This web page provides the necessary files for the CBE 459 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.
A collection of experimental tips is given here.
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:
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 "Food Grade," which contains a little bit of water. Based on previous experiences, it is a good approximation to take the glycerin to be 98% glycerin and 2% water by weight. It is important to keep the tank sealed, because if exposed to air glycerin will absorb up to 20% by weight water!
A last note on properties: there is a significant temperature increase on mixing for water/glycerin solutions (a nice chart is given on the Dow website). You can actually kill this off if you dilute the glycerin with water of an appropriate (cold) temperature, or you can just deal with the slightly hot mixture (but you will then get both some stratification and boundary layer flows at the walls). The required degree of subcooling of water is just the mixing delta T (from the website chart) * heat capacity of mixture / (heat capacity of water * mass fraction of water). A function based on digitizing the website chart is given here: temprise.m. The required degree of subcooling (as well as the calculation of characteristic profile widths and velocities) is provided by the matlab function uclycalc.m. Note that you will need to modify this to get the Uc and Ly of your power and composition, and you will want to calculate Tc as well. All are functions of the experimental parameters!
There are four PIV analysis programs in the subdirectory pivanal. 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. 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! Note that the directory also contains some sample images that the programs could be used to analyze. For these images the center of the image was 3.3cm above the wire (information required by pivplot.m) and the file base name is "sample". A comparison of the data to the theoretical model may be obtained by running comparison.m. The graphical output of this program consists of vertical, horizontal, and quiver velocity plots. You will need to heavily modify this last program to answer the questions posed in the problem statement.
The programs which generate the theoretical velocity field are given in the subdirectory theory. The programs 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.
