Showing papers on "Turbulence published in 1974"

A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers.

Abstract: Turbulence models centered on hypotheses by Rotta and Kolmogoroff are complex. In the present paper we consider systematic simplifications based on the observation that parameters governing the degree of anisotropy are small. Hopefully, we shall discern a level of complexity which is intuitively attractive and which optimizes computational speed and convenience without unduly sacrificing accuracy. Discussion is focused on density stratified flow due to temperature. However, other dependent variables—such as water vapor and droplet density—can be treated in analogous fashion. It is, in fact, the anticipation of additional physical complexity in modeling turbulent flow fields that partially motivates the interest in an organized process of analytical simplification. For the problem of a planetary boundary layer subject to a diurnally varying surface heat flux or surface temperature, three models of varying complexity have been integrated for 10 days. All of the models incorporate identical empirica...

Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number

Abstract: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.

A Laboratory Model of the Unstable Planetary Boundary Layer

Abstract: Experimental details of a laboratory model of the unstable planetary boundary layer are given. Measurements of vertical profiles of mean temperature and heat flux, and of velocity and temperature fluctuations are presented and compared with atmospheric observations. Good agreement exists between the model measurements and the atmospheric observations when the variables are appropriately scaled with the depth of the mixed layer zi, and the convective velocity and temperature scales w* and T*. Turbulence kinetic energy budgets for the mixed layer turbulence are presented. The buoyant energy production decreases nearly linearly with height, while the rate of dissipation of kinetic energy is found to be about constant with height. Horizontal temperature spectra at three heights are presented. The temperature spectrum for a height neat the middle of the mixed layer suggests the existence of an inertial subrange as well as a viscous-convective subrange. The temperature spectrum calculated from horizont...

Computation of Turbulent Flows

Abstract: Substantial advances made over the past decade in the prediction of turbulent flows are discussed. There was extensive work in the development of turbulence models, particularly for use in boundary layer calculations. Basic aspects of several important methods based on partial differential equations for the mean velocity field and turbulence quantities, including the relationship between the methods and suggestions for future development were reviewed. Work on three-dimensional time-dependent large eddy simulations is discussed. The emphasis is on the hydrodynamics of incompressible flows, but sources for consideration of heat transfer and compressibility are mentioned.

Low Reynolds number flow over a plane symmetric sudden expansion

Abstract: Flow visualization and laser-anemometry measurements are reported in the flow downstream of a plane 3: 1 symmetric expansion in a duct with an aspect ratio of 9·2: 1 downstream of the expansion. The flow was found to be markedly dependent on Reynolds number, and strongly three-dimensional even well away from the channel corners except at the lowest measurable velocities. The measurements at a Reynolds number of 56 indicated that the separation regions behind each step were of equal length. Symmetric velocity profiles existed from the expansion to a fully developed, parabolic profile far downstream, although there were substantial three-dimensional effects in the vicinity of the separation regions. The velocity profiles were in good agreement with those obtained by solving the two-dimensional momentum equation. At a Reynolds number of 114, the two separation regions were of different lengths, leading to asymmetric velocity profiles; three dimensional effects were much more pronounced. At a Reynolds number of 252, a third separation zone was found on one wall, downstream of the smaller of the two separation zones adjacent to the steps. As at the lower Reynolds numbers, the flow was very stable. At higher Reynolds numbers the flow became less stable and periodicity became increasingly important in the main stream; this was accompanied by a highly disturbed fluid motion in the separation zones, as the flow tended towards turbulence.

Three-dimensional numerical study of turbulence in an entraining mixed layer

Abstract: The mean structure calculated by a three-dimensional numerical model of a heated planetary boundary layer, in simulation of DAY 33 of the Australian Wangara data, has been previously described. The present study supplements it by describing properties of the calculated turbulence.

Natural Convection Adjacent to Horizontal Surface of Various Planforms

Abstract: Natural convection adjacent to horizontal surfaces of circular, square, rectangular, and right triangular planforms has been studied experimentally. Electrochemical techniques were employed involving a fluid with a Schmidt number of about 2200. The results encompass a wide range of Rayleigh numbers thus providing information on both the laminar and the turbulent regimes. The data for all planforms are reduced to a single correlation in the laminar and turbulent regimes using the characteristic length, as recommended by Goldstein, Sparrow, and Jones. L* = A/p, where A is the surface area and p is the surface perimeter. The laminar data for all planforms are correlated by the expression Sh = 0.54 Ra1/4 (2.2 × 104 ≤ Ra ≤ 8 × 106) and the data for the turbulent regime are correlated by the expression Sh = 0.15 Ra1/3 (8 × 106 ≤ 1.6 × 109) Transition is found to occur at about Ra = 8 × 106 . The present work thus significantly extends the Rayleigh number range of validity for the use of L* through the 1/4 power laminar regime into the turbulent 1/3 power regime. It also demonstrates the validity of the use of L* to correlate natural convection transfer coefficients for highly unsymmetrical planforms, which heretofore had not been demonstrated. Comparisons to analytical solutions and other experimental heat and mass transfer data are presented.

The effects of surface roughness and tunnel blockage on the flow past spheres

Abstract: The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

The Structure of the Two-Dimensional Internal Boundary Layer over a Sudden Change of Surface Roughness

Abstract: The effects of an abrupt change of surface roughness on the mean flow and turbulence structure in the neutral surface layer are numerically investigated by a higher-order turbulence closure theory, which includes dynamical equations for Reynolds stresses and the viscous dissipation rate. The closed system of governing equations, together with the specified initial and boundary conditions, is solved by an explicit finite-difference method on a digital computer. The numerical model predicts the distributions of mean wind, shear stress, turbulent energy and other quantities, with no a priori assumptions regarding the distributions of any of these variables in the transition region. The distributions of the nondimensional wind shear, the dissipation and mixing length scales, and the ratio of stress to turbulent kinetic energy are shown to differ significantly from their equilibrium flow variations.

Vorticity Associated with a Jet in a Cross Flow

Abstract: An extensive wind-tunnel test of a round turbulent jet directed normally through a flat plate into a subsonic cross flow has been conducted. The results of the velocity field measurements are presented in a concise and usable form through the use of simple models to relate the velocity field to empirical values for the strength and location of the pair of contrarotating vortices associated with the jet.

Approach of axisymmetric turbulence to isotropy

Abstract: The approach of axisymmetric, homogeneous turbulence to isotropy using the direct interaction approximation is investigated. The turbulence is characterized by two parameters, the spectral variance transverse and parallel to the direction of axisymmetry. The dependence of these energy components on wave vector orientation is developed into a spherical harmonic expansion, and only low order terms are examined in detail. In terms of this characterization of the theory, the general qualitative nature of the relaxation to isotropy is discussed and numerical results for the energy spectrum and transfer functions are presented. It is shown that the simplest characterization of the theory leads to an almost linear relaxation to isotropy. The numerical results at moderate Reynolds numbers are compared to the phenomenological theory of Rotta [J. C. Rotta, Z. Physik 129, 547 (1951)]. A simple analytic estimate of the Rotta relaxation rate is also presented.

Decay of two-dimensional homogeneous turbulence

Abstract: The decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model. The calculations cover the range of Reynolds numbers 50 ≤ RL ≤ 100. Comparison of spectral methods with finite-difference methods shows that one of the former with a given resolution is equivalent in accuracy to one of the latter with twice the resolution. The numerical simulations at the larger Reynolds numbers suggest that earlier reported simulations cannot be used in testing inertial-range theories. However, the large-scale features of the flow field appear to be remarkably independent of Reynolds number.The direct-interaction approximation is in satisfactory agreement with simulations in the energy-containing range, but grossly underestimates enstrophy transfer at high wavenumbers. The latter failing is traced to an inability to distinguish between convection and intrinsic distortion of small parcels of fluid. The test-field model on the other hand appears to be in excellent agreement with simulations at all wavenumbers, and for all Reynolds numbers investigated.

Turbulent vortex rings

Abstract: We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.

Centerline Velocity Decay of Compressible Free Jets

Abstract: Theme A empirically determined formulation for the eddy viscosity is introduced into the turbulent axially symmetric compressible free jet theory of Kleinstein. * The easily evaluated algebraic equation that results shows excellent agreement with an extensive compilation of experimental data for the centerline velocity decay in the main region. It is found that the eddy viscosity can be treated as constant, with functional dependence on only the exit Mach number and the jet-to-freestream density ratio. The theory presented is applicable to the main region of most classes of free jets, including heterogeneous, nonisothermal, and subsonic and properly-expanded supersonic flows.

Stratospheric Mixing Estimated from High-Altitude Turbulence Measurements

Abstract: Vertical diffusion coefficients in the stratosphere are estimated from data obtained in the High Altitude Clear Air Turbulence (HICAT) investigation. The HICAT data sample was obtained from 285 flights of over 800,000 km distance, containing 24,000 flight kilometers of turbulence between 14 and 21 km MSL, and is the only such collection of fine-scale, true gust velocities in the stratosphere. One of the HICAT program objectives was to compute power spectral densities from each of the gust velocity component measurements over the wavelength range 30–15,000 m. The square roots of the integrals of these spectra for wavelengths <610 m, designated vi (for the ith component of velocity), were computed and related to the dissipation of kinetic energy, ϵ by use of the inertial range assumption in the form ϵ = [2υi2/(3ai)]½k.Here k is the lower wavenumber limit of the spectral integration (2π/610 m), and ai is equal to 0.5 for the longitudinal component and 0.65 for the lateral and vertical components, or...

Impinging Circular Turbulent Jets

Abstract: The normal impingement of turbulent circular jets on smooth walls is studied both experimentally and analytically. This type of flow can be divided into three distinct flow regions: the free-jet region; the impingement region; and the wall-jet region. The impingement region is the most important. It is shown that the impingement region occupies about 14% of the impingement height above the wall, whereas it extends about 22% of the impingement height radially. Semi-empirical methods to predict axail variations of velocity and static pressure are developed. Similarity of velocity and static pressure profiles is investigated and it is shown that these profiles are well described by the Gaussian error function. Variation of pertinent length scales are obtained empirically using dimensional analysis so that the time-averaged velocity and pressure fields in the impingement region can be predicted. A method to predict the wall shear stress in the impingement region is developed.

Some properties of truncated turbulence signals in bounded shear flows

Abstract: Measurement results of turbulent shear flows are re-examined. Various statistical properties of the truncated streamwise and normal velocity components u and v and of their product uv have been determined in an attempt to characterize quantitatively the motions of the flow. Average values and probability density distributions both of the truncated and untruncated signals have been taken.

Wakes behind two-dimensional surface obstacles in turbulent boundary layers

Abstract: By making simple assumptions, an analytical theory is deduced for the mean velocity behind a two-dimensional obstacle (of height h) placed on a rigid plane over which flows a turbulent boundary layer (of thickness δ). It is assumed that h [Gt ] δ, and that the wake can be divided into three regions. The velocity deficit − u is greatest in the two regions in which the change in shear stress is important, a wall region (W) close to the wall and a mixing region (M) spreading from the top of the obstacle. Above these is the external region (E) in which the velocity field is an inviscid perturbation on the incident boundary-layer velocity, which is taken to have a power-law profile U(y) = U∞(y − y1)n/δn, where n [Gt ] 1. In (M), assuming that an eddy viscosity (= KhU(h)) can be defined for the perturbed flow in terms of the incident boundary-layer flow and that the velocity is self-preserving, it is found that u(x,y) has the form , and the constant which defines the strength of the wake is , where u = uE(x, y) as y → 0 in region (E).In region (W), u(y) is proportional to In y. By considering a large control surface enclosing the obstacle it is shown that the constant of the wake flow is not simply related to the drag of the obstacle, but is equal to the sum of the couple on the obstacle and an integral of the pressure field on the surface near the body.New wind-tunnel measurements of mean and turbulent velocities and Reynolds stresses in the wake behind a two-dimensional rectangular block on a roughened surface are presented. The turbulent boundary layer is artificially developed by well-established methods (Counihan 1969) in such a way that δ = 8h. These measurements are compared with the theory, with other wind-tunnel measurements and also with full-scale measurements of the wind behind windbreaks.It is found that the theory describes the distribution of mean velocity reasonably well, in particular the (x/h)−1 decay law is well confirmed. The theory gives the correct self-preserving form for the distribution of Reynolds stress and the maximum increase of the mean-square turbulent velocity is found to decay downstream approximately as in accordance with the theory. The theory also suggests that the velocity deficit is affected by the roughness of the terrain (as measured by the roughness length y0) in proportion to In (h/y0), and there seems to be some experimental support for this hypothesis.

Measurements of the nearly isotropic turbulence behind a uniform jet grid

Abstract: Wind-tunnel turbulence behind a parallel-rod grid with jets evenly distributed along each rod is nearly isotropic. Homogeneity improvement over prior related experiments was attained by the use of controllable nozzles. Compared with the ‘passive’ case, the downwind-jet ‘active’ grid has a smaller static pressure drop across it and gives a smaller turbulence level at a prescribed distance from it, while the upwind-jet grid gives a larger static pressure drop and larger turbulence level. ‘Counterflow injection’ generates larger turbulence energy and larger scales, both events being evidently associated with instability of the jet system. This behaviour is much like that commonly observed behind passive grids of higher solidities.If the turbulent kinetic energy is approximated as an inverse power law in distance, the (positive) exponent decreases with increasing (downwind or upwind) jet strength, corresponding to slower absolute decay rates. No peculiar decay behaviour occurs when the jet grid is ‘self-propelled’ (zero net average force), or when the static pressure drop across it is zero.The injection does not change the general behaviour of the energy spectra, although the absolute spectra change inasmuch as the turbulence kinetic energy changes.

The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers

Abstract: It is now well known that the turbulence structure of thin shear layers can be strongly affected by the application of extra rates of strain in addition to the shear velocity gradient. Examples of such extra strain rates include lateral divergence or convergence, and streamline curvature in the plane of the mean shear. The changes in Reynolds stress are an order of magnitude larger than would be expected from the explicit extra terms in the Reynolds-stress transport equations, and therefore an order of magnitude larger than predicted by conventional calculation methods. In the present paper, one of a series on ‘complex’ turbulent flows, we show that bulk compression or dilatation (i.e. an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatation. The fractional change in Reynolds stress is an order of magnitude larger than the fractional change in volume of a fluid element. The physical mechanism is probably analogous to that responsible for the large effects of divergence or convergence in incompressible flow. Because the phenomenon seems to be of great practical importance we discuss it in the context of engineering calculation methods. An empirical correction formula, analogous to those used to allow for divergence or curvature effects, greatly reduces the large discrepancies found between recent experiments on supersonic boundary layers and calculations by conventional extensions of successful incompressible-flow methods.

Diffusion experiments with numerically integrated isotropic turbulence.

Abstract: Results are presented of computer simulations of particle diffusion on a numerically integrated, decaying isotropic turbulent flow field. The diffusion of both fluid particles and “small” spherical particles is studied. Comparisons are made of the various temporal autocorrelation coefficients. It is found that for “short” times, the Lagrangian (fluid point) velocity correlation is larger than the Eulerian correlation, while for longer times the opposite is true. It is also found in the “small” spherical particle case that as the response time of the particle is increased, the velocity autocorrelation coefficient increases.

The evolution of a convective planetary boundary layer — A higher-order-closure model study

Abstract: The evolution of the boundary layer on day 33 of the Wangara experiment in southeast Australia is calculated with a higher-order-closure turbulence model. This model, which includes equations for the mean field as well as the second moments of the turbulent field, is described in detail. The mean profiles of wind, temperature, and humidity, the profiles of heat and humidity fluxes, the Reynolds stress distributions, and the height of the boundary layer are shown between 10 a.m. and 6 p.m. The results agree well with those from Deardorff's 3-D simulation and take relatively little computer time.

Combined dye-streak and hydrogen-bubble visual observations of a turbulent boundary layer

Abstract: The turbulent boundary layer over a flat plate was observed visually using two dye injectors and a normal bubble wire. One dye injector was a standard wall slot; the other one was a small Pitot probe which could be placed anywhere in the flow. The purpose of these experiments was to improve understanding of the relationships between the bursting of low-speed streaks near the wall and the flow field farther away from the wall.On the basis of these observations, it seems that (i) each lift-up is associated with a disturbance which originates in the logarithmic region and is characterized by a mean motion towards the wall, and that (ii) such disturbances are generated by the interaction of an earlier burst from further upstream with the fluid motion in the logarithmic region.

The Interference of Two-Dimensional Parallel Jets : 2nd Report, Experiments on the Combined Flow of Dual Jet

Abstract: Experiments on dual jet, issued from two parallel slot nozzles set on a common end wall, were reported in the 1st report. In this report, the measurement of flow in hte combined flow region of the dual jet are discussed. From these measurements, effects of distance between these two nozzles on the flow field were studied and the characteristics of combined flow are compared with those of a single jet. A summary of the results is as follows : (1) The velocity profiles of the combined flow are similar and agree well with the theoretical profile of the single jet, but the distributions of the turbulence intensities show a different property from those of the single jet. (2) The width of combined jet spreads linearly in the downstream direction and inceases with the distance between two nozzles. (3) Because of the negative pressure distribution in the combined jet, the total momentum fluxes in the downstream direction are not conserved, and the decay of the maximum velocity is stronger than that of a single jet.

Spatial waves in turbulent jets

Abstract: Measurements of the spatial development of disturbance pressure waves in a low‐speed axisymmetric turbulent free jet have been carried out. The results show that the wavenumbers of the pressure waves increase monotonically, while the phase velocities decrease as the Strouhal number of the jet increases. The pressure disturbance grows to a maximum at some distance downstream from the nozzle and then decays. The distributions of the amplitude of the pressure waves along the jet are similar if the data are plotted against a normalized distance St x/D. The most amplified mode is at a Strouhal number of 0.5 for the shear layer and 0.35 for the center line. The wave characteristics follow closely the linear stability theory of an inviscid diverged shear flow.