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 :
- In the Model section, right-click Definition and choose Model Coupling>General Project.
- Go to General Projection settings, select the domain as 1 (all domain) in the Selection section.
- Write shown parameters : Source map x-expression: z ,Source map y-expression: r, Destination Map x-expression: z
- x-expression in Source Map represents the axes that is the direction of integration (interval)
- y-expression in Source Map represents the lines that will be integrated
- x-expression in Destination Map represents the axes that the results of integration will take place
- Right-click Result section, choose 1D Plot Group.
- Right-click 1D Plot Group choose Line Graph
- Go to Settings of the 1D Plot Group
- Select the Boundary 4 (wall of pipe) for Selection location
- 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 -)
- Click the Description box and write Average Velocity vs z
- Click the Coloring and Style section and Width edit field type, 4
- Click Plot button
- Click the 1D Plot Groupand go to Settings window
- Click Manual axis limits box in the Axis section
- Type the suitable numbers in the order
- 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
- Right-click Result section, choose 1D Plot Group.
- Right-click new 1D Plot Group choose Line Graph
- Go to Settings of the new 1D Plot Group
- Select the Boundary 4 (wall of pipe) for Selection location
- 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)
- Click the Description box and write Friction factor (from dw/dr) vs z
- Click the Coloring and Style section and Width edit field type, 4
- Click Plot button
- Click the 1D Plot Group and go to Settings window
- Click Manual axis limits box in the Axis section
- Type the suitable numbers in the order
- Click Plot button