Five different mesh is chosen as follows

发现mesh1,mesh2的结果与mesh3~mesh5有明显差别，而mesh3和mesh4,mesh5相差很小。且mesh3的网格尺寸较少，综合计算精度和计算效率，采用mesh3的网格结构。Mesh5的提高，已经收益不明显，而且可能是网格过细，导致的计算误差。

下图是y=-0.9位置的压力梯度分布图，之所以用y=-0.9这个位置，是因为最早用y=-1时，看velocity图时，纵轴一直是0.估计有附面层的影响，所以调整成了y=-0.9。我刚试验过，用y=-1的pressure gradient图也是可以的。

得到压力云图，It can be seen that the pressure tends to decrease from inlet to a minimum value just before the step and then increase to a constant value on the rest of the region.The pressure drop rate could be directly effected by the sudden expansion of the cross-section at the step. After the pressure drops to zero, a reversible pressure rise can be noticed near the step due to Bernouli effect, associated with the decrease in a mean velocity due to the expansion.

The velocity contour shows that the velocity begans to decrese after the step. The flow has been developed completely. The velocity near the step region is almost zero. The air velocity is evenly distributed at the inlet of the domain. As the flow develops inside the domain, uneven velocity gradient forms with lower velocity near wall due to the fluid viscosity and higher velocity at the center. Since the flow distribution remains unchanged at the region before the step, the flow is thus taken to be fully developed and the length between the inlet and the step is deemed to be sufficient. Due to the sudden expansion of the cross-section, the flow separates at the step and continues moving forward due to inertia. The flow gradually reattached to the bottom wall before existing the computational domain.

As the flow separates at the step, the recirculation region grows as indicated by the reciculation zone illustrated below using the velocity streamlines.

This is a 3D streamline which starts from the inlet and symmetry. If the symmetry is not chosen, the recirculation region could not be observed.Why?难道这是在周围引射过来的气流？Is this the airflow that is emitted around?

It is a bit different from the book that I must choose a height just a little above the bottom surface so that I could get the figure same to the book.

e1.2.2.3 CFD Results and Discussion

❏ Tasks to be carried out

For Reynolds number of 100,

a. run the simulations using five different sets of mesh and obtain the location of the flow reattachment point behind to step for each case;

b. conduct mesh independence test and determine the sensitivity of the mesh fineness to the location of the reattachment point;

c. discuss this change in reattachment location with the mesh refinement, and choose the appropriate mesh for the next stage of the investigation;

d. use the selected mesh to continue and obtain the velocity and pressure contours and the velocity vectors; (Ensure that the developed flow is present at the outlet and/or at least a close-to-developed flow is present prior to the step.

e. discuss any observed flow characteristics using the physical parameters.For Reynolds number of 50, 150 and 200,

f. repeat the simulations for Re=50, 150, and 200 using the selected mesh;

g. discuss the relationship between Reynolds numbers and reattachment points, using physical parameters to explain the phenomenon. Provide your own conclusions on this observation.

Three Reynolds number from 50,100 and 200 are listed below. It can be oberved that the attachment point becomes farther as the Reynolds number increases.

The relation between the pressure gradient and the x direction length is below.

❏ How to identify the reattachment point?

By Using fitting function.

Exploratory questions:

❏ Change the ‘Top’ boundary condition from ‘Non-slip’ wall to ‘Specifiedshear’(maintaining shear stresses of X and Y components at 0 Pa) for the Reynolds number Re=50 case and solve for the solution. Discuss the

results obtained there in relation to the results from the previous ‘Non-slip’ boundary-condition model of same Reynolds number Re=50 case.

Solution： After changing the Top boundary condition, the condition at specifiedshear shows that recirculation region begins to enlarge obviously. The velocity at the center of the recirculation region is nearly zero, and the reattachment point is twice as long as the original case. The high velocity region at section begins to move to the top instead of the middle due to the no frictions at the top wall.

From next figure ,we can conclude that the velocity profile has changed totally with the maximum at Top wall for the ‘Specifiedshear’ case.