William K. George

Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet

The turbulent flow resulting from a top-hat jet exhausting into a large room was investigated. The Reynolds number based on exit conditions was approximately 10 5 . Velocity moments to third order were obtained using flying and stationary hot-wire and burst-mode laser-Doppler anemometry (LDA) techniques. The entire room was fully seeded for the LDA measurements. The measurements are shown to satisfy the differential and integral momentum equations for a round jet in an infinite environment. The results differ substantially from those reported by some earlier investigators, both in the level and shape of the profiles. These differences are attributed to the smaller enclosures used in the earlier works and the recirculation within them. Also, the flying hot-wire and burst-mode LDA measurements made here differ from the stationary wire measurements, especially the higher moments and away from the flow centreline. These differences are attributed to the cross-flow and rectification errors on the latter at the high turbulence intensities present in this flow (30% minimum at centreline). The measurements are used, together with recent dissipation measurements, to compute the energy balance for the jet, and an attempt is made to estimate the pressure-velocity and pressure-strain rate correlations.

Zero-Pressure-Gradient Turbulent Boundary Layer

Of the many aspects of the long-studied field of turbulence, the zero-pressure-gradient boundary layer is probably the most investigated, and perhaps also the most reviewed. Turbulence is a fluid-dynamical phenomenon for which the dynamical equations are generally believed to be the Navier-Stokes equations, at least for a single-phase, Newtonian fluid. Despite this fact, these governing equations have been used in only the most cursory manner in the development of theories for the boundary layer, or in the validation of experimental data-bases. This article uses the Reynolds-averaged Navier-Stokes equations as the primary tool for evaluating theories and experiments for the zero-pressure-gradient turbulent boundary layer. Both classical and new theoretical ideas are reviewed, and most are found wanting. The experimental data as well is shown to have been contaminated by too much effort to confirm the classical theory and too little regard for the governing equations. Theoretical concepts and experiments are identified, however, which are consistent-both with each other and with the governing equations. This article has 77 references.

The decay of homogeneous isotropic turbulence

A new theory for the decay of homogeneous, isotropic turbulence is proposed in which truly self‐preserving solutions to the spectral energy equation are found that are valid at all scales of motion. The approach differs from the classical approach in that the spectrum and the nonlinear spectral transfer terms are not assumed a priori to scale with a single length and velocity scale. Like the earlier efforts, the characteristic velocity scale is defined from the turbulence kinetic energy and the characteristic length scale is shown to be the Taylor microscale, which grows as the square root of time (or distance). Unlike the earlier efforts, however, the decay rate is shown to be of power‐law form, and to depend on the initial conditions so that the decay rate constants cannot be universal except possibly in the limit of infinite Reynolds number. Another consequence of the theory is that the velocity derivative skewness increases during decay, at least until a limiting value is reached. An extensive review ...

Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition

Experimental data are presented from 138 synchronized channels of hot-wire anemometry in an investigation of the large-scale, or coherent, structures in a high Reynolds number fully developed, turbulent axisymmetric shear layer. The dynamics of the structures are obtained from instantaneous realizations of the streamwise velocity field in a single plane, x/D = 3, downstream of a round jet nozzle. The Proper Orthogonal Decomposition (POD) technique is applied to an ensemble of these realizations to determine optimal representations of the velocity field, in a mean-square sense, in terms of an orthogonal basis. The coefficients of the orthogonal functions, which describe the temporal evolution of the POD eigenfunctions, are determined by projecting instantaneous realizations of the velocity field onto the basis.Evidence is presented to show that with a partial reconstruction of the velocity field, using only the first radial POD mode, the large-scale structure is objectively educed from the turbulent field. Further, it is shown that only five azimuthal Fourier modes (0,3,4,5,6) are necessary to represent the evolution of the large-scale structure. The results of the velocity reconstruction using the POD provide evidence for azimuthally coherent structures that exist near the potential core. In addition to the azimuthal structures near the potential core, evidence is also found for the presence of counter-rotating, streamwise vortex pairs (or ribs) in the region between successive azimuthally coherent structures as well as coexisting for short periods with them. The large-scale structure cycle, which includes the appearance of the ring structure, the advection of fluid by the ribs in the braid region and their advection toward the outside of the layer by a following ring structure, repeats approximately every one integral time scale. One surprising result was that the most spatially correlated structure in the flow, the coherent ring near the potential core which ejects fluid in the streamwise direction in a volcano-like eruption, is also the one with the shortest time scale.

Locally axisymmetric turbulence

The failure of local isotropy to describe the experimentally obtained derivative moments in turbulent shear flows has previously been well-documented, but is briefly reviewed. The same data are then used to evaluate the hypothesis that the turbulence is locally axisymmetric. Locally axisymmetric turbulence is defined herein as turbulence which is locally invariant to rotations about a preferred axis. The derivative moment relations are derived from the general form of the two-point velocity correlation tensor near the origin for axisymmetric turbulence. These are used to derive relations for the rate of dissipation of kinetic energy, the mean-square vorticity, and the components of each. Almost all of the experimental derivative moment data are shown to be consistent with these equations, and thus with local axisymmetry.

Pressure spectra in turbulent free shear flows

Spectral models for turbulent pressure fluctuations are developed by directly Fourier transforming the integral solution to the Poisson equation for a homogeneous constantmean-shear flow. The turbulence-turbulence interaction is seen to possess the well-known k −7/3 inertial subrange and to dominate the high-wavenumber region. The turbulence–mean-shear contribution is seen to be dominant in the energy-containing range and falls off as

A theory for turbulent pipe and channel flows

k^{-\frac{11}{3}}

Experiments on a round turbulent buoyant plume

in the inertial subrange. The subrange constants and the mean-square pressure fluctuation are evaluated using a spectral model for the velocity. A spectral analysis of the velocity contamination of a pressure probe is also presented. Results are compared with spectral measurements with a static-pressure probe in the mixing layer of an axisymmetric jet.

Similarity Analysis for Turbulent Boundary Layer with Pressure Gradient: Outer Flow

A theory for fully developed turbulent pipe and channel flows is proposed which extends the classical analysis to include the effects of finite Reynolds number. The proper scaling for these flows at finite Reynolds number is developed from dimensional and physical considerations using the Reynolds-averaged Navier–Stokes equations. In the limit of infinite Reynolds number, these reduce to the familiar law of the wall and velocity deficit law respectively. The fact that both scaled profiles describe the entire flow for finite values of Reynolds number but reduce to inner and outer profiles is used to determine their functional forms in the ‘overlap’ region which both retain in the limit. This overlap region corresponds to the constant, Reynolds shear stress region (30 y + R + approximately, where R + = u * R / v ). The profiles in this overlap region are logarithmic, but in the variable y + a where a is an offset. Unlike the classical theory, the additive parameters, B i , B o , and log coefficient, 1/κ, depend on R + . They are asymptotically constant, however, and are linked by a constraint equation. The corresponding friction law is also logarithmic and entirely determined by the velocity profile parameters, or vice versa. It is also argued that there exists a mesolayer near the bottom of the overlap region approximately bounded by 30 y + < 300 where there is not the necessary scale separation between the energy and dissipation ranges for inertially dominated turbulence. As a consequence, the Reynolds stress and mean flow retain a Reynolds number dependence, even though the terms explicitly containing the viscosity are negligible in the single-point Reynolds-averaged equations. A simple turbulence model shows that the offset parameter a accounts for the mesolayer, and because of it a logarithmic behaviour in y applies only beyond y + > 300, well outside where it has commonly been sought. The experimental data from the superpipe experiment and DNS of channel flow are carefully examined and shown to be in excellent agreement with the new theory over the entire range 1.8 × 10 2 R + 5 . The Reynolds number dependence of all the parameters and the friction law can be determined from the single empirical function, H = A /(ln R + ) α for α > 0, just as for boundary layers. The Reynolds number dependence of the parameters diminishes very slowly with increasing Reynolds number, and the asymptotic behaviour is reached only when R + [Gt ] 10 5 .

Recent Advancements Toward the Understanding of Turbulent Boundary Layers

This paper reports a comprehensive set of hot-wire measurements of a round buoyant plume which was generated by forcing a jet of hot air vertically up into quiescent environment. The boundary conditions of the experiment were measured, and are documented in the present paper in an attempt to sort out the contradictory mean flow results from the earlier studies. The ambient temperature was monitored to insure that the facility was not stratified and that the experiment was conducted in a neutral environment. The axisymmetry of the flow was checked by using a planar array of sixteen thermocouples and the mean temperature measurements from these are used to supplement the hot-wire measurements. The source flow conditions were measured so as to ascertain the rate at which the buoyancy was added to the flow. The measurements conserve buoyancy within 10 percent. The results are used to carry out the balances of the mean energy and momentum differential equations. In the mean energy equation it is found that the vertical advection of the energy is primarily balanced by the radial turbulent transport. In the mean momentum equation the vertical advection of momentum and the buoyancy force balance the radial turbulent transport. The buoyancy force is the second largest term in this balance and is responsible for the wider (and higher) velocity profiles in plumes as compared to jets. Budgets of the temperature variance and turbulence kinetic energy are also carried out in which thermal and mechanical dissipation rates are obtained as the closing terms. Similarities and differences between the two balances are discussed. It is found that even though the direct affect of buoyancy on turbulence, as evidenced by the buoyancy production term, is substantial, most of the turbulence is produced by shear. This is in contrast to the mean velocity field where the affect of buoyancy force is quite strong. Therefore, it is concluded that in a buoyant plume the primary affect of buoyancy on turbulence is indirect, and enters through the mean velocity field (giving larger shear production).