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Construction of the prediction model between pressure and flow rate for pulsating flows based on the Greenfield-Fry model concerning wave dispersion

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Abstract

Wave dispersion is the key feature in understanding pulsating flows in a rigid circular pipe with small diameter. The wave dispersion makes flow signals distorted in the pulsating flows by boundary conditions due to pipe surface. Detailed description of this phenomenon can make the Greenfield-Fry model more practical. This model describes the relationship between the pressure gradient and the flow rate in the rigid circular pipe. Because pressure gradient measurement requires more than two pressure transducers, it would become more practical if only one pressure transducer is needed by applying the Taylor’s frozen field hypothesis. This implies that only one pressure transducer is satisfactory for predicting flow signals with the Greenfield-Fry model. By applying the frequency variant convection velocity to consider the wave dispersion, the Taylor’s frozen field hypothesis can relate the pressure signals with the flow signals according to the Greenfield-Fry model. In this study, the Taylor’s frozen field hypothesis is reformulated into a simpler functional form with the frequency variant convection velocity in a zero-dimensional model with the Newtonian fluid, uniform, laminar, axially and one-dimensional pulsatile flow assumption. An experiment with a blood flow simulator is exemplified to demonstrate its usefulness to predict the flow signals from the pressure signals with the Greenfield-Fry model. Moreover, the three-element Windkessel model is compared to emphasize the importance of the physical model derived from the Navier–Stokes equation, such as the Greenfield-Fry model for the pulsating flows.

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Acknowledgements

This work was supported by “Establishment of National Physical Measurement Standards and Improvement of Calibration Measurement Capability” (Grant No. 17011008) as a national project conducted by KRISS in Republic of Korea.

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Authors and Affiliations

  1. Division of Physical Metrology, Center for Fluid Flow and Acoustics, Korea Research Institute of Standards and Science, 267, Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea

    Sejong Chun & Wan-Ho Cho

  2. Division of Physical Metrology, Center for Length, Korea Research Institute of Standards and Science, 267, Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea

    Jonghan Jin

  3. University of Science and Technology, 217, Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea

    Jonghan Jin

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  1. Sejong Chun
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  2. Jonghan Jin
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Correspondence to Wan-Ho Cho.

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Chun, S., Jin, J. & Cho, WH. Construction of the prediction model between pressure and flow rate for pulsating flows based on the Greenfield-Fry model concerning wave dispersion. Exp Fluids 58, 37 (2017). https://doi.org/10.1007/s00348-017-2327-9

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  • DOI: https://doi.org/10.1007/s00348-017-2327-9

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