# Oscillating Laminar Flow Around a Circular Cylinder

In this application, AcuSolve is used to simulate two dimensional, laminar flow over a cylinder to predict separation of flow from the cylinder surface and the flow in the wake area. AcuSolve results are compared with experimental results as described in Tritton (1959). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with unsteady oscillating vortex streets.

## Problem Description

The problem consists of a cylinder located in a rectangular domain, as shown in the following image, which is not drawn to scale. A fluid enters the domain with a low velocity (v) of 0.5 m/s. The diameter (D) of the cylinder is 20 cm. The domain extends 10 X D upstream of the cylinder center, 5D above and below the cylinder center, and 40D downstream of the cylinder center. The density of the working fluid is 1 kg/m3 and the viscosity is 0.001 kg/m-s. The Reynolds number for this problem is 100.
The simulation was performed as a two dimensional problem by constructing a volume mesh that contains a single layer of elements in the extruded direction, normal to the flow plane, and by imposing symmetry boundary conditions on the extruded planes.

## AcuSolve Results

The simulation was run as transient for a time record sufficient to ensure that the vortex shedding in the wake reached a stabilized oscillation frequency. The AcuSolve solution shows an unsteady, oscillating flow field with flow around the cylinder separating from the cylinder surface. A wake area is developed downstream of the cylinder with alternating vortices shedding at a regular frequency from the top and bottom of the cylinder surface. This results in oscillating lift forces that act on the cylinder as shown in the following images.
The Strouhal number for this simulation, a dimensionless number describing oscillating flows, is used to validate AcuSolve results. The experimental Strouhal number for this problem is given by(1)
$St=\frac{\omega *L}{v}=0.165$

where ω is the dominant frequency of oscillations, L is the diameter of the cylinder, and v is the flow velocity.

The peak frequency of the oscillating lift force was computed by transforming the time dependent data into frequency space with a Fourier transform. From the Fourier transform, the AcuSolve-based Strouhal number was calculated. The table below shows the comparison of the Strouhal number provided by the AcuSolve prediction and the measurement given by Tritton (1959).
Table 1.
Experimental AcuSolve
Strouhal number 0.165 0.173

## Summary

In this application, two dimensional flow over a cylinder is achieved by enforcing symmetry conditions on the front and back surfaces of the flow domain. The laminar, unsteady simulation shows the flow separation that leads to alternating vortex shedding. Frequency of the lift force acting on the cylinder is calculated to evaluate the Strouhal number. The AcuSolve solution compares well with results reported by Tritton (1959), differing slightly from the experimental results. In this application, AcuSolve demonstrates the ability to accurately predict oscillating laminar flow around a circular cylinder.

## Simulation Settings for Oscillating Laminar Flow Around a Circular Cylinder

HyperWorks CFD database file: <your working directory>\cylinder_laminar\cylinder_laminar.hm

Global

• Problem Description
• Analysis type - Transient
• Turbulence equation - Laminar
• Auto Solution Strategy
• Analysis type - Transient
• Max time - 600 sec
• Initial time increment - 0.1 sec
• Material Model
• Fluid
• Density - 1.0 kg/m3
• Viscosity - 1.0e-3 kg/m-sec

Model

• Volumes
• Volume
• Element Set
• Material model - Fluid
• Surfaces
• Back
• Simple Boundary Condition
• Type - Symmetry
• Base
• Simple Boundary Condition
• Type - Slip
• Front
• Simple Boundary Condition
• Type - Symmetry
• Inflow
• Simple Boundary Condition
• Type - Inflow
• Inflow Type - Average velocity
• Average Velocity - 0.5 m/sec
• Outflow
• Simple Boundary Condition
• Type - Outflow
• Top
• Simple Boundary Condition
• Type - Slip

## References

D.J. Tritton. "Experiments on the Flow around a Circular Cylinder at Low Reynolds Number". Journal of Fluid Mech. 6(04):547-567. 1959