EXPERIMENT NO. 4

ELEMENTARY STUDY OF LASER DOPPLER ANEMOMETRY

Submitted by: CAROL GEARY

AEROSPACE AND OCEAN ENGINEERING DEPARTMENT VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY

BLACKSBURG, VIRGINIA 20 MARCH, 2014

EXPERIMENT PERFORMED 5 MARCH, 2014 LAB INSTRUCTOR: ALEX FRIEDMAN

Honor Pledge:

By electronically submitting this report I pledge that I have neither given nor received unauthorized assistance on this assignment.

905545831 3/20/14

1: INTRODUCTION The aims of this study are:

1) To determine the 2-D shape and form of the circular cylinder wake at the center span at a fixed velocity.

2) To examine the flow over the front of the cylinder at the center-span at a set velocity and compare to ideal flow theory.

These objectives were achieved by performing a series experiments measuring velocity vectors, and analysis of a cylinder facing a flow at a set velocity and laser Doppler anemometry. The general background to laser Doppler anemometry is summarized below.

**1.1 Basic Principles of the laser Doppler anemometry **

In general the most common flow velocity measurement device is he static probe. static tubes are rugged and inexpensive and give accurate velocity measurements. But, Pitot-static probes cannot measure velocity fluctuations that goes with the turbulence or unsteady flows. A laser Doppler anemometer measures the velocity at a point in flow using laser beams. The components of velocity, measures the component in a series of bursts. The laser does not disturb the flow and is used in flows of unknown directions to give accurate measurements in unsteady turbulent flows. This particular laser Doppler anemometer is a dual beam that uses two beams of equal intensity. These are generated from a single laser and split into three beams using a beam splitter these beams are focused using a lens this lens crosses and changes the direction of the beams causing them to cross at the particular point where they are focused.

The crossing of the two light beams creates a set of equally spaced fringes. A measurement is made when a particle is passing between these fringes. The light reflected off of the particle is

detected by the fringes when the light fluctuates. That frequency of the fluctuation is proportional to the velocity of the particle.

The most prevalent source of error associated with the Laser Doppler anemometers is particle averaging bias where when the flow velocity is high, more particles pass through the volume in a given time when it is low, when taking the average of the velocity samples there will be an estimate of the mean velocity that is too high.

**1.2 Ideal Flow Model past a Circular Cylinder **

Ideal flow past a circular cylinder can be modeled by irrotational incompressible flow without circulation (Hallauer and Devenport, 2006). This flow is generated by adding a uniform flow that is orientated in the positive x direction to a doublet at an origin directed in the negative x direction. The velocity distribution predicted by the theory is given in

Cartesian coordinates centered on cylinder axis in the equations below.

= 1 − _{(} _{)} (1)

= − _{(} _{)} (2)
Where u (m/s) is the velocity in the x direction, u (m/s) is the velocity in the y direction,
(m/s) is the freestream velocity of the flow and R is the cylinder radius (D/2 with units of
meters).These equations give the foundation for an ideal flow over a cylinder.

In the following study these theories are applied to estimate and calculate the flow across a cylinder. Uncertainty analysis is used to determine how accurate the flow velocity across the cylinder compares to idealized flow velocity. The following section includes a detailed description of the water tunnel, Laser Doppler Anemometry system, and the procedure. The results are presented in section 3 along with uncertainty estimates.

2. APPARATUS AND TECHNIQUES

**2.1 Water Tunnel and Cylinder **

A 6”x6” (Hallauer and Devenport, 2006) cross section water tunnel was used and built by Engineering Laboratory and Design Inc. that has a vertical closed circuit arrangement. The normal flow is propelled by a pump that delivers 280 gallons per minute. The water flows

through honeycombed screens to help make the flow more uniform and reduce turbulence levels. The flow speed varies between 0 to .52 m/s. The general turbulence intensity is defined as the root mean square of the fluctuating component of velocity signal. The circular cylinder

.018542±.0005 meters in diameter mounted to the approximate mid height of the test section. It is manufactured from brass and spans the test section width.

**2.2 The Laser Doppler Anemometer System **

We used a three-beam, two-component LDA system to measure flow velocities. The system is designed and build by the Aerospace and Ocean Engineering Department here at Virginia Tech (Figure 1). The top of the cart contains the optical table that splits a laser beam into equal intensity using mirrors and laser beam splitter optics. The LDA probe positions the three beams and focuses them using a sending lens so the beams cross at a single microscopic volume, that crossing point is called the measurement volume which is located approximately 300mm from the sending lens (Hallauer and Devenport, 2006). The light scattered by particles in the water passing through the measurement volume is collected by the sending lens. These light signals are focused towards another optical fiber that carries the light to the photomultiplier tube (PMT). Signals from the PMT are amplified and sent to the computer and processed by LDA data acquisition software (developed by Applied University Research Inc), the software detects the valid bursts and is interfaced with LabView for data processing. The overall probe (figure 2)

is mounted on a three axis, motorized BiSlide transverse (model no. MN10-0150-E01-21) has a 2-phase stepping motor that advances 0.00635mm per step with a range of motion of

approximate 43.18 cm in each of the three coordinate directionsThe equipment on the middle shelf of the cart (figure 1) includes two Bragg cell power supplies, three-axis traverse controller, and the laser power supply.

**2.3 Other Equipment Used **

Digital camera (canon A510) was used to photography the instrumentation. A Steel ruler with a tolerance of ± 1.5875mm, dial caliper with a tolerance of ±0.127mm, and a digital

thermometer from Radioshack ±.05 degrees Celsius.

Some primary uncertainties introduced is the root mean squared velocity (±.08 m/s) which leads to an uncertainty in the mean velocity. Measuring the diameter of the cylinder with a uncertainty of ±.000127 meters, free stream velocity ±.05 m/s.

3. RESULTS AND DISCUSSION

The general procedure is as follows. First define the coordinate system to have to origin as close as possible to the trailing edge of the cylinder. The coordinate system is orientated such that the positive x is in the direction of freestream flow, positive y is the direction of the probe, and positive z is vertical pointing upwards. Set the pump speed at 30Hz (the fastest available) to maximize the freestream velocity of the flow which was found to be .52±.005 m/s (estimating it off plot in the lab manual). We set the origin to start measurements at 32.5±.5mm behind the trailing edge of the cylinder.

**3.1 Shape and Form of Circular Cylinder **

To find the shape and form of wake behind the circular cylinder. In order to determine the 2-d shape and form of the circular cylinder wake the vertical velocity profiles were measured

at incremental distances of 10mm in the x direction starting at the predefined origin from the trailing edge of the cylinder. This was repeated this until the LDA was 50mm from the origin. At each distance the LDA also took measurements in the z direction in 5mm increments between from -30 to 30mm vertically. A sample table is below.

Table 1: Velocity profile of various points at 20mm behind the origin

**x=20mm Velocity Profile y ****z[mm] ****U[m/s] ****V[m/s] ****U*V[m/s]^2 ***20 * 0 -30 0.5046 -0.0484 -0.0244
*20 * 0 -25 0.3664 -0.025 -0.0339
*20 * 0 -20 0.516 0.0478 0.0246
*20 * 0 -15 0.4124 0.04996 0.0206
*20 * 0 -10 0.3457 0.0319 0.0113
*20 * 0 -5 0.2622 -0.0724 -0.0189
*20 * 0 0 0.1984 -0.1826 -0.0362
*20 * 0 5 0.3293 -0.277 -0.0912
*20 * 0 10 0.4522 -0.0528 -0.0239
*20 * 0 15 0.1574 -0.7246 -0.1141
*20 * 0 20 0.5162 -0.0548 -0.02837
*20 * 0 25 0.6293 0.0291 0.0183
*20 * 0 30 0.6005 -0.0717 -0.0431

This gave the u and v components of the velocity where they were plotted at each velocity profile into Matlab and come up with a velocity profile of the wake behind the circular cylinder. As shown below because even though it’s a figure it is objective 1.

The arrows that are point in various directions up or down the flow field is the velocity vector at that particular point. They have an x and y component. There are a few points that are missing right at around the origin. This is because of the turbulence associated with the flow immediately behind a cylinder. These points that could not be measured because they did not have a steady flow therefore the LDA system could not accurately measure the points. Given the flow field above the flow became non turbulent at approximately 82±0.5mm behind the trailing edge of the cylinder. Or about 50mm away from the origin of our data collections. There was a small uncertainty associated with the measured mean velocities of ± .02236 m/s.

**3.2 Comparing with Ideal Flow **

For our final objective we examined the flow over the front of the cylinder center span at a set freestream velocity and compared it with ideal flow theory that was explained above. We redefined the location of the origin to be near the leading edge of the cylinder. We then took velocity measurements at various points around the front of the cylinder and recorded the u and v velocities. The idealized flow velocity was calculated from equations one and two above, after

defining the origin to be 52mm behind the leading edge of the cylinder. We had time for one test point and the data is shown in the table below.

Table 2: Idealized flow velocity vs measured velocity

**Idealized Flow velocity (m/s) **

**x input (m) ** z input (m) U
m/s
V
m/s
**0.011176±.000127 0.007112±.0000127** 0.521272±.04295 0.057472±.005671
** ** Measured Velocity
**x=[m] ** **z[m] ** **U[m/s] ** **V[m/s] **
**0.01117 ** 0.007 0.5543 0.1018

After doing one iteration of objective three we found an idealized flow velocity as an estimate of the measured flow velocity with an uncertainty of ±8% with respect to the U component of velocity and ±16% with respect to the V component of velocity.

4. CONCLUSIONS

An experiment has been performed to analyze the flow past a circular cylinder. Utilizing a laser Doppler anemometry system to measure velocities at different points in a flow using laser beams. Using the LDA system vertical velocity profiles were taken at incremental distances behind the trailing edge of the cylinder to map the 2-d shape and form of the wake behind the circular cylinder.

1. A map the 2-d wake behind the circular cylinder (image above) was created and estimated the flow to become non turbulent at approximately 82±0.5mm behind the cylinder.

2. The calculations for idealized flow velocity is v=0.057472±.005671 m/s and

u=0.521272±.04295 m/s, vs the measured velocity which gave V=.1018 m/s and U=.5543 m/s.

REFERENCES

*Hallauer W. L. Jr. and Davenport W.J., 2007,AOE 3054 Experimental Methods Course *

*Manual. Experiment 4–Laser Doppler Anemometry, A.O.E. Department, *

Virginia Tech. Blacksburg VA.

APPENDIX: UNCERTAINTY CALCUATIONS

Sources of uncertainty included the accuracy of the measuring tools. Specific uncertainties are given in Section 2. To obtain the uncertainties in results R derived from measurements,

uncertainties were then combined using the root sum square equation.

(3)

Where a,b,c are the measurements which R depends on. The partial derivatives are estimated numerically and the whole calculation being performed using and Excel table. Calculations for the uncertainty in mean velocities and ideal velocities in the u and v directions Tables 3-5 respectively.

**Table 3: Table for calculation of uncertainty in the mean velocity (m/s) **

** ** **PERTURBATION **

**MEASUREMENT ** **Quantity ** **Primary **

**Uncertainty **

**a+da, b ** **a, b+db **

**U_RMS (M/S): ** 0.08 0.05 0.13 0.08

**NUMBER OF SAMPLES TAKEN: ** 20 0 20 20

** **
**FINAL RESULT **
**MEAN VELOCITY: ** 0.035777 0.058138 0.035777
**CHANGE ** -0.02236 0
** **
**FINAL UNCERTAINTY: ** 0.022361

**Table 4: Table for calculation of uncertainty in ideal flow velocities in x direction (F_x) **

* * **Perturbation *** *

**Measurements Quantity ****Primary **
**Uncertainty **

**a+da,b,c,d ** **a,b+db,c,d ** **a,b,c+dc,d ** **a,b,c,d+dd **
*Diameter of *
*cylinder (m): *
0.018542 0.000127 0.018669 0.018542 0.018542 0.018542
*U_inf (m/s): * 0.52 0.05 0.52 0.57 0.52 0.52
*x input (m): * 0.011176 0.000127 0.011176 0.011176 0.011303 0.011176
*z input (m): * 0.007112 0.000127 0.007112 0.007112 0.007112 0.007239
* *
**Final Result ***IFV_x (m/s): * 0.44641 0.445399 0.489334 0.446999306 0.447319
* Change * 0.001012 -0.04292 -0.000589143 -0.00091

**Final***0.04295*

**Uncertainty:**Table 5: **Table for calculation of uncertainty in ideal flow velocities in z direction (F_z)**

* * **Perturbation *** *

**Measurements Quantity Primary **

**Uncertainty **

**a+da,b,c,d ** **a,b+db,c,d ** **a,b,c+dc,d ** **a,b,c,d+dd **
*Diameter of cylinder *
*(m): *
0.018542 0.000127 0.018669 0.018542 0.018542 0.018542
*U_inf (m/s): * 0.52 0.05 0.52 0.57 0.52 0.52
*x input (m): 0.011176 * 0.000127 0.011176 0.011176 0.011303 0.011176
*z input (m): 0.007112 * 0.000127 0.007112 0.007112 0.007112 0.007239
* *
**Final Result ***IFV_z (m/s): 0.057332 * 0.05812 0.062844 0.056434207 0.057914
* Change * -0.00079 -0.00551 0.000897593 -0.00058

**Final Uncertainty: 0.005671****Figures and Plots **

Figure 1: LDA System