The axial core of air that is flowing steadily through a long circular pipe .is a region of nearly homogeneous, isotropic turbulence. Homogeneous, isotropic turbulence is a very special type of turbulent flow which has received a great deal of attention in the literature during the last decade. The stimulus for this research was the theoretical work of G. I. Taylor ( 1 ) in 1935. However nearly all of the literature describing the development of the theory of homogeneous, isotropic turbulence (2, 3. 4, 5, 6) has dealt with the dynamics of turbulent kinetic-energy losses in grid produced turbulence in wind tunnels. On the other hand chemical engineers are usually interested in another aspect of turbulent phenomena, the dispersion of mass or heat by turbulent diffusion. The study of turbulent diffusion that is presented here was designed to obtain diffusion data in the simplest form of turbulent flow, nearly homogeneous isotropic turbulence that is stationary in time. Owing to the simplicity of the chosen experimental model, it is possible to use the theory of diffusion by continuous movements (7) as a theoretical model and to test the theoretical concepts experimentally.The objective of this work is easily stated: to determine turbulent diffusion parameters from a statisticaI description of the turbulence as measured by fixed probes. Since the turbulence considered approaches the simplest form (homogeneous and isotropic), it is surprising at first glance that theoretical attacks on this problem have all failed.Lionel V. Baldwin is at Lewis Research Center, National Aeronautics and Space Administration, Cleveland, Ohio. VOl. 7 , No. 1The basic difficulty is twofold. In the first place the statistical description of a turbulent field requires a knowledge o f the complete joint probability distribution function for the velocity components (x, y, z directions) at all points in space (3, p. 12; 2, p. 18). The statistical functions usually measured and reported are the correlation functions which refer to two points in space. The correlation (or spectrum) functions dominate current theory and experiment because of their simplicity and do not describe the turbulence completely even in a statistical manner ( 3 ) . Secondly to pass from the Eulerian description of the flow (fixed probes) to the Lagrangian description of the motion of an element of volume (turbulent diffusion) requires a solution of the Navier-Stokes equations. Thus the total difficulty is not only the nonlinearity of the partial differential equations of motion but also the incomplete initial conditions.To circumvent the missing theoretical link two distinct viewpoints of the turbulent motion are used. The Eulerian description has received the most attention (for example 2, 3 ) . In this research the authors seek empirical relations between this Eulerian description and the Lagrangian statistical functions which are used in the diffusion analysis. The following paragraph is a brief summary of the results of the Lagrangian analysis of diffusion by continuou...
A general Nusselt number correlation is presented for transverse cylinders in subsonic and supersonic air flows where dissociation is negligible. New and existing data in the following experimental range have been correlated: Mach M = 0.001 to 6.0, Reynolds NRe = 0.02 to 300,000, Knudsen NKn = 4 × 10−6 to 37. In subsonic flow, heat transfer from a cylinder yawed at an angle to the air velocity is predicted by the transverse cylinder Nusselt number correlation when the normal velocity component is used as the characteristic velocity. Finally, recovery temperature data from cylinders are divided into three regimes by a Knudsen number criterion.
Turbulent wakes formed downstream of flat, circular disks were surveyed with hot-wire anemometers in a low-speed wind tunnel. Three regions were discernible in the wake. Between the disk and x = 50 disk diameters D downstream, the turbulence was highly anisotropic and new turbulence was generated locally. An approximate similarity region (100 ≲ x/D ≲ 400) existed where isotropic turbulence relations were adequate for estimating decay. The far downstream wake (x/D ≳ 400) was highly intermittent throughout; the decay rate lessened in this final period. Over a 4-fold range of disk size and a 7 1/2-fold range of mean flow velocity, Taylor’s microscale was correlated by the mean residence time x/U∞; this relation was independent of disk size.
The wakes formed behind sharp-edged, bluff, elliptical bodies have elliptical cross-sections, but the major axis of the wake is aligned with the minor axis of the body. This effect was observed in both mean velocity and turbulent intensity data in wakes throughout the range of the experiment, from several body diameters to distances of 250 diameters downstream of the body. The turbulent energy in the wake flow near the body displayed a periodicity which was correlated using a Strouhal number. Over the Reynolds-number range from 8 × 103to 7 × 104, the Strouhal number depended only on the body eccentricity.
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