Skip to main content
Top

2021 | OriginalPaper | Chapter

7. Fundamentals of Fluid Dynamics

Author : Alister J. Bates

Published in: Clinical and Biomedical Engineering in the Human Nose

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The purpose of CFD is to map and quantify fluid flows in space and time. CFD simulations achieve this by solving the equations that govern flow: conservation of mass; balance of momentum; and conservation of energy. This chapter describes what these equations conceptually mean and how they are derived by applying basic physics statements such as Newton’s second law and the first law of thermodynamics to fluids. Fluid flow phenomena including boundary layers, turbulence, and unsteadiness are introduced and techniques to model them via CFD simulations are discussed. Turbulence models, which allow CFD simulations to achieve accurate results without having to calculate the smallest velocity fluctuations in a flow, thereby accelerating simulations, are also discussed and the most common models used in respiratory airflow simulations are compared.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference A. Bates, R. Cetto, D. Doorly, R. Schroter, N. Tolley, A. Comerford, The effects of curvature and constriction on airflow and energy loss in pathological tracheas. Respir. Physiol. Neurobiol. 234, 69–78 (2016)CrossRef A. Bates, R. Cetto, D. Doorly, R. Schroter, N. Tolley, A. Comerford, The effects of curvature and constriction on airflow and energy loss in pathological tracheas. Respir. Physiol. Neurobiol. 234, 69–78 (2016)CrossRef
2.
go back to reference A. Bates, A. Comerford, R. Cetto, R. Schroter, N. Tolley, D. Doorly, Power loss mechanisms in pathological tracheas. J. Biomech. 49(11), 2187–2192 (2016)CrossRef A. Bates, A. Comerford, R. Cetto, R. Schroter, N. Tolley, D. Doorly, Power loss mechanisms in pathological tracheas. J. Biomech. 49(11), 2187–2192 (2016)CrossRef
3.
go back to reference A. Bates, A. Comerford, R. Cetto, D. Doorly, R. Schroter, N. Tolley, Computational fluid dynamics benchmark dataset of airflow in tracheas. Data Brief 10, 101–107 (2017)CrossRef A. Bates, A. Comerford, R. Cetto, D. Doorly, R. Schroter, N. Tolley, Computational fluid dynamics benchmark dataset of airflow in tracheas. Data Brief 10, 101–107 (2017)CrossRef
4.
go back to reference A.J. Bates, D.J. Doorly, R. Cetto, H. Calmet, A. Gambaruto, N. Tolley, G. Houzeaux, R. Schroter, Dynamics of airflow in a short inhalation. J. R. Soc. Interface 12(102), 20140880 (2015)CrossRef A.J. Bates, D.J. Doorly, R. Cetto, H. Calmet, A. Gambaruto, N. Tolley, G. Houzeaux, R. Schroter, Dynamics of airflow in a short inhalation. J. R. Soc. Interface 12(102), 20140880 (2015)CrossRef
5.
go back to reference A.J. Bates, A. Schuh, K. McConnell, B.M. Williams, J.M. Lanier, M.M. Willmering, J.C. Woods, R.J. Fleck, C.L. Dumoulin, R.S. Amin, A novel method to generate dynamic boundary conditions for airway CFD by mapping upper airway movement with non-rigid registration of dynamic and static MRI. Int. J. Numer. Methods Biomed. Eng. 34(12), e3144 (2018)MathSciNetCrossRef A.J. Bates, A. Schuh, K. McConnell, B.M. Williams, J.M. Lanier, M.M. Willmering, J.C. Woods, R.J. Fleck, C.L. Dumoulin, R.S. Amin, A novel method to generate dynamic boundary conditions for airway CFD by mapping upper airway movement with non-rigid registration of dynamic and static MRI. Int. J. Numer. Methods Biomed. Eng. 34(12), e3144 (2018)MathSciNetCrossRef
6.
go back to reference A.J. Bates, A. Schuh, G. Amine-Eddine, K. McConnell, W. Loew, R.J. Fleck, J.C. Woods, C.L. Dumoulin, R.S. Amin, Assessing the relationship between movement and airflow in the upper airway using computational fluid dynamics with motion determined from magnetic resonance imaging. Clin. Biomech. 66, 88–96 (2019)CrossRef A.J. Bates, A. Schuh, G. Amine-Eddine, K. McConnell, W. Loew, R.J. Fleck, J.C. Woods, C.L. Dumoulin, R.S. Amin, Assessing the relationship between movement and airflow in the upper airway using computational fluid dynamics with motion determined from magnetic resonance imaging. Clin. Biomech. 66, 88–96 (2019)CrossRef
7.
go back to reference A.J. Bates, M.M. Willmering, R. Thomen, C. Gunatilaka, M.M. Hossain, C. Dumoulin, J. Woods, In vivo validation of upper airway respiratory computational fluid dynamics (CFD) with phase-contrast MRI of hyperpolarized 129xe, p. 4138 A.J. Bates, M.M. Willmering, R. Thomen, C. Gunatilaka, M.M. Hossain, C. Dumoulin, J. Woods, In vivo validation of upper airway respiratory computational fluid dynamics (CFD) with phase-contrast MRI of hyperpolarized 129xe, p. 4138
8.
go back to reference H. Calmet, A.M. Gambaruto, A.J. Bates, M. Vázquez, G. Houzeaux, D.J. Doorly, Large-scale CFD simulations of the transitional and turbulent regime for the large human airways during rapid inhalation. Comput. Biol. Med. 69, 166–180 (2016)CrossRef H. Calmet, A.M. Gambaruto, A.J. Bates, M. Vázquez, G. Houzeaux, D.J. Doorly, Large-scale CFD simulations of the transitional and turbulent regime for the large human airways during rapid inhalation. Comput. Biol. Med. 69, 166–180 (2016)CrossRef
9.
go back to reference H. Calmet, G. Houzeaux, M. Vázquez, B. Eguzkitza, A. Gambaruto, A. Bates, D. Doorly, Flow features and micro-particle deposition in a human respiratory system during sniffing. J. Aerosol Sci. 123, 171–184 (2018)CrossRef H. Calmet, G. Houzeaux, M. Vázquez, B. Eguzkitza, A. Gambaruto, A. Bates, D. Doorly, Flow features and micro-particle deposition in a human respiratory system during sniffing. J. Aerosol Sci. 123, 171–184 (2018)CrossRef
10.
go back to reference X.B. Chen, H.P. Lee, V.F.H. Chong, D.Y. Wang, Numerical simulation of the effects of inferior turbinate surgery on nasal airway heating capacity. Am. J. Rhinol. Allergy 24(5), e118–e122 (2010)CrossRef X.B. Chen, H.P. Lee, V.F.H. Chong, D.Y. Wang, Numerical simulation of the effects of inferior turbinate surgery on nasal airway heating capacity. Am. J. Rhinol. Allergy 24(5), e118–e122 (2010)CrossRef
11.
go back to reference G.J. Garcia, N. Bailie, D.A. Martins, J.S. Kimbell, Atrophic rhinitis: a CFD study of air conditioning in the nasal cavity. J. Appl. Physiol. 103(3), 1082–1092 (2007)CrossRef G.J. Garcia, N. Bailie, D.A. Martins, J.S. Kimbell, Atrophic rhinitis: a CFD study of air conditioning in the nasal cavity. J. Appl. Physiol. 103(3), 1082–1092 (2007)CrossRef
12.
go back to reference K. Inthavong, Z. Tian, J. Tu, CFD simulations on the heating capability in a human nasal cavity K. Inthavong, Z. Tian, J. Tu, CFD simulations on the heating capability in a human nasal cavity
13.
go back to reference K. Inthavong, J. Wen, J. Tu, Z. Tian, From CT scans to CFD modelling-fluid and heat transfer in a realistic human nasal cavity. Eng. Appl. Comput. Fluid Mech. 3(3), 321–335 (2009) K. Inthavong, J. Wen, J. Tu, Z. Tian, From CT scans to CFD modelling-fluid and heat transfer in a realistic human nasal cavity. Eng. Appl. Comput. Fluid Mech. 3(3), 321–335 (2009)
14.
go back to reference D. Joseph, S. Carmi, Stability of Poiseuille flow in pipes, annuli, and channels. Q. Appl. Math. 26(4), 575–599 (1969)CrossRef D. Joseph, S. Carmi, Stability of Poiseuille flow in pipes, annuli, and channels. Q. Appl. Math. 26(4), 575–599 (1969)CrossRef
15.
go back to reference A. Karl, F.S. Henry, A. Tsuda, Low Reynolds number viscous flow in an alveolated duct. J. Biomech. Eng. 126(4), 420–429 (2004)CrossRef A. Karl, F.S. Henry, A. Tsuda, Low Reynolds number viscous flow in an alveolated duct. J. Biomech. Eng. 126(4), 420–429 (2004)CrossRef
16.
go back to reference J. Kimbell, D. Frank, P. Laud, G. Garcia, J. Rhee, Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction. J. Biomech. 46(15), 2634–2643 (2013)CrossRef J. Kimbell, D. Frank, P. Laud, G. Garcia, J. Rhee, Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction. J. Biomech. 46(15), 2634–2643 (2013)CrossRef
17.
go back to reference P.K. Kundu, I.M. Cohen, Fluid Mechanics (Elsevier, Amsterdam, 2001) P.K. Kundu, I.M. Cohen, Fluid Mechanics (Elsevier, Amsterdam, 2001)
18.
go back to reference C.-L. Lin, M.H. Tawhai, G. McLennan, E.A. Hoffman, Characteristics of the turbulent laryngeal jet and its effect on airflow in the human intra-thoracic airways. Respir. Physiol. Neurobiol. 157(2–3), 295–309 (2007)CrossRef C.-L. Lin, M.H. Tawhai, G. McLennan, E.A. Hoffman, Characteristics of the turbulent laryngeal jet and its effect on airflow in the human intra-thoracic airways. Respir. Physiol. Neurobiol. 157(2–3), 295–309 (2007)CrossRef
19.
go back to reference F. Menter, Zonal two equation kw turbulence models for aerodynamic flows, in 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference (1993), p. 2906 F. Menter, Zonal two equation kw turbulence models for aerodynamic flows, in 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference (1993), p. 2906
20.
go back to reference F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)CrossRef F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)CrossRef
21.
go back to reference W. Pfenniger, Transition in the inlet length of tubes at high Reynolds numbers, in Boundary Layer and Flow Control, ed. by G. Lachman (1961), pp. 970–980 W. Pfenniger, Transition in the inlet length of tubes at high Reynolds numbers, in Boundary Layer and Flow Control, ed. by G. Lachman (1961), pp. 970–980
22.
go back to reference D.C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11), 1299–1310 (1988)MathSciNetCrossRef D.C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11), 1299–1310 (1988)MathSciNetCrossRef
23.
go back to reference D.C. Wilcox et al., Turbulence Modeling for CFD, vol. 2 (DCW Industries La Canada, 1998) D.C. Wilcox et al., Turbulence Modeling for CFD, vol. 2 (DCW Industries La Canada, 1998)
24.
go back to reference A. Willis, J. Peixinho, R. Kerswell, T. Mullin, Experimental and theoretical progress in pipe flow transition. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 366(1876), 2671–2684 (2008)MathSciNetCrossRef A. Willis, J. Peixinho, R. Kerswell, T. Mullin, Experimental and theoretical progress in pipe flow transition. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 366(1876), 2671–2684 (2008)MathSciNetCrossRef
25.
go back to reference Q. Xiao, R. Cetto, D.J. Doorly, A.J. Bates, J.N. Rose, C. McIntyre, A. Comerford, G. Madani, N.S. Tolley, R. Schroter, Assessing changes in airflow and energy loss in a progressive tracheal compression before and after surgical correction. Ann. Biomed. Eng. 48(2), 822–833 (2020)CrossRef Q. Xiao, R. Cetto, D.J. Doorly, A.J. Bates, J.N. Rose, C. McIntyre, A. Comerford, G. Madani, N.S. Tolley, R. Schroter, Assessing changes in airflow and energy loss in a progressive tracheal compression before and after surgical correction. Ann. Biomed. Eng. 48(2), 822–833 (2020)CrossRef
26.
go back to reference D.A. Yablonskiy, A.L. Sukstanskii, J.C. Leawoods, D.S. Gierada, G.L. Bretthorst, S.S. Lefrak, J.D. Cooper, M.S. Conradi, Quantitative in vivo assessment of lung microstructure at the alveolar level with hyperpolarized 3He diffusion MRI. Proc. Natl. Acad. Sci. 99(5), 3111–3116 (2002)CrossRef D.A. Yablonskiy, A.L. Sukstanskii, J.C. Leawoods, D.S. Gierada, G.L. Bretthorst, S.S. Lefrak, J.D. Cooper, M.S. Conradi, Quantitative in vivo assessment of lung microstructure at the alveolar level with hyperpolarized 3He diffusion MRI. Proc. Natl. Acad. Sci. 99(5), 3111–3116 (2002)CrossRef
27.
go back to reference D.A. Yablonskiy, A.L. Sukstanskii, J.C. Woods, D.S. Gierada, J.D. Quirk, J.C. Hogg, J.D. Cooper, M.S. Conradi, Quantification of lung microstructure with hyperpolarized 3He diffusion MRI. J. Appl. Physiol. 107(4), 1258–1265 (2009)CrossRef D.A. Yablonskiy, A.L. Sukstanskii, J.C. Woods, D.S. Gierada, J.D. Quirk, J.C. Hogg, J.D. Cooper, M.S. Conradi, Quantification of lung microstructure with hyperpolarized 3He diffusion MRI. J. Appl. Physiol. 107(4), 1258–1265 (2009)CrossRef
Metadata
Title
Fundamentals of Fluid Dynamics
Author
Alister J. Bates
Copyright Year
2021
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-15-6716-2_7

Premium Partners