashinostroyeniye Publ., 1982. 271 p. (In Russian).
  14. Galerkin Yu. B. Turbokompressory. Rabochiy process, raschet i proektirovaniye protochnoy chasti [Turbochargers. Workflow, calculation and design of the flow path]. Moscow, Information Publishing Center Compressor and Chemical Engineering Publ., 2010. 762 p. (In Russian).

06.05.2024