MECH5304 – Assignment 1 (Submit by February 12th, 2013, maximum 4pages)

Using CFX (or any other package available to you), simulate a three-dimensional air flow ina straight pipe section (212.75 mm length) followed by a 90o bend and another straight pipesection (85.1 mm length). The pipe has an 8.51 mm internal diameter and the bend has a47.656 mm radius of curvature. Use CFX or ICEM-CFD (or any software available to you)for meshing with biased accumulation of nodes towards the wall (inflation) and adequatebody spacing (start with 1 mm). Use air at 25 Celsius, one atm reference pressure, no heattransfer model and a k-ε turbulence model.

The boundary conditions are:

• Inlet conditions: top hat profile (constant normal velocity distribution equivalent toReynolds number, Re=10,000)

• Wall boundaries: no slip, default 2D region

• Outlet conditions: zero gauge average static pressure

Figure 1: Bend Geometry.

From the simulation results:

a) Determine the pressure drop, ∆p, through the pipe-bend-pipe section and compare yourresults with empirical estimates. Remember that the outlet gauge pressure was set to zero.

For a straight pipe, the empirically-defined solution to the problem is:

∆p = fL

DρU2b

2(1)

2

where the Blasius friction factor, f = 0.316/Re1/4 (for turb. flows in smooth pipes).

For the bend portion, the empirically-defined solution to the problem is::

∆p = KρU2b

2(2)

with the resistance coefficient estimated to be K = 0.4.

b) Is the pipe flow fully developed when it enters the 90o bend?

For turbulent flow, the development length is defined as Le/D ≈ 4.4Re1/6, where Re =ρUbD/µ = UbD/ν is the Reynolds number. Here ρ is the density, Ub is the bulk velocity, Dis the pipe diameter, µ is the air viscosity and ν is the air kinematic viscosity.

For the fully developed radial distribution, we have

u+ = y+ (for y+ < 5) (3)

u+ = −3.05 + 5.0ln(y+) (for 5 < y+ < 30)

u+ = 5.5 + 2.5ln(y+) (for y+ > 30)

where u+ = u/u∗ is the dimensionless axial velocity, u∗ = uavg(0.03955Re−0.25)0.5 is thefriction velocity, and y+ = yu∗/ν is the dimensionless distance from the wall.

At the estimated development length, does the velocity profile match the above-defineddistribution? Export the velocity profile from CFX and plot against the above distributionin Excel, Tecplot, Matlab, etc.

c) Describe the flow after the 90o bend.

d) Verify the simulation against another turbulence model (for example the the k-ω shearstress transport model, SST).

e) Change the inlet Reynolds number to Re=1,000. Describe the flow.

Note: 1) Assignments should have: course #, date, student name and ID # (all on thefirst page), abstract, introduction (with background, literature search when necessary andstatement of the problem), methods (with equations, refer to the CFX theory or equivalent),results and discussion (with verification and validation), conclusions and references.