The Hot-Wire Anemometer in Supersonic Flow

The hot-wire anemometer has proved to be a most valuable tool for turbulence research in the low-speed range. As interest grows in the problem of turbulence at supersonic velocities, it would appear natural to see whether the hot-wire anemometer could not also be used at higher speeds. However, a number of fundamental problems must be solved before the hot-wire can be considered as a successful instrument in the supersonic laboratory. The first problem to be solved is that of obtaining adequate frequency response of the hot-wire equipment in order to resolve the turbulent fluctuations in space which are swept by the wire at high velocity in a supersonic flow. Encouraging progress has been made in using extremely fine wires and in developing electronic equipment that will compensate for the thermal lag of the wire at very high frequencies without interference from noise. As yet, there is only a small amount of information available tha t can be used to predict the response of a hot-wire anemometer a t such speeds. Because of the great difficulties of the theory of real compressible flows, most of the data will have to be obtained experimentally. The author has conducted systematic experiments to determine the law governing the heat loss from a hot-wire in a supersonic flow up to Mach Numbers of 2.0. I t was found that the heat loss, expressed in the form of a Nusselt Number, is a unique function of the square root of the Reynolds Number when free-stream velocity and density are used and the viscosity and conductivity corresponds to stagnation conditions. This law is valid only in the case of small temperature loadings. For large temperature differences, a nonlinearity appears in sharp contrast to King's law, which has been found to be linear with temperature difference over a wide range of temperature loadings. The third problem that has been encountered is that of interpreting the hot-wire fluctuations when the number of flow parameters is large. Velocity, density, and temperature all contribute to the hot-wire reading, and it is believed that in some cases these effects may be separated. When the velocity field is a lowintensity turbulence (not random sound waves), the separation of measured fluctuations is accomplished.