Dispersion In Boundary Layers Research Articles

Development and evaluation of a new particle tracking solver for hydrodynamic and mass transport characterization of porous media – A case study on periodic open cellular structures

The detailed understanding of local mass transport characteristics in porous catalyst supports is essential for the evaluation of their performance in reaction engineering applications. This applies particularly for the development and assessment of novel concepts such as additively manufactured periodic open cellular structures (POCS). A major drawback of the frequently used Eulerian based mass transport simulation methods is their tendency to overestimate molecular diffusion due to artificial numerical diffusion, especially in the range of high Péclet numbers (boundary-layer dispersion and pure mechanical dispersion regime) that is often encountered in industrial applications.To overcome this problem, we present a new efficient solver implementation for the OpenFOAM® simulation toolbox based on the Lagrangian Random Walk Particle Tracking method to calculate the mass transport via a deterministic convective and a stochastic diffusion term. Besides the numerical calculation of effective diffusion as well as dispersion coefficients, the new solver is also capable of analyzing residence time behavior, flow tortuosity and contact patterns with catalytically active surfaces of catalyst support structures in detail. Following a thorough validation study, we demonstrate the evaluation options provided by the results of this new solver named disTrackFoam on the example of three POCS with distinct unit cell types.

Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio l / h between 1 and 8, where l is the spanwise dimension of the obstacles and h is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10h was used as the approaching flow, and a line source of passive tracer was placed 2h upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for l/h=2 the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend.

Stable Stratification Effects on Flow and Pollutant Dispersion in Boundary Layers Entering a Generic Urban Environment

Large-eddy simulations (LES) are used to investigate the effect of stable stratification on rural-to-urban roughness transitions. Smooth-wall turbulent boundary layers are subjected to a generic urban roughness consisting of cubes in an in-line arrangement. Two line sources of pollutant are added to investigate the effect on pollutant dispersion. Firstly, the LES method is validated with data from wind-tunnel experiments on fully-developed flow over cubical roughness. Good agreement is found for the vertical profiles of the mean streamwise velocity component and mean Reynolds stress. Subsequently, roughness transition simulations are done for both neutral and stable conditions. Results are compared with fully-developed simulations with conventional double-periodic boundary conditions. In stable conditions, at the end of the domain the streamwise velocity component has not yet reached the fully-developed state even though the surface forces are nearly constant. Moreover, the internal boundary layer is shallower than in the neutral case. Furthermore, an investigation of the turbulence kinetic energy budget shows that the buoyancy destruction term is reduced in the internal boundary layer, above which it is equal to the undisturbed (smooth wall) value. In addition, in stable conditions pollutants emitted above the urban canopy enter the canopy farther downstream due to decreased vertical mixing. Pollutants emitted below the top of the urban canopy are 85 % higher in concentration in stable conditions mostly due to decreased advection. If this is taken into account concentrations remain 17 % greater in stable conditions due to less rapid internal boundary-layer growth. Finally, it is concluded that in the first seven streets the vertical advective pollutant flux is significant, in contrast to the fully-developed case.

Hydrodynamic and boundary-layer dispersion in bidisperse porous media

The small grains in a bidisperse porous medium have the greater influence on the permeability, while the large grains are more effective in dispersing chemical tracers. We compute the dispersion induced by a dilute array of large spheres in a Brinkman medium whose permeability is determined by the radii and volume fraction of the small spheres. The effective diffusivity contains a purely hydrodynamic contribution proportional to Ua1ϕ1 and an O(Ua1ϕ1 ln (Ua1/D)) contribution from the mass transfer boundary layers near the spheres. Here, U is the mean velocity in the medium, a1 and ϕ1 are the radii and volume fraction of the large spheres and D is the molecular diffusivity. The boundary-layer dispersion is small when the Brinkman screening length κ (or square root of permeability) is much smaller than a1, but is important for κ[ges ]O(a1). Experimental results for the dispersion due to flow through a bidisperse packed bed are reported and compared with the theoretical predictions. In addition to its application to bidisperse porous media, the present calculation allows an extension of Koch & Brady's (1985) analysis of monodisperse fixed beds to include higher-order terms in the expansion for small particle volume fraction.

Hydraulic Jump and Undular Bore Formation on a Shelf Break

Abstract The evolution of the semidiurnal internal tide as it propagates across the Australian North West Shelf is discussed analytically. As the tide is of long wavelength and small amplitude, this evolution is described by a perturbed extended Korteweg-de Vries equation. It is found that the flow is dominated by nonlinearity, and hence is hydraulic, except in the neighborhood of any shocks predicted by hydraulic theory. Hydraulic theory predicts the formation of two shocks in each period of the tide. The inclusion of dispersion in boundary layers around the shocks results in one of these shocks breaking up into an undular bore. Good agreement is found with observations by Holloway of the semidiurnal internal tide on the Australian North West Shelf.

An experiment on boundary mixing: mean circulation and transport rates

An experiment is described in which a turbulent boundary layer was generated along a sloping wall of a laboratory tank containing salt-stratified fluid. Initially, the pycnocline separating the upper fresh-water layer from the lower saline layer was relatively thin; it thickened in response to the mixing as the experiment proceeded. Two types of mean circulation developed as a result of the boundary mixing. In the boundary layer, counterflowing mean streams were observed that augmented the diffusion of salt up- and downslope. This augmented dispersion in turn tended to spread the salt beyond the depth range of the pycnocline in the ambient fluid, producing a mean convergence in the boundary layer and intrusions from the layer into the ambient fluid.The evolving density structure in the ambient fluid was measured by conductivity-probe traverses, from which the net buoyancy flux (or salt flux) and volume flux in the boundary layer were determined. The level of zero volume flux was found to coincide closely with the level of maximum stability frequency N, so that the buoyancy transport across this level was entirely the result of turbulent dispersion in the boundary layer. At other levels, the convective transports up and down contribute significantly. A simple theory provides scaling in terms of the laboratory parameters; in terms of the inferred overall turbulent viscosity νe, the buoyancy transport resulting from boundary-layer dispersion was found to be \[ F_{\rm B} = 0.60 \left\{\frac{\nu_{\rm e}N(z)}{\sin\theta}\right\}^{\frac{3}{2}}\cos^2\theta, \] and the intrusion velocity into the ambient fluid is \[ v_1 = 0.42\frac{\nu_{\rm e}^{\frac{3}{2}}}{N^{\frac{1}{2}}h^2}\frac{\cos^2\theta}{(\sin\theta)^{\frac{3}{2}}}, \] where θ is the angle of the sloping bed. These expressions must become invalid when θ becomes vanishingly small; their application to estuarine and continental slope flows is discussed briefly.