Lecture G2: Survey of Flow Diagnostic Techniques
Lecture B1: Digital Signal Processing.
Deadline for completing the answers to these questions
is Feb. 12. However, deadline for discussion questions is Feb. 7.
1. You are asked to measure the temperature inside a gas turbine combustion chamber. There is hydrocarbon fuel being burned in air, with the mixture ratio being close to "stoichiometric" (that's when there is enough H and C to soak up all the O and O2 to form H2O and CO2). The temperature is expected to reach the "adiabatic flame temperature" (that's the temperature reached when all the heat released in reaction goes to heat up the reactants, including the products, and none is wasted in losses to the surroundings. For given composition, its a function of pressure: generally increases as pressure increases). The pressure inside the combustion chamber is 20 atmospheres, and the adiabatic flame temperature is roughly 1900K. The flow velocity is roughly 50 m/s. and highly turbulent.
There are several kinds of regions where the measurements are to be
made.
a) Exhaust gas (turbine inlet temperature). Here the temperature is
sort-of steady. The interest is in capturing the time-averaged temperature
here.
b) In the flame region. Here there are frequent occurrences of unburnt
reactants, at roughly 600K, and burnt products at 1900K, and the flame
sheet itself, which is perhaps 2000 K. The flame sheet is generally very
thin, of the order of 1mm or even less. So, the temperature at a given
point fluctuates wildly. There may be some glowing carbon particles (sub-micron)
flying around too. The interest here is in capturing the detailed time-variation
of temperature, from which various conclusions can be drawn regarding the
reaction rate, etc.
a) Discuss how to make measurements in both regions. Need not be the same device that is used.
b) Try calculating the time constant of an S-Type thermocouple, with a bead diameter of 75 microns. See how much it might vary when the mean temperature changes from 600K to 1900K.
c) Will such a thermocouple survive when the flame sheet zips by it? Discuss.
d) Discuss whether Rayleigh scattering might be a good technique to apply in either of these regions, and how you might set up such a measurement. From a search of the internet, find & discuss other techniques which might be appropriate.
2. In the above situation (see Qn. 1c), assume that the flamelets are moving past the temperature measuring device (which is assumed for this question to have infinitely fast frequency response) at a speed of 50 meters/second. Construct the expected form of the histogram of temperature. Hint: think about what percentage of the time the sensor is immersed in fluid at each temperature..