This web page provides the necessary files for the CBE 40459 experiment on Particle Image Velocimetry, a technique for measuring the velocity profile in a two-dimensional flow field. In this case, the flow field is the natural convection flow produced by a wire dissipating electrical energy as heat. The files are divided into four sections:
The detailed description of the experiment and the theory behind the natural convection model are given here in pdf format.
There are many things you can examine in comparing experiment to theory. A suggested list of questions (not exhaustive, by any means, but a good starting point) is given here.
You can download all the programs described below (needed for the analysis of your data) in a single zip file. The file is programs.zip.
You will be using mixtures of glycerin and water. Because the natural convection depends strongly on parameters such as viscosity, thermal expansion, heat capacity, thermal conductivity, and density, you need to know what these are! To make your life easier we've written a series of programs which take the data from the Dow website (and heat capacity data from Perry's) to allow you to get the properties at concentrations and temperatures you will be examining:
Most of these functions are self-explanatory, yielding the material properties as a function of concentration. The last of these is the temperature rise of a solution due to heat of mixing, which must be corrected for to avoid thermal stratification problems affecting your results.
Note that you will need to determine the mass concentration of your solutions (it is easier to prepare them using volume fraction). The glycerin you are using is either "Food Grade," which contains about 2% water, or USP grade which is 99.7% glycerin (much drier). It is important to keep the tank sealed, because if exposed to air glycerin will absorb up to 20% by weight water!
In addition to these material property functions, you actually need to calculate things from them! I have provided two scripts which should be useful. The first is subcool.m which determines the degree to which the water needs to be sub cooled so that when mixed with glycerin at various volume fractions the mixture will come out at room temperature. You can sub cool the water by just mixing appropriate amounts of tap water and ice water - a lot faster than putting it in the fridge!.
The second material property script is even more useful: uclycalc.m. As you will learn from studying the theoretical analysis of natural convection, the characteristic velocity and length scale are both functions of the material properties as well as the power supplied to the wire (the magnitude of the source of energy driving the flow). This script calculates these scaling quantities for a particular power and a range of compositions. You will want to modify the script to yield Uc and Ly for the specific conditions you are investigating.
A final material property script is useful for determining if the tracer particles are following the fluid (a fundamental assumption of PIV). The script, sedvel.m, calculates the Stokes sedimentation velocity for the chalk particles in different fluid compositions. You will want to compare this to your measured velocities when interpreting your results.
There are four PIV analysis programs. These are:
The first of these, calibration.m, is used to calibrate the images and determine image
location relative to the energy source. The second (pivanal.m) analyzes a sequence of images and
determines particle locations and links between particles in successive frames: e.g., the
tracking algorithm. You will likely want to change the variable "npics" near the top of the function to match the number of frames you have exported from iMovie (up to 99, or about 3 seconds worth of data). The third (pivplot.m) takes the files of locations and links generated
by pivanal.m and generates velocities as a function of position. Your job is to take the
pictures, run the programs, generate the velocity fields, and then use them to compare
the experiment to the theoretical model.
Don't forget to put the correct calibration information into pivplot.m, and also to enter the location of the center of the image
While you will be analyzing your own data, of course, you may want to play with a sample set of images close to the wire. These pictures are in the zip file samplepics.zip which can be downloaded, unzipped, and put into the same directory containing the analysis programs. This experiment was run with an 11.6cm length wire at a power of 3.5W in a fluid which was 33.3% glycerin by volume.
You will need to compare your results quantitatively with the theoretical model. An example of such a comparison may be obtained by running comparison.m. You will need to heavily modify this last program to answer the questions posed in the problem statement, and in particular you will need to put in the correct file name and the correct values for Uc and Ly corresponding to your experimental conditions. This code is just provided as an example: use it to get ideas for how you can use all this stuff to figure out what is going on in your experiment!
You will also need to have run the theoretical programs described below to generate the data file of theory necessary for the comparison. The programs which generate the theoretical velocity field consist of the main script heatedwire.m, and the subroutines delta.m and fderiv.m. They should be self-explanatory (at least after reading the writeup!). Again, simply save the programs into the appropriate directory with the appropriate file names and run the main script. You will need to run the code for the particular Pr of your fluid (it is a very weak function of Pr), but as it uses the value of the Pr as a part of the saved file name, only enter integer values.
The video lectures describing the theory, experiment, and analysis programs are given here.