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A numerical investigation of wake and mixing layer interactions of flow past a square cylinder

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Abstract

The aim of the present study is to simulate and analyze the interaction of two dimensional flow past a square cylinder in a laminar regime with an upstream mixing layer developed by an axis symmetrical horizontal splitter plate. The mixing layer is generated upstream of the square cylinder by mixing two uniform streams of fluid with different velocities above and below the splitter plate. A range of upstream domain lengths, distances between the splitter plate and the square cylinder, and upstream velocity ratios between the two streams of fluid are analyzed. Unconfined flow over a square cylinder placed in uniform upstream flow is initially analyzed as it plays a crucial role in understanding the properties of the wake. The results are compared with the existing literature to validate the code developed and they are found to be in very good agreement. It is observed from the present study that at smaller velocity ratios, the vortices shed into the wake consist of both clockwise and anticlockwise moment vortices. As velocity ratio is increased only clockwise moment vortices are shed downstream and anticlockwise vortices are shed as Kelvin–Helmholtz instabilities. In all simulations undertaken the same phenomena is observed independent of the upstream Reynolds number, indicating that velocity ratio is a primary parameter influencing the flow. Different instability modes were observed and they were highly dependent on the upstream velocity ratio.

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Abbreviations

a:

Side of the square cylinder

A:

Dimensional side of the square cylinder (m)

CD :

Drag coefficient

CL :

Lift coefficient

f:

Dimensional frequency (Hz)

FD :

Dimensional drag force (N)

Ff :

Flux through face f of the control volume

FL :

Dimensional lift force (N)

H:

Height of the domain

L:

Length of the domain

\({\hat{\text{n}}}\) :

Outward normal of the surface S

p:

Non dimensional pressure

r:

Ratio of Reynolds number above and below the splitter plate

Re:

Reynolds number

S:

Surface onto the control volume

St:

Strouhal number

spl:

Length of the flat plate

t:

Non-dimensional time

ul:

Upstream length of the physical domain

dl:

Downstream length of the physical domain

dt:

Non dimensional time step

u:

Non-dimensional velocity in X direction below the splitter plate

U:

Free stream velocity in X direction at the inlet below the splitter plate (m/s)

v:

Non-dimensional velocity in Y direction

\(\forall\) :

Control volume

x:

Non-dimensional Eulerian coordinates in horizontal direction

y:

Non-dimensional Eulerian coordinates in vertical direction

ρ:

Fluid density (kg/m3)

μ:

Fluid viscosity [kg/(m s)]

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Authors and Affiliations

  1. Fluid Mechanics Department, Technical University of Catalunya, 08222, Terrassa, Barcelona, Spain

    Aditya Mushyam & Josep M. Bergada

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  1. Aditya Mushyam
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  2. Josep M. Bergada
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Correspondence to Josep M. Bergada.

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Mushyam, A., Bergada, J.M. A numerical investigation of wake and mixing layer interactions of flow past a square cylinder. Meccanica 52, 107–123 (2017). https://doi.org/10.1007/s11012-016-0400-8

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