Copyright © 1999, 2000, 2002-2005, 2009 by H. McMahon, 1 J. Jagoda, N. Komerath and J. Seitzman. All rights reserved. AE3051 Experimental Fluid Dynamics UNSTEADY VELOCITY MEASUREMENTS IN A JET USING A HOT WIRE ANEMOMETER Objective The objective of this laboratory experience is to familiarize the student with the theory and operation of a hot-wire/hot-film anemometer system, which is a standard technique for measuring fluctuating flow (gas) velocities. Here, the system will be used to measure the mean and root-mean-square velocity profiles across a jet of air. The jet is produced by the exhaust of a round pipe centered in a small, low-speed wind tunnel. Note: the anemometer is a very delicate and expensive device. Please use extreme care in handling the probe and the sensor, and be sure to read and understand the instructions and the principles of operation well before you start the experiment! If you run into trouble, do not turn any knobs on a trial basis! Ask for assistance; the sensor and the instrument circuit can be quite easily burned out. The sensor is very fragile, so do not shake it or touch it. Background Rapid fluctuations in velocity occur in most flows of practical interest. Examples are: the boundary layer above wings and fuselage surfaces, the wakes behind obstacles in flows, jets from the nozzles of rockets and gas-turbine engines, and flows inside engine components. These fluctuations have profound effects on such things as drag, surface shear stress, boundary layer separation, mixing between fuel and air in engines, and vibrations of turbomachines and control surfaces. To understand such phenomena, we must be able to measure velocity fluctuations accurately. There are several difficulties in making such measurements. First, we must find a sensor that has a measurable change in output for small changes in velocity (good signal sensitivity), and which will survive in a fluctuating flowfield (robust). Second, the device must respond faithfully, and perhaps without any time lag, to rapid fluctuations (good temporal resolution orAE 3051 Unsteady Velocity Measurements in a Jet Using a Hot Wire Anemometer 2good high frequency response). Third, the measurement device should not interfere with the flowfield and change the quantities being measured (nonintrusive). For a physical probe, this means it must be small or properly shaped. Fourth, the device must respond only to the velocity in a very small, and precisely known, region (good spatial resolution). Hot Wire/Film Description The hot wire is a delicate device that provides velocity data (under certain limitations). Its small, almost “microscopic” size gives it good spatial resolution and high frequency response. In addition, it is highly sensitive. The sensing element is a long circular cylinder, typically a tungsten or platinum wire of diameter in the range of 5 to 20 µm (2-8 × 10-4 inches). Slightly more rugged hot-film sensors are also commonly used. These are glass rods, ~50 µm in diameter, with platinum films, typically 10 Å thick (Å = Angstrom = 10-10 m), coated on the surface. In either case, the wire or the glass rod is fixed to two gold-plated steel needles which serve as the electric contacts to the sensor. The wire or film is kept heated by an electric current, to temperatures of 200 to 300 °C (and sometimes up to 800 °C). When air flows over the wire, energy in the form of heat is carried away by the much colder air stream (forced convection) because of the temperature difference between the (hot) sensor and (cold) air. A typical probe and a flow pattern over a sensor are shown in Figure 1. The sensor is so small that the Reynolds number of the flow is usually very low, and so the flow pattern over the sensor can be assumed to be symmetrical and quasi-steady,1 as shown in the figure. Heat Transfer Analysis The length of the sensor wire (or rod) is much greater than its diameter. Hence, it may be assumed that heat losses by conduction2 through the ends are negligible, and the relations for heat transfer from an infinite cylinder may be applied. However, note that not all of the length of the wire is actually used as the sensor. In fact, the wire (or rod) is coated with a relatively thick layer of highly conductive gold or silver, except for a small length at the center. This center portion has a significant electrical resistance and acts as the sensor. Thus, the spatial 1In this case, quasi-steady means that the flow changes slowly compared to the rate at which the heat transfer processes can adjust. Therefore a simple steady-state analysis can be performed. The smaller the probe, generally the faster the heat transfer processes can adjust. 2Conduction is heat transfer through the material by diffusion, e.g., in one-dimension the heat flux (energy per unit time per unit area) is governed by the equation ()dxdTkdtdq −=.AE 3051 Unsteady Velocity Measurements in a Jet Using a Hot Wire Anemometer 3resolution of the sensor is kept high. The convective heat transfer rate, Q⋅conv (e.g., Watts or Joules/second) for a flow is generally given by an expression of the form Q⋅conv ()fssTThA−=, where h is a convective heat transfer coefficient, As is the surface area of the body gaining/losing energy, Ts is the temperature of the surface and Tf is the temperature of the fluid flowing over the body. For a cylinder in cross-flow (flow perpendicular to the axis of the cylinder), the solution for the convective heat transfer coefficient leads to the following expression for the rate (with subscripts substituted for our conditions), Q⋅conv ()()awnTTBuA −+= (1) where Tw is the temperature of the wire, Ta is the temperature of the air, and u is the mean velocity of the air flow. The values A, B and n are constants, valid for a given value of Tw, Ta and a given wire. They can be determined by calibration of the sensor. Physically these constants include the effects of such things as the thermal conductivity of the sensor, the Nusselt number of the flow, and the size of the sensor. Unless one is researching the construction of these probes, it is not usually easy to calculate from first principles the sensitivity of a given sensor, since the property values will depend strongly on the manufacturing processes used. So, it is far easier to obtain A, B, and n by calibration against some other velocity standard, for example a Pitot-static probe, in a simple, nearly steady