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Pressure and shear stress analysis in a normal triangular tube bundle based on experimental flow velocity field

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Abstract

This paper presents the experimental vector velocity field obtained through the spatial filter velocimetry technique in a normal triangular tube bundle test section with tubes of 20 mm O.D. and transverse pitch of 25.2 mm. The experiments were conducted for water flows and Reynolds numbers ranging from 447 to 1842. The pressure field was estimated based on the velocity results by solving the Poisson equation. The shear stress around the tubes was analyzed calculating the viscous and Reynolds stresses. The results for turbulence strength and flow vorticity were calculated and discussed. All the analyses were performed using a second-order finite difference scheme to estimate the partial derivatives. The results indicate that the spatial filter velocimetry technique provides accurate velocity data and is suitable to be applied to complex geometries. In addition, the obtained velocity fields show that the SFV technique is capable of capturing asymmetric flow distributions, which switch from time to time, indicating a suitable spatial and temporal resolution for the experimental conditions evaluated in the present study.

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Abbreviations

\(\bar{P}\) :

Average pressure (Pa)

x :

Relative to x axis (m)

y :

Relative to y axis (m)

z :

Relative to z axis (m)

V :

Actual velocity (m/s)

\(\bar{V}\) :

Average velocity (m/s)

v :

Velocity fluctuation (m/s)

u rms :

Turbulence strength (m/s)

I :

Image intensity (–)

F :

Filter (–)

t :

Time (s)

f :

Frequency (Hz)

L :

Spacing between each strip of the spatial filter (μm)

Q :

Volumetric flow rate (l/min)

d :

Tube diameter

j :

Superficial velocity (m/s)

Re:

Reynolds number based on superficial velocity and tube diameter (= j.d/ν) (–)

\(\rho\) :

Density (kg/m3)

\(\tau\) :

Shear stress (Pa)

\(\mu\) :

Dynamic viscosity (Pa.s)

\(\nu\) :

Kinetic viscosity (m2/s)

\(\omega\) :

Vorticity (1/s)

ε :

Relative error (–)

i :

Index notation

j :

Index notation

l:

Relative to liquid phase

D:

Dominant frequency

sf:

Spatial filter applied

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Acknowledgements

The authors gratefully acknowledge FAPESP (State of São Paulo research foundation agency, Brazil) for the doctorate scholarship (Contract Number 2016/20200-2) of the first author, Douglas Martins Rocha, and for the internship at Kobe University (Contract Number 2015/00854-5) of the second author, Fabio Toshio Kanizawa. The authors also appreciate the supports by FAPERJ, Grant Number FAPERJ E-26/203.261/2017 (234197) and CNPq, Grant Number 305673/2017-3. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

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Authors and Affiliations

  1. Heat Transfer Research Group, Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, São Carlos, SP, Brazil

    Douglas Martins Rocha & Gherhardt Ribatski

  2. Department of Mechanical Engineering, School of Engineering, Universidade Federal Fluminense, Niterói, RJ, Brazil

    Fabio Toshio Kanizawa

  3. Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan

    Kosuke Hayashi & Akio Tomiyama

  4. Faculty of Societal Safety Science, Kansai University, 7-1 Hakubai, Takatsuki, Osaka, 569-1098, Japan

    Shigeo Hosokawa

Authors
  1. Douglas Martins Rocha
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  2. Fabio Toshio Kanizawa
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  3. Kosuke Hayashi
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  4. Shigeo Hosokawa
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  6. Gherhardt Ribatski
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Correspondence to Douglas Martins Rocha.

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Technical Editor: William Wolf, Ph.D.

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Rocha, D.M., Kanizawa, F.T., Hayashi, K. et al. Pressure and shear stress analysis in a normal triangular tube bundle based on experimental flow velocity field. J Braz. Soc. Mech. Sci. Eng. 42, 201 (2020). https://doi.org/10.1007/s40430-020-02293-7

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