Reinvestigation of Hot-Wire Anemometry Applicable to Subsonic Compressible Flows Using Fluctuation Diagrams

Abstract

Much has been written about the improbability and impossibility of obtaining solutions to the mean square equation for constant current anemometry in subsonic slip and transonic flows. For these flow conditions, the voltage across a heated wire mounted normal to the flow is a function of velocity, density, and total temperature. In principal, the fluctuations of these quantities can be measured; however, to date there are no known acceptable solutions to the mean square equation in these flow regimes. In this study, data presented in the 1950’s by Spangenberg were used to compute the sensitivities of a heated wire to changes in velocity, density, and total temperature. These results indicated that there was a large region in the Nusselt number-Reynolds number or Nusselt number-Knudsen number regimes where the velocity and density sensitivities were different, a condition required for solutions to the mean square equation. A second necessary condition for a solution was also noted. The possible existence of a solution to the mean square equation was based on the evaluation of the condition number of the sensitivity matrix. The condition numbers obtained from Spangenberg’s data were very large and near perfect data would be required to obtain accurate measurements of the fluctuations.