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Analysis of vortex core generation in pipe flows under different Reynolds number conditions

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Abstract

Pipe flow is a well-documented case widely studied in both theoretical and practical applications. The present work aims at studying the influence of the Reynolds number on turbulent vortex distribution using Large Eddy Simulations (LES). Features such as the mean velocity profiles and root mean squared velocity are first numerically investigated for different fluid properties involving Reynolds numbers ranging from 5,925 to 15,190 in order to verify the law-of-the-wall and turbulence statistics with experimental and DNS data. Once the simulations are validated, the vortex core generation within the flow is studied through a detection algorithm based on the \({\lambda }_{2}\) criterion with two different approaches, first using an absolute threshold value and then using a relative threshold value depending on the turbulent intensity. Results are compared in terms of number of structures and Probability Density Functions for both the size and the radial distributions. Finally, results are compared for one condition with the Q-criterion to assess the results obtained resulting in practically identical volume and radial distributions. These results are deemed to shed light on the vortex formation and location to generate proper inflow boundary conditions to highly resolved simulations in varied engineering applications.

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Data availability

Data will be made available on request.

Code availability

The code used is OpenFOAM v3.0.0.

Abbreviations

DNS:

Direct Numerical Simulations

ECN:

Engine Combustion Network

SGS:

SubGrid Scale

WALE:

Wall Adapting Local Eddy-viscosity

LES:

Large Eddy Simulations

CFL:

Courant-Friedrich-Lewis

PDF:

Probability Density Function

\({u}_{\tau }\) :

Friction velocity

\(R\) :

Pipe radius

\(R{e}_{\tau }\) :

Kármán number

\(R{e}_{D}\) :

Reynolds number

\(L\) :

Pipe length

\(D\) :

Pipe diameter

\({\overline{u} }_{i}\) :

Resolved velocity vector

\(\overline{p }\) :

Modified kinetic pressure

\({C}_{w}\) :

WALE constant

\({\overline{S} }_{ij}\) :

Resolved strain rate tensor

\(S\) :

Symmetric strain rate tensor

\({U}_{b}\) :

Bulk velocity

\({y}^{+}\) :

Non-dimensional distance to the wall

\({r}_{wall}^{+}\) :

Cell size in radial direction on the wall in wall units

\({x}^{+}\) :

Cell size in axial direction in wall units

\(r\) :

Radial position

\({u}_{x}\) :

Axial velocity

\({u}_{x,cl}\) :

Axial velocity on the centerline

\({u}_{x}^{+}\) :

Axial velocity in wall units

\({u}_{x,rms}^{+}\) :

Axial root mean squared velocity in wall units

\(f\) :

Friction factor

\({N}_{s}\) :

Number of structures

\({\tau }_{w}\) :

Wall shear stress

\(\rho\) :

Density

\(\nu\) :

Kinematic viscosity

\({\nu }_{t}\) :

Turbulent viscosity

\(\Delta\) :

Width of the LES filter

\(\Omega\) :

Antisymmetric rate-of-rotation tensor

\(\mu\) :

Dynamic viscosity

\({\omega }_{wall}^{+}\) :

Cell size in azimuthal direction on the wall in wall units

\(\xi\) :

Non-dimensional radial position

\({\xi }^{+}\) :

Non-dimensional radial position in wall units

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Funding

This research has been funded by the Spanish Ministerio de Economía y Competitividad through the project RTI2018-099706-B-100: “Estudio de la atomización primaria mediante simulaciones DNS y técnicas ópticas de muy alta resolución” and the Spanish Ministerio de Ciencia e innovación through the project EQC2018-004605-P: “Estudio del proceso de inyección en atmosferas presurizadas”. The authors thankfully acknowledge the computer resources from the Rigel cluster at UPV (Spain) and the Bebop cluster from the Laboratory Computing Resource Center at Argonne National Laboratory (USA). L.A. González-Montero is partially supported through the contract FPI - Subprograma 2 of the Universitat Politècnica de València.

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  1. CMT-Motores Térmicos, Universitat Politècnica de València, Camino de Vera S/N, 46022, Valencia, Spain

    F. J. Salvador, M. Carreres, P. Quintero & L. A. González-Montero

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  1. F. J. Salvador
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  2. M. Carreres
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  3. P. Quintero
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  4. L. A. González-Montero
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Correspondence to L. A. González-Montero.

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Salvador, F.J., Carreres, M., Quintero, P. et al. Analysis of vortex core generation in pipe flows under different Reynolds number conditions. J Braz. Soc. Mech. Sci. Eng. 43, 297 (2021). https://doi.org/10.1007/s40430-021-03007-3

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