COMSOL Multiphysics

COMSOL 

"Calculation of average velocity in flow direction in the in pipe with using general projection tool of COMSOL Multiphysics"

Average velocity

The geometry of pipe is constructed in 2D-axisymetrix 

Calculation of average velocity :

1.  In the Model section, right-click Definition and choose Model Coupling>General Project.
2. Go to General Projection settings, select the domain as 1 (all domain) in the Selection section.
3. Write shown parameters : Source map x-expression: z ,Source map y-expression: r,  Destination Map x-expression: z
4. x-expression in Source Map represents the axes that is the direction of integration (interval)
5. y-expression in Source Map represents the lines that will be integrated
6. x-expression in Destination Map represents the axes that the results of integration will take place
7. Right-click Result section, choose 1D Plot Group.
8. Right-click 1D Plot Group choose Line Graph
9. Go to Settings of the 1D Plot Group
10. Select the Boundary 4 (wall of pipe) for Selection location
11. In the Expression edit field, type -2*genproj1(w*r) /0.01^2   (Average velocity in z direction is calculated with this formula where w is the velocity in z direction and R=0.01) --  (The velocity is in –z direction therefore to make the average velocity positive, the equation is multiplied with -)
12. Click the Description box and write Average Velocity vs z
13. Click the Coloring and Style section and Width edit field type, 4 
14. Click Plot button 
15. Click the 1D Plot Groupand go to Settings window
16. Click Manual axis limits box in the Axis section
17. Type the suitable numbers in the order
18. Click Plot button 

"Calculation of friction factor in flow direction in the in pipe with using general projection tool of COMSOL Multiphysics"

Friction factor from derivation of velocity

1. Right-click Result section, choose 1D Plot Group. 
2. Right-click new 1D Plot Group choose Line Graph
3. Go to Settings of the new 1D Plot Group 
4. Select the Boundary 4 (wall of pipe) for Selection location
5. In the Expression edit field, type 8*spf.mu*wr/spf.rho/(2*genproj1(w*r) /0.01^2)^2  (Friction factor formula (f) in z direction the below formula is used where wr is dw/dr)(The velocity is in –z direction therefore to make the friction factor positive, the equation is multiplied with -) ---  f=[−8*mu*(dV/dr)_r=R ] / [ rho*(V_mean)^2]   (Friction factor for laminar flow taken from Bergman T.L., Lavine A.S., Incropera F.P., DeWitt D.P. (2007) “Fundamentals of Heat and Mass Transfer” John Wiley)
6. Click the Description box and write Friction factor (from dw/dr) vs z
7. Click the Coloring and Style section and Width edit field type, 4 
8. Click Plot button 
9. Click the 1D Plot Group and go to Settings window
10. Click Manual axis limits box in the Axis section 
11. Type the suitable numbers in the order
12. Click Plot button