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Experiments in Fluids

, Volume 34, Issue 4, pp 494–503 | Cite as

4D Magnetic resonance velocimetry for mean velocity measurements in complex turbulent flows

  • C. J. Elkins
  • M. Markl
  • N. Pelc
  • J. K. EatonEmail author
Article

Abstract

An adaptation of a medical magnetic resonance imaging system to the noninvasive measurement of three-component mean velocity fields in complex turbulent engineering flows is described. The aim of this paper is to evaluate the capabilities of the technique with respect to its accuracy, time efficiency and applicability as a design tool for complex turbulent internal geometries. The technique, called 4D magnetic resonance velocimetry (4D-MRV), is used to measure the mean flow in fully developed low-Reynolds number turbulent pipe flow, Re=6400 based on bulk mean velocity and diameter, and in a model of a gas turbine blade internal cooling geometry with four serpentine passages, Re=10,000 and 15,000 based on bulk mean velocity and hydraulic diameter. 4D-MRV is capable of completing full-field measurements in three-dimensional volumes with sizes on the order of the magnet bore diameter in less than one hour. Such measurements can include over 2 million independent mean velocity vectors. Velocities measured in round pipe flow agreed with previous experimental results to within 10%. In the turbulent cooling passage flow, the average flow rates calculated from the 4D-MRV velocity profiles agreed with ultrasonic flowmeter measurements to within 7%. The measurements lend excellent qualitative insight into flow structures even in the highly complex 180° bends. Accurate quantitative measurements were obtained throughout the Re=10,000 flow and in the Re=15,000 flow except in the most complex regions, areas just downstream of high-speed bends, where velocities and velocity fluctuations exceeded MRV capabilities for the chosen set of scan parameters. General guidelines for choosing scanning parameters and suggestions for future development are presented.

Keywords

Particle Image Velocimetry Integral Time Scale Magnetic Resonance Velocimetry Secondary Flow Structure Complex Turbulent Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Christopher J. Elkins and John K. Eaton were supported by a grant from the General Electric Aircraft Engines as part of the GE–University Strategic Alliance. Use of the facilities at the Richard M. Lucas Center for Magnetic Resonance Spectroscopy and Imaging is gratefully acknowledged. The flow model was manufactured by Professor Ryan Wicker, Mr. Francisco Medina, and Mr. Erasmo Lopez at the University of Texas at El Paso.

References

  1. Bogren HG, Buonocore MH (1999) 4D magnetic resonance velocity mapping of blood flow patterns in the aorta in young vs. elderly normal subjects. J Magn Reson Imag 10:861–869CrossRefGoogle Scholar
  2. Ebbers T, Wigstrom L, Bolger AF, Engvall J, Karlsson M (2001) Estimation of relative cardiovascular pressures using time-resolved three-dimensional phase contrast MRI. Magn Res Med 45:872–879CrossRefGoogle Scholar
  3. Eggels JGM, Unger F, Weiss MH, Westerweel J, Adrian RJ, Friedrich R, Nieuwstadt FTM (1994) Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J Fluid Mech 268:175–209Google Scholar
  4. Fukushima E (1999) Nuclear magnetic resonance as a tool to study flow. Ann Rev Fluid Mech 31:95–123CrossRefGoogle Scholar
  5. Gach HM, Lowe IJ (2000) Measuring flow reattachment lengths downstream of a stenosis using MRI. J Magn Reson Imag 12:939–948CrossRefGoogle Scholar
  6. Gatenby JC, Gore JC (1996) Echo-planar-imaging studies of turbulent flow. J Magn Reson A 121:193–200CrossRefGoogle Scholar
  7. Haacke M, Brown R, Thompson M, Venkatesan R (1999) Magnetic Resonance Imaging. Wiley-Liss, New YorkGoogle Scholar
  8. Kuethe DO (1989) Measuring distributions of diffusivity in turbulent fluids with magnetic resonance imaging. Physiol Rev 40:4542–4551CrossRefGoogle Scholar
  9. Kozerke S, Hasenkam JM, Pedersen EM, Boesiger P (2001) Visualization of flow patterns distal to aortic valve prostheses in humans using a fast approach for cine 3D velocity mapping. J Magn Reson Imag 13:690–698CrossRefGoogle Scholar
  10. Ku DN, Biancheri CL, Pettigrew RI, Peifer JW, Markou CP, Engels H (1990) Evaluation of magnetic resonance velocimetry for steady flow. J Biomech Eng 112:464–72PubMedGoogle Scholar
  11. Li TQ, Seymour JD, Powell RL, McCarthy KL, Odberg L, McCarthy MJ (1994) Turbulent pipe flow studied by time-averaged NMR imaging: measurements of velocity profile and turbulent intensity. Magn Reson Imag 12:923–34Google Scholar
  12. Markl M, Chan FP, Alley MT, Wedding KL, Draney MT, Elkins CJ, Parker DW, Wicker R, Taylor CA, Herfkens RJ, Pelc NJ (2003) Time resolved three dimensional phase contrast MRI (4D-flow). J Magn Reson Imaging, in pressGoogle Scholar
  13. Markl M, Draney MT, Pelc NJ (2002) Analysis and correction of the effect of spatial gradient field distortions on velocity measurements with phase contrast MRI. In: Proc 10th Scientific Meeting International Society of Magnetic Resonance in Medicine, Honolulu, USA, 18–24 May 2002Google Scholar
  14. Nalcioglu O, Guo Q, Buxton R (1990) Measurement of eddy diffusivity by NMR imaging. Proc SPIE 1231:150Google Scholar
  15. Oshinski JN, Ku DN, Pettigrew RI (1995) Turbulent fluctuation velocity: the most significant determinant of signal loss in stenotic vessels. Magn Res Med 33:193–199Google Scholar
  16. Pelc NJ, Herfkens RJ, Shimakawa A, Enzmann DR (1991) Phase contrast cine magnetic resonance imaging. Magn Reson Q 7:229–54PubMedGoogle Scholar
  17. Pelc NJ, Sommer FG, Li KCP, Brosnan TJ, Herfkens RJ, Enzmann DR (1994) Quantitative magnetic resonance flow imaging. Magn Reson Q 10:125–47PubMedGoogle Scholar
  18. von Schulthess G, Hennig J (1998) Functional imaging. Lippincott-Raven, Philadelphia, pp 261–390Google Scholar
  19. Seigel JM, Oshinski JN, Pettigrew RI, Ku DN (1996) The accuracy of magnetic resonance phase velocity measurements in stenotic flow. J Biomechan 29:1665–1672CrossRefGoogle Scholar
  20. Seymour JD, Callaghan PT (1997) Generalized approach to NMR analysis of flow and dispersion in porous media. AIChE J 43:2096–2111Google Scholar
  21. Stark D, Bradley W (1999) Magnetic resonance imaging. Mosby-Year Book, St LouisGoogle Scholar
  22. Taylor GI (1921) Diffusion by continuous movement. Proc Roy Soc Ser A 20:196–211Google Scholar
  23. Tse DGN, Steuber G (1996) Flow in rotating serpentine coolant passages with skewed trip strips. NASA CR-198530 Google Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • C. J. Elkins
    • 1
  • M. Markl
    • 2
  • N. Pelc
    • 2
  • J. K. Eaton
    • 1
    Email author
  1. 1.Mechanical Engineering Dept.Stanford UniversityStanfordUSA
  2. 2.Dept. of Radiology, Lucas MRI/S CenterStanford UniversityStanfordUSA

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