I. Extended Applications of the Hotwire Anemometer. II. Investigations of the Flow in Round, Turbulent Jets

Citation

Corrsin, Stanley (1947) I. Extended Applications of the Hotwire Anemometer. II. Investigations of the Flow in Round, Turbulent Jets. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NB53-K411. https://resolver.caltech.edu/CaltechETD:etd-12092008-105044

Abstract

Part 1: Two new fields of application of the hot-wire anemometer are proposed, and the appropriate response equations and measuring procedures are developed. The first analysis leads to a method for the measurement of physically significant statistical quantities in a turbulent flow with heat transfer: for example the turbulence levels, the temperature fluctuation level, the turbulent heat transfer coefficient, the velocity scale, the temperature scale and some spectra. The second analysis involves the use of the hot-wire in the turbulent isothermal mixing of two appropriately different gases. If the thermal conductivity of the mixture is known and is a monotonic function of the relative concentration, it is possible to measure the mean velocity and mean concentration at any point. If no data are available on the thermal conductivity of the mixture, this additional unknown can be determined by an additional measurement. Furthermore, it is also possible to measure the various statistical functions of the fluctuating velocities and the local concentration fluctuation, provided, again, that the thermal conductivity is a known monotonic function of the concentration. Although the details of the present analysis are dependent upon the accuracy of King's equation for the rate of heat loss from fine wires, the general approach is equally valid for any (possibly more accurate) equation that may be deduced. Part 2: A detailed investigation has been made of the flow in a round turbulent air jet, heated slightly to permit measurement of mean temperature. Oscillograms of the velocity fluctuation plus direct measurement of the turbulent shear both show that the flow in a fully developed "turbulent" jet is completely turbulent only out to approximately the radius at which the extreme outer edge is in the nature of a "laminar collar", with predominantly radial (inward) mean velocity, and in between the turbulent core and the laminar collar is a rather wide annular transition region. A study of the downstream history of the radial distribution of turbulent velocity shows that the fully developed state of this round jet is reached between 15 and 20 diameters. This conclusion is corroborated by examination of the partition between turbulent motion and mean motion, of total kinetic energy crossing planes perpendicular to the axis in unit time. The directly measured shear distribution is checked roughly by a computation of the same quantity from the mean velocity distribution. A measurement of the double correlation function between points symmetrical about the jet axis shows considerable similarity to the corresponding function in isotropic turbulence, and permits calculation of scale and microscale. With the assumption of constant microscale across a section, a rough estimate is made of the energy balance distribution of production, dissipation and diffusion of turbulent energy. A comparison with momentum transfer, modified vorticity transfer and constant exchange coefficient theories show that none of them is satisfactory. A comparison of mean velocity and temperature distributions verifies Ruden's result that the lateral rate of heat transfer in turbulent shear flow is appreciably greater that the lateral rate of momentum transfer. The use of considerably increased heating, in a second jet unit, has permitted direct measurement of the temperature fluctuation level. Velocity fluctuations were also measured in this case for comparison, and they were found to be the same order of magnitude. The final result is the direct measurement of temperature-velocity correlation and of velocity correlation in the hot jet. This gives a direct measure of the turbulent heat transfer and momentum transfer in the jet, and directly verifies the fact that the former is appreciably greater than the latter.

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