Computational Fluid Dynamics

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Computational Fluid Dynamics

Baimaganbetova Sholpan

Lab Exercice 1. The axysimmetric expansion flow

Question 1. Once the computational domain has been created, display it in your Word report and exit DesignModeler.

a)

b)

Figure 1: Сomputational domain. a) GUI of DesignModeler; b) Graphics view

Question 2. Try generate meshes with various cell sizes. Display the resulting meshes in your Word report with the corresponding number of cells (Elements) and vertices (Nodes) given in the Statistics detail view of the mesh.

a)

b)

Figure 2: Mesh generation. a) The quad mesh generated with Element Size=0.05 m; b) Statistics detail view of the mesh

Question 3. Once the mesh is created and the boundary conditions labeled, display the mesh in your Word report, give the mesh statistics and exit Ansys Meshing.

a)

b)

c)

Figure 3: Mesh generation. a) GUI of Ansys Meshing; b) Zoom of the mesh near the singular expansion; c) Statistics detail view of the mesh

Question 4. We consider the flow of water (с = 998.2 kg/m3, µ = 0.001003 kg/m.s) with inlet velocity uinlet = 1.5 Ч 10-3 m/s. Compute the Reynolds number in the upstream pipe (based on its diameter). Infer the flow regime and the relevant flow simplifications.

Reynolds Number Formula:

where, fluid density, fluid dynamic viscosity, inlet velocity, upstream pipe diameter.

Reynolds number in the upstream pipe:

If Reynolds number is less than 2,300 then it has a laminar flow. On the other hand, if it is more than 4,000 then it indicates turbulent flow. Besides, the values in between 2,300 to 4,000 indicate transient flow that means the fluid flow is transitioning between the laminar and turbulent flow.

Since the Reynolds number in the upstream pipe () is less than 2300, the fluid flow regime will be laminar.

Question 5. Check the mesh. Verify that the domain dimensions are the same as in Fig.3 and report the mesh characteristics on your Word report.

Figure 4: Mesh characteristics (Graphics window and TUI window)

Question 6. Perform a computation of the expansion flow with the convergence threshold for all flow equations. Display the residual monitoring plot in your Word report.

a)

b)

c)

Figure 5: Computation of the expansion flow: a) Task panel; b) TUI window; c) Residual monitoring plot for a laminar flow computation

Question 7. Zoom in the computational domain to observe the recirculation zone of the flow (see Fig. 1). Use the Scale options of the Vectors dialog box if the vectors are too small. Display this plot in your Word report.

a)

b)

c)

Figure 6: Velocity vector visualization: a) all zone of the flow; b-c) recirculation zone of the flow

Question 8. Display the isobaric lines of the flow near the contraction. Export the graphics to your Word report. At what distance downstream of the singularity we get the isobaric lines of the Hagen-Poiseuille flow in a straight pipe?

a)

b)

c)

Figure 7: Isocontour visualization: a) Contours of Static pressure; b) Contours of Total pressure; c) Contours of Total pressure near the expansion

Question 9. Plot the velocity profiles on Sections x = 6.0, 6.5, 7., 7.5 and pressure outlet. (Give them a meaningful name!). Check that the Poiseuille velocity profile is obtained on these sections. Export the graphics to your Word report.

Figure 8: The velocity profiles on Sections x = 6.0, 6.5, 7., 7.5 (in my case: the origin x=2, so Sections x = 9.0, 9.5, 10.0, 10.5) and pressure outlet.

Question 10. Plot the velocity and (static) pressure along the sections of Question 9. Export the graphics to your Word report. Do these profiles correspond to a fully developed Poiseuille flow?

a)

b)

Figure 9: The 1D velocity (a) and static pressure (b) profiles on Sections x = 6.0, 6.5, 7., 7.5 (in my case: the origin x=2, so Sections x = 9.0, 9.5, 10.0, 10.5) and pressure outlet

From the flow symmetry condition, the maximum velocity appears in the center of the pipe, the (static) pressure is constant in the radial direction. Therefore, these profiles correspond to the fully developed Poiseuille flow.

Question 11. Define the new function tau_xy that calculates the shear stress in cylindrical coordinates:

Plot the shear stress profile on the vertical sections of Question 9 and along the upper wall. Export the graphics to your Word report.

cylindrical formula vector visualization

a)

b)

Figure 10: Shear stress profile on the vertical sections of Question 9 (a) and along the upper wall (b)

Question 12. Verify that the mean flow velocity is constant on the sections of Question 9. Report these values in your Word report.

a)

b)

Figure 11: Area-Weighted Average: a)Velocity (a) and Total pressure (b) on the sections of Question 9

Question 13. According to the previous questions, the flow is fully developed between the zones of the pipe. Use Fluent to calculate the total pressure in various sections of the fully developed region, and give the corresponding value of . Compare your results with the empiric relations obtained in a straight pipe:

· Poiseuille formula for laminar flows, :

,

· Blasius formula for turbulent flows, :

Table 1

:

Table 2

Relative measurement error:

Question 14. Calculate the Reynolds number. Deduce the flow regime and the flow equations to solve.

Reynolds Number Formula:

where, fluid density, fluid dynamic viscosity, inlet velocity, upstream pipe diameter.

Reynolds number in the upstream pipe:

If Reynolds number is less than 2,300 then it has a laminar flow. On the other hand, if it is more than 4,000 then it indicates turbulent flow. Besides, the values in between 2,300 to 4,000 indicate transient flow that means the fluid flow is transitioning between the laminar and turbulent flow.

Since the Reynolds number in the upstream pipe () is more than 4000, the fluid flow regime will be turbulent. The flow regime is turbulent, so we use the Standard k-е model. In addition to the averaged Navier-Stokes equations, transport equations for k-е are solved:

Question 15. Starting from rest, compute the solution with residual threshold for all equations. Export the residual history to your Word report.

a)

b)

Figure 12: Residual history

Question 16. Verify that the flow is fully developed at the outlet. Display in the 2D domain the velocity profiles near inlet (several sections in the upstream pipe) and outlet (sections of Question 9). Report these results in your Word report.

a)

b)

Figure 12: 2D domain the velocity profiles (a) near inlet (several sections in the upstream pipe) and (a) outlet (sections of Question 9)

Question 17. From the head losses given by your numerical solution, calculate the headloss coefficient о and compare with the analytical value. The difficulty is to estimate the abscissa x2 where the streamlines do reattach. To estimate x2, you may use the property that the shear stress is zero at a separation point (where flow separates or reattaches, see Fig. 14): the value of x2 is then obtain by plotting the computed shear stress along the upper wall (cf. Question 11)

Figure 13: Shear stress

When we look at the Figure 13, shear stress equals to zero at x = 3.8. So

Table 3

:

Velocity at .

Total pressure at

Relative measurement error:

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