Turbulent Transport Coefficients Research Articles

Spectrum of turbulence with temperature gradient (in the atmosphere)

The problem of calculating the energy spectra of velocity and temperature fluctuations in a turbulence which is maintained by a permanent, large scale temperature gradient is studied, using a repeated cascade theory. A pair of coupled spectral equations is derived containing a turbulent momentum transport coefficient, which is identified as the eddy viscosity. An equation is formed which, when solved, leads immediately to an expression for the eddy viscosity. Solutions for the velocity and temperature spectra are found in the production-transfer, inertial and dissipation subranges. The Kolmogorov spectrum is recovered in the inertial subrange. The spectra have the form of power laws with exponents ranging from -1 to -7. Some observed spectra illustrate the predicted behaviour.

A non-linear theory of the trapped-particle interchange mode

In studying the non-linear evolution of non-resonant trapped-particle instabilities, it is desirable to exploit the fact that their frequencies are smaller than the bounce frequency by employing a kinetic equation for the bounce-averaged distribution function. Such an equation for trapped particles is derived in axisymmetric toroidal geometry by transforming the familiar drift-kinetic equation to toroidal co-ordinates and employing an annihilation operator. The “bounce-averaged drift-kinetic equation” facilitates the application of Dupree's strong turbulence formalism in toroidal geometry, under the assumption that turbulent scattering of particles out of the magnetic well is unimportant. On the basis of this formalism, the trapped-particle interchange mode is analysed. The saturation amplitude of the instability and the corresponding turbulent transport coefficients are obtained.

Numerical computation of momentum jets and forced plums

A numerical study of vertical momentum jets and forced plumes issuing to similar receiving media is presented. The complete partial differential equations governing steady, incompressible, turbulent flow are solved in axisymmetric coordinates using finite-difference techniques. Solutions were based on the stream function-vorticity transport approach for a Boussinesq fluid. Buoyant driving forces were coupled to the vorticity equation by a buoyancy transport equation wich included effects of temperature and other constituents. Turbulent transport coefficients were computed iteratively using the Prandt eddy diffusivitiy model. Results for the momentum jet, axial and radial distributions of velocity and concentration, show excellent agreement with published data. Forced plum computations are presented which include similar results for densimetric Froude numbers ranging from 1 to 1000.

Turbulent transport coefficients for mine workings and tunnels

Turbulent transport coefficients for mine workings and tunnels

Turbulent transport coefficients for compressible heterogeneous mixing

Turbulent transport coefficients for compressible heterogeneous mixing

Temperature fluctuations (flickering) of catalytic wires and gauzes—I Theoretical investigation

When chemical reactions occur on catalytic wires or gauzes random surface temperature fluctuations are sometimes observed, and this “flickering” is most predominant in ammonia oxidation convertors. It is shown that the large temperature oscillations of the catalytic surface are most probably due to the coupling between the chemical reaction and the fluctuating turbulent transport coefficients. The computations indicate that the flickering should be rather sensitive to the frequency of the turbulence and dependent on the turbulence intensity and the heat capacity of the wire, as well as on the operating conditions and specific reaction. Large temperature fluctuations are most likely to occur at conditions close to the extinction temperature and they may cause a premature extinction.

Turbulent Transport Equations and Kubo Formulae for Eddy Transport Coefficients

Kubo type time correlation formulae for turbulent transport coefficients in incompressible but heat conducting fluids are derived, especially for eddy viscosity, eddy heat conductivity, and pressure. The connection to the cascade method as well as its equivalence to the methods of closure of hierarchy are established. Lagrangean time integration is used. If the retarded Green’s function has exponential time behaviour the damping constant Γq can be calculated explicitely. In this approximation in the inertial range one finds the Kolmogoroff k-5/3 spectrum including its numerical factor (C=1.53). This induces a frequency spectrum ∼ ω -2.

Statistical characteristics of the temperature field in the pipe flow of a gas-water mixture

An experimental study of the statistical characteristics of the temperature field for a flow of a water and gas mixture in a pipe discloses a significant increase in the turbulent transport coefficient and a change in the structure of the water flow in the presence of the gaseous phase.

Temperature Microstructure in a Fresh Water Thermocline

RECENT measurements of microstructure in the ocean1–4 have led to considerable speculation about physical processes that lead to a steplike distribution of temperature, salinity and velocity. Briefly, one school of thought explains the microstructure in terms of interleaving of layers originating at different locations1,2. The other school suggests that the transport processes responsible for the vertical diffusion of heat, salt and momentum may inevitably result in the development of layers; the most striking theory, the so-called salt finger mechanism developed by Turner, Stommel and Stern5–7, depends on the difference between the molecular diffusivities for salt and heat. This mechanism works only in a statically stable ocean where the temperature gradient is stable, but the salinity gradient is unstable, or in the reverse situation. Tait and Howe3 have recently published profiles that strongly favour the salt-fingering process for layers under the Mediterranean outflow, but regular steps in temperature and salt of this kind are rare: the great majority of ocean microstructure is much more variable. Dr R. W. Stewart (private communication) has suggested that this microstructure is caused by the difference between the (turbulent) transport coefficients for buoyancy and momentum. No adequate theory for this buoyancy–momentum process has yet been developed, but the low Reynolds number turbulent spots discovered by Woods8,9 may be important. Temperature microstructure in a freshwater lake at least demonstrates that salinity gradients are not an essential factor in the generation of ocean microstructure. The occurrence of such microstructure in freshwater lakes seems likely from transparency observations made by Whitney11.

Model Equation for Nonhomogeneous Turbulence

The equation for the one-point turbulent distribution function is closed by assuming a relaxation model for the pressure fluctuation term and several other less critical approximations. The resulting equation is solved for a class of rectilinear flows and for decay of a periodic wake. Good agreement with available experiments is found. A theory of turbulent transport coefficients is derived in a certain approximation.

Turbulent transport coefficients in supersonic flow

Hypersonic ramjets employing supersonic combustion of hydrogen fuel have attractive potentialities for future aircraft or launching systems. The object of the present work §§This work was sponsored by the Office of Aeronautical Research, Office of Advanced Research and Technology, National Aeronautics and Space Administration, Washington, D.C. The Applied Physics Laboratory operates under Contract NOw 62-064c with the Bureau of Naval Weapons, Department of the Navy. was to study quantitatively the effects of fuel injection parameters on the mixing of gaseous hydrogen fuel with a supersonic air stream confined within a cylindrical duct, to provide some of the fundamental background needed for the design of supersonic combustors for high-performance engines. Hydrogen was injected at sonic velocities into Mach 2 and Mach 3 air streams, at overall equivalence ratios of 0.17 to 0.50, in both radial and axial (downstream) directions from circumferential wall slots. Results showed that considerably better mixing occurred in the case of radial injection, although the decrease in stagnation pressure also was greater for this case.The eddy diffusivity of mass, Ed (turbulent diffusion coefficient) and radial velocity, Vr, were determined by differentiating experimental concentration, velocity and density profiles, obtained at various axial distances from the injection station. For the radial injection case, with a 1-in i.d. test section, a simple model in which Ed varied only in the radial direction and Vr varied only in the axial direction, allowed reasonable correlation of the experimental results. The validity of the trends obtained in Ed and Vr were checked by numerical integration of the diffusion equation, and simultaneous solution of the diffusion and momentum equations; computed profiles agreed reasonably well with downstream experimental concentration and velocity profiles. A method for solving turbulent mixing problems by simultaneous solution of the diffusion, momentum and energy equations is presented.

Turbulent transport properties for axisymmetric heterogeneous mixing

Abstract : An experimental investigation of the turbulent mixing of two dissimilar gases for both subsonic and supersonic flows is presented. This investigation was carried out in order to determine the turbulent transport coefficients for hydrogen-, helium-, and argon-air mixtures in the mixing region of two coaxial jets. The basic differential equations describ ing the mean flow properties are solved for the transport coefficients. The convective derivatives which are needed in the solution of the equations are determined from the velocity and concentration profiles measured in the experiments. Values of the eddy viscosity, turbulent diffusion coefficient, and Lewis number were evaluated in this manner and the eddy viscosity so obtained is then compared with existing formulations. A new formulation for the eddy viscosity is then given whereby existing theories may still be used in analyzing the mixing process. Finally, the influence of similar velocity and concentration profiles on the transport properties is discussed and similarity parameters in both axial and radial directions are then shown to be valid for various injected gases. (Author)