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CFD modelling of helically coiled tube flocculators for velocity gradient assessment

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Abstract

Helical tubes are used as reactors in applications such as food processing and water and wastewater treatment. In water and wastewater treatment plants, helically coiled tube flocculators (HCTFs) provide efficiency gains over the more traditionally used baffled tanks. Their superior performance has been credited to more favourable velocity gradients (G) but detailed fluid dynamics information on the response of such reactors to varying design and operational conditions is still lacking. In this study, three-dimensional computational fluid dynamics (CFD) simulations were conducted to address this shortcoming. A validated CFD model of HCTFs was applied to assess the impact of varying reactor diameter and operating flow rate on the distributions of G, axial velocity and secondary flow structures. The developed flow region of the reactor was characterised for the occurrence and corresponding response of two cross-section zones, which govern the reactor efficiency. An equation is proposed associating G with a normalised parameter involving the reactor torsion, curvature and Reynolds number, which can be used to support the rational design, optimisation and operation control of HCTFs.

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Abbreviations

a, b :

Regression function coefficients (dimensionless)

d :

Helical tube diameter (m)

D :

Helical tube curvature diameter (m)

G :

Velocity gradient (s−1)

\(\overline{G}\) :

Mean velocity gradient (s−1)

G p :

Local velocity gradient (s−1)

K :

Energy dissipation parameter (dimensionless)

K′ :

Adapted K parameter (dimensionless)

p :

Distance between consecutive passes divided by 2π (m)

P :

Instantaneous static pressure (Pa)

Q :

Flow rate (m3 s−1)

r :

Helical tube radius (m)

R :

Helical tube curvature radius (m)

R 2 :

Determination coefficient in regression analysis (dimensionless)

Re:

Reynolds number (dimensionless)

S M :

Momentum source term (kg m−2 s−2)

u, v, w :

Velocity components in the Cartesian coordinate system (m s−1)

U i :

Component of instantaneous velocity in ith direction (m s−1)

\(\overline{V}\) :

Mean axial velocity (m s−1)

\(\kappa\) :

Helical tube curvature (dimensionless)

\(\lambda\) :

Ratio between curvature and torsion (dimensionless)

\(\mu\) :

Dynamic viscosity of the fluid (Pa s)

\(\rho\) :

Specific mass of the fluid (kg m−3)

\(\tau\) :

Helical tube torsion (dimensionless)

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Authors and Affiliations

  1. Universidade Federal do Espírito Santo, Av. Fernando Ferrari, Vitoria, ES, 29060-970, Brazil

    M. Sartori, D. S. Oliveira, E. C. Teixeira & N. C. Reis Jr.

  2. Universidade Positivo, R. Prof. Pedro V. P. de Souza, 5300, Curitiba, PR, 81280-330, Brazil

    W. B. Rauen

Authors
  1. M. Sartori
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  2. D. S. Oliveira
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  3. E. C. Teixeira
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  4. W. B. Rauen
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  5. N. C. Reis Jr.
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Correspondence to W. B. Rauen.

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Technical Editor: Francisco Ricardo Cunha.

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Sartori, M., Oliveira, D.S., Teixeira, E.C. et al. CFD modelling of helically coiled tube flocculators for velocity gradient assessment. J Braz. Soc. Mech. Sci. Eng. 37, 187–198 (2015). https://doi.org/10.1007/s40430-014-0141-3

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  • DOI: https://doi.org/10.1007/s40430-014-0141-3

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