Some properties of boundary layer flow during the transition from laminar to turbulent motion

Transition in the boundary layer on a flat plate is examined from the point of view of intermittent production of turbulent spots. On the hypothesis of localized laminar breakdown, for which there is some expermental evidence, Emmons’ probability calculations can be extended to explain the observed statistical similarity of transition regions. Application of these ideas allows detailed calculations of the boundary layer parameters including mean velocity profiles and skin friction during transition. The mean velocity profiles belong to a universal one-parameter family with the intermittency factor as the parameter. From an examination of experimental data the probable existence of a relation between the transition Reynolds number and the rate of production of the turbulent spots is deduced. A simple new technique for the measurement of the intermittency factor by a Pitot tube is reported.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure

A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Plume structure in high-Rayleigh-number convection

Near-wall structures in turbulent natural convection at Rayleigh numbers of $10^{10}$ to $10^{11}$ at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log–normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.

Universality and scaling behavior of injected power in elastic turbulence in wormlike micellar gel

We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a wormlike micellar gel formed by surfactant cetyltrimethylammonium tosylate. At sufficiently high Weissenberg numbers the shear rate, and hence the injected power p(t), at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian PDFs can be well described by a universal, large deviation functional form given by the generalized Gumbel distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.

Turbulent flow computations using upwind RANS technique for a flat plate and an airfoil

Reynolds Averaged Navier Stokes (RANS) equations are solved using third order upwind biased Roe's scheme for the inviscid fluxes and second order central difference scheme for the viscous fluxes. The Baldwin & Lomax turbulence model is employed for Reynolds stresses. The governing equations are solved using finite-volume implicit scheme in body fitted curvilinear coordinate O-grid system. Computations axe reported for a flat plate apart from RAE 2822 and NACA 0012 airfoils. Results for the flat plate at M = 0.3, R-c = 4.0 x 10(6) compare favourably with the analytical solution. Results for the two airfoils are compared with experiment. There is a good agreement in C-p distribution between experiment and computation for both the airfoils. Comparison of C-f distribution with experiment for RAE 2822 airfoil is reasonable.

Continued self-similar breakup of drops in viscous continuous phase in agitated vessels

Drop breakup inviscous liquids in agitated vessels occurs in elongational flow around impeller blade edges. The drop size distributions measured over extended periods for impellers of different sizes show that breakup process continues up to 15-20 h, before a steady state is reached. The size distributions evolve in a self-similar way till the steady state is reached. The scaled size distributions vary with impeller size and impeller speed, in contrast with the near universal scaling known for drop breakup in turbulent flows. The steady state size of the largest drop follows inverse scaling with impeller tip velocity. The breadth of the scaled size distributions also shows a monotonic relationship with impeller tip velocity only. (C) 2011 Elsevier Ltd. All rights reserved.

Shear banding in a yield stress bearing Langmuir monolayer

We examine the shear-thinning behaviour of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs, showing coexistence of the fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile, which is linear at low shear rates, becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behaviour like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation.

Nitrogen and carbon flows through Belandur lake - Role of Bellandur lake as a natural wetland treating Bangalore wastewater

Much of the Bangalore sewage is treated in three streams namely Bellandur (K&C Valley),Vrishabhavati and Hebbal-Nagavara stream systems. Among these it is estimated that out of a total of about 500MLD of partially treated sewage is let into the Bellandur tank. We estimate that a total of about 77t N non-industrial anthropogenic nitrogen efflux (mainly urine and excreta) in Bangalore city. This is distributed between that handled by the three sewage streams, soak-pits and land deposition. About 17-24.5t N enters the Bellandur tank daily. This has been happening over few decades and our observations suggest that this approximately 380ha tank is functioning as a C and N removal system with reasonable efficiency. The ammoniacal and nitrate nitrogen content of the water at the discharge points were estimated and found that over 80% of the nitrogen influx and over 75% of the C influx is removed by this tank system. We observed that there are three nitrogen sinks namely bacterial, micro-algal and macrophytes. The micro-algal fraction is dominated by Microcystis and Euglenophyceae members and they appear to constitute a significant fraction. Water hyacinth represents the single largest representative of the macrophytes. This tank has been functioning in this manner for over three decades. We attempt to study this phenomenon from a material balance approach and show that it is functioning with a reasonable degree of satisfaction as a natural wetland. As the population served and concomitant influx into this wetland increases, there is a potential for the system to be overloaded and to collapse. Therefore a better understanding of its function and the need for maintenance is discussed in the paper.

Modeling of nonreacting and reacting turbulent spray jets using a fully stochastic separated flow approach

Numerical modeling of several turbulent nonreacting and reacting spray jets is carried out using a fully stochastic separated flow (FSSF) approach. As is widely used, the carrier-phase is considered in an Eulerian framework, while the dispersed phase is tracked in a Lagrangian framework following the stochastic separated flow (SSF) model. Various interactions between the two phases are taken into account by means of two-way coupling. Spray evaporation is described using a thermal model with an infinite conductivity in the liquid phase. The gas-phase turbulence terms are closed using the k-epsilon model. A novel mixture fraction based approach is used to stochastically model the fluctuating temperature and composition in the gas phase and these are then used to refine the estimates of the heat and mass transfer rates between the droplets and the surrounding gas-phase. In classical SSF (CSSF) methods, stochastic fluctuations of only the gas-phase velocity are modeled. Successful implementation of the FSSF approach to turbulent nonreacting and reacting spray jets is demonstrated. Results are compared against experimental measurements as well as with predictions using the CSSF approach for both nonreacting and reacting spray jets. The FSSF approach shows little difference from the CSSF predictions for nonreacting spray jets but differences are significant for reacting spray jets. In general, the FSSF approach gives good predictions of the flame length and structure but further improvements in modeling may be needed to improve the accuracy of some details of the Predictions. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.