We are interested in examining the long-time decay rate of a passive scalar in two-dimensional flows. The focus is on the effect of boundary conditions for kinematically prescribed velocity fields with random or periodic time dependence. Scalar evolution is followed numerically in a periodic geometry for families of flows that have either a slip or a no-slip boundary condition on a square or plane layer subdomain D. The boundary conditions on the passive scalar are imposed on the boundary C of the domain D by restricting to a subclass invariant under certain symmetry transformations. The scalar field obeys constant (Dirichlet) or no-flux (Neumann) conditions exactly for a flow with the slip boundary condition and approximately in the no-slip case. At late times the decay of a passive scalar, for example temperature, is exponential in time with a decay rate gamma(kappa), where kappa is the molecular diffusivity. Scaling laws of the form gamma(kappa) ~ C*kappa^alpha for small kappa are obtained numerically for a variety of boundary conditions on flow and scalar, and supporting theoretical arguments are presented. In particular when the scalar field satisfies a Neumann condition on all boundaries, alpha ~ 0 for a slip flow condition; for a no-slip condition we confirm results in the literature that alpha ~ 1/2 for a plane layer, but find alpha ~ 2/3 in a square subdomain D where the decay is controlled by stagnant flow in the corners. For cases where there is a Dirichlet boundary condition on one or more sides of the subdomain D, the exponent measuring the decay of the scalar field is alpha ~ 1/2 for a slip flow condition and alpha ~ 3/4 for a no-slip condition. The scaling law exponents alpha for chaotic time-periodic flows are compared with those for similarly constructed random flows. Motivated by the theory of passive scalar field, in Part II of this work we extend the investigation of the evolution of passive scalar for the flows addressed specifically in Part I. Based on an ensemble averaging over random velocity fields, the theoretical results obtained confirm the scaling laws computed numerically for a single, long realisation of random flows. In analogy with Lebedev and Turitsyn (2004) and Salman and Haynes (2007) our results show very good agreement between such an ensemble theory and applications. In part III of our study, we expand upon the work set out in the previous parts of this thesis in terms of the polar-co-ordinate system. We analyse the structures of flows driven near to a corner with a link to Moffatt corner eddies. A long-time exponential decay rate gamma(kappa)=C*kappa^alpha has been obtained confirming our numerical and theoretical results predicted in Part I and Part II in this work. The exponent alpha is determined in a structure of Moffatt corner eddies.

"Passive scalar concentration and velocity fields of isolated turbulent puffs were examined experimentally using the planar laser Mie scattering and PIV techniques, respectively. Work in WPI laboratories on reacting, fully-modulated jets has indicated significantly reduced flame lengths for compact puffs in comparison with steady and pulsed jets. Of particular interest is the entrainment and mixing of isolated turbulent puffs away from the nozzle. The present experiments were carried out in order to enhance fundamental understanding of the velocity fields associated with isolated, turbulent puffs. Puffs were generated by injecting air through a 5 mm diameter nozzle into a flow chamber with a weak co-flow. The injection time was varied by the use of a fast-response solenoid valve from 20 ms to 161 ms. Puffs with a Reynolds number of 5,000 were examined in the range of 25 - 75 diameters downstream of the nozzle. The results indicate that as the injection volume increases, puffs evolve from a spherical geometry to one with a tail. The distribution of a passive scalar within the examined turbulent puffs is unlike that in turbulent vortex rings. The half-width of radial concentration profile through the puff center decreases as the injection volume increases. On the other hand, the puff length in the axial direction increases with the injection volume. The results from phase-locked PIV measurements indicate that the largest axial mean velocities and the radial velocity fluctuation are within the central portion of the puff and the largest axial velocity fluctuation are typically present above the puff center. The turbulent shear stress profiles within puffs are antisymmetric about the centerline and the maximum magnitude for the smallest injection volume is 2.5 times the steady jet value. The vorticity fields calculated from phase-locked velocity field data indicate the presence of vorticity throughout the puff volume. The ratio of puff volume flow rate to steady jet at the puff center location was largest for the smallest injection volume. The majority of entrainment into the puff occurs below the puff center while the puff cap pushes out into surrounding fluid. In general, the puff characteristics did not reveal an internal structure analogous to that in the turbulent vortex ring."

This project will investigate mixing in microchannels. Specifically, the advection and diffusion of a passive scalar, using a split step Monte Carlo method. Numerically the implementation of this method is well understood. The current experimental geometry is a rectangular pipe with grooves on one wall. Mixing results with straight walls agree closely with experiment. The velocity field over grooves is also studied.

The dispersion and mixing of passive scalars released from two concentrated sources into open-channel and homogeneous isotropic turbulent flows are studied using direct numerical simulation (DNS). The simulations are conducted using two fully-parallelized in-house codes developed using the FORTRAN 90/95 programming language. A comparative study has been conducted to investigate the effects of the source separation distance, Reynolds number, relative length scales of the plume and turbulent flow, and source elevation on the dispersion and mixing of two plumes. For both flow configurations, four distinct stages in the downwind development of the cross correlation between the fluctuating concentration fields have been identified which feature zero, destructive and constructive interferences and a complete mixing state. Differences between the exceedance probability of concentrations for the single and total plumes are highlighted and analyzed, and the effects of destructive and constructive interference on the exceedance probabilities for the total plume are used to explain these differences. It is found that the relationship between the third- and fourth-order concentration moments and the second-order concentration moment can be well predicted using a clipped-gamma model. This leads to an interesting conclusion that all the higher-order (third-order and above) moments of the total concentration can be inferred from a knowledge of only the first- and second-order concentration moments of each single plume and of the cross correlation coefficient. From a spectral analysis, it is observed that there exists a range of `leading scales' at which the rate of turbulent mixing of the two plumes becomes the most efficient and the coherency spectrum of the plumes approaches the asymptotic value of unity quicker than at any other scales. / October 2016

Study of passive dispersion of a neutral scalar in turbulentflows is highly important due to its numerous applications in the areas of turbulent flow visualization, turbulent heat transfer and transport of pollutants and other substances in the environment. Over the past few decades, many analytical, numerical, and experimental studies have been conducted on this topic to obtain a better understanding of the physical process. In the present work, Large Eddy Simulations (LES) of scalar dispersion in turbulent flow over smooth and rough channels is conducted to contribute to the further understanding of the relation between the turbulent velocity field and the concentration field. The LES results from the present work showed good agreement with a recently com-pleted experimental study(Rahman and Webster [2005]). An in-depth comparison of in-stantaneous concentration and velocity fields revealed thecorrelation between scalar dis-persion and coherent structures of the turbulent flow. Also,a three dimensional visual-ization of concentration iso-surfaces at different instants provided a good picture of the concentration structures transported as a result of hairpin vortices of turbulent flow, which is quite difficult to accomplish using experimental studies.

The gas transfer process across the air-water interface in a buoyant-convective environment has been investigated by Direct Numerical Simulation (DNS) to gain improved understanding of the mechanisms that control the process. The process is controlled by a combination of molecular diffusion and turbulent transport by natural convection. The convection when a water surface is cooled is combination of the Rayleigh-B´enard convection and the Rayleigh-Taylor instability. It is therefore necessary to accurately resolve the flow field as well as the molecular diffusion and the turbulent transport which contribute to the total flux. One of the challenges from a numerical point of view is to handle the very different levels of diffusion when solving the convection-diffusion equation. The temperature diffusion in water is relatively high whereas the molecular diffusion for most environmentally important gases is very low. This low molecular diffusion leads to steep gradients in the gas concentration, especially near the interface. Resolving the steep gradients is the limiting factor for an accurate resolution of the gas concentration field. Therefore a detailed study has been carried out to find the limits of an accurate resolution of the transport for a low diffusivity scalar. This problem of diffusive scalar transport was studied in numerous 1D, 2D and 3D numerical simulations. A fifth-order weighted non-oscillatory scheme (WENO) was deployed to solve the convection of the scalars, in this case gas concentration and temperature. The WENO-scheme was modified and tested in 1D scalar transport to work on non-uniform meshes. To solve the 2D and 3D velocity field the incompressible Navier-Stokes equations were solved on a staggered mesh. The convective terms were solved using a fourth-order accurate kinetic energy conserving discretization while the diffusive terms were solved using a fourth-order central method. The diffusive terms were discretized using a fourth-order central finite difference method for the second derivative. For the time-integration of the velocity field a second-order Adams-Bashworth method was employed. The Boussinesq approximation was employed to model the buoyancy due to temperature differences in the water. A linear relationship between temperature and density was assumed. A mesh sensitivity study found that the velocity field is fully resolved on a relatively coarse mesh as the level of turbulence is relatively low. However a finer mesh for the gas concentration field is required to fully capture the steep gradients that occur because of its low diffusivity. A combined dual meshing approach was used where the velocity field was solved on a coarser mesh and the scalar field (gas concentration and temperature) was solved on an overlaying finer submesh. The velocities were interpolated by a second-order method onto the finer sub-mesh. A mesh sensitivity study identified a minimum mesh size required for an accurate solution of the scalar field for a range of Schmidt numbers from Sc = 20 to Sc = 500. Initially the Rayleigh-B´enard convection leads to very fine plumes of cold liquid of high gas concentration that penetrate the deeper regions. High concentration areas remain in fine tubes that are fed from the surface. The temperature however diffuses much stronger and faster over time and the results show that temperature alone is not a good identifier for detailed high concentration areas when the gas transfer is investigated experimentally. For large timescales the temperature field becomes much more homogeneous whereas the concentration field stays more heterogeneous. However, the temperature can be used to estimate the overall transfer velocity KL. If the temperature behaves like a passive scalar a relation between Schmidt or Prandtl number and KL is evident. A qualitative comparison of the numerical results from this work to existing experiments was also carried out. Laser Induced Fluorescence (LIF) images of the oxygen concentration field and Schlieren photography has been compared to the results from the 3D simulations, which were found to be in good agreement. A detailed quantitative analysis of the process was carried out. A study of the horizontally averaged convective and diffusive mass flux enabled the calculation of transfer velocity KL at the interface. With KL known the renewal rate r for the so called surface renewal model could be determined. It was found that the renewal rates are higher than in experiments in a grid stirred tank. The horizontally averaged mean and fluctuating concentration profiles were analysed and from that the boundary layer thickness could be accurately monitored over time. A lot of this new DNS data obtained in this research might be inaccessible in experiments and reveal previously unknown details of the gas transfer at the air water interface.

No description available.

This study analyzes a turbulent passive scalar field using two-point and three-point correlations of the fluctuating scalar field. Multipoint correlation functions are investigated because they retain scaling property information and simultaneously probe the concentration field for the spatial structure of the scalar filaments. Thus, multipoint correlation functions provide unique information about the spatial properties of the concentration filaments. The concentration field is created by the iso-kinetic release of a high Schmidt number dye into a fully developed turbulent boundary layer of an open channel flow. The concentration fields were previously measured using the planar laser-induced fluorescence technique. The two-point correlations of the fluctuating scalar field indicate that as the scalar field evolves downstream, the anisotropic influence of the tracer injection method diminishes, and the scalar field becomes dominated by the mean velocity shear. As the scalar filaments align with the mean velocity gradient, the elliptical shape associated with the contours of the correlation function tilts in the direction of the mean velocity gradient. As a result, the two-point correlation contours of the concentration fluctuations indicate that anisotropic conditions (i.e. the tilted, asymmetric, elliptical shape) develop as a consequence of the mean velocity shear. Three-point correlations of the fluctuating scalar field are calculated based on configuration geometries defined by previous researchers. The first configuration follows Mydlarski and Warhaft (1998), which employs two cold-wire measurements and Taylor's frozen turbulence hypothesis. The three-point correlation contours of the concentration fluctuations associated with the cold-wire measurements exhibit a symmetric characteristic V-shape. Similar symmetric properties are observed in the current study. The second set of configurations follows on recent theoretical predictions, which indicate that the three-point correlation of the fluctuating scalar field is dependent on the size, shape, and orientation of the triangle created by the three points. The current study analyzes two geometric configurations (isosceles and collinear). The geometric configurations are defined to ensure that the influence of the shape remains constant as the configuration is rotated, translated, and dilated. Additionally, the scaling exponent in the inertial-convective regime is calculated to determine the dependence of the correlation function on the size of the triangle pattern.

<p>Despite its importance in various industrial applications there is still a lack of experimental studies on the dynamic and thermal field of swirling jets in the near-field region. The present study is an attempt to close this lack and provide new insights on the effect of rotation on the turbulent mixing of a <i>passive scalar</i>, on turbulence (joint) statistics as well as the turbulence structure.</p><p>Swirl is known to increase the spreading of free turbulent jets and hence to entrain more ambient fluid. Contrary to previous experiments, which leave traces of the swirl generating method especially in the near-field, the swirl was imparted by discharging a slightly heated air flow from an axially rotating and thermally insulated pipe (6 m long, diameter 60 mm). This gives well-defined axisymmetric streamwise and azimuthal velocity distributions as well as a well-defined temperature profile at the jet outlet. The experiments were performed at a <i>Reynolds</i> number of 24000 and a swirl number (ratio between the angular velocity of the pipe wall and the bulk velocity in the pipe) of 0.5.</p><p>By means of a specially designed combined X-wire and cold-wire probe it was possible to simultaneously acquire the instantaneous axial and azimuthal velocity components as well as the temperature and compensate the former against temperature variations. The comparison of the swirling and non-swirling cases clearly indicates a modification of the turbulence structure to that effect that the swirling jet spreads and mixes faster than its non-swirling counterpart. It is also shown that the streamwise velocity and temperature fluctuations are highly correlated and that the addition of swirl drastically increases the streamwise<i> passive scalar</i> flux in the near field.</p>

Le mélange d'un scalaire passif par un écoulement turbulent est étudié. D'abord, la simulation numérique directe (DNS), la simulation des grandes échelles (LES) et des arguments dimensionnels sont employés pour étudier le spectre du flux de scalaire dans une turbulence isotrope avec un gradient moyen uniforme de scalaire. Une loi d'échelle est dérivée. Cette loi conduit à des pentes du spectre variant entre -5/3 et -7/3 en zone inertielle. De premiers résultats de LES plaident en faveur d'un comportement en K^-2. Ensuite, en utilisant une fermeture en deux points (EDQNM), nous montrons qu'aux nombres de Reynolds très élevés, le spectre de flux de scalaire dans la zone intertielle se comporte en K^-7/3. Ce résultat est en accord avec l'analyse dimensionnelle classique de Lumley (1967). Aux nombres de Reynolds correspondant aux expériences de laboratoire, la fermeture conduit à des spectres plus près de K^-2. Nous montrons ensuite que le comportement en K^-2 trouvé en LES est induit par le forçage à grande échelle. La fermeture est alors appliquée au cas des écoulements homogènes cisaillés et les spectres du flux de scalaire longitudinal et transverse sont étudiés. Le spectre du flux longitudinal est trouvé proportionnelle à K^-23/9. Ce résultat est en accord avec l'expérience mais est en désaccord avec l'analyse dimensionnelle classique. Finalement, nous montrons que le lien entre la dispersion de particules et le mélange d'un scalaire permet de formuler une fermeture en deux points et un temps qui ne nécessite l'introduction d'aucune constante dans le modèle.