FLOWLAB SOLUTION
9.113 Investigate the differences between inviscid and viscous flow fields by using the
clarky FlowLab template. Set the following conditions: default chord length c =
0.4036 m, flight altitude h = 3,000 m, flight Mach number Ma = 0.3, and angle of attack
α = 0. Run simulations for both inviscid flow and viscous flow with the medium grid
resolution. Plot surface pressure coefficient values, Cp = p/(ρU 2/2), for both the inviscid
and viscous cases and discuss the results. Record the final lift and drag coefficients for
both the inviscid and viscous cases and provide answers to the following questions. (a)
Why is the lift coefficient for the inviscid case larger than for the viscous case? (b) Why
does the inviscid case have a non-zero value for the drag coefficient even though the
viscosity is zero? (c) How and why would the lift and drag coefficient values change for
both inviscid and viscous flow if the angle of attack were increased to α = 10?
Problem Setup
For this problem, the default geometry from FlowLab was used:
The flow was set to either Inviscid or Viscous and the Boundary Condition settings were
altered to achieve the stated flight conditions.
For this problem, the Boundary Condition settings are shown below:
For all simulations, the medium mesh resolution was used for the grid setup. A sample of
this grid is shown in the following figure.
A close-up of the grid around the airfoil is shown in the following figure.
Answer
For the simulations, the default convergence limit was set to 1x10-4. Plots of the residual
history for both the inviscid and viscous cases are shown below.
Inviscid
Viscous
The first part of the problem asks the students to plot the surface pressure coefficient
values for both the inviscid and viscous solutions. These plots are shown below.
Inviscid
Viscous
The surface pressure coefficient data for both simulations was exported through the File
button on the XY Plot and imported into a spreadsheet application. The figure below
shows the comparison of the CP curves for the inviscid and viscous cases.
0.8
0.6
0.4
Cp
0.2
0
-0.25
-0.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Inviscid
Viscous
-0.4
-0.6
-0.8
-1
Chord location (m)
As expected, the surface pressure curves match quite well. The students could discuss
that the pressure acts normal to the surface and the CP curve is dependent on the shape
and orientation of the body. Including viscous effects does not have a significant impact
on the pressure results, at least at these conditions. In general, the lift on an airfoil, which
primarily comes from the pressure distribution, can be reasonably approximated with an
inviscid solution as long as the airfoil is below the stall region.
The students are to record the final lift and drag coefficients for both the inviscid and
viscous cases, which are given below. Note that for the inviscid case, FlowLab does not
include output for the wall shear stress and the skin friction factor, which are shown for
the viscous output.
Inviscid
Viscous
The students are required to answer several questions on the differences between the
above results. For parts a) and b), the student should discuss the issues of aerodynamic
forces from pressure and shear stress. For a streamlined body a majority of the lift comes
from the pressure distribution and a majority of the drag comes from the shear stress, as
discussed in Chapter 9 of the text. However, the pressure distribution can make a minor
contribution to the drag and the shear stress distribution can have a minor impact on the
lift.
Part c) asks how these lift and drag coefficient values would change if the angle of attack
was increased to 10º. The results for this angle of attack are shown below. The
coefficients of lift compare well since this angle of attack is still below the stall. The
inviscid coefficient of drag shows a significant increase since the pressure distribution at
this angle has a much larger contribution in the direction of the drag force.
Inviscid
Viscous