MEEG 481 / MEEG 681
Computer Solution of Engineering Problems
Computer Session 12

Project Presentations: Wednesday, May 23nd, 11:00 AM, 115 Gore
 

Back to Simple Problems - Important Physical Insights

In this session we will demonstrate how to couple physical insights of a problem with FIDAP solutions. The case problem is the study of friction and heat transfer in fully developed flows through tubes and channels.

Cross-flow diemnsion = 1, mean velocity = 1, density=1

conductivity = 1, specific heat = 1, wall heat flux = 1

Viscosity = 1/Re

Laminar flow in a circular pipe - GAMBIT file , FIDAP file

Domain size: D/2 X 20D

Laminar flow in a 2-D channel - FIDAP file

Domain size: D/2 X 20D

Turbulent flow in a circular pipe - Gambit file, FIDAP file

Domain size: D/2 X 100D

 
 

Important physical insights which allow us to check and interpret our laminar flow solutions
 

Laminar flow in a circular pipe Laminar flow in a 2D channel
Pressure gradient (normalized)        -  32/Re    -  12/Re
Surface to volume ratio         2/R = 4  (R is pipe radius)    1/b = 2  (b is half the channel gap)
dT/dx (under unit wall heat flux)           4     2.0

Turbulent flow: pressure drop or the friction factor

Three Reynolds numbers are studied: Re= 10,000, e= 100,000 and Re= 1,000,000

Build a good mesh: What is a good mesh?
Different mesh distribution: 

/  Re = 10 K
edge mesh "edge.3" "edge.2" firstlast ratio1 0.3 intervals 8
/  Re = 100 K
edge mesh "edge.3" "edge.2" firstlast ratio1 5 intervals 20
/  Re = 1000 K
edge mesh "edge.3" "edge.2" firstlast ratio1 69 intervals 20

Check y+ for the wall layer: the good range is 30 to 300.

What should be the size of the computational domain?

D/2 X 100D

 
 


Figure 1: Convergence history


Figure 2: pressure on centerline


Figure 3: K.E. on centerline


Figure 4: Dissipation rate on centerline

How good is the result? 

         
 COMPARISON OF FRICTION FACTOR
===================================

Re              Observation      FIDAP        % error        y+

100              0.64		0.6394        -0.09%

1,000           0.064		0.06403       +0.05%  

10,000         0.0309		0.0328        +6.1%       32 to 55

100,000        0.0178  		0.0190        +6.7%       32 to 45

1,000,000      0.0116  		0.0123        +6.0%       49 to 62


Friction factor: Comparing FIDAP solutions with observations



Comparing profiles at different Reynolds numbers


Mean velocity


Turbulent kinetic energy


Turbulent dissipation rate



Transient laminar pipe flow driven by pressure gradient

D/2 X 1.5D
FIDAP file

Analytical solution in terms of Bessel functions


Velocity Profiles

The message of the course