Cover Page for Precalculations – Individual Portion
Flow Visualization in a Water Channel
Prepared by Professor J. M. Cimbala, Penn State University
Latest revision: 11 January 2012
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Section number:
ME 325._____
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Precalculations
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Precalculations
A.
Laser Velocimeter
(10)
1.
In this lab, freestream velocity will be measured with a laser velocimetry (LV) system (also called a laser Doppler
velocimetry (LDV) system. The main advantage of this technique is that there is no probe of any kind to disturb
the flow – only laser beams enter the flow field. Using the listed references as needed (or some other reference if
preferred), provide in the space below a brief description (including sketches) of how a laser velocimeter system
works.
(4)
2.
The LV system used in this lab is a fiber optic system, which enables some of the optical components (such as the
focusing lens and the photodetector) to be permanently mounted on a portable probe. The probe is in turn
mounted on a traversing system so that it can be easily moved around to measure velocity in different parts of the
flow field. In the space below, list some other advantages of a fiber optic LV system, as compared to a standard
optical LV system:
B.
Reynolds number considerations
(2)
1.
Water at room temperature has a kinematic viscosity of  = 1  10-6 m2/s. As mentioned above, the maximum
freestream speed of our facility is around 1.3 m/s. With these fixed parameters, estimate the diameter of a smooth
sphere required to observe a “drag crisis”. Hint: from Figure 1 of the Background section, a Reynolds number Re d
= Vd/ of around 4  105 is required. Show all your work in the space below:
drequired =
(1)
2.
inches
Is this feasible in our water channel, where the test section is only 6  6 inches square in cross section?
Clearly, we can not observe a natural drag crisis on a smooth sphere in our water channel. Let us now examine
whether we may be able to observe the drag crisis on a golf ball, which has a very rough surface.
(3)
3.
Using the published data of Figure 1, the known maximum speed of our water channel (1.3 m/s), and the known
diameter of a golf ball (d = 1.68 inches), will you be able to observe the drag crisis on a golf ball in our water
channel? Show all your work in the space below:
(3)
4.
According to Figure 1, the drag crisis on a golf ball is not fully complete until Re d  6  104. Using your
knowledge of dimensional analysis and modeling, what would be the required diameter of a geometrically similar
scaled-up golf ball model in order to achieve this Reynolds number in our water channel?
drequired =
inches
While this model is small enough to fit in our 6  6 inch channel, the blockage would be significant. To account
somewhat for blockage effects, a blockage correction is applied. Namely, the velocity of water actually passing
around the sphere must be somewhat greater than the freestream velocity V, in order to satisfy conservation of
mass. Specifically the effective freestream velocity Veffective can be estimated as
Veffective 
VAchannel
Achannel  A
(1)
where Achannel is the cross-sectional area of the water channel (6  6 inches), and A is the projected frontal area of
the sphere (A = d2/4). Next, an effective Reynolds number, Red,effective = Veffectived/, is defined. Clearly, higher
effective Reynolds numbers result from the blockage.
(2)
5.
Estimate the maximum effective Reynolds number achievable with a golf ball (d = 1.68 inches) in our water
channel. (Assume again that the maximum flow speed is V = 1.3 m/s.)
Red,effective, max =
.
Is this Reynolds number high enough for a complete drag crisis to be observed?
(5)
6.
.
Also available in the lab are two yellow-orange balls, with diameters of 2.83 inches (almost identical to that of a
baseball). One of them is smooth, while the other has been artificially roughened. Assuming that the normalized
average roughness height /d on this roughened sphere matches that of a golf ball, should it be possible to observe
a drag crisis with this ball in our water channel? Use the effective Reynolds number, and show all your work in
the space below:
Experimental Objectives
a.
b.
c.
Visualize flow separation on various spheres over a range of Reynolds numbers. Observe a drag crisis if possible.
Visualize flow over a model car, and observe whether or not the flow separates.
Observe flow separation over an airfoil at large angles of attack, and observe the phenomenon of “stall”.