Group Image 1 Report

Transcription

1 THE UNIVERSITY OF COLORADO Group Image 1 Report Multiple Internal Refraction of Laer Light in Laminar Flow Chritopher Francklyn 3/14/2013 MCEN 4151 Flow Viualization Spring 2013

2 1. Purpoe of Image The image for thi report wa captured for the initial group aignment for The Univerity of Colorado, Boulder MCEN 4151: Flow Viualization coure. The cla i deigned to encompa multiple dicipline ranging from engineer to viual art tudent. For the firt group aignment, tudent were aked to oberve a fluid phenomenon of interet and document it through whatever viual medium he or he thought bet repreented the fluid flow. For the image taken, the fluid flow in quetion pertained to internal refraction of laer. Three eparate laer (red, green, and blue) were projected at different angle into a laminar flow of water. At the onet of fluid flow, the laer are cleanly reflected by the interior wall of the water jet. A the fluid jet become le laminar and more turbulent, the beam become ditorted and combine to form a uniform bright, almot white color. The image nicely yntheize fluid flow aociated with laminar jet with optical refraction aociated with Snell law. 2. Image Set Up and Approach A complex etup wa required for the production of the image, and wa accomplihed with help from employee of the phyic department (Michael Thomaon), who provided the pace and equipment for the experiment. The fluid tank wa mounted on a tand approximately one foot above the urface of the table. The tank itelf wa approximately two and a half inche deep, eighteen inche tall, and twelve inche long. Located on the bottom end of the narrow face of the tank (nearet the cloed ide), wa a 0.5 inch diameter orifice. At thi part of the wall, the thickne had been tapered and eventually removed, and had been replaced by an approximately 0.1 inch thick piece of aluminum. Thi thin wall allowed for flow effect around the orifice to be minimized. Thi helped enure a laminar flow of water out of the opening. A rubber plug filled thi hole in order to control when fluid flow occurred. Each laer wa mounted on a eparate vertical tand in line with the tank orifice and fluid jet. The laer were individually turned on, and manually adjuted o that the beam of each laer impinged onto the ame point on the orifice plug. Although each laer impact the ame point on the plane of the plug, due to the difference in incoming angle, each beam impacted a different urface of the fluid jet. The reult wa that the laer eemed to piral around one another. Figure 1: Red laer contacting the rubber plug The fluid tank wa then filled to the brim with water. Approximately a 1/8 cup of pine ol wa then added to the water. The pine ol a mall colloidal particle gave each laer a medium to be viualized on. If plain water wa ued, the path of the laer would be inviible to the naked eye, and only the final point of the path would be viible. A a laer beam encounter a mall colloidal particle (in thi cae the pine ol olution) a mall portion of the light i cattered. Thi allow the beam to become viible. Immediately after adding and tirring the pine ol in the water, the olution contain a large amount of bubble. To obtain the bet image, thee bubble were allowed to ettle, leaving a clear fluid 1

3 Laer (Green, Blue, Red) Laer (Green, Blue, Red) Tank Fluid Jet Figure 2: Actual Set-Up (Left), Set-Up Schematic (Right) olution. However, in the choen image, thi proce had not been allowed to reach a teady tate or equilibrated point, and mall bubble were till preent in the fluid. While thee particle adverely affect the harpne and reolution of the image, they alo allow the fluid dynamic to be better viualized. A the fluid in the tank exited the tank, the urrounding bubble are pulled along with it. In the image, thi create motion blur due to the long expoure time required to correctly viualize the laer beam. The cloer a particle i to the exit orifice, the more motion blur it induce in the image (fluid velocity i greatet urrounding the exit hole). 3. The Phyic behind the Flow The bulk of the fluid flow propertie for thi image are determined by the velocity of the free jet of water exiting the tank. Through rearranging Bernoulli equation for a large, open reervoir exiting into the atmophere, one can derive the free jet equation. Thi equation i hown below, and will be ued to calculate the velocity of the tream, which will help determine the Reynold number of the flow. Where the above variable are defined a: V = Fluid Jet Velocity, Unkown g = Acceleration due to Gravity = 32.2 ft 2 Free Jet: V = 2gh [4] h = Head Height of Fluid Tank = 0.5 ft (Approx. height of fluid at image capture) The free jet velocity i then calculated to be: V = 2gh = ft ft 2 (.5 ft) =

4 To minimize any potential vena contracta effect decreae in the area of the jet with repect to the exit orifice caued by a harp corner at the exit location, the tank wa contructed o that the acrylic wall moothly taper down to the exit hole. At thi location, a quare of the acrylic wall wa removed and replaced by a very thin piece of aluminum with the appropriate ized hole. Thi thin material enure that the fluid flow ha much le of a 90 turn to make a it exit the tank, and reduce the amount of vena contracta that i preent (ie C c 1.0) [4]. The free jet velocity found above can then be ued to calculate the Reynold number (a dimenionle ratio of the fluid inertial force to the fluid vicou force)of the fluid flow. In order to properly internally refract the laer beam, the fluid flow mut be laminar in nature (ie low Reynold number). Where the above variable are defined a: Re = VD ν [4] V = Average Velocity = ft (Calculated from Free Jet Equation) D = Diameter of Free Jet = ft ν = Kinematic Vicoity = 1.664E 5 ft2 (Water, At Room Temperature 40 C, [3]) Reynold number i then calculated to be: Re = VD ν ft ( ft) = E 5 ft2 The critical Reynold number allowed for laminar flow i Since thi number i much greater than that value (~4x), the fluid i mathematically claified a behaving in a turbulent manner. However, the empirical evidence and nature of the experiment were that the free jet flow wa laminar in nature. Somewhere within the calculation of either the free jet velocity or the Reynold number lay an inconitency which i generating thi incorrect mathematical reult. It i difficult to identify directly a there are few independent variable within the equation, and all are known to a relatively high level of confidence. In order to achieve a fluid flow on the boundary of being turbulent, either a head height of 0.15 inche, or an orifice ize of 0.08 inche in diameter. Neither of thee criteria are feaible, o that calculation wa left a i. 4. Viualization Technique To viualize the flow, mall bubble were employed to act a particle marker. Each bubble wa mall enough that it did not over power or degrade the image, but large enough that the generated 3

5 motion blur wa enough to demontrate the fluid flow. The laer nicely illuminated the et-up, with the combination of the red and blue laer providing a nice purple hue within the image. Unfortunately, ome apect of the image are out of focu uch a the acrylic tank. The intended focal point of the image wa the refracted laer path on the right hand ide of the image, o the tank became le defined. A fair amount of motion blur alo exit in two place: on the left hand ide in the form of particle motion, and on the right in the form of free jet fluid flow. Both of thee area of motion blur provided a ene of peed and motion to the image, which aid the overall effect. 5. Photographic Technique The camera ued to capture thi image wa a Nikon D2x. The camera len wa a 60mm Macro- Nikkor F28 len. The camera itelf wa fixed to the extended boom of a three-leg tripod. The image wa captured a a RAW file and wa pot proceed a a.tif. The camera etting were an ISO 1600, a focal length of 105 mm, an aperture ize of f/4.5, and a hutter peed of 1/20ec. The field of view i approximately 10 quare inche. No pot proceing occurred. The original image i hown below. Figure 3: Unedited Image 4

6 6. Concluion Thi image i a unique example of fluid phenomena internal refraction of light. Additionally, the mall bubble that exit in the image help build a ene of flow a the image progree left to right. The depth of color i fairly rich, with a color palate which i nicely contrated by the black backdrop. The way in which the two beam of light twit around each other i alo telling of the beauty that get created a the light i refracted by the internal wall of the fluid flow. While the image could ideally be a little harper in ome area (uch a the wall of the container), it hould be taken into conideration that a fair amount of motion blur exit within both halve of the image (particle and free jet flow). Overall, the image nicely repreent fluid dynamic. 5

7 Work Cited [1] [2] [3] [4] Young., Munon,, Okiihi,, & Huebch, (2007). A brief introduction to fluid mechanic. (4th ed.). Hoboken, NJ: Wiley. [5] 6