Overview

Test Case

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

The domain consists of a box (the channel) with an inflow at prescribed velocity and an outflow at prescribed pressure. The lateral sides of the boundary (the channel walls) and the cylinder feature a non-slip condition. The domain size and relevant quantities are shown in Figure 151. As you can see, the cylinder location is not perfectly symmetrical with respect to the channel height in the y direction. For this test case, all units of measure are consistent (length = m, time = s, mass = kg, force = N, pressure = Pa).

Figure 151: Problem Sketch: Domain Geometry and Main Dimensions

Analysis Assumptions and Modeling Notes

Two meshing boxes have been used to selectively refine the mesh around the cylinder and its wake (see Figure 152).

Figure 152: Meshing Boxes Layout for Mesh Refinement

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

(20)

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

(21)

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

(22)

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

In this test, values of drag, and lift coefficients (respectively, and ) are compared to the same values available in the reference.

The nondimensional coefficients are evaluated using the following relationship:

(23)

where is the relative dimensional force on the cylinder surface. Note that the drag force is the resultant force on the cylinder in the asymptotic flow direction (x direction), the 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 rear points of the cylinder (, , ) = (0.45, 0.2, 0.205) and (, , ) = (0.55, 0.2, 0.205), respectively.

A picture of the domain's mesh is shown in Figure 153, while Figure 154 shows a detail of the mesh refinement around the cylinder and the channel's walls.

Figure 153: Problem Setup

Figure 154: Mesh Detail

Results Comparison

Figure 155 shows the flow velocity contours on the channels' outer surfaces and on a transparent section in the x-y plane for z = 0.205. You can see the symmetric laminar steady separation downstream of the cylinder as well as the boundary layer developing along the channel's walls. Likewise, Figure 156 shows the pressure contours.

Figure 155: Fluid Velocity Contours

Figure 156: Fluid Pressure Contours

The results table shows a comparison of 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 in the target column is the average between the upper and lower bounds for each variable.

Result	Target	LS-DYNA	Error (%)
	6.1500	6.1244	1.41%
	0.0090	0.0088	1.57%
	0.1750	0.17004	2.83%