*Look at file for easy viewing*
Assignment: Using the supplied excel sheet you will complete the lab journal section, compute thecalculations and create the graphs outlined in the Problem section below. Submit your excelspreadsheet and dimensional analysis work, along with a brief write-up - 1 page or less - ofyour findings and the meaning of the pi groups found.
Background:
Determining the shedding frequency at the model scale is useful in understanding the dynamicsat play for actual systems. Vortices can create lift-induced drag on an aircraft and createvibrations against skyscrapers that can possibly cause the failure of the structure. Vortices alsocause vibrations as water flows past blunt obstructions. This creates flow separation and aboundary layer to form with strong flow oscillations in the wake area behind the body. Theunsteady separation of flow is known as a Karman vortex street.
The following gives a brief overview of the model setup used to create a Karman vortex street.
Model Objectives: Under certain conditions, the flow of fluid past a circular cylinder will produce a Karmanvortex street behind the cylinder. As shown in the figure below, this vortex street consists of aset of vortices (swirls) that are shed alternately from opposite sides of the cylinder and thenswept downstream with the fluid. The purpose of this experiment is to determine the sheddingfrequency, cycles (vortices) per second, of these vortices as a function of the pi groups formedusing dimensionless analysis.
Equipment that would be used to set up the model: Water channel with an adjustable flowrate; flow meter; set of four different diameter cylinders;dye injection system; stopwatch.
Theoretical Experimental Procedure: Insert a cylinder of diameter D into the holder on the bottom of the water channel. Adjust thecontrol valve and the downstream gate on the channel to produce the desired flowrate, Q, andvelocity, V. Make sure that the flow-straightening screens (not shown in the figure) are in placeto reduce unwanted turbulence in the flowing water. Measure the width, b, of the channel andthe depth, y, of the water in the channel so that the water velocity in the channel V = Q/(b*y),can be determined. Carefully adjust the control valve on the dye injection system to inject a thinstream of dye slightly upstream of the cylinder. By viewing down onto the top of the waterchannel, observe the vortex shedding and measure the time, t, that it takes for N vortices to beshed from the cylinder. For a given flowrate, repeat the experiment for different diametercylinders. Repeat the experiment using different flowrates and depths of the water in thechannel. Measure the water temperature so that the viscosity can be looked up in Table 1.4.
(Refer to file for side/top view pictures)
Pilot vs model: Length of the model is scaled by 5 for the pilot. Use the fluid properties of water for the modeland fluid properties of sea water for the pilot.
Hints:
Hint 1: We want to study system behavior by looking at dimensionless numbers involving V and w. Because V is included, Q, b and y should no longer be included in the dimensionless numbers. Similarly, because w is included, N and t should not be included.
Hint 2: the dimensionless numbers you will find should match some of the well knowndimensionless numbers we introduced in the course
Hint 3: watch out for the difference between dynamic and kinematic viscosity and their units
Problem:
1. Use Buckingham Pi Theorem and the details provided above to determine thedimensionless pi groups you will use for the model experiment.
2. Using the virtual lab excel sheet to simulate the experimental procedure, alter thediameter, D, using the following values to be tested in the model system: [0.02 0.03140.0421 0.0518] (ft). Calculate a minimum of 4 trials for each diameter varying Q and/or y and record the results to the lab journal section.
3. For each trial:
a. Calculate the vortex shedding frequency, w = N/t
b. Calculate the pi groups
c. On a single graph, plot the vortex shedding frequency, w as ordinates and watervelocity, V, as abscissas. Plot each of the four cylinders as their own series.
d. On another graph, plot one dimensionless number, pi1, versus the other, pi2, as ascatter plot. 4. Based on the D values given above what are the diameter values associated with thepilot system?
5. Given a real velocity range of 1-6.5 ft/s in the pilot system, what should be the range ofvelocities to be tested in the model system?
6. For a model velocity of 0.14 ft/s and D of 0.045 ft, calculate your dimensionless number,read off the figure you created in 2(c) and estimate the model w. What will be the corresponding w of the pilot system?
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