March 27, 2022
Vibrations of the optical system are driven by wind loading. The terminology used here is to define 'dynamic pressure'. The total pressure on a surface is a combination of PV=nRT type motions due to thermal energy content in a parcel of gas that is not moving, plus a dynamic term P_d=(1/2) rho * v^2 which is the kinetic energy per unit volume of the material. This dynamic pressure exerts a force F=P_d*A on the projected surface A. That holds for incompressible fluids. For compressible gases P_d=(1/2)M^2 * gamma * P where M is the flow's dimensionless Mach number M=v/c with c being speed of sound, gamma =1.4 for air is the ratio of specific heats, and P is the static pressure in Pascals.
If the flow field u(x,y,z) was totally time-independent, then the dynamic pressure is steady in time and the mirror support system would compensate. Our problem arises from variations in the dynamic pressure at frequencies above the bandwidth of the active mirror support systems.
It's easier to measure wind speed than it is to measure pressure. Pitot tubes measure static vs. dynamic pressure, but as a quasistatic quantity.
Hot wire anemometers are a traditional way to measure turbulence and have good frequency response. This is effectively the use of a thermistor in a regime where self-heating is high, and the equilibration temperature is determined mainly by convective heat loss into the surrounding flowing air.
Bought this item on eBay:
So it's a Platinum wire of diameter 0.4 mils and length of about 0.125 inches (8/64 = 1/8 inch).
Resistance at 20C is 2.69 Ohms and lead resistance is 1.89 Ohms. Temperature coefficient of resistance at 20C is 0.39% per degree. Yes, the resistance increases with temperature. If we ran at constant current, since P=I^2R we'd get thermal runaway. Operating at constant voltage avoids this, since P=V^2/R as temperature goes up the resistance increases and power dissipation goes down.
Kielbasa (10267-Volume59_Issue2-13_paper.pdf) gives a good description of how to run one of these devices. There is an optimum bias voltage to obtain maximum sensitivity to airflow. Using an op amp circuit to maintain constant temperature, i.e. constant resistance, seems the normal configuration:
(Figure 8 from Kielbasa)
Note the resistive element is wired to ground. That matters! Can't put it in the upper leg of the Wheatstone bridge!
Both Tungsten and Platinum has positive temperature coefficient of resistance. He used Tungsten, of diameter 5 microns and resistance of 4.82 Ohms. Note that I think only wire diameter and resistivity matters here, not the length. Both power dissipation and heat leak are proportional to length, so it should wash out.
Our wire has diameter of 10 microns, so if resistivity of materials was equal we'd expect a resistance of 4.82(d1/d2)^2 = 4.82/4 = 1.2 Ohms. Is resistivity of Platinum 2.69/1.2 = 2.24 times higher than Tungsten?
Tungsten is 5.6e-8 Ohm-m at 20C and Platinum is 10.5 E-8 . Ratio is 1.9. So OK to roundoff error I think.
Tungsten tempco is 4.5e-3, Pt is 3.9E-3 so not that different.
A good operating point is when wire resistance is twice as large as zero-current value in still air. Using the local derivative R=dV/dI as the definition of resistance, and R20=2.69 Ohms for wire and Rlead=1.89 Ohms,
Here's a plot of resistance vs. wire temperature, including the effect of the lead resistance.
More simply, we want to operate with a total resistance of 1.89+2*2.69 = 7.27 Ohms.
Imagine this happens at a bias current of 30 mA. The voltage across the hot wire resistance is then 30mA * ~7 Ohms ~ 200 mV. Power dissipated in wire is 900E-6*7 ~ 6 mW.
Typical NTC thermistors have 3.8% per degree at 20C, ten times the tempco of platinum. So put one of those in the upper arm of wheatstone bridge to do temperature compensation, sort of?
What we really want is to sustain constant delta-T relative to ambient air temperature, since that temperature difference is what drives heat flow and thermal equilibration.
If we want resistance twice ambient, how hot is that? Around 180C! So: if we servo to constant resistance on hot wire, even if ambient changes by 20 degrees, delta-T between hot wire and air only goes from 160C to 180C, not a large difference.
We can just measure air temperature and correct for delta-T.
So:
1) measure IV curve of hot wire device, not to exceed 50 mA. Find excitation current where resistance is 2X that of ambient no-heating value. Should be around 30-40 mA Be sure to correct for lead resistance in series!
2) set up op amp circuit to