Overview

Test Case

This test case reproduces a two-dimensional, unsteady, incompressible laminar flow around a cylinder inside a channel. The purpose is to validate the maximum drag and lift force coefficients and the pressure difference between the front and end points of the cylinder.

The domain consists of a rectangular box (the channel) with an inflow of prescribed velocity, an outflow of prescribed pressure, and the two remaining sides of the boundary (the channel's walls) with non-slip conditions. The cylinder also features a non-slip condition. The domain size and relevant quantities are shown in Figure 139. The cylinder location, as you can see, is not perfectly symmetrical with respect to the channel height. Two meshing boxes have been used to selectively refine the mesh around the cylinder and its wake.

For this test case, all units of measure are consistent (length = m, time = s, mass = kg, force = N, pressure = Pa).

Figure 139: Problem Sketch: Domain geometry and main dimensions

Analysis Assumptions and Modeling Notes

The behavior of the flow is characterized by the Reynolds number:

(13)

where ρ is the fluid's density, D is the characteristic length of the problem (that is, the cylinder diameter), and μ is the dynamic viscosity of the flow. is the flow mean velocity field at the channel's inlet:

(14)

where U is the (unsteady) velocity field in the channel's axial direction which is imposed at the inlet (x = 0). The complete inflow velocity field relation is:

(15)

Where is the maximum inflow velocity in the channel's axial direction. This yields a maximum Reynolds number .

In this study, the time interval is . The values of drag, and lift coefficients (respectively, and ) will be plotted, and their maximum value ( and ) will be compared to the values in the reference.

Note that the nondimensional coefficients are evaluated using the following relation:

(16)

where is the maximum of for the considered time interval and is the relative dimensional force on the cylinder surface. It's important to understand that the drag force is the resultant force on the cylinder in the asymptotic flow direction (x direction), lift force is the resultant force on the cylinder orthogonal to the asymptotic flow direction (y direction), and both forces are the sum of pressure and viscous forces.

As a further reference value, the pressure difference is defined, with the front and end points of the cylinder, and , respectively. Value will be compared to the same value in the reference.

A picture of the domain's mesh is shown in Figure 140, while Figure 141 shows a detail of the mesh refinement around the cylinder and the channel's walls.

Figure 140: Problem setup in LS-DYNA

Figure 141: Mesh detail

Results Comparison

Figure 142 shows the flow velocity contour in the channel's axial direction at different times. The development of unsteady vortices in the cylinder wake is evident.

Figure 142: Fluid velocity contour (channel axial direction) for different times

Figure 143 and Figure 144 show, respectively, the drag and lift coefficients over time. The table below shows a comparison of the maximum drag and lift coefficients ( and ) and pressure difference between the present analysis and the reference. The reference proposes a comparison of the same values calculated with a variety of different numerical methods. The value shown below in the target column for each variable is the average between its upper and lower bounds.

Figure 143: Drag coefficient versus time

Figure 144: Lift coefficient versus time

Result	Target	LS-DYNA	Error (%)
	2.9500	2.9399	0,34%
	0.4800	0.4760	0.83%
	- 0.1100	-0.1118	1.63%