Showing papers on "Turbulence published in 1973"

Turbulent Diffusion in the Environment

Abstract: I Molecular Diffusion- 11 Introduction- 12 Concentration- 13 Flux- 14 Fick's Law- 15 Conservation of Mass- 16 Instantaneous Plane Source- 17 Some Simple Examples- 18 Diffusion of Finite Size Cloud- 19 'Reflection' at Boundary- 110 Two- and Three-Dimensional Problems- 111 Continuous Sources- 112 Source in Uniform Wind- Appendix to Chapter I- Exercises- References- II Statistical Theory of Diffusion and Brownian Motion- 21 Introduction- 22 Dispersion Through Random Movements- 23 Diffusion with Stationary Velocities- 24 Brownian Motion- 25 Dispersion of Brownian Particles- 26 Simple Random Walk Model- 27 Reflecting Barrier- 28 Absorbing Barrier- 29 Connection of Random Walk to Diffusion Equation- 210 Deposition on Vertical Surfaces- 211 Deposition on Horizontal Surfaces- Exercises- References- III Turbulent Diffusion: Elementary Statistical Theory and Atmospheric Applications- 31 Fundamental Concepts of Turbulence- 32 Field Measurements of Concentration and Dosage- 33 The Statistical Approach to Environmental Diffusion- 34 'Lagrangian' Properties of Turbulence- 35 Consequences of Taylor's Theorem- 36 The Form of the Particle-Displacement Probability Distribution- 37 Mean Concentration Field of Continuous Sources- 38 Apparent Eddy Diffusivity- 39 Application to Laboratory Experiments- 310 Application to Atmospheric Diffusion- 311 Initial Phase of Continuous Plumes- 312 Atmospheric Cloud Growth far from Concentrated Sources- 313 The Non-Stationary Character of Atmospheric Turbulence- 314 The Hay-Pasquill Method of Cloud-Spread Prediction- Exercise- References- IV 'Relative' Diffusion and Oceanic Applications- 41 Experimental Basis- 42 Mean Concentration Field in a Frame of Reference Attached to the Center of Gravity- 43 Probability Distributions of Particle Displacements- 44 Kinematics of Particle Movements in a Moving Frame- 45 Phases of Cloud Growth- 46 History of a Concentrated Puff- 47 Initially Finite Size Cloud- 48 Use of the Diffusion Equation- 49 Horizontal Diffusion in the Ocean and Large Lakes- 410 Application to Diffusion of Sewage Plumes- 411 Vertical Diffusion in Lakes and Oceans- Exercise- References- V Dispersion in Shear Flow- 51 Introduction- 52 Properties of the Planetary Boundary Layer- 53 Particle Displacements in a Wall Layer- 54 Continuous Ground-Level Line Source- 55 Flux and Eddy Diffusivity- 56 Comparison with Experiment- 57 Continuous Point Source at Ground Level- 58 Use of the Diffusion Equation- 59 Elevated Sources- 510 Longitudinal Dispersion in Shear Flow- 511 Shear-Augmented Diffusion in a Channel- 512 Dispersion in Natural Streams- 513 Shear-Augmented Dispersion in Unlimited Parallel Flow- 514 Diffusion in Skewed Shear Flow- References- VI Effects of Density Differences on Environmental Diffusion- 61 Introduction- 62 Fundamental Equations- 63 Approximate Forms of the Equations- 64 Equations for Turbulent Flow- 65 Turbulent Energy Equation- 66 Diffusion Floors and Ceilings- 67 Diffusion in a Continuously Stratified Fluid- 68 Velocity Autocorrelation and Particle Spread in Stratified Fluid Model- 69 Bodily Motion of Buoyant and Heavy Plumes- 610 Dynamics of a Line Thermal- 611 Similarity Theory- 612 Bent-Over Chimney Plumes- 613 Theory of Buoyancy Dominated Plumes in a Neutral Atmosphere- 614 Comparison with Observation- 615 Flow Pattern within a Plume- 616 Effect of Atmospheric Stratification- 617 Approximate Arguments for Plumes in Stratified Surroundings- 618 Engineering Assessment of Ground Level Pollution from Buoyancy Dominated Plumes- 619 Effects of Plume Rise on Ground-Level Concentration- Appendix to Chapter VI- A61 Momentum Plumes- Exercise- References- VII The Fluctuation Problem in Turbulent Diffusion- 71 Introduction- 72 Probability Distribution of Concentration- 73 The Functional Form of the Probability Distribution- 74 Hazard Assessment on the Basis of Concentration Probabilities- 75 The Variance of Concentration Fluctuations- 76 Self-Similar Fluctuation Intensity Distribution- 77 Fluctuating Plume Model- References

The deepening of the wind-Mixed layer

Abstract: A simple model is given that describes the response of the upper ocean to an imposed wind stress. The stress drives both mean and turbulent flow near the surface, which is taken to mix thoroughly a layer of depth h, and to erode the stably stratified fluid below. A marginal stability criterion based on a Froude number is used to close the problem, and it is suggested that the mean momentum has a strong role in the mixing process. The initial deepening is predicted to obey where u. is the friction velocity of the imposed stress, N the ambient buoyancy frequency, and t the time. After one-half inertial period the deepening is arrested by rotadeon at a depth h = 22/4 u.{(Nf)+ where f is the Coriolis frequency. The flow is then a “mixed Ekman” layer, with strong inertial oscillations superimposed on it. Three quarters of the mean energy of the deepening layer is found to be kinetic, and only one-quarter potential. Heating and cooling are included in the model, but stress dominates for time-scales of ...

On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

Abstract: Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally at Re > 5 × 104. Transition could be initiated at lower Re by introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.Mixed laminar and turbulent flows were observed far downstream for \[ 2000 < Re < 2700 \] when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lower Re. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.

The nature of saltation and of ‘bed-load’ transport in water

Abstract: Owing to observational difficulties the distinction between a ‘suspended’ load of solids transported by a stream and a ‘ bed-load ’ has long remained undefined. Recently, however, certain critical experiments have thrown much light on the nature of bed-load transport. In particular, it has been shown that bed-load transport, by saltation, occurs in the absence of fluid turbulence and must therefore be due to a separate dynamic process from that of transport in suspension by the internal eddy motion of a turbulent fluid. It has been further shown that the forward motion of saltating solids is opposed by a frictional force of the same order as the immersed weight of the solids, the friction coefficient approximating to that given by the angle of slip. The maintenance of steady motion therefore requires a predictable rate of energy dissipation by the transporting fluid. The fluid thrust necessary to maintain the motion is shown to be exerted by virtue of a mean slip velocity which is predictable in the same way as, and approxim ates to, the terminal fall velocity of the solid. The mean thrust, and therefore the transport rate of saltating solids, are therefore predictable in terms of the fluid velocity close to the bed, at a distance from it, within the saltation zone, of a ‘centre of fluid thrust’ analogous to the ‘centre of pressure’. This velocity, which is not directly measurable in water streams, can be got from a knowledge of stream depth and mean flow velocity. Thus a basic energy equation is obtained relating the rate of transporting work done to available fluid transporting power. This is shown to be applicable to the transport both of wind-blown sand, and of water-driven solids of all sizes and larger than that of medium sand. Though the mean flow velocity is itself unpredictable, the total stream power, which is the product of this quantity times the bed shear stress, is readily measurable. But since the mean flow velocity is an increasing function of flow depth, the transport of solids expressed in terms of total stream power must decrease with increasing flow depth/grain size ratio. This considerable variation with flow depth has not been previously recognised. It explains the gross inconsistencies found in the existing experimental data. The theoretical variation is shown to approximate very closely to that found in recent critical experiments in which transport rates were measured at different constant flow depths. The theory, which is largely confirmed by these and other earlier experiments, indicates that suspension by fluid turbulence of mineral solids larger than those of medium sands does not become appreciable until the bed shear stress is increased to a value exceeding 12 times its threshold value for the bed material considered. This range of unsuspended transport decreases rapidly, however, as the grain size is reduced till, at a certain critical size, suspension should occur at the threshold of bed movement.

Effects of Streamline Curvature on Turbulent Flow.

Abstract: : Streamline curvature in the plane of the mean shear produces large changes in the turbulence structure of shear layers, usually an order of magnitude more important than normal pressure gradients and other terms in the mean-motion equations for curved flows. The effects on momentum and heat transfer in boundary layers are noticeable on typical wing sections and are very important on highly-cambered turbomachine blades: turbulence may be nearly eliminated on highly-convex surfaces, while on highly-concave surfaces momentum transfer by quasi-steady longitudinal vortices dominates the ordinary turbulence processes. The greatly enhanced mixing rates of swirling jets and the characteristic non-turbulent cores of trailing vortices are also consequences of the effects of streamline curvature on the turbulence structure. A progress report, comprises a review of current knowledge, a discussion of methods of predicting curvature effects, and a presentation of principles for the guidance of future workers.

Drag reduction in turbulent flow by polymer additives

Abstract: A brief survey is given of the drag reduction phenomenon, emphasizing the aspects which must be explained by any theory: onset, the existence of intrinsic drag reduction, the Newtonian plug, saturation with increasing concentration, and the maximum drag reduction asymptote. In addition, the polymer properties observed to be favorable are noted. Experimental and theoretical arguments are cited, indicating that sublayer stability arguments are not relevant. Recent evidence is given, linking the onset phenom-enon to a molecular time scale. The behavior of isolated molecules in flow fields is briefly surveyed, indicating the possibility of large increases in viscosity in relatively rotation free strain rate fields; indirect experimental evidence for such behavior is cited, and it is shown how, by reducing the intensity of the smallest eddies, this can explain the various aspects noted. The maximum drag reduction asymptote is discussed, in connection with recent measurements of turbulent fluctuations in drag reducing flows, and it is shown how both of these may be related to changes in the large eddy structure caused by the polymer induced changes in the small eddies.

Biasing correction for individual realization of laser anemometer measurements in turbulent flows

Abstract: In turbulent flow situations the histograms constructed in the individual realization mode of laser anemometry are biased. The biasing occurs because a larger than average volume of fluid, and hence a larger than average number of scattering centers, pass through the probe volume during periods when the velocity is faster than the mean. Similarly, a smaller volume of fluid and a smaller number of scattering particles pass through the probe volume during periods when the velocity is slower than the mean. The proper weighting function needed to correct the biased data is the inverse of the instantaneous velocity vector. However, an analysis using turbulent flow models show that corrections based only upon the streamwise component of the velocity vector are adequate for many flow situations.

Mechanism of detachment of colloidal particles from a flat substrate in a turbulent flow

Abstract: Visser [J. Colloid Interface Sci. 34, 26 (1970)] has used hydrodynamic techniques, i.e., rotating cylinders, to study the removal of submicron particles from various substrates. He developed empirical relationships which relate the force of adhesion to the viscous drag experienced by the particle, which is assumed to be embedded in a steady, viscous sublayer. Although this technique is a valuable experimental tool, the question of how a particle is moved is evaded. Detailed investigations of the turbulent boundary layer (reported in the fluid mechanics literature) have shown that the viscous sublayer is anything but steady, and is continually disrupted by turbulent “bursts.” These bursts, which are not unlike miniature tornados, may cause instantaneous lift forces sufficient to detach a particle. This model of an unsteady sublayer has been used to predict the possible lift forces acting on the particle. These can arise either from impulsive motions or from the generation of a quasi-steady updraft over a particle by a burst. From these predicted lift forces, a removal criterion is obtained which for a given fluid reduces to τωd4/3 ⩾ constant where τω is wall shear stress and d is particle diameter. This result is shown to be in general agreement with previous empirical studies. The rate of removal can be predicted by combining this analysis of lift forces with literature data on the size and frequency of bursts. Although this latter information is taken from studies in pipe-flow and flow over a flat-plate, the predicted rates are in qualitative agreement with the experimental data from rotational instruments.

Experiments on instability and turbulence in a stratified shear flow

Abstract: This is a study of turbulence which results from Kelvin—Helmholtz instability at the interface between two miscible fluids in a two-dimensional shear flow in the laboratory. The growth of two-dimensional ‘billows’, their disruption by turbulence, and the eventual decay of this turbulence and the re-establishment of a gravitationally and kinematically stable interface are described. Continuous measurements of density and horizontal velocity from both fixed and vertically moving probes have been made, and the records obtained are presented, together with photographs showing the simultaneous appearance of the flow, which serve to identify the physical nature of events seen in the records. The measurements show how the fine-structure of the density field described in earlier experiments is related to velocity fluctuations. The vertical length scales of the final mean velocity and density structure are found to be different, and to depend on the Richardson number at which instability first occurred. The eventual Richardson number at the centre of layer is, however, not dependent on the initial Richardson number and has a value of about one third. The implications of these results to the eddy diffusion coefficients, to the energy exchange, and to turbulence in the ocean and the atmosphere are discussed.

A theory of turbulent flow round two-dimensional bluff bodies

Abstract: By generalizing the theory of ‘rapid distortion’ of turbulence developed by Batchelor & Proudman (1954) it is shown in this paper that the turbulent velocity around a bluff body placed in a turbulent flow can be calculated outside and upstream of the regions of separated flow, if the incident turbulent flow satisfies the following conditions: (i) if a/Lx [Lt ] 1 or = O(1), Re−1 is the r.m.s. velocity of the homogeneous incident turbulence, a is a transverse dimension of the body (the radius in the case of a circular cylinder), Lx is the integral scale of the incident turbulence and v is the kinematic viscosity.Detailed calculations are given for the flow around a circular cylinder with particular emphasis on the turbulence very close to the surface. (The results can be generalized to other cylindrical bodies.) Mean-square values and spectra of velocity have been found only in the limiting situations where the turbulence scale is very much larger or smaller than the size of the body, i.e. Lx [Gt ] a or Lx [Lt ] a. But, whatever the value of a/Lx, if the frequency is sufficiently large the results for spectra tend to those of the limiting situation where Lx [Lt ] a. The reason why the turbulence velocities have not been calculated for intermediate values of a/Lx is that closed-form solutions cannot be found and that the computing time then required is quite excessive. However, some computed results are used in the paper to suggest the qualitative behaviour of the turbulence when Lx is of order a. An important result of the theory is that it illuminates and distinguishes between the governing physical processes of distortion of the turbulence by the mean flow, the direct ‘blocking’ of the turbulence by the body, and concentration of vortex lines at the body's surface.The results of the theory have many applications, for example in calculating turbulent dispersion and fluctuating pressures on the body, as shown elsewhere by Hunt & Mulhearn (1973) and Hunt (1973).In conclusion the theoretical results are briefly compared with experimental measurements of turbulent flows round non-circular cylinders. A detailed comparison with measurements round circular cylinders will be published later by Petty (1974).

A Preliminary Numerical Study of Atmospheric Turbulent Flows in the Idealized Planetary Boundary Layer

Abstract: A turbulent transport model is developed to study atmospheric turbulence in the planetary boundary layer. A total of nine equations governing the mean motion, mean turbulent stresses, and turbulence length scale are integrated numerically. In this preliminary study, only the ideal case of neutral lapse rate, barotropic, statistically stationary, and horizontally homogeneous conditions is treated. The height of the boundary layer is investigated and found to be about 0.5 u*/f, where u* and f are the friction velocity and Coriolis force parameter, respectively. The computed friction coefficient, the crossisobaric angle, the vertical profiles of mean wind, mean turbulent stresses, the turbulent length scale, and eddy coefficients agree well with observations and with Deardorff's results. Various terms in the turbulent stress equations, which are difficult to measure, are discussed. The direction of the stresses seems to align with the direction of the wind shear. The profiles of the turbulent diffus...

A survey of the mean turbulent field closure models.

Abstract: C solutions to the differential boundary-layer equations have for some years now been applied to turbulent boundary layers where relief from the difficulty of solution permits more concern for the physical elements of models which purport to simulate some statistical features of turbulent flowfields. A first step has been accomplished; that is, accurate, quite versatile, and practically/useful computer programs have been combined with rather simple and successful empirical statements" which allow one to estimate the Reynolds shear stress in the equations for the mean velocity field. We call this Mean Velocity Field (MVF) closure since it predicts only the mean velocity field in addition to the mean shear stress. For boundarylayer flows a set of empirical constants must be selected. However, it is then possible to accurately predict flows with wall transpiration, heat transfer, and a variety of other boundary conditions, and, remarkably, with no adjustment in the constants. However, the constants must be adjusted for, say, pipe or channel flow or free shear flows. By moving on to the more complicated Mean Turbulent Field (MTF) closure there is some hope of discovering increasingly universal models and a greater range of predictability. There are two other incentives: First, it is rather comforting actually to compute the turbulent kinetic energy; it is, after all, the premier property that distinguishes turbulent from laminar flow. Second, it appears possible to include body forcelike effects such as curvature, buoyancy, and Coriolis effects with no further empiricism. The latter is a line of thought that is not new,' and it has occupied the present authors' interest for some time. However, in this paper we avoid these topics in order to simplify discussion of an already complicated field. We also assume that the fluid is incompressible. Extension to high Mach number flows does not, however, seem to be a major problem. A basis for MTF calculations began appropriately enough with the semiheuristic models of Kolmogoroff and Prandtl in the early 1940's; they include the turbulent kinetic energy transport equation, a turbulent-energy-related eddy viscosity, and either a prescribed length scale function or a differential equation for a length scale. We wish to call this Mean Turbulent Energy (MTE) closure which together with Mean Reynolds Stress (MRS) closure forms two subsets of MTF closure.* MRS closure implies a closed set of equations which include equations for all nonzero components of the Reynolds stress tensor. Chou' seems to be the first to initiate a study of the full set of equations with an eye towards closure. However, it was Rotta in 1951 who laid the foundation for almost all of the current models. In the Reynolds stress tensor equation (the tensor equation for the single-point, double-velocity correlations, the trace of which is the kinetic energy equation) there appear pressure-velocity gradient correlations, (pdujdxj), which Rotta called the energy redistribution terms and which he argued should be proportional to the deviation from isotropy — dtj(uky/3. On the whole, the assumption seems physically correct, but of further importance is the fact that it provides a unity that was lacking, say, in the 1940's.f Thus, the Reynolds shear stress is now determined as a part of the whole; MTE closure can be obtained as an analytic simplification of MRS closure, and, furthermore, MVF closure (that is, eddy viscosity or mixing length concepts) can be viewed as a further simplification. We shall follow this process of simplification in this paper. Despite the unity of thought provided by Rotta's basic assumption, it is, of course, an approximation to nature and is subject to modification in the hands of investigators eager to achieve agreement with data. Furthermore, there are other terms in the Reynolds stress equations, such as the dissipation and diffusion terms, which are modeled differently by different investigators and represent some impass to a consensus theory such as is the near state of MVF closure. In the present development we have attempted to present the basic ideas and a core model for MRS and MTE closure and

Prediction of free shear flows: A comparison of the performance of six turbulence models

Abstract: The performance is evaluated of three distinct classes of turbulence model. These classes are: (1) Turbulent-viscosity models in which the length scale of turbulence is found by way of algebraic formulas, (2) turbulent-viscosity models in which the length scale of turbulence is found from a partial differential equation of transport, and (3) models in which the shear stress itself is the dependent variable of a partial differential conservation equation. Two models were examined in each class; thus, six different models were tested. A complete mathematical statement of these models is provided and a brief commentary on the models is included.

Drag reduction of a submersible hull by electrolysis

Abstract: Viscous drag reduction of a fully-submerged body of revolution is obtained by creating hydrogen gas on the hull by electrolysis. The bubbles alter both the laminar and turbulent boundary-layer characteristics resulting in a significant reduction in the viscous drag on the 3-foot model up to a speed of 8.5 feet per second, the maximum test velocity. Results show that the amount of drag reduction depends on the ratio of the mass flow of water in the wake to the time-rate of hydrogen mass produced beneath the boundary-layer. The results presented herein are model results and should NOT be considered directly applicable to any existing prototype.

The origin of secondary flow in turbulent flow along a corner

Abstract: The mechanisms which initiate secondary flow in developing turbulent flow along a corner are examined on the basis of both energy and vorticity considerations. This is done by experimentally evaluating the terms of an energy balance and vorticity balance applied to the mean motion along a corner bisector. The results show that a transverse flow is initiated and directed towards the corner as a direct result of turbulent shear stress gradients normal to the bisector. The results further indicate that anisotropy of the turbulent normal stresses does not play a major role in the generation of secondary flow. Possible extensions of the present results to other related flow situations are ahstrated and discussed.

Analytic Prediction of the Properties of Stratified Planetary Surface Layers

Abstract: By considering the complex of one-point, turbulent moment equations for velocity, pressure and temperature, it appears possible to predict some properties of diabatic, density-stratified planetary layers using empirical information obtained from laboratory turbulence data in the absence of density stratification. In this paper attention is focused on the near-surface, constant-flux layer. The results, like the empirical input, are simple and, hopefully, will be instructive and useful in the formulation of improved and possibly more complicated models in the future.

Relaminarization in highly accelerated turbulent boundary layers

Abstract: The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

Experiment on convex curvature effects in turbulent boundary layers

Abstract: Turbulent boundary layers along a convex surface of varying curvature were investigated in a specially designed boundary-layer tunnel. A fairly complete set of turbulence measurements was obtained. The effect of curvature is striking. For example, along a convex wall the Reynolds stress is decreased near the wall and vanishes about midway between the wall and the edge of a boundary layer where there exists a velocity profile gradient created upstream of the curved wall.

Prediction of turbulent boundary layers and wakes in compressible flow by a lag-entrainment method

Abstract: : A rapid method is presented for predicting the development of turbulent boundary layers and wakes taking account of the influence of the upstream flow history on the turbulent stresses. The method employs the momentum integral equation, the entrainment equation and an equation for the streamwise rate of change of entrainment coefficient. This last, developed from the equation for shear stress which Bradshaw, Ferriss and Atwell derived from the turbulent kinetic energy equation, explicitly represents the balance between the advection, production, diffusion and dissipation of turbulent kinetic energy. The application of the method to two-dimensional and axisymmetric flows is described, and it is shown how secondary influences on the turbulence structure such as longitudinal surface curvature, can be logically taken into account. Comparisons with experiment show that, for incompressible flow, the method is fully comparable comparable in accuracy with the best of the methods assessed at the Stanford Conference of 1968. For compressible flow, the accuracy of the method in flow at constant pressure is ensured by its derivation, but the available experimental data do not enable its accuracy in flows with strong pressure gradients to be assessed with any finality. (Author)

The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment

Abstract: The interaction of a vortex ring with a sharp density interface is investigated in the laboratory. Attention is restricted to the case where the Froude number based on the density difference across the interface, the velocity of propagation of the ring normal to the interface and the diameter of the ring is less than unity. It is found that the depth of maximum penetration of the ring, and the diameter of the region of contact between the ring and the interface, are functions of the Froude number. A simple model of the ring-interface interaction which accounts for the observed motion is proposed. This model is then used to calculate the volume rate of entrainment produced by the vortex rings. It is found that this rate of entrainment is proportional to the cube of the Froude number, a result which agrees with measurements of entrainment across density interfaces caused by grid-generated turbulence (Turner 1968) and by a plume incident on the interface (Baines 1973). Thus the vortex ring would appear to be a good approximation to a turbulent eddy in these situations. The main feature of the model is that it identifies the way in which the kinetic energy of the turbulence is converted into potential energy by entraining fluid across the interface. In particular, it indicates that the essential force balance is inertial, and that it is possible to discuss entrainment across a sharp density interface without explicitly invoking either viscosity or molecular diffusion.

The laser-doppler velocimeter and its application to the measurement of turbulence

Abstract: The paper examines the spatial and temporal resolution of the laser-Doppler velocimeter. Criteria for meaningful measurements are established. The effect of the random phase fluctuations introduced by the Doppler ambiguity on attempts to measure statistical quantities in turbulent flow is examined. An operational laser-Doppler velocimeter is described and measurements in both laminar and turbulent flow are presented.

Pressure distributions on circular cylinders at critical Reynolds numbers

Abstract: Measurements have been made of the mean and fluctuating pressure distributions on long circular cylinders, having smooth and rough surfaces, at Reynolds numbers of 1·11 × 105 and 2·35 × 105 in both uniform and turbulent streams. The presence of free-stream turbulence a t these Reynolds numbers was found to suppress coherent vortex shedding on the smooth cylinder and give rise to a complex pressure field in which the mean pressure distribution was almost independent of Reynolds number over the small range of Reynolds numbers tested. The pressure distributions on the rough cylinder were found to be completely different in uniform and turbulent streams; the presence of turbulence gave rise to an increase in the level of vortex shedding energy, and produced mean pressure distributions similar to those obtained on smooth cylinders at Reynolds numbers of the order of 107.

Measurements in a self-preserving plane wall jet in a positive pressure gradient

Abstract: Measurements of a wall jet in a self-preserving pressure gradient are described. The quantities measured with a linearized hot-wire anemometer were the mean velocity, the turbulence stresses, triple and quadruple velocity correlations, intermittency and spectra of the longitudinal turbulence intensity. The turbulence, as well as the mean flow, reached a self-preserving state in which the ratio of the maximum velocity to the free-stream velocity was 2·65. Skin friction was also measured using the razor-blade technique in the viscous sublayer and buffer region. The values of the constants in the logarithmic law of the wall are found to be similar to those in boundary-layer and pipe flows. The skin-friction coefficient is slightly lower than that found for the wall jet in still air (Guitton 1970), but close to the formula of Bradshaw & Gee (1962) for the wall jet in an external stream with zero pressure gradient.A balance of the terms in the turbulence energy equation is presented and discussed. The shearing stress is not zero at the point of maximum velocity but is of opposite sign to that at the wall and hence the contribution of this stress to turbulence production is negative in the outer part of the boundary-layer region. However, the total turbulence production remains positive because the contribution of the normal stresses is positive and slightly larger. The pressure—velocity gradient correlations are evaluated by difference from the Reynolds stress equations and are compared with the theoretical model of Hanjalic & Launder (1972b). Agreement is quite good in the outer region of the wall jet. The above model is also compared with the triple velocity correlations and again found to be in fair agreement.